From 9b97b50b1816b74b694a1a702e7a84e79964d94a Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Fri, 21 Apr 2023 05:56:57 +0200 Subject: [PATCH 01/48] Add num additions to r1cs info --- src/r1cs_info.js | 72 +++++++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 71 insertions(+), 1 deletion(-) diff --git a/src/r1cs_info.js b/src/r1cs_info.js index f144fb2f..58769ba5 100644 --- a/src/r1cs_info.js +++ b/src/r1cs_info.js @@ -18,15 +18,28 @@ */ import { Scalar } from "ffjavascript"; -import { readR1cs } from "r1csfile"; +import { readR1cs, readR1csFd } from "r1csfile"; + +import { + getFFlonkAdditionConstraint, + getFFlonkConstantConstraint, + getFFlonkMultiplicationConstraint +} from "./plonk_equation.js"; +import {r1csConstraintProcessor} from "./r1cs_constraint_processor.js"; +import * as binFileUtils from "@iden3/binfileutils"; + +import {readBinFile} from "@iden3/binfileutils"; const bls12381r = Scalar.e("73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001", 16); const bn128r = Scalar.e("21888242871839275222246405745257275088548364400416034343698204186575808495617"); + export default async function r1csInfo(r1csName, logger) { const cir = await readR1cs(r1csName); + const {nAdditions: additions} = await countConstraints(cir.F, r1csName, logger); + if (Scalar.eq(cir.prime, bn128r)) { if (logger) logger.info("Curve: bn-128"); } else if (Scalar.eq(cir.prime, bls12381r)) { @@ -36,6 +49,7 @@ export default async function r1csInfo(r1csName, logger) { } if (logger) logger.info(`# of Wires: ${cir.nVars}`); if (logger) logger.info(`# of Constraints: ${cir.nConstraints}`); + if (logger) logger.info(`# of Additions: ${additions}`); if (logger) logger.info(`# of Private Inputs: ${cir.nPrvInputs}`); if (logger) logger.info(`# of Public Inputs: ${cir.nPubInputs}`); if (logger) logger.info(`# of Labels: ${cir.nLabels}`); @@ -43,3 +57,59 @@ export default async function r1csInfo(r1csName, logger) { return cir; } + +async function countConstraints(Fr, r1csFilename, logger) { + const {fd: fdR1cs, sections: sectionsR1cs} = await readBinFile(r1csFilename, "r1cs", 1, 1 << 22, 1 << 24); + const r1cs = await readR1csFd(fdR1cs, sectionsR1cs, {loadConstraints: false, loadCustomGates: true}); + + // Add all constraints from r1cs file + const r1csProcessor = new r1csConstraintProcessor(Fr, getFFlonkConstantConstraint, getFFlonkAdditionConstraint, getFFlonkMultiplicationConstraint, logger); + + const bR1cs = await binFileUtils.readSection(fdR1cs, sectionsR1cs, 2); + let bR1csPos = 0; + let settings = { + nVars: 0 + }; + + let nConstraints = 0; + let nAdditions = 0; + + for (let i = 0; i < r1cs.nConstraints; i++) { + const [constraints, additions] = r1csProcessor.processR1csConstraint(settings, ...readConstraint()); + + nConstraints += constraints.length; + nAdditions += additions.length; + } + + await fdR1cs.close(); + + return {nConstraints, nAdditions}; + + function readConstraint() { + const c = []; + c[0] = readLC(); + c[1] = readLC(); + c[2] = readLC(); + return c; + } + + function readLC() { + const lc = {}; + + const buffUL32 = bR1cs.slice(bR1csPos, bR1csPos + 4); + bR1csPos += 4; + const buffUL32V = new DataView(buffUL32.buffer); + const nIdx = buffUL32V.getUint32(0, true); + + const buff = bR1cs.slice(bR1csPos, bR1csPos + (4 + r1cs.n8) * nIdx); + bR1csPos += (4 + r1cs.n8) * nIdx; + const buffV = new DataView(buff.buffer); + for (let i = 0; i < nIdx; i++) { + const idx = buffV.getUint32(i * (4 + r1cs.n8), true); + const val = r1cs.F.fromRprLE(buff, i * (4 + r1cs.n8) + 4); + lc[idx] = val; + } + return lc; + } +} + From 8702b3a36155b7329bba2e05ba3f50c81b15cc82 Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Fri, 21 Apr 2023 04:44:23 +0000 Subject: [PATCH 02/48] add checkAddtions as optional flag --- cli.js | 7 +++--- src/r1cs_info.js | 56 ++++++++++++++++++++++++++++++------------------ 2 files changed, 39 insertions(+), 24 deletions(-) diff --git a/cli.js b/cli.js index 0bb7972a..21a00a31 100755 --- a/cli.js +++ b/cli.js @@ -138,6 +138,7 @@ const commands = [ cmd: "r1cs info [circuit.r1cs]", description: "Print statistiscs of a circuit", alias: ["ri", "info -r|r1cs:circuit.r1cs"], + options: "-checkadditions|ca", action: r1csInfo }, { @@ -390,11 +391,11 @@ function changeExt(fileName, newExt) { // r1cs export circomJSON [circuit.r1cs] [circuit.json] async function r1csInfo(params, options) { const r1csName = params[0] || "circuit.r1cs"; + let checkAdditions = false; - if (options.verbose) Logger.setLogLevel("DEBUG"); - - await r1cs.info(r1csName, logger); + if (options.checkadditions) checkAdditions = true; + await r1cs.info(r1csName, checkAdditions, logger); return 0; } diff --git a/src/r1cs_info.js b/src/r1cs_info.js index 58769ba5..6e160bbf 100644 --- a/src/r1cs_info.js +++ b/src/r1cs_info.js @@ -18,49 +18,61 @@ */ import { Scalar } from "ffjavascript"; -import { readR1cs, readR1csFd } from "r1csfile"; +import { readR1cs, readR1csFd } from "r1csfile"; import { getFFlonkAdditionConstraint, getFFlonkConstantConstraint, getFFlonkMultiplicationConstraint } from "./plonk_equation.js"; -import {r1csConstraintProcessor} from "./r1cs_constraint_processor.js"; +import { r1csConstraintProcessor } from "./r1cs_constraint_processor.js"; import * as binFileUtils from "@iden3/binfileutils"; -import {readBinFile} from "@iden3/binfileutils"; +import { readBinFile } from "@iden3/binfileutils"; const bls12381r = Scalar.e("73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001", 16); const bn128r = Scalar.e("21888242871839275222246405745257275088548364400416034343698204186575808495617"); -export default async function r1csInfo(r1csName, logger) { +export default async function r1csInfo(r1csName, checkAdditions, logger) { + const cir = await readR1cs(r1csName, false); - const cir = await readR1cs(r1csName); - - const {nAdditions: additions} = await countConstraints(cir.F, r1csName, logger); + let nConstraints, nAdditions; + if (checkAdditions) { + ({ nConstraints, nAdditions } = await countConstraints(cir.F, r1csName, logger)); + } + let curve; if (Scalar.eq(cir.prime, bn128r)) { - if (logger) logger.info("Curve: bn-128"); + curve = "Curve: bn-128"; } else if (Scalar.eq(cir.prime, bls12381r)) { - if (logger) logger.info("Curve: bls12-381"); + curve = "Curve: bls12-381"; } else { - if (logger) logger.info(`Unknown Curve. Prime: ${Scalar.toString(cir.prime)}`); + curve = `Unknown. Prime: ${Scalar.toString(cir.prime)}`; + } + + if (logger) { + logger.info("----------------------------"); + logger.info(" R1CS INFO"); + + logger.info(` Curve: ${curve}`); + logger.info(` # of Wires: ${cir.nVars}`); + logger.info(` # of Constraints: ${cir.nConstraints}`); + if (checkAdditions) logger.info(`# of Additions: ${nAdditions}`); + logger.info(` # of Private Inputs: ${cir.nPrvInputs}`); + logger.info(` # of Public Inputs: ${cir.nPubInputs}`); + logger.info(` # of Labels: ${cir.nLabels}`); + logger.info(` # of Outputs: ${cir.nOutputs}`); + + logger.info("----------------------------"); } - if (logger) logger.info(`# of Wires: ${cir.nVars}`); - if (logger) logger.info(`# of Constraints: ${cir.nConstraints}`); - if (logger) logger.info(`# of Additions: ${additions}`); - if (logger) logger.info(`# of Private Inputs: ${cir.nPrvInputs}`); - if (logger) logger.info(`# of Public Inputs: ${cir.nPubInputs}`); - if (logger) logger.info(`# of Labels: ${cir.nLabels}`); - if (logger) logger.info(`# of Outputs: ${cir.nOutputs}`); return cir; } async function countConstraints(Fr, r1csFilename, logger) { - const {fd: fdR1cs, sections: sectionsR1cs} = await readBinFile(r1csFilename, "r1cs", 1, 1 << 22, 1 << 24); - const r1cs = await readR1csFd(fdR1cs, sectionsR1cs, {loadConstraints: false, loadCustomGates: true}); + const { fd: fdR1cs, sections: sectionsR1cs } = await readBinFile(r1csFilename, "r1cs", 1, 1 << 22, 1 << 24); + const r1cs = await readR1csFd(fdR1cs, sectionsR1cs, { loadConstraints: false, loadCustomGates: true }); // Add all constraints from r1cs file const r1csProcessor = new r1csConstraintProcessor(Fr, getFFlonkConstantConstraint, getFFlonkAdditionConstraint, getFFlonkMultiplicationConstraint, logger); @@ -75,15 +87,17 @@ async function countConstraints(Fr, r1csFilename, logger) { let nAdditions = 0; for (let i = 0; i < r1cs.nConstraints; i++) { + if (i !== 0 && i % 100000 === 0) { + if (logger) logger.info(`Processed ${i}/${r1cs.nConstraints} constraints`); + } const [constraints, additions] = r1csProcessor.processR1csConstraint(settings, ...readConstraint()); - nConstraints += constraints.length; nAdditions += additions.length; } await fdR1cs.close(); - return {nConstraints, nAdditions}; + return { nConstraints, nAdditions }; function readConstraint() { const c = []; From 8e9e23d5fa297633e0af58cb091b6c409bb8da1b Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Fri, 21 Apr 2023 04:52:09 +0000 Subject: [PATCH 03/48] add total constraints in info --- src/r1cs_info.js | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/src/r1cs_info.js b/src/r1cs_info.js index 6e160bbf..106c9a77 100644 --- a/src/r1cs_info.js +++ b/src/r1cs_info.js @@ -58,7 +58,10 @@ export default async function r1csInfo(r1csName, checkAdditions, logger) { logger.info(` Curve: ${curve}`); logger.info(` # of Wires: ${cir.nVars}`); logger.info(` # of Constraints: ${cir.nConstraints}`); - if (checkAdditions) logger.info(`# of Additions: ${nAdditions}`); + if (checkAdditions) { + logger.info(` # of Additions: ${nAdditions}`); + logger.info(` # total constraints: ${cir.nConstraints + nAdditions}`); + } logger.info(` # of Private Inputs: ${cir.nPrvInputs}`); logger.info(` # of Public Inputs: ${cir.nPubInputs}`); logger.info(` # of Labels: ${cir.nLabels}`); From 5add066dc776a32bf2d059fe3e2eeba8a07e3cfb Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Sun, 30 Apr 2023 18:11:28 +0200 Subject: [PATCH 04/48] Plonk refactored with new clsses and working --- package-lock.json | 2 + src/plonk.js | 17 + src/plonk_prove.js | 1194 +++++++++++++++------------------- src/polynomial/polynomial.js | 3 +- src/proof.js | 18 +- src/zkey_utils.js | 2 +- 6 files changed, 572 insertions(+), 664 deletions(-) diff --git a/package-lock.json b/package-lock.json index 32225357..0bf223ad 100644 --- a/package-lock.json +++ b/package-lock.json @@ -4960,6 +4960,7 @@ "resolved": "https://registry.npmjs.org/bufferutil/-/bufferutil-4.0.5.tgz", "integrity": "sha512-HTm14iMQKK2FjFLRTM5lAVcyaUzOnqbPtesFIvREgXpJHdQm8bWS+GkQgIkfaBYRHuCnea7w8UVNfwiAQhlr9A==", "dev": true, + "hasInstallScript": true, "optional": true, "dependencies": { "node-gyp-build": "^4.3.0" @@ -5322,6 +5323,7 @@ "resolved": "https://registry.npmjs.org/utf-8-validate/-/utf-8-validate-5.0.7.tgz", "integrity": "sha512-vLt1O5Pp+flcArHGIyKEQq883nBt8nN8tVBcoL0qUXj2XT1n7p70yGIq2VK98I5FdZ1YHc0wk/koOnHjnXWk1Q==", "dev": true, + "hasInstallScript": true, "optional": true, "dependencies": { "node-gyp-build": "^4.3.0" diff --git a/src/plonk.js b/src/plonk.js index b02d2e4b..ecf7240f 100644 --- a/src/plonk.js +++ b/src/plonk.js @@ -17,6 +17,23 @@ along with snarkJS. If not, see . */ +// ZKEY constants +export const ZKEY_PL_NSECTIONS = 13; + +export const ZKEY_PL_HEADER_SECTION = 2; +export const ZKEY_PL_ADDITIONS_SECTION = 3; +export const ZKEY_PL_A_MAP_SECTION = 4; +export const ZKEY_PL_B_MAP_SECTION = 5; +export const ZKEY_PL_C_MAP_SECTION = 6; +export const ZKEY_PL_QM_SECTION = 7; +export const ZKEY_PL_QL_SECTION = 8; +export const ZKEY_PL_QR_SECTION = 9; +export const ZKEY_PL_QO_SECTION = 10; +export const ZKEY_PL_QC_SECTION = 11; +export const ZKEY_PL_SIGMA_SECTION = 12; +export const ZKEY_PL_LAGRANGE_SECTION = 13; +export const ZKEY_PL_PTAU_SECTION = 14; + export {default as setup} from "./plonk_setup.js"; export {default as fullProve} from "./plonk_fullprove.js"; export {default as prove} from "./plonk_prove.js"; diff --git a/src/plonk_prove.js b/src/plonk_prove.js index a0b31c22..da5193bf 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -22,20 +22,40 @@ import * as binFileUtils from "@iden3/binfileutils"; import * as zkeyUtils from "./zkey_utils.js"; import * as wtnsUtils from "./wtns_utils.js"; -import { getCurveFromQ as getCurve } from "./curves.js"; import { Scalar, utils, BigBuffer } from "ffjavascript"; const {stringifyBigInts} = utils; -import jsSha3 from "js-sha3"; -const { keccak256 } = jsSha3; - +import { Proof } from "./proof.js"; +import { Keccak256Transcript } from "./Keccak256Transcript.js"; +import { MulZ } from "./mul_z.js"; +import { ZKEY_PL_HEADER_SECTION, + ZKEY_PL_ADDITIONS_SECTION, + ZKEY_PL_A_MAP_SECTION, + ZKEY_PL_B_MAP_SECTION, + ZKEY_PL_C_MAP_SECTION, + ZKEY_PL_QM_SECTION, + ZKEY_PL_QL_SECTION, + ZKEY_PL_QR_SECTION, + ZKEY_PL_QO_SECTION, + ZKEY_PL_QC_SECTION, + ZKEY_PL_SIGMA_SECTION, + ZKEY_PL_LAGRANGE_SECTION, + ZKEY_PL_PTAU_SECTION, + } from "./plonk.js"; + import { Polynomial } from "./polynomial/polynomial.js"; + import { Evaluations } from "./polynomial/evaluations.js"; + export default async function plonk16Prove(zkeyFileName, witnessFileName, logger) { const {fd: fdWtns, sections: sectionsWtns} = await binFileUtils.readBinFile(witnessFileName, "wtns", 2, 1<<25, 1<<23); + // Read witness file + if (logger) logger.debug("> Reading witness file"); const wtns = await wtnsUtils.readHeader(fdWtns, sectionsWtns); - const {fd: fdZKey, sections: sectionsZKey} = await binFileUtils.readBinFile(zkeyFileName, "zkey", 2, 1<<25, 1<<23); + // Read zkey file + if (logger) logger.debug("> Reading zkey file"); + const {fd: fdZKey, sections: zkeySections} = await binFileUtils.readBinFile(zkeyFileName, "zkey", 2, 1<<25, 1<<23); - const zkey = await zkeyUtils.readHeader(fdZKey, sectionsZKey); + const zkey = await zkeyUtils.readHeader(fdZKey, zkeySections); if (zkey.protocol != "plonk") { throw new Error("zkey file is not plonk"); } @@ -49,42 +69,65 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } const curve = zkey.curve; + const Fr = curve.Fr; - const G1 = curve.G1; const n8r = curve.Fr.n8; + const sDomain = zkey.domainSize * n8r; + + if (logger) { + logger.info("----------------------------"); + logger.info(" PLONK PROVE SETTINGS"); + logger.info(` Curve: ${curve.name}`); + logger.info(` Circuit power: ${zkey.power}`); + logger.info(` Domain size: ${zkey.domainSize}`); + logger.info(` Vars: ${zkey.nVars}`); + logger.info(` Public vars: ${zkey.nPublic}`); + logger.info(` Constraints: ${zkey.nConstraints}`); + logger.info(` Additions: ${zkey.nAdditions}`); + logger.info("----------------------------"); + } - if (logger) logger.debug("Reading Wtns"); + //Read witness data + if (logger) logger.info("> Reading witness file data"); const buffWitness = await binFileUtils.readSection(fdWtns, sectionsWtns, 2); + // First element in plonk is not used and can be any value. (But always the same). // We set it to zero to go faster in the exponentiations. buffWitness.set(Fr.zero, 0); const buffInternalWitness = new BigBuffer(n8r*zkey.nAdditions); - await calculateAdditions(); + let buffers = {}; + let polynomials = {}; + let evaluations = {}; - let A,B,C,Z; - let A4, B4, C4, Z4; - let pol_a,pol_b,pol_c, pol_z, pol_t, pol_r; - let proof = {}; + let challenges = {}; + let proof = new Proof(curve, logger); + const transcript = new Keccak256Transcript(curve); - const sigmaBuff = new BigBuffer(zkey.domainSize*n8r*4*3); - let o = sectionsZKey[12][0].p + zkey.domainSize*n8r; - await fdZKey.readToBuffer(sigmaBuff, 0 , zkey.domainSize*n8r*4, o); - o += zkey.domainSize*n8r*5; - await fdZKey.readToBuffer(sigmaBuff, zkey.domainSize*n8r*4 , zkey.domainSize*n8r*4, o); - o += zkey.domainSize*n8r*5; - await fdZKey.readToBuffer(sigmaBuff, zkey.domainSize*n8r*8 , zkey.domainSize*n8r*4, o); + if (logger) logger.info(`> Reading Section ${ZKEY_PL_ADDITIONS_SECTION}. Additions`); + await calculateAdditions(); - const pol_s1 = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_s1, 0 , zkey.domainSize*n8r, sectionsZKey[12][0].p); + if (logger) logger.info(`> Reading Section ${ZKEY_PL_SIGMA_SECTION}. Sigma1, Sigma2 & Sigma 3`); + if (logger) logger.info("··· Reading Sigma polynomials "); + polynomials.Sigma1 = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.Sigma2 = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.Sigma3 = new Polynomial(new BigBuffer(sDomain), curve, logger); - const pol_s2 = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_s2, 0 , zkey.domainSize*n8r, sectionsZKey[12][0].p + 5*zkey.domainSize*n8r); + await fdZKey.readToBuffer(polynomials.Sigma1.coef, 0, sDomain, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.Sigma2.coef, 0, sDomain, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 5 * sDomain); + await fdZKey.readToBuffer(polynomials.Sigma3.coef, 0, sDomain, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 10 * sDomain); - const PTau = await binFileUtils.readSection(fdZKey, sectionsZKey, 14); + if (logger) logger.info("··· Reading Sigma evaluations"); + evaluations.Sigma1 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.Sigma2 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.Sigma3 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + await fdZKey.readToBuffer(evaluations.Sigma1.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + sDomain); + await fdZKey.readToBuffer(evaluations.Sigma2.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 6 * sDomain); + await fdZKey.readToBuffer(evaluations.Sigma3.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 11 * sDomain); - const ch = {}; + if (logger) logger.info(`> Reading Section ${ZKEY_PL_PTAU_SECTION}. Powers of Tau`); + const PTau = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_PTAU_SECTION); await round1(); await round2(); @@ -92,14 +135,10 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger await round4(); await round5(); - /////////////////////// // Final adjustments // /////////////////////// - proof.protocol = "plonk"; - proof.curve = curve.name; - await fdZKey.close(); await fdWtns.close(); @@ -110,79 +149,46 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger publicSignals.push(Scalar.fromRprLE(pub)); } - proof.A = G1.toObject(proof.A); - proof.B = G1.toObject(proof.B); - proof.C = G1.toObject(proof.C); - proof.Z = G1.toObject(proof.Z); - - proof.T1 = G1.toObject(proof.T1); - proof.T2 = G1.toObject(proof.T2); - proof.T3 = G1.toObject(proof.T3); - - proof.eval_a = Fr.toObject(proof.eval_a); - proof.eval_b = Fr.toObject(proof.eval_b); - proof.eval_c = Fr.toObject(proof.eval_c); - proof.eval_s1 = Fr.toObject(proof.eval_s1); - proof.eval_s2 = Fr.toObject(proof.eval_s2); - proof.eval_zw = Fr.toObject(proof.eval_zw); - proof.eval_t = Fr.toObject(proof.eval_t); - proof.eval_r = Fr.toObject(proof.eval_r); - - proof.Wxi = G1.toObject(proof.Wxi); - proof.Wxiw = G1.toObject(proof.Wxiw); - - delete proof.eval_t; - - proof = stringifyBigInts(proof); - publicSignals = stringifyBigInts(publicSignals); - - return {proof, publicSignals}; + // Prepare proof + let _proof = proof.toObjectProof(false); + _proof.protocol = "plonk"; + _proof.curve = curve.name; + + return { + proof: stringifyBigInts(_proof), + publicSignals: stringifyBigInts(publicSignals) + }; async function calculateAdditions() { - const additionsBuff = await binFileUtils.readSection(fdZKey, sectionsZKey, 3); - - const sSum = 8+curve.Fr.n8*2; - - for (let i=0; i Computing A, B, C wire polynomials"); + await computeWirePolynomials(); + + // The first output of the prover is ([A]_1, [B]_1, [C]_1) + let commitA = await polynomials.A.multiExponentiation(PTau, "A"); + let commitB = await polynomials.B.multiExponentiation(PTau, "B"); + let commitC = await polynomials.C.multiExponentiation(PTau, "C"); - - proof.A = await expTau(pol_a, "multiexp A"); - proof.B = await expTau(pol_b, "multiexp B"); - proof.C = await expTau(pol_c, "multiexp C"); + proof.addPolynomial("A", commitA); + proof.addPolynomial("B", commitB); + proof.addPolynomial("C", commitC); + + return 0; + } + + async function computeWirePolynomials() { + if (logger) logger.info("··· Reading data from zkey file"); + // Build A, B and C evaluations buffer from zkey and witness files + buffers.A = new BigBuffer(sDomain); + buffers.B = new BigBuffer(sDomain); + buffers.C = new BigBuffer(sDomain); + + const aMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_A_MAP_SECTION); + const bMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_B_MAP_SECTION); + const cMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_C_MAP_SECTION); + + // Compute all witness from signal ids and set them to A,B & C buffers + for (let i = 0; i < zkey.nConstraints; i++) { + const i_sFr = i * n8r; + const offset = i * 4; + + // Compute A value from a signal id + const signalIdA = readUInt32(aMapBuff, offset); + buffers.A.set(getWitness(signalIdA), i_sFr); + + // Compute B value from a signal id + const signalIdB = readUInt32(bMapBuff, offset); + buffers.B.set(getWitness(signalIdB), i_sFr); + + // Compute C value from a signal id + const signalIdC = readUInt32(cMapBuff, offset); + buffers.C.set(getWitness(signalIdC), i_sFr); + } + + buffers.A = await Fr.batchToMontgomery(buffers.A); + buffers.B = await Fr.batchToMontgomery(buffers.B); + buffers.C = await Fr.batchToMontgomery(buffers.C); + + // Compute the coefficients of the wire polynomials a(X), b(X) and c(X) from A,B & C buffers + if (logger) logger.info("··· Computing A ifft"); + polynomials.A = await Polynomial.fromEvaluations(buffers.A, curve, logger); + if (logger) logger.info("··· Computing B ifft"); + polynomials.B = await Polynomial.fromEvaluations(buffers.B, curve, logger); + if (logger) logger.info("··· Computing C ifft"); + polynomials.C = await Polynomial.fromEvaluations(buffers.C, curve, logger); + + // Compute extended evaluations of a(X), b(X) and c(X) polynomials + if (logger) logger.info("··· Computing A fft"); + evaluations.A = await Evaluations.fromPolynomial(polynomials.A, 4, curve, logger); + if (logger) logger.info("··· Computing B fft"); + evaluations.B = await Evaluations.fromPolynomial(polynomials.B, 4, curve, logger); + if (logger) logger.info("··· Computing C fft"); + evaluations.C = await Evaluations.fromPolynomial(polynomials.C, 4, curve, logger); + + // Blind a(X), b(X) and c(X) polynomials coefficients with blinding scalars b + polynomials.A.blindCoefficients([challenges.b[2], challenges.b[1]]); + polynomials.B.blindCoefficients([challenges.b[4], challenges.b[3]]); + polynomials.C.blindCoefficients([challenges.b[6], challenges.b[5]]); + + // // Check degrees + if (polynomials.A.degree() >= zkey.domainSize + 2) { + throw new Error("A Polynomial is not well calculated"); + } + if (polynomials.B.degree() >= zkey.domainSize + 2) { + throw new Error("B Polynomial is not well calculated"); + } + if (polynomials.C.degree() >= zkey.domainSize + 2) { + throw new Error("C Polynomial is not well calculated"); + } } async function round2() { + // STEP 2.1 - Compute permutation challenge beta and gamma ∈ F + // Compute permutation challenge beta + if (logger) logger.debug("> Computing challenges beta and gamma"); + transcript.reset(); + + // TODO Add circuit dependent commitment to the transcript!!!!! + //transcript.addPolCommitment(zkey.?????); - const transcript1 = new Uint8Array(zkey.nPublic*n8r + G1.F.n8*2*3); - for (let i=0; i Computing Z polynomial"); + await computeZ(); + + // The second output of the prover is ([Z]_1) + let commitZ = await polynomials.Z.multiExponentiation(PTau, "Z"); + + proof.addPolynomial("Z", commitZ); + } + async function computeZ() { + if (logger) logger.info("··· Computing Z evaluations"); + + let numArr = new BigBuffer(sDomain); + let denArr = new BigBuffer(sDomain); + + // Set the first values to 1 numArr.set(Fr.one, 0); denArr.set(Fr.one, 0); + // Set initial omega let w = Fr.one; - for (let i=0; i0)&&(Fr.isZero(p.slice(deg*n8r, deg*n8r+n8r)))) deg--; - return deg; - } + let den = Fr.mul(d1, Fr.mul(d2, d3)); - function printPol(P) { - const n=(P.byteLength/n8r); - console.log("["); - for (let i=0; i= zkey.domainSize + 3) { + throw new Error("Z Polynomial is not well calculated"); + } - const Z2 = [ - Fr.zero, - Fr.add(Fr.zero, Fr.mul(Fr.e(-2), Fr.w[2])), - Fr.e(4), - Fr.sub(Fr.zero, Fr.mul(Fr.e(-2), Fr.w[2])), - ]; + delete buffers.Z; + } - const Z3 = [ - Fr.zero, - Fr.add(Fr.e(2), Fr.mul(Fr.e(2), Fr.w[2])), - Fr.e(-8), - Fr.sub(Fr.e(2), Fr.mul(Fr.e(2), Fr.w[2])), - ]; + async function round3() { + if (logger) logger.debug("> Computing challenge alpha"); + // STEP 3.1 - Compute evaluation challenge xi ∈ S + transcript.reset(); + transcript.addPolCommitment(proof.getPolynomial("Z")); + + challenges.alpha = transcript.getChallenge(); + challenges.alpha2 = Fr.square(challenges.alpha); + if (logger) logger.debug("··· challenges.alpha: " + Fr.toString(challenges.alpha)); + + if (logger) logger.info(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + + `, ${ZKEY_PL_QM_SECTION}, ${ZKEY_PL_QO_SECTION}, ${ZKEY_PL_QC_SECTION}. Q selectors`); + // Reserve memory for Q's evaluations + evaluations.QL = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.QR = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.QM = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.QO = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.QC = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + + // Read Q's evaluations from zkey file + await fdZKey.readToBuffer(evaluations.QL.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_QL_SECTION][0].p + sDomain); + await fdZKey.readToBuffer(evaluations.QR.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_QR_SECTION][0].p + sDomain); + await fdZKey.readToBuffer(evaluations.QM.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_QM_SECTION][0].p + sDomain); + await fdZKey.readToBuffer(evaluations.QO.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_QO_SECTION][0].p + sDomain); + await fdZKey.readToBuffer(evaluations.QC.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_QC_SECTION][0].p + sDomain); + + // Read Lagrange polynomials & evaluations from zkey file + evaluations.Lagrange = new Evaluations(new BigBuffer(sDomain * 4 * zkey.nPublic), curve, logger); + + for (let i = 0; i < zkey.nPublic; i++) { + await fdZKey.readToBuffer(evaluations.Lagrange.eval, i * sDomain * 4, sDomain * 4, zkeySections[ZKEY_PL_LAGRANGE_SECTION][0].p + i * 5 * sDomain + sDomain); + } - const T = new BigBuffer(zkey.domainSize*4*n8r); - const Tz = new BigBuffer(zkey.domainSize*4*n8r); + buffers.T = new BigBuffer(sDomain * 4); + buffers.Tz = new BigBuffer(sDomain * 4); let w = Fr.one; for (let i=0; i (zkey.domainSize*3 -4) ) { - if (!Fr.isZero(a)) { - throw new Error("T Polynomial is not divisible"); - } - } - } + // Add the polynomial T1z to T1 to get the final polynomial T1 + polynomials.T.add(polynomials.Tz); - if (logger) logger.debug("ifft Tz"); - const tz = await Fr.ifft(Tz); - for (let i=0; i (zkey.domainSize*3 +5) ) { - if (!Fr.isZero(a)) { - throw new Error("Tz Polynomial is not well calculated"); - } - } else { - t.set( - Fr.add( - t.slice(i*n8r, (i+1)*n8r), - a - ), - i*n8r - ); - } + // Check degree + if (polynomials.T.degree() >= zkey.domainSize * 3 + 6) { + throw new Error("T Polynomial is not well calculated"); } - - pol_t = t.slice(0, (zkey.domainSize * 3 + 6) * n8r); - + // t(x) has degree 3n + 5, we are going to split t(x) into three smaller polynomials: - // t'_low and t'_mid with a degree < n and t'_high with a degree n+5 - // such that t(x) = t'_low(X) + X^n t'_mid(X) + X^{2n} t'_hi(X) + // T1' and T2' with a degree < n and T3' with a degree n+5 + // such that t(x) = T1'(X) + X^n T2'(X) + X^{2n} T3'(X) // To randomize the parts we use blinding scalars b_10 and b_11 in a way that doesn't change t(X): - // t_low(X) = t'_low(X) + b_10 X^n - // t_mid(X) = t'_mid(X) - b_10 + b_11 X^n - // t_high(X) = t'_high(X) - b_11 + // T1(X) = T1'(X) + b_10 X^n + // T2(X) = T2'(X) - b_10 + b_11 X^n + // T3(X) = T3'(X) - b_11 // such that - // t(X) = t_low(X) + X^n t_mid(X) + X^2n t_high(X) + // t(X) = T1(X) + X^n T2(X) + X^2n T3(X) + + polynomials.T1 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); + polynomials.T2 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); + polynomials.T3 = new Polynomial(new BigBuffer((zkey.domainSize + 6) * n8r), curve, logger); + + polynomials.T1.coef.set(polynomials.T.coef.slice(0, sDomain), 0); + polynomials.T2.coef.set(polynomials.T.coef.slice(sDomain, sDomain * 2), 0); + polynomials.T3.coef.set(polynomials.T.coef.slice(sDomain * 2, sDomain * 3 + 6 * n8r), 0); - // compute t_low(X) - let polTLow = new BigBuffer((zkey.domainSize + 1) * n8r); - polTLow.set(t.slice(0, zkey.domainSize * n8r), 0); // Add blinding scalar b_10 as a new coefficient n - polTLow.set(ch.b[10], zkey.domainSize * n8r); + polynomials.T1.setCoef(zkey.domainSize, challenges.b[10]); // compute t_mid(X) - let polTMid = new BigBuffer((zkey.domainSize + 1) * n8r); - polTMid.set(t.slice(zkey.domainSize * n8r, zkey.domainSize * 2 * n8r), 0); // Subtract blinding scalar b_10 to the lowest coefficient of t_mid - const lowestMid = Fr.sub(polTMid.slice(0, n8r), ch.b[10]); - polTMid.set(lowestMid, 0); - // Add blinding scalar b_11 as a new coefficient n - polTMid.set(ch.b[11], zkey.domainSize * n8r); + const lowestMid = Fr.sub(polynomials.T2.getCoef(0), challenges.b[10]); + polynomials.T2.setCoef(0, lowestMid); + polynomials.T2.setCoef(zkey.domainSize, challenges.b[11]); // compute t_high(X) - let polTHigh = new BigBuffer((zkey.domainSize + 6) * n8r); - polTHigh.set(t.slice(zkey.domainSize * 2 * n8r, (zkey.domainSize * 3 + 6) * n8r), 0); //Subtract blinding scalar b_11 to the lowest coefficient of t_high - const lowestHigh = Fr.sub(polTHigh.slice(0, n8r), ch.b[11]); - polTHigh.set(lowestHigh, 0); - - proof.T1 = await expTau(polTLow, "multiexp T1"); - proof.T2 = await expTau(polTMid, "multiexp T2"); - proof.T3 = await expTau(polTHigh, "multiexp T3"); - - function mul2(a,b, ap, bp, p) { - let r, rz; - - - const a_b = Fr.mul(a,b); - const a_bp = Fr.mul(a,bp); - const ap_b = Fr.mul(ap,b); - const ap_bp = Fr.mul(ap,bp); - - r = a_b; + const lowestHigh = Fr.sub(polynomials.T3.getCoef(0), challenges.b[11]); + polynomials.T3.setCoef(0, lowestHigh); - let a0 = Fr.add(a_bp, ap_b); - - let a1 = ap_bp; - - rz = a0; - if (p) { - rz = Fr.add(rz, Fr.mul(Z1[p], a1)); - } - - return [r, rz]; - } - - function mul4(a,b,c,d, ap, bp, cp, dp, p) { - let r, rz; - - - const a_b = Fr.mul(a,b); - const a_bp = Fr.mul(a,bp); - const ap_b = Fr.mul(ap,b); - const ap_bp = Fr.mul(ap,bp); - - const c_d = Fr.mul(c,d); - const c_dp = Fr.mul(c,dp); - const cp_d = Fr.mul(cp,d); - const cp_dp = Fr.mul(cp,dp); - - r = Fr.mul(a_b, c_d); - - let a0 = Fr.mul(ap_b, c_d); - a0 = Fr.add(a0, Fr.mul(a_bp, c_d)); - a0 = Fr.add(a0, Fr.mul(a_b, cp_d)); - a0 = Fr.add(a0, Fr.mul(a_b, c_dp)); - - let a1 = Fr.mul(ap_bp, c_d); - a1 = Fr.add(a1, Fr.mul(ap_b, cp_d)); - a1 = Fr.add(a1, Fr.mul(ap_b, c_dp)); - a1 = Fr.add(a1, Fr.mul(a_bp, cp_d)); - a1 = Fr.add(a1, Fr.mul(a_bp, c_dp)); - a1 = Fr.add(a1, Fr.mul(a_b, cp_dp)); - - let a2 = Fr.mul(a_bp, cp_dp); - a2 = Fr.add(a2, Fr.mul(ap_b, cp_dp)); - a2 = Fr.add(a2, Fr.mul(ap_bp, c_dp)); - a2 = Fr.add(a2, Fr.mul(ap_bp, cp_d)); - - let a3 = Fr.mul(ap_bp, cp_dp); - - rz = a0; - if (p) { - rz = Fr.add(rz, Fr.mul(Z1[p], a1)); - rz = Fr.add(rz, Fr.mul(Z2[p], a2)); - rz = Fr.add(rz, Fr.mul(Z3[p], a3)); - } + // The third output of the prover is ([T1]_1, [T2]_1, [T3]_1) + let commitT1 = await polynomials.T1.multiExponentiation(PTau, "T1"); + let commitT2 = await polynomials.T2.multiExponentiation(PTau, "T2"); + let commitT3 = await polynomials.T3.multiExponentiation(PTau, "T3"); - return [r, rz]; - } + proof.addPolynomial("T1", commitT1); + proof.addPolynomial("T2", commitT2); + proof.addPolynomial("T3", commitT3); } async function round4() { - const pol_qm = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_qm, 0 , zkey.domainSize*n8r, sectionsZKey[7][0].p); - - const pol_ql = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_ql, 0 , zkey.domainSize*n8r, sectionsZKey[8][0].p); - - const pol_qr = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_qr, 0 , zkey.domainSize*n8r, sectionsZKey[9][0].p); - - const pol_qo = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_qo, 0 , zkey.domainSize*n8r, sectionsZKey[10][0].p); - - const pol_qc = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_qc, 0 , zkey.domainSize*n8r, sectionsZKey[11][0].p); - - const pol_s3 = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_s3, 0 , zkey.domainSize*n8r, sectionsZKey[12][0].p + 10*zkey.domainSize*n8r); - - const transcript4 = new Uint8Array(G1.F.n8*2*3); - G1.toRprUncompressed(transcript4, 0, proof.T1); - G1.toRprUncompressed(transcript4, G1.F.n8*2, proof.T2); - G1.toRprUncompressed(transcript4, G1.F.n8*4, proof.T3); - ch.xi = hashToFr(transcript4); - - if (logger) logger.debug("xi: " + Fr.toString(ch.xi)); - - proof.eval_a = evalPol(pol_a, ch.xi); - proof.eval_b = evalPol(pol_b, ch.xi); - proof.eval_c = evalPol(pol_c, ch.xi); - proof.eval_s1 = evalPol(pol_s1, ch.xi); - proof.eval_s2 = evalPol(pol_s2, ch.xi); - proof.eval_t = evalPol(pol_t, ch.xi); - proof.eval_zw = evalPol(pol_z, Fr.mul(ch.xi, Fr.w[zkey.power])); - - const coef_ab = Fr.mul(proof.eval_a, proof.eval_b); + if (logger) logger.debug("> Computing challenge xi"); + // STEP 3.1 - Compute evaluation challenge xi ∈ S + transcript.reset(); + transcript.addPolCommitment(proof.getPolynomial("T1")); + transcript.addPolCommitment(proof.getPolynomial("T2")); + transcript.addPolCommitment(proof.getPolynomial("T3")); + + challenges.xi = transcript.getChallenge(); + challenges.xiw = Fr.mul(challenges.xi, Fr.w[zkey.power]); + if (logger) logger.debug("··· challenges.xi: " + Fr.toString(challenges.xi)); + + // Reserve memory for Q's polynomials + polynomials.QL = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.QR = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.QM = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.QO = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.QC = new Polynomial(new BigBuffer(sDomain), curve, logger); + + // Read Q's evaluations from zkey file + await fdZKey.readToBuffer(polynomials.QL.coef, 0, sDomain, zkeySections[ZKEY_PL_QL_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.QR.coef, 0, sDomain, zkeySections[ZKEY_PL_QR_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.QM.coef, 0, sDomain, zkeySections[ZKEY_PL_QM_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.QO.coef, 0, sDomain, zkeySections[ZKEY_PL_QO_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.QC.coef, 0, sDomain, zkeySections[ZKEY_PL_QC_SECTION][0].p); + + proof.addEvaluation("eval_a", polynomials.A.evaluate(challenges.xi)); + proof.addEvaluation("eval_b", polynomials.B.evaluate(challenges.xi)); + proof.addEvaluation("eval_c", polynomials.C.evaluate(challenges.xi)); + proof.addEvaluation("eval_s1", polynomials.Sigma1.evaluate(challenges.xi)); + proof.addEvaluation("eval_s2", polynomials.Sigma2.evaluate(challenges.xi)); + proof.addEvaluation("eval_t", polynomials.T.evaluate(challenges.xi)); + proof.addEvaluation("eval_zw", polynomials.Z.evaluate(challenges.xiw)); + + const coef_ab = Fr.mul(proof.evaluations.eval_a, proof.evaluations.eval_b); - let e2a = proof.eval_a; - const betaxi = Fr.mul(ch.beta, ch.xi); + let e2a = proof.evaluations.eval_a; + const betaxi = Fr.mul(challenges.beta, challenges.xi); e2a = Fr.add( e2a, betaxi); - e2a = Fr.add( e2a, ch.gamma); + e2a = Fr.add( e2a, challenges.gamma); - let e2b = proof.eval_b; + let e2b = proof.evaluations.eval_b; e2b = Fr.add( e2b, Fr.mul(betaxi, zkey.k1)); - e2b = Fr.add( e2b, ch.gamma); + e2b = Fr.add( e2b, challenges.gamma); - let e2c = proof.eval_c; + let e2c = proof.evaluations.eval_c; e2c = Fr.add( e2c, Fr.mul(betaxi, zkey.k2)); - e2c = Fr.add( e2c, ch.gamma); + e2c = Fr.add( e2c, challenges.gamma); - const e2 = Fr.mul(Fr.mul(Fr.mul(e2a, e2b), e2c), ch.alpha); + const e2 = Fr.mul(Fr.mul(Fr.mul(e2a, e2b), e2c), challenges.alpha); - let e3a = proof.eval_a; - e3a = Fr.add( e3a, Fr.mul(ch.beta, proof.eval_s1)); - e3a = Fr.add( e3a, ch.gamma); + let e3a = proof.evaluations.eval_a; + e3a = Fr.add( e3a, Fr.mul(challenges.beta, proof.evaluations.eval_s1)); + e3a = Fr.add( e3a, challenges.gamma); - let e3b = proof.eval_b; - e3b = Fr.add( e3b, Fr.mul(ch.beta, proof.eval_s2)); - e3b = Fr.add( e3b, ch.gamma); + let e3b = proof.evaluations.eval_b; + e3b = Fr.add( e3b, Fr.mul(challenges.beta, proof.evaluations.eval_s2)); + e3b = Fr.add( e3b, challenges.gamma); let e3 = Fr.mul(e3a, e3b); - e3 = Fr.mul(e3, ch.beta); - e3 = Fr.mul(e3, proof.eval_zw); - e3 = Fr.mul(e3, ch.alpha); + e3 = Fr.mul(e3, challenges.beta); + e3 = Fr.mul(e3, proof.evaluations.eval_zw); + e3 = Fr.mul(e3, challenges.alpha); - ch.xim= ch.xi; - for (let i=0; i Computing challenge v"); + + transcript.reset(); + transcript.addScalar(proof.getEvaluation("eval_a")); + transcript.addScalar(proof.getEvaluation("eval_b")); + transcript.addScalar(proof.getEvaluation("eval_c")); + transcript.addScalar(proof.getEvaluation("eval_s1")); + transcript.addScalar(proof.getEvaluation("eval_s2")); + transcript.addScalar(proof.getEvaluation("eval_zw")); + transcript.addScalar(proof.getEvaluation("eval_r")); + + challenges.v = []; + challenges.v[1] = transcript.getChallenge(); + if (logger) logger.debug("··· challenges.v: " + Fr.toString(challenges.v)); + + for (let i=2; i<=6; i++ ) challenges.v[i] = Fr.mul(challenges.v[i-1], challenges.v[1]); - let pol_wxi = new BigBuffer((zkey.domainSize+6)*n8r); - - const xi2m = Fr.mul(ch.xim, ch.xim); - - for (let i = 0; i < zkey.domainSize + 6; i++) { - let w = Fr.zero; - - const polTHigh = pol_t.slice((zkey.domainSize * 2 + i) * n8r, (zkey.domainSize * 2 + i + 1) * n8r); - w = Fr.add(w, Fr.mul(xi2m, polTHigh)); - - if (i < zkey.domainSize + 3) { - w = Fr.add(w, Fr.mul(ch.v[1], pol_r.slice(i * n8r, (i + 1) * n8r))); - } - - if (i < zkey.domainSize + 2) { - w = Fr.add(w, Fr.mul(ch.v[2], pol_a.slice(i * n8r, (i + 1) * n8r))); - w = Fr.add(w, Fr.mul(ch.v[3], pol_b.slice(i * n8r, (i + 1) * n8r))); - w = Fr.add(w, Fr.mul(ch.v[4], pol_c.slice(i * n8r, (i + 1) * n8r))); - } - - if (i < zkey.domainSize) { - const polTLow = pol_t.slice(i * n8r, (i + 1) * n8r); - w = Fr.add(w, polTLow); - - const polTMid = pol_t.slice((zkey.domainSize + i) * n8r, (zkey.domainSize + i + 1) * n8r); - w = Fr.add(w, Fr.mul(ch.xim, polTMid)); - - w = Fr.add(w, Fr.mul(ch.v[5], pol_s1.slice(i * n8r, (i + 1) * n8r))); - w = Fr.add(w, Fr.mul(ch.v[6], pol_s2.slice(i * n8r, (i + 1) * n8r))); - } - - // b_10 and b_11 blinding scalars were applied on round 3 to randomize the polynomials t_low, t_mid, t_high - // Subtract blinding scalar b_10 and b_11 to the lowest coefficient - if (i === 0) { - w = Fr.sub(w, Fr.mul(xi2m, ch.b[11])); - w = Fr.sub(w, Fr.mul(ch.xim, ch.b[10])); - } - - // Add blinding scalars b_10 and b_11 to the coefficient n - if (i === zkey.domainSize) { - w = Fr.add(w, ch.b[10]); - w = Fr.add(w, Fr.mul(ch.xim, ch.b[11])); - } - - pol_wxi.set(w, i * n8r); - } - - let w0 = pol_wxi.slice(0, n8r); - w0 = Fr.sub(w0, proof.eval_t); - w0 = Fr.sub(w0, Fr.mul(ch.v[1], proof.eval_r)); - w0 = Fr.sub(w0, Fr.mul(ch.v[2], proof.eval_a)); - w0 = Fr.sub(w0, Fr.mul(ch.v[3], proof.eval_b)); - w0 = Fr.sub(w0, Fr.mul(ch.v[4], proof.eval_c)); - w0 = Fr.sub(w0, Fr.mul(ch.v[5], proof.eval_s1)); - w0 = Fr.sub(w0, Fr.mul(ch.v[6], proof.eval_s2)); - pol_wxi.set(w0, 0); - - pol_wxi= divPol1(pol_wxi, ch.xi); - - proof.Wxi = await expTau(pol_wxi, "multiexp Wxi"); - - let pol_wxiw = new BigBuffer((zkey.domainSize+3)*n8r); - for (let i=0; i=0; i--) { - res = Fr.add(Fr.mul(res, x), P.slice(i*n8r, (i+1)*n8r)); - } - return res; - } - - function divPol1(P, d) { - const n = P.byteLength/n8r; - const res = new BigBuffer(n*n8r); - res.set(Fr.zero, (n-1) *n8r); - res.set(P.slice((n-1)*n8r, n*n8r), (n-2)*n8r); - for (let i=n-3; i>=0; i--) { - res.set( - Fr.add( - P.slice((i+1)*n8r, (i+2)*n8r), - Fr.mul( - d, - res.slice((i+1)*n8r, (i+2)*n8r) - ) - ), - i*n8r - ); - } - if (!Fr.eq( - P.slice(0, n8r), - Fr.mul( - Fr.neg(d), - res.slice(0, n8r) - ) - )) { - throw new Error("Polinomial does not divide"); - } - return res; - } - - async function expTau(b, name) { - const n = b.byteLength/n8r; - const PTauN = PTau.slice(0, n*curve.G1.F.n8*2); - const bm = await curve.Fr.batchFromMontgomery(b); - let res = await curve.G1.multiExpAffine(PTauN, bm, logger, name); - res = curve.G1.toAffine(res); - return res; - } - - - async function to4T(A, pz) { - pz = pz || []; - let a = await Fr.ifft(A); - const a4 = new BigBuffer(n8r*zkey.domainSize*4); - a4.set(a, 0); - - const a1 = new BigBuffer(n8r*(zkey.domainSize + pz.length)); - a1.set(a, 0); - for (let i= 0; i { - res.polynomials[key] = this.curve.G1.toObject(this.polynomials[key]); + const value = this.curve.G1.toObject(this.polynomials[key]); + if(splitFields) { + res.polynomials[key] = value; + } else { + res[key] = value; + } }); Object.keys(this.evaluations).forEach(key => { - res.evaluations[key] = this.curve.Fr.toObject(this.evaluations[key]); + const value = this.curve.Fr.toObject(this.evaluations[key]); + if(splitFields) { + res.polynomials[key] = value; + } else { + res[key] = value; + } }); return res; diff --git a/src/zkey_utils.js b/src/zkey_utils.js index 7f1124c9..bea870df 100644 --- a/src/zkey_utils.js +++ b/src/zkey_utils.js @@ -279,7 +279,7 @@ async function readHeaderPlonk(fd, sections, toObject) { zkey.domainSize = await fd.readULE32(); zkey.power = log2(zkey.domainSize); zkey.nAdditions = await fd.readULE32(); - zkey.nConstrains = await fd.readULE32(); + zkey.nConstraints = await fd.readULE32(); zkey.k1 = await fd.read(n8r); zkey.k2 = await fd.read(n8r); From 44b1efb611947b5abde82bd76535e52a28fcf34b Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Mon, 1 May 2023 09:21:19 +0200 Subject: [PATCH 05/48] change logger.in -> logger.debug --- src/plonk_prove.js | 98 ++++++++++++++++++++++++++-------------------- 1 file changed, 55 insertions(+), 43 deletions(-) diff --git a/src/plonk_prove.js b/src/plonk_prove.js index da5193bf..777a7770 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -75,20 +75,20 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger const sDomain = zkey.domainSize * n8r; if (logger) { - logger.info("----------------------------"); - logger.info(" PLONK PROVE SETTINGS"); - logger.info(` Curve: ${curve.name}`); - logger.info(` Circuit power: ${zkey.power}`); - logger.info(` Domain size: ${zkey.domainSize}`); - logger.info(` Vars: ${zkey.nVars}`); - logger.info(` Public vars: ${zkey.nPublic}`); - logger.info(` Constraints: ${zkey.nConstraints}`); - logger.info(` Additions: ${zkey.nAdditions}`); - logger.info("----------------------------"); + logger.debug("----------------------------"); + logger.debug(" PLONK PROVE SETTINGS"); + logger.debug(` Curve: ${curve.name}`); + logger.debug(` Circuit power: ${zkey.power}`); + logger.debug(` Domain size: ${zkey.domainSize}`); + logger.debug(` Vars: ${zkey.nVars}`); + logger.debug(` Public vars: ${zkey.nPublic}`); + logger.debug(` Constraints: ${zkey.nConstraints}`); + logger.debug(` Additions: ${zkey.nAdditions}`); + logger.debug("----------------------------"); } //Read witness data - if (logger) logger.info("> Reading witness file data"); + if (logger) logger.debug("> Reading witness file data"); const buffWitness = await binFileUtils.readSection(fdWtns, sectionsWtns, 2); // First element in plonk is not used and can be any value. (But always the same). @@ -104,11 +104,11 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger let proof = new Proof(curve, logger); const transcript = new Keccak256Transcript(curve); - if (logger) logger.info(`> Reading Section ${ZKEY_PL_ADDITIONS_SECTION}. Additions`); + if (logger) logger.debug(`> Reading Section ${ZKEY_PL_ADDITIONS_SECTION}. Additions`); await calculateAdditions(); - if (logger) logger.info(`> Reading Section ${ZKEY_PL_SIGMA_SECTION}. Sigma1, Sigma2 & Sigma 3`); - if (logger) logger.info("··· Reading Sigma polynomials "); + if (logger) logger.debug(`> Reading Section ${ZKEY_PL_SIGMA_SECTION}. Sigma1, Sigma2 & Sigma 3`); + if (logger) logger.debug("··· Reading Sigma polynomials "); polynomials.Sigma1 = new Polynomial(new BigBuffer(sDomain), curve, logger); polynomials.Sigma2 = new Polynomial(new BigBuffer(sDomain), curve, logger); polynomials.Sigma3 = new Polynomial(new BigBuffer(sDomain), curve, logger); @@ -117,7 +117,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger await fdZKey.readToBuffer(polynomials.Sigma2.coef, 0, sDomain, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 5 * sDomain); await fdZKey.readToBuffer(polynomials.Sigma3.coef, 0, sDomain, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 10 * sDomain); - if (logger) logger.info("··· Reading Sigma evaluations"); + if (logger) logger.debug("··· Reading Sigma evaluations"); evaluations.Sigma1 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); evaluations.Sigma2 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); evaluations.Sigma3 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); @@ -126,13 +126,23 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger await fdZKey.readToBuffer(evaluations.Sigma2.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 6 * sDomain); await fdZKey.readToBuffer(evaluations.Sigma3.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 11 * sDomain); - if (logger) logger.info(`> Reading Section ${ZKEY_PL_PTAU_SECTION}. Powers of Tau`); + if (logger) logger.debug(`> Reading Section ${ZKEY_PL_PTAU_SECTION}. Powers of Tau`); const PTau = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_PTAU_SECTION); + if (logger) logger.debug(""); + if (logger) logger.debug("> ROUND 1"); await round1(); + + if (logger) logger.debug("> ROUND 2"); await round2(); + + if (logger) logger.debug("> ROUND 3"); await round3(); + + if (logger) logger.debug("> ROUND 4"); await round4(); + + if (logger) logger.debug("> ROUND 5"); await round5(); /////////////////////// @@ -154,13 +164,15 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger _proof.protocol = "plonk"; _proof.curve = curve.name; + if (logger) logger.debug("PLONK PROVER FINISHED"); + return { proof: stringifyBigInts(_proof), publicSignals: stringifyBigInts(publicSignals) }; async function calculateAdditions() { - if (logger) logger.info("··· Computing additions"); + if (logger) logger.debug("··· Computing additions"); const additionsBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_ADDITIONS_SECTION); // sizes: wireId_x = 4 bytes (32 bits), factor_x = field size bits @@ -168,7 +180,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger const sSum = 8 + n8r * 2; for (let i = 0; i < zkey.nAdditions; i++) { - if (logger && (0 !== i) && (i % 100000 === 0)) logger.info(` addition ${i}/${zkey.nAdditions}`); + if (logger && (0 !== i) && (i % 100000 === 0)) logger.debug(` addition ${i}/${zkey.nAdditions}`); // Read addition values let offset = i * sSum; @@ -214,7 +226,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } // STEP 1.2 - Compute wire polynomials a(X), b(X) and c(X) - if (logger) logger.info("> Computing A, B, C wire polynomials"); + if (logger) logger.debug("> Computing A, B, C wire polynomials"); await computeWirePolynomials(); // The first output of the prover is ([A]_1, [B]_1, [C]_1) @@ -230,7 +242,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } async function computeWirePolynomials() { - if (logger) logger.info("··· Reading data from zkey file"); + if (logger) logger.debug("··· Reading data from zkey file"); // Build A, B and C evaluations buffer from zkey and witness files buffers.A = new BigBuffer(sDomain); buffers.B = new BigBuffer(sDomain); @@ -263,19 +275,19 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger buffers.C = await Fr.batchToMontgomery(buffers.C); // Compute the coefficients of the wire polynomials a(X), b(X) and c(X) from A,B & C buffers - if (logger) logger.info("··· Computing A ifft"); + if (logger) logger.debug("··· Computing A ifft"); polynomials.A = await Polynomial.fromEvaluations(buffers.A, curve, logger); - if (logger) logger.info("··· Computing B ifft"); + if (logger) logger.debug("··· Computing B ifft"); polynomials.B = await Polynomial.fromEvaluations(buffers.B, curve, logger); - if (logger) logger.info("··· Computing C ifft"); + if (logger) logger.debug("··· Computing C ifft"); polynomials.C = await Polynomial.fromEvaluations(buffers.C, curve, logger); // Compute extended evaluations of a(X), b(X) and c(X) polynomials - if (logger) logger.info("··· Computing A fft"); + if (logger) logger.debug("··· Computing A fft"); evaluations.A = await Evaluations.fromPolynomial(polynomials.A, 4, curve, logger); - if (logger) logger.info("··· Computing B fft"); + if (logger) logger.debug("··· Computing B fft"); evaluations.B = await Evaluations.fromPolynomial(polynomials.B, 4, curve, logger); - if (logger) logger.info("··· Computing C fft"); + if (logger) logger.debug("··· Computing C fft"); evaluations.C = await Evaluations.fromPolynomial(polynomials.C, 4, curve, logger); // Blind a(X), b(X) and c(X) polynomials coefficients with blinding scalars b @@ -324,7 +336,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger if (logger) logger.debug("··· challenges.gamma: " + Fr.toString(challenges.gamma)); // STEP 2.2 - Compute permutation polynomial z(X) - if (logger) logger.info("> Computing Z polynomial"); + if (logger) logger.debug("> Computing Z polynomial"); await computeZ(); // The second output of the prover is ([Z]_1) @@ -334,7 +346,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } async function computeZ() { - if (logger) logger.info("··· Computing Z evaluations"); + if (logger) logger.debug("··· Computing Z evaluations"); let numArr = new BigBuffer(sDomain); let denArr = new BigBuffer(sDomain); @@ -411,11 +423,11 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } // Compute polynomial coefficients z(X) from buffers.Z - if (logger) logger.info("··· Computing Z ifft"); + if (logger) logger.debug("··· Computing Z ifft"); polynomials.Z = await Polynomial.fromEvaluations(buffers.Z, curve, logger); // Compute extended evaluations of z(X) polynomial - if (logger) logger.info("··· Computing Z fft"); + if (logger) logger.debug("··· Computing Z fft"); evaluations.Z = await Evaluations.fromPolynomial(polynomials.Z, 4, curve, logger); // Blind z(X) polynomial coefficients with blinding scalars b @@ -439,7 +451,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger challenges.alpha2 = Fr.square(challenges.alpha); if (logger) logger.debug("··· challenges.alpha: " + Fr.toString(challenges.alpha)); - if (logger) logger.info(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + + if (logger) logger.debug(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + `, ${ZKEY_PL_QM_SECTION}, ${ZKEY_PL_QO_SECTION}, ${ZKEY_PL_QC_SECTION}. Q selectors`); // Reserve memory for Q's evaluations evaluations.QL = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); @@ -467,7 +479,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger let w = Fr.one; for (let i=0; i Date: Tue, 2 May 2023 15:52:07 +0200 Subject: [PATCH 06/48] update protocol to last version --- src/plonk_prove.js | 245 ++++++++++++++++++++++++++------------------ src/plonk_verify.js | 230 ++++++++++++++++++----------------------- 2 files changed, 244 insertions(+), 231 deletions(-) diff --git a/src/plonk_prove.js b/src/plonk_prove.js index 777a7770..94e54074 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -129,6 +129,13 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger if (logger) logger.debug(`> Reading Section ${ZKEY_PL_PTAU_SECTION}. Powers of Tau`); const PTau = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_PTAU_SECTION); + let publicSignals = []; + + for (let i=1; i<= zkey.nPublic; i++) { + const pub = buffWitness.slice(i*Fr.n8, i*Fr.n8+Fr.n8); + publicSignals.push(Scalar.fromRprLE(pub)); + } + if (logger) logger.debug(""); if (logger) logger.debug("> ROUND 1"); await round1(); @@ -152,13 +159,6 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger await fdZKey.close(); await fdWtns.close(); - let publicSignals = []; - - for (let i=1; i<= zkey.nPublic; i++) { - const pub = buffWitness.slice(i*Fr.n8, i*Fr.n8+Fr.n8); - publicSignals.push(Scalar.fromRprLE(pub)); - } - // Prepare proof let _proof = proof.toObjectProof(false); _proof.protocol = "plonk"; @@ -222,7 +222,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger async function round1() { challenges.b = []; for (let i=1; i<=11; i++) { - challenges.b[i] = curve.Fr.one;//curve.Fr.random(); + challenges.b[i] = curve.Fr.random(); } // STEP 1.2 - Compute wire polynomials a(X), b(X) and c(X) @@ -327,13 +327,13 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger transcript.addPolCommitment(proof.getPolynomial("C")); challenges.beta = transcript.getChallenge(); - if (logger) logger.debug("··· challenges.beta: " + Fr.toString(challenges.beta)); + if (logger) logger.debug("··· challenges.beta: " + Fr.toString(challenges.beta, 16)); // Compute permutation challenge gamma transcript.reset(); transcript.addScalar(challenges.beta); challenges.gamma = transcript.getChallenge(); - if (logger) logger.debug("··· challenges.gamma: " + Fr.toString(challenges.gamma)); + if (logger) logger.debug("··· challenges.gamma: " + Fr.toString(challenges.gamma, 16)); // STEP 2.2 - Compute permutation polynomial z(X) if (logger) logger.debug("> Computing Z polynomial"); @@ -449,7 +449,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger challenges.alpha = transcript.getChallenge(); challenges.alpha2 = Fr.square(challenges.alpha); - if (logger) logger.debug("··· challenges.alpha: " + Fr.toString(challenges.alpha)); + if (logger) logger.debug("··· challenges.alpha: " + Fr.toString(challenges.alpha, 16)); if (logger) logger.debug(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + `, ${ZKEY_PL_QM_SECTION}, ${ZKEY_PL_QO_SECTION}, ${ZKEY_PL_QC_SECTION}. Q selectors`); @@ -637,7 +637,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger const lowestHigh = Fr.sub(polynomials.T3.getCoef(0), challenges.b[11]); polynomials.T3.setCoef(0, lowestHigh); - // The third output of the prover is ([T1]_1, [T2]_1, [T3]_1) + // Third output of the prover is ([T1]_1, [T2]_1, [T3]_1) let commitT1 = await polynomials.T1.multiExponentiation(PTau, "T1"); let commitT2 = await polynomials.T2.multiExponentiation(PTau, "T2"); let commitT3 = await polynomials.T3.multiExponentiation(PTau, "T3"); @@ -649,6 +649,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger async function round4() { if (logger) logger.debug("> Computing challenge xi"); + // STEP 3.1 - Compute evaluation challenge xi ∈ S transcript.reset(); transcript.addPolCommitment(proof.getPolynomial("T1")); @@ -657,8 +658,55 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger challenges.xi = transcript.getChallenge(); challenges.xiw = Fr.mul(challenges.xi, Fr.w[zkey.power]); - if (logger) logger.debug("··· challenges.xi: " + Fr.toString(challenges.xi)); + + if (logger) logger.debug("··· challenges.xi: " + Fr.toString(challenges.xi, 16)); + + // Fourth output of the prover is ( a(xi), b(xi), c(xi), s1(xi), s2(xi), z(xiw) ) + proof.addEvaluation("eval_a", polynomials.A.evaluate(challenges.xi)); + proof.addEvaluation("eval_b", polynomials.B.evaluate(challenges.xi)); + proof.addEvaluation("eval_c", polynomials.C.evaluate(challenges.xi)); + proof.addEvaluation("eval_s1", polynomials.Sigma1.evaluate(challenges.xi)); + proof.addEvaluation("eval_s2", polynomials.Sigma2.evaluate(challenges.xi)); + proof.addEvaluation("eval_zw", polynomials.Z.evaluate(challenges.xiw)); + } + + async function round5() { + if (logger) logger.debug("> Computing challenge v"); + transcript.reset(); + transcript.addScalar(proof.getEvaluation("eval_a")); + transcript.addScalar(proof.getEvaluation("eval_b")); + transcript.addScalar(proof.getEvaluation("eval_c")); + transcript.addScalar(proof.getEvaluation("eval_s1")); + transcript.addScalar(proof.getEvaluation("eval_s2")); + transcript.addScalar(proof.getEvaluation("eval_zw")); + + challenges.v = []; + challenges.v[1] = transcript.getChallenge(); + if (logger) logger.debug("··· challenges.v: " + Fr.toString(challenges.v[1], 16)); + + for (let i = 2; i < 6; i++) { + challenges.v[i] = Fr.mul(challenges.v[i - 1], challenges.v[1]); + } + + await computeR(); + + computeWxi(); + + // Compute opening proof polynomial Wxiω(X) + computeWxiw(); + + // Fifth output of the prover is ([Wxi]_1, [Wxiw]_1) + let commitWxi = await polynomials.Wxi.multiExponentiation(PTau, "Wxi"); + let commitWxiw = await polynomials.Wxiw.multiExponentiation(PTau, "Wxiw"); + + proof.addPolynomial("Wxi", commitWxi); + proof.addPolynomial("Wxiw", commitWxiw); + } + + async function computeR() { + const Fr = curve.Fr; + // Reserve memory for Q's polynomials polynomials.QL = new Polynomial(new BigBuffer(sDomain), curve, logger); polynomials.QR = new Polynomial(new BigBuffer(sDomain), curve, logger); @@ -671,129 +719,126 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger await fdZKey.readToBuffer(polynomials.QR.coef, 0, sDomain, zkeySections[ZKEY_PL_QR_SECTION][0].p); await fdZKey.readToBuffer(polynomials.QM.coef, 0, sDomain, zkeySections[ZKEY_PL_QM_SECTION][0].p); await fdZKey.readToBuffer(polynomials.QO.coef, 0, sDomain, zkeySections[ZKEY_PL_QO_SECTION][0].p); - await fdZKey.readToBuffer(polynomials.QC.coef, 0, sDomain, zkeySections[ZKEY_PL_QC_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.QC.coef, 0, sDomain, zkeySections[ZKEY_PL_QC_SECTION][0].p); + + challenges.xin = challenges.xi; + for (let i = 0; i < zkey.power; i++) { + challenges.xin = Fr.square(challenges.xin); + } - proof.addEvaluation("eval_a", polynomials.A.evaluate(challenges.xi)); - proof.addEvaluation("eval_b", polynomials.B.evaluate(challenges.xi)); - proof.addEvaluation("eval_c", polynomials.C.evaluate(challenges.xi)); - proof.addEvaluation("eval_s1", polynomials.Sigma1.evaluate(challenges.xi)); - proof.addEvaluation("eval_s2", polynomials.Sigma2.evaluate(challenges.xi)); - proof.addEvaluation("eval_t", polynomials.T.evaluate(challenges.xi)); - proof.addEvaluation("eval_zw", polynomials.Z.evaluate(challenges.xiw)); + challenges.zh = Fr.sub(challenges.xin, Fr.one); + + const L = []; + + const n = Fr.e(zkey.domainSize); + let w = Fr.one; + for (let i = 1; i <= Math.max(1, zkey.nPublic); i++) { + L[i] = Fr.div(Fr.mul(w, challenges.zh), Fr.mul(n, Fr.sub(challenges.xi, w))); + w = Fr.mul(w, Fr.w[zkey.power]); + } + + const eval_l1 = Fr.div( + Fr.sub(challenges.xin, Fr.one), + Fr.mul(n, Fr.sub(challenges.xi, Fr.one)) + ); + + if (logger) { + logger.debug("Lagrange Evaluations: "); + for (let i=1; i Computing challenge v"); + let r0 = Fr.sub(eval_pi, Fr.mul(e3, Fr.add(proof.evaluations.eval_c, challenges.gamma))); + r0 = Fr.sub(r0, e4); - transcript.reset(); - transcript.addScalar(proof.getEvaluation("eval_a")); - transcript.addScalar(proof.getEvaluation("eval_b")); - transcript.addScalar(proof.getEvaluation("eval_c")); - transcript.addScalar(proof.getEvaluation("eval_s1")); - transcript.addScalar(proof.getEvaluation("eval_s2")); - transcript.addScalar(proof.getEvaluation("eval_zw")); - transcript.addScalar(proof.getEvaluation("eval_r")); + logger.debug("r0: " + Fr.toString(r0, 16)); - challenges.v = []; - challenges.v[1] = transcript.getChallenge(); - if (logger) logger.debug("··· challenges.v: " + Fr.toString(challenges.v[1])); + polynomials.R.addScalar(r0); + } - for (let i=2; i<=6; i++ ) { - challenges.v[i] = Fr.mul(challenges.v[i-1], challenges.v[1]); - } - + function computeWxi() { polynomials.Wxi = new Polynomial(new BigBuffer(sDomain + 6 * n8r), curve, logger); - polynomials.Wxi.add(polynomials.T1); - polynomials.Wxi.add(polynomials.T2, challenges.xim); - polynomials.Wxi.add(polynomials.T3, Fr.square(challenges.xim)); - polynomials.Wxi.add(polynomials.R, challenges.v[1]); - polynomials.Wxi.add(polynomials.A, challenges.v[2]); - polynomials.Wxi.add(polynomials.B, challenges.v[3]); - polynomials.Wxi.add(polynomials.C, challenges.v[4]); - polynomials.Wxi.add(polynomials.Sigma1, challenges.v[5]); - polynomials.Wxi.add(polynomials.Sigma2, challenges.v[6]); - - polynomials.Wxi.subScalar(proof.evaluations.eval_t); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[1], proof.evaluations.eval_r)); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[2], proof.evaluations.eval_a)); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[3], proof.evaluations.eval_b)); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[4], proof.evaluations.eval_c)); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[5], proof.evaluations.eval_s1)); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[6], proof.evaluations.eval_s2)); + polynomials.Wxi.add(polynomials.R); + polynomials.Wxi.add(polynomials.A, challenges.v[1]); + polynomials.Wxi.add(polynomials.B, challenges.v[2]); + polynomials.Wxi.add(polynomials.C, challenges.v[3]); + polynomials.Wxi.add(polynomials.Sigma1, challenges.v[4]); + polynomials.Wxi.add(polynomials.Sigma2, challenges.v[5]); + + polynomials.Wxi.subScalar(Fr.mul(challenges.v[1], proof.evaluations.eval_a)); + polynomials.Wxi.subScalar(Fr.mul(challenges.v[2], proof.evaluations.eval_b)); + polynomials.Wxi.subScalar(Fr.mul(challenges.v[3], proof.evaluations.eval_c)); + polynomials.Wxi.subScalar(Fr.mul(challenges.v[4], proof.evaluations.eval_s1)); + polynomials.Wxi.subScalar(Fr.mul(challenges.v[5], proof.evaluations.eval_s2)); polynomials.Wxi.divByZerofier(1, challenges.xi); + } - // Compute opening proof polynomial Wxiω(X) + async function computeWxiw() { polynomials.Wxiw = Polynomial.fromPolynomial(polynomials.Z, curve, logger); polynomials.Wxiw.subScalar(proof.evaluations.eval_zw); polynomials.Wxiw.divByZerofier(1, challenges.xiw); - - // The fifth output of the prover is ([Wxi]_1, [Wxiw]_1) - let commitWxi = await polynomials.Wxi.multiExponentiation(PTau, "Wxi"); - let commitWxiw = await polynomials.Wxiw.multiExponentiation(PTau, "Wxiw"); - - proof.addPolynomial("Wxi", commitWxi); - proof.addPolynomial("Wxiw", commitWxiw); } -} \ No newline at end of file +} diff --git a/src/plonk_verify.js b/src/plonk_verify.js index 2859fccf..27196607 100644 --- a/src/plonk_verify.js +++ b/src/plonk_verify.js @@ -26,9 +26,10 @@ import jsSha3 from "js-sha3"; const { keccak256 } = jsSha3; + export default async function plonkVerify(_vk_verifier, _publicSignals, _proof, logger) { let vk_verifier = unstringifyBigInts(_vk_verifier); - let proof = unstringifyBigInts(_proof); + _proof = unstringifyBigInts(_proof); let publicSignals = unstringifyBigInts(_publicSignals); const curve = await curves.getCurveFromName(vk_verifier.curve); @@ -36,31 +37,35 @@ export default async function plonkVerify(_vk_verifier, _publicSignals, _proof, const Fr = curve.Fr; const G1 = curve.G1; - proof = fromObjectProof(curve,proof); + if (logger) logger.info("PLONK VERIFIER STARTED"); + + let proof = fromObjectProof(curve,_proof); vk_verifier = fromObjectVk(curve, vk_verifier); + if (!isWellConstructed(curve, proof)) { logger.error("Proof is not well constructed"); return false; } + if (publicSignals.length != vk_verifier.nPublic) { logger.error("Invalid number of public inputs"); return false; } - const challanges = calculateChallanges(curve, proof, publicSignals); + const challenges = calculatechallenges(curve, proof, publicSignals); if (logger) { - logger.debug("beta: " + Fr.toString(challanges.beta, 16)); - logger.debug("gamma: " + Fr.toString(challanges.gamma, 16)); - logger.debug("alpha: " + Fr.toString(challanges.alpha, 16)); - logger.debug("xi: " + Fr.toString(challanges.xi, 16)); - logger.debug("v1: " + Fr.toString(challanges.v[1], 16)); - logger.debug("v6: " + Fr.toString(challanges.v[6], 16)); - logger.debug("u: " + Fr.toString(challanges.u, 16)); + logger.debug("beta: " + Fr.toString(challenges.beta, 16)); + logger.debug("gamma: " + Fr.toString(challenges.gamma, 16)); + logger.debug("alpha: " + Fr.toString(challenges.alpha, 16)); + logger.debug("xi: " + Fr.toString(challenges.xi, 16)); + for(let i=1;i<6;i++) { + if (logger) logger.debug("v: " + Fr.toString(challenges.v[i], 16)); + } + logger.debug("u: " + Fr.toString(challenges.u, 16)); } - const L = calculateLagrangeEvaluations(curve, challanges, vk_verifier); + const L = calculateLagrangeEvaluations(curve, challenges, vk_verifier); if (logger) { - logger.debug("Lagrange Evaluations: "); for (let i=1; i Date: Tue, 2 May 2023 17:46:21 +0200 Subject: [PATCH 07/48] Refactor Fiat-Shamir adding preprocessed circuit dependent values --- src/plonk_prove.js | 163 ++++++++++++++++++++++++++++---------------- src/plonk_verify.js | 106 +++++++++++++++------------- 2 files changed, 162 insertions(+), 107 deletions(-) diff --git a/src/plonk_prove.js b/src/plonk_prove.js index 94e54074..833a45df 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -28,21 +28,21 @@ import { Proof } from "./proof.js"; import { Keccak256Transcript } from "./Keccak256Transcript.js"; import { MulZ } from "./mul_z.js"; import { ZKEY_PL_HEADER_SECTION, - ZKEY_PL_ADDITIONS_SECTION, - ZKEY_PL_A_MAP_SECTION, - ZKEY_PL_B_MAP_SECTION, - ZKEY_PL_C_MAP_SECTION, - ZKEY_PL_QM_SECTION, - ZKEY_PL_QL_SECTION, - ZKEY_PL_QR_SECTION, - ZKEY_PL_QO_SECTION, - ZKEY_PL_QC_SECTION, - ZKEY_PL_SIGMA_SECTION, - ZKEY_PL_LAGRANGE_SECTION, - ZKEY_PL_PTAU_SECTION, - } from "./plonk.js"; - import { Polynomial } from "./polynomial/polynomial.js"; - import { Evaluations } from "./polynomial/evaluations.js"; + ZKEY_PL_ADDITIONS_SECTION, + ZKEY_PL_A_MAP_SECTION, + ZKEY_PL_B_MAP_SECTION, + ZKEY_PL_C_MAP_SECTION, + ZKEY_PL_QM_SECTION, + ZKEY_PL_QL_SECTION, + ZKEY_PL_QR_SECTION, + ZKEY_PL_QO_SECTION, + ZKEY_PL_QC_SECTION, + ZKEY_PL_SIGMA_SECTION, + ZKEY_PL_LAGRANGE_SECTION, + ZKEY_PL_PTAU_SECTION, +} from "./plonk.js"; +import { Polynomial } from "./polynomial/polynomial.js"; +import { Evaluations } from "./polynomial/evaluations.js"; export default async function plonk16Prove(zkeyFileName, witnessFileName, logger) { const {fd: fdWtns, sections: sectionsWtns} = await binFileUtils.readBinFile(witnessFileName, "wtns", 2, 1<<25, 1<<23); @@ -220,6 +220,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } async function round1() { + // STEP 1.1 - Generate random blinding scalars (b1, ..., b11) ∈ F challenges.b = []; for (let i=1; i<=11; i++) { challenges.b[i] = curve.Fr.random(); @@ -229,11 +230,13 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger if (logger) logger.debug("> Computing A, B, C wire polynomials"); await computeWirePolynomials(); - // The first output of the prover is ([A]_1, [B]_1, [C]_1) + // STEP 1.3 - Compute [a]_1, [b]_1, [c]_1 + if (logger) logger.debug("> Computing A, B, C MSM"); let commitA = await polynomials.A.multiExponentiation(PTau, "A"); let commitB = await polynomials.B.multiExponentiation(PTau, "B"); let commitC = await polynomials.C.multiExponentiation(PTau, "C"); + // First output of the prover is ([A]_1, [B]_1, [C]_1) proof.addPolynomial("A", commitA); proof.addPolynomial("B", commitB); proof.addPolynomial("C", commitC); @@ -243,11 +246,13 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger async function computeWirePolynomials() { if (logger) logger.debug("··· Reading data from zkey file"); + // Build A, B and C evaluations buffer from zkey and witness files buffers.A = new BigBuffer(sDomain); buffers.B = new BigBuffer(sDomain); buffers.C = new BigBuffer(sDomain); + // Read zkey file to the buffers const aMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_A_MAP_SECTION); const bMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_B_MAP_SECTION); const cMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_C_MAP_SECTION); @@ -295,7 +300,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger polynomials.B.blindCoefficients([challenges.b[4], challenges.b[3]]); polynomials.C.blindCoefficients([challenges.b[6], challenges.b[5]]); - // // Check degrees + // Check degrees if (polynomials.A.degree() >= zkey.domainSize + 2) { throw new Error("A Polynomial is not well calculated"); } @@ -313,8 +318,14 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger if (logger) logger.debug("> Computing challenges beta and gamma"); transcript.reset(); - // TODO Add circuit dependent commitment to the transcript!!!!! - //transcript.addPolCommitment(zkey.?????); + transcript.addPolCommitment(zkey.Qm); + transcript.addPolCommitment(zkey.Ql); + transcript.addPolCommitment(zkey.Qr); + transcript.addPolCommitment(zkey.Qo); + transcript.addPolCommitment(zkey.Ql); + transcript.addPolCommitment(zkey.S1); + transcript.addPolCommitment(zkey.S2); + transcript.addPolCommitment(zkey.S3); // Add A to the transcript for (let i = 0; i < zkey.nPublic; i++) { @@ -339,9 +350,11 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger if (logger) logger.debug("> Computing Z polynomial"); await computeZ(); - // The second output of the prover is ([Z]_1) + // STEP 2.3 - Compute permutation [z]_1 + if (logger) logger.debug("> Computing Z MSM"); let commitZ = await polynomials.Z.multiExponentiation(PTau, "Z"); + // Second output of the prover is ([Z]_1) proof.addPolynomial("Z", commitZ); } @@ -443,16 +456,37 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger async function round3() { if (logger) logger.debug("> Computing challenge alpha"); - // STEP 3.1 - Compute evaluation challenge xi ∈ S + + // STEP 3.1 - Compute evaluation challenge alpha ∈ F transcript.reset(); + transcript.addScalar(challenges.beta); + transcript.addScalar(challenges.gamma); transcript.addPolCommitment(proof.getPolynomial("Z")); challenges.alpha = transcript.getChallenge(); challenges.alpha2 = Fr.square(challenges.alpha); if (logger) logger.debug("··· challenges.alpha: " + Fr.toString(challenges.alpha, 16)); - if (logger) logger.debug(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + - `, ${ZKEY_PL_QM_SECTION}, ${ZKEY_PL_QO_SECTION}, ${ZKEY_PL_QC_SECTION}. Q selectors`); + // Compute quotient polynomial T(X) + if (logger) logger.debug("> Computing T polynomial"); + await computeT(); + + // Compute [T1]_1, [T2]_1, [T3]_1 + if (logger) logger.debug("> Computing T MSM"); + let commitT1 = await polynomials.T1.multiExponentiation(PTau, "T1"); + let commitT2 = await polynomials.T2.multiExponentiation(PTau, "T2"); + let commitT3 = await polynomials.T3.multiExponentiation(PTau, "T3"); + + // Third output of the prover is ([T1]_1, [T2]_1, [T3]_1) + proof.addPolynomial("T1", commitT1); + proof.addPolynomial("T2", commitT2); + proof.addPolynomial("T3", commitT3); + } + + async function computeT() { + if (logger) + logger.debug(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + + `, ${ZKEY_PL_QM_SECTION}, ${ZKEY_PL_QO_SECTION}, ${ZKEY_PL_QC_SECTION}. Q selectors`); // Reserve memory for Q's evaluations evaluations.QL = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); evaluations.QR = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); @@ -477,9 +511,12 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger buffers.T = new BigBuffer(sDomain * 4); buffers.Tz = new BigBuffer(sDomain * 4); + if (logger) logger.debug("··· Computing T evaluations"); + let w = Fr.one; - for (let i=0; i= zkey.domainSize * 3 + 6) { throw new Error("T Polynomial is not well calculated"); } - + // t(x) has degree 3n + 5, we are going to split t(x) into three smaller polynomials: // T1' and T2' with a degree < n and T3' with a degree n+5 // such that t(x) = T1'(X) + X^n T2'(X) + X^{2n} T3'(X) @@ -614,7 +659,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger // T3(X) = T3'(X) - b_11 // such that // t(X) = T1(X) + X^n T2(X) + X^2n T3(X) - + logger.debug("··· Computing T1, T2, T3 polynomials"); polynomials.T1 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); polynomials.T2 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); polynomials.T3 = new Polynomial(new BigBuffer((zkey.domainSize + 6) * n8r), curve, logger); @@ -636,22 +681,14 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger //Subtract blinding scalar b_11 to the lowest coefficient of t_high const lowestHigh = Fr.sub(polynomials.T3.getCoef(0), challenges.b[11]); polynomials.T3.setCoef(0, lowestHigh); - - // Third output of the prover is ([T1]_1, [T2]_1, [T3]_1) - let commitT1 = await polynomials.T1.multiExponentiation(PTau, "T1"); - let commitT2 = await polynomials.T2.multiExponentiation(PTau, "T2"); - let commitT3 = await polynomials.T3.multiExponentiation(PTau, "T3"); - - proof.addPolynomial("T1", commitT1); - proof.addPolynomial("T2", commitT2); - proof.addPolynomial("T3", commitT3); } async function round4() { if (logger) logger.debug("> Computing challenge xi"); - // STEP 3.1 - Compute evaluation challenge xi ∈ S + // STEP 4.1 - Compute evaluation challenge xi ∈ F transcript.reset(); + transcript.addScalar(challenges.alpha); transcript.addPolCommitment(proof.getPolynomial("T1")); transcript.addPolCommitment(proof.getPolynomial("T2")); transcript.addPolCommitment(proof.getPolynomial("T3")); @@ -672,8 +709,10 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger async function round5() { if (logger) logger.debug("> Computing challenge v"); - + + // STEP 5.1 - Compute evaluation challenge v ∈ F transcript.reset(); + transcript.addScalar(challenges.xi); transcript.addScalar(proof.getEvaluation("eval_a")); transcript.addScalar(proof.getEvaluation("eval_b")); transcript.addScalar(proof.getEvaluation("eval_c")); @@ -689,17 +728,23 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger challenges.v[i] = Fr.mul(challenges.v[i - 1], challenges.v[1]); } + // STEP 5.2 Compute linearisation polynomial r(X) + if (logger) logger.debug("> Computing linearisation polynomial R(X)"); await computeR(); + //STEP 5.3 Compute opening proof polynomial Wxi(X) + if (logger) logger.debug("> Computing opening proof polynomial Wxi(X) polynomial"); computeWxi(); - // Compute opening proof polynomial Wxiω(X) + //STEP 5.4 Compute opening proof polynomial Wxiw(X) + if (logger) logger.debug("> Computing opening proof polynomial Wxiw(X) polynomial"); computeWxiw(); - // Fifth output of the prover is ([Wxi]_1, [Wxiw]_1) + if (logger) logger.debug("> Computing Wxi, Wxiw MSM"); let commitWxi = await polynomials.Wxi.multiExponentiation(PTau, "Wxi"); let commitWxiw = await polynomials.Wxiw.multiExponentiation(PTau, "Wxiw"); + // Fifth output of the prover is ([Wxi]_1, [Wxiw]_1) proof.addPolynomial("Wxi", commitWxi); proof.addPolynomial("Wxiw", commitWxiw); } diff --git a/src/plonk_verify.js b/src/plonk_verify.js index 27196607..212782d0 100644 --- a/src/plonk_verify.js +++ b/src/plonk_verify.js @@ -18,12 +18,10 @@ */ /* Implementation of this paper: https://eprint.iacr.org/2019/953.pdf */ -import { Scalar } from "ffjavascript"; import * as curves from "./curves.js"; import { utils } from "ffjavascript"; const {unstringifyBigInts} = utils; -import jsSha3 from "js-sha3"; -const { keccak256 } = jsSha3; +import { Keccak256Transcript } from "./Keccak256Transcript.js"; @@ -51,7 +49,8 @@ export default async function plonkVerify(_vk_verifier, _publicSignals, _proof, logger.error("Invalid number of public inputs"); return false; } - const challenges = calculatechallenges(curve, proof, publicSignals); + const challenges = calculatechallenges(curve, proof, publicSignals, vk_verifier); + if (logger) { logger.debug("beta: " + Fr.toString(challenges.beta, 16)); logger.debug("gamma: " + Fr.toString(challenges.gamma, 16)); @@ -169,53 +168,69 @@ function isWellConstructed(curve, proof) { return true; } -function calculatechallenges(curve, proof, publicSignals) { - const G1 = curve.G1; +function calculatechallenges(curve, proof, publicSignals, vk) { const Fr = curve.Fr; - const n8r = curve.Fr.n8; const res = {}; - - const transcript1 = new Uint8Array(publicSignals.length*n8r + G1.F.n8*2*3); - for (let i=0; i Date: Sat, 6 May 2023 07:04:53 +0200 Subject: [PATCH 08/48] Add check functions in js and sc --- src/fflonk_verify.js | 50 ++++++++++++++++++++++++++++-- src/groth16_verify.js | 28 +++++++++++++++++ src/plonk_verify.js | 42 +++++++++++++++++++++++-- templates/verifier_fflonk.sol.ejs | 11 +++++-- templates/verifier_groth16.sol.ejs | 47 ++++++++++++++++++++++++++++ templates/verifier_plonk.sol.ejs | 37 ++++++++++++++++++++-- 6 files changed, 206 insertions(+), 9 deletions(-) diff --git a/src/fflonk_verify.js b/src/fflonk_verify.js index e8809836..3d866e53 100644 --- a/src/fflonk_verify.js +++ b/src/fflonk_verify.js @@ -22,6 +22,7 @@ import { BigBuffer, utils } from "ffjavascript"; import { Proof } from "./proof.js"; import { Keccak256Transcript } from "./Keccak256Transcript.js"; import { Polynomial } from "./polynomial/polynomial.js"; +import { Scalar } from "ffjavascript"; const { unstringifyBigInts } = utils; @@ -62,15 +63,23 @@ export default async function fflonkVerify(_vk_verifier, _publicSignals, _proof, // STEP 1 - Validate that all polynomial commitments ∈ G_1 if (logger) logger.info("> Checking commitments belong to G1"); if (!commitmentsBelongToG1(curve, proof, vk)) { - logger.error("Proof is not well constructed"); + if (logger) logger.error("Proof commitments are not valid"); return false; } - // TODO // STEP 2 - Validate that all evaluations ∈ F + if (logger) logger.info("> Checking evaluations belong to F"); + if (!evaluationsAreValid(curve, proof)) { + if (logger) logger.error("Proof evaluations are not valid."); + return false; + } - // TODO // STEP 3 - Validate that w_i ∈ F for i ∈ [l] + if (logger) logger.info("> Checking public inputs belong to F"); + if (!publicInputsAreValid(curve, publicSignals)) { + if (logger) logger.error("Public inputs are not valid."); + return false; + } // STEP 4 - Compute the challenges: beta, gamma, xi, alpha and y ∈ F // as in prover description, from the common preprocessed inputs, public inputs and elements of π_SNARK @@ -152,6 +161,41 @@ function commitmentsBelongToG1(curve, proof, vk) { && G1.isValid(vk.C0); } +function checkValueBelongToField(curve, value) { + return Scalar.lt(value, curve.r); +} + +function checkEvaluationIsValid(curve, evaluation) { + return checkValueBelongToField(curve, Scalar.fromRprLE(evaluation)); +} + +function evaluationsAreValid(curve, proof) { + return checkEvaluationIsValid(curve, proof.evaluations.ql) + && checkEvaluationIsValid(curve, proof.evaluations.qr) + && checkEvaluationIsValid(curve, proof.evaluations.qm) + && checkEvaluationIsValid(curve, proof.evaluations.qo) + && checkEvaluationIsValid(curve, proof.evaluations.qc) + && checkEvaluationIsValid(curve, proof.evaluations.s1) + && checkEvaluationIsValid(curve, proof.evaluations.s2) + && checkEvaluationIsValid(curve, proof.evaluations.s3) + && checkEvaluationIsValid(curve, proof.evaluations.a) + && checkEvaluationIsValid(curve, proof.evaluations.b) + && checkEvaluationIsValid(curve, proof.evaluations.c) + && checkEvaluationIsValid(curve, proof.evaluations.z) + && checkEvaluationIsValid(curve, proof.evaluations.zw) + && checkEvaluationIsValid(curve, proof.evaluations.t1w) + && checkEvaluationIsValid(curve, proof.evaluations.t2w); +} + +function publicInputsAreValid(curve, publicInputs) { + for(let i = 0; i < publicInputs.length; i++) { + if(!checkValueBelongToField(curve, publicInputs[i])) { + return false; + } + } + return true; +} + function computeChallenges(curve, proof, vk, publicSignals, logger) { const Fr = curve.Fr; diff --git a/src/groth16_verify.js b/src/groth16_verify.js index f4936fa7..d2101a45 100644 --- a/src/groth16_verify.js +++ b/src/groth16_verify.js @@ -41,6 +41,11 @@ export default async function groth16Verify(_vk_verifier, _publicSignals, _proof const IC = new Uint8Array(curve.G1.F.n8*2 * publicSignals.length); const w = new Uint8Array(curve.Fr.n8 * publicSignals.length); + if (!publicInputsAreValid(curve, publicSignals)) { + if (logger) logger.error("Public inputs are not valid."); + return false; + } + for (let i=0; i, @@ -238,9 +268,26 @@ contract Verifier { proof.B = Pairing.G2Point([b[0][0], b[0][1]], [b[1][0], b[1][1]]); proof.C = Pairing.G1Point(c[0], c[1]); uint[] memory inputValues = new uint[](input.length); + + // Check public inputs belong to field for(uint i = 0; i < input.length; i++){ inputValues[i] = input[i]; + checkField(inputValues[i]); } + + // Check G1 points coordinates belong to field + checkField(a[0]); + checkField(a[1]); + checkField(b[0][0]); + checkField(b[0][1]); + checkField(b[1][0]); + checkField(b[1][1]); + checkField(c[0]); + checkField(c[1]); + + checkPointBelongsToBN128Curve(proof.A); + checkPointBelongsToBN128Curve(proof.C); + if (verify(inputValues, proof) == 0) { return true; } else { diff --git a/templates/verifier_plonk.sol.ejs b/templates/verifier_plonk.sol.ejs index c6d8452e..af188d05 100644 --- a/templates/verifier_plonk.sol.ejs +++ b/templates/verifier_plonk.sol.ejs @@ -182,11 +182,46 @@ contract PlonkVerifier { } } + function checkPointBelongsToBN128Curve(p) { + let x := mload(p) + let y := mload(add(p, 32)) + + // Check that the point is on the curve + // y^2 = x^3 + 3 + let x3_3 := addmod(mulmod(x, mulmod(x, x, qf), qf), 3, qf) + let y2 := mulmod(y, y, qf) + + if iszero(eq(x3_3, y2)) { + mstore(0, 0) + return(0, 0x20) + } + } + function checkInput(pProof) { if iszero(eq(mload(pProof), 800 )) { mstore(0, 0) return(0,0x20) } + + checkField(mload(add(pProof, pA))) + checkField(mload(add(pProof, add(pA, 32)))) + checkField(mload(add(pProof, pB))) + checkField(mload(add(pProof, add(pB, 32)))) + checkField(mload(add(pProof, pC))) + checkField(mload(add(pProof, add(pC, 32)))) + checkField(mload(add(pProof, pZ))) + checkField(mload(add(pProof, add(pZ, 32)))) + checkField(mload(add(pProof, pT1))) + checkField(mload(add(pProof, add(pT1, 32)))) + checkField(mload(add(pProof, pT2))) + checkField(mload(add(pProof, add(pT2, 32)))) + checkField(mload(add(pProof, pT3))) + checkField(mload(add(pProof, add(pT3, 32)))) + checkField(mload(add(pProof, pWxi))) + checkField(mload(add(pProof, add(pWxi, 32)))) + checkField(mload(add(pProof, pWxiw))) + checkField(mload(add(pProof, add(pWxiw, 32)))) + checkField(mload(add(pProof, pEval_a))) checkField(mload(add(pProof, pEval_b))) checkField(mload(add(pProof, pEval_c))) @@ -194,8 +229,6 @@ contract PlonkVerifier { checkField(mload(add(pProof, pEval_s2))) checkField(mload(add(pProof, pEval_zw))) checkField(mload(add(pProof, pEval_r))) - - // Points are checked in the point operations precompiled smart contracts } function calculateChallanges(pProof, pMem, pPublic) { From 80e7ce114e288c5d9132a9a2899031669692c109 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Thu, 11 May 2023 09:11:04 +0200 Subject: [PATCH 09/48] refactor groth16 smart contract to assembly code --- .vscode/launch.json | 91 ++++++ templates/verifier_groth16.sol.ejs | 452 +++++++++++------------------ 2 files changed, 255 insertions(+), 288 deletions(-) diff --git a/.vscode/launch.json b/.vscode/launch.json index dd59ba47..1074b58f 100644 --- a/.vscode/launch.json +++ b/.vscode/launch.json @@ -12,6 +12,97 @@ "/**" ], "type": "node" + }, + { + "type": "node", + "request": "launch", + "name": "groth16 setup", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "groth16", "setup", + "test/groth16/circuit.r1cs", + "test/plonk_circuit/powersOfTau15_final.ptau", + "test/groth16/circuit.zkey" + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 prove", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "groth16", "prove", + "test/groth16/circuit.zkey", + "test/groth16/witness.wtns", + "test/groth16/proof.json", + "test/groth16/public.json", + "-v" + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 export vk", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "zkev", + "test/groth16/circuit.zkey", + "test/groth16/verification_key.json", + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 verify", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "groth16", "verify", + "test/groth16/verification_key.json", + "test/groth16/public.json", + "test/groth16/proof.json", + "-v" + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 solidity verifier", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "zkesv", + "test/groth16/circuit.zkey", + "test/groth16/verifier.sol", + ] + }, + + { + "type": "node", + "request": "launch", + "name": "groth16 solidity calldata", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "zkesc", + "test/groth16/public.json", + "test/groth16/proof.json", + ] }, { "type": "node", diff --git a/templates/verifier_groth16.sol.ejs b/templates/verifier_groth16.sol.ejs index eba018e7..12503206 100644 --- a/templates/verifier_groth16.sol.ejs +++ b/templates/verifier_groth16.sol.ejs @@ -1,297 +1,173 @@ -// -// Copyright 2017 Christian Reitwiessner -// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: -// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. -// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. -// -// 2019 OKIMS -// ported to solidity 0.6 -// fixed linter warnings -// added requiere error messages -// -// // SPDX-License-Identifier: GPL-3.0 -pragma solidity ^0.6.11; -library Pairing { - struct G1Point { - uint X; - uint Y; - } - // Encoding of field elements is: X[0] * z + X[1] - struct G2Point { - uint[2] X; - uint[2] Y; - } - /// @return the generator of G1 - function P1() internal pure returns (G1Point memory) { - return G1Point(1, 2); - } - /// @return the generator of G2 - function P2() internal pure returns (G2Point memory) { - // Original code point - return G2Point( - [11559732032986387107991004021392285783925812861821192530917403151452391805634, - 10857046999023057135944570762232829481370756359578518086990519993285655852781], - [4082367875863433681332203403145435568316851327593401208105741076214120093531, - 8495653923123431417604973247489272438418190587263600148770280649306958101930] - ); - /* - // Changed by Jordi point - return G2Point( - [10857046999023057135944570762232829481370756359578518086990519993285655852781, - 11559732032986387107991004021392285783925812861821192530917403151452391805634], - [8495653923123431417604973247489272438418190587263600148770280649306958101930, - 4082367875863433681332203403145435568316851327593401208105741076214120093531] - ); + Copyright 2021 0KIMS association. + + This file is generated with [snarkJS](https://github.com/iden3/snarkjs). + + snarkJS is a free software: you can redistribute it and/or modify it + under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + snarkJS is distributed in the hope that it will be useful, but WITHOUT + ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public + License for more details. + + You should have received a copy of the GNU General Public License + along with snarkJS. If not, see . */ - } - /// @return r the negation of p, i.e. p.addition(p.negate()) should be zero. - function negate(G1Point memory p) internal pure returns (G1Point memory r) { - // The prime q in the base field F_q for G1 - uint q = 21888242871839275222246405745257275088696311157297823662689037894645226208583; - if (p.X == 0 && p.Y == 0) - return G1Point(0, 0); - return G1Point(p.X, q - (p.Y % q)); - } - /// @return r the sum of two points of G1 - function addition(G1Point memory p1, G1Point memory p2) internal view returns (G1Point memory r) { - uint[4] memory input; - input[0] = p1.X; - input[1] = p1.Y; - input[2] = p2.X; - input[3] = p2.Y; - bool success; - // solium-disable-next-line security/no-inline-assembly - assembly { - success := staticcall(sub(gas(), 2000), 6, input, 0xc0, r, 0x60) - // Use "invalid" to make gas estimation work - switch success case 0 { invalid() } - } - require(success,"pairing-add-failed"); - } - /// @return r the product of a point on G1 and a scalar, i.e. - /// p == p.scalar_mul(1) and p.addition(p) == p.scalar_mul(2) for all points p. - function scalar_mul(G1Point memory p, uint s) internal view returns (G1Point memory r) { - uint[3] memory input; - input[0] = p.X; - input[1] = p.Y; - input[2] = s; - bool success; - // solium-disable-next-line security/no-inline-assembly - assembly { - success := staticcall(sub(gas(), 2000), 7, input, 0x80, r, 0x60) - // Use "invalid" to make gas estimation work - switch success case 0 { invalid() } - } - require (success,"pairing-mul-failed"); - } - /// @return the result of computing the pairing check - /// e(p1[0], p2[0]) * .... * e(p1[n], p2[n]) == 1 - /// For example pairing([P1(), P1().negate()], [P2(), P2()]) should - /// return true. - function pairing(G1Point[] memory p1, G2Point[] memory p2) internal view returns (bool) { - require(p1.length == p2.length,"pairing-lengths-failed"); - uint elements = p1.length; - uint inputSize = elements * 6; - uint[] memory input = new uint[](inputSize); - for (uint i = 0; i < elements; i++) - { - input[i * 6 + 0] = p1[i].X; - input[i * 6 + 1] = p1[i].Y; - input[i * 6 + 2] = p2[i].X[0]; - input[i * 6 + 3] = p2[i].X[1]; - input[i * 6 + 4] = p2[i].Y[0]; - input[i * 6 + 5] = p2[i].Y[1]; - } - uint[1] memory out; - bool success; - // solium-disable-next-line security/no-inline-assembly - assembly { - success := staticcall(sub(gas(), 2000), 8, add(input, 0x20), mul(inputSize, 0x20), out, 0x20) - // Use "invalid" to make gas estimation work - switch success case 0 { invalid() } - } - require(success,"pairing-opcode-failed"); - return out[0] != 0; - } - /// Convenience method for a pairing check for two pairs. - function pairingProd2(G1Point memory a1, G2Point memory a2, G1Point memory b1, G2Point memory b2) internal view returns (bool) { - G1Point[] memory p1 = new G1Point[](2); - G2Point[] memory p2 = new G2Point[](2); - p1[0] = a1; - p1[1] = b1; - p2[0] = a2; - p2[1] = b2; - return pairing(p1, p2); - } - /// Convenience method for a pairing check for three pairs. - function pairingProd3( - G1Point memory a1, G2Point memory a2, - G1Point memory b1, G2Point memory b2, - G1Point memory c1, G2Point memory c2 - ) internal view returns (bool) { - G1Point[] memory p1 = new G1Point[](3); - G2Point[] memory p2 = new G2Point[](3); - p1[0] = a1; - p1[1] = b1; - p1[2] = c1; - p2[0] = a2; - p2[1] = b2; - p2[2] = c2; - return pairing(p1, p2); - } - /// Convenience method for a pairing check for four pairs. - function pairingProd4( - G1Point memory a1, G2Point memory a2, - G1Point memory b1, G2Point memory b2, - G1Point memory c1, G2Point memory c2, - G1Point memory d1, G2Point memory d2 - ) internal view returns (bool) { - G1Point[] memory p1 = new G1Point[](4); - G2Point[] memory p2 = new G2Point[](4); - p1[0] = a1; - p1[1] = b1; - p1[2] = c1; - p1[3] = d1; - p2[0] = a2; - p2[1] = b2; - p2[2] = c2; - p2[3] = d2; - return pairing(p1, p2); - } -} -contract Verifier { - uint256 constant p_bn128 = 21888242871839275222246405745257275088548364400416034343698204186575808495617; - uint256 constant q_bn128 = 21888242871839275222246405745257275088696311157297823662689037894645226208583; - - using Pairing for *; - struct VerifyingKey { - Pairing.G1Point alfa1; - Pairing.G2Point beta2; - Pairing.G2Point gamma2; - Pairing.G2Point delta2; - Pairing.G1Point[] IC; - } - struct Proof { - Pairing.G1Point A; - Pairing.G2Point B; - Pairing.G1Point C; - } - - function checkField(uint v) internal pure returns (uint) { + +pragma solidity >=0.7.0 <0.9.0; + +import "hardhat/console.sol"; + +contract Groth16Verifier { + // Scalar field size + uint256 constant r = 21888242871839275222246405745257275088548364400416034343698204186575808495617; + // Base field size + uint256 constant q = 21888242871839275222246405745257275088696311157297823662689037894645226208583; + + // Verification Key data + uint256 constant alphax = <%= vk_alpha_1[0] %>; + uint256 constant alphay = <%= vk_alpha_1[1] %>; + uint256 constant betax1 = <%= vk_beta_2[0][1] %>; + uint256 constant betax2 = <%= vk_beta_2[0][0] %>; + uint256 constant betay1 = <%= vk_beta_2[1][1] %>; + uint256 constant betay2 = <%= vk_beta_2[1][0] %>; + uint256 constant gammax1 = <%= vk_gamma_2[0][1] %>; + uint256 constant gammax2 = <%= vk_gamma_2[0][0] %>; + uint256 constant gammay1 = <%= vk_gamma_2[1][1] %>; + uint256 constant gammay2 = <%= vk_gamma_2[1][0] %>; + uint256 constant deltax1 = <%= vk_delta_2[0][1] %>; + uint256 constant deltax2 = <%= vk_delta_2[0][0] %>; + uint256 constant deltay1 = <%= vk_delta_2[1][1] %>; + uint256 constant deltay2 = <%= vk_delta_2[1][0] %>; + + <% for (let i=0; i + uint256 constant IC<%=i%>x = <%=IC[i][0]%>; + uint256 constant IC<%=i%>y = <%=IC[i][1]%>; + <% } %> + + // Proof calldata + // Byte offset of every parameter of the calldata + uint16 constant pA = <%=4 + 0%>; // [A]_1 + uint16 constant pB = <%=4 + 32*2%>; // [B]_2 + uint16 constant pC = <%=4 + 32*6%>; // [C]_1 + + // Memory data + uint16 constant pVk = 0; + uint16 constant pPairing = 128; + + uint16 constant pLastMem = 896; + + function verifyProof(bytes32[8] calldata _proof, bytes32[<%=IC.length-1%>] calldata _pubSignals) public view returns (bool) { assembly { - if iszero(lt(v, p_bn128)) { - mstore(0, 0) - return(0, 0x20) + function checkField(v) { + if iszero(lt(v, q)) { + mstore(0, 0) + return(0, 0x20) + } } - } - } + + // G1 function to multiply a G1 value(x,y) to value in an address + function g1_mulAccC(pR, x, y, s) { + let success + let mIn := mload(0x40) + mstore(mIn, x) + mstore(add(mIn, 32), y) + mstore(add(mIn, 64), s) - function checkPointBelongsToBN128Curve(Pairing.G1Point memory p) internal pure returns (uint) { - assembly { - let x := mload(p) - let y := mload(add(p,0x20)) + success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } - // Check that the point is on the curve - // y^2 = x^3 + 3 - let x3_3 := addmod(mulmod(x, mulmod(x, x, q_bn128), q_bn128), 3, q_bn128) - let y2 := mulmod(y, y, q_bn128) + mstore(add(mIn, 64), mload(pR)) + mstore(add(mIn, 96), mload(add(pR, 32))) - if iszero(eq(x3_3, y2)) { - mstore(0, 0) - return(0, 0x20) + success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } } - } - } - - function verifyingKey() internal pure returns (VerifyingKey memory vk) { - vk.alfa1 = Pairing.G1Point( - <%=vk_alpha_1[0]%>, - <%=vk_alpha_1[1]%> - ); - - vk.beta2 = Pairing.G2Point( - [<%=vk_beta_2[0][1]%>, - <%=vk_beta_2[0][0]%>], - [<%=vk_beta_2[1][1]%>, - <%=vk_beta_2[1][0]%>] - ); - vk.gamma2 = Pairing.G2Point( - [<%=vk_gamma_2[0][1]%>, - <%=vk_gamma_2[0][0]%>], - [<%=vk_gamma_2[1][1]%>, - <%=vk_gamma_2[1][0]%>] - ); - vk.delta2 = Pairing.G2Point( - [<%=vk_delta_2[0][1]%>, - <%=vk_delta_2[0][0]%>], - [<%=vk_delta_2[1][1]%>, - <%=vk_delta_2[1][0]%>] - ); - vk.IC = new Pairing.G1Point[](<%=IC.length%>); - <% for (let i=0; i - vk.IC[<%=i%>] = Pairing.G1Point( - <%=IC[i][0]%>, - <%=IC[i][1]%> - ); - <% } %> - } - function verify(uint[] memory input, Proof memory proof) internal view returns (uint) { - uint256 snark_scalar_field = 21888242871839275222246405745257275088548364400416034343698204186575808495617; - VerifyingKey memory vk = verifyingKey(); - require(input.length + 1 == vk.IC.length,"verifier-bad-input"); - // Compute the linear combination vk_x - Pairing.G1Point memory vk_x = Pairing.G1Point(0, 0); - for (uint i = 0; i < input.length; i++) { - require(input[i] < snark_scalar_field,"verifier-gte-snark-scalar-field"); - vk_x = Pairing.addition(vk_x, Pairing.scalar_mul(vk.IC[i + 1], input[i])); - } - vk_x = Pairing.addition(vk_x, vk.IC[0]); - if (!Pairing.pairingProd4( - Pairing.negate(proof.A), proof.B, - vk.alfa1, vk.beta2, - vk_x, vk.gamma2, - proof.C, vk.delta2 - )) return 1; - return 0; - } - /// @return r bool true if proof is valid - function verifyProof( - uint[2] memory a, - uint[2][2] memory b, - uint[2] memory c, - uint[<%=IC.length-1%>] memory input - ) public view returns (bool r) { - Proof memory proof; - proof.A = Pairing.G1Point(a[0], a[1]); - proof.B = Pairing.G2Point([b[0][0], b[0][1]], [b[1][0], b[1][1]]); - proof.C = Pairing.G1Point(c[0], c[1]); - uint[] memory inputValues = new uint[](input.length); - - // Check public inputs belong to field - for(uint i = 0; i < input.length; i++){ - inputValues[i] = input[i]; - checkField(inputValues[i]); - } - - // Check G1 points coordinates belong to field - checkField(a[0]); - checkField(a[1]); - checkField(b[0][0]); - checkField(b[0][1]); - checkField(b[1][0]); - checkField(b[1][1]); - checkField(c[0]); - checkField(c[1]); - - checkPointBelongsToBN128Curve(proof.A); - checkPointBelongsToBN128Curve(proof.C); - - if (verify(inputValues, proof) == 0) { - return true; - } else { - return false; - } - } -} + + function checkPairing(proof, pubSignals, pMem) -> isOk { + let _pPairing := add(pMem, pPairing) + let _pVk := add(pMem, pVk) + + mstore(_pVk, IC0x) + mstore(add(_pVk, 32), IC0y) + + // Compute the linear combination vk_x + <% for (let i = 1; i <= nPublic; i++) { %> + g1_mulAccC(_pVk, IC<%=i%>x, IC<%=i%>y, calldataload(add(pubSignals, <%=(i-1)*32%>))) + <% } %> + + // -A + mstore(_pPairing, calldataload(pA)) + mstore(add(_pPairing, 32), mod(sub(q, calldataload(add(pA, 32))), q)) + + // B + mstore(add(_pPairing, 64), calldataload(pB)) + mstore(add(_pPairing, 96), calldataload(add(pB, 32))) + mstore(add(_pPairing, 128), calldataload(add(pB, 64))) + mstore(add(_pPairing, 160), calldataload(add(pB, 96))) + + // alpha1 + mstore(add(_pPairing, 192), alphax) + mstore(add(_pPairing, 224), alphay) + + // beta2 + mstore(add(_pPairing, 256), betax1) + mstore(add(_pPairing, 288), betax2) + mstore(add(_pPairing, 320), betay1) + mstore(add(_pPairing, 352), betay2) + + // vk_x + mstore(add(_pPairing, 384), mload(add(pMem, pVk))) + mstore(add(_pPairing, 416), mload(add(pMem, add(pVk, 32)))) + + + // gamma2 + mstore(add(_pPairing, 448), gammax1) + mstore(add(_pPairing, 480), gammax2) + mstore(add(_pPairing, 512), gammay1) + mstore(add(_pPairing, 544), gammay2) + + // C + mstore(add(_pPairing, 576), calldataload(pC)) + mstore(add(_pPairing, 608), calldataload(add(pC, 32))) + + // delta2 + mstore(add(_pPairing, 640), deltax1) + mstore(add(_pPairing, 672), deltax2) + mstore(add(_pPairing, 704), deltay1) + mstore(add(_pPairing, 736), deltay2) + + + let success := staticcall(sub(gas(), 2000), 8, _pPairing, 768, _pPairing, 0x20) + + isOk := and(success, mload(_pPairing)) + } + + let pMem := mload(0x40) + mstore(0x40, add(pMem, pLastMem)) + + // Validate that all evaluations ∈ F + <% for (let i=0; i + checkField(calldataload(add(_pubSignals, <%=i*32%>))) + <% } %> + + // Validate all evaluations + let isValid := checkPairing(_proof, _pubSignals, pMem) + + mstore(0, isValid) + return(0, 0x20) + } + } + } From aadeb25162dd2c960b29541f59f52a48259699c8 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Thu, 11 May 2023 09:31:56 +0200 Subject: [PATCH 10/48] fix calldata types and test passing --- smart_contract_tests/test/smart_contracts.test.js | 2 +- templates/verifier_groth16.sol.ejs | 12 +++--------- 2 files changed, 4 insertions(+), 10 deletions(-) diff --git a/smart_contract_tests/test/smart_contracts.test.js b/smart_contract_tests/test/smart_contracts.test.js index 43191590..5bc057ef 100644 --- a/smart_contract_tests/test/smart_contracts.test.js +++ b/smart_contract_tests/test/smart_contracts.test.js @@ -54,7 +54,7 @@ describe("Smart contracts test suite", function () { await run("compile"); // Deploy mock groth16 verifier - const VerifierFactory = await ethers.getContractFactory("Verifier"); + const VerifierFactory = await ethers.getContractFactory("Groth16Verifier"); verifierContract = await VerifierFactory.deploy(); // Verifiy the proof in the smart contract diff --git a/templates/verifier_groth16.sol.ejs b/templates/verifier_groth16.sol.ejs index 12503206..7c9687ac 100644 --- a/templates/verifier_groth16.sol.ejs +++ b/templates/verifier_groth16.sol.ejs @@ -48,12 +48,6 @@ contract Groth16Verifier { uint256 constant IC<%=i%>x = <%=IC[i][0]%>; uint256 constant IC<%=i%>y = <%=IC[i][1]%>; <% } %> - - // Proof calldata - // Byte offset of every parameter of the calldata - uint16 constant pA = <%=4 + 0%>; // [A]_1 - uint16 constant pB = <%=4 + 32*2%>; // [B]_2 - uint16 constant pC = <%=4 + 32*6%>; // [C]_1 // Memory data uint16 constant pVk = 0; @@ -61,7 +55,7 @@ contract Groth16Verifier { uint16 constant pLastMem = 896; - function verifyProof(bytes32[8] calldata _proof, bytes32[<%=IC.length-1%>] calldata _pubSignals) public view returns (bool) { + function verifyProof(uint[2] calldata _pA, uint[2][2] calldata _pB, uint[2] calldata _pC, uint[<%=IC.length-1%>] calldata _pubSignals) public view returns (bool) { assembly { function checkField(v) { if iszero(lt(v, q)) { @@ -96,7 +90,7 @@ contract Groth16Verifier { } } - function checkPairing(proof, pubSignals, pMem) -> isOk { + function checkPairing(pA, pB, pC, pubSignals, pMem) -> isOk { let _pPairing := add(pMem, pPairing) let _pVk := add(pMem, pVk) @@ -164,7 +158,7 @@ contract Groth16Verifier { <% } %> // Validate all evaluations - let isValid := checkPairing(_proof, _pubSignals, pMem) + let isValid := checkPairing(_pA, _pB, _pC, _pubSignals, pMem) mstore(0, isValid) return(0, 0x20) From 37fbbdee38a9f8e2a3097ff36a68223785ab6c12 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Fri, 12 May 2023 07:00:49 +0000 Subject: [PATCH 11/48] fix errors. working --- src/plonk_prove.js | 4 ++-- src/proof.js | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/src/plonk_prove.js b/src/plonk_prove.js index 833a45df..ab48a4c6 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -659,7 +659,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger // T3(X) = T3'(X) - b_11 // such that // t(X) = T1(X) + X^n T2(X) + X^2n T3(X) - logger.debug("··· Computing T1, T2, T3 polynomials"); + if (logger) logger.debug("··· Computing T1, T2, T3 polynomials"); polynomials.T1 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); polynomials.T2 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); polynomials.T3 = new Polynomial(new BigBuffer((zkey.domainSize + 6) * n8r), curve, logger); @@ -856,7 +856,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger let r0 = Fr.sub(eval_pi, Fr.mul(e3, Fr.add(proof.evaluations.eval_c, challenges.gamma))); r0 = Fr.sub(r0, e4); - logger.debug("r0: " + Fr.toString(r0, 16)); + if (logger) logger.debug("r0: " + Fr.toString(r0, 16)); polynomials.R.addScalar(r0); } diff --git a/src/proof.js b/src/proof.js index d8ca1f21..ba7d96d1 100644 --- a/src/proof.js +++ b/src/proof.js @@ -73,7 +73,7 @@ export class Proof { Object.keys(this.evaluations).forEach(key => { const value = this.curve.Fr.toObject(this.evaluations[key]); if(splitFields) { - res.polynomials[key] = value; + res.evaluations[key] = value; } else { res[key] = value; } From dbe718d19d06158d62d0fd906d8c484ad30c62a7 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Fri, 12 May 2023 07:01:48 +0000 Subject: [PATCH 12/48] wip --- src/plonk_prove.js | 2 +- src/plonk_verify.js | 2 +- templates/verifier_plonk.sol.ejs | 433 ++++++++++---------- test/plonk_circuit/circuit.zkey | Bin 14916 -> 14748 bytes test/plonk_circuit/proof.json | 49 ++- test/plonk_circuit/verification_key.json | 35 +- test/plonk_circuit/verifier.sol | 477 ++++++++++++----------- 7 files changed, 526 insertions(+), 472 deletions(-) diff --git a/src/plonk_prove.js b/src/plonk_prove.js index ab48a4c6..6c3409f7 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -322,7 +322,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger transcript.addPolCommitment(zkey.Ql); transcript.addPolCommitment(zkey.Qr); transcript.addPolCommitment(zkey.Qo); - transcript.addPolCommitment(zkey.Ql); + transcript.addPolCommitment(zkey.Qc); transcript.addPolCommitment(zkey.S1); transcript.addPolCommitment(zkey.S2); transcript.addPolCommitment(zkey.S3); diff --git a/src/plonk_verify.js b/src/plonk_verify.js index 212782d0..31692b76 100644 --- a/src/plonk_verify.js +++ b/src/plonk_verify.js @@ -178,7 +178,7 @@ function calculatechallenges(curve, proof, publicSignals, vk) { transcript.addPolCommitment(vk.Ql); transcript.addPolCommitment(vk.Qr); transcript.addPolCommitment(vk.Qo); - transcript.addPolCommitment(vk.Ql); + transcript.addPolCommitment(vk.Qc); transcript.addPolCommitment(vk.S1); transcript.addPolCommitment(vk.S2); transcript.addPolCommitment(vk.S3); diff --git a/templates/verifier_plonk.sol.ejs b/templates/verifier_plonk.sol.ejs index c6d8452e..6485cc0c 100644 --- a/templates/verifier_plonk.sol.ejs +++ b/templates/verifier_plonk.sol.ejs @@ -75,7 +75,6 @@ contract PlonkVerifier { uint16 constant pEval_s1 = 704; uint16 constant pEval_s2 = 736; uint16 constant pEval_zw = 768; - uint16 constant pEval_r = 800; uint16 constant pAlpha = 0; uint16 constant pBeta = 32; @@ -90,16 +89,18 @@ contract PlonkVerifier { uint16 constant pV5 = 320; uint16 constant pV6 = 352; uint16 constant pU = 384; - uint16 constant pPl = 416; - uint16 constant pEval_t = 448; - uint16 constant pA1 = 480; - uint16 constant pB1 = 544; - uint16 constant pZh = 608; - uint16 constant pZhInv = 640; + uint16 constant pPI = 416; + uint16 constant pEval_r0 = 448; + uint16 constant pD = 480; + uint16 constant pF = 544; + uint16 constant pE = 608; + uint16 constant pTmp = 672; + uint16 constant pZh = 736; + uint16 constant pZhInv = 768; <% for (let i=1; i<=Math.max(nPublic, 1); i++) { %> - uint16 constant pEval_l<%=i%> = <%=640+i*32%>; + uint16 constant pEval_l<%=i%> = <%=768+i*32%>; <% } %> - <% let pLastMem = 672+32*Math.max(nPublic,1) %> + <% let pLastMem = 800+32*Math.max(nPublic,1) %> uint16 constant lastMem = <%=pLastMem%>; @@ -193,7 +194,6 @@ contract PlonkVerifier { checkField(mload(add(pProof, pEval_s1))) checkField(mload(add(pProof, pEval_s2))) checkField(mload(add(pProof, pEval_zw))) - checkField(mload(add(pProof, pEval_r))) // Points are checked in the point operations precompiled smart contracts } @@ -203,23 +203,69 @@ contract PlonkVerifier { let a let b + // Challenges.beta + mstore( add(pMem, <%=pLastMem%> ), Qmx) + mstore( add(pMem, <%=pLastMem + 32%> ), Qmy) + mstore( add(pMem, <%=pLastMem + 64%> ), Qlx) + mstore( add(pMem, <%=pLastMem + 96%> ), Qly) + mstore( add(pMem, <%=pLastMem + 128%> ), Qrx) + mstore( add(pMem, <%=pLastMem + 160%> ), Qry) + mstore( add(pMem, <%=pLastMem + 192%> ), Qox) + mstore( add(pMem, <%=pLastMem + 224%> ), Qoy) + mstore( add(pMem, <%=pLastMem + 256%> ), Qcx) + mstore( add(pMem, <%=pLastMem + 288%> ), Qcy) + mstore( add(pMem, <%=pLastMem + 320%> ), S1x) + mstore( add(pMem, <%=pLastMem + 352%> ), S1x) + mstore( add(pMem, <%=pLastMem + 384%> ), S2x) + mstore( add(pMem, <%=pLastMem + 416%> ), S2x) + mstore( add(pMem, <%=pLastMem + 448%> ), S3x) + mstore( add(pMem, <%=pLastMem + 480%> ), S3x) + <%for (let i=0; i - mstore( add(pMem, <%=pLastMem + i*32%> ), mload( add( pPublic, <%=i*32 + 32%>))) + mstore( add(pMem, <%=pLastMem + 512 + i*32%> ), mload( add( pPublic, <%=i*32 + 32%>))) <%}%> - mstore( add(pMem, <%=pLastMem + nPublic*32 +0%> ), mload( add( pProof, pA))) - mstore( add(pMem, <%=pLastMem + nPublic*32 +32%> ), mload( add( pProof, add(pA,32)))) - mstore( add(pMem, <%=pLastMem + nPublic*32 +64%> ), mload( add( pProof, add(pA,64)))) - mstore( add(pMem, <%=pLastMem + nPublic*32 +96%> ), mload( add( pProof, add(pA,96)))) - mstore( add(pMem, <%=pLastMem + nPublic*32 +128%> ), mload( add( pProof, add(pA,128)))) - mstore( add(pMem, <%=pLastMem + nPublic*32 +160%> ), mload( add( pProof, add(pA,160)))) - - b := mod(keccak256(add(pMem, lastMem), <%= 192 + 32*nPublic %>), q) - mstore( add(pMem, pBeta), b) - mstore( add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) - mstore( add(pMem, pAlpha), mod(keccak256(add(pProof, pZ), 64), q)) - - a := mod(keccak256(add(pProof, pT1), 192), q) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +0%> ), mload( add( pProof, pA))) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +32%> ), mload( add( pProof, add(pA,32)))) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +64%> ), mload( add( pProof, pB))) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +96%> ), mload( add( pProof, add(pB, 32)))) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +128%> ), mload( add( pProof, pC))) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +160%> ), mload( add( pProof, add(pC, 32)))) + + b := mod(keccak256(add(pMem, lastMem), <%= 704 + 32*nPublic %>), q) + mstore(add(pMem, pBeta), b) + + // Challenges.gamma + mstore(add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) + + // Challenges.alpha + mstore(add(pMem, <%=pLastMem%>), mload(add(pMem, pBeta))) + mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pMem, pGamma))) + mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, pZ))) + mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, add(pZ, 32)))) + a := mod(keccak256(add(pMem, lastMem), 128), q) + mstore(add(pMem, pAlpha), a) + + mstore(add(pMem, <%=pLastMem%>), mload(add(pMem, pAlpha))) + mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pProof, pT1))) + mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, add(pT1, 32)))) + mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, pT2))) + mstore(add(pMem, <%=pLastMem + 128%>), mload(add(pProof, add(pT2, 32)))) + mstore(add(pMem, <%=pLastMem + 160%>), mload(add(pProof, pT3))) + mstore(add(pMem, <%=pLastMem + 192%>), mload(add(pProof, add(pT3, 32)))) + a := mod(keccak256(add(pMem, lastMem), 224), q) mstore( add(pMem, pXi), a) + + mstore(add(pMem, <%=pLastMem%>), a) + mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pProof, pEval_a))) + mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, pEval_b))) + mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, pEval_c))) + mstore(add(pMem, <%=pLastMem + 128%>), mload(add(pProof, pEval_s1))) + mstore(add(pMem, <%=pLastMem + 160%>), mload(add(pProof, pEval_s2))) + mstore(add(pMem, <%=pLastMem + 192%>), mload(add(pProof, pEval_zw))) + let v1 := mod(keccak256(add(pMem, lastMem), 224), q) + mstore(add(pMem, pV1), v1) + + // Compute betaxi mstore( add(pMem, pBetaXi), mulmod(b, a, q)) <%for (let i=0; i a:= mulmod(a, a, q) @@ -228,9 +274,7 @@ contract PlonkVerifier { a:= mod(add(sub(a, 1),q), q) mstore( add(pMem, pZh), a) mstore( add(pMem, pZhInv), a) // We will invert later together with lagrange pols - - let v1 := mod(keccak256(add(pProof, pEval_a), 224), q) - mstore( add(pMem, pV1), v1) + a := mulmod(v1, v1, q) mstore( add(pMem, pV2), a) a := mulmod(a, v1, q) @@ -307,7 +351,7 @@ contract PlonkVerifier { } - function calculatePl(pMem, pPub) { + function calculatePI(pMem, pPub) { let pl := 0 <% for (let i=0; i @@ -327,88 +371,43 @@ contract PlonkVerifier { ) <% } %> - mstore(add(pMem, pPl), pl) + mstore(add(pMem, pPI), pl) } - function calculateT(pProof, pMem) { - let t - let t1 - let t2 - t := addmod( - mload(add(pProof, pEval_r)), - mload(add(pMem, pPl)), - q - ) - - t1 := mulmod( - mload(add(pProof, pEval_s1)), - mload(add(pMem, pBeta)), - q - ) + function calculateR0(pProof, pMem) { + let alpha2 := mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q) + let e1 := mload(add(pMem, pPI)) - t1 := addmod( - t1, - mload(add(pProof, pEval_a)), - q - ) - - t1 := addmod( - t1, - mload(add(pMem, pGamma)), - q - ) + let e2 := mulmod(mload(add(pMem, pEval_l1)), alpha2, q) - t2 := mulmod( - mload(add(pProof, pEval_s2)), - mload(add(pMem, pBeta)), - q - ) + let e3a := addmod( + mload(add(pProof, pEval_a)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), + q) + e3a := addmod(e3a, mload(add(pMem, pGamma)), q) - t2 := addmod( - t2, + let e3b := addmod( mload(add(pProof, pEval_b)), - q - ) - - t2 := addmod( - t2, - mload(add(pMem, pGamma)), - q - ) - - t1 := mulmod(t1, t2, q) - - t2 := addmod( + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), + q) + e3b := addmod(e3b, mload(add(pMem, pGamma)), q) + + let e3c := addmod( mload(add(pProof, pEval_c)), mload(add(pMem, pGamma)), - q - ) + q) - t1 := mulmod(t1, t2, q) - t1 := mulmod(t1, mload(add(pProof, pEval_zw)), q) - t1 := mulmod(t1, mload(add(pMem, pAlpha)), q) - - t2 := mulmod( - mload(add(pMem, pEval_l1)), - mload(add(pMem, pAlpha)), - q - ) - - t2 := mulmod( - t2, - mload(add(pMem, pAlpha)), - q - ) + let e3 := mulmod(mulmod(e3a, e3b, q), e3c, q) - t1 := addmod(t1, t2, q) - - t := mod(sub(add(t, q), t1), q) - t := mulmod(t, mload(add(pMem, pZhInv)), q) + e3 := mulmod(e3, mload(add(pProof, pEval_zw)), q) + e3 := mulmod(e3, mload(add(pMem, pAlpha)), q) + + let r0 := mod(sub(e1, e2), q) + r0 := mod(sub(r0, e3), q) - mstore( add(pMem, pEval_t) , t) - + mstore(add(pMem, pEval_r0) , r0) } function g1_set(pR, pP) { @@ -497,119 +496,146 @@ contract PlonkVerifier { } } + function calculateD(pProof, pMem) { + let p:= add(pMem, pD) + let mIn := mload(0x40) + + g1_mulSetC(p, Qmx, Qmy, mulmod(mload(add(pProof, pEval_a)), mload(add(pProof, pEval_b)), q)) + g1_mulAccC(p, Qlx, Qly, mload(add(pProof, pEval_a))) + g1_mulAccC(p, Qrx, Qry, mload(add(pProof, pEval_b))) + g1_mulAccC(p, Qox, Qoy, mload(add(pProof, pEval_c))) + g1_mulAccC(p, Qcx, Qcy, 1) - function calculateA1(pProof, pMem) { - let p := add(pMem, pA1) - g1_set(p, add(pProof, pWxi)) - g1_mulAcc(p, add(pProof, pWxiw), mload(add(pMem, pU))) - } - + let val1 := addmod( + addmod(mload(add(pProof, pEval_a)), mload(add(pMem, pBetaXi)), q), + mload(add(pMem, pGamma)), + q) + + let val2 := addmod( + addmod( + mload(add(pProof, pEval_b)), + mulmod(mload(add(pMem, pBetaXi)), k1, q), + q), + mload(add(pMem, pGamma)), + q) + + let val3 := addmod( + addmod( + mload(add(pProof, pEval_c)), + mulmod(mload(add(pMem, pBetaXi)), k2, q), + q), + mload(add(pMem, pGamma)), + q) + + let d2a := mulmod( + mulmod(mulmod(val1, val2, q), val3, q), + mload(add(pMem, pAlpha)), + q + ) + + let d2b := mulmod( + mload(add(pMem, pEval_l1)), + mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q), + q + ) + + // We'll use pF to save d2 + g1_mulAcc( + add(pMem, pF), + add(pProof, pZ), + addmod(addmod(d2a, d2b, q), mload(add(pMem, pU)), q)) - function calculateB1(pProof, pMem) { - let s - let s1 - let p := add(pMem, pB1) - - // Calculate D - s := mulmod( mload(add(pProof, pEval_a)), mload(add(pMem, pV1)), q) - g1_mulSetC(p, Qlx, Qly, s) + val1 := addmod( + addmod( + mload(add(pProof, pEval_a)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), + q), + mload(add(pMem, pGamma)), + q) - s := mulmod( s, mload(add(pProof, pEval_b)), q) - g1_mulAccC(p, Qmx, Qmy, s) + val2 := addmod( + addmod( + mload(add(pProof, pEval_b)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), + q), + mload(add(pMem, pGamma)), + q) + + val3 := mulmod( + mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pBeta)), q), + mload(add(pProof, pEval_zw)), q) + - s := mulmod( mload(add(pProof, pEval_b)), mload(add(pMem, pV1)), q) - g1_mulAccC(p, Qrx, Qry, s) - - s := mulmod( mload(add(pProof, pEval_c)), mload(add(pMem, pV1)), q) - g1_mulAccC(p, Qox, Qoy, s) - - s :=mload(add(pMem, pV1)) - g1_mulAccC(p, Qcx, Qcy, s) - - s := addmod(mload(add(pProof, pEval_a)), mload(add(pMem, pBetaXi)), q) - s := addmod(s, mload(add(pMem, pGamma)), q) - s1 := mulmod(k1, mload(add(pMem, pBetaXi)), q) - s1 := addmod(s1, mload(add(pProof, pEval_b)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s1 := mulmod(k2, mload(add(pMem, pBetaXi)), q) - s1 := addmod(s1, mload(add(pProof, pEval_c)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s := mulmod(s, mload(add(pMem, pAlpha)), q) - s := mulmod(s, mload(add(pMem, pV1)), q) - s1 := mulmod(mload(add(pMem, pEval_l1)), mload(add(pMem, pAlpha)), q) - s1 := mulmod(s1, mload(add(pMem, pAlpha)), q) - s1 := mulmod(s1, mload(add(pMem, pV1)), q) - s := addmod(s, s1, q) - s := addmod(s, mload(add(pMem, pU)), q) - g1_mulAcc(p, add(pProof, pZ), s) - - s := mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q) - s := addmod(s, mload(add(pProof, pEval_a)), q) - s := addmod(s, mload(add(pMem, pGamma)), q) - s1 := mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q) - s1 := addmod(s1, mload(add(pProof, pEval_b)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s := mulmod(s, mload(add(pMem, pAlpha)), q) - s := mulmod(s, mload(add(pMem, pV1)), q) - s := mulmod(s, mload(add(pMem, pBeta)), q) - s := mulmod(s, mload(add(pProof, pEval_zw)), q) - s := mod(sub(q, s), q) - g1_mulAccC(p, S3x, S3y, s) - - - // calculate F - g1_acc(p , add(pProof, pT1)) - - s := mload(add(pMem, pXin)) - g1_mulAcc(p, add(pProof, pT2), s) - - s := mulmod(s, s, q) - g1_mulAcc(p, add(pProof, pT3), s) - - g1_mulAcc(p, add(pProof, pA), mload(add(pMem, pV2))) - g1_mulAcc(p, add(pProof, pB), mload(add(pMem, pV3))) - g1_mulAcc(p, add(pProof, pC), mload(add(pMem, pV4))) - g1_mulAccC(p, S1x, S1y, mload(add(pMem, pV5))) - g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV6))) - - // calculate E - s := mload(add(pMem, pEval_t)) - s := addmod(s, mulmod(mload(add(pProof, pEval_r)), mload(add(pMem, pV1)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_a)), mload(add(pMem, pV2)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_b)), mload(add(pMem, pV3)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_c)), mload(add(pMem, pV4)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s1)), mload(add(pMem, pV5)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s2)), mload(add(pMem, pV6)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_zw)), mload(add(pMem, pU)), q), q) - s := mod(sub(q, s), q) - g1_mulAccC(p, G1x, G1y, s) - - - // Last part of B - s := mload(add(pMem, pXi)) - g1_mulAcc(p, add(pProof, pWxi), s) + // We'll use pE to save d3 + g1_mulAccC( + add(pMem, pE), + S3x, + S3y, + mulmod(mulmod(val1, val2, q), val3, q)) - s := mulmod(mload(add(pMem, pU)), mload(add(pMem, pXi)), q) - s := mulmod(s, w1, q) - g1_mulAcc(p, add(pProof, pWxiw), s) + // We'll use pTmp to save d4 + g1_set(add(pMem, pTmp), add(pProof, pT1)) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT2), add(pMem, pXin)) + let xin2 := mulmod(add(pMem, pXin), add(pMem, pXin), q) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) + + g1_mulAcc(mIn, add(pMem, pTmp), add(pMem, pZh)) + + mstore(add(add(pMem, pE), 32), mod(sub(qf, mload(add(add(pMem, pE), 32))), qf)) + mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) + g1_acc(add(pMem, pD), add(pMem, pF)) + g1_acc(add(pMem, pD), add(pMem, pE)) + g1_acc(add(pMem, pD), add(pMem, mIn)) } - function checkPairing(pMem) -> isOk { + function calculateF(pProof, pMem) { + let p := add(pMem, pF) + + g1_set(p, add(pMem, pD)) + g1_mulAcc(p, add(pProof, pA), mload(add(pMem, pV1))) + g1_mulAcc(p, add(pProof, pB), mload(add(pMem, pV2))) + g1_mulAcc(p, add(pProof, pC), mload(add(pMem, pV3))) + g1_mulAccC(p, S1x, S1y, mload(add(pMem, pV4))) + g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV5))) + } + + function calculateE(pProof, pMem) { + let s := mod(sub(q, mload(add(pMem, pEval_r0))), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_a)), mload(add(pMem, pV1)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_b)), mload(add(pMem, pV2)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_c)), mload(add(pMem, pV3)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_s1)), mload(add(pMem, pV4)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_s2)), mload(add(pMem, pV5)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_zw)), mload(add(pMem, pU)), q), q) + g1_mulAccC(add(pMem, pE), G1x, G1y, s) + } + + function checkPairing(pProof, pMem) -> isOk { let mIn := mload(0x40) - mstore(mIn, mload(add(pMem, pA1))) - mstore(add(mIn,32), mload(add(add(pMem, pA1), 32))) + + // A1 + g1_mulAcc(mIn, add(pProof, pWxiw), add(pMem, pU)) + g1_acc(mIn, add(pProof, pWxi)) + mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) + + // [X]_2 mstore(add(mIn,64), X2x2) mstore(add(mIn,96), X2x1) mstore(add(mIn,128), X2y2) mstore(add(mIn,160), X2y1) - mstore(add(mIn,192), mload(add(pMem, pB1))) - let s := mload(add(add(pMem, pB1), 32)) - s := mod(sub(qf, s), qf) - mstore(add(mIn,224), s) + + // B1 + g1_mulAcc(add(mIn, 192), add(pMem, pWxi), mload(add(pMem, pXi))) + let s := mulmod(mload(mload(add(pMem, pU))), mload(mload(add(pMem, pXi))), q) + s := mulmod(s, w1, q) + g1_mulAcc(add(mIn, 256), add(pProof, pWxiw), s) + g1_acc(add(mIn, 192), add(mIn, 256)) + g1_acc(add(mIn, 192), add(pMem, pF)) + g1_acc(add(mIn, 192), add(pMem, pE)) + + // [1]_2 mstore(add(mIn,256), G2x2) mstore(add(mIn,288), G2x1) mstore(add(mIn,320), G2y2) @@ -617,7 +643,7 @@ contract PlonkVerifier { let success := staticcall(sub(gas(), 2000), 8, mIn, 384, mIn, 0x20) - isOk := and(success, mload(mIn)) + isOk := and(success, mload(mIn)) } let pMem := mload(0x40) @@ -626,11 +652,12 @@ contract PlonkVerifier { checkInput(proof) calculateChallanges(proof, pMem, pubSignals) calculateLagrange(pMem) - calculatePl(pMem, pubSignals) - calculateT(proof, pMem) - calculateA1(proof, pMem) - calculateB1(proof, pMem) - let isValid := checkPairing(pMem) + calculatePI(pMem, pubSignals) + calculateR0(proof, pMem) + calculateD(proof, pMem) + calculateF(proof, pMem) + calculateE(proof, pMem) + let isValid := checkPairing(proof, pMem) mstore(0x40, sub(pMem, lastMem)) mstore(0, isValid) diff --git a/test/plonk_circuit/circuit.zkey b/test/plonk_circuit/circuit.zkey index 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"4789447887245439838828293816801085734534480786500369542683260813915807895018", - "5743534347322910212791948378800524709212623490686788228035168007519506810508", + "13971416223242651542366715728368906359640038706276531500429531708796073258277", + "10421443948033763642149912846113365572165014601716715331224624947552460520043", "1" ], "Wxiw": [ - "19379972490037320589254794886333437175961689166573424007077500138714809349682", - "12523908414418029668596495120104904066342410136497532239942511327769729048404", + "17765787784457670830871593390874368837165912572092183824115141625095019062878", + "1923706056001260011656416104295967740181091112784478760912734896662208628583", "1" ], + "eval_a": "10799560112054680901137226204213873700826592739080369812528079446253216295813", + "eval_b": "7877313129049829225962721657498993624288591252629781090410265210156591091645", + "eval_c": "19262479669546615646866494950794050991978938609429436242634904528122872883540", + "eval_s1": "9943707996031584540773781677363098084929121111061462884057666436801558016467", + "eval_s2": "20442292478151764537886021535271741908528859398849641563695916267470568099112", + "eval_zw": "2514741082646163896220326677313738849736483859214666037715057616704431674465", "protocol": "plonk", "curve": "bn128" } \ No newline at end of file diff --git a/test/plonk_circuit/verification_key.json b/test/plonk_circuit/verification_key.json index 63321622..419cf6c4 100644 --- a/test/plonk_circuit/verification_key.json +++ b/test/plonk_circuit/verification_key.json @@ -6,43 +6,43 @@ "k1": "2", "k2": "3", "Qm": [ - "4574976860925876233715815557145957880705707179788243092345689458042383890488", - "4280641572679440220740870768701934042005081764212788702122100316880968332003", + "17953645607507459900286185560951810786731058999325781923205502055353263497291", + "19385486967908870028674938916390954985705306268782601788969000107603897770767", "1" ], "Ql": [ - "965658296392348546197801330054212493203716810675203464920320569299615906620", - "2656007013467620250344837426700774817845582578535592475523934494973414078961", + "11940858774017579942566450477449012460918017239896733829055270107468309760540", + "947254594125514574342968640034741130676940992205538578216940265903584710169", "1" ], "Qr": [ - "9466120146806803512081752933000124200435544680867502413168004293837549973279", - "21718061423910769411439185483074527939398926867139106591112998426662463026765", + "16057511199156614460548645536725007313348939819318943470685206502402956172907", + "10506209454111335156976278630909826596572196999531725341452203577193363727183", "1" ], "Qo": [ - "14232475876760437187555678371073865360567175818750566973123447255794615727867", - "12884948380030714721172201264029036846611910042838904312559968631894569296588", + "17157624048880737579826278328189066542171805404376573481770268188483838847757", + "18514386016535062016800932564037101304017747936838789635283796814642720512673", "1" ], "Qc": [ - "14611255151810715369553599153356422265550902840832241273629187752840438096443", - "9099095607583972457036848580058361056377035074964862926640921566382822995435", + "9425204922382128984212419080680000340238602060329517997301340801336513664736", + "9167308630107900718125273932943677561306913176994118892249570126249686869364", "1" ], "S1": [ - "14533465958261944855196820716374074689704505288368818447966063234824080424576", - "12453353674569653145950160230568106433424266373528956571501497772329286407421", + "10782085188530267881189340256496934831907742532399561656521702603135823217637", + "12403008688044971496101927450821599344745023222457894394078671019783662128471", "1" ], "S2": [ - "19581287390493194877650947725652399954855738146667446650367315521331119724530", - "13292535777423157488265774466403939589622049710743071078999542362804505686482", + "9279525915934333912510150900730589708299616165652915633005823194068751444534", + "17339946533833948904498037980944354287085405669808936769308277491115888828896", "1" ], "S3": [ - "7628615832235497959754170049702774596960536866278288444040861507702299255530", - "6061093738111279431632848690609155827426019335581022466737969401920480256170", + "10636394165993966883449775646752541022226109588433686577933510456646304718904", + "18335534742276222998450555199564351867006746787413781617417650248398260441193", "1" ], "X_2": [ @@ -58,5 +58,6 @@ "1", "0" ] - ] + ], + "w": "19540430494807482326159819597004422086093766032135589407132600596362845576832" } \ No newline at end of file diff --git a/test/plonk_circuit/verifier.sol b/test/plonk_circuit/verifier.sol index 9e2a122d..5b02324a 100644 --- a/test/plonk_circuit/verifier.sol +++ b/test/plonk_circuit/verifier.sol @@ -27,22 +27,22 @@ contract PlonkVerifier { uint16 constant nPublic = 2; uint16 constant nLagrange = 2; - uint256 constant Qmx = 4574976860925876233715815557145957880705707179788243092345689458042383890488; - uint256 constant Qmy = 4280641572679440220740870768701934042005081764212788702122100316880968332003; - uint256 constant Qlx = 965658296392348546197801330054212493203716810675203464920320569299615906620; - uint256 constant Qly = 2656007013467620250344837426700774817845582578535592475523934494973414078961; - uint256 constant Qrx = 9466120146806803512081752933000124200435544680867502413168004293837549973279; - uint256 constant Qry = 21718061423910769411439185483074527939398926867139106591112998426662463026765; - uint256 constant Qox = 14232475876760437187555678371073865360567175818750566973123447255794615727867; - uint256 constant Qoy = 12884948380030714721172201264029036846611910042838904312559968631894569296588; - uint256 constant Qcx = 14611255151810715369553599153356422265550902840832241273629187752840438096443; - uint256 constant Qcy = 9099095607583972457036848580058361056377035074964862926640921566382822995435; - uint256 constant S1x = 14533465958261944855196820716374074689704505288368818447966063234824080424576; - uint256 constant S1y = 12453353674569653145950160230568106433424266373528956571501497772329286407421; - uint256 constant S2x = 19581287390493194877650947725652399954855738146667446650367315521331119724530; - uint256 constant S2y = 13292535777423157488265774466403939589622049710743071078999542362804505686482; - uint256 constant S3x = 7628615832235497959754170049702774596960536866278288444040861507702299255530; - uint256 constant S3y = 6061093738111279431632848690609155827426019335581022466737969401920480256170; + uint256 constant Qmx = 17953645607507459900286185560951810786731058999325781923205502055353263497291; + uint256 constant Qmy = 19385486967908870028674938916390954985705306268782601788969000107603897770767; + uint256 constant Qlx = 11940858774017579942566450477449012460918017239896733829055270107468309760540; + uint256 constant Qly = 947254594125514574342968640034741130676940992205538578216940265903584710169; + uint256 constant Qrx = 16057511199156614460548645536725007313348939819318943470685206502402956172907; + uint256 constant Qry = 10506209454111335156976278630909826596572196999531725341452203577193363727183; + uint256 constant Qox = 17157624048880737579826278328189066542171805404376573481770268188483838847757; + uint256 constant Qoy = 18514386016535062016800932564037101304017747936838789635283796814642720512673; + uint256 constant Qcx = 9425204922382128984212419080680000340238602060329517997301340801336513664736; + uint256 constant Qcy = 9167308630107900718125273932943677561306913176994118892249570126249686869364; + uint256 constant S1x = 10782085188530267881189340256496934831907742532399561656521702603135823217637; + uint256 constant S1y = 12403008688044971496101927450821599344745023222457894394078671019783662128471; + uint256 constant S2x = 9279525915934333912510150900730589708299616165652915633005823194068751444534; + uint256 constant S2y = 17339946533833948904498037980944354287085405669808936769308277491115888828896; + uint256 constant S3x = 10636394165993966883449775646752541022226109588433686577933510456646304718904; + uint256 constant S3y = 18335534742276222998450555199564351867006746787413781617417650248398260441193; uint256 constant k1 = 2; uint256 constant k2 = 3; uint256 constant X2x1 = 18029695676650738226693292988307914797657423701064905010927197838374790804409; @@ -75,7 +75,6 @@ contract PlonkVerifier { uint16 constant pEval_s1 = 704; uint16 constant pEval_s2 = 736; uint16 constant pEval_zw = 768; - uint16 constant pEval_r = 800; uint16 constant pAlpha = 0; uint16 constant pBeta = 32; @@ -90,20 +89,22 @@ contract PlonkVerifier { uint16 constant pV5 = 320; uint16 constant pV6 = 352; uint16 constant pU = 384; - uint16 constant pPl = 416; - uint16 constant pEval_t = 448; - uint16 constant pA1 = 480; - uint16 constant pB1 = 544; - uint16 constant pZh = 608; - uint16 constant pZhInv = 640; + uint16 constant pPI = 416; + uint16 constant pEval_r0 = 448; + uint16 constant pD = 480; + uint16 constant pF = 544; + uint16 constant pE = 608; + uint16 constant pTmp = 672; + uint16 constant pZh = 736; + uint16 constant pZhInv = 768; - uint16 constant pEval_l1 = 672; + uint16 constant pEval_l1 = 800; - uint16 constant pEval_l2 = 704; + uint16 constant pEval_l2 = 832; - uint16 constant lastMem = 736; + uint16 constant lastMem = 864; function verifyProof(bytes memory proof, uint[] memory pubSignals) public view returns (bool) { assembly { @@ -195,7 +196,6 @@ contract PlonkVerifier { checkField(mload(add(pProof, pEval_s1))) checkField(mload(add(pProof, pEval_s2))) checkField(mload(add(pProof, pEval_zw))) - checkField(mload(add(pProof, pEval_r))) // Points are checked in the point operations precompiled smart contracts } @@ -205,25 +205,71 @@ contract PlonkVerifier { let a let b - - mstore( add(pMem, 736 ), mload( add( pPublic, 32))) - - mstore( add(pMem, 768 ), mload( add( pPublic, 64))) - - mstore( add(pMem, 800 ), mload( add( pProof, pA))) - mstore( add(pMem, 832 ), mload( add( pProof, add(pA,32)))) - mstore( add(pMem, 864 ), mload( add( pProof, add(pA,64)))) - mstore( add(pMem, 896 ), mload( add( pProof, add(pA,96)))) - mstore( add(pMem, 928 ), mload( add( pProof, add(pA,128)))) - mstore( add(pMem, 960 ), mload( add( pProof, add(pA,160)))) - - b := mod(keccak256(add(pMem, lastMem), 256), q) - mstore( add(pMem, pBeta), b) - mstore( add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) - mstore( add(pMem, pAlpha), mod(keccak256(add(pProof, pZ), 64), q)) - - a := mod(keccak256(add(pProof, pT1), 192), q) + // Challenges.beta + mstore( add(pMem, 864 ), Qmx) + mstore( add(pMem, 896 ), Qmy) + mstore( add(pMem, 928 ), Qlx) + mstore( add(pMem, 960 ), Qly) + mstore( add(pMem, 992 ), Qrx) + mstore( add(pMem, 1024 ), Qry) + mstore( add(pMem, 1056 ), Qox) + mstore( add(pMem, 1088 ), Qoy) + mstore( add(pMem, 1120 ), Qcx) + mstore( add(pMem, 1152 ), Qcy) + mstore( add(pMem, 1184 ), S1x) + mstore( add(pMem, 1216 ), S1x) + mstore( add(pMem, 1248 ), S2x) + mstore( add(pMem, 1280 ), S2x) + mstore( add(pMem, 1312 ), S3x) + mstore( add(pMem, 1344 ), S3x) + + + mstore( add(pMem, 1376 ), mload( add( pPublic, 32))) + + mstore( add(pMem, 1408 ), mload( add( pPublic, 64))) + + mstore( add(pMem, 1440 ), mload( add( pProof, pA))) + mstore( add(pMem, 1472 ), mload( add( pProof, add(pA,32)))) + mstore( add(pMem, 1504 ), mload( add( pProof, pB))) + mstore( add(pMem, 1536 ), mload( add( pProof, add(pB, 32)))) + mstore( add(pMem, 1568 ), mload( add( pProof, pC))) + mstore( add(pMem, 1600 ), mload( add( pProof, add(pC, 32)))) + + b := mod(keccak256(add(pMem, lastMem), 768), q) + mstore(add(pMem, pBeta), b) + + // Challenges.gamma + mstore(add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) + + // Challenges.alpha + mstore(add(pMem, 864), mload(add(pMem, pBeta))) + mstore(add(pMem, 896), mload(add(pMem, pGamma))) + mstore(add(pMem, 928), mload(add(pProof, pZ))) + mstore(add(pMem, 960), mload(add(pProof, add(pZ, 32)))) + a := mod(keccak256(add(pMem, lastMem), 128), q) + mstore(add(pMem, pAlpha), a) + + mstore(add(pMem, 864), mload(add(pMem, pAlpha))) + mstore(add(pMem, 896), mload(add(pProof, pT1))) + mstore(add(pMem, 928), mload(add(pProof, add(pT1, 32)))) + mstore(add(pMem, 960), mload(add(pProof, pT2))) + mstore(add(pMem, 992), mload(add(pProof, add(pT2, 32)))) + mstore(add(pMem, 1024), mload(add(pProof, pT3))) + mstore(add(pMem, 1056), mload(add(pProof, add(pT3, 32)))) + a := mod(keccak256(add(pMem, lastMem), 224), q) mstore( add(pMem, pXi), a) + + mstore(add(pMem, 864), a) + mstore(add(pMem, 896), mload(add(pProof, pEval_a))) + mstore(add(pMem, 928), mload(add(pProof, pEval_b))) + mstore(add(pMem, 960), mload(add(pProof, pEval_c))) + mstore(add(pMem, 992), mload(add(pProof, pEval_s1))) + mstore(add(pMem, 1024), mload(add(pProof, pEval_s2))) + mstore(add(pMem, 1056), mload(add(pProof, pEval_zw))) + let v1 := mod(keccak256(add(pMem, lastMem), 224), q) + mstore(add(pMem, pV1), v1) + + // Compute betaxi mstore( add(pMem, pBetaXi), mulmod(b, a, q)) a:= mulmod(a, a, q) @@ -236,9 +282,7 @@ contract PlonkVerifier { a:= mod(add(sub(a, 1),q), q) mstore( add(pMem, pZh), a) mstore( add(pMem, pZhInv), a) // We will invert later together with lagrange pols - - let v1 := mod(keccak256(add(pProof, pEval_a), 224), q) - mstore( add(pMem, pV1), v1) + a := mulmod(v1, v1, q) mstore( add(pMem, pV2), a) a := mulmod(a, v1, q) @@ -337,7 +381,7 @@ contract PlonkVerifier { } - function calculatePl(pMem, pPub) { + function calculatePI(pMem, pPub) { let pl := 0 @@ -372,88 +416,43 @@ contract PlonkVerifier { ) - mstore(add(pMem, pPl), pl) + mstore(add(pMem, pPI), pl) } - function calculateT(pProof, pMem) { - let t - let t1 - let t2 - t := addmod( - mload(add(pProof, pEval_r)), - mload(add(pMem, pPl)), - q - ) - - t1 := mulmod( - mload(add(pProof, pEval_s1)), - mload(add(pMem, pBeta)), - q - ) + function calculateR0(pProof, pMem) { + let alpha2 := mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q) + let e1 := mload(add(pMem, pPI)) - t1 := addmod( - t1, - mload(add(pProof, pEval_a)), - q - ) - - t1 := addmod( - t1, - mload(add(pMem, pGamma)), - q - ) + let e2 := mulmod(mload(add(pMem, pEval_l1)), alpha2, q) - t2 := mulmod( - mload(add(pProof, pEval_s2)), - mload(add(pMem, pBeta)), - q - ) + let e3a := addmod( + mload(add(pProof, pEval_a)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), + q) + e3a := addmod(e3a, mload(add(pMem, pGamma)), q) - t2 := addmod( - t2, + let e3b := addmod( mload(add(pProof, pEval_b)), - q - ) - - t2 := addmod( - t2, - mload(add(pMem, pGamma)), - q - ) - - t1 := mulmod(t1, t2, q) - - t2 := addmod( + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), + q) + e3b := addmod(e3b, mload(add(pMem, pGamma)), q) + + let e3c := addmod( mload(add(pProof, pEval_c)), mload(add(pMem, pGamma)), - q - ) + q) - t1 := mulmod(t1, t2, q) - t1 := mulmod(t1, mload(add(pProof, pEval_zw)), q) - t1 := mulmod(t1, mload(add(pMem, pAlpha)), q) - - t2 := mulmod( - mload(add(pMem, pEval_l1)), - mload(add(pMem, pAlpha)), - q - ) - - t2 := mulmod( - t2, - mload(add(pMem, pAlpha)), - q - ) + let e3 := mulmod(mulmod(e3a, e3b, q), e3c, q) - t1 := addmod(t1, t2, q) - - t := mod(sub(add(t, q), t1), q) - t := mulmod(t, mload(add(pMem, pZhInv)), q) + e3 := mulmod(e3, mload(add(pProof, pEval_zw)), q) + e3 := mulmod(e3, mload(add(pMem, pAlpha)), q) + + let r0 := mod(sub(e1, e2), q) + r0 := mod(sub(r0, e3), q) - mstore( add(pMem, pEval_t) , t) - + mstore(add(pMem, pEval_r0) , r0) } function g1_set(pR, pP) { @@ -542,119 +541,146 @@ contract PlonkVerifier { } } + function calculateD(pProof, pMem) { + let p:= add(pMem, pD) + let mIn := mload(0x40) + + g1_mulSetC(p, Qmx, Qmy, mulmod(mload(add(pProof, pEval_a)), mload(add(pProof, pEval_b)), q)) + g1_mulAccC(p, Qlx, Qly, mload(add(pProof, pEval_a))) + g1_mulAccC(p, Qrx, Qry, mload(add(pProof, pEval_b))) + g1_mulAccC(p, Qox, Qoy, mload(add(pProof, pEval_c))) + g1_mulAccC(p, Qcx, Qcy, 1) + + let val1 := addmod( + addmod(mload(add(pProof, pEval_a)), mload(add(pMem, pBetaXi)), q), + mload(add(pMem, pGamma)), + q) + + let val2 := addmod( + addmod( + mload(add(pProof, pEval_b)), + mulmod(mload(add(pMem, pBetaXi)), k1, q), + q), + mload(add(pMem, pGamma)), + q) + + let val3 := addmod( + addmod( + mload(add(pProof, pEval_c)), + mulmod(mload(add(pMem, pBetaXi)), k2, q), + q), + mload(add(pMem, pGamma)), + q) + + let d2a := mulmod( + mulmod(mulmod(val1, val2, q), val3, q), + mload(add(pMem, pAlpha)), + q + ) + + let d2b := mulmod( + mload(add(pMem, pEval_l1)), + mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q), + q + ) + + // We'll use pF to save d2 + g1_mulAcc( + add(pMem, pF), + add(pProof, pZ), + addmod(addmod(d2a, d2b, q), mload(add(pMem, pU)), q)) + + val1 := addmod( + addmod( + mload(add(pProof, pEval_a)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), + q), + mload(add(pMem, pGamma)), + q) - function calculateA1(pProof, pMem) { - let p := add(pMem, pA1) - g1_set(p, add(pProof, pWxi)) - g1_mulAcc(p, add(pProof, pWxiw), mload(add(pMem, pU))) + val2 := addmod( + addmod( + mload(add(pProof, pEval_b)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), + q), + mload(add(pMem, pGamma)), + q) + + val3 := mulmod( + mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pBeta)), q), + mload(add(pProof, pEval_zw)), q) + + + // We'll use pE to save d3 + g1_mulAccC( + add(pMem, pE), + S3x, + S3y, + mulmod(mulmod(val1, val2, q), val3, q)) + + + // We'll use pTmp to save d4 + g1_set(add(pMem, pTmp), add(pProof, pT1)) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT2), add(pMem, pXin)) + let xin2 := mulmod(add(pMem, pXin), add(pMem, pXin), q) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) + + g1_mulAcc(mIn, add(pMem, pTmp), add(pMem, pZh)) + + mstore(add(add(pMem, pE), 32), mod(sub(qf, mload(add(add(pMem, pE), 32))), qf)) + mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) + g1_acc(add(pMem, pD), add(pMem, pF)) + g1_acc(add(pMem, pD), add(pMem, pE)) + g1_acc(add(pMem, pD), add(pMem, mIn)) } + function calculateF(pProof, pMem) { + let p := add(pMem, pF) + + g1_set(p, add(pMem, pD)) + g1_mulAcc(p, add(pProof, pA), mload(add(pMem, pV1))) + g1_mulAcc(p, add(pProof, pB), mload(add(pMem, pV2))) + g1_mulAcc(p, add(pProof, pC), mload(add(pMem, pV3))) + g1_mulAccC(p, S1x, S1y, mload(add(pMem, pV4))) + g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV5))) + } - function calculateB1(pProof, pMem) { - let s - let s1 - let p := add(pMem, pB1) - - // Calculate D - s := mulmod( mload(add(pProof, pEval_a)), mload(add(pMem, pV1)), q) - g1_mulSetC(p, Qlx, Qly, s) - - s := mulmod( s, mload(add(pProof, pEval_b)), q) - g1_mulAccC(p, Qmx, Qmy, s) - - s := mulmod( mload(add(pProof, pEval_b)), mload(add(pMem, pV1)), q) - g1_mulAccC(p, Qrx, Qry, s) - - s := mulmod( mload(add(pProof, pEval_c)), mload(add(pMem, pV1)), q) - g1_mulAccC(p, Qox, Qoy, s) - - s :=mload(add(pMem, pV1)) - g1_mulAccC(p, Qcx, Qcy, s) - - s := addmod(mload(add(pProof, pEval_a)), mload(add(pMem, pBetaXi)), q) - s := addmod(s, mload(add(pMem, pGamma)), q) - s1 := mulmod(k1, mload(add(pMem, pBetaXi)), q) - s1 := addmod(s1, mload(add(pProof, pEval_b)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s1 := mulmod(k2, mload(add(pMem, pBetaXi)), q) - s1 := addmod(s1, mload(add(pProof, pEval_c)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s := mulmod(s, mload(add(pMem, pAlpha)), q) - s := mulmod(s, mload(add(pMem, pV1)), q) - s1 := mulmod(mload(add(pMem, pEval_l1)), mload(add(pMem, pAlpha)), q) - s1 := mulmod(s1, mload(add(pMem, pAlpha)), q) - s1 := mulmod(s1, mload(add(pMem, pV1)), q) - s := addmod(s, s1, q) - s := addmod(s, mload(add(pMem, pU)), q) - g1_mulAcc(p, add(pProof, pZ), s) - - s := mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q) - s := addmod(s, mload(add(pProof, pEval_a)), q) - s := addmod(s, mload(add(pMem, pGamma)), q) - s1 := mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q) - s1 := addmod(s1, mload(add(pProof, pEval_b)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s := mulmod(s, mload(add(pMem, pAlpha)), q) - s := mulmod(s, mload(add(pMem, pV1)), q) - s := mulmod(s, mload(add(pMem, pBeta)), q) - s := mulmod(s, mload(add(pProof, pEval_zw)), q) - s := mod(sub(q, s), q) - g1_mulAccC(p, S3x, S3y, s) - - - // calculate F - g1_acc(p , add(pProof, pT1)) - - s := mload(add(pMem, pXin)) - g1_mulAcc(p, add(pProof, pT2), s) - - s := mulmod(s, s, q) - g1_mulAcc(p, add(pProof, pT3), s) - - g1_mulAcc(p, add(pProof, pA), mload(add(pMem, pV2))) - g1_mulAcc(p, add(pProof, pB), mload(add(pMem, pV3))) - g1_mulAcc(p, add(pProof, pC), mload(add(pMem, pV4))) - g1_mulAccC(p, S1x, S1y, mload(add(pMem, pV5))) - g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV6))) - - // calculate E - s := mload(add(pMem, pEval_t)) - s := addmod(s, mulmod(mload(add(pProof, pEval_r)), mload(add(pMem, pV1)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_a)), mload(add(pMem, pV2)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_b)), mload(add(pMem, pV3)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_c)), mload(add(pMem, pV4)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s1)), mload(add(pMem, pV5)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s2)), mload(add(pMem, pV6)), q), q) + function calculateE(pProof, pMem) { + let s := mod(sub(q, mload(add(pMem, pEval_r0))), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_a)), mload(add(pMem, pV1)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_b)), mload(add(pMem, pV2)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_c)), mload(add(pMem, pV3)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_s1)), mload(add(pMem, pV4)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_s2)), mload(add(pMem, pV5)), q), q) s := addmod(s, mulmod(mload(add(pProof, pEval_zw)), mload(add(pMem, pU)), q), q) - s := mod(sub(q, s), q) - g1_mulAccC(p, G1x, G1y, s) - - - // Last part of B - s := mload(add(pMem, pXi)) - g1_mulAcc(p, add(pProof, pWxi), s) - - s := mulmod(mload(add(pMem, pU)), mload(add(pMem, pXi)), q) - s := mulmod(s, w1, q) - g1_mulAcc(p, add(pProof, pWxiw), s) - + g1_mulAccC(add(pMem, pE), G1x, G1y, s) } - function checkPairing(pMem) -> isOk { + function checkPairing(pProof, pMem) -> isOk { let mIn := mload(0x40) - mstore(mIn, mload(add(pMem, pA1))) - mstore(add(mIn,32), mload(add(add(pMem, pA1), 32))) + + // A1 + g1_mulAcc(mIn, add(pProof, pWxiw), add(pMem, pU)) + g1_acc(mIn, add(pProof, pWxi)) + mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) + + // [X]_2 mstore(add(mIn,64), X2x2) mstore(add(mIn,96), X2x1) mstore(add(mIn,128), X2y2) mstore(add(mIn,160), X2y1) - mstore(add(mIn,192), mload(add(pMem, pB1))) - let s := mload(add(add(pMem, pB1), 32)) - s := mod(sub(qf, s), qf) - mstore(add(mIn,224), s) + + // B1 + g1_mulAcc(add(mIn, 192), add(pMem, pWxi), mload(add(pMem, pXi))) + let s := mulmod(mload(mload(add(pMem, pU))), mload(mload(add(pMem, pXi))), q) + s := mulmod(s, w1, q) + g1_mulAcc(add(mIn, 256), add(pProof, pWxiw), s) + g1_acc(add(mIn, 192), add(mIn, 256)) + g1_acc(add(mIn, 192), add(pMem, pF)) + g1_acc(add(mIn, 192), add(pMem, pE)) + + // [1]_2 mstore(add(mIn,256), G2x2) mstore(add(mIn,288), G2x1) mstore(add(mIn,320), G2y2) @@ -662,7 +688,7 @@ contract PlonkVerifier { let success := staticcall(sub(gas(), 2000), 8, mIn, 384, mIn, 0x20) - isOk := and(success, mload(mIn)) + isOk := and(success, mload(mIn)) } let pMem := mload(0x40) @@ -671,11 +697,12 @@ contract PlonkVerifier { checkInput(proof) calculateChallanges(proof, pMem, pubSignals) calculateLagrange(pMem) - calculatePl(pMem, pubSignals) - calculateT(proof, pMem) - calculateA1(proof, pMem) - calculateB1(proof, pMem) - let isValid := checkPairing(pMem) + calculatePI(pMem, pubSignals) + calculateR0(proof, pMem) + calculateD(proof, pMem) + calculateF(proof, pMem) + calculateE(proof, pMem) + let isValid := checkPairing(proof, pMem) mstore(0x40, sub(pMem, lastMem)) mstore(0, isValid) From bd57b81f02c537617ed97af559d3ea2b4e8181b3 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Sat, 13 May 2023 06:08:33 +0200 Subject: [PATCH 13/48] add debug function --- templates/verifier_plonk.sol.ejs | 29 +++++++++++++++++++++++++---- 1 file changed, 25 insertions(+), 4 deletions(-) diff --git a/templates/verifier_plonk.sol.ejs b/templates/verifier_plonk.sol.ejs index 6485cc0c..b4f301e2 100644 --- a/templates/verifier_plonk.sol.ejs +++ b/templates/verifier_plonk.sol.ejs @@ -21,6 +21,8 @@ pragma solidity >=0.7.0 <0.9.0; +import "hardhat/console.sol"; + contract PlonkVerifier { uint32 constant n = <%=2**power%>; @@ -104,7 +106,7 @@ contract PlonkVerifier { uint16 constant lastMem = <%=pLastMem%>; - function verifyProof(bytes memory proof, uint[] memory pubSignals) public view returns (bool) { + function verifyProof(bytes memory proof, uint[] memory pubSignals) public /*view*/ returns (bool) { assembly { ///////// // Computes the inverse using the extended euclidean algorithm @@ -658,11 +660,30 @@ contract PlonkVerifier { calculateF(proof, pMem) calculateE(proof, pMem) let isValid := checkPairing(proof, pMem) - - mstore(0x40, sub(pMem, lastMem)) + + sstore(0, mload(add(pMem, pGamma))) + } + + bytes32 value = debug(); + console.logBytes32(value); + + assembly { + mstore(0, true) + return(0,0x20) + } + } + + function debug() public view returns (bytes32 result) { + assembly { + result := sload(0) + } + } +} + + /*mstore(0x40, sub(pMem, lastMem)) mstore(0, isValid) return(0,0x20) } } -} +}/* From cc771d48602df41624cb22ca3b6b649b51c889e4 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Sat, 13 May 2023 06:09:20 +0200 Subject: [PATCH 14/48] remove console.log import --- templates/verifier_groth16.sol.ejs | 2 -- 1 file changed, 2 deletions(-) diff --git a/templates/verifier_groth16.sol.ejs b/templates/verifier_groth16.sol.ejs index 7c9687ac..32c260ed 100644 --- a/templates/verifier_groth16.sol.ejs +++ b/templates/verifier_groth16.sol.ejs @@ -20,8 +20,6 @@ pragma solidity >=0.7.0 <0.9.0; -import "hardhat/console.sol"; - contract Groth16Verifier { // Scalar field size uint256 constant r = 21888242871839275222246405745257275088548364400416034343698204186575808495617; From 1218180329898e3461db727ccb12f97c9127434a Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Wed, 17 May 2023 11:25:22 +0200 Subject: [PATCH 15/48] Plonk smart contracte refactored. --- src/plonk_exportsoliditycalldata.js | 39 +- templates/verifier_plonk.sol.ejs | 571 ++++++++++++++-------------- 2 files changed, 312 insertions(+), 298 deletions(-) diff --git a/src/plonk_exportsoliditycalldata.js b/src/plonk_exportsoliditycalldata.js index 48d437fd..d1bcce37 100644 --- a/src/plonk_exportsoliditycalldata.js +++ b/src/plonk_exportsoliditycalldata.js @@ -46,27 +46,20 @@ export default async function plonkExportSolidityCallData(_proof, _pub) { inputs = inputs + p256(pub[i]); } - const proofBuff = new Uint8Array(G1.F.n8*2*9 + Fr.n8*7); - G1.toRprUncompressed(proofBuff, 0, G1.e(proof.A)); - G1.toRprUncompressed(proofBuff, G1.F.n8*2, G1.e(proof.B)); - G1.toRprUncompressed(proofBuff, G1.F.n8*4, G1.e(proof.C)); - G1.toRprUncompressed(proofBuff, G1.F.n8*6, G1.e(proof.Z)); - G1.toRprUncompressed(proofBuff, G1.F.n8*8, G1.e(proof.T1)); - G1.toRprUncompressed(proofBuff, G1.F.n8*10, G1.e(proof.T2)); - G1.toRprUncompressed(proofBuff, G1.F.n8*12, G1.e(proof.T3)); - G1.toRprUncompressed(proofBuff, G1.F.n8*14, G1.e(proof.Wxi)); - G1.toRprUncompressed(proofBuff, G1.F.n8*16, G1.e(proof.Wxiw)); - Fr.toRprBE(proofBuff, G1.F.n8*18 , Fr.e(proof.eval_a)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8, Fr.e(proof.eval_b)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8*2, Fr.e(proof.eval_c)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8*3, Fr.e(proof.eval_s1)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8*4, Fr.e(proof.eval_s2)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8*5, Fr.e(proof.eval_zw)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8*6, Fr.e(proof.eval_r)); - - const proofHex = Array.from(proofBuff).map(i2hex).join(""); - - const S="0x"+proofHex+",["+inputs+"]"; - - return S; + return `[${p256(proof.A[0])}, ${p256(proof.A[1])},` + + `${p256(proof.B[0])},${p256(proof.B[1])},` + + `${p256(proof.C[0])},${p256(proof.C[1])},` + + `${p256(proof.Z[0])},${p256(proof.Z[1])},` + + `${p256(proof.T1[0])},${p256(proof.T1[1])},` + + `${p256(proof.T2[0])},${p256(proof.T2[1])},` + + `${p256(proof.T3[0])},${p256(proof.T3[1])},` + + `${p256(proof.Wxi[0])},${p256(proof.Wxi[1])},` + + `${p256(proof.Wxiw[0])},${p256(proof.Wxiw[1])},` + + `${p256(proof.eval_a)},` + + `${p256(proof.eval_b)},` + + `${p256(proof.eval_c)},` + + `${p256(proof.eval_s1)},` + + `${p256(proof.eval_s2)},` + + `${p256(proof.eval_zw)}]` + + `[${inputs}]`; } diff --git a/templates/verifier_plonk.sol.ejs b/templates/verifier_plonk.sol.ejs index b4f301e2..25f38eb1 100644 --- a/templates/verifier_plonk.sol.ejs +++ b/templates/verifier_plonk.sol.ejs @@ -24,81 +24,95 @@ pragma solidity >=0.7.0 <0.9.0; import "hardhat/console.sol"; contract PlonkVerifier { - - uint32 constant n = <%=2**power%>; - uint16 constant nPublic = <%=nPublic%>; - uint16 constant nLagrange = <%=Math.max(nPublic, 1)%>; - - uint256 constant Qmx = <%=Qm[0]%>; - uint256 constant Qmy = <%=Qm[0] == "0" ? "0" : Qm[1]%>; - uint256 constant Qlx = <%=Ql[0]%>; - uint256 constant Qly = <%=Ql[0] == "0" ? "0" : Ql[1]%>; - uint256 constant Qrx = <%=Qr[0]%>; - uint256 constant Qry = <%=Qr[0] == "0" ? "0" : Qr[1]%>; - uint256 constant Qox = <%=Qo[0]%>; - uint256 constant Qoy = <%=Qo[0] == "0" ? "0" : Qo[1]%>; - uint256 constant Qcx = <%=Qc[0]%>; - uint256 constant Qcy = <%=Qc[0] == "0" ? "0" : Qc[1]%>; - uint256 constant S1x = <%=S1[0]%>; - uint256 constant S1y = <%=S1[0] == "0" ? "0" : S1[1]%>; - uint256 constant S2x = <%=S2[0]%>; - uint256 constant S2y = <%=S2[0] == "0" ? "0" : S2[1]%>; - uint256 constant S3x = <%=S3[0]%>; - uint256 constant S3y = <%=S3[0] == "0" ? "0" : S3[1]%>; - uint256 constant k1 = 2; - uint256 constant k2 = 3; - uint256 constant X2x1 = <%=X_2[0][0]%>; - uint256 constant X2x2 = <%=X_2[0][1]%>; - uint256 constant X2y1 = <%=X_2[1][0]%>; - uint256 constant X2y2 = <%=X_2[1][1]%>; - - uint256 constant q = 21888242871839275222246405745257275088548364400416034343698204186575808495617; - uint256 constant qf = 21888242871839275222246405745257275088696311157297823662689037894645226208583; + // Omega uint256 constant w1 = <%=w%>; + // Scalar field size + uint256 constant q = 21888242871839275222246405745257275088548364400416034343698204186575808495617; + // Base field size + uint256 constant qf = 21888242871839275222246405745257275088696311157297823662689037894645226208583; + // [1]_1 uint256 constant G1x = 1; uint256 constant G1y = 2; + // [1]_2 uint256 constant G2x1 = 10857046999023057135944570762232829481370756359578518086990519993285655852781; uint256 constant G2x2 = 11559732032986387107991004021392285783925812861821192530917403151452391805634; uint256 constant G2y1 = 8495653923123431417604973247489272438418190587263600148770280649306958101930; uint256 constant G2y2 = 4082367875863433681332203403145435568316851327593401208105741076214120093531; - uint16 constant pA = 32; - uint16 constant pB = 96; - uint16 constant pC = 160; - uint16 constant pZ = 224; - uint16 constant pT1 = 288; - uint16 constant pT2 = 352; - uint16 constant pT3 = 416; - uint16 constant pWxi = 480; - uint16 constant pWxiw = 544; - uint16 constant pEval_a = 608; - uint16 constant pEval_b = 640; - uint16 constant pEval_c = 672; - uint16 constant pEval_s1 = 704; - uint16 constant pEval_s2 = 736; - uint16 constant pEval_zw = 768; - uint16 constant pAlpha = 0; - uint16 constant pBeta = 32; - uint16 constant pGamma = 64; - uint16 constant pXi = 96; - uint16 constant pXin = 128; + // Verification Key data + uint32 constant n = <%=2**power%>; + uint16 constant nPublic = <%=nPublic%>; + uint16 constant nLagrange = <%=Math.max(nPublic, 1)%>; + + uint256 constant Qmx = <%=Qm[0]%>; + uint256 constant Qmy = <%=Qm[0] == "0" ? "0" : Qm[1]%>; + uint256 constant Qlx = <%=Ql[0]%>; + uint256 constant Qly = <%=Ql[0] == "0" ? "0" : Ql[1]%>; + uint256 constant Qrx = <%=Qr[0]%>; + uint256 constant Qry = <%=Qr[0] == "0" ? "0" : Qr[1]%>; + uint256 constant Qox = <%=Qo[0]%>; + uint256 constant Qoy = <%=Qo[0] == "0" ? "0" : Qo[1]%>; + uint256 constant Qcx = <%=Qc[0]%>; + uint256 constant Qcy = <%=Qc[0] == "0" ? "0" : Qc[1]%>; + uint256 constant S1x = <%=S1[0]%>; + uint256 constant S1y = <%=S1[0] == "0" ? "0" : S1[1]%>; + uint256 constant S2x = <%=S2[0]%>; + uint256 constant S2y = <%=S2[0] == "0" ? "0" : S2[1]%>; + uint256 constant S3x = <%=S3[0]%>; + uint256 constant S3y = <%=S3[0] == "0" ? "0" : S3[1]%>; + uint256 constant k1 = <%=k1%>; + uint256 constant k2 = <%=k2%>; + uint256 constant X2x1 = <%=X_2[0][0]%>; + uint256 constant X2x2 = <%=X_2[0][1]%>; + uint256 constant X2y1 = <%=X_2[1][0]%>; + uint256 constant X2y2 = <%=X_2[1][1]%>; + + // Proof calldata + // Byte offset of every parameter of the calldata + // Polynomial commitments + uint16 constant pA = 4 + 0; + uint16 constant pB = 4 + 64; + uint16 constant pC = 4 + 128; + uint16 constant pZ = 4 + 192; + uint16 constant pT1 = 4 + 256; + uint16 constant pT2 = 4 + 320; + uint16 constant pT3 = 4 + 384; + uint16 constant pWxi = 4 + 448; + uint16 constant pWxiw = 4 + 512; + // Opening evaluations + uint16 constant pEval_a = 4 + 576; + uint16 constant pEval_b = 4 + 608; + uint16 constant pEval_c = 4 + 640; + uint16 constant pEval_s1 = 4 + 672; + uint16 constant pEval_s2 = 4 + 704; + uint16 constant pEval_zw = 4 + 736; + + // Memory data + // Challenges + uint16 constant pAlpha = 0; + uint16 constant pBeta = 32; + uint16 constant pGamma = 64; + uint16 constant pXi = 96; + uint16 constant pXin = 128; uint16 constant pBetaXi = 160; - uint16 constant pV1 = 192; - uint16 constant pV2 = 224; - uint16 constant pV3 = 256; - uint16 constant pV4 = 288; - uint16 constant pV5 = 320; - uint16 constant pV6 = 352; - uint16 constant pU = 384; - uint16 constant pPI = 416; - uint16 constant pEval_r0 = 448; - uint16 constant pD = 480; - uint16 constant pF = 544; - uint16 constant pE = 608; - uint16 constant pTmp = 672; - uint16 constant pZh = 736; - uint16 constant pZhInv = 768; + uint16 constant pV1 = 192; + uint16 constant pV2 = 224; + uint16 constant pV3 = 256; + uint16 constant pV4 = 288; + uint16 constant pV5 = 320; + uint16 constant pU = 352; + + uint16 constant pPI = 384; + uint16 constant pEval_r0 = 416; + uint16 constant pD = 448; + uint16 constant pF = 512; + uint16 constant pE = 576; + uint16 constant pTmp = 640; + uint16 constant pAlpha2 = 704; + uint16 constant pZh = 736; + uint16 constant pZhInv = 768; + <% for (let i=1; i<=Math.max(nPublic, 1); i++) { %> uint16 constant pEval_l<%=i%> = <%=768+i*32%>; <% } %> @@ -106,7 +120,7 @@ contract PlonkVerifier { uint16 constant lastMem = <%=pLastMem%>; - function verifyProof(bytes memory proof, uint[] memory pubSignals) public /*view*/ returns (bool) { + function verifyProof(uint256[24] calldata _proof, uint256[<%=nPublic%>] calldata _pubSignals) public view returns (bool) { assembly { ///////// // Computes the inverse using the extended euclidean algorithm @@ -185,114 +199,123 @@ contract PlonkVerifier { } } - function checkInput(pProof) { - if iszero(eq(mload(pProof), 800 )) { - mstore(0, 0) - return(0,0x20) - } - checkField(mload(add(pProof, pEval_a))) - checkField(mload(add(pProof, pEval_b))) - checkField(mload(add(pProof, pEval_c))) - checkField(mload(add(pProof, pEval_s1))) - checkField(mload(add(pProof, pEval_s2))) - checkField(mload(add(pProof, pEval_zw))) - - // Points are checked in the point operations precompiled smart contracts + function checkInput() { + checkField(calldataload(pEval_a)) + checkField(calldataload(pEval_b)) + checkField(calldataload(pEval_c)) + checkField(calldataload(pEval_s1)) + checkField(calldataload(pEval_s2)) + checkField(calldataload(pEval_zw)) } - function calculateChallanges(pProof, pMem, pPublic) { - - let a - let b - - // Challenges.beta - mstore( add(pMem, <%=pLastMem%> ), Qmx) - mstore( add(pMem, <%=pLastMem + 32%> ), Qmy) - mstore( add(pMem, <%=pLastMem + 64%> ), Qlx) - mstore( add(pMem, <%=pLastMem + 96%> ), Qly) - mstore( add(pMem, <%=pLastMem + 128%> ), Qrx) - mstore( add(pMem, <%=pLastMem + 160%> ), Qry) - mstore( add(pMem, <%=pLastMem + 192%> ), Qox) - mstore( add(pMem, <%=pLastMem + 224%> ), Qoy) - mstore( add(pMem, <%=pLastMem + 256%> ), Qcx) - mstore( add(pMem, <%=pLastMem + 288%> ), Qcy) - mstore( add(pMem, <%=pLastMem + 320%> ), S1x) - mstore( add(pMem, <%=pLastMem + 352%> ), S1x) - mstore( add(pMem, <%=pLastMem + 384%> ), S2x) - mstore( add(pMem, <%=pLastMem + 416%> ), S2x) - mstore( add(pMem, <%=pLastMem + 448%> ), S3x) - mstore( add(pMem, <%=pLastMem + 480%> ), S3x) + function calculateChallenges(pMem, pPublic) { + let beta + let aux + + let mIn := mload(0x40) // Pointer to the next free memory position + + // Compute challenge.beta & challenge.gamma + mstore(mIn, Qmx) + mstore(add(mIn, 32), Qmy) + mstore(add(mIn, 64), Qlx) + mstore(add(mIn, 96), Qly) + mstore(add(mIn, 128), Qrx) + mstore(add(mIn, 160), Qry) + mstore(add(mIn, 192), Qox) + mstore(add(mIn, 224), Qoy) + mstore(add(mIn, 256), Qcx) + mstore(add(mIn, 288), Qcy) + mstore(add(mIn, 320), S1x) + mstore(add(mIn, 352), S1y) + mstore(add(mIn, 384), S2x) + mstore(add(mIn, 416), S2y) + mstore(add(mIn, 448), S3x) + mstore(add(mIn, 480), S3y) <%for (let i=0; i - mstore( add(pMem, <%=pLastMem + 512 + i*32%> ), mload( add( pPublic, <%=i*32 + 32%>))) + mstore(add(mIn, <%= 512 + i*32 %>), calldataload(add(pPublic, <%=i*32%>))) <%}%> - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +0%> ), mload( add( pProof, pA))) - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +32%> ), mload( add( pProof, add(pA,32)))) - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +64%> ), mload( add( pProof, pB))) - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +96%> ), mload( add( pProof, add(pB, 32)))) - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +128%> ), mload( add( pProof, pC))) - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +160%> ), mload( add( pProof, add(pC, 32)))) + mstore(add(mIn, <%= 512 + nPublic*32 + 0 %> ), calldataload(pA)) + mstore(add(mIn, <%= 512 + nPublic*32 + 32 %> ), calldataload(add(pA, 32))) + mstore(add(mIn, <%= 512 + nPublic*32 + 64 %> ), calldataload(pB)) + mstore(add(mIn, <%= 512 + nPublic*32 + 96 %> ), calldataload(add(pB, 32))) + mstore(add(mIn, <%= 512 + nPublic*32 + 128 %> ), calldataload(pC)) + mstore(add(mIn, <%= 512 + nPublic*32 + 160 %> ), calldataload(add(pC, 32))) - b := mod(keccak256(add(pMem, lastMem), <%= 704 + 32*nPublic %>), q) - mstore(add(pMem, pBeta), b) + beta := mod(keccak256(mIn, <%= 704 + 32 * nPublic %>), q) + mstore(add(pMem, pBeta), beta) - // Challenges.gamma + // challenges.gamma mstore(add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) - // Challenges.alpha - mstore(add(pMem, <%=pLastMem%>), mload(add(pMem, pBeta))) - mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pMem, pGamma))) - mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, pZ))) - mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, add(pZ, 32)))) - a := mod(keccak256(add(pMem, lastMem), 128), q) - mstore(add(pMem, pAlpha), a) - - mstore(add(pMem, <%=pLastMem%>), mload(add(pMem, pAlpha))) - mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pProof, pT1))) - mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, add(pT1, 32)))) - mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, pT2))) - mstore(add(pMem, <%=pLastMem + 128%>), mload(add(pProof, add(pT2, 32)))) - mstore(add(pMem, <%=pLastMem + 160%>), mload(add(pProof, pT3))) - mstore(add(pMem, <%=pLastMem + 192%>), mload(add(pProof, add(pT3, 32)))) - a := mod(keccak256(add(pMem, lastMem), 224), q) - mstore( add(pMem, pXi), a) - - mstore(add(pMem, <%=pLastMem%>), a) - mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pProof, pEval_a))) - mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, pEval_b))) - mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, pEval_c))) - mstore(add(pMem, <%=pLastMem + 128%>), mload(add(pProof, pEval_s1))) - mstore(add(pMem, <%=pLastMem + 160%>), mload(add(pProof, pEval_s2))) - mstore(add(pMem, <%=pLastMem + 192%>), mload(add(pProof, pEval_zw))) - let v1 := mod(keccak256(add(pMem, lastMem), 224), q) + // challenges.alpha + mstore(mIn, mload(add(pMem, pBeta))) + mstore(add(mIn, 32), mload(add(pMem, pGamma))) + mstore(add(mIn, 64), calldataload(pZ)) + mstore(add(mIn, 96), calldataload(add(pZ, 32))) + + aux := mod(keccak256(mIn, 128), q) + mstore(add(pMem, pAlpha), aux) + mstore(add(pMem, pAlpha2), mulmod(aux, aux, q)) + + // challenges.xi + mstore(mIn, aux) + mstore(add(mIn, 32), calldataload(pT1)) + mstore(add(mIn, 64), calldataload(add(pT1, 32))) + mstore(add(mIn, 96), calldataload(pT2)) + mstore(add(mIn, 128), calldataload(add(pT2, 32))) + mstore(add(mIn, 160), calldataload(pT3)) + mstore(add(mIn, 192), calldataload(add(pT3, 32))) + + aux := mod(keccak256(mIn, 224), q) + mstore( add(pMem, pXi), aux) + + // challenges.v + mstore(mIn, aux) + mstore(add(mIn, 32), calldataload(pEval_a)) + mstore(add(mIn, 64), calldataload(pEval_b)) + mstore(add(mIn, 96), calldataload(pEval_c)) + mstore(add(mIn, 128), calldataload(pEval_s1)) + mstore(add(mIn, 160), calldataload(pEval_s2)) + mstore(add(mIn, 192), calldataload(pEval_zw)) + + let v1 := mod(keccak256(mIn, 224), q) mstore(add(pMem, pV1), v1) - // Compute betaxi - mstore( add(pMem, pBetaXi), mulmod(b, a, q)) + // challenges.beta * challenges.xi + mstore(add(pMem, pBetaXi), mulmod(beta, aux, q)) + + // challenges.xi^n <%for (let i=0; i - a:= mulmod(a, a, q) + aux:= mulmod(aux, aux, q) <%}%> - mstore( add(pMem, pXin), a) - a:= mod(add(sub(a, 1),q), q) - mstore( add(pMem, pZh), a) - mstore( add(pMem, pZhInv), a) // We will invert later together with lagrange pols + mstore(add(pMem, pXin), aux) + + // Zh + aux:= mod(add(sub(aux, 1), q), q) + mstore(add(pMem, pZh), aux) + mstore(add(pMem, pZhInv), aux) // We will invert later together with lagrange pols - a := mulmod(v1, v1, q) - mstore( add(pMem, pV2), a) - a := mulmod(a, v1, q) - mstore( add(pMem, pV3), a) - a := mulmod(a, v1, q) - mstore( add(pMem, pV4), a) - a := mulmod(a, v1, q) - mstore( add(pMem, pV5), a) - a := mulmod(a, v1, q) - mstore( add(pMem, pV6), a) - - mstore( add(pMem, pU), mod(keccak256(add(pProof, pWxi), 128), q)) + // challenges.v^2, challenges.v^3, challenges.v^4, challenges.v^5 + aux := mulmod(v1, v1, q) + mstore(add(pMem, pV2), aux) + aux := mulmod(aux, v1, q) + mstore(add(pMem, pV3), aux) + aux := mulmod(aux, v1, q) + mstore(add(pMem, pV4), aux) + aux := mulmod(aux, v1, q) + mstore(add(pMem, pV5), aux) + + // challenges.u + mstore(mIn, calldataload(pWxi)) + mstore(add(mIn, 32), calldataload(add(pWxi, 32))) + mstore(add(mIn, 64), calldataload(pWxiw)) + mstore(add(mIn, 96), calldataload(add(pWxiw, 32))) + + mstore(add(pMem, pU), mod(keccak256(mIn, 128), q)) } function calculateLagrange(pMem) { - let w := 1 <% for (let i=1; i<=Math.max(nPublic, 1); i++) { %> mstore( @@ -363,7 +386,7 @@ contract PlonkVerifier { pl, mulmod( mload(add(pMem, pEval_l<%=i+1%>)), - mload(add(pPub, <%=32+i*32%>)), + calldataload(add(pPub, <%=i*32%>)), q ) ), @@ -374,40 +397,36 @@ contract PlonkVerifier { <% } %> mstore(add(pMem, pPI), pl) - - } - function calculateR0(pProof, pMem) { - let alpha2 := mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q) + function calculateR0(pMem) { let e1 := mload(add(pMem, pPI)) - let e2 := mulmod(mload(add(pMem, pEval_l1)), alpha2, q) + let e2 := mulmod(mload(add(pMem, pEval_l1)), mload(add(pMem, pAlpha2)), q) let e3a := addmod( - mload(add(pProof, pEval_a)), - mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), + calldataload(pEval_a), + mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s1), q), q) e3a := addmod(e3a, mload(add(pMem, pGamma)), q) let e3b := addmod( - mload(add(pProof, pEval_b)), - mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), + calldataload(pEval_b), + mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s2), q), q) e3b := addmod(e3b, mload(add(pMem, pGamma)), q) let e3c := addmod( - mload(add(pProof, pEval_c)), + calldataload(pEval_c), mload(add(pMem, pGamma)), q) let e3 := mulmod(mulmod(e3a, e3b, q), e3c, q) - - e3 := mulmod(e3, mload(add(pProof, pEval_zw)), q) + e3 := mulmod(e3, calldataload(pEval_zw), q) e3 := mulmod(e3, mload(add(pMem, pAlpha)), q) - let r0 := mod(sub(e1, e2), q) - r0 := mod(sub(r0, e3), q) + let r0 := addmod(e1, mod(sub(q, e2), q), q) + r0 := addmod(r0, mod(sub(q, e3), q), q) mstore(add(pMem, pEval_r0) , r0) } @@ -415,6 +434,16 @@ contract PlonkVerifier { function g1_set(pR, pP) { mstore(pR, mload(pP)) mstore(add(pR, 32), mload(add(pP,32))) + } + + function g1_setC(pR, x, y) { + mstore(pR, x) + mstore(add(pR, 32), y) + } + + function g1_calldataSet(pR, pP) { + mstore(pR, calldataload(pP)) + mstore(add(pR, 32), calldataload(add(pP, 32))) } function g1_acc(pR, pP) { @@ -498,36 +527,38 @@ contract PlonkVerifier { } } - function calculateD(pProof, pMem) { - let p:= add(pMem, pD) + function g1_mulSet(pR, pP, s) { + g1_mulSetC(pR, mload(pP), mload(add(pP, 32)), s) + } + + function calculateD(pMem) { + let _pD:= add(pMem, pD) + let gamma := mload(add(pMem, pGamma)) let mIn := mload(0x40) + mstore(0x40, add(mIn, 256)) // d1, d2, d3 & d4 (4*64 bytes) - g1_mulSetC(p, Qmx, Qmy, mulmod(mload(add(pProof, pEval_a)), mload(add(pProof, pEval_b)), q)) - g1_mulAccC(p, Qlx, Qly, mload(add(pProof, pEval_a))) - g1_mulAccC(p, Qrx, Qry, mload(add(pProof, pEval_b))) - g1_mulAccC(p, Qox, Qoy, mload(add(pProof, pEval_c))) - g1_mulAccC(p, Qcx, Qcy, 1) + g1_setC(_pD, Qcx, Qcy) + g1_mulAccC(_pD, Qmx, Qmy, mulmod(calldataload(pEval_a), calldataload(pEval_b), q)) + g1_mulAccC(_pD, Qlx, Qly, calldataload(pEval_a)) + g1_mulAccC(_pD, Qrx, Qry, calldataload(pEval_b)) + g1_mulAccC(_pD, Qox, Qoy, calldataload(pEval_c)) + let betaxi := mload(add(pMem, pBetaXi)) let val1 := addmod( - addmod(mload(add(pProof, pEval_a)), mload(add(pMem, pBetaXi)), q), - mload(add(pMem, pGamma)), - q) + addmod(calldataload(pEval_a), betaxi, q), + gamma, q) let val2 := addmod( addmod( - mload(add(pProof, pEval_b)), - mulmod(mload(add(pMem, pBetaXi)), k1, q), - q), - mload(add(pMem, pGamma)), - q) + calldataload(pEval_b), + mulmod(betaxi, k1, q), + q), gamma, q) let val3 := addmod( addmod( - mload(add(pProof, pEval_c)), - mulmod(mload(add(pMem, pBetaXi)), k2, q), - q), - mload(add(pMem, pGamma)), - q) + calldataload(pEval_c), + mulmod(betaxi, k2, q), + q), gamma, q) let d2a := mulmod( mulmod(mulmod(val1, val2, q), val3, q), @@ -537,89 +568,96 @@ contract PlonkVerifier { let d2b := mulmod( mload(add(pMem, pEval_l1)), - mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q), + mload(add(pMem, pAlpha2)), q ) - // We'll use pF to save d2 - g1_mulAcc( - add(pMem, pF), - add(pProof, pZ), + // We'll use mIn to save d2 + g1_calldataSet(add(mIn, 192), pZ) + g1_mulSet( + mIn, + add(mIn, 192), addmod(addmod(d2a, d2b, q), mload(add(pMem, pU)), q)) - + + val1 := addmod( addmod( - mload(add(pProof, pEval_a)), - mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), - q), - mload(add(pMem, pGamma)), - q) + calldataload(pEval_a), + mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s1), q), + q), gamma, q) val2 := addmod( addmod( - mload(add(pProof, pEval_b)), - mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), - q), - mload(add(pMem, pGamma)), - q) + calldataload(pEval_b), + mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s2), q), + q), gamma, q) val3 := mulmod( mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pBeta)), q), - mload(add(pProof, pEval_zw)), q) + calldataload(pEval_zw), q) - // We'll use pE to save d3 - g1_mulAccC( - add(pMem, pE), + // We'll use mIn + 64 to save d3 + g1_mulSetC( + add(mIn, 64), S3x, S3y, mulmod(mulmod(val1, val2, q), val3, q)) + // We'll use mIn + 128 to save d4 + g1_calldataSet(add(mIn, 128), pT1) - // We'll use pTmp to save d4 - g1_set(add(pMem, pTmp), add(pProof, pT1)) - g1_mulAcc(add(pMem, pTmp), add(pProof, pT2), add(pMem, pXin)) - let xin2 := mulmod(add(pMem, pXin), add(pMem, pXin), q) - g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) - g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) + g1_mulAccC(add(mIn, 128), calldataload(pT2), calldataload(add(pT2, 32)), mload(add(pMem, pXin))) + let xin2 := mulmod(mload(add(pMem, pXin)), mload(add(pMem, pXin)), q) + g1_mulAccC(add(mIn, 128), calldataload(pT3), calldataload(add(pT3, 32)) , xin2) - g1_mulAcc(mIn, add(pMem, pTmp), add(pMem, pZh)) + g1_mulSetC(add(mIn, 128), mload(add(mIn, 128)), mload(add(mIn, 160)), mload(add(pMem, pZh))) - mstore(add(add(pMem, pE), 32), mod(sub(qf, mload(add(add(pMem, pE), 32))), qf)) - mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) - g1_acc(add(pMem, pD), add(pMem, pF)) - g1_acc(add(pMem, pD), add(pMem, pE)) - g1_acc(add(pMem, pD), add(pMem, mIn)) + mstore(add(add(mIn, 64), 32), mod(sub(qf, mload(add(add(mIn, 64), 32))), qf)) + mstore(add(mIn, 160), mod(sub(qf, mload(add(mIn, 160))), qf)) + g1_acc(_pD, mIn) + g1_acc(_pD, add(mIn, 64)) + g1_acc(_pD, add(mIn, 128)) } - function calculateF(pProof, pMem) { + function calculateF(pMem) { let p := add(pMem, pF) g1_set(p, add(pMem, pD)) - g1_mulAcc(p, add(pProof, pA), mload(add(pMem, pV1))) - g1_mulAcc(p, add(pProof, pB), mload(add(pMem, pV2))) - g1_mulAcc(p, add(pProof, pC), mload(add(pMem, pV3))) + g1_mulAccC(p, calldataload(pA), calldataload(add(pA, 32)), mload(add(pMem, pV1))) + g1_mulAccC(p, calldataload(pB), calldataload(add(pB, 32)), mload(add(pMem, pV2))) + g1_mulAccC(p, calldataload(pC), calldataload(add(pC, 32)), mload(add(pMem, pV3))) g1_mulAccC(p, S1x, S1y, mload(add(pMem, pV4))) - g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV5))) + g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV5))) } - function calculateE(pProof, pMem) { + function calculateE(pMem) { let s := mod(sub(q, mload(add(pMem, pEval_r0))), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_a)), mload(add(pMem, pV1)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_b)), mload(add(pMem, pV2)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_c)), mload(add(pMem, pV3)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s1)), mload(add(pMem, pV4)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s2)), mload(add(pMem, pV5)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_zw)), mload(add(pMem, pU)), q), q) - g1_mulAccC(add(pMem, pE), G1x, G1y, s) + + s := addmod(s, mulmod(calldataload(pEval_a), mload(add(pMem, pV1)), q), q) + s := addmod(s, mulmod(calldataload(pEval_b), mload(add(pMem, pV2)), q), q) + s := addmod(s, mulmod(calldataload(pEval_c), mload(add(pMem, pV3)), q), q) + s := addmod(s, mulmod(calldataload(pEval_s1), mload(add(pMem, pV4)), q), q) + s := addmod(s, mulmod(calldataload(pEval_s2), mload(add(pMem, pV5)), q), q) + s := addmod(s, mulmod(calldataload(pEval_zw), mload(add(pMem, pU)), q), q) + + g1_mulSetC(add(pMem, pE), G1x, G1y, s) } - function checkPairing(pProof, pMem) -> isOk { + function checkPairing(pMem) -> isOk { let mIn := mload(0x40) - + mstore(0x40, add(mIn, 576)) // [0..383] = pairing data, [384..447] = pWxi, [448..512] = pWxiw + + let _pWxi := add(mIn, 384) + let _pWxiw := add(mIn, 448) + let _aux := add(mIn, 512) + + g1_calldataSet(_pWxi, pWxi) + g1_calldataSet(_pWxiw, pWxiw) + // A1 - g1_mulAcc(mIn, add(pProof, pWxiw), add(pMem, pU)) - g1_acc(mIn, add(pProof, pWxi)) + g1_mulSet(mIn, _pWxiw, mload(add(pMem, pU))) + g1_acc(mIn, _pWxi) mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) // [X]_2 @@ -629,12 +667,14 @@ contract PlonkVerifier { mstore(add(mIn,160), X2y1) // B1 - g1_mulAcc(add(mIn, 192), add(pMem, pWxi), mload(add(pMem, pXi))) - let s := mulmod(mload(mload(add(pMem, pU))), mload(mload(add(pMem, pXi))), q) + g1_mulSet(add(mIn, 192), _pWxi, mload(add(pMem, pXi))) + + let s := mulmod(mload(add(pMem, pU)), mload(add(pMem, pXi)), q) s := mulmod(s, w1, q) - g1_mulAcc(add(mIn, 256), add(pProof, pWxiw), s) - g1_acc(add(mIn, 192), add(mIn, 256)) + g1_mulSet(_aux, _pWxiw, s) + g1_acc(add(mIn, 192), _aux) g1_acc(add(mIn, 192), add(pMem, pF)) + mstore(add(pMem, add(pE, 32)), mod(sub(qf, mload(add(pMem, add(pE, 32)))), qf)) g1_acc(add(mIn, 192), add(pMem, pE)) // [1]_2 @@ -645,45 +685,26 @@ contract PlonkVerifier { let success := staticcall(sub(gas(), 2000), 8, mIn, 384, mIn, 0x20) - isOk := and(success, mload(mIn)) + isOk := and(success, mload(mIn)) } let pMem := mload(0x40) mstore(0x40, add(pMem, lastMem)) - checkInput(proof) - calculateChallanges(proof, pMem, pubSignals) + checkInput() + calculateChallenges(pMem, _pubSignals) calculateLagrange(pMem) - calculatePI(pMem, pubSignals) - calculateR0(proof, pMem) - calculateD(proof, pMem) - calculateF(proof, pMem) - calculateE(proof, pMem) - let isValid := checkPairing(proof, pMem) + calculatePI(pMem, _pubSignals) + calculateR0(pMem) + calculateD(pMem) + calculateF(pMem) + calculateE(pMem) + let isValid := checkPairing(pMem) - sstore(0, mload(add(pMem, pGamma))) - } - - bytes32 value = debug(); - console.logBytes32(value); - - assembly { - mstore(0, true) - return(0,0x20) - } - } - - function debug() public view returns (bytes32 result) { - assembly { - result := sload(0) - } - } -} - - /*mstore(0x40, sub(pMem, lastMem)) + mstore(0x40, sub(pMem, lastMem)) mstore(0, isValid) return(0,0x20) } } -}/* +} From b6f96555746aeabdd92d7d430d59c0191808c7b1 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Wed, 17 May 2023 11:26:08 +0200 Subject: [PATCH 16/48] Added test with circuits using +1 inputs --- test/smart_contracts.test.js | 75 +++++++++++++++++++++++++----------- 1 file changed, 53 insertions(+), 22 deletions(-) diff --git a/test/smart_contracts.test.js b/test/smart_contracts.test.js index f856634a..81ea4ce4 100644 --- a/test/smart_contracts.test.js +++ b/test/smart_contracts.test.js @@ -33,11 +33,51 @@ describe("Smart contracts test suite", function () { await curve.terminate(); }); - it("Groth16 smart contract", async () => { + it("Groth16 smart contract 1 input", async () => { + expect(await groth16Verify( + path.join("test", "groth16", "circuit.r1cs"), + path.join("test", "groth16", "witness.wtns") + )).to.be.equal(true); + }); + + it("Groth16 smart contract 3 inputs", async () => { + expect(await groth16Verify( + path.join("test", "circuit2", "circuit.r1cs"), + path.join("test", "circuit2", "witness.wtns") + )).to.be.equal(true); + }); + + it("Plonk smart contract 1 input", async () => { + expect(await plonkVerify( + path.join("test", "plonk_circuit", "circuit.r1cs"), + path.join("test", "plonk_circuit", "witness.wtns") + )).to.be.equal(true); + }); + + it("Plonk smart contract 3 inputs", async () => { + expect(await plonkVerify( + path.join("test", "circuit2", "circuit.r1cs"), + path.join("test", "circuit2", "witness.wtns") + )).to.be.equal(true); + }); + + it("Fflonk smart contract 1 input", async () => { + expect(await fflonkVerify( + path.join("test", "fflonk", "circuit.r1cs"), + path.join("test", "fflonk", "witness.wtns") + )).to.be.equal(true); + }); + + it("Fflonk smart contract 3 inputs", async () => { + expect(await fflonkVerify( + path.join("test", "circuit2", "circuit.r1cs"), + path.join("test", "circuit2", "witness.wtns") + )).to.be.equal(true); + }); + + async function groth16Verify(r1csFilename, wtnsFilename) { const solidityVerifierFilename = path.join("test", "smart_contracts", "contracts", "groth16.sol"); - const r1csFilename = path.join("test", "groth16", "circuit.r1cs"); - const wtnsFilename = path.join("test", "groth16", "witness.wtns"); const zkeyFilename = { type: "mem" }; await snarkjs.zKey.newZKey(r1csFilename, ptauFilename, zkeyFilename); @@ -58,15 +98,12 @@ describe("Smart contracts test suite", function () { const VerifierFactory = await ethers.getContractFactory("Verifier"); verifierContract = await VerifierFactory.deploy(); - // Verifiy the proof in the smart contract - expect(await verifierContract.verifyProof(proofA, proofB, proofC, publicInputs)).to.be.equal(true); - }); + return await verifierContract.verifyProof(proofA, proofB, proofC, publicInputs); + } - it("plonk smart contract", async () => { + async function plonkVerify(r1csFilename, wtnsFilename) { const solidityVerifierFilename = path.join("test", "smart_contracts", "contracts", "plonk.sol"); - const r1csFilename = path.join("test", "plonk_circuit", "circuit.r1cs"); - const wtnsFilename = path.join("test", "plonk_circuit", "witness.wtns"); const zkeyFilename = { type: "mem" }; await snarkjs.plonk.setup(r1csFilename, ptauFilename, zkeyFilename); @@ -84,9 +121,7 @@ describe("Smart contracts test suite", function () { verifierContract = await VerifierFactory.deploy(); // Verifiy the proof in the smart contract - const arrayStrings = Array(25).fill("bytes32"); - const proof = ethers.utils.defaultAbiCoder.encode( - arrayStrings, + const proof = [ ethers.utils.hexZeroPad(ethers.BigNumber.from(proofJson.A[0]).toHexString(), 32), ethers.utils.hexZeroPad(ethers.BigNumber.from(proofJson.A[1]).toHexString(), 32), @@ -113,18 +148,14 @@ describe("Smart contracts test suite", function () { ethers.utils.hexZeroPad(ethers.BigNumber.from(proofJson.eval_s1).toHexString(), 32), ethers.utils.hexZeroPad(ethers.BigNumber.from(proofJson.eval_s2).toHexString(), 32), ethers.utils.hexZeroPad(ethers.BigNumber.from(proofJson.eval_zw).toHexString(), 32), - ethers.utils.hexZeroPad(ethers.BigNumber.from(proofJson.eval_r).toHexString(), 32), - ], - ); + ]; - expect(await verifierContract.verifyProof(proof, publicInputs)).to.be.equal(true); - }); + return await verifierContract.verifyProof(proof, publicInputs); + }; - it("fflonk smart contract", async () => { + async function fflonkVerify(r1csFilename, wtnsFilename) { const solidityVerifierFilename = path.join("test", "smart_contracts", "contracts", "fflonk.sol"); - const r1csFilename = path.join("test", "fflonk", "circuit.r1cs"); - const wtnsFilename = path.join("test", "fflonk", "witness.wtns"); const zkeyFilename = { type: "mem" }; await snarkjs.fflonk.fflonkSetupCmd(r1csFilename, ptauFilename, zkeyFilename); @@ -174,6 +205,6 @@ describe("Smart contracts test suite", function () { ], ); - expect(await verifierContract.verifyProof(proof, publicInputs)).to.be.equal(true); - }); + return await verifierContract.verifyProof(proof, publicInputs); + }; }); \ No newline at end of file From b22da8603d7aba3a3dd384284b6d2f903e08dd23 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Wed, 17 May 2023 11:28:19 +0200 Subject: [PATCH 17/48] Added cricuits tests with +1 inputs --- src/fflonk_prove.js | 2 +- test/circuit2/circuit.circom | 17 + test/circuit2/circuit.r1cs | Bin 0 -> 164180 bytes test/circuit2/circuit.zkey | Bin 0 -> 4160728 bytes test/circuit2/circuit_js/circuit.wasm | Bin 0 -> 38826 bytes test/circuit2/circuit_js/generate_witness.cjs | 20 ++ .../circuit_js/witness_calculator.cjs | 337 ++++++++++++++++++ test/circuit2/input.json | 5 + test/circuit2/witness.wtns | Bin 0 -> 32204 bytes 9 files changed, 380 insertions(+), 1 deletion(-) create mode 100644 test/circuit2/circuit.circom create mode 100644 test/circuit2/circuit.r1cs create mode 100644 test/circuit2/circuit.zkey create mode 100644 test/circuit2/circuit_js/circuit.wasm create mode 100644 test/circuit2/circuit_js/generate_witness.cjs create mode 100644 test/circuit2/circuit_js/witness_calculator.cjs create mode 100644 test/circuit2/input.json create mode 100644 test/circuit2/witness.wtns diff --git a/src/fflonk_prove.js b/src/fflonk_prove.js index 9d23673b..b4c35f2d 100644 --- a/src/fflonk_prove.js +++ b/src/fflonk_prove.js @@ -1209,7 +1209,7 @@ export default async function fflonkProve(zkeyFileName, witnessFileName, logger) for (let i = 0; i < size; i++) { toInverse["Li_" + (i + 1)] = Fr.mul(Fr.e(zkey.domainSize), Fr.sub(challenges.xi, w)); - w = Fr.mul(w, zkey.w); + w = Fr.mul(w, Fr.w[zkey.power]); } let mulAccumulator = Fr.one; diff --git a/test/circuit2/circuit.circom b/test/circuit2/circuit.circom new file mode 100644 index 00000000..98763ffe --- /dev/null +++ b/test/circuit2/circuit.circom @@ -0,0 +1,17 @@ +template Multiplier(n) { + signal input a; + signal input b; + signal input c; + signal output d; + + signal int[n]; + + int[0] <== a * a + b * 2 + c + 3; + for (var i = 1; i < n; i++) { + int[i] <== int[i-1] * int[i-1] + b + 4; + } + + d <== int[n-1]; +} + +component main {public [a, b, c]} = Multiplier(1000); 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fix(cli): Correctly return status codes instead of values (#369) --- build/cli.cjs | 63 ++++++++++++++++++++++++++++++++++++++++----------- cli.js | 63 ++++++++++++++++++++++++++++++++++++++++----------- 2 files changed, 100 insertions(+), 26 deletions(-) diff --git a/build/cli.cjs b/build/cli.cjs index 064fa977..51e9e4fe 100755 --- a/build/cli.cjs +++ b/build/cli.cjs @@ -12913,7 +12913,10 @@ async function powersOfTauNew(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return await newAccumulator(curve, power, ptauName, logger); + // Discard firstChallengeHash + await newAccumulator(curve, power, ptauName, logger); + + return 0; } async function powersOfTauExportChallenge(params, options) { @@ -12930,7 +12933,10 @@ async function powersOfTauExportChallenge(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return await exportChallenge(ptauName, challengeName, logger); + // Discard curChallengeHash + await exportChallenge(ptauName, challengeName, logger); + + return 0; } // powersoftau challenge contribute [response] @@ -12950,7 +12956,9 @@ async function powersOfTauChallengeContribute(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return await challengeContribute(curve, challengeName, responseName, options.entropy, logger); + await challengeContribute(curve, challengeName, responseName, options.entropy, logger); + + return 0; } @@ -12972,6 +12980,7 @@ async function powersOfTauImport(params, options) { const res = await importResponse(oldPtauName, response, newPtauName, options.name, importPoints, logger); + // TODO: This seems wrong if (res) return res; if (!doCheck) return; @@ -13006,7 +13015,10 @@ async function powersOfTauBeacon(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return await beacon$1(oldPtauName, newPtauName, options.name, beaconHashStr, numIterationsExp, logger); + // Discard hashResponse + await beacon$1(oldPtauName, newPtauName, options.name, beaconHashStr, numIterationsExp, logger); + + return 0; } async function powersOfTauContribute(params, options) { @@ -13018,7 +13030,10 @@ async function powersOfTauContribute(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return await contribute(oldPtauName, newPtauName, options.name, options.entropy, logger); + // Discard hashResponse + await contribute(oldPtauName, newPtauName, options.name, options.entropy, logger); + + return 0; } async function powersOfTauPreparePhase2(params, options) { @@ -13030,7 +13045,9 @@ async function powersOfTauPreparePhase2(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return await preparePhase2(oldPtauName, newPtauName, logger); + await preparePhase2(oldPtauName, newPtauName, logger); + + return 0; } async function powersOfTauConvert(params, options) { @@ -13042,7 +13059,9 @@ async function powersOfTauConvert(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return await convert(oldPtauName, newPtauName, logger); + await convert(oldPtauName, newPtauName, logger); + + return 0; } @@ -13058,7 +13077,10 @@ async function powersOfTauTruncate(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return await truncate(ptauName, template, logger); + // Discard `true` + await truncate(ptauName, template, logger); + + return 0; } // powersoftau export json ", @@ -13103,7 +13125,10 @@ async function zkeyNew(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return newZKey(r1csName, ptauName, zkeyName, logger); + // Discard csHash + await newZKey(r1csName, ptauName, zkeyName, logger); + + return 0; } // zkey export bellman [circuit_0000.zkey] [circuit.mpcparams] @@ -13121,8 +13146,9 @@ async function zkeyExportBellman(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return phase2exportMPCParams(zkeyName, mpcparamsName, logger); + await phase2exportMPCParams(zkeyName, mpcparamsName, logger); + return 0; } @@ -13225,7 +13251,10 @@ async function zkeyContribute(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return phase2contribute(zkeyOldName, zkeyNewName, options.name, options.entropy, logger); + // Discard contribuionHash + await phase2contribute(zkeyOldName, zkeyNewName, options.name, options.entropy, logger); + + return 0; } // zkey beacon @@ -13242,7 +13271,10 @@ async function zkeyBeacon(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return await beacon(zkeyOldName, zkeyNewName, options.name, beaconHashStr, numIterationsExp, logger); + // Discard contribuionHash + await beacon(zkeyOldName, zkeyNewName, options.name, beaconHashStr, numIterationsExp, logger); + + return 0; } @@ -13263,7 +13295,10 @@ async function zkeyBellmanContribute(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); - return bellmanContribute(curve, challengeName, responseName, options.entropy, logger); + // Discard contributionHash + await bellmanContribute(curve, challengeName, responseName, options.entropy, logger); + + return 0; } @@ -13293,6 +13328,7 @@ async function plonkSetup(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); + // TODO: Make plonk.setup reject instead of returning -1 or null return plonkSetup$1(r1csName, ptauName, zkeyName, logger); } @@ -13367,6 +13403,7 @@ async function fflonkSetup(params, options) { if (options.verbose) Logger__default["default"].setLogLevel("DEBUG"); + // TODO: Make fflonk.setup return valuable information or nothing at all return await fflonkSetup$1(r1csFilename, ptauFilename, zkeyFilename, logger); } diff --git a/cli.js b/cli.js index fa4e0962..4f9ce292 100755 --- a/cli.js +++ b/cli.js @@ -712,7 +712,10 @@ async function powersOfTauNew(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return await powersOfTau.newAccumulator(curve, power, ptauName, logger); + // Discard firstChallengeHash + await powersOfTau.newAccumulator(curve, power, ptauName, logger); + + return 0; } async function powersOfTauExportChallenge(params, options) { @@ -729,7 +732,10 @@ async function powersOfTauExportChallenge(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return await powersOfTau.exportChallenge(ptauName, challengeName, logger); + // Discard curChallengeHash + await powersOfTau.exportChallenge(ptauName, challengeName, logger); + + return 0; } // powersoftau challenge contribute [response] @@ -749,7 +755,9 @@ async function powersOfTauChallengeContribute(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return await powersOfTau.challengeContribute(curve, challengeName, responseName, options.entropy, logger); + await powersOfTau.challengeContribute(curve, challengeName, responseName, options.entropy, logger); + + return 0; } @@ -771,6 +779,7 @@ async function powersOfTauImport(params, options) { const res = await powersOfTau.importResponse(oldPtauName, response, newPtauName, options.name, importPoints, logger); + // TODO: This seems wrong if (res) return res; if (!doCheck) return; @@ -805,7 +814,10 @@ async function powersOfTauBeacon(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return await powersOfTau.beacon(oldPtauName, newPtauName, options.name, beaconHashStr, numIterationsExp, logger); + // Discard hashResponse + await powersOfTau.beacon(oldPtauName, newPtauName, options.name, beaconHashStr, numIterationsExp, logger); + + return 0; } async function powersOfTauContribute(params, options) { @@ -817,7 +829,10 @@ async function powersOfTauContribute(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return await powersOfTau.contribute(oldPtauName, newPtauName, options.name, options.entropy, logger); + // Discard hashResponse + await powersOfTau.contribute(oldPtauName, newPtauName, options.name, options.entropy, logger); + + return 0; } async function powersOfTauPreparePhase2(params, options) { @@ -829,7 +844,9 @@ async function powersOfTauPreparePhase2(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return await powersOfTau.preparePhase2(oldPtauName, newPtauName, logger); + await powersOfTau.preparePhase2(oldPtauName, newPtauName, logger); + + return 0; } async function powersOfTauConvert(params, options) { @@ -841,7 +858,9 @@ async function powersOfTauConvert(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return await powersOfTau.convert(oldPtauName, newPtauName, logger); + await powersOfTau.convert(oldPtauName, newPtauName, logger); + + return 0; } @@ -857,7 +876,10 @@ async function powersOfTauTruncate(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return await powersOfTau.truncate(ptauName, template, logger); + // Discard `true` + await powersOfTau.truncate(ptauName, template, logger); + + return 0; } // powersoftau export json ", @@ -902,7 +924,10 @@ async function zkeyNew(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return zkey.newZKey(r1csName, ptauName, zkeyName, logger); + // Discard csHash + await zkey.newZKey(r1csName, ptauName, zkeyName, logger); + + return 0; } // zkey export bellman [circuit_0000.zkey] [circuit.mpcparams] @@ -920,8 +945,9 @@ async function zkeyExportBellman(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return zkey.exportBellman(zkeyName, mpcparamsName, logger); + await zkey.exportBellman(zkeyName, mpcparamsName, logger); + return 0; } @@ -1024,7 +1050,10 @@ async function zkeyContribute(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return zkey.contribute(zkeyOldName, zkeyNewName, options.name, options.entropy, logger); + // Discard contribuionHash + await zkey.contribute(zkeyOldName, zkeyNewName, options.name, options.entropy, logger); + + return 0; } // zkey beacon @@ -1041,7 +1070,10 @@ async function zkeyBeacon(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return await zkey.beacon(zkeyOldName, zkeyNewName, options.name, beaconHashStr, numIterationsExp, logger); + // Discard contribuionHash + await zkey.beacon(zkeyOldName, zkeyNewName, options.name, beaconHashStr, numIterationsExp, logger); + + return 0; } @@ -1062,7 +1094,10 @@ async function zkeyBellmanContribute(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); - return zkey.bellmanContribute(curve, challengeName, responseName, options.entropy, logger); + // Discard contributionHash + await zkey.bellmanContribute(curve, challengeName, responseName, options.entropy, logger); + + return 0; } @@ -1092,6 +1127,7 @@ async function plonkSetup(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); + // TODO: Make plonk.setup reject instead of returning -1 or null return plonk.setup(r1csName, ptauName, zkeyName, logger); } @@ -1166,6 +1202,7 @@ async function fflonkSetup(params, options) { if (options.verbose) Logger.setLogLevel("DEBUG"); + // TODO: Make fflonk.setup return valuable information or nothing at all return await fflonk.setup(r1csFilename, ptauFilename, zkeyFilename, logger); } From e094f553c0cded760432f0ad9068a143dbed107f Mon Sep 17 00:00:00 2001 From: Blaine Bublitz Date: Thu, 18 May 2023 04:53:45 +0100 Subject: [PATCH 20/48] feat: Use WebCrypto if available (#364) chore: Increase eslint ecmaVersion to 2022 chore: Lint cleanup --- .eslintrc.cjs | 2 +- build/cli.cjs | 61 ++++++++++++++++++++++---------- build/main.cjs | 61 ++++++++++++++++++++++---------- build/snarkjs.js | 69 ++++++++++++++++++++++++------------- build/snarkjs.min.js | 4 +-- src/misc.js | 37 +++++++++++++++++--- src/plonk_prove.js | 1 - src/powersoftau_beacon.js | 2 +- src/powersoftau_utils.js | 4 +-- src/powersoftau_verify.js | 11 +++--- src/zkey_verify_frominit.js | 9 ++--- test/fullprocess.js | 3 +- 12 files changed, 176 insertions(+), 88 deletions(-) diff --git a/.eslintrc.cjs b/.eslintrc.cjs index fc5127cd..2a39d0d1 100644 --- a/.eslintrc.cjs +++ b/.eslintrc.cjs @@ -8,7 +8,7 @@ module.exports = { "mocha": true }, "parserOptions": { - "ecmaVersion": 2020, + "ecmaVersion": 2022, "sourceType": "module" }, "extends": "eslint:recommended", diff --git a/build/cli.cjs b/build/cli.cjs index 51e9e4fe..0a60da0c 100755 --- a/build/cli.cjs +++ b/build/cli.cjs @@ -279,26 +279,53 @@ function askEntropy() { } } +function getRandomBytes(n) { + let array = new Uint8Array(n); + if (typeof globalThis.crypto !== "undefined") { // Supported + globalThis.crypto.getRandomValues(array); + } else { // NodeJS + crypto__default["default"].randomFillSync(array); + } + return array; +} + +async function sha256digest(data) { + if (typeof globalThis.crypto !== "undefined" && typeof globalThis.crypto.subtle !== "undefined") { // Supported + const buffer = await globalThis.crypto.subtle.digest("SHA-256", data.buffer); + return new Uint8Array(buffer); + } else { // NodeJS + return crypto__default["default"].createHash("sha256").update(data).digest(); + } +} + +/** + * @param {Uint8Array} data + * @param {number} offset + */ +function readUInt32BE(data, offset) { + return new DataView(data.buffer).getUint32(offset, false); +} + async function getRandomRng(entropy) { // Generate a random Rng while (!entropy) { entropy = await askEntropy(); } const hasher = Blake2b__default["default"](64); - hasher.update(crypto__default["default"].randomBytes(64)); + hasher.update(getRandomBytes(64)); const enc = new TextEncoder(); // always utf-8 hasher.update(enc.encode(entropy)); - const hash = Buffer.from(hasher.digest()); + const hash = hasher.digest(); const seed = []; for (let i=0;i<8;i++) { - seed[i] = hash.readUInt32BE(i*4); + seed[i] = readUInt32BE(hash, i*4); } const rng = new ffjavascript.ChaCha(seed); return rng; } -function rngFromBeaconParams(beaconHash, numIterationsExp) { +async function rngFromBeaconParams(beaconHash, numIterationsExp) { let nIterationsInner; let nIterationsOuter; if (numIterationsExp<32) { @@ -312,7 +339,7 @@ function rngFromBeaconParams(beaconHash, numIterationsExp) { let curHash = beaconHash; for (let i=0; i0) { const firstBase = G.fromRprLEM(bases, 0); - const r = crypto__default["default"].randomBytes(4).readUInt32BE(0, true); + const r = readUInt32BE(getRandomBytes(4), 0); R1 = G.add(R1, G.timesScalar(lastBase, r)); R2 = G.add(R2, G.timesScalar(firstBase, r)); @@ -1940,7 +1965,7 @@ async function verify(tauFilename, logger) { const seed= new Array(8); for (let i=0; i<8; i++) { - seed[i] = crypto__default["default"].randomBytes(4).readUInt32BE(0, true); + seed[i] = readUInt32BE(getRandomBytes(4), 0); } for (let p=0; p<= power; p ++) { @@ -2262,7 +2287,7 @@ async function beacon$1(oldPtauFilename, newPTauFilename, name, beaconHashStr,n lastChallengeHash = calculateFirstChallengeHash(curve, power, logger); } - curContribution.key = keyFromBeacon(curve, lastChallengeHash, beaconHash, numIterationsExp); + curContribution.key = await keyFromBeacon(curve, lastChallengeHash, beaconHash, numIterationsExp); const responseHasher = new Blake2b__default["default"](64); responseHasher.update(lastChallengeHash); @@ -4564,7 +4589,7 @@ async function phase2verifyFromInit(initFileName, pTauFileName, zkeyFileName, lo } if (c.type == 1) { - const rng = rngFromBeaconParams(c.beaconHash, c.numIterationsExp); + const rng = await rngFromBeaconParams(c.beaconHash, c.numIterationsExp); const expected_prvKey = curve.Fr.fromRng(rng); const expected_g1_s = curve.G1.toAffine(curve.G1.fromRng(rng)); const expected_g1_sx = curve.G1.toAffine(curve.G1.timesFr(expected_g1_s, expected_prvKey)); @@ -4740,9 +4765,7 @@ async function phase2verifyFromInit(initFileName, pTauFileName, zkeyFileName, lo const bases1 = await fd1.read(n*sG); const bases2 = await fd2.read(n*sG); - const scalars = new Uint8Array(4*n); - crypto__default["default"].randomFillSync(scalars); - + const scalars = getRandomBytes(4*n); const r1 = await G.multiExpAffine(bases1, scalars); const r2 = await G.multiExpAffine(bases2, scalars); @@ -4773,7 +4796,7 @@ async function phase2verifyFromInit(initFileName, pTauFileName, zkeyFileName, lo const seed= new Array(8); for (let i=0; i<8; i++) { - seed[i] = crypto__default["default"].randomBytes(4).readUInt32BE(0, true); + seed[i] = readUInt32BE(getRandomBytes(4), 0); } const rng = new ffjavascript.ChaCha(seed); for (let i=0; i0) { const firstBase = G.fromRprLEM(bases, 0); - const r = crypto__default["default"].randomBytes(4).readUInt32BE(0, true); + const r = readUInt32BE(getRandomBytes(4), 0); R1 = G.add(R1, G.timesScalar(lastBase, r)); R2 = G.add(R2, G.timesScalar(firstBase, r)); @@ -2648,7 +2673,7 @@ async function verify(tauFilename, logger) { const seed= new Array(8); for (let i=0; i<8; i++) { - seed[i] = crypto__default["default"].randomBytes(4).readUInt32BE(0, true); + seed[i] = readUInt32BE(getRandomBytes(4), 0); } for (let p=0; p<= power; p ++) { @@ -2970,7 +2995,7 @@ async function beacon$1(oldPtauFilename, newPTauFilename, name, beaconHashStr,n lastChallengeHash = calculateFirstChallengeHash(curve, power, logger); } - curContribution.key = keyFromBeacon(curve, lastChallengeHash, beaconHash, numIterationsExp); + curContribution.key = await keyFromBeacon(curve, lastChallengeHash, beaconHash, numIterationsExp); const responseHasher = new Blake2b__default["default"](64); responseHasher.update(lastChallengeHash); @@ -5283,7 +5308,7 @@ async function phase2verifyFromInit(initFileName, pTauFileName, zkeyFileName, lo } if (c.type == 1) { - const rng = rngFromBeaconParams(c.beaconHash, c.numIterationsExp); + const rng = await rngFromBeaconParams(c.beaconHash, c.numIterationsExp); const expected_prvKey = curve.Fr.fromRng(rng); const expected_g1_s = curve.G1.toAffine(curve.G1.fromRng(rng)); const expected_g1_sx = curve.G1.toAffine(curve.G1.timesFr(expected_g1_s, expected_prvKey)); @@ -5459,9 +5484,7 @@ async function phase2verifyFromInit(initFileName, pTauFileName, zkeyFileName, lo const bases1 = await fd1.read(n*sG); const bases2 = await fd2.read(n*sG); - const scalars = new Uint8Array(4*n); - crypto__default["default"].randomFillSync(scalars); - + const scalars = getRandomBytes(4*n); const r1 = await G.multiExpAffine(bases1, scalars); const r2 = await G.multiExpAffine(bases2, scalars); @@ -5492,7 +5515,7 @@ async function phase2verifyFromInit(initFileName, pTauFileName, zkeyFileName, lo const seed= new Array(8); for (let i=0; i<8; i++) { - seed[i] = crypto__default["default"].randomBytes(4).readUInt32BE(0, true); + seed[i] = readUInt32BE(getRandomBytes(4), 0); } const rng = new ffjavascript.ChaCha(seed); for (let i=0; i0) { const firstBase = G.fromRprLEM(bases, 0); - const r = crypto.randomBytes(4).readUInt32BE(0, true); + const r = readUInt32BE(getRandomBytes(4), 0); R1 = G.add(R1, G.timesScalar(lastBase, r)); R2 = G.add(R2, G.timesScalar(firstBase, r)); @@ -21869,7 +21894,7 @@ var snarkjs = (function (exports) { const seed= new Array(8); for (let i=0; i<8; i++) { - seed[i] = crypto.randomBytes(4).readUInt32BE(0, true); + seed[i] = readUInt32BE(getRandomBytes(4), 0); } for (let p=0; p<= power; p ++) { @@ -22191,7 +22216,7 @@ var snarkjs = (function (exports) { lastChallengeHash = calculateFirstChallengeHash(curve, power, logger); } - curContribution.key = keyFromBeacon(curve, lastChallengeHash, beaconHash, numIterationsExp); + curContribution.key = await keyFromBeacon(curve, lastChallengeHash, beaconHash, numIterationsExp); const responseHasher = new blake2bWasm.exports(64); responseHasher.update(lastChallengeHash); @@ -24854,7 +24879,7 @@ var snarkjs = (function (exports) { } if (c.type == 1) { - const rng = rngFromBeaconParams(c.beaconHash, c.numIterationsExp); + const rng = await rngFromBeaconParams(c.beaconHash, c.numIterationsExp); const expected_prvKey = curve.Fr.fromRng(rng); const expected_g1_s = curve.G1.toAffine(curve.G1.fromRng(rng)); const expected_g1_sx = curve.G1.toAffine(curve.G1.timesFr(expected_g1_s, expected_prvKey)); @@ -25030,9 +25055,7 @@ var snarkjs = (function (exports) { const bases1 = await fd1.read(n*sG); const bases2 = await fd2.read(n*sG); - const scalars = new Uint8Array(4*n); - crypto.randomFillSync(scalars); - + const scalars = getRandomBytes(4*n); const r1 = await G.multiExpAffine(bases1, scalars); const r2 = await G.multiExpAffine(bases2, scalars); @@ -25063,7 +25086,7 @@ var snarkjs = (function (exports) { const seed= new Array(8); for (let i=0; i<8; i++) { - seed[i] = crypto.randomBytes(4).readUInt32BE(0, true); + seed[i] = readUInt32BE(getRandomBytes(4), 0); } const rng = new ChaCha(seed); for (let i=0; i>BigInt(e)}const c=r,d=s;function u(t){return(BigInt(t)&BigInt(1))==BigInt(1)}function g(t){let e=BigInt(t);const 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a=8*t.modules[e].n64,i=t.addFunction(e+"_batchInverse");i.addParam("pIn","i32"),i.addParam("inStep","i32"),i.addParam("n","i32"),i.addParam("pOut","i32"),i.addParam("outStep","i32"),i.addLocal("itAux","i32"),i.addLocal("itIn","i32"),i.addLocal("itOut","i32"),i.addLocal("i","i32");const 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W=function(t,e,a,i,o,n){void 0===n&&(n=ie?1:-1}function tt(t){return t*t}function et(t){return t%2n!==0n}function at(t){return t%2n===0n}function it(t){return t<0n}function ot(t){return t>0n}function nt(t){return it(t)?t.toString(2).length-1:t.toString(2).length}function lt(t){return t<0n?-t:t}function rt(t){return 1n===lt(t)}function st(t,e){for(var a,i,o,n=0n,l=1n,r=e,s=lt(t);0n!==s;)a=r/s,i=n,o=r,n=l,r=s,l=i-a*l,s=o-a*s;if(!rt(r))throw new Error(t.toString()+" and "+e.toString()+" are not co-prime");return-1===X(n,0n)&&(n+=e),it(t)?-n:n}function ct(t,e,a){if(0n===a)throw new Error("Cannot take modPow with modulus 0");var i=1n,o=t%a;for(it(e)&&(e*=-1n,o=st(o,a));ot(e);){if(0n===o)return 0n;et(e)&&(i=i*o%a),e/=2n,o=tt(o)%a}return i}function dt(t,e){return 0n!==e&&(!!rt(e)||(0===function(t,e){return(t=t>=0n?t:-t)===(e=e>=0n?e:-e)?0:t>e?1:-1}(e,2n)?at(t):t%e===0n))}function ut(t,e){for(var a,i,o,n=function(t){return 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e=t.addFunction(s+"_add");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const a=e.getCodeBuilder();e.addCode(a.if(a.call(c+"_add",a.getLocal("x"),a.getLocal("y"),a.getLocal("r")),a.drop(a.call(c+"_sub",a.getLocal("r"),a.i32_const(d),a.getLocal("r"))),a.if(a.call(c+"_gte",a.getLocal("r"),a.i32_const(d)),a.drop(a.call(c+"_sub",a.getLocal("r"),a.i32_const(d),a.getLocal("r"))))))}(),function(){const e=t.addFunction(s+"_sub");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const a=e.getCodeBuilder();e.addCode(a.if(a.call(c+"_sub",a.getLocal("x"),a.getLocal("y"),a.getLocal("r")),a.drop(a.call(c+"_add",a.getLocal("r"),a.i32_const(d),a.getLocal("r")))))}(),function(){const e=t.addFunction(s+"_neg");e.addParam("x","i32"),e.addParam("r","i32");const a=e.getCodeBuilder();e.addCode(a.call(s+"_sub",a.i32_const(f),a.getLocal("x"),a.getLocal("r")))}(),function(){const e=t.alloc(l*l*8),a=t.addFunction(s+"_mReduct");a.addParam("t","i32"),a.addParam("r","i32"),a.addLocal("np32","i64"),a.addLocal("c","i64"),a.addLocal("m","i64");const i=a.getCodeBuilder(),n=Number(0x100000000n-Lt(o,0x100000000n));a.addCode(i.setLocal("np32",i.i64_const(n)));for(let t=0;t=l&&e.addCode(a.i64_store32(a.getLocal("r"),4*(t-l),a.getLocal(h))),[h,_]=[_,h],e.addCode(a.setLocal(_,a.i64_shr_u(a.getLocal(h),a.i64_const(32))))}e.addCode(a.i64_store32(a.getLocal("r"),4*l-4,a.getLocal(h))),e.addCode(a.if(a.i32_wrap_i64(a.getLocal(_)),a.drop(a.call(c+"_sub",a.getLocal("r"),a.i32_const(d),a.getLocal("r"))),a.if(a.call(c+"_gte",a.getLocal("r"),a.i32_const(d)),a.drop(a.call(c+"_sub",a.getLocal("r"),a.i32_const(d),a.getLocal("r"))))))}(),function(){const e=t.addFunction(s+"_square");e.addParam("x","i32"),e.addParam("r","i32"),e.addLocal("c0","i64"),e.addLocal("c1","i64"),e.addLocal("c0_old","i64"),e.addLocal("c1_old","i64"),e.addLocal("np32","i64");for(let t=0;t>1&&i>1,t>>1)))),e.addCode(a.setLocal(h,a.i64_add(a.getLocal(h),a.i64_shr_u(a.getLocal(f),a.i64_const(32)))))),t>0&&(e.addCode(a.setLocal(f,a.i64_add(a.i64_and(a.getLocal(f),a.i64_const(4294967295)),a.i64_and(a.getLocal(_),a.i64_const(4294967295))))),e.addCode(a.setLocal(h,a.i64_add(a.i64_add(a.getLocal(h),a.i64_shr_u(a.getLocal(f),a.i64_const(32))),a.getLocal(p)))));for(let i=Math.max(1,t-l+1);i<=t&&i=l&&e.addCode(a.i64_store32(a.getLocal("r"),4*(t-l),a.getLocal(f))),e.addCode(a.setLocal(_,a.getLocal(h)),a.setLocal(p,a.i64_shr_u(a.getLocal(_),a.i64_const(32))))}e.addCode(a.i64_store32(a.getLocal("r"),4*l-4,a.getLocal(_))),e.addCode(a.if(a.i32_wrap_i64(a.getLocal(p)),a.drop(a.call(c+"_sub",a.getLocal("r"),a.i32_const(d),a.getLocal("r"))),a.if(a.call(c+"_gte",a.getLocal("r"),a.i32_const(d)),a.drop(a.call(c+"_sub",a.getLocal("r"),a.i32_const(d),a.getLocal("r"))))))}(),function(){const e=t.addFunction(s+"_squareOld");e.addParam("x","i32"),e.addParam("r","i32");const a=e.getCodeBuilder();e.addCode(a.call(s+"_mul",a.getLocal("x"),a.getLocal("x"),a.getLocal("r")))}(),function(){const e=t.addFunction(s+"_toMontgomery");e.addParam("x","i32"),e.addParam("r","i32");const a=e.getCodeBuilder();e.addCode(a.call(s+"_mul",a.getLocal("x"),a.i32_const(u),a.getLocal("r")))}(),function(){const e=t.alloc(2*r),a=t.addFunction(s+"_fromMontgomery");a.addParam("x","i32"),a.addParam("r","i32");const i=a.getCodeBuilder();a.addCode(i.call(c+"_copy",i.getLocal("x"),i.i32_const(e))),a.addCode(i.call(c+"_zero",i.i32_const(e+r))),a.addCode(i.call(s+"_mReduct",i.i32_const(e),i.getLocal("r")))}(),function(){const e=t.addFunction(s+"_isNegative");e.addParam("x","i32"),e.setReturnType("i32");const a=e.getCodeBuilder(),i=a.i32_const(t.alloc(r));e.addCode(a.call(s+"_fromMontgomery",a.getLocal("x"),i),a.call(c+"_gte",i,a.i32_const(w)))}(),function(){const e=t.addFunction(s+"_sign");e.addParam("x","i32"),e.setReturnType("i32");const a=e.getCodeBuilder(),i=a.i32_const(t.alloc(r));e.addCode(a.if(a.call(c+"_isZero",a.getLocal("x")),a.ret(a.i32_const(0))),a.call(s+"_fromMontgomery",a.getLocal("x"),i),a.if(a.call(c+"_gte",i,a.i32_const(w)),a.ret(a.i32_const(-1))),a.ret(a.i32_const(1)))}(),function(){const e=t.addFunction(s+"_inverse");e.addParam("x","i32"),e.addParam("r","i32");const a=e.getCodeBuilder();e.addCode(a.call(s+"_fromMontgomery",a.getLocal("x"),a.getLocal("r"))),e.addCode(a.call(c+"_inverseMod",a.getLocal("r"),a.i32_const(d),a.getLocal("r"))),e.addCode(a.call(s+"_toMontgomery",a.getLocal("r"),a.getLocal("r")))}(),function(){const e=t.addFunction(s+"_one");e.addParam("pr","i32");const a=e.getCodeBuilder();e.addCode(a.call(c+"_copy",a.i32_const(g),a.getLocal("pr")))}(),function(){const e=t.addFunction(s+"_load");e.addParam("scalar","i32"),e.addParam("scalarLen","i32"),e.addParam("r","i32"),e.addLocal("p","i32"),e.addLocal("l","i32"),e.addLocal("i","i32"),e.addLocal("j","i32");const a=e.getCodeBuilder(),i=a.i32_const(t.alloc(r)),o=t.alloc(r),n=a.i32_const(o);e.addCode(a.call(c+"_zero",a.getLocal("r")),a.setLocal("i",a.i32_const(r)),a.setLocal("p",a.getLocal("scalar")),a.block(a.loop(a.br_if(1,a.i32_gt_u(a.getLocal("i"),a.getLocal("scalarLen"))),a.if(a.i32_eq(a.getLocal("i"),a.i32_const(r)),a.call(s+"_one",i),a.call(s+"_mul",i,a.i32_const(u),i)),a.call(s+"_mul",a.getLocal("p"),i,n),a.call(s+"_add",a.getLocal("r"),n,a.getLocal("r")),a.setLocal("p",a.i32_add(a.getLocal("p"),a.i32_const(r))),a.setLocal("i",a.i32_add(a.getLocal("i"),a.i32_const(r))),a.br(0))),a.setLocal("l",a.i32_rem_u(a.getLocal("scalarLen"),a.i32_const(r))),a.if(a.i32_eqz(a.getLocal("l")),a.ret([])),a.call(c+"_zero",n),a.setLocal("j",a.i32_const(0)),a.block(a.loop(a.br_if(1,a.i32_eq(a.getLocal("j"),a.getLocal("l"))),a.i32_store8(a.getLocal("j"),o,a.i32_load8_u(a.getLocal("p"))),a.setLocal("p",a.i32_add(a.getLocal("p"),a.i32_const(1))),a.setLocal("j",a.i32_add(a.getLocal("j"),a.i32_const(1))),a.br(0))),a.if(a.i32_eq(a.getLocal("i"),a.i32_const(r)),a.call(s+"_one",i),a.call(s+"_mul",i,a.i32_const(u),i)),a.call(s+"_mul",n,i,n),a.call(s+"_add",a.getLocal("r"),n,a.getLocal("r")))}(),function(){const e=t.addFunction(s+"_timesScalar");e.addParam("x","i32"),e.addParam("scalar","i32"),e.addParam("scalarLen","i32"),e.addParam("r","i32");const a=e.getCodeBuilder(),i=a.i32_const(t.alloc(r));e.addCode(a.call(s+"_load",a.getLocal("scalar"),a.getLocal("scalarLen"),i),a.call(s+"_toMontgomery",i,i),a.call(s+"_mul",a.getLocal("x"),i,a.getLocal("r")))}(),_t(t,s),pt(t,s+"_batchToMontgomery",s+"_toMontgomery",r,r),pt(t,s+"_batchFromMontgomery",s+"_fromMontgomery",r,r),pt(t,s+"_batchNeg",s+"_neg",r,r),mt(t,s+"_batchAdd",s+"_add",r,r),mt(t,s+"_batchSub",s+"_sub",r,r),mt(t,s+"_batchMul",s+"_mul",r,r),t.exportFunction(s+"_add"),t.exportFunction(s+"_sub"),t.exportFunction(s+"_neg"),t.exportFunction(s+"_isNegative"),t.exportFunction(s+"_isOne"),t.exportFunction(s+"_sign"),t.exportFunction(s+"_mReduct"),t.exportFunction(s+"_mul"),t.exportFunction(s+"_square"),t.exportFunction(s+"_squareOld"),t.exportFunction(s+"_fromMontgomery"),t.exportFunction(s+"_toMontgomery"),t.exportFunction(s+"_inverse"),t.exportFunction(s+"_one"),t.exportFunction(s+"_load"),t.exportFunction(s+"_timesScalar"),ht(t,s+"_exp",r,s+"_mul",s+"_square",c+"_copy",s+"_one"),t.exportFunction(s+"_exp"),t.exportFunction(s+"_batchInverse"),At(o)&&(!function(){const e=t.addFunction(s+"_sqrt");e.addParam("n","i32"),e.addParam("r","i32"),e.addLocal("m","i32"),e.addLocal("i","i32"),e.addLocal("j","i32");const a=e.getCodeBuilder(),i=a.i32_const(g),o=a.i32_const(t.alloc(r)),n=a.i32_const(t.alloc(r)),l=a.i32_const(t.alloc(r)),c=a.i32_const(t.alloc(r)),d=a.i32_const(t.alloc(r));e.addCode(a.if(a.call(s+"_isZero",a.getLocal("n")),a.ret(a.call(s+"_zero",a.getLocal("r")))),a.setLocal("m",a.i32_const(b)),a.call(s+"_copy",a.i32_const(I),o),a.call(s+"_exp",a.getLocal("n"),a.i32_const(y),a.i32_const(r),n),a.call(s+"_exp",a.getLocal("n"),a.i32_const(x),a.i32_const(r),l),a.block(a.loop(a.br_if(1,a.call(s+"_eq",n,i)),a.call(s+"_square",n,c),a.setLocal("i",a.i32_const(1)),a.block(a.loop(a.br_if(1,a.call(s+"_eq",c,i)),a.call(s+"_square",c,c),a.setLocal("i",a.i32_add(a.getLocal("i"),a.i32_const(1))),a.br(0))),a.call(s+"_copy",o,d),a.setLocal("j",a.i32_sub(a.i32_sub(a.getLocal("m"),a.getLocal("i")),a.i32_const(1))),a.block(a.loop(a.br_if(1,a.i32_eqz(a.getLocal("j"))),a.call(s+"_square",d,d),a.setLocal("j",a.i32_sub(a.getLocal("j"),a.i32_const(1))),a.br(0))),a.setLocal("m",a.getLocal("i")),a.call(s+"_square",d,o),a.call(s+"_mul",n,o,n),a.call(s+"_mul",l,d,l),a.br(0))),a.if(a.call(s+"_isNegative",l),a.call(s+"_neg",l,a.getLocal("r")),a.call(s+"_copy",l,a.getLocal("r"))))}(),function(){const e=t.addFunction(s+"_isSquare");e.addParam("n","i32"),e.setReturnType("i32");const a=e.getCodeBuilder(),i=a.i32_const(g),o=a.i32_const(t.alloc(r));e.addCode(a.if(a.call(s+"_isZero",a.getLocal("n")),a.ret(a.i32_const(1))),a.call(s+"_exp",a.getLocal("n"),a.i32_const(p),a.i32_const(r),o),a.call(s+"_eq",o,i))}(),t.exportFunction(s+"_sqrt"),t.exportFunction(s+"_isSquare")),t.exportFunction(s+"_batchToMontgomery"),t.exportFunction(s+"_batchFromMontgomery"),s};const Ft=It,{bitLength:xt}=J;var Et=function(t,e,a,i,o){const n=BigInt(e),l=Math.floor((xt(n-1n)-1)/64)+1,r=8*l,s=a||"f1";if(t.modules[s])return s;t.modules[s]={n64:l};const c=o||"int",d=Ft(t,n,i,c),u=t.modules[d].pR2,g=t.modules[d].pq,f=t.modules[d].pePlusOne;return function(){const e=t.alloc(r),a=t.addFunction(s+"_mul");a.addParam("x","i32"),a.addParam("y","i32"),a.addParam("r","i32");const i=a.getCodeBuilder();a.addCode(i.call(d+"_mul",i.getLocal("x"),i.getLocal("y"),i.i32_const(e))),a.addCode(i.call(d+"_mul",i.i32_const(e),i.i32_const(u),i.getLocal("r")))}(),function(){const e=t.addFunction(s+"_square");e.addParam("x","i32"),e.addParam("r","i32");const a=e.getCodeBuilder();e.addCode(a.call(s+"_mul",a.getLocal("x"),a.getLocal("x"),a.getLocal("r")))}(),function(){const e=t.addFunction(s+"_inverse");e.addParam("x","i32"),e.addParam("r","i32");const a=e.getCodeBuilder();e.addCode(a.call(c+"_inverseMod",a.getLocal("x"),a.i32_const(g),a.getLocal("r")))}(),function(){const e=t.addFunction(s+"_isNegative");e.addParam("x","i32"),e.setReturnType("i32");const a=e.getCodeBuilder();e.addCode(a.call(c+"_gte",a.getLocal("x"),a.i32_const(f)))}(),t.exportFunction(d+"_add",s+"_add"),t.exportFunction(d+"_sub",s+"_sub"),t.exportFunction(d+"_neg",s+"_neg"),t.exportFunction(s+"_mul"),t.exportFunction(s+"_square"),t.exportFunction(s+"_inverse"),t.exportFunction(s+"_isNegative"),t.exportFunction(d+"_copy",s+"_copy"),t.exportFunction(d+"_zero",s+"_zero"),t.exportFunction(d+"_one",s+"_one"),t.exportFunction(d+"_isZero",s+"_isZero"),t.exportFunction(d+"_eq",s+"_eq"),s};const vt=H,Bt=Z,St=K;var Pt=function(t,e,a,i){if(t.modules[a])return a;const o=8*t.modules[i].n64,n=t.modules[i].q;return t.modules[a]={n64:2*t.modules[i].n64},function(){const e=t.addFunction(a+"_isZero");e.addParam("x","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.i32_and(n.call(i+"_isZero",l),n.call(i+"_isZero",r)))}(),function(){const e=t.addFunction(a+"_isOne");e.addParam("x","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.ret(n.i32_and(n.call(i+"_isOne",l),n.call(i+"_isZero",r))))}(),function(){const e=t.addFunction(a+"_zero");e.addParam("x","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.call(i+"_zero",l),n.call(i+"_zero",r))}(),function(){const e=t.addFunction(a+"_one");e.addParam("x","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.call(i+"_one",l),n.call(i+"_zero",r))}(),function(){const e=t.addFunction(a+"_copy");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_copy",l,s),n.call(i+"_copy",r,c))}(),function(){const n=t.addFunction(a+"_mul");n.addParam("x","i32"),n.addParam("y","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.getLocal("y"),d=l.i32_add(l.getLocal("y"),l.i32_const(o)),u=l.getLocal("r"),g=l.i32_add(l.getLocal("r"),l.i32_const(o)),f=l.i32_const(t.alloc(o)),h=l.i32_const(t.alloc(o)),_=l.i32_const(t.alloc(o)),p=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_mul",r,c,f),l.call(i+"_mul",s,d,h),l.call(i+"_add",r,s,_),l.call(i+"_add",c,d,p),l.call(i+"_mul",_,p,_),l.call(e,h,u),l.call(i+"_add",f,u,u),l.call(i+"_add",f,h,g),l.call(i+"_sub",_,g,g))}(),function(){const e=t.addFunction(a+"_mul1");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("y"),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_mul",l,s,c),n.call(i+"_mul",r,s,d))}(),function(){const n=t.addFunction(a+"_square");n.addParam("x","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.getLocal("r"),d=l.i32_add(l.getLocal("r"),l.i32_const(o)),u=l.i32_const(t.alloc(o)),g=l.i32_const(t.alloc(o)),f=l.i32_const(t.alloc(o)),h=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_mul",r,s,u),l.call(i+"_add",r,s,g),l.call(e,s,f),l.call(i+"_add",r,f,f),l.call(e,u,h),l.call(i+"_add",h,u,h),l.call(i+"_mul",g,f,c),l.call(i+"_sub",c,h,c),l.call(i+"_add",u,u,d))}(),function(){const e=t.addFunction(a+"_add");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("y"),c=n.i32_add(n.getLocal("y"),n.i32_const(o)),d=n.getLocal("r"),u=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_add",l,s,d),n.call(i+"_add",r,c,u))}(),function(){const e=t.addFunction(a+"_sub");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("y"),c=n.i32_add(n.getLocal("y"),n.i32_const(o)),d=n.getLocal("r"),u=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_sub",l,s,d),n.call(i+"_sub",r,c,u))}(),function(){const e=t.addFunction(a+"_neg");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_neg",l,s),n.call(i+"_neg",r,c))}(),function(){const e=t.addFunction(a+"_conjugate");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_copy",l,s),n.call(i+"_neg",r,c))}(),function(){const e=t.addFunction(a+"_toMontgomery");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_toMontgomery",l,s),n.call(i+"_toMontgomery",r,c))}(),function(){const e=t.addFunction(a+"_fromMontgomery");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_fromMontgomery",l,s),n.call(i+"_fromMontgomery",r,c))}(),function(){const e=t.addFunction(a+"_eq");e.addParam("x","i32"),e.addParam("y","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("y"),c=n.i32_add(n.getLocal("y"),n.i32_const(o));e.addCode(n.i32_and(n.call(i+"_eq",l,s),n.call(i+"_eq",r,c)))}(),function(){const n=t.addFunction(a+"_inverse");n.addParam("x","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.getLocal("r"),d=l.i32_add(l.getLocal("r"),l.i32_const(o)),u=l.i32_const(t.alloc(o)),g=l.i32_const(t.alloc(o)),f=l.i32_const(t.alloc(o)),h=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_square",r,u),l.call(i+"_square",s,g),l.call(e,g,f),l.call(i+"_sub",u,f,f),l.call(i+"_inverse",f,h),l.call(i+"_mul",r,h,c),l.call(i+"_mul",s,h,d),l.call(i+"_neg",d,d))}(),function(){const e=t.addFunction(a+"_timesScalar");e.addParam("x","i32"),e.addParam("scalar","i32"),e.addParam("scalarLen","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_timesScalar",l,n.getLocal("scalar"),n.getLocal("scalarLen"),s),n.call(i+"_timesScalar",r,n.getLocal("scalar"),n.getLocal("scalarLen"),c))}(),function(){const e=t.addFunction(a+"_sign");e.addParam("x","i32"),e.addLocal("s","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.setLocal("s",n.call(i+"_sign",r)),n.if(n.getLocal("s"),n.ret(n.getLocal("s"))),n.ret(n.call(i+"_sign",l)))}(),function(){const e=t.addFunction(a+"_isNegative");e.addParam("x","i32"),e.setReturnType("i32");const 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l=e.getCodeBuilder(),r=l.i32_const(t.alloc(St.bigInt2BytesLE((BigInt(n||0)-3n)/4n,o))),s=l.i32_const(t.alloc(St.bigInt2BytesLE((BigInt(n||0)-1n)/2n,o))),c=l.getLocal("a"),d=l.i32_const(t.alloc(2*o)),u=l.i32_const(t.alloc(2*o)),g=l.i32_const(t.alloc(2*o)),f=t.alloc(2*o),h=l.i32_const(f),_=l.i32_const(f),p=l.i32_const(f+o),m=l.i32_const(t.alloc(2*o)),w=l.i32_const(t.alloc(2*o));e.addCode(l.call(a+"_one",h),l.call(a+"_neg",h,h),l.call(a+"_exp",c,r,l.i32_const(o),d),l.call(a+"_square",d,u),l.call(a+"_mul",c,u,u),l.call(a+"_conjugate",u,g),l.call(a+"_mul",g,u,g),l.if(l.call(a+"_eq",g,h),l.unreachable()),l.call(a+"_mul",d,c,m),l.if(l.call(a+"_eq",u,h),[...l.call(i+"_zero",_),...l.call(i+"_one",p),...l.call(a+"_mul",h,m,l.getLocal("pr"))],[...l.call(a+"_one",w),...l.call(a+"_add",w,u,w),...l.call(a+"_exp",w,s,l.i32_const(o),w),...l.call(a+"_mul",w,m,l.getLocal("pr"))]))}(),function(){const e=t.addFunction(a+"_isSquare");e.addParam("a","i32"),e.setReturnType("i32");const i=e.getCodeBuilder(),l=i.i32_const(t.alloc(St.bigInt2BytesLE((BigInt(n||0)-3n)/4n,o))),r=i.getLocal("a"),s=i.i32_const(t.alloc(2*o)),c=i.i32_const(t.alloc(2*o)),d=i.i32_const(t.alloc(2*o)),u=t.alloc(2*o),g=i.i32_const(u);e.addCode(i.call(a+"_one",g),i.call(a+"_neg",g,g),i.call(a+"_exp",r,l,i.i32_const(o),s),i.call(a+"_square",s,c),i.call(a+"_mul",r,c,c),i.call(a+"_conjugate",c,d),i.call(a+"_mul",d,c,d),i.if(i.call(a+"_eq",d,g),i.ret(i.i32_const(0))),i.ret(i.i32_const(1)))}(),t.exportFunction(a+"_exp"),t.exportFunction(a+"_timesScalar"),t.exportFunction(a+"_batchInverse"),t.exportFunction(a+"_sqrt"),t.exportFunction(a+"_isSquare"),t.exportFunction(a+"_isNegative"),a};const Gt=H,zt=Z;var Ot=function(t,e,a,i){if(t.modules[a])return a;const o=8*t.modules[i].n64;return t.modules[a]={n64:3*t.modules[i].n64},function(){const e=t.addFunction(a+"_isZero");e.addParam("x","i32"),e.setReturnType("i32");const 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l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.i32_add(l.getLocal("x"),l.i32_const(2*o)),d=l.getLocal("y"),u=l.i32_add(l.getLocal("y"),l.i32_const(o)),g=l.i32_add(l.getLocal("y"),l.i32_const(2*o)),f=l.getLocal("r"),h=l.i32_add(l.getLocal("r"),l.i32_const(o)),_=l.i32_add(l.getLocal("r"),l.i32_const(2*o)),p=l.i32_const(t.alloc(o)),m=l.i32_const(t.alloc(o)),w=l.i32_const(t.alloc(o)),L=l.i32_const(t.alloc(o)),b=l.i32_const(t.alloc(o)),A=l.i32_const(t.alloc(o)),y=l.i32_const(t.alloc(o)),C=l.i32_const(t.alloc(o)),I=l.i32_const(t.alloc(o)),F=l.i32_const(t.alloc(o)),x=l.i32_const(t.alloc(o)),E=l.i32_const(t.alloc(o)),v=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_mul",r,d,p),l.call(i+"_mul",s,u,m),l.call(i+"_mul",c,g,w),l.call(i+"_add",r,s,L),l.call(i+"_add",d,u,b),l.call(i+"_add",r,c,A),l.call(i+"_add",d,g,y),l.call(i+"_add",s,c,C),l.call(i+"_add",u,g,I),l.call(i+"_add",p,m,F),l.call(i+"_add",p,w,x),l.call(i+"_add",m,w,E),l.call(i+"_mul",C,I,f),l.call(i+"_sub",f,E,f),l.call(e,f,f),l.call(i+"_add",p,f,f),l.call(i+"_mul",L,b,h),l.call(i+"_sub",h,F,h),l.call(e,w,v),l.call(i+"_add",h,v,h),l.call(i+"_mul",A,y,_),l.call(i+"_sub",_,x,_),l.call(i+"_add",_,m,_))}(),function(){const n=t.addFunction(a+"_square");n.addParam("x","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.i32_add(l.getLocal("x"),l.i32_const(2*o)),d=l.getLocal("r"),u=l.i32_add(l.getLocal("r"),l.i32_const(o)),g=l.i32_add(l.getLocal("r"),l.i32_const(2*o)),f=l.i32_const(t.alloc(o)),h=l.i32_const(t.alloc(o)),_=l.i32_const(t.alloc(o)),p=l.i32_const(t.alloc(o)),m=l.i32_const(t.alloc(o)),w=l.i32_const(t.alloc(o)),L=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_square",r,f),l.call(i+"_mul",r,s,h),l.call(i+"_add",h,h,_),l.call(i+"_sub",r,s,p),l.call(i+"_add",p,c,p),l.call(i+"_square",p,p),l.call(i+"_mul",s,c,m),l.call(i+"_add",m,m,w),l.call(i+"_square",c,L),l.call(e,w,d),l.call(i+"_add",f,d,d),l.call(e,L,u),l.call(i+"_add",_,u,u),l.call(i+"_add",f,L,g),l.call(i+"_sub",w,g,g),l.call(i+"_add",p,g,g),l.call(i+"_add",_,g,g))}(),function(){const e=t.addFunction(a+"_add");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("y"),d=n.i32_add(n.getLocal("y"),n.i32_const(o)),u=n.i32_add(n.getLocal("y"),n.i32_const(2*o)),g=n.getLocal("r"),f=n.i32_add(n.getLocal("r"),n.i32_const(o)),h=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_add",l,c,g),n.call(i+"_add",r,d,f),n.call(i+"_add",s,u,h))}(),function(){const e=t.addFunction(a+"_sub");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("y"),d=n.i32_add(n.getLocal("y"),n.i32_const(o)),u=n.i32_add(n.getLocal("y"),n.i32_const(2*o)),g=n.getLocal("r"),f=n.i32_add(n.getLocal("r"),n.i32_const(o)),h=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_sub",l,c,g),n.call(i+"_sub",r,d,f),n.call(i+"_sub",s,u,h))}(),function(){const e=t.addFunction(a+"_neg");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o)),u=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_neg",l,c),n.call(i+"_neg",r,d),n.call(i+"_neg",s,u))}(),function(){const e=t.addFunction(a+"_sign");e.addParam("x","i32"),e.addLocal("s","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o));e.addCode(n.setLocal("s",n.call(i+"_sign",s)),n.if(n.getLocal("s"),n.ret(n.getLocal("s"))),n.setLocal("s",n.call(i+"_sign",r)),n.if(n.getLocal("s"),n.ret(n.getLocal("s"))),n.ret(n.call(i+"_sign",l)))}(),function(){const e=t.addFunction(a+"_toMontgomery");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o)),u=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_toMontgomery",l,c),n.call(i+"_toMontgomery",r,d),n.call(i+"_toMontgomery",s,u))}(),function(){const e=t.addFunction(a+"_fromMontgomery");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o)),u=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_fromMontgomery",l,c),n.call(i+"_fromMontgomery",r,d),n.call(i+"_fromMontgomery",s,u))}(),function(){const e=t.addFunction(a+"_eq");e.addParam("x","i32"),e.addParam("y","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("y"),d=n.i32_add(n.getLocal("y"),n.i32_const(o)),u=n.i32_add(n.getLocal("y"),n.i32_const(2*o));e.addCode(n.i32_and(n.i32_and(n.call(i+"_eq",l,c),n.call(i+"_eq",r,d)),n.call(i+"_eq",s,u)))}(),function(){const n=t.addFunction(a+"_inverse");n.addParam("x","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.i32_add(l.getLocal("x"),l.i32_const(2*o)),d=l.getLocal("r"),u=l.i32_add(l.getLocal("r"),l.i32_const(o)),g=l.i32_add(l.getLocal("r"),l.i32_const(2*o)),f=l.i32_const(t.alloc(o)),h=l.i32_const(t.alloc(o)),_=l.i32_const(t.alloc(o)),p=l.i32_const(t.alloc(o)),m=l.i32_const(t.alloc(o)),w=l.i32_const(t.alloc(o)),L=l.i32_const(t.alloc(o)),b=l.i32_const(t.alloc(o)),A=l.i32_const(t.alloc(o)),y=l.i32_const(t.alloc(o)),C=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_square",r,f),l.call(i+"_square",s,h),l.call(i+"_square",c,_),l.call(i+"_mul",r,s,p),l.call(i+"_mul",r,c,m),l.call(i+"_mul",s,c,w),l.call(e,w,L),l.call(i+"_sub",f,L,L),l.call(e,_,b),l.call(i+"_sub",b,p,b),l.call(i+"_sub",h,m,A),l.call(i+"_mul",c,b,y),l.call(i+"_mul",s,A,C),l.call(i+"_add",y,C,y),l.call(e,y,y),l.call(i+"_mul",r,L,C),l.call(i+"_add",C,y,y),l.call(i+"_inverse",y,y),l.call(i+"_mul",y,L,d),l.call(i+"_mul",y,b,u),l.call(i+"_mul",y,A,g))}(),function(){const e=t.addFunction(a+"_timesScalar");e.addParam("x","i32"),e.addParam("scalar","i32"),e.addParam("scalarLen","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o)),u=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_timesScalar",l,n.getLocal("scalar"),n.getLocal("scalarLen"),c),n.call(i+"_timesScalar",r,n.getLocal("scalar"),n.getLocal("scalarLen"),d),n.call(i+"_timesScalar",s,n.getLocal("scalar"),n.getLocal("scalarLen"),u))}(),function(){const e=t.addFunction(a+"_isNegative");e.addParam("x","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o));e.addCode(n.if(n.call(i+"_isZero",s),n.if(n.call(i+"_isZero",r),n.ret(n.call(i+"_isNegative",l)),n.ret(n.call(i+"_isNegative",r)))),n.ret(n.call(i+"_isNegative",s)))}(),t.exportFunction(a+"_isZero"),t.exportFunction(a+"_isOne"),t.exportFunction(a+"_zero"),t.exportFunction(a+"_one"),t.exportFunction(a+"_copy"),t.exportFunction(a+"_mul"),t.exportFunction(a+"_square"),t.exportFunction(a+"_add"),t.exportFunction(a+"_sub"),t.exportFunction(a+"_neg"),t.exportFunction(a+"_sign"),t.exportFunction(a+"_fromMontgomery"),t.exportFunction(a+"_toMontgomery"),t.exportFunction(a+"_eq"),t.exportFunction(a+"_inverse"),zt(t,a),Gt(t,a+"_exp",3*o,a+"_mul",a+"_square",a+"_copy",a+"_one"),t.exportFunction(a+"_exp"),t.exportFunction(a+"_timesScalar"),t.exportFunction(a+"_batchInverse"),t.exportFunction(a+"_isNegative"),a};const Ut=function(t,e,a,i,o,n,l,r){const s=t.addFunction(e);s.addParam("base","i32"),s.addParam("scalar","i32"),s.addParam("scalarLength","i32"),s.addParam("r","i32"),s.addLocal("old0","i32"),s.addLocal("nbits","i32"),s.addLocal("i","i32"),s.addLocal("last","i32"),s.addLocal("cur","i32"),s.addLocal("carry","i32"),s.addLocal("p","i32");const c=s.getCodeBuilder(),d=c.i32_const(t.alloc(a));function u(t){return c.i32_and(c.i32_shr_u(c.i32_load(c.i32_add(c.getLocal("scalar"),c.i32_and(c.i32_shr_u(t,c.i32_const(3)),c.i32_const(4294967292)))),c.i32_and(t,c.i32_const(31))),c.i32_const(1))}function 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n=8*t.modules[e].n64;function l(){const i=t.addFunction(a);i.addParam("pBases","i32"),i.addParam("pScalars","i32"),i.addParam("scalarSize","i32"),i.addParam("n","i32"),i.addParam("pr","i32"),i.addLocal("chunkSize","i32"),i.addLocal("nChunks","i32"),i.addLocal("itScalar","i32"),i.addLocal("endScalar","i32"),i.addLocal("itBase","i32"),i.addLocal("itBit","i32"),i.addLocal("i","i32"),i.addLocal("j","i32"),i.addLocal("nTable","i32"),i.addLocal("pTable","i32"),i.addLocal("idx","i32"),i.addLocal("pIdxTable","i32");const o=i.getCodeBuilder(),l=o.i32_const(t.alloc(n)),r=t.alloc([17,17,17,17,17,17,17,17,17,17,16,16,15,14,13,13,12,11,10,9,8,7,7,6,5,4,3,2,1,1,1,1]);i.addCode(o.call(e+"_zero",o.getLocal("pr")),o.if(o.i32_eqz(o.getLocal("n")),o.ret([])),o.setLocal("chunkSize",o.i32_load8_u(o.i32_clz(o.getLocal("n")),r)),o.setLocal("nChunks",o.i32_add(o.i32_div_u(o.i32_sub(o.i32_shl(o.getLocal("scalarSize"),o.i32_const(3)),o.i32_const(1)),o.getLocal("chunkSize")),o.i32_const(1))),o.setLocal("itBit",o.i32_mul(o.i32_sub(o.getLocal("nChunks"),o.i32_const(1)),o.getLocal("chunkSize"))),o.block(o.loop(o.br_if(1,o.i32_lt_s(o.getLocal("itBit"),o.i32_const(0))),o.if(o.i32_eqz(o.call(e+"_isZero",o.getLocal("pr"))),[...o.setLocal("j",o.i32_const(0)),...o.block(o.loop(o.br_if(1,o.i32_eq(o.getLocal("j"),o.getLocal("chunkSize"))),o.call(e+"_double",o.getLocal("pr"),o.getLocal("pr")),o.setLocal("j",o.i32_add(o.getLocal("j"),o.i32_const(1))),o.br(0)))]),o.call(a+"_chunk",o.getLocal("pBases"),o.getLocal("pScalars"),o.getLocal("scalarSize"),o.getLocal("n"),o.getLocal("itBit"),o.getLocal("chunkSize"),l),o.call(e+"_add",o.getLocal("pr"),l,o.getLocal("pr")),o.setLocal("itBit",o.i32_sub(o.getLocal("itBit"),o.getLocal("chunkSize"))),o.br(0))))}!function(){const e=t.addFunction(a+"_getChunk");e.addParam("pScalar","i32"),e.addParam("scalarSize","i32"),e.addParam("startBit","i32"),e.addParam("chunkSize","i32"),e.addLocal("bitsToEnd","i32"),e.addLocal("mask","i32"),e.setReturnType("i32");const i=e.getCodeBuilder();e.addCode(i.setLocal("bitsToEnd",i.i32_sub(i.i32_mul(i.getLocal("scalarSize"),i.i32_const(8)),i.getLocal("startBit"))),i.if(i.i32_gt_s(i.getLocal("chunkSize"),i.getLocal("bitsToEnd")),i.setLocal("mask",i.i32_sub(i.i32_shl(i.i32_const(1),i.getLocal("bitsToEnd")),i.i32_const(1))),i.setLocal("mask",i.i32_sub(i.i32_shl(i.i32_const(1),i.getLocal("chunkSize")),i.i32_const(1)))),i.i32_and(i.i32_shr_u(i.i32_load(i.i32_add(i.getLocal("pScalar"),i.i32_shr_u(i.getLocal("startBit"),i.i32_const(3))),0,0),i.i32_and(i.getLocal("startBit"),i.i32_const(7))),i.getLocal("mask")))}(),function(){const i=t.addFunction(a+"_reduceTable");i.addParam("pTable","i32"),i.addParam("p","i32"),i.addLocal("half","i32"),i.addLocal("it1","i32"),i.addLocal("it2","i32"),i.addLocal("pAcc","i32");const o=i.getCodeBuilder();i.addCode(o.if(o.i32_eq(o.getLocal("p"),o.i32_const(1)),o.ret([])),o.setLocal("half",o.i32_shl(o.i32_const(1),o.i32_sub(o.getLocal("p"),o.i32_const(1)))),o.setLocal("it1",o.getLocal("pTable")),o.setLocal("it2",o.i32_add(o.getLocal("pTable"),o.i32_mul(o.getLocal("half"),o.i32_const(n)))),o.setLocal("pAcc",o.i32_sub(o.getLocal("it2"),o.i32_const(n))),o.block(o.loop(o.br_if(1,o.i32_eq(o.getLocal("it1"),o.getLocal("pAcc"))),o.call(e+"_add",o.getLocal("it1"),o.getLocal("it2"),o.getLocal("it1")),o.call(e+"_add",o.getLocal("pAcc"),o.getLocal("it2"),o.getLocal("pAcc")),o.setLocal("it1",o.i32_add(o.getLocal("it1"),o.i32_const(n))),o.setLocal("it2",o.i32_add(o.getLocal("it2"),o.i32_const(n))),o.br(0))),o.call(a+"_reduceTable",o.getLocal("pTable"),o.i32_sub(o.getLocal("p"),o.i32_const(1))),o.setLocal("p",o.i32_sub(o.getLocal("p"),o.i32_const(1))),o.block(o.loop(o.br_if(1,o.i32_eqz(o.getLocal("p"))),o.call(e+"_double",o.getLocal("pAcc"),o.getLocal("pAcc")),o.setLocal("p",o.i32_sub(o.getLocal("p"),o.i32_const(1))),o.br(0))),o.call(e+"_add",o.getLocal("pTable"),o.getLocal("pAcc"),o.getLocal("pTable")))}(),function(){const l=t.addFunction(a+"_chunk");l.addParam("pBases","i32"),l.addParam("pScalars","i32"),l.addParam("scalarSize","i32"),l.addParam("n","i32"),l.addParam("startBit","i32"),l.addParam("chunkSize","i32"),l.addParam("pr","i32"),l.addLocal("nChunks","i32"),l.addLocal("itScalar","i32"),l.addLocal("endScalar","i32"),l.addLocal("itBase","i32"),l.addLocal("i","i32"),l.addLocal("j","i32"),l.addLocal("nTable","i32"),l.addLocal("pTable","i32"),l.addLocal("idx","i32"),l.addLocal("pIdxTable","i32");const r=l.getCodeBuilder();l.addCode(r.if(r.i32_eqz(r.getLocal("n")),[...r.call(e+"_zero",r.getLocal("pr")),...r.ret([])]),r.setLocal("nTable",r.i32_shl(r.i32_const(1),r.getLocal("chunkSize"))),r.setLocal("pTable",r.i32_load(r.i32_const(0))),r.i32_store(r.i32_const(0),r.i32_add(r.getLocal("pTable"),r.i32_mul(r.getLocal("nTable"),r.i32_const(n)))),r.setLocal("j",r.i32_const(0)),r.block(r.loop(r.br_if(1,r.i32_eq(r.getLocal("j"),r.getLocal("nTable"))),r.call(e+"_zero",r.i32_add(r.getLocal("pTable"),r.i32_mul(r.getLocal("j"),r.i32_const(n)))),r.setLocal("j",r.i32_add(r.getLocal("j"),r.i32_const(1))),r.br(0))),r.setLocal("itBase",r.getLocal("pBases")),r.setLocal("itScalar",r.getLocal("pScalars")),r.setLocal("endScalar",r.i32_add(r.getLocal("pScalars"),r.i32_mul(r.getLocal("n"),r.getLocal("scalarSize")))),r.block(r.loop(r.br_if(1,r.i32_eq(r.getLocal("itScalar"),r.getLocal("endScalar"))),r.setLocal("idx",r.call(a+"_getChunk",r.getLocal("itScalar"),r.getLocal("scalarSize"),r.getLocal("startBit"),r.getLocal("chunkSize"))),r.if(r.getLocal("idx"),[...r.setLocal("pIdxTable",r.i32_add(r.getLocal("pTable"),r.i32_mul(r.i32_sub(r.getLocal("idx"),r.i32_const(1)),r.i32_const(n)))),...r.call(i,r.getLocal("pIdxTable"),r.getLocal("itBase"),r.getLocal("pIdxTable"))]),r.setLocal("itScalar",r.i32_add(r.getLocal("itScalar"),r.getLocal("scalarSize"))),r.setLocal("itBase",r.i32_add(r.getLocal("itBase"),r.i32_const(o))),r.br(0))),r.call(a+"_reduceTable",r.getLocal("pTable"),r.getLocal("chunkSize")),r.call(e+"_copy",r.getLocal("pTable"),r.getLocal("pr")),r.i32_store(r.i32_const(0),r.getLocal("pTable")))}(),l(),t.exportFunction(a),t.exportFunction(a+"_chunk")};var qt=function(t,e,a,i){const o=t.modules[a].n64,n=8*o;if(t.modules[e])return e;return t.modules[e]={n64:3*o},function(){const i=t.addFunction(e+"_isZeroAffine");i.addParam("p1","i32"),i.setReturnType("i32");const o=i.getCodeBuilder();i.addCode(o.i32_and(o.call(a+"_isZero",o.getLocal("p1")),o.call(a+"_isZero",o.i32_add(o.getLocal("p1"),o.i32_const(n)))))}(),function(){const i=t.addFunction(e+"_isZero");i.addParam("p1","i32"),i.setReturnType("i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_isZero",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))))}(),function(){const i=t.addFunction(e+"_zeroAffine");i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_zero",o.getLocal("pr"))),i.addCode(o.call(a+"_zero",o.i32_add(o.getLocal("pr"),o.i32_const(n))))}(),function(){const i=t.addFunction(e+"_zero");i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_zero",o.getLocal("pr"))),i.addCode(o.call(a+"_one",o.i32_add(o.getLocal("pr"),o.i32_const(n)))),i.addCode(o.call(a+"_zero",o.i32_add(o.getLocal("pr"),o.i32_const(2*n))))}(),function(){const a=t.addFunction(e+"_copyAffine");a.addParam("ps","i32"),a.addParam("pd","i32");const i=a.getCodeBuilder();for(let t=0;t<2*o;t++)a.addCode(i.i64_store(i.getLocal("pd"),8*t,i.i64_load(i.getLocal("ps"),8*t)))}(),function(){const a=t.addFunction(e+"_copy");a.addParam("ps","i32"),a.addParam("pd","i32");const i=a.getCodeBuilder();for(let t=0;t<3*o;t++)a.addCode(i.i64_store(i.getLocal("pd"),8*t,i.i64_load(i.getLocal("ps"),8*t)))}(),function(){const i=t.addFunction(e+"_toJacobian");i.addParam("p1","i32"),i.addParam("pr","i32");const 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o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n));i.addCode(o.setLocal("z1",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))));const s=o.getLocal("z1"),c=o.getLocal("p2"),d=o.i32_add(o.getLocal("p2"),o.i32_const(n)),u=o.i32_const(t.alloc(n)),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),o.ret(o.call(e+"_isZeroAffine",o.getLocal("p2")))),o.if(o.call(e+"_isZeroAffine",o.getLocal("p2")),o.ret(o.i32_const(0))),o.if(o.call(a+"_isOne",s),o.ret(o.call(e+"_eqAffine",o.getLocal("p1"),o.getLocal("p2")))),o.call(a+"_square",s,u),o.call(a+"_mul",c,u,g),o.call(a+"_mul",s,u,f),o.call(a+"_mul",d,f,h),o.if(o.call(a+"_eq",l,g),o.if(o.call(a+"_eq",r,h),o.ret(o.i32_const(1)))),o.ret(o.i32_const(0)))}(),function(){const i=t.addFunction(e+"_eq");i.addParam("p1","i32"),i.addParam("p2","i32"),i.setReturnType("i32"),i.addLocal("z1","i32"),i.addLocal("z2","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n));i.addCode(o.setLocal("z1",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))));const s=o.getLocal("z1"),c=o.getLocal("p2"),d=o.i32_add(o.getLocal("p2"),o.i32_const(n));i.addCode(o.setLocal("z2",o.i32_add(o.getLocal("p2"),o.i32_const(2*n))));const u=o.getLocal("z2"),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n)),m=o.i32_const(t.alloc(n)),w=o.i32_const(t.alloc(n)),L=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),o.ret(o.call(e+"_isZero",o.getLocal("p2")))),o.if(o.call(e+"_isZero",o.getLocal("p2")),o.ret(o.i32_const(0))),o.if(o.call(a+"_isOne",s),o.ret(o.call(e+"_eqMixed",o.getLocal("p2"),o.getLocal("p1")))),o.if(o.call(a+"_isOne",u),o.ret(o.call(e+"_eqMixed",o.getLocal("p1"),o.getLocal("p2")))),o.call(a+"_square",s,g),o.call(a+"_square",u,f),o.call(a+"_mul",l,f,h),o.call(a+"_mul",c,g,_),o.call(a+"_mul",s,g,p),o.call(a+"_mul",u,f,m),o.call(a+"_mul",r,m,w),o.call(a+"_mul",d,p,L),o.if(o.call(a+"_eq",h,_),o.if(o.call(a+"_eq",w,L),o.ret(o.i32_const(1)))),o.ret(o.i32_const(0)))}(),function(){const i=t.addFunction(e+"_doubleAffine");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.getLocal("pr"),c=o.i32_add(o.getLocal("pr"),o.i32_const(n)),d=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),u=o.i32_const(t.alloc(n)),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZeroAffine",o.getLocal("p1")),[...o.call(e+"_toJacobian",o.getLocal("p1"),o.getLocal("pr")),...o.ret([])]),o.call(a+"_square",l,u),o.call(a+"_square",r,g),o.call(a+"_square",g,f),o.call(a+"_add",l,g,h),o.call(a+"_square",h,h),o.call(a+"_sub",h,u,h),o.call(a+"_sub",h,f,h),o.call(a+"_add",h,h,h),o.call(a+"_add",u,u,_),o.call(a+"_add",_,u,_),o.call(a+"_add",r,r,d),o.call(a+"_square",_,s),o.call(a+"_sub",s,h,s),o.call(a+"_sub",s,h,s),o.call(a+"_add",f,f,p),o.call(a+"_add",p,p,p),o.call(a+"_add",p,p,p),o.call(a+"_sub",h,s,c),o.call(a+"_mul",c,_,c),o.call(a+"_sub",c,p,c))}(),function(){const i=t.addFunction(e+"_double");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.i32_add(o.getLocal("p1"),o.i32_const(2*n)),c=o.getLocal("pr"),d=o.i32_add(o.getLocal("pr"),o.i32_const(n)),u=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n)),m=o.i32_const(t.alloc(n)),w=o.i32_const(t.alloc(n)),L=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),[...o.call(e+"_copy",o.getLocal("p1"),o.getLocal("pr")),...o.ret([])]),o.if(o.call(a+"_isOne",s),[...o.ret(o.call(e+"_doubleAffine",o.getLocal("p1"),o.getLocal("pr"))),...o.ret([])]),o.call(a+"_square",l,g),o.call(a+"_square",r,f),o.call(a+"_square",f,h),o.call(a+"_add",l,f,_),o.call(a+"_square",_,_),o.call(a+"_sub",_,g,_),o.call(a+"_sub",_,h,_),o.call(a+"_add",_,_,_),o.call(a+"_add",g,g,p),o.call(a+"_add",p,g,p),o.call(a+"_square",p,m),o.call(a+"_mul",r,s,w),o.call(a+"_add",_,_,c),o.call(a+"_sub",m,c,c),o.call(a+"_add",h,h,L),o.call(a+"_add",L,L,L),o.call(a+"_add",L,L,L),o.call(a+"_sub",_,c,d),o.call(a+"_mul",d,p,d),o.call(a+"_sub",d,L,d),o.call(a+"_add",w,w,u))}(),function(){const i=t.addFunction(e+"_addAffine");i.addParam("p1","i32"),i.addParam("p2","i32"),i.addParam("pr","i32"),i.addLocal("z1","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n));i.addCode(o.setLocal("z1",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))));const s=o.getLocal("p2"),c=o.i32_add(o.getLocal("p2"),o.i32_const(n)),d=o.getLocal("pr"),u=o.i32_add(o.getLocal("pr"),o.i32_const(n)),g=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n)),m=o.i32_const(t.alloc(n)),w=o.i32_const(t.alloc(n)),L=o.i32_const(t.alloc(n)),b=o.i32_const(t.alloc(n)),A=o.i32_const(t.alloc(n)),y=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZeroAffine",o.getLocal("p1")),[...o.call(e+"_copyAffine",o.getLocal("p2"),o.getLocal("pr")),...o.call(a+"_one",o.i32_add(o.getLocal("pr"),o.i32_const(2*n))),...o.ret([])]),o.if(o.call(e+"_isZeroAffine",o.getLocal("p2")),[...o.call(e+"_copyAffine",o.getLocal("p1"),o.getLocal("pr")),...o.call(a+"_one",o.i32_add(o.getLocal("pr"),o.i32_const(2*n))),...o.ret([])]),o.if(o.call(a+"_eq",l,s),o.if(o.call(a+"_eq",r,c),[...o.call(e+"_doubleAffine",o.getLocal("p2"),o.getLocal("pr")),...o.ret([])])),o.call(a+"_sub",s,l,f),o.call(a+"_sub",c,r,_),o.call(a+"_square",f,h),o.call(a+"_add",h,h,p),o.call(a+"_add",p,p,p),o.call(a+"_mul",f,p,m),o.call(a+"_add",_,_,w),o.call(a+"_mul",l,p,b),o.call(a+"_square",w,L),o.call(a+"_add",b,b,A),o.call(a+"_sub",L,m,d),o.call(a+"_sub",d,A,d),o.call(a+"_mul",r,m,y),o.call(a+"_add",y,y,y),o.call(a+"_sub",b,d,u),o.call(a+"_mul",u,w,u),o.call(a+"_sub",u,y,u),o.call(a+"_add",f,f,g))}(),function(){const i=t.addFunction(e+"_addMixed");i.addParam("p1","i32"),i.addParam("p2","i32"),i.addParam("pr","i32"),i.addLocal("z1","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n));i.addCode(o.setLocal("z1",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))));const s=o.getLocal("z1"),c=o.getLocal("p2"),d=o.i32_add(o.getLocal("p2"),o.i32_const(n)),u=o.getLocal("pr"),g=o.i32_add(o.getLocal("pr"),o.i32_const(n)),f=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),h=o.i32_const(t.alloc(n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n)),m=o.i32_const(t.alloc(n)),w=o.i32_const(t.alloc(n)),L=o.i32_const(t.alloc(n)),b=o.i32_const(t.alloc(n)),A=o.i32_const(t.alloc(n)),y=o.i32_const(t.alloc(n)),C=o.i32_const(t.alloc(n)),I=o.i32_const(t.alloc(n)),F=o.i32_const(t.alloc(n)),x=o.i32_const(t.alloc(n)),E=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),[...o.call(e+"_copyAffine",o.getLocal("p2"),o.getLocal("pr")),...o.call(a+"_one",o.i32_add(o.getLocal("pr"),o.i32_const(2*n))),...o.ret([])]),o.if(o.call(e+"_isZeroAffine",o.getLocal("p2")),[...o.call(e+"_copy",o.getLocal("p1"),o.getLocal("pr")),...o.ret([])]),o.if(o.call(a+"_isOne",s),[...o.call(e+"_addAffine",l,c,u),...o.ret([])]),o.call(a+"_square",s,h),o.call(a+"_mul",c,h,_),o.call(a+"_mul",s,h,p),o.call(a+"_mul",d,p,m),o.if(o.call(a+"_eq",l,_),o.if(o.call(a+"_eq",r,m),[...o.call(e+"_doubleAffine",o.getLocal("p2"),o.getLocal("pr")),...o.ret([])])),o.call(a+"_sub",_,l,w),o.call(a+"_sub",m,r,b),o.call(a+"_square",w,L),o.call(a+"_add",L,L,A),o.call(a+"_add",A,A,A),o.call(a+"_mul",w,A,y),o.call(a+"_add",b,b,C),o.call(a+"_mul",l,A,F),o.call(a+"_square",C,I),o.call(a+"_add",F,F,x),o.call(a+"_sub",I,y,u),o.call(a+"_sub",u,x,u),o.call(a+"_mul",r,y,E),o.call(a+"_add",E,E,E),o.call(a+"_sub",F,u,g),o.call(a+"_mul",g,C,g),o.call(a+"_sub",g,E,g),o.call(a+"_add",s,w,f),o.call(a+"_square",f,f),o.call(a+"_sub",f,h,f),o.call(a+"_sub",f,L,f))}(),function(){const i=t.addFunction(e+"_add");i.addParam("p1","i32"),i.addParam("p2","i32"),i.addParam("pr","i32"),i.addLocal("z1","i32"),i.addLocal("z2","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n));i.addCode(o.setLocal("z1",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))));const s=o.getLocal("z1"),c=o.getLocal("p2"),d=o.i32_add(o.getLocal("p2"),o.i32_const(n));i.addCode(o.setLocal("z2",o.i32_add(o.getLocal("p2"),o.i32_const(2*n))));const u=o.getLocal("z2"),g=o.getLocal("pr"),f=o.i32_add(o.getLocal("pr"),o.i32_const(n)),h=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n)),m=o.i32_const(t.alloc(n)),w=o.i32_const(t.alloc(n)),L=o.i32_const(t.alloc(n)),b=o.i32_const(t.alloc(n)),A=o.i32_const(t.alloc(n)),y=o.i32_const(t.alloc(n)),C=o.i32_const(t.alloc(n)),I=o.i32_const(t.alloc(n)),F=o.i32_const(t.alloc(n)),x=o.i32_const(t.alloc(n)),E=o.i32_const(t.alloc(n)),v=o.i32_const(t.alloc(n)),B=o.i32_const(t.alloc(n)),S=o.i32_const(t.alloc(n)),P=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),[...o.call(e+"_copy",o.getLocal("p2"),o.getLocal("pr")),...o.ret([])]),o.if(o.call(e+"_isZero",o.getLocal("p2")),[...o.call(e+"_copy",o.getLocal("p1"),o.getLocal("pr")),...o.ret([])]),o.if(o.call(a+"_isOne",s),[...o.call(e+"_addMixed",c,l,g),...o.ret([])]),o.if(o.call(a+"_isOne",u),[...o.call(e+"_addMixed",l,c,g),...o.ret([])]),o.call(a+"_square",s,_),o.call(a+"_square",u,p),o.call(a+"_mul",l,p,m),o.call(a+"_mul",c,_,w),o.call(a+"_mul",s,_,L),o.call(a+"_mul",u,p,b),o.call(a+"_mul",r,b,A),o.call(a+"_mul",d,L,y),o.if(o.call(a+"_eq",m,w),o.if(o.call(a+"_eq",A,y),[...o.call(e+"_double",o.getLocal("p1"),o.getLocal("pr")),...o.ret([])])),o.call(a+"_sub",w,m,C),o.call(a+"_sub",y,A,I),o.call(a+"_add",C,C,F),o.call(a+"_square",F,F),o.call(a+"_mul",C,F,x),o.call(a+"_add",I,I,E),o.call(a+"_mul",m,F,B),o.call(a+"_square",E,v),o.call(a+"_add",B,B,S),o.call(a+"_sub",v,x,g),o.call(a+"_sub",g,S,g),o.call(a+"_mul",A,x,P),o.call(a+"_add",P,P,P),o.call(a+"_sub",B,g,f),o.call(a+"_mul",f,E,f),o.call(a+"_sub",f,P,f),o.call(a+"_add",s,u,h),o.call(a+"_square",h,h),o.call(a+"_sub",h,_,h),o.call(a+"_sub",h,p,h),o.call(a+"_mul",h,C,h))}(),function(){const i=t.addFunction(e+"_negAffine");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.getLocal("pr"),c=o.i32_add(o.getLocal("pr"),o.i32_const(n));i.addCode(o.call(a+"_copy",l,s),o.call(a+"_neg",r,c))}(),function(){const i=t.addFunction(e+"_neg");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.i32_add(o.getLocal("p1"),o.i32_const(2*n)),c=o.getLocal("pr"),d=o.i32_add(o.getLocal("pr"),o.i32_const(n)),u=o.i32_add(o.getLocal("pr"),o.i32_const(2*n));i.addCode(o.call(a+"_copy",l,c),o.call(a+"_neg",r,d),o.call(a+"_copy",s,u))}(),function(){const a=t.addFunction(e+"_subAffine");a.addParam("p1","i32"),a.addParam("p2","i32"),a.addParam("pr","i32");const i=a.getCodeBuilder(),o=i.i32_const(t.alloc(3*n));a.addCode(i.call(e+"_negAffine",i.getLocal("p2"),o),i.call(e+"_addAffine",i.getLocal("p1"),o,i.getLocal("pr")))}(),function(){const a=t.addFunction(e+"_subMixed");a.addParam("p1","i32"),a.addParam("p2","i32"),a.addParam("pr","i32");const i=a.getCodeBuilder(),o=i.i32_const(t.alloc(3*n));a.addCode(i.call(e+"_negAffine",i.getLocal("p2"),o),i.call(e+"_addMixed",i.getLocal("p1"),o,i.getLocal("pr")))}(),function(){const a=t.addFunction(e+"_sub");a.addParam("p1","i32"),a.addParam("p2","i32"),a.addParam("pr","i32");const i=a.getCodeBuilder(),o=i.i32_const(t.alloc(3*n));a.addCode(i.call(e+"_neg",i.getLocal("p2"),o),i.call(e+"_add",i.getLocal("p1"),o,i.getLocal("pr")))}(),function(){const i=t.addFunction(e+"_fromMontgomeryAffine");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_fromMontgomery",o.getLocal("p1"),o.getLocal("pr")));for(let t=1;t<2;t++)i.addCode(o.call(a+"_fromMontgomery",o.i32_add(o.getLocal("p1"),o.i32_const(t*n)),o.i32_add(o.getLocal("pr"),o.i32_const(t*n))))}(),function(){const i=t.addFunction(e+"_fromMontgomery");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_fromMontgomery",o.getLocal("p1"),o.getLocal("pr")));for(let t=1;t<3;t++)i.addCode(o.call(a+"_fromMontgomery",o.i32_add(o.getLocal("p1"),o.i32_const(t*n)),o.i32_add(o.getLocal("pr"),o.i32_const(t*n))))}(),function(){const i=t.addFunction(e+"_toMontgomeryAffine");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_toMontgomery",o.getLocal("p1"),o.getLocal("pr")));for(let t=1;t<2;t++)i.addCode(o.call(a+"_toMontgomery",o.i32_add(o.getLocal("p1"),o.i32_const(t*n)),o.i32_add(o.getLocal("pr"),o.i32_const(t*n))))}(),function(){const i=t.addFunction(e+"_toMontgomery");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_toMontgomery",o.getLocal("p1"),o.getLocal("pr")));for(let t=1;t<3;t++)i.addCode(o.call(a+"_toMontgomery",o.i32_add(o.getLocal("p1"),o.i32_const(t*n)),o.i32_add(o.getLocal("pr"),o.i32_const(t*n))))}(),function(){const i=t.addFunction(e+"_toAffine");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.i32_add(o.getLocal("p1"),o.i32_const(2*n)),c=o.getLocal("pr"),d=o.i32_add(o.getLocal("pr"),o.i32_const(n)),u=o.i32_const(t.alloc(n)),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),[...o.call(a+"_zero",c),...o.call(a+"_zero",d)],[...o.call(a+"_inverse",s,u),...o.call(a+"_square",u,g),...o.call(a+"_mul",u,g,f),...o.call(a+"_mul",l,g,c),...o.call(a+"_mul",r,f,d)]))}(),function(){const o=t.addFunction(e+"_inCurveAffine");o.addParam("pIn","i32"),o.setReturnType("i32");const l=o.getCodeBuilder(),r=l.getLocal("pIn"),s=l.i32_add(l.getLocal("pIn"),l.i32_const(n)),c=l.i32_const(t.alloc(n)),d=l.i32_const(t.alloc(n));o.addCode(l.call(a+"_square",s,c),l.call(a+"_square",r,d),l.call(a+"_mul",r,d,d),l.call(a+"_add",d,l.i32_const(i),d),l.ret(l.call(a+"_eq",c,d)))}(),function(){const a=t.addFunction(e+"_inCurve");a.addParam("pIn","i32"),a.setReturnType("i32");const i=a.getCodeBuilder(),o=i.i32_const(t.alloc(2*n));a.addCode(i.call(e+"_toAffine",i.getLocal("pIn"),o),i.ret(i.call(e+"_inCurveAffine",o)))}(),function(){const i=t.addFunction(e+"_batchToAffine");i.addParam("pIn","i32"),i.addParam("n","i32"),i.addParam("pOut","i32"),i.addLocal("pAux","i32"),i.addLocal("itIn","i32"),i.addLocal("itAux","i32"),i.addLocal("itOut","i32"),i.addLocal("i","i32");const o=i.getCodeBuilder(),l=o.i32_const(t.alloc(n));i.addCode(o.setLocal("pAux",o.i32_load(o.i32_const(0))),o.i32_store(o.i32_const(0),o.i32_add(o.getLocal("pAux"),o.i32_mul(o.getLocal("n"),o.i32_const(n)))),o.call(a+"_batchInverse",o.i32_add(o.getLocal("pIn"),o.i32_const(2*n)),o.i32_const(3*n),o.getLocal("n"),o.getLocal("pAux"),o.i32_const(n)),o.setLocal("itIn",o.getLocal("pIn")),o.setLocal("itAux",o.getLocal("pAux")),o.setLocal("itOut",o.getLocal("pOut")),o.setLocal("i",o.i32_const(0)),o.block(o.loop(o.br_if(1,o.i32_eq(o.getLocal("i"),o.getLocal("n"))),o.if(o.call(a+"_isZero",o.getLocal("itAux")),[...o.call(a+"_zero",o.getLocal("itOut")),...o.call(a+"_zero",o.i32_add(o.getLocal("itOut"),o.i32_const(n)))],[...o.call(a+"_mul",o.getLocal("itAux"),o.i32_add(o.getLocal("itIn"),o.i32_const(n)),l),...o.call(a+"_square",o.getLocal("itAux"),o.getLocal("itAux")),...o.call(a+"_mul",o.getLocal("itAux"),o.getLocal("itIn"),o.getLocal("itOut")),...o.call(a+"_mul",o.getLocal("itAux"),l,o.i32_add(o.getLocal("itOut"),o.i32_const(n)))]),o.setLocal("itIn",o.i32_add(o.getLocal("itIn"),o.i32_const(3*n))),o.setLocal("itOut",o.i32_add(o.getLocal("itOut"),o.i32_const(2*n))),o.setLocal("itAux",o.i32_add(o.getLocal("itAux"),o.i32_const(n))),o.setLocal("i",o.i32_add(o.getLocal("i"),o.i32_const(1))),o.br(0))),o.i32_store(o.i32_const(0),o.getLocal("pAux")))}(),function(){const i=t.addFunction(e+"_normalize");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.i32_add(o.getLocal("p1"),o.i32_const(2*n)),c=o.getLocal("pr"),d=o.i32_add(o.getLocal("pr"),o.i32_const(n)),u=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),o.call(e+"_zero",o.getLocal("pr")),[...o.call(a+"_inverse",s,g),...o.call(a+"_square",g,f),...o.call(a+"_mul",g,f,h),...o.call(a+"_mul",l,f,c),...o.call(a+"_mul",r,h,d),...o.call(a+"_one",u)]))}(),function(){const a=t.addFunction(e+"__reverseBytes");a.addParam("pIn","i32"),a.addParam("n","i32"),a.addParam("pOut","i32"),a.addLocal("itOut","i32"),a.addLocal("itIn","i32");const i=a.getCodeBuilder();a.addCode(i.setLocal("itOut",i.i32_sub(i.i32_add(i.getLocal("pOut"),i.getLocal("n")),i.i32_const(1))),i.setLocal("itIn",i.getLocal("pIn")),i.block(i.loop(i.br_if(1,i.i32_lt_s(i.getLocal("itOut"),i.getLocal("pOut"))),i.i32_store8(i.getLocal("itOut"),i.i32_load8_u(i.getLocal("itIn"))),i.setLocal("itOut",i.i32_sub(i.getLocal("itOut"),i.i32_const(1))),i.setLocal("itIn",i.i32_add(i.getLocal("itIn"),i.i32_const(1))),i.br(0))))}(),function(){const a=t.addFunction(e+"_LEMtoU");a.addParam("pIn","i32"),a.addParam("pOut","i32");const i=a.getCodeBuilder(),o=t.alloc(2*n),l=i.i32_const(o),r=i.i32_const(o),s=i.i32_const(o+n);a.addCode(i.if(i.call(e+"_isZeroAffine",i.getLocal("pIn")),[...i.call(e+"_zeroAffine",i.getLocal("pOut")),...i.i32_store8(i.getLocal("pOut"),i.i32_const(64)),...i.ret([])]),i.call(e+"_fromMontgomeryAffine",i.getLocal("pIn"),l),i.call(e+"__reverseBytes",r,i.i32_const(n),i.getLocal("pOut")),i.call(e+"__reverseBytes",s,i.i32_const(n),i.i32_add(i.getLocal("pOut"),i.i32_const(n))))}(),function(){const i=t.addFunction(e+"_LEMtoC");i.addParam("pIn","i32"),i.addParam("pOut","i32");const o=i.getCodeBuilder(),l=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("pIn")),[...o.call(a+"_zero",o.getLocal("pOut")),...o.i32_store8(o.getLocal("pOut"),o.i32_const(64)),...o.ret([])]),o.call(a+"_fromMontgomery",o.getLocal("pIn"),l),o.call(e+"__reverseBytes",l,o.i32_const(n),o.getLocal("pOut")),o.if(o.i32_eq(o.call(a+"_sign",o.i32_add(o.getLocal("pIn"),o.i32_const(n))),o.i32_const(-1)),o.i32_store8(o.getLocal("pOut"),o.i32_or(o.i32_load8_u(o.getLocal("pOut")),o.i32_const(128)))))}(),function(){const a=t.addFunction(e+"_UtoLEM");a.addParam("pIn","i32"),a.addParam("pOut","i32");const i=a.getCodeBuilder(),o=t.alloc(2*n),l=i.i32_const(o),r=i.i32_const(o),s=i.i32_const(o+n);a.addCode(i.if(i.i32_and(i.i32_load8_u(i.getLocal("pIn")),i.i32_const(64)),[...i.call(e+"_zeroAffine",i.getLocal("pOut")),...i.ret([])]),i.call(e+"__reverseBytes",i.getLocal("pIn"),i.i32_const(n),r),i.call(e+"__reverseBytes",i.i32_add(i.getLocal("pIn"),i.i32_const(n)),i.i32_const(n),s),i.call(e+"_toMontgomeryAffine",l,i.getLocal("pOut")))}(),function(){const o=t.addFunction(e+"_CtoLEM");o.addParam("pIn","i32"),o.addParam("pOut","i32"),o.addLocal("firstByte","i32"),o.addLocal("greatest","i32");const l=o.getCodeBuilder(),r=t.alloc(2*n),s=l.i32_const(r),c=l.i32_const(r+n);o.addCode(l.setLocal("firstByte",l.i32_load8_u(l.getLocal("pIn"))),l.if(l.i32_and(l.getLocal("firstByte"),l.i32_const(64)),[...l.call(e+"_zeroAffine",l.getLocal("pOut")),...l.ret([])]),l.setLocal("greatest",l.i32_and(l.getLocal("firstByte"),l.i32_const(128))),l.call(a+"_copy",l.getLocal("pIn"),c),l.i32_store8(c,l.i32_and(l.getLocal("firstByte"),l.i32_const(63))),l.call(e+"__reverseBytes",c,l.i32_const(n),s),l.call(a+"_toMontgomery",s,l.getLocal("pOut")),l.call(a+"_square",l.getLocal("pOut"),c),l.call(a+"_mul",l.getLocal("pOut"),c,c),l.call(a+"_add",c,l.i32_const(i),c),l.call(a+"_sqrt",c,c),l.call(a+"_neg",c,s),l.if(l.i32_eq(l.call(a+"_sign",c),l.i32_const(-1)),l.if(l.getLocal("greatest"),l.call(a+"_copy",c,l.i32_add(l.getLocal("pOut"),l.i32_const(n))),l.call(a+"_neg",c,l.i32_add(l.getLocal("pOut"),l.i32_const(n)))),l.if(l.getLocal("greatest"),l.call(a+"_neg",c,l.i32_add(l.getLocal("pOut"),l.i32_const(n))),l.call(a+"_copy",c,l.i32_add(l.getLocal("pOut"),l.i32_const(n))))))}(),Qt(t,e+"_batchLEMtoU",e+"_LEMtoU",2*n,2*n),Qt(t,e+"_batchLEMtoC",e+"_LEMtoC",2*n,n),Qt(t,e+"_batchUtoLEM",e+"_UtoLEM",2*n,2*n),Qt(t,e+"_batchCtoLEM",e+"_CtoLEM",n,2*n,!0),Qt(t,e+"_batchToJacobian",e+"_toJacobian",2*n,3*n,!0),Tt(t,e,e+"_multiexp",e+"_add",3*n),Tt(t,e,e+"_multiexpAffine",e+"_addMixed",2*n),Ut(t,e+"_timesScalar",3*n,e+"_add",e+"_double",e+"_sub",e+"_copy",e+"_zero"),Ut(t,e+"_timesScalarAffine",2*n,e+"_addMixed",e+"_double",e+"_subMixed",e+"_copyAffine",e+"_zero"),t.exportFunction(e+"_isZero"),t.exportFunction(e+"_isZeroAffine"),t.exportFunction(e+"_eq"),t.exportFunction(e+"_eqMixed"),t.exportFunction(e+"_eqAffine"),t.exportFunction(e+"_copy"),t.exportFunction(e+"_copyAffine"),t.exportFunction(e+"_zero"),t.exportFunction(e+"_zeroAffine"),t.exportFunction(e+"_double"),t.exportFunction(e+"_doubleAffine"),t.exportFunction(e+"_add"),t.exportFunction(e+"_addMixed"),t.exportFunction(e+"_addAffine"),t.exportFunction(e+"_neg"),t.exportFunction(e+"_negAffine"),t.exportFunction(e+"_sub"),t.exportFunction(e+"_subMixed"),t.exportFunction(e+"_subAffine"),t.exportFunction(e+"_fromMontgomery"),t.exportFunction(e+"_fromMontgomeryAffine"),t.exportFunction(e+"_toMontgomery"),t.exportFunction(e+"_toMontgomeryAffine"),t.exportFunction(e+"_timesScalar"),t.exportFunction(e+"_timesScalarAffine"),t.exportFunction(e+"_normalize"),t.exportFunction(e+"_LEMtoU"),t.exportFunction(e+"_LEMtoC"),t.exportFunction(e+"_UtoLEM"),t.exportFunction(e+"_CtoLEM"),t.exportFunction(e+"_batchLEMtoU"),t.exportFunction(e+"_batchLEMtoC"),t.exportFunction(e+"_batchUtoLEM"),t.exportFunction(e+"_batchCtoLEM"),t.exportFunction(e+"_toAffine"),t.exportFunction(e+"_toJacobian"),t.exportFunction(e+"_batchToAffine"),t.exportFunction(e+"_batchToJacobian"),t.exportFunction(e+"_inCurve"),t.exportFunction(e+"_inCurveAffine"),e};const{isOdd:Mt,modInv:kt,modPow:Rt}=J,Dt=K;var Nt=function(t,e,a,i,o){const n=8*t.modules[i].n64,l=8*t.modules[a].n64,r=t.modules[i].q;let s=r-1n,c=0;for(;!Mt(s);)c++,s>>=1n;let d=2n;for(;1n===Rt(d,r>>1n,r);)d+=1n;const u=new Array(c+1);u[c]=Rt(d,s,r);let g=c-1;for(;g>=0;)u[g]=Rt(u[g+1],2n,r),g--;const f=[],h=(1n<>a);return e}const F=Array(256);for(let t=0;t<256;t++)F[t]=I(t);const x=t.alloc(F);function E(){const a=t.addFunction(e+"_fft");a.addParam("px","i32"),a.addParam("n","i32"),a.addLocal("bits","i32");const o=a.getCodeBuilder(),l=o.i32_const(t.alloc(n));a.addCode(o.setLocal("bits",o.call(e+"__log2",o.getLocal("n"))),o.call(i+"_one",l),o.call(e+"_rawfft",o.getLocal("px"),o.getLocal("bits"),o.i32_const(0),l))}!function(){const a=t.addFunction(e+"__rev");a.addParam("x","i32"),a.addParam("bits","i32"),a.setReturnType("i32");const i=a.getCodeBuilder();a.addCode(i.i32_rotl(i.i32_add(i.i32_add(i.i32_shl(i.i32_load8_u(i.i32_and(i.getLocal("x"),i.i32_const(255)),x,0),i.i32_const(24)),i.i32_shl(i.i32_load8_u(i.i32_and(i.i32_shr_u(i.getLocal("x"),i.i32_const(8)),i.i32_const(255)),x,0),i.i32_const(16))),i.i32_add(i.i32_shl(i.i32_load8_u(i.i32_and(i.i32_shr_u(i.getLocal("x"),i.i32_const(16)),i.i32_const(255)),x,0),i.i32_const(8)),i.i32_load8_u(i.i32_and(i.i32_shr_u(i.getLocal("x"),i.i32_const(24)),i.i32_const(255)),x,0))),i.getLocal("bits")))}(),function(){const i=t.addFunction(e+"__reversePermutation");i.addParam("px","i32"),i.addParam("bits","i32"),i.addLocal("n","i32"),i.addLocal("i","i32"),i.addLocal("ri","i32"),i.addLocal("idx1","i32"),i.addLocal("idx2","i32");const o=i.getCodeBuilder(),n=o.i32_const(t.alloc(l));i.addCode(o.setLocal("n",o.i32_shl(o.i32_const(1),o.getLocal("bits"))),o.setLocal("i",o.i32_const(0)),o.block(o.loop(o.br_if(1,o.i32_eq(o.getLocal("i"),o.getLocal("n"))),o.setLocal("idx1",o.i32_add(o.getLocal("px"),o.i32_mul(o.getLocal("i"),o.i32_const(l)))),o.setLocal("ri",o.call(e+"__rev",o.getLocal("i"),o.getLocal("bits"))),o.setLocal("idx2",o.i32_add(o.getLocal("px"),o.i32_mul(o.getLocal("ri"),o.i32_const(l)))),o.if(o.i32_lt_u(o.getLocal("i"),o.getLocal("ri")),[...o.call(a+"_copy",o.getLocal("idx1"),n),...o.call(a+"_copy",o.getLocal("idx2"),o.getLocal("idx1")),...o.call(a+"_copy",n,o.getLocal("idx2"))]),o.setLocal("i",o.i32_add(o.getLocal("i"),o.i32_const(1))),o.br(0))))}(),function(){const n=t.addFunction(e+"__fftFinal");n.addParam("px","i32"),n.addParam("bits","i32"),n.addParam("reverse","i32"),n.addParam("mulFactor","i32"),n.addLocal("n","i32"),n.addLocal("ndiv2","i32"),n.addLocal("pInv2","i32"),n.addLocal("i","i32"),n.addLocal("mask","i32"),n.addLocal("idx1","i32"),n.addLocal("idx2","i32");const r=n.getCodeBuilder(),s=r.i32_const(t.alloc(l));n.addCode(r.if(r.i32_and(r.i32_eqz(r.getLocal("reverse")),r.call(i+"_isOne",r.getLocal("mulFactor"))),r.ret([])),r.setLocal("n",r.i32_shl(r.i32_const(1),r.getLocal("bits"))),r.setLocal("mask",r.i32_sub(r.getLocal("n"),r.i32_const(1))),r.setLocal("i",r.i32_const(1)),r.setLocal("ndiv2",r.i32_shr_u(r.getLocal("n"),r.i32_const(1))),r.block(r.loop(r.br_if(1,r.i32_ge_u(r.getLocal("i"),r.getLocal("ndiv2"))),r.setLocal("idx1",r.i32_add(r.getLocal("px"),r.i32_mul(r.getLocal("i"),r.i32_const(l)))),r.setLocal("idx2",r.i32_add(r.getLocal("px"),r.i32_mul(r.i32_sub(r.getLocal("n"),r.getLocal("i")),r.i32_const(l)))),r.if(r.getLocal("reverse"),r.if(r.call(i+"_isOne",r.getLocal("mulFactor")),[...r.call(a+"_copy",r.getLocal("idx1"),s),...r.call(a+"_copy",r.getLocal("idx2"),r.getLocal("idx1")),...r.call(a+"_copy",s,r.getLocal("idx2"))],[...r.call(a+"_copy",r.getLocal("idx1"),s),...r.call(o,r.getLocal("idx2"),r.getLocal("mulFactor"),r.getLocal("idx1")),...r.call(o,s,r.getLocal("mulFactor"),r.getLocal("idx2"))]),r.if(r.call(i+"_isOne",r.getLocal("mulFactor")),[],[...r.call(o,r.getLocal("idx1"),r.getLocal("mulFactor"),r.getLocal("idx1")),...r.call(o,r.getLocal("idx2"),r.getLocal("mulFactor"),r.getLocal("idx2"))])),r.setLocal("i",r.i32_add(r.getLocal("i"),r.i32_const(1))),r.br(0))),r.if(r.call(i+"_isOne",r.getLocal("mulFactor")),[],[...r.call(o,r.getLocal("px"),r.getLocal("mulFactor"),r.getLocal("px")),...r.setLocal("idx2",r.i32_add(r.getLocal("px"),r.i32_mul(r.getLocal("ndiv2"),r.i32_const(l)))),...r.call(o,r.getLocal("idx2"),r.getLocal("mulFactor"),r.getLocal("idx2"))]))}(),function(){const r=t.addFunction(e+"_rawfft");r.addParam("px","i32"),r.addParam("bits","i32"),r.addParam("reverse","i32"),r.addParam("mulFactor","i32"),r.addLocal("s","i32"),r.addLocal("k","i32"),r.addLocal("j","i32"),r.addLocal("m","i32"),r.addLocal("mdiv2","i32"),r.addLocal("n","i32"),r.addLocal("pwm","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l)),u=s.i32_const(t.alloc(l));r.addCode(s.call(e+"__reversePermutation",s.getLocal("px"),s.getLocal("bits")),s.setLocal("n",s.i32_shl(s.i32_const(1),s.getLocal("bits"))),s.setLocal("s",s.i32_const(1)),s.block(s.loop(s.br_if(1,s.i32_gt_u(s.getLocal("s"),s.getLocal("bits"))),s.setLocal("m",s.i32_shl(s.i32_const(1),s.getLocal("s"))),s.setLocal("pwm",s.i32_add(s.i32_const(_),s.i32_mul(s.getLocal("s"),s.i32_const(n)))),s.setLocal("k",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_ge_u(s.getLocal("k"),s.getLocal("n"))),s.call(i+"_one",c),s.setLocal("mdiv2",s.i32_shr_u(s.getLocal("m"),s.i32_const(1))),s.setLocal("j",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_ge_u(s.getLocal("j"),s.getLocal("mdiv2"))),s.setLocal("idx1",s.i32_add(s.getLocal("px"),s.i32_mul(s.i32_add(s.getLocal("k"),s.getLocal("j")),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("idx1"),s.i32_mul(s.getLocal("mdiv2"),s.i32_const(l)))),s.call(o,s.getLocal("idx2"),c,d),s.call(a+"_copy",s.getLocal("idx1"),u),s.call(a+"_add",u,d,s.getLocal("idx1")),s.call(a+"_sub",u,d,s.getLocal("idx2")),s.call(i+"_mul",c,s.getLocal("pwm"),c),s.setLocal("j",s.i32_add(s.getLocal("j"),s.i32_const(1))),s.br(0))),s.setLocal("k",s.i32_add(s.getLocal("k"),s.getLocal("m"))),s.br(0))),s.setLocal("s",s.i32_add(s.getLocal("s"),s.i32_const(1))),s.br(0))),s.call(e+"__fftFinal",s.getLocal("px"),s.getLocal("bits"),s.getLocal("reverse"),s.getLocal("mulFactor")))}(),function(){const a=t.addFunction(e+"__log2");a.addParam("n","i32"),a.setReturnType("i32"),a.addLocal("bits","i32"),a.addLocal("aux","i32");const i=a.getCodeBuilder();a.addCode(i.setLocal("aux",i.i32_shr_u(i.getLocal("n"),i.i32_const(1)))),a.addCode(i.setLocal("bits",i.i32_const(0))),a.addCode(i.block(i.loop(i.br_if(1,i.i32_eqz(i.getLocal("aux"))),i.setLocal("aux",i.i32_shr_u(i.getLocal("aux"),i.i32_const(1))),i.setLocal("bits",i.i32_add(i.getLocal("bits"),i.i32_const(1))),i.br(0)))),a.addCode(i.if(i.i32_ne(i.getLocal("n"),i.i32_shl(i.i32_const(1),i.getLocal("bits"))),i.unreachable())),a.addCode(i.if(i.i32_gt_u(i.getLocal("bits"),i.i32_const(c)),i.unreachable())),a.addCode(i.getLocal("bits"))}(),E(),function(){const a=t.addFunction(e+"_ifft");a.addParam("px","i32"),a.addParam("n","i32"),a.addLocal("bits","i32"),a.addLocal("pInv2","i32");const i=a.getCodeBuilder();a.addCode(i.setLocal("bits",i.call(e+"__log2",i.getLocal("n"))),i.setLocal("pInv2",i.i32_add(i.i32_const(w),i.i32_mul(i.getLocal("bits"),i.i32_const(n)))),i.call(e+"_rawfft",i.getLocal("px"),i.getLocal("bits"),i.i32_const(1),i.getLocal("pInv2")))}(),function(){const r=t.addFunction(e+"_fftJoin");r.addParam("pBuff1","i32"),r.addParam("pBuff2","i32"),r.addParam("n","i32"),r.addParam("first","i32"),r.addParam("inc","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32"),r.addLocal("i","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l)),u=s.i32_const(t.alloc(l));r.addCode(s.call(i+"_copy",s.getLocal("first"),c),s.setLocal("i",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("i"),s.getLocal("n"))),s.setLocal("idx1",s.i32_add(s.getLocal("pBuff1"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("pBuff2"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.call(o,s.getLocal("idx2"),c,d),s.call(a+"_copy",s.getLocal("idx1"),u),s.call(a+"_add",u,d,s.getLocal("idx1")),s.call(a+"_sub",u,d,s.getLocal("idx2")),s.call(i+"_mul",c,s.getLocal("inc"),c),s.setLocal("i",s.i32_add(s.getLocal("i"),s.i32_const(1))),s.br(0))))}(),function(){const r=t.addFunction(e+"_fftJoinExt");r.addParam("pBuff1","i32"),r.addParam("pBuff2","i32"),r.addParam("n","i32"),r.addParam("first","i32"),r.addParam("inc","i32"),r.addParam("totalBits","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32"),r.addLocal("i","i32"),r.addLocal("pShiftToM","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l));r.addCode(s.setLocal("pShiftToM",s.i32_add(s.i32_const(y),s.i32_mul(s.getLocal("totalBits"),s.i32_const(n)))),s.call(i+"_copy",s.getLocal("first"),c),s.setLocal("i",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("i"),s.getLocal("n"))),s.setLocal("idx1",s.i32_add(s.getLocal("pBuff1"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("pBuff2"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.call(a+"_add",s.getLocal("idx1"),s.getLocal("idx2"),d),s.call(o,s.getLocal("idx2"),s.getLocal("pShiftToM"),s.getLocal("idx2")),s.call(a+"_add",s.getLocal("idx1"),s.getLocal("idx2"),s.getLocal("idx2")),s.call(o,s.getLocal("idx2"),c,s.getLocal("idx2")),s.call(a+"_copy",d,s.getLocal("idx1")),s.call(i+"_mul",c,s.getLocal("inc"),c),s.setLocal("i",s.i32_add(s.getLocal("i"),s.i32_const(1))),s.br(0))))}(),function(){const r=t.addFunction(e+"_fftJoinExtInv");r.addParam("pBuff1","i32"),r.addParam("pBuff2","i32"),r.addParam("n","i32"),r.addParam("first","i32"),r.addParam("inc","i32"),r.addParam("totalBits","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32"),r.addLocal("i","i32"),r.addLocal("pShiftToM","i32"),r.addLocal("pSConst","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l));r.addCode(s.setLocal("pShiftToM",s.i32_add(s.i32_const(y),s.i32_mul(s.getLocal("totalBits"),s.i32_const(n)))),s.setLocal("pSConst",s.i32_add(s.i32_const(C),s.i32_mul(s.getLocal("totalBits"),s.i32_const(n)))),s.call(i+"_copy",s.getLocal("first"),c),s.setLocal("i",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("i"),s.getLocal("n"))),s.setLocal("idx1",s.i32_add(s.getLocal("pBuff1"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("pBuff2"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.call(o,s.getLocal("idx2"),c,d),s.call(a+"_sub",s.getLocal("idx1"),d,s.getLocal("idx2")),s.call(o,s.getLocal("idx2"),s.getLocal("pSConst"),s.getLocal("idx2")),s.call(o,s.getLocal("idx1"),s.getLocal("pShiftToM"),s.getLocal("idx1")),s.call(a+"_sub",d,s.getLocal("idx1"),s.getLocal("idx1")),s.call(o,s.getLocal("idx1"),s.getLocal("pSConst"),s.getLocal("idx1")),s.call(i+"_mul",c,s.getLocal("inc"),c),s.setLocal("i",s.i32_add(s.getLocal("i"),s.i32_const(1))),s.br(0))))}(),function(){const r=t.addFunction(e+"_fftMix");r.addParam("pBuff","i32"),r.addParam("n","i32"),r.addParam("exp","i32"),r.addLocal("nGroups","i32"),r.addLocal("nPerGroup","i32"),r.addLocal("nPerGroupDiv2","i32"),r.addLocal("pairOffset","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32"),r.addLocal("i","i32"),r.addLocal("j","i32"),r.addLocal("pwm","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l)),u=s.i32_const(t.alloc(l));r.addCode(s.setLocal("nPerGroup",s.i32_shl(s.i32_const(1),s.getLocal("exp"))),s.setLocal("nPerGroupDiv2",s.i32_shr_u(s.getLocal("nPerGroup"),s.i32_const(1))),s.setLocal("nGroups",s.i32_shr_u(s.getLocal("n"),s.getLocal("exp"))),s.setLocal("pairOffset",s.i32_mul(s.getLocal("nPerGroupDiv2"),s.i32_const(l))),s.setLocal("pwm",s.i32_add(s.i32_const(_),s.i32_mul(s.getLocal("exp"),s.i32_const(n)))),s.setLocal("i",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("i"),s.getLocal("nGroups"))),s.call(i+"_one",c),s.setLocal("j",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("j"),s.getLocal("nPerGroupDiv2"))),s.setLocal("idx1",s.i32_add(s.getLocal("pBuff"),s.i32_mul(s.i32_add(s.i32_mul(s.getLocal("i"),s.getLocal("nPerGroup")),s.getLocal("j")),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("idx1"),s.getLocal("pairOffset"))),s.call(o,s.getLocal("idx2"),c,d),s.call(a+"_copy",s.getLocal("idx1"),u),s.call(a+"_add",u,d,s.getLocal("idx1")),s.call(a+"_sub",u,d,s.getLocal("idx2")),s.call(i+"_mul",c,s.getLocal("pwm"),c),s.setLocal("j",s.i32_add(s.getLocal("j"),s.i32_const(1))),s.br(0))),s.setLocal("i",s.i32_add(s.getLocal("i"),s.i32_const(1))),s.br(0))))}(),function(){const i=t.addFunction(e+"_fftFinal");i.addParam("pBuff","i32"),i.addParam("n","i32"),i.addParam("factor","i32"),i.addLocal("idx1","i32"),i.addLocal("idx2","i32"),i.addLocal("i","i32"),i.addLocal("ndiv2","i32");const n=i.getCodeBuilder(),r=n.i32_const(t.alloc(l));i.addCode(n.setLocal("ndiv2",n.i32_shr_u(n.getLocal("n"),n.i32_const(1))),n.if(n.i32_and(n.getLocal("n"),n.i32_const(1)),n.call(o,n.i32_add(n.getLocal("pBuff"),n.i32_mul(n.getLocal("ndiv2"),n.i32_const(l))),n.getLocal("factor"),n.i32_add(n.getLocal("pBuff"),n.i32_mul(n.getLocal("ndiv2"),n.i32_const(l))))),n.setLocal("i",n.i32_const(0)),n.block(n.loop(n.br_if(1,n.i32_ge_u(n.getLocal("i"),n.getLocal("ndiv2"))),n.setLocal("idx1",n.i32_add(n.getLocal("pBuff"),n.i32_mul(n.getLocal("i"),n.i32_const(l)))),n.setLocal("idx2",n.i32_add(n.getLocal("pBuff"),n.i32_mul(n.i32_sub(n.i32_sub(n.getLocal("n"),n.i32_const(1)),n.getLocal("i")),n.i32_const(l)))),n.call(o,n.getLocal("idx2"),n.getLocal("factor"),r),n.call(o,n.getLocal("idx1"),n.getLocal("factor"),n.getLocal("idx2")),n.call(a+"_copy",r,n.getLocal("idx1")),n.setLocal("i",n.i32_add(n.getLocal("i"),n.i32_const(1))),n.br(0))))}(),function(){const r=t.addFunction(e+"_prepareLagrangeEvaluation");r.addParam("pBuff1","i32"),r.addParam("pBuff2","i32"),r.addParam("n","i32"),r.addParam("first","i32"),r.addParam("inc","i32"),r.addParam("totalBits","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32"),r.addLocal("i","i32"),r.addLocal("pShiftToM","i32"),r.addLocal("pSConst","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l));r.addCode(s.setLocal("pShiftToM",s.i32_add(s.i32_const(y),s.i32_mul(s.getLocal("totalBits"),s.i32_const(n)))),s.setLocal("pSConst",s.i32_add(s.i32_const(C),s.i32_mul(s.getLocal("totalBits"),s.i32_const(n)))),s.call(i+"_copy",s.getLocal("first"),c),s.setLocal("i",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("i"),s.getLocal("n"))),s.setLocal("idx1",s.i32_add(s.getLocal("pBuff1"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("pBuff2"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.call(o,s.getLocal("idx1"),s.getLocal("pShiftToM"),d),s.call(a+"_sub",s.getLocal("idx2"),d,d),s.call(a+"_sub",s.getLocal("idx1"),s.getLocal("idx2"),s.getLocal("idx2")),s.call(o,d,s.getLocal("pSConst"),s.getLocal("idx1")),s.call(o,s.getLocal("idx2"),c,s.getLocal("idx2")),s.call(i+"_mul",c,s.getLocal("inc"),c),s.setLocal("i",s.i32_add(s.getLocal("i"),s.i32_const(1))),s.br(0))))}(),t.exportFunction(e+"_fft"),t.exportFunction(e+"_ifft"),t.exportFunction(e+"_rawfft"),t.exportFunction(e+"_fftJoin"),t.exportFunction(e+"_fftJoinExt"),t.exportFunction(e+"_fftJoinExtInv"),t.exportFunction(e+"_fftMix"),t.exportFunction(e+"_fftFinal"),t.exportFunction(e+"_prepareLagrangeEvaluation")},Vt=function(t,e,a){const i=8*t.modules[a].n64;return function(){const o=t.addFunction(e+"_zero");o.addParam("px","i32"),o.addParam("n","i32"),o.addLocal("lastp","i32"),o.addLocal("p","i32");const n=o.getCodeBuilder();o.addCode(n.setLocal("p",n.getLocal("px")),n.setLocal("lastp",n.i32_add(n.getLocal("px"),n.i32_mul(n.getLocal("n"),n.i32_const(i)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("p"),n.getLocal("lastp"))),n.call(a+"_zero",n.getLocal("p")),n.setLocal("p",n.i32_add(n.getLocal("p"),n.i32_const(i))),n.br(0))))}(),function(){const o=t.addFunction(e+"_constructLC");o.addParam("ppolynomials","i32"),o.addParam("psignals","i32"),o.addParam("nSignals","i32"),o.addParam("pres","i32"),o.addLocal("i","i32"),o.addLocal("j","i32"),o.addLocal("pp","i32"),o.addLocal("ps","i32"),o.addLocal("pd","i32"),o.addLocal("ncoefs","i32");const n=o.getCodeBuilder(),l=n.i32_const(t.alloc(i));o.addCode(n.setLocal("i",n.i32_const(0)),n.setLocal("pp",n.getLocal("ppolynomials")),n.setLocal("ps",n.getLocal("psignals")),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("i"),n.getLocal("nSignals"))),n.setLocal("ncoefs",n.i32_load(n.getLocal("pp"))),n.setLocal("pp",n.i32_add(n.getLocal("pp"),n.i32_const(4))),n.setLocal("j",n.i32_const(0)),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("j"),n.getLocal("ncoefs"))),n.setLocal("pd",n.i32_add(n.getLocal("pres"),n.i32_mul(n.i32_load(n.getLocal("pp")),n.i32_const(i)))),n.setLocal("pp",n.i32_add(n.getLocal("pp"),n.i32_const(4))),n.call(a+"_mul",n.getLocal("ps"),n.getLocal("pp"),l),n.call(a+"_add",l,n.getLocal("pd"),n.getLocal("pd")),n.setLocal("pp",n.i32_add(n.getLocal("pp"),n.i32_const(i))),n.setLocal("j",n.i32_add(n.getLocal("j"),n.i32_const(1))),n.br(0))),n.setLocal("ps",n.i32_add(n.getLocal("ps"),n.i32_const(i))),n.setLocal("i",n.i32_add(n.getLocal("i"),n.i32_const(1))),n.br(0))))}(),t.exportFunction(e+"_zero"),t.exportFunction(e+"_constructLC"),e},$t=function(t,e,a){const i=8*t.modules[a].n64;return function(){const o=t.addFunction(e+"_buildABC");o.addParam("pCoefs","i32"),o.addParam("nCoefs","i32"),o.addParam("pWitness","i32"),o.addParam("pA","i32"),o.addParam("pB","i32"),o.addParam("pC","i32"),o.addParam("offsetOut","i32"),o.addParam("nOut","i32"),o.addParam("offsetWitness","i32"),o.addParam("nWitness","i32"),o.addLocal("it","i32"),o.addLocal("ita","i32"),o.addLocal("itb","i32"),o.addLocal("last","i32"),o.addLocal("m","i32"),o.addLocal("c","i32"),o.addLocal("s","i32"),o.addLocal("pOut","i32");const n=o.getCodeBuilder(),l=n.i32_const(t.alloc(i));o.addCode(n.setLocal("ita",n.getLocal("pA")),n.setLocal("itb",n.getLocal("pB")),n.setLocal("last",n.i32_add(n.getLocal("pA"),n.i32_mul(n.getLocal("nOut"),n.i32_const(i)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("ita"),n.getLocal("last"))),n.call(a+"_zero",n.getLocal("ita")),n.call(a+"_zero",n.getLocal("itb")),n.setLocal("ita",n.i32_add(n.getLocal("ita"),n.i32_const(i))),n.setLocal("itb",n.i32_add(n.getLocal("itb"),n.i32_const(i))),n.br(0))),n.setLocal("it",n.getLocal("pCoefs")),n.setLocal("last",n.i32_add(n.getLocal("pCoefs"),n.i32_mul(n.getLocal("nCoefs"),n.i32_const(i+12)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("it"),n.getLocal("last"))),n.setLocal("s",n.i32_load(n.getLocal("it"),8)),n.if(n.i32_or(n.i32_lt_u(n.getLocal("s"),n.getLocal("offsetWitness")),n.i32_ge_u(n.getLocal("s"),n.i32_add(n.getLocal("offsetWitness"),n.getLocal("nWitness")))),[...n.setLocal("it",n.i32_add(n.getLocal("it"),n.i32_const(i+12))),...n.br(1)]),n.setLocal("m",n.i32_load(n.getLocal("it"))),n.if(n.i32_eq(n.getLocal("m"),n.i32_const(0)),n.setLocal("pOut",n.getLocal("pA")),n.if(n.i32_eq(n.getLocal("m"),n.i32_const(1)),n.setLocal("pOut",n.getLocal("pB")),[...n.setLocal("it",n.i32_add(n.getLocal("it"),n.i32_const(i+12))),...n.br(1)])),n.setLocal("c",n.i32_load(n.getLocal("it"),4)),n.if(n.i32_or(n.i32_lt_u(n.getLocal("c"),n.getLocal("offsetOut")),n.i32_ge_u(n.getLocal("c"),n.i32_add(n.getLocal("offsetOut"),n.getLocal("nOut")))),[...n.setLocal("it",n.i32_add(n.getLocal("it"),n.i32_const(i+12))),...n.br(1)]),n.setLocal("pOut",n.i32_add(n.getLocal("pOut"),n.i32_mul(n.i32_sub(n.getLocal("c"),n.getLocal("offsetOut")),n.i32_const(i)))),n.call(a+"_mul",n.i32_add(n.getLocal("pWitness"),n.i32_mul(n.i32_sub(n.getLocal("s"),n.getLocal("offsetWitness")),n.i32_const(i))),n.i32_add(n.getLocal("it"),n.i32_const(12)),l),n.call(a+"_add",n.getLocal("pOut"),l,n.getLocal("pOut")),n.setLocal("it",n.i32_add(n.getLocal("it"),n.i32_const(i+12))),n.br(0))),n.setLocal("ita",n.getLocal("pA")),n.setLocal("itb",n.getLocal("pB")),n.setLocal("it",n.getLocal("pC")),n.setLocal("last",n.i32_add(n.getLocal("pA"),n.i32_mul(n.getLocal("nOut"),n.i32_const(i)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("ita"),n.getLocal("last"))),n.call(a+"_mul",n.getLocal("ita"),n.getLocal("itb"),n.getLocal("it")),n.setLocal("ita",n.i32_add(n.getLocal("ita"),n.i32_const(i))),n.setLocal("itb",n.i32_add(n.getLocal("itb"),n.i32_const(i))),n.setLocal("it",n.i32_add(n.getLocal("it"),n.i32_const(i))),n.br(0))))}(),function(){const o=t.addFunction(e+"_joinABC");o.addParam("pA","i32"),o.addParam("pB","i32"),o.addParam("pC","i32"),o.addParam("n","i32"),o.addParam("pP","i32"),o.addLocal("ita","i32"),o.addLocal("itb","i32"),o.addLocal("itc","i32"),o.addLocal("itp","i32"),o.addLocal("last","i32");const n=o.getCodeBuilder(),l=n.i32_const(t.alloc(i));o.addCode(n.setLocal("ita",n.getLocal("pA")),n.setLocal("itb",n.getLocal("pB")),n.setLocal("itc",n.getLocal("pC")),n.setLocal("itp",n.getLocal("pP")),n.setLocal("last",n.i32_add(n.getLocal("pA"),n.i32_mul(n.getLocal("n"),n.i32_const(i)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("ita"),n.getLocal("last"))),n.call(a+"_mul",n.getLocal("ita"),n.getLocal("itb"),l),n.call(a+"_sub",l,n.getLocal("itc"),n.getLocal("itp")),n.setLocal("ita",n.i32_add(n.getLocal("ita"),n.i32_const(i))),n.setLocal("itb",n.i32_add(n.getLocal("itb"),n.i32_const(i))),n.setLocal("itc",n.i32_add(n.getLocal("itc"),n.i32_const(i))),n.setLocal("itp",n.i32_add(n.getLocal("itp"),n.i32_const(i))),n.br(0))))}(),function(){const o=t.addFunction(e+"_batchAdd");o.addParam("pa","i32"),o.addParam("pb","i32"),o.addParam("n","i32"),o.addParam("pr","i32"),o.addLocal("ita","i32"),o.addLocal("itb","i32"),o.addLocal("itr","i32"),o.addLocal("last","i32");const n=o.getCodeBuilder();o.addCode(n.setLocal("ita",n.getLocal("pa")),n.setLocal("itb",n.getLocal("pb")),n.setLocal("itr",n.getLocal("pr")),n.setLocal("last",n.i32_add(n.getLocal("pa"),n.i32_mul(n.getLocal("n"),n.i32_const(i)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("ita"),n.getLocal("last"))),n.call(a+"_add",n.getLocal("ita"),n.getLocal("itb"),n.getLocal("itr")),n.setLocal("ita",n.i32_add(n.getLocal("ita"),n.i32_const(i))),n.setLocal("itb",n.i32_add(n.getLocal("itb"),n.i32_const(i))),n.setLocal("itr",n.i32_add(n.getLocal("itr"),n.i32_const(i))),n.br(0))))}(),t.exportFunction(e+"_buildABC"),t.exportFunction(e+"_joinABC"),t.exportFunction(e+"_batchAdd"),e},jt=function(t,e,a,i,o,n,l,r){const s=t.addFunction(e);s.addParam("pIn","i32"),s.addParam("n","i32"),s.addParam("pFirst","i32"),s.addParam("pInc","i32"),s.addParam("pOut","i32"),s.addLocal("pOldFree","i32"),s.addLocal("i","i32"),s.addLocal("pFrom","i32"),s.addLocal("pTo","i32");const c=s.getCodeBuilder(),d=c.i32_const(t.alloc(l));s.addCode(c.setLocal("pFrom",c.getLocal("pIn")),c.setLocal("pTo",c.getLocal("pOut"))),s.addCode(c.call(i+"_copy",c.getLocal("pFirst"),d)),s.addCode(c.setLocal("i",c.i32_const(0)),c.block(c.loop(c.br_if(1,c.i32_eq(c.getLocal("i"),c.getLocal("n"))),c.call(r,c.getLocal("pFrom"),d,c.getLocal("pTo")),c.setLocal("pFrom",c.i32_add(c.getLocal("pFrom"),c.i32_const(o))),c.setLocal("pTo",c.i32_add(c.getLocal("pTo"),c.i32_const(n))),c.call(i+"_mul",d,c.getLocal("pInc"),d),c.setLocal("i",c.i32_add(c.getLocal("i"),c.i32_const(1))),c.br(0)))),t.exportFunction(e)};const Kt=K,Ht=It,Zt=Et,Wt=Pt,Yt=Ot,Jt=qt,Xt=Nt,te=Vt,ee=$t,ae=jt,{bitLength:ie,modInv:oe,isOdd:ne,isNegative:le}=J;const re=K,se=It,ce=Et,de=Pt,ue=Ot,ge=qt,fe=Nt,he=Vt,_e=$t,pe=jt,{bitLength:me,isOdd:we,isNegative:Le}=J;var be=function(t,e){const a=e||"bn128";if(t.modules[a])return a;const i=21888242871839275222246405745257275088696311157297823662689037894645226208583n,o=21888242871839275222246405745257275088548364400416034343698204186575808495617n,n=Math.floor((ie(i-1n)-1)/64)+1,l=8*n,r=l,s=l,c=2*s,d=12*s,u=t.alloc(Kt.bigInt2BytesLE(o,r)),g=Ht(t,i,"f1m");Zt(t,o,"fr","frm");const f=t.alloc(Kt.bigInt2BytesLE(L(3n),s)),h=Jt(t,"g1m","f1m",f);Xt(t,"frm","frm","frm","frm_mul"),te(t,"pol","frm"),ee(t,"qap","frm");const _=Wt(t,"f1m_neg","f2m","f1m"),p=t.alloc([...Kt.bigInt2BytesLE(L(19485874751759354771024239261021720505790618469301721065564631296452457478373n),s),...Kt.bigInt2BytesLE(L(266929791119991161246907387137283842545076965332900288569378510910307636690n),s)]),m=Jt(t,"g2m","f2m",p);function w(e,a){const i=t.addFunction(e);i.addParam("pG","i32"),i.addParam("pFr","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),n=o.i32_const(t.alloc(l));i.addCode(o.call("frm_fromMontgomery",o.getLocal("pFr"),n),o.call(a,o.getLocal("pG"),n,o.i32_const(l),o.getLocal("pr"))),t.exportFunction(e)}function L(t){return BigInt(t)*(1n<0n;)ne(e)?a.push(1):a.push(0),e>>=1n;return a}(29793968203157093288n),Q=t.alloc(U),T=3*c,q=U.length-1,M=U.reduce(((t,e)=>t+(0!=e?1:0)),0),k=6*l,R=3*l*2+(M+q+1)*T;t.modules[a]={n64:n,pG1gen:A,pG1zero:C,pG1b:f,pG2gen:F,pG2zero:E,pG2b:p,pq:t.modules.f1m.pq,pr:u,pOneT:v,prePSize:k,preQSize:R,r:o.toString(),q:i.toString()};const D=4965661367192848881n;function N(e){const 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r=l.getCodeBuilder();for(let a=0;a<6;a++){const i=0==a?r.getLocal("x"):r.i32_add(r.getLocal("x"),r.i32_const(a*c)),u=i,f=r.i32_add(r.getLocal("x"),r.i32_const(a*c+s)),h=0==a?r.getLocal("r"):r.i32_add(r.getLocal("r"),r.i32_const(a*c)),p=h,m=r.i32_add(r.getLocal("r"),r.i32_const(a*c+s)),w=d(o[Math.floor(a/3)][e%12],n[a%3][e%6]),b=t.alloc([...Kt.bigInt2BytesLE(L(w[0]),32),...Kt.bigInt2BytesLE(L(w[1]),32)]);e%2==1?l.addCode(r.call(g+"_copy",u,p),r.call(g+"_neg",f,m),r.call(_+"_mul",h,r.i32_const(b),h)):l.addCode(r.call(_+"_mul",i,r.i32_const(b),h))}function d(t,e){const a=BigInt(t[0]),o=BigInt(t[1]),n=BigInt(e[0]),l=BigInt(e[1]),r=[(a*n-o*l)%i,(a*l+o*n)%i];return le(r[0])&&(r[0]=r[0]+i),r}}function V(e,i){const o=function(t){let e=t;const a=[];for(;e>0n;){if(ne(e)){const t=2-Number(e%4n);a.push(t),e-=BigInt(t)}else a.push(0);e>>=1n}return 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i=e.getCodeBuilder(),o=i.getLocal("x"),n=i.getLocal("r"),l=i.i32_const(t.alloc(d)),r=i.i32_const(t.alloc(d)),s=i.i32_const(t.alloc(d)),u=i.i32_const(t.alloc(d)),g=i.i32_const(t.alloc(d)),f=i.i32_const(t.alloc(d)),h=i.i32_const(t.alloc(d)),p=i.i32_const(t.alloc(d)),m=i.i32_const(t.alloc(d)),w=i.i32_const(t.alloc(d)),L=i.i32_const(t.alloc(d)),b=i.i32_const(t.alloc(d)),A=i.i32_const(t.alloc(d)),y=i.i32_const(t.alloc(d)),C=i.i32_const(t.alloc(d)),I=i.i32_const(t.alloc(d)),F=i.i32_const(t.alloc(d)),x=i.i32_const(t.alloc(d)),E=i.i32_const(t.alloc(d)),v=i.i32_const(t.alloc(d)),S=i.i32_const(t.alloc(d));e.addCode(i.call(a+"__cyclotomicExp_w0",o,l),i.call(O+"_conjugate",l,l),i.call(a+"__cyclotomicSquare",l,r),i.call(a+"__cyclotomicSquare",r,s),i.call(O+"_mul",s,r,u),i.call(a+"__cyclotomicExp_w0",u,g),i.call(O+"_conjugate",g,g),i.call(a+"__cyclotomicSquare",g,f),i.call(a+"__cyclotomicExp_w0",f,h),i.call(O+"_conjugate",h,h),i.call(O+"_conjugate",u,p),i.call(O+"_conjugate",h,m),i.call(O+"_mul",m,g,w),i.call(O+"_mul",w,p,L),i.call(O+"_mul",L,r,b),i.call(O+"_mul",L,g,A),i.call(O+"_mul",A,o,y),i.call(a+"__frobeniusMap1",b,C),i.call(O+"_mul",C,y,I),i.call(a+"__frobeniusMap2",L,F),i.call(O+"_mul",F,I,x),i.call(O+"_conjugate",o,E),i.call(O+"_mul",E,b,v),i.call(a+"__frobeniusMap3",v,S),i.call(O+"_mul",S,x,n))}const 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c=n.getCodeBuilder();for(let i=0;i<6;i++){const u=0==i?c.getLocal("x"):c.i32_add(c.getLocal("x"),c.i32_const(i*s)),g=u,f=c.i32_add(c.getLocal("x"),c.i32_const(i*s+r)),_=0==i?c.getLocal("r"):c.i32_add(c.getLocal("r"),c.i32_const(i*s)),p=_,w=c.i32_add(c.getLocal("r"),c.i32_const(i*s+r)),L=d(a[Math.floor(i/3)][e%12],o[i%3][e%6]),b=t.alloc([...re.bigInt2BytesLE(A(L[0]),l),...re.bigInt2BytesLE(A(L[1]),l)]);e%2==1?n.addCode(c.call(h+"_copy",g,p),c.call(h+"_neg",f,w),c.call(m+"_mul",_,c.i32_const(b),_)):n.addCode(c.call(m+"_mul",u,c.i32_const(b),_))}function d(t,e){const a=t[0],o=t[1],n=e[0],l=e[1],r=[(a*n-o*l)%i,(a*l+o*n)%i];return Le(r[0])&&(r[0]=r[0]+i),r}}function V(e,i,o){const n=function(t){let e=t;const a=[];for(;e>0n;){if(we(e)){const t=2-Number(e%4n);a.push(t),e-=BigInt(t)}else a.push(0);e>>=1n}return a}(e).map((t=>-1==t?255:t)),l=t.alloc(n),r=t.addFunction(a+"__cyclotomicExp_"+o);r.addParam("x","i32"),r.addParam("r","i32"),r.addLocal("bit","i32"),r.addLocal("i","i32");const s=r.getCodeBuilder(),d=s.getLocal("x"),u=s.getLocal("r"),g=s.i32_const(t.alloc(c));r.addCode(s.call(z+"_conjugate",d,g),s.call(z+"_one",u),s.if(s.teeLocal("bit",s.i32_load8_s(s.i32_const(n.length-1),l)),s.if(s.i32_eq(s.getLocal("bit"),s.i32_const(1)),s.call(z+"_mul",u,d,u),s.call(z+"_mul",u,g,u))),s.setLocal("i",s.i32_const(n.length-2)),s.block(s.loop(s.call(a+"__cyclotomicSquare",u,u),s.if(s.teeLocal("bit",s.i32_load8_s(s.getLocal("i"),l)),s.if(s.i32_eq(s.getLocal("bit"),s.i32_const(1)),s.call(z+"_mul",u,d,u),s.call(z+"_mul",u,g,u))),s.br_if(1,s.i32_eqz(s.getLocal("i"))),s.setLocal("i",s.i32_sub(s.getLocal("i"),s.i32_const(1))),s.br(0)))),i&&r.addCode(s.call(z+"_conjugate",u,u))}t.modules[a]={n64q:n,n64r:d,n8q:l,n8r:u,pG1gen:C,pG1zero:F,pG1b:_,pG2gen:E,pG2zero:B,pG2b:w,pq:t.modules.f1m.pq,pr:f,pOneT:S,r:o,q:i,prePSize:M,preQSize:k},function(){const e=t.addFunction(G+"_mul1");e.addParam("pA","i32"),e.addParam("pC1","i32"),e.addParam("pR","i32");const a=e.getCodeBuilder(),i=a.getLocal("pA"),o=a.i32_add(a.getLocal("pA"),a.i32_const(2*r)),n=a.i32_add(a.getLocal("pA"),a.i32_const(4*r)),l=a.getLocal("pC1"),s=a.getLocal("pR"),c=a.i32_add(a.getLocal("pR"),a.i32_const(2*r)),d=a.i32_add(a.getLocal("pR"),a.i32_const(4*r)),u=a.i32_const(t.alloc(2*r)),g=a.i32_const(t.alloc(2*r));e.addCode(a.call(m+"_add",i,o,u),a.call(m+"_add",o,n,g),a.call(m+"_mul",o,l,d),a.call(m+"_mul",g,l,s),a.call(m+"_sub",s,d,s),a.call(m+"_mulNR",s,s),a.call(m+"_mul",u,l,c),a.call(m+"_sub",c,d,c))}(),function(){const e=t.addFunction(G+"_mul01");e.addParam("pA","i32"),e.addParam("pC0","i32"),e.addParam("pC1","i32"),e.addParam("pR","i32");const a=e.getCodeBuilder(),i=a.getLocal("pA"),o=a.i32_add(a.getLocal("pA"),a.i32_const(2*r)),n=a.i32_add(a.getLocal("pA"),a.i32_const(4*r)),l=a.getLocal("pC0"),s=a.getLocal("pC1"),c=a.getLocal("pR"),d=a.i32_add(a.getLocal("pR"),a.i32_const(2*r)),u=a.i32_add(a.getLocal("pR"),a.i32_const(4*r)),g=a.i32_const(t.alloc(2*r)),f=a.i32_const(t.alloc(2*r)),h=a.i32_const(t.alloc(2*r)),_=a.i32_const(t.alloc(2*r));e.addCode(a.call(m+"_mul",i,l,g),a.call(m+"_mul",o,s,f),a.call(m+"_add",i,o,h),a.call(m+"_add",i,n,_),a.call(m+"_add",o,n,c),a.call(m+"_mul",c,s,c),a.call(m+"_sub",c,f,c),a.call(m+"_mulNR",c,c),a.call(m+"_add",c,g,c),a.call(m+"_add",l,s,d),a.call(m+"_mul",d,h,d),a.call(m+"_sub",d,g,d),a.call(m+"_sub",d,f,d),a.call(m+"_mul",_,l,u),a.call(m+"_sub",u,g,u),a.call(m+"_add",u,f,u))}(),function(){const e=t.addFunction(z+"_mul014");e.addParam("pA","i32"),e.addParam("pC0","i32"),e.addParam("pC1","i32"),e.addParam("pC4","i32"),e.addParam("pR","i32");const a=e.getCodeBuilder(),i=a.getLocal("pA"),o=a.i32_add(a.getLocal("pA"),a.i32_const(6*r)),n=a.getLocal("pC0"),l=a.getLocal("pC1"),s=a.getLocal("pC4"),c=a.i32_const(t.alloc(6*r)),d=a.i32_const(t.alloc(6*r)),u=a.i32_const(t.alloc(2*r)),g=a.getLocal("pR"),f=a.i32_add(a.getLocal("pR"),a.i32_const(6*r));e.addCode(a.call(G+"_mul01",i,n,l,c),a.call(G+"_mul1",o,s,d),a.call(m+"_add",l,s,u),a.call(G+"_add",o,i,f),a.call(G+"_mul01",f,n,u,f),a.call(G+"_sub",f,c,f),a.call(G+"_sub",f,d,f),a.call(G+"_copy",d,g),a.call(G+"_mulNR",g,g),a.call(G+"_add",g,c,g))}(),function(){const e=t.addFunction(a+"_ell");e.addParam("pP","i32"),e.addParam("pCoefs","i32"),e.addParam("pF","i32");const i=e.getCodeBuilder(),o=i.getLocal("pP"),n=i.i32_add(i.getLocal("pP"),i.i32_const(l)),s=i.getLocal("pF"),c=i.getLocal("pCoefs"),d=i.i32_add(i.getLocal("pCoefs"),i.i32_const(r)),u=i.i32_add(i.getLocal("pCoefs"),i.i32_const(2*r)),g=i.i32_add(i.getLocal("pCoefs"),i.i32_const(3*r)),f=i.i32_add(i.getLocal("pCoefs"),i.i32_const(4*r)),_=t.alloc(2*r),p=i.i32_const(_),m=i.i32_const(_),w=i.i32_const(_+r),L=t.alloc(2*r),b=i.i32_const(L),A=i.i32_const(L),y=i.i32_const(L+r);e.addCode(i.call(h+"_mul",c,n,m),i.call(h+"_mul",d,n,w),i.call(h+"_mul",u,o,A),i.call(h+"_mul",g,o,y),i.call(z+"_mul014",s,f,b,p,s))}();const $=t.alloc(M),j=t.alloc(k);function K(e){const i=t.addFunction(a+"_pairingEq"+e);for(let t=0;t>=BigInt(32)):l+2<=e?(n.setUint16(l,Number(a&BigInt(65535)),!0),l+=2,a>>=BigInt(16)):(n.setUint8(l,Number(a&BigInt(255)),!0),l+=1,a>>=BigInt(8));if(a)throw new Error("Number does not fit in this length");return i}const Ce=[];for(let t=0;t<256;t++)Ce[t]=Ie(t,8);function Ie(t,e){let a=0,i=t;for(let t=0;t>=1;return a}function Fe(t,e){return(Ce[t>>>24]|Ce[t>>>16&255]<<8|Ce[t>>>8&255]<<16|Ce[255&t]<<24)>>>32-e}function xe(t){return(0!=(4294901760&t)?(t&=4294901760,16):0)|(0!=(4278255360&t)?(t&=4278255360,8):0)|(0!=(4042322160&t)?(t&=4042322160,4):0)|(0!=(3435973836&t)?(t&=3435973836,2):0)|0!=(2863311530&t)}function Ee(t,e){const a=t.byteLength/e,i=xe(a);if(a!=1<a){const i=t.slice(o*e,(o+1)*e);t.set(t.slice(a*e,(a+1)*e),o*e),t.set(i,a*e)}}}function ve(t,e){const a=new Uint8Array(e*t.length);for(let i=0;i{a[i]=t(e[i])})),a}return e},unstringifyBigInts:function t(e){if("string"==typeof e&&/^[0-9]+$/.test(e))return BigInt(e);if("string"==typeof e&&/^0x[0-9a-fA-F]+$/.test(e))return BigInt(e);if(Array.isArray(e))return e.map(t);if("object"==typeof e){if(null===e)return null;const a={};return Object.keys(e).forEach((i=>{a[i]=t(e[i])})),a}return e},beBuff2int:function(t){let e=BigInt(0),a=t.length,i=0;const o=new 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Ge{constructor(t){this.buffers=[],this.byteLength=t;for(let e=0;e0;){const t=l+r>Pe?Pe-l:r,e=new Uint8Array(this.buffers[n].buffer,this.buffers[n].byteOffset+l,t);if(t==a)return e.slice();o||(o=a<=Pe?new Uint8Array(a):new Ge(a)),o.set(e,a-r),r-=t,n++,l=0}return o}set(t,e){void 0===e&&(e=0);const a=t.byteLength;if(0==a)return;const i=Math.floor(e/Pe);if(i==Math.floor((e+a-1)/Pe))return t instanceof Ge&&1==t.buffers.length?this.buffers[i].set(t.buffers[0],e%Pe):this.buffers[i].set(t,e%Pe);let o=i,n=e%Pe,l=a;for(;l>0;){const e=n+l>Pe?Pe-n:l,i=t.slice(a-l,a-l+e);new Uint8Array(this.buffers[o].buffer,this.buffers[o].byteOffset+n,e).set(i),l-=e,o++,n=0}}}function ze(t,e,a,i){return async function(o){const n=Math.floor(o.byteLength/a);if(n*a!==o.byteLength)throw new Error("Invalid buffer size");const l=Math.floor(n/t.concurrency),r=[];for(let s=0;s=0;t--)this.w[t]=this.square(this.w[t+1]);if(!this.eq(this.w[0],this.one))throw new Error("Error calculating roots of 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B(E(this.fromMontgomery(t),0),e)}fromRng(t){let e;const a=new Uint8Array(this.n8);do{e=P;for(let a=0;ai.buffer.byteLength){const o=i.buffer.byteLength/65536;let n=Math.floor((a[0]+t)/65536)+1;n>e&&(n=e),i.grow(n-o)}return o}function l(t){const e=n(t.byteLength);return s(e,t),e}function r(t,e){const a=new Uint8Array(i.buffer);return new Uint8Array(a.buffer,a.byteOffset+t,e)}function s(t,e){new Uint8Array(i.buffer).set(new Uint8Array(e),t)}function c(t){if("INIT"==t[0].cmd)return o(t[0]);const e={vars:[],out:[]},c=new Uint32Array(i.buffer,0,1)[0];for(let i=0;i{this.reject=e,this.resolve=t}))}}var Ne;const Ve="data:application/javascript;base64,"+(Ne="("+qe.toString()+")(self)",globalThis.btoa(Ne));class $e{constructor(){this.actionQueue=[],this.oldPFree=0}startSyncOp(){if(0!=this.oldPFree)throw new Error("Sync operation in progress");this.oldPFree=this.u32[0]}endSyncOp(){if(0==this.oldPFree)throw new Error("No sync operation in 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a=t[e],i=t.Fr,o=t.tm;t[e].batchApplyKey=async function(t,n,l,r,s){let c,d,u,g,f;if(r=r||"affine",s=s||"affine","G1"==e)"jacobian"==r?(u=3*a.F.n8,c="g1m_batchApplyKey"):(u=2*a.F.n8,c="g1m_batchApplyKeyMixed"),g=3*a.F.n8,"jacobian"==s?f=3*a.F.n8:(d="g1m_batchToAffine",f=2*a.F.n8);else if("G2"==e)"jacobian"==r?(u=3*a.F.n8,c="g2m_batchApplyKey"):(u=2*a.F.n8,c="g2m_batchApplyKeyMixed"),g=3*a.F.n8,"jacobian"==s?f=3*a.F.n8:(d="g2m_batchToAffine",f=2*a.F.n8);else{if("Fr"!=e)throw new Error("Invalid group: "+e);c="frm_batchApplyKey",u=a.n8,g=a.n8,f=a.n8}const h=Math.floor(t.byteLength/u),_=Math.floor(h/o.concurrency),p=[];l=i.e(l);let m=i.e(n);for(let e=0;e=0;t--){if(!a.isZero(_))for(let t=0;tc&&(_=c),_<1024&&(_=1024);const p=[];for(let e=0;e(r&&r.debug(`Multiexp end: ${s}: ${e}/${u}`),t))))}const m=await Promise.all(p);let w=a.zero;for(let t=m.length-1;t>=0;t--)w=a.add(w,m[t]);return w}a.multiExp=async function(t,e,a,i){return await n(t,e,"jacobian",a,i)},a.multiExpAffine=async function(t,e,a,i){return await n(t,e,"affine",a,i)}}function Ze(t,e){const a=t[e],i=t.Fr,o=a.tm;async function n(t,r,s,c,d,u){s=s||"affine",c=c||"affine";let g,f,h,_,p,m,w,L;"G1"==e?("affine"==s?(g=2*a.F.n8,_="g1m_batchToJacobian"):g=3*a.F.n8,f=3*a.F.n8,r&&(L="g1m_fftFinal"),w="g1m_fftJoin",m="g1m_fftMix","affine"==c?(h=2*a.F.n8,p="g1m_batchToAffine"):h=3*a.F.n8):"G2"==e?("affine"==s?(g=2*a.F.n8,_="g2m_batchToJacobian"):g=3*a.F.n8,f=3*a.F.n8,r&&(L="g2m_fftFinal"),w="g2m_fftJoin",m="g2m_fftMix","affine"==c?(h=2*a.F.n8,p="g2m_batchToAffine"):h=3*a.F.n8):"Fr"==e&&(g=a.n8,f=a.n8,h=a.n8,r&&(L="frm_fftFinal"),m="frm_fftMix",w="frm_fftJoin");let b=!1;Array.isArray(t)?(t=ve(t,g),b=!0):t=t.slice(0,t.byteLength);const A=t.byteLength/g,y=xe(A);if(1<1<<28?new Ge(2*u[0].byteLength):new Uint8Array(2*u[0].byteLength);return g.set(u[0]),g.set(u[1],u[0].byteLength),g}(t,s,c,d,u):await async function(t,e,a,o,r){let s,c;s=t.slice(0,t.byteLength/2),c=t.slice(t.byteLength/2,t.byteLength);const d=[];[s,c]=await l(s,c,"fftJoinExt",i.one,i.shift,e,"jacobian",o,r),d.push(n(s,!1,"jacobian",a,o,r)),d.push(n(c,!1,"jacobian",a,o,r));const u=await Promise.all(d);let g;g=u[0].byteLength>1<<28?new Ge(2*u[0].byteLength):new Uint8Array(2*u[0].byteLength);return g.set(u[0]),g.set(u[1],u[0].byteLength),g}(t,s,c,d,u),b?Be(e,h):e}let C,I,F;r&&(C=i.inv(i.e(A))),Ee(t,g);let x=Math.min(16384,A),E=A/x;for(;E=16;)E*=2,x/=2;const v=xe(x),B=[];for(let e=0;e(d&&d.debug(`${u}: fft ${y} mix end: ${e}/${E}`),t))))}F=await Promise.all(B);for(let t=0;t(d&&d.debug(`${u}: fft ${y} join ${t}/${y} ${l+1}/${e} ${r}/${a/2}`),i))))}const l=await Promise.all(n);for(let t=0;t0;e--)I.set(F[e],t),t+=x*h,delete F[e];I.set(F[0].slice(0,(x-1)*h),t),delete F[0]}else for(let t=0;t65536&&(b=65536);const A=[];for(let e=0;e(u&&u.debug(`${g}: fftJoinExt End: ${e}/${L}`),t))))}const y=await Promise.all(A);let C,I;L*p>1<<28?(C=new Ge(L*p),I=new Ge(L*p)):(C=new Uint8Array(L*p),I=new Uint8Array(L*p));let F=0;for(let t=0;ti.s+1)throw s&&s.error("lagrangeEvaluations input too big"),new Error("lagrangeEvaluations input too big");let f=t.slice(0,t.byteLength/2),h=t.slice(t.byteLength/2,t.byteLength);const _=i.exp(i.shift,u/2),p=i.inv(i.sub(i.one,_));[f,h]=await l(f,h,"prepareLagrangeEvaluation",p,i.shiftInv,o,"jacobian",s,c+" prep");const m=[];let w;return m.push(n(f,!0,"jacobian",r,s,c+" t0")),m.push(n(h,!0,"jacobian",r,s,c+" t1")),[f,h]=await Promise.all(m),w=f.byteLength>1<<28?new Ge(2*f.byteLength):new Uint8Array(2*f.byteLength),w.set(f),w.set(h,f.byteLength),w},a.fftMix=async function(t){const n=3*a.F.n8;let l,r;if("G1"==e)l="g1m_fftMix",r="g1m_fftJoin";else if("G2"==e)l="g2m_fftMix",r="g2m_fftJoin";else{if("Fr"!=e)throw new Error("Invalid group");l="frm_fftMix",r="frm_fftJoin"}const s=Math.floor(t.byteLength/n),c=xe(s);let d=1<=0;t--)f.set(g[t][0],h),h+=g[t][0].byteLength;return f}}async function We(t){const e=await async function(t,e){const a=new $e;a.memory=new WebAssembly.Memory({initial:Re}),a.u8=new Uint8Array(a.memory.buffer),a.u32=new Uint32Array(a.memory.buffer);const i=await WebAssembly.compile(t.code);if(a.instance=await WebAssembly.instantiate(i,{env:{memory:a.memory}}),a.singleThread=e,a.initalPFree=a.u32[0],a.pq=t.pq,a.pr=t.pr,a.pG1gen=t.pG1gen,a.pG1zero=t.pG1zero,a.pG2gen=t.pG2gen,a.pG2zero=t.pG2zero,a.pOneT=t.pOneT,e)a.code=t.code,a.taskManager=qe(),await a.taskManager([{cmd:"INIT",init:Re,code:a.code.slice()}]),a.concurrency=1;else{let e;a.workers=[],a.pendingDeferreds=[],a.working=[],e="object"==typeof navigator&&navigator.hardwareConcurrency?navigator.hardwareConcurrency:Me.cpus().length,0==e&&(e=2),e>64&&(e=64),a.concurrency=e;for(let t=0;t>8n&0xFFn)),e.push(Number(a>>16n&0xFFn)),e.push(Number(a>>24n&0xFFn)),e}function ea(t){const e=function(t){for(var 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sa{constructor(t){this.func=t,this.functionName=t.functionName,this.module=t.module}setLocal(t,e){const a=this.func.localIdxByName[t];if(void 0===a)throw new Error(`Local Variable not defined: Function: ${this.functionName} local: ${t} `);return[...e,33,...la(a)]}teeLocal(t,e){const a=this.func.localIdxByName[t];if(void 0===a)throw new Error(`Local Variable not defined: Function: ${this.functionName} local: ${t} `);return[...e,34,...la(a)]}getLocal(t){const e=this.func.localIdxByName[t];if(void 0===e)throw new Error(`Local Variable not defined: Function: ${this.functionName} local: ${t} `);return[32,...la(e)]}i64_load8_s(t,e,a){return[...t,48,void 0===a?0:a,...la(e||0)]}i64_load8_u(t,e,a){return[...t,49,void 0===a?0:a,...la(e||0)]}i64_load16_s(t,e,a){return[...t,50,void 0===a?1:a,...la(e||0)]}i64_load16_u(t,e,a){return[...t,51,void 0===a?1:a,...la(e||0)]}i64_load32_s(t,e,a){return[...t,52,void 0===a?2:a,...la(e||0)]}i64_load32_u(t,e,a){return[...t,53,void 0===a?2:a,...la(e||0)]}i64_load(t,e,a){return[...t,41,void 0===a?3:a,...la(e||0)]}i64_store(t,e,a,i){let o,n,l;return Array.isArray(e)?(o=0,n=3,l=e):Array.isArray(a)?(o=e,n=3,l=a):Array.isArray(i)&&(o=e,n=a,l=i),[...t,...l,55,n,...la(o)]}i64_store32(t,e,a,i){let o,n,l;return Array.isArray(e)?(o=0,n=2,l=e):Array.isArray(a)?(o=e,n=2,l=a):Array.isArray(i)&&(o=e,n=a,l=i),[...t,...l,62,n,...la(o)]}i64_store16(t,e,a,i){let o,n,l;return Array.isArray(e)?(o=0,n=1,l=e):Array.isArray(a)?(o=e,n=1,l=a):Array.isArray(i)&&(o=e,n=a,l=i),[...t,...l,61,n,...la(o)]}i64_store8(t,e,a,i){let o,n,l;return Array.isArray(e)?(o=0,n=0,l=e):Array.isArray(a)?(o=e,n=0,l=a):Array.isArray(i)&&(o=e,n=a,l=i),[...t,...l,60,n,...la(o)]}i32_load8_s(t,e,a){return[...t,44,void 0===a?0:a,...la(e||0)]}i32_load8_u(t,e,a){return[...t,45,void 0===a?0:a,...la(e||0)]}i32_load16_s(t,e,a){return[...t,46,void 0===a?1:a,...la(e||0)]}i32_load16_u(t,e,a){return[...t,47,void 0===a?1:a,...la(e||0)]}i32_load(t,e,a){return[...t,40,void 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a?[...t,4,64,...e,5,...a,11]:[...t,4,64,...e,11]}block(t){return[2,64,...t,11]}loop(...t){return[3,64,...[].concat(...t),11]}br_if(t,e){return[...e,13,...la(t)]}br(t){return[12,...la(t)]}ret(t){return[...t,15]}drop(t){return[...t,26]}i64_const(t){return[66,...na(t)]}i32_const(t){return[65,...oa(t)]}i64_eqz(t){return[...t,80]}i64_eq(t,e){return[...t,...e,81]}i64_ne(t,e){return[...t,...e,82]}i64_lt_s(t,e){return[...t,...e,83]}i64_lt_u(t,e){return[...t,...e,84]}i64_gt_s(t,e){return[...t,...e,85]}i64_gt_u(t,e){return[...t,...e,86]}i64_le_s(t,e){return[...t,...e,87]}i64_le_u(t,e){return[...t,...e,88]}i64_ge_s(t,e){return[...t,...e,89]}i64_ge_u(t,e){return[...t,...e,90]}i64_add(t,e){return[...t,...e,124]}i64_sub(t,e){return[...t,...e,125]}i64_mul(t,e){return[...t,...e,126]}i64_div_s(t,e){return[...t,...e,127]}i64_div_u(t,e){return[...t,...e,128]}i64_rem_s(t,e){return[...t,...e,129]}i64_rem_u(t,e){return[...t,...e,130]}i64_and(t,e){return[...t,...e,131]}i64_or(t,e){return[...t,...e,132]}i64_xor(t,e){return[...t,...e,133]}i64_shl(t,e){return[...t,...e,134]}i64_shr_s(t,e){return[...t,...e,135]}i64_shr_u(t,e){return[...t,...e,136]}i64_extend_i32_s(t){return[...t,172]}i64_extend_i32_u(t){return[...t,173]}i64_clz(t){return[...t,121]}i64_ctz(t){return[...t,122]}i32_eqz(t){return[...t,69]}i32_eq(t,e){return[...t,...e,70]}i32_ne(t,e){return[...t,...e,71]}i32_lt_s(t,e){return[...t,...e,72]}i32_lt_u(t,e){return[...t,...e,73]}i32_gt_s(t,e){return[...t,...e,74]}i32_gt_u(t,e){return[...t,...e,75]}i32_le_s(t,e){return[...t,...e,76]}i32_le_u(t,e){return[...t,...e,77]}i32_ge_s(t,e){return[...t,...e,78]}i32_ge_u(t,e){return[...t,...e,79]}i32_add(t,e){return[...t,...e,106]}i32_sub(t,e){return[...t,...e,107]}i32_mul(t,e){return[...t,...e,108]}i32_div_s(t,e){return[...t,...e,109]}i32_div_u(t,e){return[...t,...e,110]}i32_rem_s(t,e){return[...t,...e,111]}i32_rem_u(t,e){return[...t,...e,112]}i32_and(t,e){return[...t,...e,113]}i32_or(t,e){return[...t,...e,114]}i32_xor(t,e){return[...t,...e,115]}i32_shl(t,e){return[...t,...e,116]}i32_shr_s(t,e){return[...t,...e,117]}i32_shr_u(t,e){return[...t,...e,118]}i32_rotl(t,e){return[...t,...e,119]}i32_rotr(t,e){return[...t,...e,120]}i32_wrap_i64(t){return[...t,167]}i32_clz(t){return[...t,103]}i32_ctz(t){return[...t,104]}unreachable(){return[0]}current_memory(){return[63,0]}comment(){return[]}}const ca={i32:127,i64:126,f32:125,f64:124,anyfunc:112,func:96,emptyblock:64};class da{constructor(t,e,a,i,o){if("import"==a)this.fnType="import",this.moduleName=i,this.fieldName=o;else{if("internal"!=a)throw new Error("Invalid function fnType: "+a);this.fnType="internal"}this.module=t,this.fnName=e,this.params=[],this.locals=[],this.localIdxByName={},this.code=[],this.returnType=null,this.nextLocal=0}addParam(t,e){if(this.localIdxByName[t])throw new Error(`param already exists. Function: ${this.fnName}, Param: ${t} `);const a=this.nextLocal++;this.localIdxByName[t]=a,this.params.push({type:e})}addLocal(t,e,a){const i=a||1;if(this.localIdxByName[t])throw new Error(`local already exists. Function: ${this.fnName}, Param: ${t} `);const o=this.nextLocal++;this.localIdxByName[t]=o,this.locals.push({type:e,length:i})}setReturnType(t){if(this.returnType)throw new Error(`returnType already defined. Function: ${this.fnName}`);this.returnType=t}getSignature(){return[96,...[...la(this.params.length),...this.params.map((t=>ca[t.type]))],...this.returnType?[1,ca[this.returnType]]:[0]]}getBody(){const t=this.locals.map((t=>[...la(t.length),ca[t.type]])),e=[...la(this.locals.length),...[].concat(...t),...this.code,11];return[...la(e.length),...e]}addCode(...t){this.code.push(...[].concat(...t))}getCodeBuilder(){return new sa(this)}}class ua{constructor(){this.functions=[],this.functionIdxByName={},this.nImportFunctions=0,this.nInternalFunctions=0,this.memory={pagesSize:1,moduleName:"env",fieldName:"memory"},this.free=8,this.datas=[],this.modules={},this.exports=[],this.functionsTable=[]}build(){return this._setSignatures(),new Uint8Array([...ta(1836278016),...ta(1),...this._buildType(),...this._buildImport(),...this._buildFunctionDeclarations(),...this._buildFunctionsTable(),...this._buildExports(),...this._buildElements(),...this._buildCode(),...this._buildData()])}addFunction(t){if(void 0!==this.functionIdxByName[t])throw new Error(`Function already defined: ${t}`);const e=this.functions.length;return this.functionIdxByName[t]=e,this.functions.push(new da(this,t,"internal")),this.nInternalFunctions++,this.functions[e]}addIimportFunction(t,e,a){if(void 0!==this.functionIdxByName[t])throw new Error(`Function already defined: ${t}`);if(this.functions.length>0&&"internal"==this.functions[this.functions.length-1].type)throw new Error(`Import functions must be declared before internal: ${t}`);let i=a||t;const o=this.functions.length;return this.functionIdxByName[t]=o,this.functions.push(new da(this,t,"import",e,i)),this.nImportFunctions++,this.functions[o]}setMemory(t,e,a){this.memory={pagesSize:t,moduleName:e||"env",fieldName:a||"memory"}}exportFunction(t,e){const a=e||t;if(void 0===this.functionIdxByName[t])throw new Error(`Function not defined: ${t}`);const i=this.functionIdxByName[t];a!=t&&(this.functionIdxByName[a]=i),this.exports.push({exportName:a,idx:i})}addFunctionToTable(t){const e=this.functionIdxByName[t];this.functionsTable.push(e)}addData(t,e){this.datas.push({offset:t,bytes:e})}alloc(t,e){let a,i;(Array.isArray(t)||ArrayBuffer.isView(t))&&void 0===e?(a=t.length,i=t):(a=t,i=e),a=1+(a-1>>3)<<3;const o=this.free;return this.free+=a,i&&this.addData(o,i),o}allocString(t){const e=(new globalThis.TextEncoder).encode(t);return this.alloc([...e,0])}_setSignatures(){this.signatures=[];const t={};if(this.functionsTable.length>0){const e=this.functions[this.functionsTable[0]].getSignature();t["s_"+ra(e)]=0,this.signatures.push(e)}for(let e=0;e{e.pendingLoads.push({page:t,resolve:a,reject:i})}));return e.__statusPage("After Load request: ",t),a}__statusPage(t,e){const a=[],i=this;if(!i.logHistory)return;a.push("=="+t+" "+e);let o="";for(let t=0;t "+e.history[t][a][i])}_triggerLoad(){const t=this;if(t.reading)return;if(0==t.pendingLoads.length)return;const e=Object.keys(t.pages),a=[];for(let i=0;i0&&(void 0!==t.pages[t.pendingLoads[0].page]||i>0||a.length>0);){const e=t.pendingLoads.shift();if(void 0!==t.pages[e.page]){t.pages[e.page].pendingOps++;const i=a.indexOf(e.page);i>=0&&a.splice(i,1),t.pages[e.page].loading?t.pages[e.page].loading.push(e):e.resolve(),t.__statusPage("After Load (cached): ",e.page)}else{if(i)i--;else{const e=a.shift();t.__statusPage("Before Unload: ",e),t.avBuffs.unshift(t.pages[e]),delete t.pages[e],t.__statusPage("After Unload: ",e)}e.page>=t.totalPages?(t.pages[e.page]=n(),e.resolve(),t.__statusPage("After Load (new): ",e.page)):(t.reading=!0,t.pages[e.page]=n(),t.pages[e.page].loading=[e],o.push(t.fd.read(t.pages[e.page].buff,0,t.pageSize,e.page*t.pageSize).then((a=>{t.pages[e.page].size=a.bytesRead;const i=t.pages[e.page].loading;delete t.pages[e.page].loading;for(let t=0;t{e.reject(t)}))),t.__statusPage("After Load (loading): ",e.page))}}function n(){if(t.avBuffs.length>0){const e=t.avBuffs.shift();return e.dirty=!1,e.pendingOps=1,e.size=0,e}return{dirty:!1,buff:new Uint8Array(t.pageSize),pendingOps:1,size:0}}Promise.all(o).then((()=>{t.reading=!1,t.pendingLoads.length>0&&setImmediate(t._triggerLoad.bind(t)),t._tryClose()}))}_triggerWrite(){const t=this;if(t.writing)return;const e=Object.keys(t.pages),a=[];for(let i=0;i{o.writing=!1}),(e=>{console.log("ERROR Writing: "+e),t.error=e,t._tryClose()}))))}t.writing&&Promise.all(a).then((()=>{t.writing=!1,setImmediate(t._triggerWrite.bind(t)),t._tryClose(),t.pendingLoads.length>0&&setImmediate(t._triggerLoad.bind(t))}))}_getDirtyPage(){for(let t in this.pages)if(this.pages[t].dirty)return t;return-1}async write(t,e){if(0==t.byteLength)return;const a=this;if(void 0===e&&(e=a.pos),a.pos=e+t.byteLength,a.totalSize0;){await n[l-i];const e=r+s>a.pageSize?a.pageSize-r:s,o=t.slice(t.byteLength-s,t.byteLength-s+e);new Uint8Array(a.pages[l].buff.buffer,r,e).set(o),a.pages[l].dirty=!0,a.pages[l].pendingOps--,a.pages[l].size=Math.max(r+e,a.pages[l].size),l>=a.totalPages&&(a.totalPages=l+1),s-=e,l++,r=0,a.writing||setImmediate(a._triggerWrite.bind(a))}}async read(t,e){let a=new Uint8Array(t);return await this.readToBuffer(a,0,t,e),a}async readToBuffer(t,e,a,i){if(0==a)return;const o=this;if(a>o.pageSize*o.maxPagesLoaded*.8){const t=Math.floor(1.1*a);this.maxPagesLoaded=Math.floor(t/o.pageSize)+1}if(void 0===i&&(i=o.pos),o.pos=i+a,o.pendingClose)throw new Error("Reading a closing file");const n=Math.floor(i/o.pageSize),l=Math.floor((i+a-1)/o.pageSize),r=[];for(let t=n;t<=l;t++)r.push(o._loadPage(t));o._triggerLoad();let s=n,c=i%o.pageSize,d=i+a>o.totalSize?a-(i+a-o.totalSize):a;for(;d>0;){await r[s-n],o.__statusPage("After Await (read): ",s);const i=c+d>o.pageSize?o.pageSize-c:d,l=new Uint8Array(o.pages[s].buff.buffer,o.pages[s].buff.byteOffset+c,i);t.set(l,e+a-d),o.pages[s].pendingOps--,o.__statusPage("After Op done: ",s),d-=i,s++,c=0,o.pendingLoads.length>0&&setImmediate(o._triggerLoad.bind(o))}this.pos=i+a}_tryClose(){const t=this;if(!t.pendingClose)return;t.error&&t.pendingCloseReject(t.error);t._getDirtyPage()>=0||t.writing||t.reading||t.pendingLoads.length>0||t.pendingClose()}close(){const t=this;if(t.pendingClose)throw new Error("Closing the file twice");return new Promise(((e,a)=>{t.pendingClose=e,t.pendingCloseReject=a,t._tryClose()})).then((()=>{t.fd.close()}),(e=>{throw t.fd.close(),e}))}async discard(){await this.close(),await wa.promises.unlink(this.fileName)}async writeULE32(t,e){const a=new Uint8Array(4);new DataView(a.buffer).setUint32(0,t,!0),await this.write(a,e)}async writeUBE32(t,e){const a=new Uint8Array(4);new DataView(a.buffer).setUint32(0,t,!1),await this.write(a,e)}async writeULE64(t,e){const a=new Uint8Array(8),i=new DataView(a.buffer);i.setUint32(0,4294967295&t,!0),i.setUint32(4,Math.floor(t/4294967296),!0),await this.write(a,e)}async readULE32(t){const e=await this.read(4,t);return new Uint32Array(e.buffer)[0]}async readUBE32(t){const e=await this.read(4,t);return new DataView(e.buffer).getUint32(0,!1)}async readULE64(t){const e=await this.read(8,t),a=new Uint32Array(e.buffer);return 4294967296*a[1]+a[0]}async readString(t){const e=this;if(e.pendingClose)throw new Error("Reading a closing file");let a=void 0===t?e.pos:t,i=Math.floor(a/e.pageSize),o=!1,n="";for(;!o;){let t=e._loadPage(i);e._triggerLoad(),await t,e.__statusPage("After Await (read): ",i);let l=a%e.pageSize;const r=new Uint8Array(e.pages[i].buff.buffer,e.pages[i].buff.byteOffset+l,e.pageSize-l);let s=r.findIndex((t=>0===t));o=-1!==s,o?(n+=(new TextDecoder).decode(r.slice(0,s)),e.pos=i*this.pageSize+l+s+1):(n+=(new TextDecoder).decode(r),e.pos=i*this.pageSize+l+r.length),e.pages[i].pendingOps--,e.__statusPage("After Op done: ",i),a=e.pos,i++,e.pendingLoads.length>0&&setImmediate(e._triggerLoad.bind(e))}return n}}const Aa=new Uint8Array(4),ya=new DataView(Aa.buffer),Ca=new Uint8Array(8),Ia=new DataView(Ca.buffer);class Fa{constructor(){this.pageSize=16384}_resizeIfNeeded(t){if(t>this.allocSize){const e=Math.max(this.allocSize+(1<<20),Math.floor(1.1*this.allocSize),t),a=new Uint8Array(e);a.set(this.o.data),this.o.data=a,this.allocSize=e}}async write(t,e){if(void 0===e&&(e=this.pos),this.readOnly)throw new Error("Writing a read only file");this._resizeIfNeeded(e+t.byteLength),this.o.data.set(t.slice(),e),e+t.byteLength>this.totalSize&&(this.totalSize=e+t.byteLength),this.pos=e+t.byteLength}async readToBuffer(t,e,a,i){if(void 0===i&&(i=this.pos),this.readOnly&&i+a>this.totalSize)throw new Error("Reading out of bounds");this._resizeIfNeeded(i+a);const o=new Uint8Array(this.o.data.buffer,this.o.data.byteOffset+i,a);t.set(o,e),this.pos=i+a}async read(t,e){const a=new Uint8Array(t);return await this.readToBuffer(a,0,t,e),a}close(){this.o.data.byteLength!=this.totalSize&&(this.o.data=this.o.data.slice(0,this.totalSize))}async discard(){}async writeULE32(t,e){ya.setUint32(0,t,!0),await this.write(Aa,e)}async writeUBE32(t,e){ya.setUint32(0,t,!1),await this.write(Aa,e)}async writeULE64(t,e){Ia.setUint32(0,4294967295&t,!0),Ia.setUint32(4,Math.floor(t/4294967296),!0),await this.write(Ca,e)}async readULE32(t){const e=await this.read(4,t);return new Uint32Array(e.buffer)[0]}async readUBE32(t){const e=await this.read(4,t);return new DataView(e.buffer).getUint32(0,!1)}async readULE64(t){const e=await this.read(8,t),a=new Uint32Array(e.buffer);return 4294967296*a[1]+a[0]}async readString(t){const e=this;let a=void 0===t?e.pos:t;if(a>this.totalSize){if(this.readOnly)throw new Error("Reading out of bounds");this._resizeIfNeeded(t)}const i=new Uint8Array(e.o.data.buffer,a,this.totalSize-a);let o=i.findIndex((t=>0===t)),n="";return-1!==o?(n=(new TextDecoder).decode(i.slice(0,o)),e.pos=a+o+1):e.pos=a,n}}const xa=1<<22;const Ea=new Uint8Array(4),va=new DataView(Ea.buffer),Ba=new Uint8Array(8),Sa=new DataView(Ba.buffer);class Pa{constructor(){this.pageSize=16384}_resizeIfNeeded(t){if(t<=this.totalSize)return;if(this.readOnly)throw new Error("Reading out of file bounds");const e=Math.floor((t-1)/xa)+1;for(let a=Math.max(this.o.data.length-1,0);a0;){const e=o+n>xa?xa-o:n,l=t.slice(t.byteLength-n,t.byteLength-n+e);new Uint8Array(a.o.data[i].buffer,o,e).set(l),n-=e,i++,o=0}this.pos=e+t.byteLength}async readToBuffer(t,e,a,i){const o=this;if(void 0===i&&(i=o.pos),this.readOnly&&i+a>this.totalSize)throw new Error("Reading out of bounds");this._resizeIfNeeded(i+a);let n=Math.floor(i/xa),l=i%xa,r=a;for(;r>0;){const i=l+r>xa?xa-l:r,s=new Uint8Array(o.o.data[n].buffer,l,i);t.set(s,e+a-r),r-=i,n++,l=0}this.pos=i+a}async read(t,e){const a=new Uint8Array(t);return await this.readToBuffer(a,0,t,e),a}close(){}async discard(){}async writeULE32(t,e){va.setUint32(0,t,!0),await this.write(Ea,e)}async writeUBE32(t,e){va.setUint32(0,t,!1),await this.write(Ea,e)}async writeULE64(t,e){Sa.setUint32(0,4294967295&t,!0),Sa.setUint32(4,Math.floor(t/4294967296),!0),await this.write(Ba,e)}async readULE32(t){const e=await this.read(4,t);return new Uint32Array(e.buffer)[0]}async readUBE32(t){const e=await this.read(4,t);return new DataView(e.buffer).getUint32(0,!1)}async readULE64(t){const e=await this.read(8,t),a=new Uint32Array(e.buffer);return 4294967296*a[1]+a[0]}async readString(t){const e=this;let a=void 0===t?e.pos:t;if(a>this.totalSize){if(this.readOnly)throw new Error("Reading out of bounds");this._resizeIfNeeded(t)}let i=!1,o="";for(;!i;){let t=Math.floor(a/xa),n=a%xa;if(void 0===e.o.data[t])throw new Error("ERROR");let l=Math.min(2048,e.o.data[t].length-n);const r=new Uint8Array(e.o.data[t].buffer,n,l);let s=r.findIndex((t=>0===t));i=-1!==s,i?(o+=(new TextDecoder).decode(r.slice(0,s)),e.pos=t*xa+n+s+1):(o+=(new TextDecoder).decode(r),e.pos=t*xa+n+r.length),a=e.pos}return o}}const Ga=1024,za=512,Oa=2,Ua=0,Qa=65536,Ta=8192;async function qa(t,e,a){if("string"==typeof t&&(t={type:"file",fileName:t,cacheSize:e||Qa,pageSize:a||Ta}),"file"==t.type)return await La(t.fileName,Ga|za|Oa,t.cacheSize,t.pageSize);if("mem"==t.type)return function(t){const e=t.initialSize||1<<20,a=new Fa;return a.o=t,a.o.data=new Uint8Array(e),a.allocSize=e,a.totalSize=0,a.readOnly=!1,a.pos=0,a}(t);if("bigMem"==t.type)return function(t){const e=t.initialSize||0,a=new Pa;a.o=t;const i=e?Math.floor((e-1)/xa)+1:0;a.o.data=[];for(let t=0;ta)throw new Error("Version not supported");const s=await n.readULE32();let c=[];for(let t=0;t1)throw new Error(t.fileName+": Section Duplicated "+a);t.pos=e[a][0].p,t.readingSection=e[a][0]}async function $a(t,e){if(void 0===t.readingSection)throw new Error("Not reading a section");if(!e&&t.pos-t.readingSection.p!=t.readingSection.size)throw new Error("Invalid section size reading");delete t.readingSection}async function ja(t,e,a,i){const o=new Uint8Array(a);pa.toRprLE(o,0,e,a),await t.write(o,i)}async function Ka(t,e,a){const i=await t.read(e,a);return pa.fromRprLE(i,0,e)}async function Ha(t,e,a,i,o){void 0===o&&(o=e[i][0].size);const n=t.pageSize;await Va(t,e,i),await Da(a,i);for(let e=0;ee[a][0].size)throw new Error("Reading out of the range of the section");let n;return n=o<1<<30?new Uint8Array(o):new Ge(o),await t.readToBuffer(n,0,o,e[a][0].p+i),n}async function Wa(t,e,a,i,o){const n=16*t.pageSize;if(await Va(t,e,o),await Va(a,i,o),e[o][0].size!=i[o][0].size)return!1;const l=e[o][0].size;for(let e=0;e=0)e=await ga();else{if(!(["BLS12381"].indexOf(a)>=0))throw new Error(`Curve not supported: ${t}`);e=await fa()}return e}var ii={exports:{}},oi=function t(e,a){if(!e){var 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")}}),a=e(),i=WebAssembly.compile(a);return Ai=async t=>(await WebAssembly.instantiate(await i,t)).exports}()().then((t=>{xi=t})),vi=64,Bi=[];ii.exports=Qi;var Si=ii.exports.BYTES_MIN=16,Pi=ii.exports.BYTES_MAX=64;ii.exports.BYTES=32;var Gi=ii.exports.KEYBYTES_MIN=16,zi=ii.exports.KEYBYTES_MAX=64;ii.exports.KEYBYTES=32;var Oi=ii.exports.SALTBYTES=16,Ui=ii.exports.PERSONALBYTES=16;function Qi(t,e,a,i,o){if(!(this instanceof Qi))return new Qi(t,e,a,i,o);if(!xi)throw new Error("WASM not loaded. Wait for Blake2b.ready(cb)");t||(t=32),!0!==o&&(Ii(t>=Si,"digestLength must be at least "+Si+", was given "+t),Ii(t<=Pi,"digestLength must be at most "+Pi+", was given "+t),null!=e&&(Ii(e instanceof Uint8Array,"key must be Uint8Array or Buffer"),Ii(e.length>=Gi,"key must be at least "+Gi+", was given "+e.length),Ii(e.length<=zi,"key must be at least "+zi+", was given "+e.length)),null!=a&&(Ii(a instanceof Uint8Array,"salt must be Uint8Array or Buffer"),Ii(a.length===Oi,"salt must be exactly "+Oi+", was given "+a.length)),null!=i&&(Ii(i instanceof Uint8Array,"personal must be Uint8Array or Buffer"),Ii(i.length===Ui,"personal must be exactly "+Ui+", was given "+i.length))),Bi.length||(Bi.push(vi),vi+=216),this.digestLength=t,this.finalized=!1,this.pointer=Bi.pop(),this._memory=new Uint8Array(xi.memory.buffer),this._memory.fill(0,0,64),this._memory[0]=this.digestLength,this._memory[1]=e?e.length:0,this._memory[2]=1,this._memory[3]=1,a&&this._memory.set(a,32),i&&this._memory.set(i,48),this.pointer+216>this._memory.length&&this._realloc(this.pointer+216),xi.blake2b_init(this.pointer,this.digestLength),e&&(this.update(e),this._memory.fill(0,vi,vi+e.length),this._memory[this.pointer+200]=128)}function Ti(){}function qi(t){return(0!=(4294901760&t)?(t&=4294901760,16):0)|(0!=(4278255360&t)?(t&=4278255360,8):0)|(0!=(4042322160&t)?(t&=4042322160,4):0)|(0!=(3435973836&t)?(t&=3435973836,2):0)|0!=(2863311530&t)}function Mi(t,e){const a=new DataView(t.buffer,t.byteOffset,t.byteLength);let i="";for(let t=0;t<4;t++){t>0&&(i+="\n"),i+="\t\t";for(let e=0;e<4;e++)e>0&&(i+=" "),i+=a.getUint32(16*t+4*e).toString(16).padStart(8,"0")}return e&&(i=e+"\n"+i),i}function ki(t,e){if(t.byteLength!=e.byteLength)return!1;for(var a=new Int8Array(t),i=new Int8Array(e),o=0;o!=t.byteLength;o++)if(a[o]!=i[o])return!1;return!0}function Ri(t){const e=t.getPartialHash(),a=ii.exports(64);return a.setPartialHash(e),a}async function Di(t,e,a,i,o){if(t.G1.isZero(e))return!1;if(t.G1.isZero(a))return!1;if(t.G2.isZero(i))return!1;if(t.G2.isZero(o))return!1;return await t.pairingEq(e,o,t.G1.neg(a),i)}async function Ni(t){for(;!t;)t=await window.prompt("Enter a random text. (Entropy): ","");const e=ii.exports(64);e.update(q.randomBytes(64));const a=new TextEncoder;e.update(a.encode(t));const i=Buffer.from(e.digest()),o=[];for(let t=0;t<8;t++)o[t]=i.readUInt32BE(4*t);return new T(o)}function Vi(t,e){let a,i;e<32?(a=1<>>0,i=1):(a=4294967296,i=1<>>0);let o=t;for(let t=0;t{a[i]=Ki(t,e[i])})),a}return"bigint"==typeof e||void 0!==e.eq?e.toString(10):e}Qi.prototype._realloc=function(t){xi.memory.grow(Math.max(0,Math.ceil(Math.abs(t-this._memory.length)/65536))),this._memory=new Uint8Array(xi.memory.buffer)},Qi.prototype.update=function(t){return Ii(!1===this.finalized,"Hash instance finalized"),Ii(t instanceof Uint8Array,"input must be Uint8Array or Buffer"),vi+t.length>this._memory.length&&this._realloc(vi+t.length),this._memory.set(t,vi),xi.blake2b_update(this.pointer,vi,vi+t.length),this},Qi.prototype.digest=function(t){if(Ii(!1===this.finalized,"Hash instance finalized"),this.finalized=!0,Bi.push(this.pointer),xi.blake2b_final(this.pointer),!t||"binary"===t)return this._memory.slice(this.pointer+128,this.pointer+128+this.digestLength);if("string"==typeof t)return Fi.toString(this._memory,t,this.pointer+128,this.pointer+128+this.digestLength);Ii(t instanceof Uint8Array&&t.length>=this.digestLength,"input must be Uint8Array or Buffer");for(var e=0;et()),t):t(new Error("WebAssembly not supported"))},Qi.prototype.ready=Qi.ready,Qi.prototype.getPartialHash=function(){return this._memory.slice(this.pointer,this.pointer+216)},Qi.prototype.setPartialHash=function(t){this._memory.set(t,this.pointer)};const Hi=1,Zi=1,Wi=2,Yi=10,Ji=3,Xi=17,to=2,eo=3,ao=4,io=5,oo=6,no=7,lo=8,ro=9,so=10,co=11,uo=12,go=13,fo=14,ho=15,_o=16,po=17;async function mo(t,e){await Da(t,1),await t.writeULE32(1),await Na(t);const a=await ei(e.q);await Da(t,2);const i=a.q,o=8*(Math.floor((pa.bitLength(i)-1)/64)+1),n=a.r,l=8*(Math.floor((pa.bitLength(n)-1)/64)+1);await t.writeULE32(o),await ja(t,i,o),await t.writeULE32(l),await ja(t,n,l),await t.writeULE32(e.nVars),await t.writeULE32(e.nPublic),await t.writeULE32(e.domainSize),await wo(t,a,e.vk_alpha_1),await wo(t,a,e.vk_beta_1),await Lo(t,a,e.vk_beta_2),await Lo(t,a,e.vk_gamma_2),await wo(t,a,e.vk_delta_1),await Lo(t,a,e.vk_delta_2),await Na(t)}async function wo(t,e,a){const i=new Uint8Array(2*e.G1.F.n8);e.G1.toRprLEM(i,0,a),await t.write(i)}async function Lo(t,e,a){const i=new Uint8Array(2*e.G2.F.n8);e.G2.toRprLEM(i,0,a),await t.write(i)}async function bo(t,e,a){const i=await t.read(2*e.G1.F.n8),o=e.G1.fromRprLEM(i,0);return a?e.G1.toObject(o):o}async function Ao(t,e,a){const i=await t.read(2*e.G2.F.n8),o=e.G2.fromRprLEM(i,0);return a?e.G2.toObject(o):o}async function yo(t,e,a){await Va(t,e,1);const i=await t.readULE32();if(await $a(t),i===Zi)return await async function(t,e,a){const i={protocol:"groth16"};await Va(t,e,2);const o=await t.readULE32();i.n8q=o,i.q=await Ka(t,o);const n=await t.readULE32();return i.n8r=n,i.r=await Ka(t,n),i.curve=await ei(i.q),i.nVars=await t.readULE32(),i.nPublic=await t.readULE32(),i.domainSize=await t.readULE32(),i.power=qi(i.domainSize),i.vk_alpha_1=await bo(t,i.curve,a),i.vk_beta_1=await bo(t,i.curve,a),i.vk_beta_2=await Ao(t,i.curve,a),i.vk_gamma_2=await Ao(t,i.curve,a),i.vk_delta_1=await bo(t,i.curve,a),i.vk_delta_2=await Ao(t,i.curve,a),await $a(t),i}(t,e,a);if(i===Wi)return await async function(t,e,a){const i={protocol:"plonk"};await Va(t,e,2);const o=await t.readULE32();i.n8q=o,i.q=await Ka(t,o);const n=await t.readULE32();return i.n8r=n,i.r=await Ka(t,n),i.curve=await ei(i.q),i.nVars=await t.readULE32(),i.nPublic=await t.readULE32(),i.domainSize=await t.readULE32(),i.power=qi(i.domainSize),i.nAdditions=await t.readULE32(),i.nConstrains=await t.readULE32(),i.k1=await t.read(n),i.k2=await t.read(n),i.Qm=await bo(t,i.curve,a),i.Ql=await bo(t,i.curve,a),i.Qr=await bo(t,i.curve,a),i.Qo=await bo(t,i.curve,a),i.Qc=await bo(t,i.curve,a),i.S1=await bo(t,i.curve,a),i.S2=await bo(t,i.curve,a),i.S3=await bo(t,i.curve,a),i.X_2=await Ao(t,i.curve,a),await $a(t),i}(t,e,a);if(i===Yi)return await async function(t,e,a){const i={protocol:"fflonk"};i.protocolId=Yi,await Va(t,e,to);const o=await t.readULE32();i.n8q=o,i.q=await Ka(t,o),i.curve=await ei(i.q);const n=await t.readULE32();return i.n8r=n,i.r=await Ka(t,n),i.nVars=await t.readULE32(),i.nPublic=await t.readULE32(),i.domainSize=await t.readULE32(),i.power=qi(i.domainSize),i.nAdditions=await t.readULE32(),i.nConstraints=await t.readULE32(),i.k1=await t.read(n),i.k2=await t.read(n),i.w3=await t.read(n),i.w4=await t.read(n),i.w8=await t.read(n),i.wr=await t.read(n),i.X_2=await Ao(t,i.curve,a),i.C0=await bo(t,i.curve,a),await $a(t),i}(t,e,a);throw new Error("Protocol not supported: ")}async function Co(t,e,a){const i={delta:{}};i.deltaAfter=await bo(t,e,a),i.delta.g1_s=await bo(t,e,a),i.delta.g1_sx=await bo(t,e,a),i.delta.g2_spx=await Ao(t,e,a),i.transcript=await t.read(64),i.type=await t.readULE32();const o=await t.readULE32(),n=t.pos;let l=0;for(;t.pos-n0){const e=new Uint8Array(i);await t.writeULE32(e.byteLength),await t.write(e)}else await t.writeULE32(0)}async function xo(t,e,a){await Da(t,10),await t.write(a.csHash),await t.writeULE32(a.contributions.length);for(let i=0;i0;)a.unshift(0),n--;return a}async function Uo(t,e){e=e||{};let a,i=32767,o=!1;for(;!o;)try{a=new WebAssembly.Memory({initial:i}),o=!0}catch(t){if(1===i)throw t;console.warn("Could not allocate "+1024*i*64+" bytes. This may cause severe instability. Trying with "+1024*i*64/2+" bytes"),i=Math.floor(i/2)}const n=await WebAssembly.compile(t);let l,r="",s="",c=1,d=0,u=0;const g=await WebAssembly.instantiate(n,{env:{memory:a},runtime:{exceptionHandler:function(t){let e;throw e=1==t?"Signal not found. ":2==t?"Too many signals set. ":3==t?"Signal already set. ":4==t?"Assert Failed. ":5==t?"Not enough memory. ":6==t?"Input signal array access exceeds the size. ":"Unknown error. ",console.error("ERROR: ",t,r),new Error(e+r)},printErrorMessage:function(){r+=h()+"\n"},writeBufferMessage:function(){const t=h();"\n"===t?(console.log(s),s=""):(""!==s&&(s+=" "),s+=t)},showSharedRWMemory:function(){const t=g.exports.getFieldNumLen32(),e=new Uint32Array(t);for(let a=0;a=2&&(d>=1||u>=7)){""!==s&&(s+=" ");const t=pa.fromArray(e,4294967296).toString();s+=t}else console.log(pa.fromArray(e,4294967296))},error:function(t,a,i,o,n,r){let s;throw s=7==t?_(a)+" "+l.getFr(o).toString()+" != "+l.getFr(n).toString()+" "+_(r):9==t?_(a)+" "+l.getFr(o).toString()+" "+_(n):5==t&&e.sym?_(a)+" "+e.sym.labelIdx2Name[n]:_(a)+" "+i+" "+o+" "+n+" "+r,console.log("ERROR: ",t,s),new Error(s)},log:function(t){console.log(l.getFr(t).toString())},logGetSignal:function(t,a){e.logGetSignal&&e.logGetSignal(t,l.getFr(a))},logSetSignal:function(t,a){e.logSetSignal&&e.logSetSignal(t,l.getFr(a))},logStartComponent:function(t){e.logStartComponent&&e.logStartComponent(t)},logFinishComponent:function(t){e.logFinishComponent&&e.logFinishComponent(t)}}});"function"==typeof g.exports.getVersion&&(c=g.exports.getVersion()),"function"==typeof g.exports.getMinorVersion&&(d=g.exports.getMinorVersion()),"function"==typeof g.exports.getPatchVersion&&(u=g.exports.getPatchVersion());const f=e&&(e.sanityCheck||e.logGetSignal||e.logSetSignal||e.logStartComponent||e.logFinishComponent);return l=2===c?new To(g,f):new Qo(a,g,f),l;function h(){for(var t="",e=g.exports.getMessageChar();0!=e;)t+=String.fromCharCode(e),e=g.exports.getMessageChar();return t}function _(t){const e=new Uint8Array(a.buffer),i=[];for(let a=0;e[t+a]>0;a++)i.push(e[t+a]);return String.fromCharCode.apply(null,i)}}class Qo{constructor(t,e,a){this.memory=t,this.i32=new Uint32Array(t.buffer),this.instance=e,this.n32=(this.instance.exports.getFrLen()>>2)-2;const i=this.instance.exports.getPRawPrime(),o=new Array(this.n32);for(let t=0;t>2)+t];this.prime=pa.fromArray(o,4294967296),this.Fr=new $(this.prime),this.mask32=pa.fromString("FFFFFFFF",16),this.NVars=this.instance.exports.getNVars(),this.n64=Math.floor((this.Fr.bitLength-1)/64)+1,this.R=this.Fr.e(pa.shiftLeft(1,64*this.n64)),this.RInv=this.Fr.inv(this.R),this.sanityCheck=a}circom_version(){return 1}async _doCalculateWitness(t,e){this.instance.exports.init(this.sanityCheck||e?1:0);const a=this.allocInt(),i=this.allocFr();Object.keys(t).forEach((e=>{const o=zo(e),n=parseInt(o.slice(0,8),16),l=parseInt(o.slice(8,16),16);try{this.instance.exports.getSignalOffset32(a,0,n,l)}catch(t){throw new Error(`Signal ${e} is not an input of the circuit.`)}const r=this.getInt(a),s=Go(t[e]);for(let t=0;t>2]}setInt(t,e){this.i32[t>>2]=e}getFr(t){const e=this,a=t>>2;if(2147483648&e.i32[a+1]){const t=new Array(e.n32);for(let i=0;i>2]=o,void(a.i32[1+(t>>2)]=0)}a.i32[t>>2]=0,a.i32[1+(t>>2)]=2147483648;const n=pa.toArray(e,4294967296);for(let e=0;e>2)+e]=i>=0?n[i]:0}}}class To{constructor(t,e){this.instance=t,this.version=this.instance.exports.getVersion(),this.n32=this.instance.exports.getFieldNumLen32(),this.instance.exports.getRawPrime();const a=new Array(this.n32);for(let t=0;t{const a=zo(e),o=parseInt(a.slice(0,8),16),n=parseInt(a.slice(8,16),16),l=Go(t[e]);for(let t=0;t1)throw new Error(t.fileName+": File has more than one header");t.pos=e[1][0].p;const a=await t.readULE32(),i=await t.read(a),o=pa.fromRprLE(i),n=await ei(o);if(8*n.F1.n64!=a)throw new Error(t.fileName+": Invalid size");const l=await t.readULE32(),r=await t.readULE32();if(t.pos-e[1][0].p!=e[1][0].size)throw new Error("Invalid PTau header size");return{curve:n,power:l,ceremonyPower:r}}function Yo(t,e,a,i){const o={tau:{},alpha:{},beta:{}};return o.tau.g1_s=n(),o.tau.g1_sx=n(),o.alpha.g1_s=n(),o.alpha.g1_sx=n(),o.beta.g1_s=n(),o.beta.g1_sx=n(),o.tau.g2_spx=l(),o.alpha.g2_spx=l(),o.beta.g2_spx=l(),o;function n(){let o;return o=i?a.G1.fromRprLEM(t,e):a.G1.fromRprUncompressed(t,e),e+=2*a.G1.F.n8,o}function l(){let o;return o=i?a.G2.fromRprLEM(t,e):a.G2.fromRprUncompressed(t,e),e+=2*a.G2.F.n8,o}}function Jo(t,e,a,i,o){async function n(i){o?a.G1.toRprLEM(t,e,i):a.G1.toRprUncompressed(t,e,i),e+=2*a.F1.n8}async function l(i){o?a.G2.toRprLEM(t,e,i):a.G2.toRprUncompressed(t,e,i),e+=2*a.F2.n8}return n(i.tau.g1_s),n(i.tau.g1_sx),n(i.alpha.g1_s),n(i.alpha.g1_sx),n(i.beta.g1_s),n(i.beta.g1_sx),l(i.tau.g2_spx),l(i.alpha.g2_spx),l(i.beta.g2_spx),t}async function Xo(t,e){const a={};a.tauG1=await s(),a.tauG2=await c(),a.alphaG1=await s(),a.betaG1=await s(),a.betaG2=await c(),a.key=await async function(t,e,a){return Yo(await t.read(2*e.F1.n8*6+2*e.F2.n8*3),0,e,a)}(t,e,!0),a.partialHash=await t.read(216),a.nextChallenge=await t.read(64),a.type=await t.readULE32();const i=new Uint8Array(2*e.G1.F.n8*6+2*e.G2.F.n8*3);Jo(i,0,e,a.key,!1);const o=ii.exports(64);o.setPartialHash(a.partialHash),o.update(i),a.responseHash=o.digest();const n=await t.readULE32(),l=t.pos;let r=0;for(;t.pos-l1)throw new Error(t.fileName+": File has more than one contributions section");t.pos=a[7][0].p;const i=await t.readULE32(),o=[];for(let a=0;a0){const e=new Uint8Array(n);await t.writeULE32(e.byteLength),await t.write(e)}else await t.writeULE32(0);async function l(a){e.G1.toRprLEM(i,0,a),await t.write(i)}async function r(a){e.G2.toRprLEM(o,0,a),await t.write(o)}}async function an(t,e,a){await t.writeULE32(7);const i=t.pos;await t.writeULE64(0),await t.writeULE32(a.length);for(let i=0;i0?u[u.length-1].nextChallenge:on(c,d,n);const L=await Ra(a,"ptau",1,o?7:2);await Zo(L,c,d);const b=await m.read(64);if(ki(l,w)&&(w=b,u[u.length-1].nextChallenge=w),!ki(b,w))throw new Error("Wrong contribution. this contribution is not based on the previus hash");const A=new ii.exports(64);A.update(b);const y=[];let C;C=await x(m,L,"G1",2,2**d*2-1,[1],"tauG1"),g.tauG1=C[0],C=await x(m,L,"G2",3,2**d,[1],"tauG2"),g.tauG2=C[0],C=await x(m,L,"G1",4,2**d,[0],"alphaG1"),g.alphaG1=C[0],C=await x(m,L,"G1",5,2**d,[0],"betaG1"),g.betaG1=C[0],C=await x(m,L,"G2",6,1,[0],"betaG2"),g.betaG2=C[0],g.partialHash=A.getPartialHash();const I=await m.read(2*c.F1.n8*6+2*c.F2.n8*3);g.key=Yo(I,0,c,!1),A.update(new Uint8Array(I));const F=A.digest();if(n&&n.info(Mi(F,"Contribution Response Hash imported: ")),o){const t=new ii.exports(64);t.update(F),await E(t,L,"G1",2,2**d*2-1,"tauG1",n),await E(t,L,"G2",3,2**d,"tauG2",n),await E(t,L,"G1",4,2**d,"alphaTauG1",n),await E(t,L,"G1",5,2**d,"betaTauG1",n),await E(t,L,"G2",6,1,"betaG2",n),g.nextChallenge=t.digest(),n&&n.info(Mi(g.nextChallenge,"Next Challenge Hash: "))}else g.nextChallenge=l;return u.push(g),await an(L,c,u),await m.close(),await L.close(),await r.close(),g.nextChallenge;async function x(t,e,a,i,l,r,s){return o?await async function(t,e,a,i,o,l,r){const s=c[a],d=s.F.n8,u=2*s.F.n8,g=[];await Da(e,i);const f=Math.floor((1<<24)/u);y[i]=e.pos;for(let a=0;a=a&&e=e&&o1?s[s.length-2]:c;const u=s[s.length-1];if(e&&e.debug("Validating contribution #"+s[s.length-1].id),!await rn(n,u,d,e))return!1;const g=ii.exports(64);g.update(u.responseHash),e&&e.debug("Verifying powers in tau*G1 section");const f=await b(2,"G1","tauG1",2**l*2-1,[0,1],e);if(a=await ln(n,f.R1,f.R2,n.G2.g,u.tauG2),!0!==a)return e&&e.error("tauG1 section. Powers do not match"),!1;if(!n.G1.eq(n.G1.g,f.singularPoints[0]))return e&&e.error("First element of tau*G1 section must be the generator"),!1;if(!n.G1.eq(u.tauG1,f.singularPoints[1]))return e&&e.error("Second element of tau*G1 section does not match the one in the contribution section"),!1;e&&e.debug("Verifying powers in tau*G2 section");const h=await b(3,"G2","tauG2",2**l,[0,1],e);if(a=await ln(n,n.G1.g,u.tauG1,h.R1,h.R2),!0!==a)return e&&e.error("tauG2 section. Powers do not match"),!1;if(!n.G2.eq(n.G2.g,h.singularPoints[0]))return e&&e.error("First element of tau*G2 section must be the generator"),!1;if(!n.G2.eq(u.tauG2,h.singularPoints[1]))return e&&e.error("Second element of tau*G2 section does not match the one in the contribution section"),!1;e&&e.debug("Verifying powers in alpha*tau*G1 section");const _=await b(4,"G1","alphatauG1",2**l,[0],e);if(a=await ln(n,_.R1,_.R2,n.G2.g,u.tauG2),!0!==a)return e&&e.error("alphaTauG1 section. Powers do not match"),!1;if(!n.G1.eq(u.alphaG1,_.singularPoints[0]))return e&&e.error("First element of alpha*tau*G1 section (alpha*G1) does not match the one in the contribution section"),!1;e&&e.debug("Verifying powers in beta*tau*G1 section");const p=await b(5,"G1","betatauG1",2**l,[0],e);if(a=await ln(n,p.R1,p.R2,n.G2.g,u.tauG2),!0!==a)return e&&e.error("betaTauG1 section. Powers do not match"),!1;if(!n.G1.eq(u.betaG1,p.singularPoints[0]))return e&&e.error("First element of beta*tau*G1 section (beta*G1) does not match the one in the contribution section"),!1;const m=await async function(t){const e=n.G2,a=2*e.F.n8,l=new Uint8Array(a);if(!o[6])throw t.error("File has no BetaG2 section"),new Error("File has no BetaG2 section");if(o[6].length>1)throw t.error("File has no BetaG2 section"),new Error("File has more than one GetaG2 section");i.pos=o[6][0].p;const r=await i.read(a),s=e.fromRprLEM(r);return e.toRprUncompressed(l,0,s),g.update(l),s}(e);if(!n.G2.eq(u.betaG2,m))return e&&e.error("betaG2 element in betaG2 section does not match the one in the contribution section"),!1;const w=g.digest();if(l==r&&!ki(w,u.nextChallenge))return e&&e.error("Hash of the values does not match the next challenge of the last contributor in the contributions section"),!1;e&&e.info(Mi(w,"Next challenge hash: ")),L(u,d);for(let t=s.length-2;t>=0;t--){const a=s[t],i=t>0?s[t-1]:c;if(!await rn(n,a,i,e))return!1;L(a,i)}if(e&&e.info("-----------------------------------------------------"),o[12]&&o[13]&&o[14]&&o[15]){let t;if(t=await A("G1",2,12,"tauG1",e),!t)return!1;if(t=await A("G2",3,13,"tauG2",e),!t)return!1;if(t=await A("G1",4,14,"alphaTauG1",e),!t)return!1;if(t=await A("G1",5,15,"betaTauG1",e),!t)return!1}else e&&e.warn('this file does not contain phase2 precalculated values. Please run: \n snarkjs "powersoftau preparephase2" to prepare this file to be used in the phase2 ceremony.');return await i.close(),e&&e.info("Powers of Tau Ok!"),!0;function L(t,a){if(!e)return;e.info("-----------------------------------------------------"),e.info(`Contribution #${t.id}: ${t.name||""}`),e.info(Mi(t.nextChallenge,"Next Challenge: "));const i=new Uint8Array(2*n.G1.F.n8*6+2*n.G2.F.n8*3);Jo(i,0,n,t.key,!1);const o=ii.exports(64);o.setPartialHash(t.partialHash),o.update(i);const l=o.digest();e.info(Mi(l,"Response Hash:")),e.info(Mi(a.nextChallenge,"Response Hash:")),1==t.type&&(e.info(`Beacon generator: ${ji(t.beaconHash)}`),e.info(`Beacon iterations Exp: ${t.numIterationsExp}`))}async function b(t,e,a,l,r,s){const c=n[e],d=2*c.F.n8;await Va(i,o,t);const u=[];let f=c.zero,h=c.zero,_=c.zero;for(let t=0;t0){const t=c.fromRprLEM(o,0),e=q.randomBytes(4).readUInt32BE(0,!0);f=c.add(f,c.timesScalar(_,e)),h=c.add(h,c.timesScalar(t,e))}const m=await c.multiExpAffine(o.slice(0,(e-1)*d),p),w=await c.multiExpAffine(o.slice(d),p);f=c.add(f,m),h=c.add(h,w),_=c.fromRprLEM(o,(e-1)*d);for(let a=0;a=t&&i1;)c/=2,d+=1;if(2**d!=s)throw new Error("Invalid file size");o&&o.debug("Power to tau size: "+d);const u=await Ni(i),g=await qa(a),f=ii.exports(64);for(let t=0;t{o.debug(e+".g1_s: "+t.G1.toString(p[e].g1_s,16)),o.debug(e+".g1_sx: "+t.G1.toString(p[e].g1_sx,16)),o.debug(e+".g2_sp: "+t.G2.toString(p[e].g2_sp,16)),o.debug(e+".g2_spx: "+t.G2.toString(p[e].g2_spx,16)),o.debug("")}));const m=ii.exports(64);await g.write(_),m.update(_),await cn(n,g,m,t,"G1",2**d*2-1,t.Fr.one,p.tau.prvKey,"COMPRESSED","tauG1",o),await cn(n,g,m,t,"G2",2**d,t.Fr.one,p.tau.prvKey,"COMPRESSED","tauG2",o),await cn(n,g,m,t,"G1",2**d,p.alpha.prvKey,p.tau.prvKey,"COMPRESSED","alphaTauG1",o),await cn(n,g,m,t,"G1",2**d,p.beta.prvKey,p.tau.prvKey,"COMPRESSED","betaTauG1",o),await cn(n,g,m,t,"G2",1,p.beta.prvKey,p.tau.prvKey,"COMPRESSED","betaTauG2",o);const w=new Uint8Array(2*t.F1.n8*6+2*t.F2.n8*3);Jo(w,0,t,p,!1),await g.write(w),m.update(w);const L=m.digest();o&&o.info(Mi(L,"Contribution Response Hash: ")),await g.close(),await n.close()},beacon:async function(t,e,a,i,o,n){const l=$i(i);if(0==l.byteLength||2*l.byteLength!=i.length)return n&&n.error("Invalid Beacon Hash. (It must be a valid hexadecimal sequence)"),!1;if(l.length>=256)return n&&n.error("Maximum lenght of beacon hash is 255 bytes"),!1;if((o=parseInt(o))<10||o>63)return n&&n.error("Invalid numIterationsExp. (Must be between 10 and 63)"),!1;await ii.exports.ready();const{fd:r,sections:s}=await ka(t,"ptau",1),{curve:c,power:d,ceremonyPower:u}=await Wo(r,s);if(d!=u)return n&&n.error("This file has been reduced. You cannot contribute into a reduced file."),!1;s[12]&&n&&n.warn("Contributing into a file that has phase2 calculated. You will have to prepare phase2 again.");const g=await tn(r,c,s),f={name:a,type:1,numIterationsExp:o,beaconHash:l};let h;h=g.length>0?g[g.length-1].nextChallenge:on(c,d,n),f.key=nn(c,h,l,o);const _=new ii.exports(64);_.update(h);const p=await Ra(e,"ptau",1,7);await Zo(p,c,d);const m=[];let w;w=await y(2,"G1",2**d*2-1,c.Fr.e(1),f.key.tau.prvKey,"tauG1",n),f.tauG1=w[1],w=await y(3,"G2",2**d,c.Fr.e(1),f.key.tau.prvKey,"tauG2",n),f.tauG2=w[1],w=await y(4,"G1",2**d,f.key.alpha.prvKey,f.key.tau.prvKey,"alphaTauG1",n),f.alphaG1=w[0],w=await y(5,"G1",2**d,f.key.beta.prvKey,f.key.tau.prvKey,"betaTauG1",n),f.betaG1=w[0],w=await y(6,"G2",1,f.key.beta.prvKey,f.key.tau.prvKey,"betaTauG2",n),f.betaG2=w[0],f.partialHash=_.getPartialHash();const L=new Uint8Array(2*c.F1.n8*6+2*c.F2.n8*3);Jo(L,0,c,f.key,!1),_.update(new Uint8Array(L));const b=_.digest();n&&n.info(Mi(b,"Contribution Response Hash imported: "));const A=new ii.exports(64);return A.update(b),await C(p,"G1",2,2**d*2-1,"tauG1",n),await C(p,"G2",3,2**d,"tauG2",n),await C(p,"G1",4,2**d,"alphaTauG1",n),await C(p,"G1",5,2**d,"betaTauG1",n),await C(p,"G2",6,1,"betaG2",n),f.nextChallenge=A.digest(),n&&n.info(Mi(f.nextChallenge,"Next Challenge Hash: ")),g.push(f),await an(p,c,g),await r.close(),await p.close(),b;async function y(t,e,a,i,o,n,l){const d=[];r.pos=s[t][0].p,await Da(p,t),m[t]=p.pos;const u=c[e],g=2*u.F.n8,f=Math.floor((1<<20)/g);let h=i;for(let t=0;t0?d[d.length-1].nextChallenge:on(r,s,o),u.key=Ho(r,g,f);const h=new ii.exports(64);h.update(g);const _=await Ra(e,"ptau",1,7);await Zo(_,r,s);const p=[];let m;m=await A(2,"G1",2**s*2-1,r.Fr.e(1),u.key.tau.prvKey,"tauG1"),u.tauG1=m[1],m=await A(3,"G2",2**s,r.Fr.e(1),u.key.tau.prvKey,"tauG2"),u.tauG2=m[1],m=await A(4,"G1",2**s,u.key.alpha.prvKey,u.key.tau.prvKey,"alphaTauG1"),u.alphaG1=m[0],m=await A(5,"G1",2**s,u.key.beta.prvKey,u.key.tau.prvKey,"betaTauG1"),u.betaG1=m[0],m=await A(6,"G2",1,u.key.beta.prvKey,u.key.tau.prvKey,"betaTauG2"),u.betaG2=m[0],u.partialHash=h.getPartialHash();const w=new Uint8Array(2*r.F1.n8*6+2*r.F2.n8*3);Jo(w,0,r,u.key,!1),h.update(new Uint8Array(w));const L=h.digest();o&&o.info(Mi(L,"Contribution Response Hash imported: "));const b=new ii.exports(64);return b.update(L),await y(_,"G1",2,2**s*2-1,"tauG1"),await y(_,"G2",3,2**s,"tauG2"),await y(_,"G1",4,2**s,"alphaTauG1"),await y(_,"G1",5,2**s,"betaTauG1"),await y(_,"G2",6,1,"betaG2"),u.nextChallenge=b.digest(),o&&o.info(Mi(u.nextChallenge,"Next Challenge Hash: ")),d.push(u),await an(_,r,d),await n.close(),await _.close(),L;async function A(t,e,a,i,s,c){const d=[];n.pos=l[t][0].p,await Da(_,t),p[t]=_.pos;const u=r[e],g=2*u.F.n8,f=Math.floor((1<<20)/g);let m=i;for(let t=0;t=this.length&&(this.length=t+1),!0}getKeys(){const t=new hn;for(let e=0;e1<<20?new hn:[];for(let t=0;t1<<20?new hn:[];for(let t=0;t1<<20?new hn:[];for(let t=0;t{let i="";return Object.keys(a).forEach((o=>{let n=e.varIdx2Name[o];"one"==n&&(n="1");let l=t.curve.Fr.toString(a[o]);"1"==l&&(l=""),"-1"==l&&(l="-"),""!=i&&"-"!=l[0]&&(l="+"+l),""!=i&&(l=" "+l),i=i+l+n})),i},n=`[ ${o(i[0])} ] * [ ${o(i[1])} ] - [ ${o(i[2])} ] = 0`;a&&a.info(n)}},info:async function(t,e){const a=await Ln(t);return pa.eq(a.prime,An)?e&&e.info("Curve: bn-128"):pa.eq(a.prime,bn)?e&&e.info("Curve: bls12-381"):e&&e.info(`Unknown Curve. Prime: ${pa.toString(a.prime)}`),e&&e.info(`# of Wires: ${a.nVars}`),e&&e.info(`# of Constraints: ${a.nConstraints}`),e&&e.info(`# of Private Inputs: ${a.nPrvInputs}`),e&&e.info(`# of Public Inputs: ${a.nPubInputs}`),e&&e.info(`# of Labels: ${a.nLabels}`),e&&e.info(`# of Outputs: ${a.nOutputs}`),a},exportJson:async function(t,e){const a=await Ln(t,!0,!0,!0,e),i=a.curve.Fr;return delete a.curve,delete a.F,Ki(i,a)}});async function Cn(t){const e={labelIdx2Name:["one"],varIdx2Name:["one"],componentIdx2Name:[]},a=await Ma(t),i=await a.read(a.totalSize),o=new TextDecoder("utf-8").decode(i).split("\n");for(let t=0;t Reading r1cs file");const{fd:i,sections:o}=await ka(t,"r1cs",1),n=await wn(i,o,{loadConstraints:!1,loadCustomGates:!1});a&&a.info("> Reading witness file");const{fd:l,sections:r}=await ka(e,"wtns",2),s=await Bo(l,r);if(!pa.eq(n.prime,s.q))throw new Error("Curve of the witness does not match the curve of the proving key");const c=await Za(l,r,2);await l.close();const d=(await async function(t){let e;if(pa.eq(t,Ja))e=await ga();else{if(!pa.eq(t,Ya))throw new Error(`Curve not supported: ${pa.toString(t)}`);e=await fa()}return e}(n.prime)).Fr,u=d.n8,g=await Za(i,o,2);a&&(a.info("----------------------------"),a.info(" WITNESS CHECK"),a.info(` Curve: ${n.curve.name}`),a.info(` Vars (wires): ${n.nVars}`),a.info(` Ouputs: ${n.nOutputs}`),a.info(` Public Inputs: ${n.nPubInputs}`),a.info(` Private Inputs: ${n.nPrvInputs}`),a.info(` Labels: ${n.nLabels}`),a.info(` Constraints: ${n.nConstraints}`),a.info(` Custom Gates: ${n.useCustomGates}`),a.info("----------------------------")),a&&a.info("> Checking witness correctness");let f=0,h=!0;for(let t=0;t{const i=function(t){return d.fromRprLE(c.slice(t*u,t*u+u))}(a),o=t[a];e=d.add(e,d.mul(i,o))})),e}function p(){const t={},e=g.slice(f,f+4);f+=4;const a=new DataView(e.buffer).getUint32(0,!0),i=g.slice(f,f+(4+n.n8)*a);f+=(4+n.n8)*a;const o=new DataView(i.buffer);for(let e=0;e=this.length&&(this.length=t+1),!0}getKeys(){const t=new Bn;for(let e=0;eg)return i&&i.error(`circuit too big for this power of tau ceremony. ${_.nConstraints}*2 > 2**${g}`),-1;if(!d[12])return i&&i.error("Powers of tau is not prepared."),-1;const b=_.nOutputs+_.nPubInputs,A=2**L;await Da(p,1),await p.writeULE32(1),await Na(p),await Da(p,2);const y=u.q,C=8*(Math.floor((pa.bitLength(y)-1)/64)+1),I=u.r,F=8*(Math.floor((pa.bitLength(I)-1)/64)+1),x=pa.mod(pa.shl(1,8*F),I),E=u.Fr.e(pa.mod(pa.mul(x,x),I));let v,B,S;await p.writeULE32(C),await ja(p,y,C),await p.writeULE32(F),await ja(p,I,F),await p.writeULE32(_.nVars),await p.writeULE32(b),await p.writeULE32(A),v=await c.read(m,d[4][0].p),await p.write(v),v=await u.G1.batchLEMtoU(v),s.update(v),B=await c.read(m,d[5][0].p),await p.write(B),B=await u.G1.batchLEMtoU(B),s.update(B),S=await c.read(w,d[6][0].p),await p.write(S),S=await u.G2.batchLEMtoU(S),s.update(S);const P=new Uint8Array(m);u.G1.toRprLEM(P,0,u.G1.g);const G=new Uint8Array(w);u.G2.toRprLEM(G,0,u.G2.g);const z=new Uint8Array(m);u.G1.toRprUncompressed(z,0,u.G1.g);const O=new Uint8Array(w);u.G2.toRprUncompressed(O,0,u.G2.g),await p.write(G),await p.write(P),await p.write(G),s.update(O),s.update(z),s.update(O),await Na(p),i&&i.info("Reading r1cs");let U=await Za(f,h,2);const Q=new Bn(_.nVars),T=new Bn(_.nVars),q=new Bn(_.nVars),M=new Bn(_.nVars-b-1),k=new Array(b+1);i&&i.info("Reading tauG1");let R=await Za(c,d,12,(A-1)*m,A*m);i&&i.info("Reading tauG2");let D=await Za(c,d,13,(A-1)*w,A*w);i&&i.info("Reading alphatauG1");let N=await Za(c,d,14,(A-1)*m,A*m);i&&i.info("Reading betatauG1");let V=await Za(c,d,15,(A-1)*m,A*m);await async function(){const t=new Uint8Array(12+u.Fr.n8),e=new DataView(t.buffer),a=new Uint8Array(u.Fr.n8);u.Fr.toRprLE(a,0,u.Fr.e(1));let s=0;function c(){const t=U.slice(s,s+4);s+=4;return new DataView(t.buffer).getUint32(0,!0)}const d=new Bn;for(let t=0;t<_.nConstraints;t++){i&&t%1e4==0&&i.debug(`processing constraints: ${t}/${_.nConstraints}`);const e=c();for(let a=0;a=0?u.Fr.fromRprLE(U.slice(i[3],i[3]+u.Fr.n8),0):u.Fr.fromRprLE(a,0);const n=u.Fr.mul(o,E);u.Fr.toRprLE(t,12,n),g.set(t,h),h+=t.length}await p.write(g),await Na(p)}(),await j(3,"G1",k,"IC"),await async function(){await Da(p,9);const t=new Ge(A*m);if(L(i&&i.debug(`Writing points end ${o}: ${d}/${a.length}`),t)))),r+=n,t++}const c=await Promise.all(l);for(let t=0;t32768?(f=new Ge(_*n),h=new Ge(_*u.Fr.n8)):(f=new Uint8Array(_*n),h=new Uint8Array(_*u.Fr.n8));let p=0,m=0;const w=[R,D,N,V],L=new Uint8Array(u.Fr.n8);u.Fr.toRprLE(L,0,u.Fr.e(1));let b=0;for(let t=0;t=0?h.set(U.slice(e[t][o][2],e[t][o][2]+u.Fr.n8),b*u.Fr.n8):h.set(L,b*u.Fr.n8),b++;if(e.length>1){const t=[];t.push({cmd:"ALLOCSET",var:0,buff:f}),t.push({cmd:"ALLOCSET",var:1,buff:h}),t.push({cmd:"ALLOC",var:2,len:e.length*l}),p=0,m=0;let a=0;for(let i=0;i=0;t--){const e=d.contributions[t];i&&i.info("-------------------------"),i&&i.info(Mi(e.contributionHash,`contribution #${t+1} ${e.name?e.name:""}:`)),1==e.type&&(i&&i.info(`Beacon generator: ${ji(e.beaconHash)}`),i&&i.info(`Beacon iterations Exp: ${e.numIterationsExp}`))}return i&&i.info("-------------------------"),i&&i.info("ZKey Ok!"),!0;async function w(t,e){const a=2*s.G1.F.n8,i=t.byteLength/a,o=s.tm.concurrency,n=Math.floor(i/o),l=[];for(let a=0;a Detected protocol: "+o.protocol),"groth16"===o.protocol)n=await async function(t,e,a){const i=await ei(t.q),o=2*i.G1.F.n8,n=await i.pairing(t.vk_alpha_1,t.vk_beta_2);let l={protocol:t.protocol,curve:i.name,nPublic:t.nPublic,vk_alpha_1:i.G1.toObject(t.vk_alpha_1),vk_beta_2:i.G2.toObject(t.vk_beta_2),vk_gamma_2:i.G2.toObject(t.vk_gamma_2),vk_delta_2:i.G2.toObject(t.vk_delta_2),vk_alphabeta_12:i.Gt.toObject(n)};await Va(e,a,3),l.IC=[];for(let a=0;a<=t.nPublic;a++){const t=await e.read(o),a=i.G1.toObject(t);l.IC.push(a)}return await $a(e),l=zn(l),l}(o,a,i);else if("plonk"===o.protocol)n=await async function(t){const e=await ei(t.q);let 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a=e.getCodeBuilder(),i=a.i32_const(t.alloc(r));e.addCode(a.call(s+"_load",a.getLocal("scalar"),a.getLocal("scalarLen"),i),a.call(s+"_toMontgomery",i,i),a.call(s+"_mul",a.getLocal("x"),i,a.getLocal("r")))}(),_t(t,s),pt(t,s+"_batchToMontgomery",s+"_toMontgomery",r,r),pt(t,s+"_batchFromMontgomery",s+"_fromMontgomery",r,r),pt(t,s+"_batchNeg",s+"_neg",r,r),mt(t,s+"_batchAdd",s+"_add",r,r),mt(t,s+"_batchSub",s+"_sub",r,r),mt(t,s+"_batchMul",s+"_mul",r,r),t.exportFunction(s+"_add"),t.exportFunction(s+"_sub"),t.exportFunction(s+"_neg"),t.exportFunction(s+"_isNegative"),t.exportFunction(s+"_isOne"),t.exportFunction(s+"_sign"),t.exportFunction(s+"_mReduct"),t.exportFunction(s+"_mul"),t.exportFunction(s+"_square"),t.exportFunction(s+"_squareOld"),t.exportFunction(s+"_fromMontgomery"),t.exportFunction(s+"_toMontgomery"),t.exportFunction(s+"_inverse"),t.exportFunction(s+"_one"),t.exportFunction(s+"_load"),t.exportFunction(s+"_timesScalar"),ht(t,s+"_exp",r,s+"_mul",s+"_square",c+"_copy",s+"_one"),t.exportFunction(s+"_exp"),t.exportFunction(s+"_batchInverse"),At(o)&&(!function(){const 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a=e.getCodeBuilder(),i=a.i32_const(g),o=a.i32_const(t.alloc(r)),n=a.i32_const(t.alloc(r)),l=a.i32_const(t.alloc(r)),c=a.i32_const(t.alloc(r)),d=a.i32_const(t.alloc(r));e.addCode(a.if(a.call(s+"_isZero",a.getLocal("n")),a.ret(a.call(s+"_zero",a.getLocal("r")))),a.setLocal("m",a.i32_const(b)),a.call(s+"_copy",a.i32_const(I),o),a.call(s+"_exp",a.getLocal("n"),a.i32_const(y),a.i32_const(r),n),a.call(s+"_exp",a.getLocal("n"),a.i32_const(x),a.i32_const(r),l),a.block(a.loop(a.br_if(1,a.call(s+"_eq",n,i)),a.call(s+"_square",n,c),a.setLocal("i",a.i32_const(1)),a.block(a.loop(a.br_if(1,a.call(s+"_eq",c,i)),a.call(s+"_square",c,c),a.setLocal("i",a.i32_add(a.getLocal("i"),a.i32_const(1))),a.br(0))),a.call(s+"_copy",o,d),a.setLocal("j",a.i32_sub(a.i32_sub(a.getLocal("m"),a.getLocal("i")),a.i32_const(1))),a.block(a.loop(a.br_if(1,a.i32_eqz(a.getLocal("j"))),a.call(s+"_square",d,d),a.setLocal("j",a.i32_sub(a.getLocal("j"),a.i32_const(1))),a.br(0))),a.setLocal("m",a.getLocal("i")),a.call(s+"_square",d,o),a.call(s+"_mul",n,o,n),a.call(s+"_mul",l,d,l),a.br(0))),a.if(a.call(s+"_isNegative",l),a.call(s+"_neg",l,a.getLocal("r")),a.call(s+"_copy",l,a.getLocal("r"))))}(),function(){const e=t.addFunction(s+"_isSquare");e.addParam("n","i32"),e.setReturnType("i32");const a=e.getCodeBuilder(),i=a.i32_const(g),o=a.i32_const(t.alloc(r));e.addCode(a.if(a.call(s+"_isZero",a.getLocal("n")),a.ret(a.i32_const(1))),a.call(s+"_exp",a.getLocal("n"),a.i32_const(p),a.i32_const(r),o),a.call(s+"_eq",o,i))}(),t.exportFunction(s+"_sqrt"),t.exportFunction(s+"_isSquare")),t.exportFunction(s+"_batchToMontgomery"),t.exportFunction(s+"_batchFromMontgomery"),s};const Ft=It,{bitLength:xt}=J;var Et=function(t,e,a,i,o){const n=BigInt(e),l=Math.floor((xt(n-1n)-1)/64)+1,r=8*l,s=a||"f1";if(t.modules[s])return s;t.modules[s]={n64:l};const c=o||"int",d=Ft(t,n,i,c),u=t.modules[d].pR2,g=t.modules[d].pq,f=t.modules[d].pePlusOne;return function(){const e=t.alloc(r),a=t.addFunction(s+"_mul");a.addParam("x","i32"),a.addParam("y","i32"),a.addParam("r","i32");const i=a.getCodeBuilder();a.addCode(i.call(d+"_mul",i.getLocal("x"),i.getLocal("y"),i.i32_const(e))),a.addCode(i.call(d+"_mul",i.i32_const(e),i.i32_const(u),i.getLocal("r")))}(),function(){const e=t.addFunction(s+"_square");e.addParam("x","i32"),e.addParam("r","i32");const a=e.getCodeBuilder();e.addCode(a.call(s+"_mul",a.getLocal("x"),a.getLocal("x"),a.getLocal("r")))}(),function(){const e=t.addFunction(s+"_inverse");e.addParam("x","i32"),e.addParam("r","i32");const a=e.getCodeBuilder();e.addCode(a.call(c+"_inverseMod",a.getLocal("x"),a.i32_const(g),a.getLocal("r")))}(),function(){const e=t.addFunction(s+"_isNegative");e.addParam("x","i32"),e.setReturnType("i32");const a=e.getCodeBuilder();e.addCode(a.call(c+"_gte",a.getLocal("x"),a.i32_const(f)))}(),t.exportFunction(d+"_add",s+"_add"),t.exportFunction(d+"_sub",s+"_sub"),t.exportFunction(d+"_neg",s+"_neg"),t.exportFunction(s+"_mul"),t.exportFunction(s+"_square"),t.exportFunction(s+"_inverse"),t.exportFunction(s+"_isNegative"),t.exportFunction(d+"_copy",s+"_copy"),t.exportFunction(d+"_zero",s+"_zero"),t.exportFunction(d+"_one",s+"_one"),t.exportFunction(d+"_isZero",s+"_isZero"),t.exportFunction(d+"_eq",s+"_eq"),s};const vt=H,Bt=Z,St=K;var Pt=function(t,e,a,i){if(t.modules[a])return a;const o=8*t.modules[i].n64,n=t.modules[i].q;return t.modules[a]={n64:2*t.modules[i].n64},function(){const e=t.addFunction(a+"_isZero");e.addParam("x","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.i32_and(n.call(i+"_isZero",l),n.call(i+"_isZero",r)))}(),function(){const e=t.addFunction(a+"_isOne");e.addParam("x","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.ret(n.i32_and(n.call(i+"_isOne",l),n.call(i+"_isZero",r))))}(),function(){const e=t.addFunction(a+"_zero");e.addParam("x","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.call(i+"_zero",l),n.call(i+"_zero",r))}(),function(){const e=t.addFunction(a+"_one");e.addParam("x","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.call(i+"_one",l),n.call(i+"_zero",r))}(),function(){const e=t.addFunction(a+"_copy");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_copy",l,s),n.call(i+"_copy",r,c))}(),function(){const n=t.addFunction(a+"_mul");n.addParam("x","i32"),n.addParam("y","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.getLocal("y"),d=l.i32_add(l.getLocal("y"),l.i32_const(o)),u=l.getLocal("r"),g=l.i32_add(l.getLocal("r"),l.i32_const(o)),f=l.i32_const(t.alloc(o)),h=l.i32_const(t.alloc(o)),_=l.i32_const(t.alloc(o)),p=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_mul",r,c,f),l.call(i+"_mul",s,d,h),l.call(i+"_add",r,s,_),l.call(i+"_add",c,d,p),l.call(i+"_mul",_,p,_),l.call(e,h,u),l.call(i+"_add",f,u,u),l.call(i+"_add",f,h,g),l.call(i+"_sub",_,g,g))}(),function(){const e=t.addFunction(a+"_mul1");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("y"),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_mul",l,s,c),n.call(i+"_mul",r,s,d))}(),function(){const n=t.addFunction(a+"_square");n.addParam("x","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.getLocal("r"),d=l.i32_add(l.getLocal("r"),l.i32_const(o)),u=l.i32_const(t.alloc(o)),g=l.i32_const(t.alloc(o)),f=l.i32_const(t.alloc(o)),h=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_mul",r,s,u),l.call(i+"_add",r,s,g),l.call(e,s,f),l.call(i+"_add",r,f,f),l.call(e,u,h),l.call(i+"_add",h,u,h),l.call(i+"_mul",g,f,c),l.call(i+"_sub",c,h,c),l.call(i+"_add",u,u,d))}(),function(){const e=t.addFunction(a+"_add");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("y"),c=n.i32_add(n.getLocal("y"),n.i32_const(o)),d=n.getLocal("r"),u=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_add",l,s,d),n.call(i+"_add",r,c,u))}(),function(){const e=t.addFunction(a+"_sub");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("y"),c=n.i32_add(n.getLocal("y"),n.i32_const(o)),d=n.getLocal("r"),u=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_sub",l,s,d),n.call(i+"_sub",r,c,u))}(),function(){const e=t.addFunction(a+"_neg");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_neg",l,s),n.call(i+"_neg",r,c))}(),function(){const e=t.addFunction(a+"_conjugate");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_copy",l,s),n.call(i+"_neg",r,c))}(),function(){const e=t.addFunction(a+"_toMontgomery");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_toMontgomery",l,s),n.call(i+"_toMontgomery",r,c))}(),function(){const e=t.addFunction(a+"_fromMontgomery");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_fromMontgomery",l,s),n.call(i+"_fromMontgomery",r,c))}(),function(){const e=t.addFunction(a+"_eq");e.addParam("x","i32"),e.addParam("y","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("y"),c=n.i32_add(n.getLocal("y"),n.i32_const(o));e.addCode(n.i32_and(n.call(i+"_eq",l,s),n.call(i+"_eq",r,c)))}(),function(){const n=t.addFunction(a+"_inverse");n.addParam("x","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.getLocal("r"),d=l.i32_add(l.getLocal("r"),l.i32_const(o)),u=l.i32_const(t.alloc(o)),g=l.i32_const(t.alloc(o)),f=l.i32_const(t.alloc(o)),h=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_square",r,u),l.call(i+"_square",s,g),l.call(e,g,f),l.call(i+"_sub",u,f,f),l.call(i+"_inverse",f,h),l.call(i+"_mul",r,h,c),l.call(i+"_mul",s,h,d),l.call(i+"_neg",d,d))}(),function(){const e=t.addFunction(a+"_timesScalar");e.addParam("x","i32"),e.addParam("scalar","i32"),e.addParam("scalarLen","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.getLocal("r"),c=n.i32_add(n.getLocal("r"),n.i32_const(o));e.addCode(n.call(i+"_timesScalar",l,n.getLocal("scalar"),n.getLocal("scalarLen"),s),n.call(i+"_timesScalar",r,n.getLocal("scalar"),n.getLocal("scalarLen"),c))}(),function(){const e=t.addFunction(a+"_sign");e.addParam("x","i32"),e.addLocal("s","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.setLocal("s",n.call(i+"_sign",r)),n.if(n.getLocal("s"),n.ret(n.getLocal("s"))),n.ret(n.call(i+"_sign",l)))}(),function(){const e=t.addFunction(a+"_isNegative");e.addParam("x","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o));e.addCode(n.if(n.call(i+"_isZero",r),n.ret(n.call(i+"_isNegative",l))),n.ret(n.call(i+"_isNegative",r)))}(),t.exportFunction(a+"_isZero"),t.exportFunction(a+"_isOne"),t.exportFunction(a+"_zero"),t.exportFunction(a+"_one"),t.exportFunction(a+"_copy"),t.exportFunction(a+"_mul"),t.exportFunction(a+"_mul1"),t.exportFunction(a+"_square"),t.exportFunction(a+"_add"),t.exportFunction(a+"_sub"),t.exportFunction(a+"_neg"),t.exportFunction(a+"_sign"),t.exportFunction(a+"_conjugate"),t.exportFunction(a+"_fromMontgomery"),t.exportFunction(a+"_toMontgomery"),t.exportFunction(a+"_eq"),t.exportFunction(a+"_inverse"),Bt(t,a),vt(t,a+"_exp",2*o,a+"_mul",a+"_square",a+"_copy",a+"_one"),function(){const e=t.addFunction(a+"_sqrt");e.addParam("a","i32"),e.addParam("pr","i32");const l=e.getCodeBuilder(),r=l.i32_const(t.alloc(St.bigInt2BytesLE((BigInt(n||0)-3n)/4n,o))),s=l.i32_const(t.alloc(St.bigInt2BytesLE((BigInt(n||0)-1n)/2n,o))),c=l.getLocal("a"),d=l.i32_const(t.alloc(2*o)),u=l.i32_const(t.alloc(2*o)),g=l.i32_const(t.alloc(2*o)),f=t.alloc(2*o),h=l.i32_const(f),_=l.i32_const(f),p=l.i32_const(f+o),m=l.i32_const(t.alloc(2*o)),w=l.i32_const(t.alloc(2*o));e.addCode(l.call(a+"_one",h),l.call(a+"_neg",h,h),l.call(a+"_exp",c,r,l.i32_const(o),d),l.call(a+"_square",d,u),l.call(a+"_mul",c,u,u),l.call(a+"_conjugate",u,g),l.call(a+"_mul",g,u,g),l.if(l.call(a+"_eq",g,h),l.unreachable()),l.call(a+"_mul",d,c,m),l.if(l.call(a+"_eq",u,h),[...l.call(i+"_zero",_),...l.call(i+"_one",p),...l.call(a+"_mul",h,m,l.getLocal("pr"))],[...l.call(a+"_one",w),...l.call(a+"_add",w,u,w),...l.call(a+"_exp",w,s,l.i32_const(o),w),...l.call(a+"_mul",w,m,l.getLocal("pr"))]))}(),function(){const e=t.addFunction(a+"_isSquare");e.addParam("a","i32"),e.setReturnType("i32");const i=e.getCodeBuilder(),l=i.i32_const(t.alloc(St.bigInt2BytesLE((BigInt(n||0)-3n)/4n,o))),r=i.getLocal("a"),s=i.i32_const(t.alloc(2*o)),c=i.i32_const(t.alloc(2*o)),d=i.i32_const(t.alloc(2*o)),u=t.alloc(2*o),g=i.i32_const(u);e.addCode(i.call(a+"_one",g),i.call(a+"_neg",g,g),i.call(a+"_exp",r,l,i.i32_const(o),s),i.call(a+"_square",s,c),i.call(a+"_mul",r,c,c),i.call(a+"_conjugate",c,d),i.call(a+"_mul",d,c,d),i.if(i.call(a+"_eq",d,g),i.ret(i.i32_const(0))),i.ret(i.i32_const(1)))}(),t.exportFunction(a+"_exp"),t.exportFunction(a+"_timesScalar"),t.exportFunction(a+"_batchInverse"),t.exportFunction(a+"_sqrt"),t.exportFunction(a+"_isSquare"),t.exportFunction(a+"_isNegative"),a};const Gt=H,zt=Z;var Ot=function(t,e,a,i){if(t.modules[a])return a;const o=8*t.modules[i].n64;return t.modules[a]={n64:3*t.modules[i].n64},function(){const e=t.addFunction(a+"_isZero");e.addParam("x","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o));e.addCode(n.i32_and(n.i32_and(n.call(i+"_isZero",l),n.call(i+"_isZero",r)),n.call(i+"_isZero",s)))}(),function(){const e=t.addFunction(a+"_isOne");e.addParam("x","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o));e.addCode(n.ret(n.i32_and(n.i32_and(n.call(i+"_isOne",l),n.call(i+"_isZero",r)),n.call(i+"_isZero",s))))}(),function(){const e=t.addFunction(a+"_zero");e.addParam("x","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o));e.addCode(n.call(i+"_zero",l),n.call(i+"_zero",r),n.call(i+"_zero",s))}(),function(){const e=t.addFunction(a+"_one");e.addParam("x","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o));e.addCode(n.call(i+"_one",l),n.call(i+"_zero",r),n.call(i+"_zero",s))}(),function(){const e=t.addFunction(a+"_copy");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o)),u=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_copy",l,c),n.call(i+"_copy",r,d),n.call(i+"_copy",s,u))}(),function(){const n=t.addFunction(a+"_mul");n.addParam("x","i32"),n.addParam("y","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.i32_add(l.getLocal("x"),l.i32_const(2*o)),d=l.getLocal("y"),u=l.i32_add(l.getLocal("y"),l.i32_const(o)),g=l.i32_add(l.getLocal("y"),l.i32_const(2*o)),f=l.getLocal("r"),h=l.i32_add(l.getLocal("r"),l.i32_const(o)),_=l.i32_add(l.getLocal("r"),l.i32_const(2*o)),p=l.i32_const(t.alloc(o)),m=l.i32_const(t.alloc(o)),w=l.i32_const(t.alloc(o)),L=l.i32_const(t.alloc(o)),b=l.i32_const(t.alloc(o)),A=l.i32_const(t.alloc(o)),y=l.i32_const(t.alloc(o)),C=l.i32_const(t.alloc(o)),I=l.i32_const(t.alloc(o)),F=l.i32_const(t.alloc(o)),x=l.i32_const(t.alloc(o)),E=l.i32_const(t.alloc(o)),v=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_mul",r,d,p),l.call(i+"_mul",s,u,m),l.call(i+"_mul",c,g,w),l.call(i+"_add",r,s,L),l.call(i+"_add",d,u,b),l.call(i+"_add",r,c,A),l.call(i+"_add",d,g,y),l.call(i+"_add",s,c,C),l.call(i+"_add",u,g,I),l.call(i+"_add",p,m,F),l.call(i+"_add",p,w,x),l.call(i+"_add",m,w,E),l.call(i+"_mul",C,I,f),l.call(i+"_sub",f,E,f),l.call(e,f,f),l.call(i+"_add",p,f,f),l.call(i+"_mul",L,b,h),l.call(i+"_sub",h,F,h),l.call(e,w,v),l.call(i+"_add",h,v,h),l.call(i+"_mul",A,y,_),l.call(i+"_sub",_,x,_),l.call(i+"_add",_,m,_))}(),function(){const n=t.addFunction(a+"_square");n.addParam("x","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.i32_add(l.getLocal("x"),l.i32_const(2*o)),d=l.getLocal("r"),u=l.i32_add(l.getLocal("r"),l.i32_const(o)),g=l.i32_add(l.getLocal("r"),l.i32_const(2*o)),f=l.i32_const(t.alloc(o)),h=l.i32_const(t.alloc(o)),_=l.i32_const(t.alloc(o)),p=l.i32_const(t.alloc(o)),m=l.i32_const(t.alloc(o)),w=l.i32_const(t.alloc(o)),L=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_square",r,f),l.call(i+"_mul",r,s,h),l.call(i+"_add",h,h,_),l.call(i+"_sub",r,s,p),l.call(i+"_add",p,c,p),l.call(i+"_square",p,p),l.call(i+"_mul",s,c,m),l.call(i+"_add",m,m,w),l.call(i+"_square",c,L),l.call(e,w,d),l.call(i+"_add",f,d,d),l.call(e,L,u),l.call(i+"_add",_,u,u),l.call(i+"_add",f,L,g),l.call(i+"_sub",w,g,g),l.call(i+"_add",p,g,g),l.call(i+"_add",_,g,g))}(),function(){const e=t.addFunction(a+"_add");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("y"),d=n.i32_add(n.getLocal("y"),n.i32_const(o)),u=n.i32_add(n.getLocal("y"),n.i32_const(2*o)),g=n.getLocal("r"),f=n.i32_add(n.getLocal("r"),n.i32_const(o)),h=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_add",l,c,g),n.call(i+"_add",r,d,f),n.call(i+"_add",s,u,h))}(),function(){const e=t.addFunction(a+"_sub");e.addParam("x","i32"),e.addParam("y","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("y"),d=n.i32_add(n.getLocal("y"),n.i32_const(o)),u=n.i32_add(n.getLocal("y"),n.i32_const(2*o)),g=n.getLocal("r"),f=n.i32_add(n.getLocal("r"),n.i32_const(o)),h=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_sub",l,c,g),n.call(i+"_sub",r,d,f),n.call(i+"_sub",s,u,h))}(),function(){const e=t.addFunction(a+"_neg");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o)),u=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_neg",l,c),n.call(i+"_neg",r,d),n.call(i+"_neg",s,u))}(),function(){const e=t.addFunction(a+"_sign");e.addParam("x","i32"),e.addLocal("s","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o));e.addCode(n.setLocal("s",n.call(i+"_sign",s)),n.if(n.getLocal("s"),n.ret(n.getLocal("s"))),n.setLocal("s",n.call(i+"_sign",r)),n.if(n.getLocal("s"),n.ret(n.getLocal("s"))),n.ret(n.call(i+"_sign",l)))}(),function(){const e=t.addFunction(a+"_toMontgomery");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o)),u=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_toMontgomery",l,c),n.call(i+"_toMontgomery",r,d),n.call(i+"_toMontgomery",s,u))}(),function(){const e=t.addFunction(a+"_fromMontgomery");e.addParam("x","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o)),u=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_fromMontgomery",l,c),n.call(i+"_fromMontgomery",r,d),n.call(i+"_fromMontgomery",s,u))}(),function(){const e=t.addFunction(a+"_eq");e.addParam("x","i32"),e.addParam("y","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("y"),d=n.i32_add(n.getLocal("y"),n.i32_const(o)),u=n.i32_add(n.getLocal("y"),n.i32_const(2*o));e.addCode(n.i32_and(n.i32_and(n.call(i+"_eq",l,c),n.call(i+"_eq",r,d)),n.call(i+"_eq",s,u)))}(),function(){const n=t.addFunction(a+"_inverse");n.addParam("x","i32"),n.addParam("r","i32");const l=n.getCodeBuilder(),r=l.getLocal("x"),s=l.i32_add(l.getLocal("x"),l.i32_const(o)),c=l.i32_add(l.getLocal("x"),l.i32_const(2*o)),d=l.getLocal("r"),u=l.i32_add(l.getLocal("r"),l.i32_const(o)),g=l.i32_add(l.getLocal("r"),l.i32_const(2*o)),f=l.i32_const(t.alloc(o)),h=l.i32_const(t.alloc(o)),_=l.i32_const(t.alloc(o)),p=l.i32_const(t.alloc(o)),m=l.i32_const(t.alloc(o)),w=l.i32_const(t.alloc(o)),L=l.i32_const(t.alloc(o)),b=l.i32_const(t.alloc(o)),A=l.i32_const(t.alloc(o)),y=l.i32_const(t.alloc(o)),C=l.i32_const(t.alloc(o));n.addCode(l.call(i+"_square",r,f),l.call(i+"_square",s,h),l.call(i+"_square",c,_),l.call(i+"_mul",r,s,p),l.call(i+"_mul",r,c,m),l.call(i+"_mul",s,c,w),l.call(e,w,L),l.call(i+"_sub",f,L,L),l.call(e,_,b),l.call(i+"_sub",b,p,b),l.call(i+"_sub",h,m,A),l.call(i+"_mul",c,b,y),l.call(i+"_mul",s,A,C),l.call(i+"_add",y,C,y),l.call(e,y,y),l.call(i+"_mul",r,L,C),l.call(i+"_add",C,y,y),l.call(i+"_inverse",y,y),l.call(i+"_mul",y,L,d),l.call(i+"_mul",y,b,u),l.call(i+"_mul",y,A,g))}(),function(){const e=t.addFunction(a+"_timesScalar");e.addParam("x","i32"),e.addParam("scalar","i32"),e.addParam("scalarLen","i32"),e.addParam("r","i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o)),c=n.getLocal("r"),d=n.i32_add(n.getLocal("r"),n.i32_const(o)),u=n.i32_add(n.getLocal("r"),n.i32_const(2*o));e.addCode(n.call(i+"_timesScalar",l,n.getLocal("scalar"),n.getLocal("scalarLen"),c),n.call(i+"_timesScalar",r,n.getLocal("scalar"),n.getLocal("scalarLen"),d),n.call(i+"_timesScalar",s,n.getLocal("scalar"),n.getLocal("scalarLen"),u))}(),function(){const e=t.addFunction(a+"_isNegative");e.addParam("x","i32"),e.setReturnType("i32");const n=e.getCodeBuilder(),l=n.getLocal("x"),r=n.i32_add(n.getLocal("x"),n.i32_const(o)),s=n.i32_add(n.getLocal("x"),n.i32_const(2*o));e.addCode(n.if(n.call(i+"_isZero",s),n.if(n.call(i+"_isZero",r),n.ret(n.call(i+"_isNegative",l)),n.ret(n.call(i+"_isNegative",r)))),n.ret(n.call(i+"_isNegative",s)))}(),t.exportFunction(a+"_isZero"),t.exportFunction(a+"_isOne"),t.exportFunction(a+"_zero"),t.exportFunction(a+"_one"),t.exportFunction(a+"_copy"),t.exportFunction(a+"_mul"),t.exportFunction(a+"_square"),t.exportFunction(a+"_add"),t.exportFunction(a+"_sub"),t.exportFunction(a+"_neg"),t.exportFunction(a+"_sign"),t.exportFunction(a+"_fromMontgomery"),t.exportFunction(a+"_toMontgomery"),t.exportFunction(a+"_eq"),t.exportFunction(a+"_inverse"),zt(t,a),Gt(t,a+"_exp",3*o,a+"_mul",a+"_square",a+"_copy",a+"_one"),t.exportFunction(a+"_exp"),t.exportFunction(a+"_timesScalar"),t.exportFunction(a+"_batchInverse"),t.exportFunction(a+"_isNegative"),a};const Ut=function(t,e,a,i,o,n,l,r){const s=t.addFunction(e);s.addParam("base","i32"),s.addParam("scalar","i32"),s.addParam("scalarLength","i32"),s.addParam("r","i32"),s.addLocal("old0","i32"),s.addLocal("nbits","i32"),s.addLocal("i","i32"),s.addLocal("last","i32"),s.addLocal("cur","i32"),s.addLocal("carry","i32"),s.addLocal("p","i32");const c=s.getCodeBuilder(),d=c.i32_const(t.alloc(a));function u(t){return c.i32_and(c.i32_shr_u(c.i32_load(c.i32_add(c.getLocal("scalar"),c.i32_and(c.i32_shr_u(t,c.i32_const(3)),c.i32_const(4294967292)))),c.i32_and(t,c.i32_const(31))),c.i32_const(1))}function g(t){return[...c.i32_store8(c.getLocal("p"),c.i32_const(t)),...c.setLocal("p",c.i32_add(c.getLocal("p"),c.i32_const(1)))]}s.addCode(c.if(c.i32_eqz(c.getLocal("scalarLength")),[...c.call(r,c.getLocal("r")),...c.ret([])]),c.setLocal("nbits",c.i32_shl(c.getLocal("scalarLength"),c.i32_const(3))),c.setLocal("old0",c.i32_load(c.i32_const(0))),c.setLocal("p",c.getLocal("old0")),c.i32_store(c.i32_const(0),c.i32_and(c.i32_add(c.i32_add(c.getLocal("old0"),c.i32_const(32)),c.getLocal("nbits")),c.i32_const(4294967288))),c.setLocal("i",c.i32_const(1)),c.setLocal("last",u(c.i32_const(0))),c.setLocal("carry",c.i32_const(0)),c.block(c.loop(c.br_if(1,c.i32_eq(c.getLocal("i"),c.getLocal("nbits"))),c.setLocal("cur",u(c.getLocal("i"))),c.if(c.getLocal("last"),c.if(c.getLocal("cur"),c.if(c.getLocal("carry"),[...c.setLocal("last",c.i32_const(0)),...c.setLocal("carry",c.i32_const(1)),...g(1)],[...c.setLocal("last",c.i32_const(0)),...c.setLocal("carry",c.i32_const(1)),...g(255)]),c.if(c.getLocal("carry"),[...c.setLocal("last",c.i32_const(0)),...c.setLocal("carry",c.i32_const(1)),...g(255)],[...c.setLocal("last",c.i32_const(0)),...c.setLocal("carry",c.i32_const(0)),...g(1)])),c.if(c.getLocal("cur"),c.if(c.getLocal("carry"),[...c.setLocal("last",c.i32_const(0)),...c.setLocal("carry",c.i32_const(1)),...g(0)],[...c.setLocal("last",c.i32_const(1)),...c.setLocal("carry",c.i32_const(0)),...g(0)]),c.if(c.getLocal("carry"),[...c.setLocal("last",c.i32_const(1)),...c.setLocal("carry",c.i32_const(0)),...g(0)],[...c.setLocal("last",c.i32_const(0)),...c.setLocal("carry",c.i32_const(0)),...g(0)]))),c.setLocal("i",c.i32_add(c.getLocal("i"),c.i32_const(1))),c.br(0))),c.if(c.getLocal("last"),c.if(c.getLocal("carry"),[...g(255),...g(0),...g(1)],[...g(1)]),c.if(c.getLocal("carry"),[...g(0),...g(1)])),c.setLocal("p",c.i32_sub(c.getLocal("p"),c.i32_const(1))),c.call(l,c.getLocal("base"),d),c.call(r,c.getLocal("r")),c.block(c.loop(c.call(o,c.getLocal("r"),c.getLocal("r")),c.setLocal("cur",c.i32_load8_u(c.getLocal("p"))),c.if(c.getLocal("cur"),c.if(c.i32_eq(c.getLocal("cur"),c.i32_const(1)),c.call(i,c.getLocal("r"),d,c.getLocal("r")),c.call(n,c.getLocal("r"),d,c.getLocal("r")))),c.br_if(1,c.i32_eq(c.getLocal("old0"),c.getLocal("p"))),c.setLocal("p",c.i32_sub(c.getLocal("p"),c.i32_const(1))),c.br(0))),c.i32_store(c.i32_const(0),c.getLocal("old0")))},Tt=W,Qt=function(t,e,a,i,o){const n=8*t.modules[e].n64;function l(){const i=t.addFunction(a);i.addParam("pBases","i32"),i.addParam("pScalars","i32"),i.addParam("scalarSize","i32"),i.addParam("n","i32"),i.addParam("pr","i32"),i.addLocal("chunkSize","i32"),i.addLocal("nChunks","i32"),i.addLocal("itScalar","i32"),i.addLocal("endScalar","i32"),i.addLocal("itBase","i32"),i.addLocal("itBit","i32"),i.addLocal("i","i32"),i.addLocal("j","i32"),i.addLocal("nTable","i32"),i.addLocal("pTable","i32"),i.addLocal("idx","i32"),i.addLocal("pIdxTable","i32");const o=i.getCodeBuilder(),l=o.i32_const(t.alloc(n)),r=t.alloc([17,17,17,17,17,17,17,17,17,17,16,16,15,14,13,13,12,11,10,9,8,7,7,6,5,4,3,2,1,1,1,1]);i.addCode(o.call(e+"_zero",o.getLocal("pr")),o.if(o.i32_eqz(o.getLocal("n")),o.ret([])),o.setLocal("chunkSize",o.i32_load8_u(o.i32_clz(o.getLocal("n")),r)),o.setLocal("nChunks",o.i32_add(o.i32_div_u(o.i32_sub(o.i32_shl(o.getLocal("scalarSize"),o.i32_const(3)),o.i32_const(1)),o.getLocal("chunkSize")),o.i32_const(1))),o.setLocal("itBit",o.i32_mul(o.i32_sub(o.getLocal("nChunks"),o.i32_const(1)),o.getLocal("chunkSize"))),o.block(o.loop(o.br_if(1,o.i32_lt_s(o.getLocal("itBit"),o.i32_const(0))),o.if(o.i32_eqz(o.call(e+"_isZero",o.getLocal("pr"))),[...o.setLocal("j",o.i32_const(0)),...o.block(o.loop(o.br_if(1,o.i32_eq(o.getLocal("j"),o.getLocal("chunkSize"))),o.call(e+"_double",o.getLocal("pr"),o.getLocal("pr")),o.setLocal("j",o.i32_add(o.getLocal("j"),o.i32_const(1))),o.br(0)))]),o.call(a+"_chunk",o.getLocal("pBases"),o.getLocal("pScalars"),o.getLocal("scalarSize"),o.getLocal("n"),o.getLocal("itBit"),o.getLocal("chunkSize"),l),o.call(e+"_add",o.getLocal("pr"),l,o.getLocal("pr")),o.setLocal("itBit",o.i32_sub(o.getLocal("itBit"),o.getLocal("chunkSize"))),o.br(0))))}!function(){const e=t.addFunction(a+"_getChunk");e.addParam("pScalar","i32"),e.addParam("scalarSize","i32"),e.addParam("startBit","i32"),e.addParam("chunkSize","i32"),e.addLocal("bitsToEnd","i32"),e.addLocal("mask","i32"),e.setReturnType("i32");const i=e.getCodeBuilder();e.addCode(i.setLocal("bitsToEnd",i.i32_sub(i.i32_mul(i.getLocal("scalarSize"),i.i32_const(8)),i.getLocal("startBit"))),i.if(i.i32_gt_s(i.getLocal("chunkSize"),i.getLocal("bitsToEnd")),i.setLocal("mask",i.i32_sub(i.i32_shl(i.i32_const(1),i.getLocal("bitsToEnd")),i.i32_const(1))),i.setLocal("mask",i.i32_sub(i.i32_shl(i.i32_const(1),i.getLocal("chunkSize")),i.i32_const(1)))),i.i32_and(i.i32_shr_u(i.i32_load(i.i32_add(i.getLocal("pScalar"),i.i32_shr_u(i.getLocal("startBit"),i.i32_const(3))),0,0),i.i32_and(i.getLocal("startBit"),i.i32_const(7))),i.getLocal("mask")))}(),function(){const i=t.addFunction(a+"_reduceTable");i.addParam("pTable","i32"),i.addParam("p","i32"),i.addLocal("half","i32"),i.addLocal("it1","i32"),i.addLocal("it2","i32"),i.addLocal("pAcc","i32");const o=i.getCodeBuilder();i.addCode(o.if(o.i32_eq(o.getLocal("p"),o.i32_const(1)),o.ret([])),o.setLocal("half",o.i32_shl(o.i32_const(1),o.i32_sub(o.getLocal("p"),o.i32_const(1)))),o.setLocal("it1",o.getLocal("pTable")),o.setLocal("it2",o.i32_add(o.getLocal("pTable"),o.i32_mul(o.getLocal("half"),o.i32_const(n)))),o.setLocal("pAcc",o.i32_sub(o.getLocal("it2"),o.i32_const(n))),o.block(o.loop(o.br_if(1,o.i32_eq(o.getLocal("it1"),o.getLocal("pAcc"))),o.call(e+"_add",o.getLocal("it1"),o.getLocal("it2"),o.getLocal("it1")),o.call(e+"_add",o.getLocal("pAcc"),o.getLocal("it2"),o.getLocal("pAcc")),o.setLocal("it1",o.i32_add(o.getLocal("it1"),o.i32_const(n))),o.setLocal("it2",o.i32_add(o.getLocal("it2"),o.i32_const(n))),o.br(0))),o.call(a+"_reduceTable",o.getLocal("pTable"),o.i32_sub(o.getLocal("p"),o.i32_const(1))),o.setLocal("p",o.i32_sub(o.getLocal("p"),o.i32_const(1))),o.block(o.loop(o.br_if(1,o.i32_eqz(o.getLocal("p"))),o.call(e+"_double",o.getLocal("pAcc"),o.getLocal("pAcc")),o.setLocal("p",o.i32_sub(o.getLocal("p"),o.i32_const(1))),o.br(0))),o.call(e+"_add",o.getLocal("pTable"),o.getLocal("pAcc"),o.getLocal("pTable")))}(),function(){const l=t.addFunction(a+"_chunk");l.addParam("pBases","i32"),l.addParam("pScalars","i32"),l.addParam("scalarSize","i32"),l.addParam("n","i32"),l.addParam("startBit","i32"),l.addParam("chunkSize","i32"),l.addParam("pr","i32"),l.addLocal("nChunks","i32"),l.addLocal("itScalar","i32"),l.addLocal("endScalar","i32"),l.addLocal("itBase","i32"),l.addLocal("i","i32"),l.addLocal("j","i32"),l.addLocal("nTable","i32"),l.addLocal("pTable","i32"),l.addLocal("idx","i32"),l.addLocal("pIdxTable","i32");const r=l.getCodeBuilder();l.addCode(r.if(r.i32_eqz(r.getLocal("n")),[...r.call(e+"_zero",r.getLocal("pr")),...r.ret([])]),r.setLocal("nTable",r.i32_shl(r.i32_const(1),r.getLocal("chunkSize"))),r.setLocal("pTable",r.i32_load(r.i32_const(0))),r.i32_store(r.i32_const(0),r.i32_add(r.getLocal("pTable"),r.i32_mul(r.getLocal("nTable"),r.i32_const(n)))),r.setLocal("j",r.i32_const(0)),r.block(r.loop(r.br_if(1,r.i32_eq(r.getLocal("j"),r.getLocal("nTable"))),r.call(e+"_zero",r.i32_add(r.getLocal("pTable"),r.i32_mul(r.getLocal("j"),r.i32_const(n)))),r.setLocal("j",r.i32_add(r.getLocal("j"),r.i32_const(1))),r.br(0))),r.setLocal("itBase",r.getLocal("pBases")),r.setLocal("itScalar",r.getLocal("pScalars")),r.setLocal("endScalar",r.i32_add(r.getLocal("pScalars"),r.i32_mul(r.getLocal("n"),r.getLocal("scalarSize")))),r.block(r.loop(r.br_if(1,r.i32_eq(r.getLocal("itScalar"),r.getLocal("endScalar"))),r.setLocal("idx",r.call(a+"_getChunk",r.getLocal("itScalar"),r.getLocal("scalarSize"),r.getLocal("startBit"),r.getLocal("chunkSize"))),r.if(r.getLocal("idx"),[...r.setLocal("pIdxTable",r.i32_add(r.getLocal("pTable"),r.i32_mul(r.i32_sub(r.getLocal("idx"),r.i32_const(1)),r.i32_const(n)))),...r.call(i,r.getLocal("pIdxTable"),r.getLocal("itBase"),r.getLocal("pIdxTable"))]),r.setLocal("itScalar",r.i32_add(r.getLocal("itScalar"),r.getLocal("scalarSize"))),r.setLocal("itBase",r.i32_add(r.getLocal("itBase"),r.i32_const(o))),r.br(0))),r.call(a+"_reduceTable",r.getLocal("pTable"),r.getLocal("chunkSize")),r.call(e+"_copy",r.getLocal("pTable"),r.getLocal("pr")),r.i32_store(r.i32_const(0),r.getLocal("pTable")))}(),l(),t.exportFunction(a),t.exportFunction(a+"_chunk")};var qt=function(t,e,a,i){const o=t.modules[a].n64,n=8*o;if(t.modules[e])return e;return t.modules[e]={n64:3*o},function(){const i=t.addFunction(e+"_isZeroAffine");i.addParam("p1","i32"),i.setReturnType("i32");const o=i.getCodeBuilder();i.addCode(o.i32_and(o.call(a+"_isZero",o.getLocal("p1")),o.call(a+"_isZero",o.i32_add(o.getLocal("p1"),o.i32_const(n)))))}(),function(){const i=t.addFunction(e+"_isZero");i.addParam("p1","i32"),i.setReturnType("i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_isZero",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))))}(),function(){const i=t.addFunction(e+"_zeroAffine");i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_zero",o.getLocal("pr"))),i.addCode(o.call(a+"_zero",o.i32_add(o.getLocal("pr"),o.i32_const(n))))}(),function(){const i=t.addFunction(e+"_zero");i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_zero",o.getLocal("pr"))),i.addCode(o.call(a+"_one",o.i32_add(o.getLocal("pr"),o.i32_const(n)))),i.addCode(o.call(a+"_zero",o.i32_add(o.getLocal("pr"),o.i32_const(2*n))))}(),function(){const a=t.addFunction(e+"_copyAffine");a.addParam("ps","i32"),a.addParam("pd","i32");const i=a.getCodeBuilder();for(let t=0;t<2*o;t++)a.addCode(i.i64_store(i.getLocal("pd"),8*t,i.i64_load(i.getLocal("ps"),8*t)))}(),function(){const a=t.addFunction(e+"_copy");a.addParam("ps","i32"),a.addParam("pd","i32");const i=a.getCodeBuilder();for(let t=0;t<3*o;t++)a.addCode(i.i64_store(i.getLocal("pd"),8*t,i.i64_load(i.getLocal("ps"),8*t)))}(),function(){const i=t.addFunction(e+"_toJacobian");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.getLocal("pr"),c=o.i32_add(o.getLocal("pr"),o.i32_const(n)),d=o.i32_add(o.getLocal("pr"),o.i32_const(2*n));i.addCode(o.if(o.call(e+"_isZeroAffine",o.getLocal("p1")),o.call(e+"_zero",o.getLocal("pr")),[...o.call(a+"_one",d),...o.call(a+"_copy",r,c),...o.call(a+"_copy",l,s)]))}(),function(){const i=t.addFunction(e+"_eqAffine");i.addParam("p1","i32"),i.addParam("p2","i32"),i.setReturnType("i32"),i.addLocal("z1","i32");const o=i.getCodeBuilder();i.addCode(o.ret(o.i32_and(o.call(a+"_eq",o.getLocal("p1"),o.getLocal("p2")),o.call(a+"_eq",o.i32_add(o.getLocal("p1"),o.i32_const(n)),o.i32_add(o.getLocal("p2"),o.i32_const(n))))))}(),function(){const i=t.addFunction(e+"_eqMixed");i.addParam("p1","i32"),i.addParam("p2","i32"),i.setReturnType("i32"),i.addLocal("z1","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n));i.addCode(o.setLocal("z1",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))));const s=o.getLocal("z1"),c=o.getLocal("p2"),d=o.i32_add(o.getLocal("p2"),o.i32_const(n)),u=o.i32_const(t.alloc(n)),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),o.ret(o.call(e+"_isZeroAffine",o.getLocal("p2")))),o.if(o.call(e+"_isZeroAffine",o.getLocal("p2")),o.ret(o.i32_const(0))),o.if(o.call(a+"_isOne",s),o.ret(o.call(e+"_eqAffine",o.getLocal("p1"),o.getLocal("p2")))),o.call(a+"_square",s,u),o.call(a+"_mul",c,u,g),o.call(a+"_mul",s,u,f),o.call(a+"_mul",d,f,h),o.if(o.call(a+"_eq",l,g),o.if(o.call(a+"_eq",r,h),o.ret(o.i32_const(1)))),o.ret(o.i32_const(0)))}(),function(){const i=t.addFunction(e+"_eq");i.addParam("p1","i32"),i.addParam("p2","i32"),i.setReturnType("i32"),i.addLocal("z1","i32"),i.addLocal("z2","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n));i.addCode(o.setLocal("z1",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))));const s=o.getLocal("z1"),c=o.getLocal("p2"),d=o.i32_add(o.getLocal("p2"),o.i32_const(n));i.addCode(o.setLocal("z2",o.i32_add(o.getLocal("p2"),o.i32_const(2*n))));const u=o.getLocal("z2"),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n)),m=o.i32_const(t.alloc(n)),w=o.i32_const(t.alloc(n)),L=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),o.ret(o.call(e+"_isZero",o.getLocal("p2")))),o.if(o.call(e+"_isZero",o.getLocal("p2")),o.ret(o.i32_const(0))),o.if(o.call(a+"_isOne",s),o.ret(o.call(e+"_eqMixed",o.getLocal("p2"),o.getLocal("p1")))),o.if(o.call(a+"_isOne",u),o.ret(o.call(e+"_eqMixed",o.getLocal("p1"),o.getLocal("p2")))),o.call(a+"_square",s,g),o.call(a+"_square",u,f),o.call(a+"_mul",l,f,h),o.call(a+"_mul",c,g,_),o.call(a+"_mul",s,g,p),o.call(a+"_mul",u,f,m),o.call(a+"_mul",r,m,w),o.call(a+"_mul",d,p,L),o.if(o.call(a+"_eq",h,_),o.if(o.call(a+"_eq",w,L),o.ret(o.i32_const(1)))),o.ret(o.i32_const(0)))}(),function(){const i=t.addFunction(e+"_doubleAffine");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.getLocal("pr"),c=o.i32_add(o.getLocal("pr"),o.i32_const(n)),d=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),u=o.i32_const(t.alloc(n)),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZeroAffine",o.getLocal("p1")),[...o.call(e+"_toJacobian",o.getLocal("p1"),o.getLocal("pr")),...o.ret([])]),o.call(a+"_square",l,u),o.call(a+"_square",r,g),o.call(a+"_square",g,f),o.call(a+"_add",l,g,h),o.call(a+"_square",h,h),o.call(a+"_sub",h,u,h),o.call(a+"_sub",h,f,h),o.call(a+"_add",h,h,h),o.call(a+"_add",u,u,_),o.call(a+"_add",_,u,_),o.call(a+"_add",r,r,d),o.call(a+"_square",_,s),o.call(a+"_sub",s,h,s),o.call(a+"_sub",s,h,s),o.call(a+"_add",f,f,p),o.call(a+"_add",p,p,p),o.call(a+"_add",p,p,p),o.call(a+"_sub",h,s,c),o.call(a+"_mul",c,_,c),o.call(a+"_sub",c,p,c))}(),function(){const i=t.addFunction(e+"_double");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.i32_add(o.getLocal("p1"),o.i32_const(2*n)),c=o.getLocal("pr"),d=o.i32_add(o.getLocal("pr"),o.i32_const(n)),u=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n)),m=o.i32_const(t.alloc(n)),w=o.i32_const(t.alloc(n)),L=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),[...o.call(e+"_copy",o.getLocal("p1"),o.getLocal("pr")),...o.ret([])]),o.if(o.call(a+"_isOne",s),[...o.ret(o.call(e+"_doubleAffine",o.getLocal("p1"),o.getLocal("pr"))),...o.ret([])]),o.call(a+"_square",l,g),o.call(a+"_square",r,f),o.call(a+"_square",f,h),o.call(a+"_add",l,f,_),o.call(a+"_square",_,_),o.call(a+"_sub",_,g,_),o.call(a+"_sub",_,h,_),o.call(a+"_add",_,_,_),o.call(a+"_add",g,g,p),o.call(a+"_add",p,g,p),o.call(a+"_square",p,m),o.call(a+"_mul",r,s,w),o.call(a+"_add",_,_,c),o.call(a+"_sub",m,c,c),o.call(a+"_add",h,h,L),o.call(a+"_add",L,L,L),o.call(a+"_add",L,L,L),o.call(a+"_sub",_,c,d),o.call(a+"_mul",d,p,d),o.call(a+"_sub",d,L,d),o.call(a+"_add",w,w,u))}(),function(){const i=t.addFunction(e+"_addAffine");i.addParam("p1","i32"),i.addParam("p2","i32"),i.addParam("pr","i32"),i.addLocal("z1","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n));i.addCode(o.setLocal("z1",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))));const s=o.getLocal("p2"),c=o.i32_add(o.getLocal("p2"),o.i32_const(n)),d=o.getLocal("pr"),u=o.i32_add(o.getLocal("pr"),o.i32_const(n)),g=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n)),m=o.i32_const(t.alloc(n)),w=o.i32_const(t.alloc(n)),L=o.i32_const(t.alloc(n)),b=o.i32_const(t.alloc(n)),A=o.i32_const(t.alloc(n)),y=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZeroAffine",o.getLocal("p1")),[...o.call(e+"_copyAffine",o.getLocal("p2"),o.getLocal("pr")),...o.call(a+"_one",o.i32_add(o.getLocal("pr"),o.i32_const(2*n))),...o.ret([])]),o.if(o.call(e+"_isZeroAffine",o.getLocal("p2")),[...o.call(e+"_copyAffine",o.getLocal("p1"),o.getLocal("pr")),...o.call(a+"_one",o.i32_add(o.getLocal("pr"),o.i32_const(2*n))),...o.ret([])]),o.if(o.call(a+"_eq",l,s),o.if(o.call(a+"_eq",r,c),[...o.call(e+"_doubleAffine",o.getLocal("p2"),o.getLocal("pr")),...o.ret([])])),o.call(a+"_sub",s,l,f),o.call(a+"_sub",c,r,_),o.call(a+"_square",f,h),o.call(a+"_add",h,h,p),o.call(a+"_add",p,p,p),o.call(a+"_mul",f,p,m),o.call(a+"_add",_,_,w),o.call(a+"_mul",l,p,b),o.call(a+"_square",w,L),o.call(a+"_add",b,b,A),o.call(a+"_sub",L,m,d),o.call(a+"_sub",d,A,d),o.call(a+"_mul",r,m,y),o.call(a+"_add",y,y,y),o.call(a+"_sub",b,d,u),o.call(a+"_mul",u,w,u),o.call(a+"_sub",u,y,u),o.call(a+"_add",f,f,g))}(),function(){const i=t.addFunction(e+"_addMixed");i.addParam("p1","i32"),i.addParam("p2","i32"),i.addParam("pr","i32"),i.addLocal("z1","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n));i.addCode(o.setLocal("z1",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))));const s=o.getLocal("z1"),c=o.getLocal("p2"),d=o.i32_add(o.getLocal("p2"),o.i32_const(n)),u=o.getLocal("pr"),g=o.i32_add(o.getLocal("pr"),o.i32_const(n)),f=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),h=o.i32_const(t.alloc(n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n)),m=o.i32_const(t.alloc(n)),w=o.i32_const(t.alloc(n)),L=o.i32_const(t.alloc(n)),b=o.i32_const(t.alloc(n)),A=o.i32_const(t.alloc(n)),y=o.i32_const(t.alloc(n)),C=o.i32_const(t.alloc(n)),I=o.i32_const(t.alloc(n)),F=o.i32_const(t.alloc(n)),x=o.i32_const(t.alloc(n)),E=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),[...o.call(e+"_copyAffine",o.getLocal("p2"),o.getLocal("pr")),...o.call(a+"_one",o.i32_add(o.getLocal("pr"),o.i32_const(2*n))),...o.ret([])]),o.if(o.call(e+"_isZeroAffine",o.getLocal("p2")),[...o.call(e+"_copy",o.getLocal("p1"),o.getLocal("pr")),...o.ret([])]),o.if(o.call(a+"_isOne",s),[...o.call(e+"_addAffine",l,c,u),...o.ret([])]),o.call(a+"_square",s,h),o.call(a+"_mul",c,h,_),o.call(a+"_mul",s,h,p),o.call(a+"_mul",d,p,m),o.if(o.call(a+"_eq",l,_),o.if(o.call(a+"_eq",r,m),[...o.call(e+"_doubleAffine",o.getLocal("p2"),o.getLocal("pr")),...o.ret([])])),o.call(a+"_sub",_,l,w),o.call(a+"_sub",m,r,b),o.call(a+"_square",w,L),o.call(a+"_add",L,L,A),o.call(a+"_add",A,A,A),o.call(a+"_mul",w,A,y),o.call(a+"_add",b,b,C),o.call(a+"_mul",l,A,F),o.call(a+"_square",C,I),o.call(a+"_add",F,F,x),o.call(a+"_sub",I,y,u),o.call(a+"_sub",u,x,u),o.call(a+"_mul",r,y,E),o.call(a+"_add",E,E,E),o.call(a+"_sub",F,u,g),o.call(a+"_mul",g,C,g),o.call(a+"_sub",g,E,g),o.call(a+"_add",s,w,f),o.call(a+"_square",f,f),o.call(a+"_sub",f,h,f),o.call(a+"_sub",f,L,f))}(),function(){const i=t.addFunction(e+"_add");i.addParam("p1","i32"),i.addParam("p2","i32"),i.addParam("pr","i32"),i.addLocal("z1","i32"),i.addLocal("z2","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n));i.addCode(o.setLocal("z1",o.i32_add(o.getLocal("p1"),o.i32_const(2*n))));const s=o.getLocal("z1"),c=o.getLocal("p2"),d=o.i32_add(o.getLocal("p2"),o.i32_const(n));i.addCode(o.setLocal("z2",o.i32_add(o.getLocal("p2"),o.i32_const(2*n))));const u=o.getLocal("z2"),g=o.getLocal("pr"),f=o.i32_add(o.getLocal("pr"),o.i32_const(n)),h=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),_=o.i32_const(t.alloc(n)),p=o.i32_const(t.alloc(n)),m=o.i32_const(t.alloc(n)),w=o.i32_const(t.alloc(n)),L=o.i32_const(t.alloc(n)),b=o.i32_const(t.alloc(n)),A=o.i32_const(t.alloc(n)),y=o.i32_const(t.alloc(n)),C=o.i32_const(t.alloc(n)),I=o.i32_const(t.alloc(n)),F=o.i32_const(t.alloc(n)),x=o.i32_const(t.alloc(n)),E=o.i32_const(t.alloc(n)),v=o.i32_const(t.alloc(n)),B=o.i32_const(t.alloc(n)),S=o.i32_const(t.alloc(n)),P=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),[...o.call(e+"_copy",o.getLocal("p2"),o.getLocal("pr")),...o.ret([])]),o.if(o.call(e+"_isZero",o.getLocal("p2")),[...o.call(e+"_copy",o.getLocal("p1"),o.getLocal("pr")),...o.ret([])]),o.if(o.call(a+"_isOne",s),[...o.call(e+"_addMixed",c,l,g),...o.ret([])]),o.if(o.call(a+"_isOne",u),[...o.call(e+"_addMixed",l,c,g),...o.ret([])]),o.call(a+"_square",s,_),o.call(a+"_square",u,p),o.call(a+"_mul",l,p,m),o.call(a+"_mul",c,_,w),o.call(a+"_mul",s,_,L),o.call(a+"_mul",u,p,b),o.call(a+"_mul",r,b,A),o.call(a+"_mul",d,L,y),o.if(o.call(a+"_eq",m,w),o.if(o.call(a+"_eq",A,y),[...o.call(e+"_double",o.getLocal("p1"),o.getLocal("pr")),...o.ret([])])),o.call(a+"_sub",w,m,C),o.call(a+"_sub",y,A,I),o.call(a+"_add",C,C,F),o.call(a+"_square",F,F),o.call(a+"_mul",C,F,x),o.call(a+"_add",I,I,E),o.call(a+"_mul",m,F,B),o.call(a+"_square",E,v),o.call(a+"_add",B,B,S),o.call(a+"_sub",v,x,g),o.call(a+"_sub",g,S,g),o.call(a+"_mul",A,x,P),o.call(a+"_add",P,P,P),o.call(a+"_sub",B,g,f),o.call(a+"_mul",f,E,f),o.call(a+"_sub",f,P,f),o.call(a+"_add",s,u,h),o.call(a+"_square",h,h),o.call(a+"_sub",h,_,h),o.call(a+"_sub",h,p,h),o.call(a+"_mul",h,C,h))}(),function(){const i=t.addFunction(e+"_negAffine");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.getLocal("pr"),c=o.i32_add(o.getLocal("pr"),o.i32_const(n));i.addCode(o.call(a+"_copy",l,s),o.call(a+"_neg",r,c))}(),function(){const i=t.addFunction(e+"_neg");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.i32_add(o.getLocal("p1"),o.i32_const(2*n)),c=o.getLocal("pr"),d=o.i32_add(o.getLocal("pr"),o.i32_const(n)),u=o.i32_add(o.getLocal("pr"),o.i32_const(2*n));i.addCode(o.call(a+"_copy",l,c),o.call(a+"_neg",r,d),o.call(a+"_copy",s,u))}(),function(){const a=t.addFunction(e+"_subAffine");a.addParam("p1","i32"),a.addParam("p2","i32"),a.addParam("pr","i32");const i=a.getCodeBuilder(),o=i.i32_const(t.alloc(3*n));a.addCode(i.call(e+"_negAffine",i.getLocal("p2"),o),i.call(e+"_addAffine",i.getLocal("p1"),o,i.getLocal("pr")))}(),function(){const a=t.addFunction(e+"_subMixed");a.addParam("p1","i32"),a.addParam("p2","i32"),a.addParam("pr","i32");const i=a.getCodeBuilder(),o=i.i32_const(t.alloc(3*n));a.addCode(i.call(e+"_negAffine",i.getLocal("p2"),o),i.call(e+"_addMixed",i.getLocal("p1"),o,i.getLocal("pr")))}(),function(){const a=t.addFunction(e+"_sub");a.addParam("p1","i32"),a.addParam("p2","i32"),a.addParam("pr","i32");const i=a.getCodeBuilder(),o=i.i32_const(t.alloc(3*n));a.addCode(i.call(e+"_neg",i.getLocal("p2"),o),i.call(e+"_add",i.getLocal("p1"),o,i.getLocal("pr")))}(),function(){const i=t.addFunction(e+"_fromMontgomeryAffine");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_fromMontgomery",o.getLocal("p1"),o.getLocal("pr")));for(let t=1;t<2;t++)i.addCode(o.call(a+"_fromMontgomery",o.i32_add(o.getLocal("p1"),o.i32_const(t*n)),o.i32_add(o.getLocal("pr"),o.i32_const(t*n))))}(),function(){const i=t.addFunction(e+"_fromMontgomery");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_fromMontgomery",o.getLocal("p1"),o.getLocal("pr")));for(let t=1;t<3;t++)i.addCode(o.call(a+"_fromMontgomery",o.i32_add(o.getLocal("p1"),o.i32_const(t*n)),o.i32_add(o.getLocal("pr"),o.i32_const(t*n))))}(),function(){const i=t.addFunction(e+"_toMontgomeryAffine");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_toMontgomery",o.getLocal("p1"),o.getLocal("pr")));for(let t=1;t<2;t++)i.addCode(o.call(a+"_toMontgomery",o.i32_add(o.getLocal("p1"),o.i32_const(t*n)),o.i32_add(o.getLocal("pr"),o.i32_const(t*n))))}(),function(){const i=t.addFunction(e+"_toMontgomery");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder();i.addCode(o.call(a+"_toMontgomery",o.getLocal("p1"),o.getLocal("pr")));for(let t=1;t<3;t++)i.addCode(o.call(a+"_toMontgomery",o.i32_add(o.getLocal("p1"),o.i32_const(t*n)),o.i32_add(o.getLocal("pr"),o.i32_const(t*n))))}(),function(){const i=t.addFunction(e+"_toAffine");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.i32_add(o.getLocal("p1"),o.i32_const(2*n)),c=o.getLocal("pr"),d=o.i32_add(o.getLocal("pr"),o.i32_const(n)),u=o.i32_const(t.alloc(n)),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),[...o.call(a+"_zero",c),...o.call(a+"_zero",d)],[...o.call(a+"_inverse",s,u),...o.call(a+"_square",u,g),...o.call(a+"_mul",u,g,f),...o.call(a+"_mul",l,g,c),...o.call(a+"_mul",r,f,d)]))}(),function(){const o=t.addFunction(e+"_inCurveAffine");o.addParam("pIn","i32"),o.setReturnType("i32");const l=o.getCodeBuilder(),r=l.getLocal("pIn"),s=l.i32_add(l.getLocal("pIn"),l.i32_const(n)),c=l.i32_const(t.alloc(n)),d=l.i32_const(t.alloc(n));o.addCode(l.call(a+"_square",s,c),l.call(a+"_square",r,d),l.call(a+"_mul",r,d,d),l.call(a+"_add",d,l.i32_const(i),d),l.ret(l.call(a+"_eq",c,d)))}(),function(){const a=t.addFunction(e+"_inCurve");a.addParam("pIn","i32"),a.setReturnType("i32");const i=a.getCodeBuilder(),o=i.i32_const(t.alloc(2*n));a.addCode(i.call(e+"_toAffine",i.getLocal("pIn"),o),i.ret(i.call(e+"_inCurveAffine",o)))}(),function(){const i=t.addFunction(e+"_batchToAffine");i.addParam("pIn","i32"),i.addParam("n","i32"),i.addParam("pOut","i32"),i.addLocal("pAux","i32"),i.addLocal("itIn","i32"),i.addLocal("itAux","i32"),i.addLocal("itOut","i32"),i.addLocal("i","i32");const o=i.getCodeBuilder(),l=o.i32_const(t.alloc(n));i.addCode(o.setLocal("pAux",o.i32_load(o.i32_const(0))),o.i32_store(o.i32_const(0),o.i32_add(o.getLocal("pAux"),o.i32_mul(o.getLocal("n"),o.i32_const(n)))),o.call(a+"_batchInverse",o.i32_add(o.getLocal("pIn"),o.i32_const(2*n)),o.i32_const(3*n),o.getLocal("n"),o.getLocal("pAux"),o.i32_const(n)),o.setLocal("itIn",o.getLocal("pIn")),o.setLocal("itAux",o.getLocal("pAux")),o.setLocal("itOut",o.getLocal("pOut")),o.setLocal("i",o.i32_const(0)),o.block(o.loop(o.br_if(1,o.i32_eq(o.getLocal("i"),o.getLocal("n"))),o.if(o.call(a+"_isZero",o.getLocal("itAux")),[...o.call(a+"_zero",o.getLocal("itOut")),...o.call(a+"_zero",o.i32_add(o.getLocal("itOut"),o.i32_const(n)))],[...o.call(a+"_mul",o.getLocal("itAux"),o.i32_add(o.getLocal("itIn"),o.i32_const(n)),l),...o.call(a+"_square",o.getLocal("itAux"),o.getLocal("itAux")),...o.call(a+"_mul",o.getLocal("itAux"),o.getLocal("itIn"),o.getLocal("itOut")),...o.call(a+"_mul",o.getLocal("itAux"),l,o.i32_add(o.getLocal("itOut"),o.i32_const(n)))]),o.setLocal("itIn",o.i32_add(o.getLocal("itIn"),o.i32_const(3*n))),o.setLocal("itOut",o.i32_add(o.getLocal("itOut"),o.i32_const(2*n))),o.setLocal("itAux",o.i32_add(o.getLocal("itAux"),o.i32_const(n))),o.setLocal("i",o.i32_add(o.getLocal("i"),o.i32_const(1))),o.br(0))),o.i32_store(o.i32_const(0),o.getLocal("pAux")))}(),function(){const i=t.addFunction(e+"_normalize");i.addParam("p1","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),l=o.getLocal("p1"),r=o.i32_add(o.getLocal("p1"),o.i32_const(n)),s=o.i32_add(o.getLocal("p1"),o.i32_const(2*n)),c=o.getLocal("pr"),d=o.i32_add(o.getLocal("pr"),o.i32_const(n)),u=o.i32_add(o.getLocal("pr"),o.i32_const(2*n)),g=o.i32_const(t.alloc(n)),f=o.i32_const(t.alloc(n)),h=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("p1")),o.call(e+"_zero",o.getLocal("pr")),[...o.call(a+"_inverse",s,g),...o.call(a+"_square",g,f),...o.call(a+"_mul",g,f,h),...o.call(a+"_mul",l,f,c),...o.call(a+"_mul",r,h,d),...o.call(a+"_one",u)]))}(),function(){const a=t.addFunction(e+"__reverseBytes");a.addParam("pIn","i32"),a.addParam("n","i32"),a.addParam("pOut","i32"),a.addLocal("itOut","i32"),a.addLocal("itIn","i32");const i=a.getCodeBuilder();a.addCode(i.setLocal("itOut",i.i32_sub(i.i32_add(i.getLocal("pOut"),i.getLocal("n")),i.i32_const(1))),i.setLocal("itIn",i.getLocal("pIn")),i.block(i.loop(i.br_if(1,i.i32_lt_s(i.getLocal("itOut"),i.getLocal("pOut"))),i.i32_store8(i.getLocal("itOut"),i.i32_load8_u(i.getLocal("itIn"))),i.setLocal("itOut",i.i32_sub(i.getLocal("itOut"),i.i32_const(1))),i.setLocal("itIn",i.i32_add(i.getLocal("itIn"),i.i32_const(1))),i.br(0))))}(),function(){const a=t.addFunction(e+"_LEMtoU");a.addParam("pIn","i32"),a.addParam("pOut","i32");const i=a.getCodeBuilder(),o=t.alloc(2*n),l=i.i32_const(o),r=i.i32_const(o),s=i.i32_const(o+n);a.addCode(i.if(i.call(e+"_isZeroAffine",i.getLocal("pIn")),[...i.call(e+"_zeroAffine",i.getLocal("pOut")),...i.i32_store8(i.getLocal("pOut"),i.i32_const(64)),...i.ret([])]),i.call(e+"_fromMontgomeryAffine",i.getLocal("pIn"),l),i.call(e+"__reverseBytes",r,i.i32_const(n),i.getLocal("pOut")),i.call(e+"__reverseBytes",s,i.i32_const(n),i.i32_add(i.getLocal("pOut"),i.i32_const(n))))}(),function(){const i=t.addFunction(e+"_LEMtoC");i.addParam("pIn","i32"),i.addParam("pOut","i32");const o=i.getCodeBuilder(),l=o.i32_const(t.alloc(n));i.addCode(o.if(o.call(e+"_isZero",o.getLocal("pIn")),[...o.call(a+"_zero",o.getLocal("pOut")),...o.i32_store8(o.getLocal("pOut"),o.i32_const(64)),...o.ret([])]),o.call(a+"_fromMontgomery",o.getLocal("pIn"),l),o.call(e+"__reverseBytes",l,o.i32_const(n),o.getLocal("pOut")),o.if(o.i32_eq(o.call(a+"_sign",o.i32_add(o.getLocal("pIn"),o.i32_const(n))),o.i32_const(-1)),o.i32_store8(o.getLocal("pOut"),o.i32_or(o.i32_load8_u(o.getLocal("pOut")),o.i32_const(128)))))}(),function(){const a=t.addFunction(e+"_UtoLEM");a.addParam("pIn","i32"),a.addParam("pOut","i32");const i=a.getCodeBuilder(),o=t.alloc(2*n),l=i.i32_const(o),r=i.i32_const(o),s=i.i32_const(o+n);a.addCode(i.if(i.i32_and(i.i32_load8_u(i.getLocal("pIn")),i.i32_const(64)),[...i.call(e+"_zeroAffine",i.getLocal("pOut")),...i.ret([])]),i.call(e+"__reverseBytes",i.getLocal("pIn"),i.i32_const(n),r),i.call(e+"__reverseBytes",i.i32_add(i.getLocal("pIn"),i.i32_const(n)),i.i32_const(n),s),i.call(e+"_toMontgomeryAffine",l,i.getLocal("pOut")))}(),function(){const o=t.addFunction(e+"_CtoLEM");o.addParam("pIn","i32"),o.addParam("pOut","i32"),o.addLocal("firstByte","i32"),o.addLocal("greatest","i32");const l=o.getCodeBuilder(),r=t.alloc(2*n),s=l.i32_const(r),c=l.i32_const(r+n);o.addCode(l.setLocal("firstByte",l.i32_load8_u(l.getLocal("pIn"))),l.if(l.i32_and(l.getLocal("firstByte"),l.i32_const(64)),[...l.call(e+"_zeroAffine",l.getLocal("pOut")),...l.ret([])]),l.setLocal("greatest",l.i32_and(l.getLocal("firstByte"),l.i32_const(128))),l.call(a+"_copy",l.getLocal("pIn"),c),l.i32_store8(c,l.i32_and(l.getLocal("firstByte"),l.i32_const(63))),l.call(e+"__reverseBytes",c,l.i32_const(n),s),l.call(a+"_toMontgomery",s,l.getLocal("pOut")),l.call(a+"_square",l.getLocal("pOut"),c),l.call(a+"_mul",l.getLocal("pOut"),c,c),l.call(a+"_add",c,l.i32_const(i),c),l.call(a+"_sqrt",c,c),l.call(a+"_neg",c,s),l.if(l.i32_eq(l.call(a+"_sign",c),l.i32_const(-1)),l.if(l.getLocal("greatest"),l.call(a+"_copy",c,l.i32_add(l.getLocal("pOut"),l.i32_const(n))),l.call(a+"_neg",c,l.i32_add(l.getLocal("pOut"),l.i32_const(n)))),l.if(l.getLocal("greatest"),l.call(a+"_neg",c,l.i32_add(l.getLocal("pOut"),l.i32_const(n))),l.call(a+"_copy",c,l.i32_add(l.getLocal("pOut"),l.i32_const(n))))))}(),Tt(t,e+"_batchLEMtoU",e+"_LEMtoU",2*n,2*n),Tt(t,e+"_batchLEMtoC",e+"_LEMtoC",2*n,n),Tt(t,e+"_batchUtoLEM",e+"_UtoLEM",2*n,2*n),Tt(t,e+"_batchCtoLEM",e+"_CtoLEM",n,2*n,!0),Tt(t,e+"_batchToJacobian",e+"_toJacobian",2*n,3*n,!0),Qt(t,e,e+"_multiexp",e+"_add",3*n),Qt(t,e,e+"_multiexpAffine",e+"_addMixed",2*n),Ut(t,e+"_timesScalar",3*n,e+"_add",e+"_double",e+"_sub",e+"_copy",e+"_zero"),Ut(t,e+"_timesScalarAffine",2*n,e+"_addMixed",e+"_double",e+"_subMixed",e+"_copyAffine",e+"_zero"),t.exportFunction(e+"_isZero"),t.exportFunction(e+"_isZeroAffine"),t.exportFunction(e+"_eq"),t.exportFunction(e+"_eqMixed"),t.exportFunction(e+"_eqAffine"),t.exportFunction(e+"_copy"),t.exportFunction(e+"_copyAffine"),t.exportFunction(e+"_zero"),t.exportFunction(e+"_zeroAffine"),t.exportFunction(e+"_double"),t.exportFunction(e+"_doubleAffine"),t.exportFunction(e+"_add"),t.exportFunction(e+"_addMixed"),t.exportFunction(e+"_addAffine"),t.exportFunction(e+"_neg"),t.exportFunction(e+"_negAffine"),t.exportFunction(e+"_sub"),t.exportFunction(e+"_subMixed"),t.exportFunction(e+"_subAffine"),t.exportFunction(e+"_fromMontgomery"),t.exportFunction(e+"_fromMontgomeryAffine"),t.exportFunction(e+"_toMontgomery"),t.exportFunction(e+"_toMontgomeryAffine"),t.exportFunction(e+"_timesScalar"),t.exportFunction(e+"_timesScalarAffine"),t.exportFunction(e+"_normalize"),t.exportFunction(e+"_LEMtoU"),t.exportFunction(e+"_LEMtoC"),t.exportFunction(e+"_UtoLEM"),t.exportFunction(e+"_CtoLEM"),t.exportFunction(e+"_batchLEMtoU"),t.exportFunction(e+"_batchLEMtoC"),t.exportFunction(e+"_batchUtoLEM"),t.exportFunction(e+"_batchCtoLEM"),t.exportFunction(e+"_toAffine"),t.exportFunction(e+"_toJacobian"),t.exportFunction(e+"_batchToAffine"),t.exportFunction(e+"_batchToJacobian"),t.exportFunction(e+"_inCurve"),t.exportFunction(e+"_inCurveAffine"),e};const{isOdd:Mt,modInv:kt,modPow:Rt}=J,Dt=K;var Nt=function(t,e,a,i,o){const n=8*t.modules[i].n64,l=8*t.modules[a].n64,r=t.modules[i].q;let s=r-1n,c=0;for(;!Mt(s);)c++,s>>=1n;let d=2n;for(;1n===Rt(d,r>>1n,r);)d+=1n;const u=new Array(c+1);u[c]=Rt(d,s,r);let g=c-1;for(;g>=0;)u[g]=Rt(u[g+1],2n,r),g--;const f=[],h=(1n<>a);return e}const F=Array(256);for(let t=0;t<256;t++)F[t]=I(t);const x=t.alloc(F);function E(){const a=t.addFunction(e+"_fft");a.addParam("px","i32"),a.addParam("n","i32"),a.addLocal("bits","i32");const o=a.getCodeBuilder(),l=o.i32_const(t.alloc(n));a.addCode(o.setLocal("bits",o.call(e+"__log2",o.getLocal("n"))),o.call(i+"_one",l),o.call(e+"_rawfft",o.getLocal("px"),o.getLocal("bits"),o.i32_const(0),l))}!function(){const a=t.addFunction(e+"__rev");a.addParam("x","i32"),a.addParam("bits","i32"),a.setReturnType("i32");const i=a.getCodeBuilder();a.addCode(i.i32_rotl(i.i32_add(i.i32_add(i.i32_shl(i.i32_load8_u(i.i32_and(i.getLocal("x"),i.i32_const(255)),x,0),i.i32_const(24)),i.i32_shl(i.i32_load8_u(i.i32_and(i.i32_shr_u(i.getLocal("x"),i.i32_const(8)),i.i32_const(255)),x,0),i.i32_const(16))),i.i32_add(i.i32_shl(i.i32_load8_u(i.i32_and(i.i32_shr_u(i.getLocal("x"),i.i32_const(16)),i.i32_const(255)),x,0),i.i32_const(8)),i.i32_load8_u(i.i32_and(i.i32_shr_u(i.getLocal("x"),i.i32_const(24)),i.i32_const(255)),x,0))),i.getLocal("bits")))}(),function(){const i=t.addFunction(e+"__reversePermutation");i.addParam("px","i32"),i.addParam("bits","i32"),i.addLocal("n","i32"),i.addLocal("i","i32"),i.addLocal("ri","i32"),i.addLocal("idx1","i32"),i.addLocal("idx2","i32");const o=i.getCodeBuilder(),n=o.i32_const(t.alloc(l));i.addCode(o.setLocal("n",o.i32_shl(o.i32_const(1),o.getLocal("bits"))),o.setLocal("i",o.i32_const(0)),o.block(o.loop(o.br_if(1,o.i32_eq(o.getLocal("i"),o.getLocal("n"))),o.setLocal("idx1",o.i32_add(o.getLocal("px"),o.i32_mul(o.getLocal("i"),o.i32_const(l)))),o.setLocal("ri",o.call(e+"__rev",o.getLocal("i"),o.getLocal("bits"))),o.setLocal("idx2",o.i32_add(o.getLocal("px"),o.i32_mul(o.getLocal("ri"),o.i32_const(l)))),o.if(o.i32_lt_u(o.getLocal("i"),o.getLocal("ri")),[...o.call(a+"_copy",o.getLocal("idx1"),n),...o.call(a+"_copy",o.getLocal("idx2"),o.getLocal("idx1")),...o.call(a+"_copy",n,o.getLocal("idx2"))]),o.setLocal("i",o.i32_add(o.getLocal("i"),o.i32_const(1))),o.br(0))))}(),function(){const n=t.addFunction(e+"__fftFinal");n.addParam("px","i32"),n.addParam("bits","i32"),n.addParam("reverse","i32"),n.addParam("mulFactor","i32"),n.addLocal("n","i32"),n.addLocal("ndiv2","i32"),n.addLocal("pInv2","i32"),n.addLocal("i","i32"),n.addLocal("mask","i32"),n.addLocal("idx1","i32"),n.addLocal("idx2","i32");const r=n.getCodeBuilder(),s=r.i32_const(t.alloc(l));n.addCode(r.if(r.i32_and(r.i32_eqz(r.getLocal("reverse")),r.call(i+"_isOne",r.getLocal("mulFactor"))),r.ret([])),r.setLocal("n",r.i32_shl(r.i32_const(1),r.getLocal("bits"))),r.setLocal("mask",r.i32_sub(r.getLocal("n"),r.i32_const(1))),r.setLocal("i",r.i32_const(1)),r.setLocal("ndiv2",r.i32_shr_u(r.getLocal("n"),r.i32_const(1))),r.block(r.loop(r.br_if(1,r.i32_ge_u(r.getLocal("i"),r.getLocal("ndiv2"))),r.setLocal("idx1",r.i32_add(r.getLocal("px"),r.i32_mul(r.getLocal("i"),r.i32_const(l)))),r.setLocal("idx2",r.i32_add(r.getLocal("px"),r.i32_mul(r.i32_sub(r.getLocal("n"),r.getLocal("i")),r.i32_const(l)))),r.if(r.getLocal("reverse"),r.if(r.call(i+"_isOne",r.getLocal("mulFactor")),[...r.call(a+"_copy",r.getLocal("idx1"),s),...r.call(a+"_copy",r.getLocal("idx2"),r.getLocal("idx1")),...r.call(a+"_copy",s,r.getLocal("idx2"))],[...r.call(a+"_copy",r.getLocal("idx1"),s),...r.call(o,r.getLocal("idx2"),r.getLocal("mulFactor"),r.getLocal("idx1")),...r.call(o,s,r.getLocal("mulFactor"),r.getLocal("idx2"))]),r.if(r.call(i+"_isOne",r.getLocal("mulFactor")),[],[...r.call(o,r.getLocal("idx1"),r.getLocal("mulFactor"),r.getLocal("idx1")),...r.call(o,r.getLocal("idx2"),r.getLocal("mulFactor"),r.getLocal("idx2"))])),r.setLocal("i",r.i32_add(r.getLocal("i"),r.i32_const(1))),r.br(0))),r.if(r.call(i+"_isOne",r.getLocal("mulFactor")),[],[...r.call(o,r.getLocal("px"),r.getLocal("mulFactor"),r.getLocal("px")),...r.setLocal("idx2",r.i32_add(r.getLocal("px"),r.i32_mul(r.getLocal("ndiv2"),r.i32_const(l)))),...r.call(o,r.getLocal("idx2"),r.getLocal("mulFactor"),r.getLocal("idx2"))]))}(),function(){const r=t.addFunction(e+"_rawfft");r.addParam("px","i32"),r.addParam("bits","i32"),r.addParam("reverse","i32"),r.addParam("mulFactor","i32"),r.addLocal("s","i32"),r.addLocal("k","i32"),r.addLocal("j","i32"),r.addLocal("m","i32"),r.addLocal("mdiv2","i32"),r.addLocal("n","i32"),r.addLocal("pwm","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l)),u=s.i32_const(t.alloc(l));r.addCode(s.call(e+"__reversePermutation",s.getLocal("px"),s.getLocal("bits")),s.setLocal("n",s.i32_shl(s.i32_const(1),s.getLocal("bits"))),s.setLocal("s",s.i32_const(1)),s.block(s.loop(s.br_if(1,s.i32_gt_u(s.getLocal("s"),s.getLocal("bits"))),s.setLocal("m",s.i32_shl(s.i32_const(1),s.getLocal("s"))),s.setLocal("pwm",s.i32_add(s.i32_const(_),s.i32_mul(s.getLocal("s"),s.i32_const(n)))),s.setLocal("k",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_ge_u(s.getLocal("k"),s.getLocal("n"))),s.call(i+"_one",c),s.setLocal("mdiv2",s.i32_shr_u(s.getLocal("m"),s.i32_const(1))),s.setLocal("j",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_ge_u(s.getLocal("j"),s.getLocal("mdiv2"))),s.setLocal("idx1",s.i32_add(s.getLocal("px"),s.i32_mul(s.i32_add(s.getLocal("k"),s.getLocal("j")),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("idx1"),s.i32_mul(s.getLocal("mdiv2"),s.i32_const(l)))),s.call(o,s.getLocal("idx2"),c,d),s.call(a+"_copy",s.getLocal("idx1"),u),s.call(a+"_add",u,d,s.getLocal("idx1")),s.call(a+"_sub",u,d,s.getLocal("idx2")),s.call(i+"_mul",c,s.getLocal("pwm"),c),s.setLocal("j",s.i32_add(s.getLocal("j"),s.i32_const(1))),s.br(0))),s.setLocal("k",s.i32_add(s.getLocal("k"),s.getLocal("m"))),s.br(0))),s.setLocal("s",s.i32_add(s.getLocal("s"),s.i32_const(1))),s.br(0))),s.call(e+"__fftFinal",s.getLocal("px"),s.getLocal("bits"),s.getLocal("reverse"),s.getLocal("mulFactor")))}(),function(){const a=t.addFunction(e+"__log2");a.addParam("n","i32"),a.setReturnType("i32"),a.addLocal("bits","i32"),a.addLocal("aux","i32");const i=a.getCodeBuilder();a.addCode(i.setLocal("aux",i.i32_shr_u(i.getLocal("n"),i.i32_const(1)))),a.addCode(i.setLocal("bits",i.i32_const(0))),a.addCode(i.block(i.loop(i.br_if(1,i.i32_eqz(i.getLocal("aux"))),i.setLocal("aux",i.i32_shr_u(i.getLocal("aux"),i.i32_const(1))),i.setLocal("bits",i.i32_add(i.getLocal("bits"),i.i32_const(1))),i.br(0)))),a.addCode(i.if(i.i32_ne(i.getLocal("n"),i.i32_shl(i.i32_const(1),i.getLocal("bits"))),i.unreachable())),a.addCode(i.if(i.i32_gt_u(i.getLocal("bits"),i.i32_const(c)),i.unreachable())),a.addCode(i.getLocal("bits"))}(),E(),function(){const a=t.addFunction(e+"_ifft");a.addParam("px","i32"),a.addParam("n","i32"),a.addLocal("bits","i32"),a.addLocal("pInv2","i32");const i=a.getCodeBuilder();a.addCode(i.setLocal("bits",i.call(e+"__log2",i.getLocal("n"))),i.setLocal("pInv2",i.i32_add(i.i32_const(w),i.i32_mul(i.getLocal("bits"),i.i32_const(n)))),i.call(e+"_rawfft",i.getLocal("px"),i.getLocal("bits"),i.i32_const(1),i.getLocal("pInv2")))}(),function(){const r=t.addFunction(e+"_fftJoin");r.addParam("pBuff1","i32"),r.addParam("pBuff2","i32"),r.addParam("n","i32"),r.addParam("first","i32"),r.addParam("inc","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32"),r.addLocal("i","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l)),u=s.i32_const(t.alloc(l));r.addCode(s.call(i+"_copy",s.getLocal("first"),c),s.setLocal("i",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("i"),s.getLocal("n"))),s.setLocal("idx1",s.i32_add(s.getLocal("pBuff1"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("pBuff2"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.call(o,s.getLocal("idx2"),c,d),s.call(a+"_copy",s.getLocal("idx1"),u),s.call(a+"_add",u,d,s.getLocal("idx1")),s.call(a+"_sub",u,d,s.getLocal("idx2")),s.call(i+"_mul",c,s.getLocal("inc"),c),s.setLocal("i",s.i32_add(s.getLocal("i"),s.i32_const(1))),s.br(0))))}(),function(){const r=t.addFunction(e+"_fftJoinExt");r.addParam("pBuff1","i32"),r.addParam("pBuff2","i32"),r.addParam("n","i32"),r.addParam("first","i32"),r.addParam("inc","i32"),r.addParam("totalBits","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32"),r.addLocal("i","i32"),r.addLocal("pShiftToM","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l));r.addCode(s.setLocal("pShiftToM",s.i32_add(s.i32_const(y),s.i32_mul(s.getLocal("totalBits"),s.i32_const(n)))),s.call(i+"_copy",s.getLocal("first"),c),s.setLocal("i",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("i"),s.getLocal("n"))),s.setLocal("idx1",s.i32_add(s.getLocal("pBuff1"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("pBuff2"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.call(a+"_add",s.getLocal("idx1"),s.getLocal("idx2"),d),s.call(o,s.getLocal("idx2"),s.getLocal("pShiftToM"),s.getLocal("idx2")),s.call(a+"_add",s.getLocal("idx1"),s.getLocal("idx2"),s.getLocal("idx2")),s.call(o,s.getLocal("idx2"),c,s.getLocal("idx2")),s.call(a+"_copy",d,s.getLocal("idx1")),s.call(i+"_mul",c,s.getLocal("inc"),c),s.setLocal("i",s.i32_add(s.getLocal("i"),s.i32_const(1))),s.br(0))))}(),function(){const r=t.addFunction(e+"_fftJoinExtInv");r.addParam("pBuff1","i32"),r.addParam("pBuff2","i32"),r.addParam("n","i32"),r.addParam("first","i32"),r.addParam("inc","i32"),r.addParam("totalBits","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32"),r.addLocal("i","i32"),r.addLocal("pShiftToM","i32"),r.addLocal("pSConst","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l));r.addCode(s.setLocal("pShiftToM",s.i32_add(s.i32_const(y),s.i32_mul(s.getLocal("totalBits"),s.i32_const(n)))),s.setLocal("pSConst",s.i32_add(s.i32_const(C),s.i32_mul(s.getLocal("totalBits"),s.i32_const(n)))),s.call(i+"_copy",s.getLocal("first"),c),s.setLocal("i",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("i"),s.getLocal("n"))),s.setLocal("idx1",s.i32_add(s.getLocal("pBuff1"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("pBuff2"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.call(o,s.getLocal("idx2"),c,d),s.call(a+"_sub",s.getLocal("idx1"),d,s.getLocal("idx2")),s.call(o,s.getLocal("idx2"),s.getLocal("pSConst"),s.getLocal("idx2")),s.call(o,s.getLocal("idx1"),s.getLocal("pShiftToM"),s.getLocal("idx1")),s.call(a+"_sub",d,s.getLocal("idx1"),s.getLocal("idx1")),s.call(o,s.getLocal("idx1"),s.getLocal("pSConst"),s.getLocal("idx1")),s.call(i+"_mul",c,s.getLocal("inc"),c),s.setLocal("i",s.i32_add(s.getLocal("i"),s.i32_const(1))),s.br(0))))}(),function(){const r=t.addFunction(e+"_fftMix");r.addParam("pBuff","i32"),r.addParam("n","i32"),r.addParam("exp","i32"),r.addLocal("nGroups","i32"),r.addLocal("nPerGroup","i32"),r.addLocal("nPerGroupDiv2","i32"),r.addLocal("pairOffset","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32"),r.addLocal("i","i32"),r.addLocal("j","i32"),r.addLocal("pwm","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l)),u=s.i32_const(t.alloc(l));r.addCode(s.setLocal("nPerGroup",s.i32_shl(s.i32_const(1),s.getLocal("exp"))),s.setLocal("nPerGroupDiv2",s.i32_shr_u(s.getLocal("nPerGroup"),s.i32_const(1))),s.setLocal("nGroups",s.i32_shr_u(s.getLocal("n"),s.getLocal("exp"))),s.setLocal("pairOffset",s.i32_mul(s.getLocal("nPerGroupDiv2"),s.i32_const(l))),s.setLocal("pwm",s.i32_add(s.i32_const(_),s.i32_mul(s.getLocal("exp"),s.i32_const(n)))),s.setLocal("i",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("i"),s.getLocal("nGroups"))),s.call(i+"_one",c),s.setLocal("j",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("j"),s.getLocal("nPerGroupDiv2"))),s.setLocal("idx1",s.i32_add(s.getLocal("pBuff"),s.i32_mul(s.i32_add(s.i32_mul(s.getLocal("i"),s.getLocal("nPerGroup")),s.getLocal("j")),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("idx1"),s.getLocal("pairOffset"))),s.call(o,s.getLocal("idx2"),c,d),s.call(a+"_copy",s.getLocal("idx1"),u),s.call(a+"_add",u,d,s.getLocal("idx1")),s.call(a+"_sub",u,d,s.getLocal("idx2")),s.call(i+"_mul",c,s.getLocal("pwm"),c),s.setLocal("j",s.i32_add(s.getLocal("j"),s.i32_const(1))),s.br(0))),s.setLocal("i",s.i32_add(s.getLocal("i"),s.i32_const(1))),s.br(0))))}(),function(){const i=t.addFunction(e+"_fftFinal");i.addParam("pBuff","i32"),i.addParam("n","i32"),i.addParam("factor","i32"),i.addLocal("idx1","i32"),i.addLocal("idx2","i32"),i.addLocal("i","i32"),i.addLocal("ndiv2","i32");const n=i.getCodeBuilder(),r=n.i32_const(t.alloc(l));i.addCode(n.setLocal("ndiv2",n.i32_shr_u(n.getLocal("n"),n.i32_const(1))),n.if(n.i32_and(n.getLocal("n"),n.i32_const(1)),n.call(o,n.i32_add(n.getLocal("pBuff"),n.i32_mul(n.getLocal("ndiv2"),n.i32_const(l))),n.getLocal("factor"),n.i32_add(n.getLocal("pBuff"),n.i32_mul(n.getLocal("ndiv2"),n.i32_const(l))))),n.setLocal("i",n.i32_const(0)),n.block(n.loop(n.br_if(1,n.i32_ge_u(n.getLocal("i"),n.getLocal("ndiv2"))),n.setLocal("idx1",n.i32_add(n.getLocal("pBuff"),n.i32_mul(n.getLocal("i"),n.i32_const(l)))),n.setLocal("idx2",n.i32_add(n.getLocal("pBuff"),n.i32_mul(n.i32_sub(n.i32_sub(n.getLocal("n"),n.i32_const(1)),n.getLocal("i")),n.i32_const(l)))),n.call(o,n.getLocal("idx2"),n.getLocal("factor"),r),n.call(o,n.getLocal("idx1"),n.getLocal("factor"),n.getLocal("idx2")),n.call(a+"_copy",r,n.getLocal("idx1")),n.setLocal("i",n.i32_add(n.getLocal("i"),n.i32_const(1))),n.br(0))))}(),function(){const r=t.addFunction(e+"_prepareLagrangeEvaluation");r.addParam("pBuff1","i32"),r.addParam("pBuff2","i32"),r.addParam("n","i32"),r.addParam("first","i32"),r.addParam("inc","i32"),r.addParam("totalBits","i32"),r.addLocal("idx1","i32"),r.addLocal("idx2","i32"),r.addLocal("i","i32"),r.addLocal("pShiftToM","i32"),r.addLocal("pSConst","i32");const s=r.getCodeBuilder(),c=s.i32_const(t.alloc(n)),d=s.i32_const(t.alloc(l));r.addCode(s.setLocal("pShiftToM",s.i32_add(s.i32_const(y),s.i32_mul(s.getLocal("totalBits"),s.i32_const(n)))),s.setLocal("pSConst",s.i32_add(s.i32_const(C),s.i32_mul(s.getLocal("totalBits"),s.i32_const(n)))),s.call(i+"_copy",s.getLocal("first"),c),s.setLocal("i",s.i32_const(0)),s.block(s.loop(s.br_if(1,s.i32_eq(s.getLocal("i"),s.getLocal("n"))),s.setLocal("idx1",s.i32_add(s.getLocal("pBuff1"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.setLocal("idx2",s.i32_add(s.getLocal("pBuff2"),s.i32_mul(s.getLocal("i"),s.i32_const(l)))),s.call(o,s.getLocal("idx1"),s.getLocal("pShiftToM"),d),s.call(a+"_sub",s.getLocal("idx2"),d,d),s.call(a+"_sub",s.getLocal("idx1"),s.getLocal("idx2"),s.getLocal("idx2")),s.call(o,d,s.getLocal("pSConst"),s.getLocal("idx1")),s.call(o,s.getLocal("idx2"),c,s.getLocal("idx2")),s.call(i+"_mul",c,s.getLocal("inc"),c),s.setLocal("i",s.i32_add(s.getLocal("i"),s.i32_const(1))),s.br(0))))}(),t.exportFunction(e+"_fft"),t.exportFunction(e+"_ifft"),t.exportFunction(e+"_rawfft"),t.exportFunction(e+"_fftJoin"),t.exportFunction(e+"_fftJoinExt"),t.exportFunction(e+"_fftJoinExtInv"),t.exportFunction(e+"_fftMix"),t.exportFunction(e+"_fftFinal"),t.exportFunction(e+"_prepareLagrangeEvaluation")},Vt=function(t,e,a){const i=8*t.modules[a].n64;return function(){const o=t.addFunction(e+"_zero");o.addParam("px","i32"),o.addParam("n","i32"),o.addLocal("lastp","i32"),o.addLocal("p","i32");const n=o.getCodeBuilder();o.addCode(n.setLocal("p",n.getLocal("px")),n.setLocal("lastp",n.i32_add(n.getLocal("px"),n.i32_mul(n.getLocal("n"),n.i32_const(i)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("p"),n.getLocal("lastp"))),n.call(a+"_zero",n.getLocal("p")),n.setLocal("p",n.i32_add(n.getLocal("p"),n.i32_const(i))),n.br(0))))}(),function(){const o=t.addFunction(e+"_constructLC");o.addParam("ppolynomials","i32"),o.addParam("psignals","i32"),o.addParam("nSignals","i32"),o.addParam("pres","i32"),o.addLocal("i","i32"),o.addLocal("j","i32"),o.addLocal("pp","i32"),o.addLocal("ps","i32"),o.addLocal("pd","i32"),o.addLocal("ncoefs","i32");const n=o.getCodeBuilder(),l=n.i32_const(t.alloc(i));o.addCode(n.setLocal("i",n.i32_const(0)),n.setLocal("pp",n.getLocal("ppolynomials")),n.setLocal("ps",n.getLocal("psignals")),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("i"),n.getLocal("nSignals"))),n.setLocal("ncoefs",n.i32_load(n.getLocal("pp"))),n.setLocal("pp",n.i32_add(n.getLocal("pp"),n.i32_const(4))),n.setLocal("j",n.i32_const(0)),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("j"),n.getLocal("ncoefs"))),n.setLocal("pd",n.i32_add(n.getLocal("pres"),n.i32_mul(n.i32_load(n.getLocal("pp")),n.i32_const(i)))),n.setLocal("pp",n.i32_add(n.getLocal("pp"),n.i32_const(4))),n.call(a+"_mul",n.getLocal("ps"),n.getLocal("pp"),l),n.call(a+"_add",l,n.getLocal("pd"),n.getLocal("pd")),n.setLocal("pp",n.i32_add(n.getLocal("pp"),n.i32_const(i))),n.setLocal("j",n.i32_add(n.getLocal("j"),n.i32_const(1))),n.br(0))),n.setLocal("ps",n.i32_add(n.getLocal("ps"),n.i32_const(i))),n.setLocal("i",n.i32_add(n.getLocal("i"),n.i32_const(1))),n.br(0))))}(),t.exportFunction(e+"_zero"),t.exportFunction(e+"_constructLC"),e},$t=function(t,e,a){const i=8*t.modules[a].n64;return function(){const o=t.addFunction(e+"_buildABC");o.addParam("pCoefs","i32"),o.addParam("nCoefs","i32"),o.addParam("pWitness","i32"),o.addParam("pA","i32"),o.addParam("pB","i32"),o.addParam("pC","i32"),o.addParam("offsetOut","i32"),o.addParam("nOut","i32"),o.addParam("offsetWitness","i32"),o.addParam("nWitness","i32"),o.addLocal("it","i32"),o.addLocal("ita","i32"),o.addLocal("itb","i32"),o.addLocal("last","i32"),o.addLocal("m","i32"),o.addLocal("c","i32"),o.addLocal("s","i32"),o.addLocal("pOut","i32");const n=o.getCodeBuilder(),l=n.i32_const(t.alloc(i));o.addCode(n.setLocal("ita",n.getLocal("pA")),n.setLocal("itb",n.getLocal("pB")),n.setLocal("last",n.i32_add(n.getLocal("pA"),n.i32_mul(n.getLocal("nOut"),n.i32_const(i)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("ita"),n.getLocal("last"))),n.call(a+"_zero",n.getLocal("ita")),n.call(a+"_zero",n.getLocal("itb")),n.setLocal("ita",n.i32_add(n.getLocal("ita"),n.i32_const(i))),n.setLocal("itb",n.i32_add(n.getLocal("itb"),n.i32_const(i))),n.br(0))),n.setLocal("it",n.getLocal("pCoefs")),n.setLocal("last",n.i32_add(n.getLocal("pCoefs"),n.i32_mul(n.getLocal("nCoefs"),n.i32_const(i+12)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("it"),n.getLocal("last"))),n.setLocal("s",n.i32_load(n.getLocal("it"),8)),n.if(n.i32_or(n.i32_lt_u(n.getLocal("s"),n.getLocal("offsetWitness")),n.i32_ge_u(n.getLocal("s"),n.i32_add(n.getLocal("offsetWitness"),n.getLocal("nWitness")))),[...n.setLocal("it",n.i32_add(n.getLocal("it"),n.i32_const(i+12))),...n.br(1)]),n.setLocal("m",n.i32_load(n.getLocal("it"))),n.if(n.i32_eq(n.getLocal("m"),n.i32_const(0)),n.setLocal("pOut",n.getLocal("pA")),n.if(n.i32_eq(n.getLocal("m"),n.i32_const(1)),n.setLocal("pOut",n.getLocal("pB")),[...n.setLocal("it",n.i32_add(n.getLocal("it"),n.i32_const(i+12))),...n.br(1)])),n.setLocal("c",n.i32_load(n.getLocal("it"),4)),n.if(n.i32_or(n.i32_lt_u(n.getLocal("c"),n.getLocal("offsetOut")),n.i32_ge_u(n.getLocal("c"),n.i32_add(n.getLocal("offsetOut"),n.getLocal("nOut")))),[...n.setLocal("it",n.i32_add(n.getLocal("it"),n.i32_const(i+12))),...n.br(1)]),n.setLocal("pOut",n.i32_add(n.getLocal("pOut"),n.i32_mul(n.i32_sub(n.getLocal("c"),n.getLocal("offsetOut")),n.i32_const(i)))),n.call(a+"_mul",n.i32_add(n.getLocal("pWitness"),n.i32_mul(n.i32_sub(n.getLocal("s"),n.getLocal("offsetWitness")),n.i32_const(i))),n.i32_add(n.getLocal("it"),n.i32_const(12)),l),n.call(a+"_add",n.getLocal("pOut"),l,n.getLocal("pOut")),n.setLocal("it",n.i32_add(n.getLocal("it"),n.i32_const(i+12))),n.br(0))),n.setLocal("ita",n.getLocal("pA")),n.setLocal("itb",n.getLocal("pB")),n.setLocal("it",n.getLocal("pC")),n.setLocal("last",n.i32_add(n.getLocal("pA"),n.i32_mul(n.getLocal("nOut"),n.i32_const(i)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("ita"),n.getLocal("last"))),n.call(a+"_mul",n.getLocal("ita"),n.getLocal("itb"),n.getLocal("it")),n.setLocal("ita",n.i32_add(n.getLocal("ita"),n.i32_const(i))),n.setLocal("itb",n.i32_add(n.getLocal("itb"),n.i32_const(i))),n.setLocal("it",n.i32_add(n.getLocal("it"),n.i32_const(i))),n.br(0))))}(),function(){const o=t.addFunction(e+"_joinABC");o.addParam("pA","i32"),o.addParam("pB","i32"),o.addParam("pC","i32"),o.addParam("n","i32"),o.addParam("pP","i32"),o.addLocal("ita","i32"),o.addLocal("itb","i32"),o.addLocal("itc","i32"),o.addLocal("itp","i32"),o.addLocal("last","i32");const n=o.getCodeBuilder(),l=n.i32_const(t.alloc(i));o.addCode(n.setLocal("ita",n.getLocal("pA")),n.setLocal("itb",n.getLocal("pB")),n.setLocal("itc",n.getLocal("pC")),n.setLocal("itp",n.getLocal("pP")),n.setLocal("last",n.i32_add(n.getLocal("pA"),n.i32_mul(n.getLocal("n"),n.i32_const(i)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("ita"),n.getLocal("last"))),n.call(a+"_mul",n.getLocal("ita"),n.getLocal("itb"),l),n.call(a+"_sub",l,n.getLocal("itc"),n.getLocal("itp")),n.setLocal("ita",n.i32_add(n.getLocal("ita"),n.i32_const(i))),n.setLocal("itb",n.i32_add(n.getLocal("itb"),n.i32_const(i))),n.setLocal("itc",n.i32_add(n.getLocal("itc"),n.i32_const(i))),n.setLocal("itp",n.i32_add(n.getLocal("itp"),n.i32_const(i))),n.br(0))))}(),function(){const o=t.addFunction(e+"_batchAdd");o.addParam("pa","i32"),o.addParam("pb","i32"),o.addParam("n","i32"),o.addParam("pr","i32"),o.addLocal("ita","i32"),o.addLocal("itb","i32"),o.addLocal("itr","i32"),o.addLocal("last","i32");const n=o.getCodeBuilder();o.addCode(n.setLocal("ita",n.getLocal("pa")),n.setLocal("itb",n.getLocal("pb")),n.setLocal("itr",n.getLocal("pr")),n.setLocal("last",n.i32_add(n.getLocal("pa"),n.i32_mul(n.getLocal("n"),n.i32_const(i)))),n.block(n.loop(n.br_if(1,n.i32_eq(n.getLocal("ita"),n.getLocal("last"))),n.call(a+"_add",n.getLocal("ita"),n.getLocal("itb"),n.getLocal("itr")),n.setLocal("ita",n.i32_add(n.getLocal("ita"),n.i32_const(i))),n.setLocal("itb",n.i32_add(n.getLocal("itb"),n.i32_const(i))),n.setLocal("itr",n.i32_add(n.getLocal("itr"),n.i32_const(i))),n.br(0))))}(),t.exportFunction(e+"_buildABC"),t.exportFunction(e+"_joinABC"),t.exportFunction(e+"_batchAdd"),e},jt=function(t,e,a,i,o,n,l,r){const s=t.addFunction(e);s.addParam("pIn","i32"),s.addParam("n","i32"),s.addParam("pFirst","i32"),s.addParam("pInc","i32"),s.addParam("pOut","i32"),s.addLocal("pOldFree","i32"),s.addLocal("i","i32"),s.addLocal("pFrom","i32"),s.addLocal("pTo","i32");const c=s.getCodeBuilder(),d=c.i32_const(t.alloc(l));s.addCode(c.setLocal("pFrom",c.getLocal("pIn")),c.setLocal("pTo",c.getLocal("pOut"))),s.addCode(c.call(i+"_copy",c.getLocal("pFirst"),d)),s.addCode(c.setLocal("i",c.i32_const(0)),c.block(c.loop(c.br_if(1,c.i32_eq(c.getLocal("i"),c.getLocal("n"))),c.call(r,c.getLocal("pFrom"),d,c.getLocal("pTo")),c.setLocal("pFrom",c.i32_add(c.getLocal("pFrom"),c.i32_const(o))),c.setLocal("pTo",c.i32_add(c.getLocal("pTo"),c.i32_const(n))),c.call(i+"_mul",d,c.getLocal("pInc"),d),c.setLocal("i",c.i32_add(c.getLocal("i"),c.i32_const(1))),c.br(0)))),t.exportFunction(e)};const Kt=K,Ht=It,Zt=Et,Wt=Pt,Yt=Ot,Jt=qt,Xt=Nt,te=Vt,ee=$t,ae=jt,{bitLength:ie,modInv:oe,isOdd:ne,isNegative:le}=J;const re=K,se=It,ce=Et,de=Pt,ue=Ot,ge=qt,fe=Nt,he=Vt,_e=$t,pe=jt,{bitLength:me,isOdd:we,isNegative:Le}=J;var be=function(t,e){const a=e||"bn128";if(t.modules[a])return a;const i=21888242871839275222246405745257275088696311157297823662689037894645226208583n,o=21888242871839275222246405745257275088548364400416034343698204186575808495617n,n=Math.floor((ie(i-1n)-1)/64)+1,l=8*n,r=l,s=l,c=2*s,d=12*s,u=t.alloc(Kt.bigInt2BytesLE(o,r)),g=Ht(t,i,"f1m");Zt(t,o,"fr","frm");const f=t.alloc(Kt.bigInt2BytesLE(L(3n),s)),h=Jt(t,"g1m","f1m",f);Xt(t,"frm","frm","frm","frm_mul"),te(t,"pol","frm"),ee(t,"qap","frm");const _=Wt(t,"f1m_neg","f2m","f1m"),p=t.alloc([...Kt.bigInt2BytesLE(L(19485874751759354771024239261021720505790618469301721065564631296452457478373n),s),...Kt.bigInt2BytesLE(L(266929791119991161246907387137283842545076965332900288569378510910307636690n),s)]),m=Jt(t,"g2m","f2m",p);function w(e,a){const i=t.addFunction(e);i.addParam("pG","i32"),i.addParam("pFr","i32"),i.addParam("pr","i32");const o=i.getCodeBuilder(),n=o.i32_const(t.alloc(l));i.addCode(o.call("frm_fromMontgomery",o.getLocal("pFr"),n),o.call(a,o.getLocal("pG"),n,o.i32_const(l),o.getLocal("pr"))),t.exportFunction(e)}function L(t){return BigInt(t)*(1n<0n;)ne(e)?a.push(1):a.push(0),e>>=1n;return a}(29793968203157093288n),T=t.alloc(U),Q=3*c,q=U.length-1,M=U.reduce(((t,e)=>t+(0!=e?1:0)),0),k=6*l,R=3*l*2+(M+q+1)*Q;t.modules[a]={n64:n,pG1gen:A,pG1zero:C,pG1b:f,pG2gen:F,pG2zero:E,pG2b:p,pq:t.modules.f1m.pq,pr:u,pOneT:v,prePSize:k,preQSize:R,r:o.toString(),q:i.toString()};const D=4965661367192848881n;function N(e){const o=[[[1n,0n],[1n,0n],[1n,0n],[1n,0n],[1n,0n],[1n,0n],[1n,0n],[1n,0n],[1n,0n],[1n,0n],[1n,0n],[1n,0n]],[[1n,0n],[8376118865763821496583973867626364092589906065868298776909617916018768340080n,16469823323077808223889137241176536799009286646108169935659301613961712198316n],[21888242871839275220042445260109153167277707414472061641714758635765020556617n,0n],[11697423496358154304825782922584725312912383441159505038794027105778954184319n,303847389135065887422783454877609941456349188919719272345083954437860409601n],[21888242871839275220042445260109153167277707414472061641714758635765020556616n,0n],[3321304630594332808241809054958361220322477375291206261884409189760185844239n,5722266937896532885780051958958348231143373700109372999374820235121374419868n],[21888242871839275222246405745257275088696311157297823662689037894645226208582n,0n],[13512124006075453725662431877630910996106405091429524885779419978626457868503n,5418419548761466998357268504080738289687024511189653727029736280683514010267n],[2203960485148121921418603742825762020974279258880205651966n,0n],[10190819375481120917420622822672549775783927716138318623895010788866272024264n,21584395482704209334823622290379665147239961968378104390343953940207365798982n],[2203960485148121921418603742825762020974279258880205651967n,0n],[18566938241244942414004596690298913868373833782006617400804628704885040364344n,16165975933942742336466353786298926857552937457188450663314217659523851788715n]]],n=[[[1n,0n],[1n,0n],[1n,0n],[1n,0n],[1n,0n],[1n,0n]],[[1n,0n],[21575463638280843010398324269430826099269044274347216827212613867836435027261n,10307601595873709700152284273816112264069230130616436755625194854815875713954n],[21888242871839275220042445260109153167277707414472061641714758635765020556616n,0n],[3772000881919853776433695186713858239009073593817195771773381919316419345261n,2236595495967245188281701248203181795121068902605861227855261137820944008926n],[2203960485148121921418603742825762020974279258880205651966n,0n],[18429021223477853657660792034369865839114504446431234726392080002137598044644n,9344045779998320333812420223237981029506012124075525679208581902008406485703n]],[[1n,0n],[2581911344467009335267311115468803099551665605076196740867805258568234346338n,19937756971775647987995932169929341994314640652964949448313374472400716661030n],[2203960485148121921418603742825762020974279258880205651966n,0n],[5324479202449903542726783395506214481928257762400643279780343368557297135718n,16208900380737693084919495127334387981393726419856888799917914180988844123039n],[21888242871839275220042445260109153167277707414472061641714758635765020556616n,0n],[13981852324922362344252311234282257507216387789820983642040889267519694726527n,7629828391165209371577384193250820201684255241773809077146787135900891633097n]]],l=t.addFunction(a+"__frobeniusMap"+e);l.addParam("x","i32"),l.addParam("r","i32");const r=l.getCodeBuilder();for(let a=0;a<6;a++){const i=0==a?r.getLocal("x"):r.i32_add(r.getLocal("x"),r.i32_const(a*c)),u=i,f=r.i32_add(r.getLocal("x"),r.i32_const(a*c+s)),h=0==a?r.getLocal("r"):r.i32_add(r.getLocal("r"),r.i32_const(a*c)),p=h,m=r.i32_add(r.getLocal("r"),r.i32_const(a*c+s)),w=d(o[Math.floor(a/3)][e%12],n[a%3][e%6]),b=t.alloc([...Kt.bigInt2BytesLE(L(w[0]),32),...Kt.bigInt2BytesLE(L(w[1]),32)]);e%2==1?l.addCode(r.call(g+"_copy",u,p),r.call(g+"_neg",f,m),r.call(_+"_mul",h,r.i32_const(b),h)):l.addCode(r.call(_+"_mul",i,r.i32_const(b),h))}function d(t,e){const a=BigInt(t[0]),o=BigInt(t[1]),n=BigInt(e[0]),l=BigInt(e[1]),r=[(a*n-o*l)%i,(a*l+o*n)%i];return le(r[0])&&(r[0]=r[0]+i),r}}function V(e,i){const o=function(t){let e=t;const a=[];for(;e>0n;){if(ne(e)){const t=2-Number(e%4n);a.push(t),e-=BigInt(t)}else a.push(0);e>>=1n}return 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i=e.getCodeBuilder(),o=i.getLocal("x"),n=i.i32_add(i.getLocal("x"),i.i32_const(c)),l=i.i32_add(i.getLocal("x"),i.i32_const(2*c)),r=i.i32_add(i.getLocal("x"),i.i32_const(3*c)),s=i.i32_add(i.getLocal("x"),i.i32_const(4*c)),d=i.i32_add(i.getLocal("x"),i.i32_const(5*c)),u=i.getLocal("r"),g=i.i32_add(i.getLocal("r"),i.i32_const(c)),f=i.i32_add(i.getLocal("r"),i.i32_const(2*c)),h=i.i32_add(i.getLocal("r"),i.i32_const(3*c)),p=i.i32_add(i.getLocal("r"),i.i32_const(4*c)),m=i.i32_add(i.getLocal("r"),i.i32_const(5*c)),w=i.i32_const(t.alloc(c)),L=i.i32_const(t.alloc(c)),b=i.i32_const(t.alloc(c)),A=i.i32_const(t.alloc(c)),y=i.i32_const(t.alloc(c)),C=i.i32_const(t.alloc(c)),I=i.i32_const(t.alloc(c)),F=i.i32_const(t.alloc(c));e.addCode(i.call(_+"_mul",o,s,I),i.call(_+"_mul",s,i.i32_const(B),w),i.call(_+"_add",o,w,w),i.call(_+"_add",o,s,F),i.call(_+"_mul",F,w,w),i.call(_+"_mul",i.i32_const(B),I,F),i.call(_+"_add",I,F,F),i.call(_+"_sub",w,F,w),i.call(_+"_add",I,I,L),i.call(_+"_mul",r,l,I),i.call(_+"_mul",l,i.i32_const(B),b),i.call(_+"_add",r,b,b),i.call(_+"_add",r,l,F),i.call(_+"_mul",F,b,b),i.call(_+"_mul",i.i32_const(B),I,F),i.call(_+"_add",I,F,F),i.call(_+"_sub",b,F,b),i.call(_+"_add",I,I,A),i.call(_+"_mul",n,d,I),i.call(_+"_mul",d,i.i32_const(B),y),i.call(_+"_add",n,y,y),i.call(_+"_add",n,d,F),i.call(_+"_mul",F,y,y),i.call(_+"_mul",i.i32_const(B),I,F),i.call(_+"_add",I,F,F),i.call(_+"_sub",y,F,y),i.call(_+"_add",I,I,C),i.call(_+"_sub",w,o,u),i.call(_+"_add",u,u,u),i.call(_+"_add",w,u,u),i.call(_+"_add",L,s,p),i.call(_+"_add",p,p,p),i.call(_+"_add",L,p,p),i.call(_+"_mul",C,i.i32_const(P),F),i.call(_+"_add",F,r,h),i.call(_+"_add",h,h,h),i.call(_+"_add",F,h,h),i.call(_+"_sub",y,l,f),i.call(_+"_add",f,f,f),i.call(_+"_add",y,f,f),i.call(_+"_sub",b,n,g),i.call(_+"_add",g,g,g),i.call(_+"_add",b,g,g),i.call(_+"_add",A,d,m),i.call(_+"_add",m,m,m),i.call(_+"_add",A,m,m))}(),V(D,"w0");const e=t.addFunction(a+"__finalExponentiationLastChunk");e.addParam("x","i32"),e.addParam("r","i32");const i=e.getCodeBuilder(),o=i.getLocal("x"),n=i.getLocal("r"),l=i.i32_const(t.alloc(d)),r=i.i32_const(t.alloc(d)),s=i.i32_const(t.alloc(d)),u=i.i32_const(t.alloc(d)),g=i.i32_const(t.alloc(d)),f=i.i32_const(t.alloc(d)),h=i.i32_const(t.alloc(d)),p=i.i32_const(t.alloc(d)),m=i.i32_const(t.alloc(d)),w=i.i32_const(t.alloc(d)),L=i.i32_const(t.alloc(d)),b=i.i32_const(t.alloc(d)),A=i.i32_const(t.alloc(d)),y=i.i32_const(t.alloc(d)),C=i.i32_const(t.alloc(d)),I=i.i32_const(t.alloc(d)),F=i.i32_const(t.alloc(d)),x=i.i32_const(t.alloc(d)),E=i.i32_const(t.alloc(d)),v=i.i32_const(t.alloc(d)),S=i.i32_const(t.alloc(d));e.addCode(i.call(a+"__cyclotomicExp_w0",o,l),i.call(O+"_conjugate",l,l),i.call(a+"__cyclotomicSquare",l,r),i.call(a+"__cyclotomicSquare",r,s),i.call(O+"_mul",s,r,u),i.call(a+"__cyclotomicExp_w0",u,g),i.call(O+"_conjugate",g,g),i.call(a+"__cyclotomicSquare",g,f),i.call(a+"__cyclotomicExp_w0",f,h),i.call(O+"_conjugate",h,h),i.call(O+"_conjugate",u,p),i.call(O+"_conjugate",h,m),i.call(O+"_mul",m,g,w),i.call(O+"_mul",w,p,L),i.call(O+"_mul",L,r,b),i.call(O+"_mul",L,g,A),i.call(O+"_mul",A,o,y),i.call(a+"__frobeniusMap1",b,C),i.call(O+"_mul",C,y,I),i.call(a+"__frobeniusMap2",L,F),i.call(O+"_mul",F,I,x),i.call(O+"_conjugate",o,E),i.call(O+"_mul",E,b,v),i.call(a+"__frobeniusMap3",v,S),i.call(O+"_mul",S,x,n))}const j=t.alloc(k),K=t.alloc(R);function H(e){const i=t.addFunction(a+"_pairingEq"+e);for(let t=0;t0n;)we(e)?a.push(1):a.push(0),e>>=1n;return a}(0xd201000000010000n),U=t.alloc(O),T=3*s,Q=O.length-1,q=O.reduce(((t,e)=>t+(0!=e?1:0)),0),M=6*l,k=3*l*2+(q+Q+1)*T,R=!0,D=15132376222941642752n;function N(e){const 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c=n.getCodeBuilder();for(let i=0;i<6;i++){const u=0==i?c.getLocal("x"):c.i32_add(c.getLocal("x"),c.i32_const(i*s)),g=u,f=c.i32_add(c.getLocal("x"),c.i32_const(i*s+r)),_=0==i?c.getLocal("r"):c.i32_add(c.getLocal("r"),c.i32_const(i*s)),p=_,w=c.i32_add(c.getLocal("r"),c.i32_const(i*s+r)),L=d(a[Math.floor(i/3)][e%12],o[i%3][e%6]),b=t.alloc([...re.bigInt2BytesLE(A(L[0]),l),...re.bigInt2BytesLE(A(L[1]),l)]);e%2==1?n.addCode(c.call(h+"_copy",g,p),c.call(h+"_neg",f,w),c.call(m+"_mul",_,c.i32_const(b),_)):n.addCode(c.call(m+"_mul",u,c.i32_const(b),_))}function d(t,e){const a=t[0],o=t[1],n=e[0],l=e[1],r=[(a*n-o*l)%i,(a*l+o*n)%i];return Le(r[0])&&(r[0]=r[0]+i),r}}function V(e,i,o){const n=function(t){let e=t;const a=[];for(;e>0n;){if(we(e)){const t=2-Number(e%4n);a.push(t),e-=BigInt(t)}else a.push(0);e>>=1n}return a}(e).map((t=>-1==t?255:t)),l=t.alloc(n),r=t.addFunction(a+"__cyclotomicExp_"+o);r.addParam("x","i32"),r.addParam("r","i32"),r.addLocal("bit","i32"),r.addLocal("i","i32");const s=r.getCodeBuilder(),d=s.getLocal("x"),u=s.getLocal("r"),g=s.i32_const(t.alloc(c));r.addCode(s.call(z+"_conjugate",d,g),s.call(z+"_one",u),s.if(s.teeLocal("bit",s.i32_load8_s(s.i32_const(n.length-1),l)),s.if(s.i32_eq(s.getLocal("bit"),s.i32_const(1)),s.call(z+"_mul",u,d,u),s.call(z+"_mul",u,g,u))),s.setLocal("i",s.i32_const(n.length-2)),s.block(s.loop(s.call(a+"__cyclotomicSquare",u,u),s.if(s.teeLocal("bit",s.i32_load8_s(s.getLocal("i"),l)),s.if(s.i32_eq(s.getLocal("bit"),s.i32_const(1)),s.call(z+"_mul",u,d,u),s.call(z+"_mul",u,g,u))),s.br_if(1,s.i32_eqz(s.getLocal("i"))),s.setLocal("i",s.i32_sub(s.getLocal("i"),s.i32_const(1))),s.br(0)))),i&&r.addCode(s.call(z+"_conjugate",u,u))}t.modules[a]={n64q:n,n64r:d,n8q:l,n8r:u,pG1gen:C,pG1zero:F,pG1b:_,pG2gen:E,pG2zero:B,pG2b:w,pq:t.modules.f1m.pq,pr:f,pOneT:S,r:o,q:i,prePSize:M,preQSize:k},function(){const e=t.addFunction(G+"_mul1");e.addParam("pA","i32"),e.addParam("pC1","i32"),e.addParam("pR","i32");const a=e.getCodeBuilder(),i=a.getLocal("pA"),o=a.i32_add(a.getLocal("pA"),a.i32_const(2*r)),n=a.i32_add(a.getLocal("pA"),a.i32_const(4*r)),l=a.getLocal("pC1"),s=a.getLocal("pR"),c=a.i32_add(a.getLocal("pR"),a.i32_const(2*r)),d=a.i32_add(a.getLocal("pR"),a.i32_const(4*r)),u=a.i32_const(t.alloc(2*r)),g=a.i32_const(t.alloc(2*r));e.addCode(a.call(m+"_add",i,o,u),a.call(m+"_add",o,n,g),a.call(m+"_mul",o,l,d),a.call(m+"_mul",g,l,s),a.call(m+"_sub",s,d,s),a.call(m+"_mulNR",s,s),a.call(m+"_mul",u,l,c),a.call(m+"_sub",c,d,c))}(),function(){const e=t.addFunction(G+"_mul01");e.addParam("pA","i32"),e.addParam("pC0","i32"),e.addParam("pC1","i32"),e.addParam("pR","i32");const a=e.getCodeBuilder(),i=a.getLocal("pA"),o=a.i32_add(a.getLocal("pA"),a.i32_const(2*r)),n=a.i32_add(a.getLocal("pA"),a.i32_const(4*r)),l=a.getLocal("pC0"),s=a.getLocal("pC1"),c=a.getLocal("pR"),d=a.i32_add(a.getLocal("pR"),a.i32_const(2*r)),u=a.i32_add(a.getLocal("pR"),a.i32_const(4*r)),g=a.i32_const(t.alloc(2*r)),f=a.i32_const(t.alloc(2*r)),h=a.i32_const(t.alloc(2*r)),_=a.i32_const(t.alloc(2*r));e.addCode(a.call(m+"_mul",i,l,g),a.call(m+"_mul",o,s,f),a.call(m+"_add",i,o,h),a.call(m+"_add",i,n,_),a.call(m+"_add",o,n,c),a.call(m+"_mul",c,s,c),a.call(m+"_sub",c,f,c),a.call(m+"_mulNR",c,c),a.call(m+"_add",c,g,c),a.call(m+"_add",l,s,d),a.call(m+"_mul",d,h,d),a.call(m+"_sub",d,g,d),a.call(m+"_sub",d,f,d),a.call(m+"_mul",_,l,u),a.call(m+"_sub",u,g,u),a.call(m+"_add",u,f,u))}(),function(){const e=t.addFunction(z+"_mul014");e.addParam("pA","i32"),e.addParam("pC0","i32"),e.addParam("pC1","i32"),e.addParam("pC4","i32"),e.addParam("pR","i32");const a=e.getCodeBuilder(),i=a.getLocal("pA"),o=a.i32_add(a.getLocal("pA"),a.i32_const(6*r)),n=a.getLocal("pC0"),l=a.getLocal("pC1"),s=a.getLocal("pC4"),c=a.i32_const(t.alloc(6*r)),d=a.i32_const(t.alloc(6*r)),u=a.i32_const(t.alloc(2*r)),g=a.getLocal("pR"),f=a.i32_add(a.getLocal("pR"),a.i32_const(6*r));e.addCode(a.call(G+"_mul01",i,n,l,c),a.call(G+"_mul1",o,s,d),a.call(m+"_add",l,s,u),a.call(G+"_add",o,i,f),a.call(G+"_mul01",f,n,u,f),a.call(G+"_sub",f,c,f),a.call(G+"_sub",f,d,f),a.call(G+"_copy",d,g),a.call(G+"_mulNR",g,g),a.call(G+"_add",g,c,g))}(),function(){const e=t.addFunction(a+"_ell");e.addParam("pP","i32"),e.addParam("pCoefs","i32"),e.addParam("pF","i32");const i=e.getCodeBuilder(),o=i.getLocal("pP"),n=i.i32_add(i.getLocal("pP"),i.i32_const(l)),s=i.getLocal("pF"),c=i.getLocal("pCoefs"),d=i.i32_add(i.getLocal("pCoefs"),i.i32_const(r)),u=i.i32_add(i.getLocal("pCoefs"),i.i32_const(2*r)),g=i.i32_add(i.getLocal("pCoefs"),i.i32_const(3*r)),f=i.i32_add(i.getLocal("pCoefs"),i.i32_const(4*r)),_=t.alloc(2*r),p=i.i32_const(_),m=i.i32_const(_),w=i.i32_const(_+r),L=t.alloc(2*r),b=i.i32_const(L),A=i.i32_const(L),y=i.i32_const(L+r);e.addCode(i.call(h+"_mul",c,n,m),i.call(h+"_mul",d,n,w),i.call(h+"_mul",u,o,A),i.call(h+"_mul",g,o,y),i.call(z+"_mul014",s,f,b,p,s))}();const $=t.alloc(M),j=t.alloc(k);function K(e){const i=t.addFunction(a+"_pairingEq"+e);for(let t=0;t>=BigInt(32)):l+2<=e?(n.setUint16(l,Number(a&BigInt(65535)),!0),l+=2,a>>=BigInt(16)):(n.setUint8(l,Number(a&BigInt(255)),!0),l+=1,a>>=BigInt(8));if(a)throw new Error("Number does not fit in this length");return i}const Ce=[];for(let t=0;t<256;t++)Ce[t]=Ie(t,8);function Ie(t,e){let a=0,i=t;for(let 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0===a?2:a,...la(e||0)]}i64_load(t,e,a){return[...t,41,void 0===a?3:a,...la(e||0)]}i64_store(t,e,a,i){let o,n,l;return Array.isArray(e)?(o=0,n=3,l=e):Array.isArray(a)?(o=e,n=3,l=a):Array.isArray(i)&&(o=e,n=a,l=i),[...t,...l,55,n,...la(o)]}i64_store32(t,e,a,i){let o,n,l;return Array.isArray(e)?(o=0,n=2,l=e):Array.isArray(a)?(o=e,n=2,l=a):Array.isArray(i)&&(o=e,n=a,l=i),[...t,...l,62,n,...la(o)]}i64_store16(t,e,a,i){let o,n,l;return Array.isArray(e)?(o=0,n=1,l=e):Array.isArray(a)?(o=e,n=1,l=a):Array.isArray(i)&&(o=e,n=a,l=i),[...t,...l,61,n,...la(o)]}i64_store8(t,e,a,i){let o,n,l;return Array.isArray(e)?(o=0,n=0,l=e):Array.isArray(a)?(o=e,n=0,l=a):Array.isArray(i)&&(o=e,n=a,l=i),[...t,...l,60,n,...la(o)]}i32_load8_s(t,e,a){return[...t,44,void 0===a?0:a,...la(e||0)]}i32_load8_u(t,e,a){return[...t,45,void 0===a?0:a,...la(e||0)]}i32_load16_s(t,e,a){return[...t,46,void 0===a?1:a,...la(e||0)]}i32_load16_u(t,e,a){return[...t,47,void 0===a?1:a,...la(e||0)]}i32_load(t,e,a){return[...t,40,void 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a?[...t,4,64,...e,5,...a,11]:[...t,4,64,...e,11]}block(t){return[2,64,...t,11]}loop(...t){return[3,64,...[].concat(...t),11]}br_if(t,e){return[...e,13,...la(t)]}br(t){return[12,...la(t)]}ret(t){return[...t,15]}drop(t){return[...t,26]}i64_const(t){return[66,...na(t)]}i32_const(t){return[65,...oa(t)]}i64_eqz(t){return[...t,80]}i64_eq(t,e){return[...t,...e,81]}i64_ne(t,e){return[...t,...e,82]}i64_lt_s(t,e){return[...t,...e,83]}i64_lt_u(t,e){return[...t,...e,84]}i64_gt_s(t,e){return[...t,...e,85]}i64_gt_u(t,e){return[...t,...e,86]}i64_le_s(t,e){return[...t,...e,87]}i64_le_u(t,e){return[...t,...e,88]}i64_ge_s(t,e){return[...t,...e,89]}i64_ge_u(t,e){return[...t,...e,90]}i64_add(t,e){return[...t,...e,124]}i64_sub(t,e){return[...t,...e,125]}i64_mul(t,e){return[...t,...e,126]}i64_div_s(t,e){return[...t,...e,127]}i64_div_u(t,e){return[...t,...e,128]}i64_rem_s(t,e){return[...t,...e,129]}i64_rem_u(t,e){return[...t,...e,130]}i64_and(t,e){return[...t,...e,131]}i64_or(t,e){return[...t,...e,132]}i64_xor(t,e){return[...t,...e,133]}i64_shl(t,e){return[...t,...e,134]}i64_shr_s(t,e){return[...t,...e,135]}i64_shr_u(t,e){return[...t,...e,136]}i64_extend_i32_s(t){return[...t,172]}i64_extend_i32_u(t){return[...t,173]}i64_clz(t){return[...t,121]}i64_ctz(t){return[...t,122]}i32_eqz(t){return[...t,69]}i32_eq(t,e){return[...t,...e,70]}i32_ne(t,e){return[...t,...e,71]}i32_lt_s(t,e){return[...t,...e,72]}i32_lt_u(t,e){return[...t,...e,73]}i32_gt_s(t,e){return[...t,...e,74]}i32_gt_u(t,e){return[...t,...e,75]}i32_le_s(t,e){return[...t,...e,76]}i32_le_u(t,e){return[...t,...e,77]}i32_ge_s(t,e){return[...t,...e,78]}i32_ge_u(t,e){return[...t,...e,79]}i32_add(t,e){return[...t,...e,106]}i32_sub(t,e){return[...t,...e,107]}i32_mul(t,e){return[...t,...e,108]}i32_div_s(t,e){return[...t,...e,109]}i32_div_u(t,e){return[...t,...e,110]}i32_rem_s(t,e){return[...t,...e,111]}i32_rem_u(t,e){return[...t,...e,112]}i32_and(t,e){return[...t,...e,113]}i32_or(t,e){return[...t,...e,114]}i32_xor(t,e){return[...t,...e,115]}i32_shl(t,e){return[...t,...e,116]}i32_shr_s(t,e){return[...t,...e,117]}i32_shr_u(t,e){return[...t,...e,118]}i32_rotl(t,e){return[...t,...e,119]}i32_rotr(t,e){return[...t,...e,120]}i32_wrap_i64(t){return[...t,167]}i32_clz(t){return[...t,103]}i32_ctz(t){return[...t,104]}unreachable(){return[0]}current_memory(){return[63,0]}comment(){return[]}}const ca={i32:127,i64:126,f32:125,f64:124,anyfunc:112,func:96,emptyblock:64};class da{constructor(t,e,a,i,o){if("import"==a)this.fnType="import",this.moduleName=i,this.fieldName=o;else{if("internal"!=a)throw new Error("Invalid function fnType: "+a);this.fnType="internal"}this.module=t,this.fnName=e,this.params=[],this.locals=[],this.localIdxByName={},this.code=[],this.returnType=null,this.nextLocal=0}addParam(t,e){if(this.localIdxByName[t])throw new Error(`param already exists. Function: ${this.fnName}, Param: ${t} `);const a=this.nextLocal++;this.localIdxByName[t]=a,this.params.push({type:e})}addLocal(t,e,a){const i=a||1;if(this.localIdxByName[t])throw new Error(`local already exists. Function: ${this.fnName}, Param: ${t} `);const o=this.nextLocal++;this.localIdxByName[t]=o,this.locals.push({type:e,length:i})}setReturnType(t){if(this.returnType)throw new Error(`returnType already defined. Function: ${this.fnName}`);this.returnType=t}getSignature(){return[96,...[...la(this.params.length),...this.params.map((t=>ca[t.type]))],...this.returnType?[1,ca[this.returnType]]:[0]]}getBody(){const t=this.locals.map((t=>[...la(t.length),ca[t.type]])),e=[...la(this.locals.length),...[].concat(...t),...this.code,11];return[...la(e.length),...e]}addCode(...t){this.code.push(...[].concat(...t))}getCodeBuilder(){return new sa(this)}}class ua{constructor(){this.functions=[],this.functionIdxByName={},this.nImportFunctions=0,this.nInternalFunctions=0,this.memory={pagesSize:1,moduleName:"env",fieldName:"memory"},this.free=8,this.datas=[],this.modules={},this.exports=[],this.functionsTable=[]}build(){return this._setSignatures(),new Uint8Array([...ta(1836278016),...ta(1),...this._buildType(),...this._buildImport(),...this._buildFunctionDeclarations(),...this._buildFunctionsTable(),...this._buildExports(),...this._buildElements(),...this._buildCode(),...this._buildData()])}addFunction(t){if(void 0!==this.functionIdxByName[t])throw new Error(`Function already defined: ${t}`);const e=this.functions.length;return this.functionIdxByName[t]=e,this.functions.push(new da(this,t,"internal")),this.nInternalFunctions++,this.functions[e]}addIimportFunction(t,e,a){if(void 0!==this.functionIdxByName[t])throw new Error(`Function already defined: ${t}`);if(this.functions.length>0&&"internal"==this.functions[this.functions.length-1].type)throw new Error(`Import functions must be declared before internal: ${t}`);let i=a||t;const o=this.functions.length;return this.functionIdxByName[t]=o,this.functions.push(new da(this,t,"import",e,i)),this.nImportFunctions++,this.functions[o]}setMemory(t,e,a){this.memory={pagesSize:t,moduleName:e||"env",fieldName:a||"memory"}}exportFunction(t,e){const a=e||t;if(void 0===this.functionIdxByName[t])throw new Error(`Function not defined: ${t}`);const i=this.functionIdxByName[t];a!=t&&(this.functionIdxByName[a]=i),this.exports.push({exportName:a,idx:i})}addFunctionToTable(t){const e=this.functionIdxByName[t];this.functionsTable.push(e)}addData(t,e){this.datas.push({offset:t,bytes:e})}alloc(t,e){let a,i;(Array.isArray(t)||ArrayBuffer.isView(t))&&void 0===e?(a=t.length,i=t):(a=t,i=e),a=1+(a-1>>3)<<3;const o=this.free;return this.free+=a,i&&this.addData(o,i),o}allocString(t){const e=(new globalThis.TextEncoder).encode(t);return this.alloc([...e,0])}_setSignatures(){this.signatures=[];const t={};if(this.functionsTable.length>0){const e=this.functions[this.functionsTable[0]].getSignature();t["s_"+ra(e)]=0,this.signatures.push(e)}for(let e=0;e{e.pendingLoads.push({page:t,resolve:a,reject:i})}));return e.__statusPage("After Load request: ",t),a}__statusPage(t,e){const a=[],i=this;if(!i.logHistory)return;a.push("=="+t+" "+e);let o="";for(let t=0;t "+e.history[t][a][i])}_triggerLoad(){const t=this;if(t.reading)return;if(0==t.pendingLoads.length)return;const e=Object.keys(t.pages),a=[];for(let i=0;i0&&(void 0!==t.pages[t.pendingLoads[0].page]||i>0||a.length>0);){const e=t.pendingLoads.shift();if(void 0!==t.pages[e.page]){t.pages[e.page].pendingOps++;const i=a.indexOf(e.page);i>=0&&a.splice(i,1),t.pages[e.page].loading?t.pages[e.page].loading.push(e):e.resolve(),t.__statusPage("After Load (cached): ",e.page)}else{if(i)i--;else{const e=a.shift();t.__statusPage("Before Unload: ",e),t.avBuffs.unshift(t.pages[e]),delete t.pages[e],t.__statusPage("After Unload: ",e)}e.page>=t.totalPages?(t.pages[e.page]=n(),e.resolve(),t.__statusPage("After Load (new): ",e.page)):(t.reading=!0,t.pages[e.page]=n(),t.pages[e.page].loading=[e],o.push(t.fd.read(t.pages[e.page].buff,0,t.pageSize,e.page*t.pageSize).then((a=>{t.pages[e.page].size=a.bytesRead;const i=t.pages[e.page].loading;delete t.pages[e.page].loading;for(let t=0;t{e.reject(t)}))),t.__statusPage("After Load (loading): ",e.page))}}function n(){if(t.avBuffs.length>0){const e=t.avBuffs.shift();return e.dirty=!1,e.pendingOps=1,e.size=0,e}return{dirty:!1,buff:new Uint8Array(t.pageSize),pendingOps:1,size:0}}Promise.all(o).then((()=>{t.reading=!1,t.pendingLoads.length>0&&setImmediate(t._triggerLoad.bind(t)),t._tryClose()}))}_triggerWrite(){const t=this;if(t.writing)return;const e=Object.keys(t.pages),a=[];for(let i=0;i{o.writing=!1}),(e=>{console.log("ERROR Writing: "+e),t.error=e,t._tryClose()}))))}t.writing&&Promise.all(a).then((()=>{t.writing=!1,setImmediate(t._triggerWrite.bind(t)),t._tryClose(),t.pendingLoads.length>0&&setImmediate(t._triggerLoad.bind(t))}))}_getDirtyPage(){for(let t in this.pages)if(this.pages[t].dirty)return t;return-1}async write(t,e){if(0==t.byteLength)return;const a=this;if(void 0===e&&(e=a.pos),a.pos=e+t.byteLength,a.totalSize0;){await n[l-i];const e=r+s>a.pageSize?a.pageSize-r:s,o=t.slice(t.byteLength-s,t.byteLength-s+e);new Uint8Array(a.pages[l].buff.buffer,r,e).set(o),a.pages[l].dirty=!0,a.pages[l].pendingOps--,a.pages[l].size=Math.max(r+e,a.pages[l].size),l>=a.totalPages&&(a.totalPages=l+1),s-=e,l++,r=0,a.writing||setImmediate(a._triggerWrite.bind(a))}}async read(t,e){let a=new Uint8Array(t);return await this.readToBuffer(a,0,t,e),a}async readToBuffer(t,e,a,i){if(0==a)return;const o=this;if(a>o.pageSize*o.maxPagesLoaded*.8){const t=Math.floor(1.1*a);this.maxPagesLoaded=Math.floor(t/o.pageSize)+1}if(void 0===i&&(i=o.pos),o.pos=i+a,o.pendingClose)throw new Error("Reading a closing file");const n=Math.floor(i/o.pageSize),l=Math.floor((i+a-1)/o.pageSize),r=[];for(let t=n;t<=l;t++)r.push(o._loadPage(t));o._triggerLoad();let s=n,c=i%o.pageSize,d=i+a>o.totalSize?a-(i+a-o.totalSize):a;for(;d>0;){await r[s-n],o.__statusPage("After Await (read): ",s);const i=c+d>o.pageSize?o.pageSize-c:d,l=new Uint8Array(o.pages[s].buff.buffer,o.pages[s].buff.byteOffset+c,i);t.set(l,e+a-d),o.pages[s].pendingOps--,o.__statusPage("After Op done: ",s),d-=i,s++,c=0,o.pendingLoads.length>0&&setImmediate(o._triggerLoad.bind(o))}this.pos=i+a}_tryClose(){const t=this;if(!t.pendingClose)return;t.error&&t.pendingCloseReject(t.error);t._getDirtyPage()>=0||t.writing||t.reading||t.pendingLoads.length>0||t.pendingClose()}close(){const t=this;if(t.pendingClose)throw new Error("Closing the file twice");return new Promise(((e,a)=>{t.pendingClose=e,t.pendingCloseReject=a,t._tryClose()})).then((()=>{t.fd.close()}),(e=>{throw t.fd.close(),e}))}async discard(){await this.close(),await wa.promises.unlink(this.fileName)}async writeULE32(t,e){const a=new Uint8Array(4);new DataView(a.buffer).setUint32(0,t,!0),await this.write(a,e)}async writeUBE32(t,e){const a=new Uint8Array(4);new DataView(a.buffer).setUint32(0,t,!1),await this.write(a,e)}async writeULE64(t,e){const a=new Uint8Array(8),i=new DataView(a.buffer);i.setUint32(0,4294967295&t,!0),i.setUint32(4,Math.floor(t/4294967296),!0),await this.write(a,e)}async readULE32(t){const e=await this.read(4,t);return new Uint32Array(e.buffer)[0]}async readUBE32(t){const e=await this.read(4,t);return new DataView(e.buffer).getUint32(0,!1)}async readULE64(t){const e=await this.read(8,t),a=new Uint32Array(e.buffer);return 4294967296*a[1]+a[0]}async readString(t){const e=this;if(e.pendingClose)throw new Error("Reading a closing file");let a=void 0===t?e.pos:t,i=Math.floor(a/e.pageSize),o=!1,n="";for(;!o;){let t=e._loadPage(i);e._triggerLoad(),await t,e.__statusPage("After Await (read): ",i);let l=a%e.pageSize;const r=new Uint8Array(e.pages[i].buff.buffer,e.pages[i].buff.byteOffset+l,e.pageSize-l);let s=r.findIndex((t=>0===t));o=-1!==s,o?(n+=(new TextDecoder).decode(r.slice(0,s)),e.pos=i*this.pageSize+l+s+1):(n+=(new TextDecoder).decode(r),e.pos=i*this.pageSize+l+r.length),e.pages[i].pendingOps--,e.__statusPage("After Op done: ",i),a=e.pos,i++,e.pendingLoads.length>0&&setImmediate(e._triggerLoad.bind(e))}return n}}const Aa=new Uint8Array(4),ya=new DataView(Aa.buffer),Ca=new Uint8Array(8),Ia=new DataView(Ca.buffer);class Fa{constructor(){this.pageSize=16384}_resizeIfNeeded(t){if(t>this.allocSize){const e=Math.max(this.allocSize+(1<<20),Math.floor(1.1*this.allocSize),t),a=new Uint8Array(e);a.set(this.o.data),this.o.data=a,this.allocSize=e}}async write(t,e){if(void 0===e&&(e=this.pos),this.readOnly)throw new Error("Writing a read only file");this._resizeIfNeeded(e+t.byteLength),this.o.data.set(t.slice(),e),e+t.byteLength>this.totalSize&&(this.totalSize=e+t.byteLength),this.pos=e+t.byteLength}async readToBuffer(t,e,a,i){if(void 0===i&&(i=this.pos),this.readOnly&&i+a>this.totalSize)throw new Error("Reading out of bounds");this._resizeIfNeeded(i+a);const o=new Uint8Array(this.o.data.buffer,this.o.data.byteOffset+i,a);t.set(o,e),this.pos=i+a}async read(t,e){const a=new Uint8Array(t);return await this.readToBuffer(a,0,t,e),a}close(){this.o.data.byteLength!=this.totalSize&&(this.o.data=this.o.data.slice(0,this.totalSize))}async discard(){}async writeULE32(t,e){ya.setUint32(0,t,!0),await this.write(Aa,e)}async writeUBE32(t,e){ya.setUint32(0,t,!1),await this.write(Aa,e)}async writeULE64(t,e){Ia.setUint32(0,4294967295&t,!0),Ia.setUint32(4,Math.floor(t/4294967296),!0),await this.write(Ca,e)}async readULE32(t){const e=await this.read(4,t);return new Uint32Array(e.buffer)[0]}async readUBE32(t){const e=await this.read(4,t);return new DataView(e.buffer).getUint32(0,!1)}async readULE64(t){const e=await this.read(8,t),a=new Uint32Array(e.buffer);return 4294967296*a[1]+a[0]}async readString(t){const e=this;let a=void 0===t?e.pos:t;if(a>this.totalSize){if(this.readOnly)throw new Error("Reading out of bounds");this._resizeIfNeeded(t)}const i=new Uint8Array(e.o.data.buffer,a,this.totalSize-a);let o=i.findIndex((t=>0===t)),n="";return-1!==o?(n=(new TextDecoder).decode(i.slice(0,o)),e.pos=a+o+1):e.pos=a,n}}const xa=1<<22;const Ea=new Uint8Array(4),va=new DataView(Ea.buffer),Ba=new Uint8Array(8),Sa=new DataView(Ba.buffer);class Pa{constructor(){this.pageSize=16384}_resizeIfNeeded(t){if(t<=this.totalSize)return;if(this.readOnly)throw new Error("Reading out of file bounds");const e=Math.floor((t-1)/xa)+1;for(let a=Math.max(this.o.data.length-1,0);a0;){const e=o+n>xa?xa-o:n,l=t.slice(t.byteLength-n,t.byteLength-n+e);new Uint8Array(a.o.data[i].buffer,o,e).set(l),n-=e,i++,o=0}this.pos=e+t.byteLength}async readToBuffer(t,e,a,i){const o=this;if(void 0===i&&(i=o.pos),this.readOnly&&i+a>this.totalSize)throw new Error("Reading out of bounds");this._resizeIfNeeded(i+a);let n=Math.floor(i/xa),l=i%xa,r=a;for(;r>0;){const i=l+r>xa?xa-l:r,s=new Uint8Array(o.o.data[n].buffer,l,i);t.set(s,e+a-r),r-=i,n++,l=0}this.pos=i+a}async read(t,e){const a=new Uint8Array(t);return await this.readToBuffer(a,0,t,e),a}close(){}async discard(){}async writeULE32(t,e){va.setUint32(0,t,!0),await this.write(Ea,e)}async writeUBE32(t,e){va.setUint32(0,t,!1),await this.write(Ea,e)}async writeULE64(t,e){Sa.setUint32(0,4294967295&t,!0),Sa.setUint32(4,Math.floor(t/4294967296),!0),await this.write(Ba,e)}async readULE32(t){const e=await this.read(4,t);return new Uint32Array(e.buffer)[0]}async readUBE32(t){const e=await this.read(4,t);return new DataView(e.buffer).getUint32(0,!1)}async readULE64(t){const e=await this.read(8,t),a=new Uint32Array(e.buffer);return 4294967296*a[1]+a[0]}async readString(t){const e=this;let a=void 0===t?e.pos:t;if(a>this.totalSize){if(this.readOnly)throw new Error("Reading out of bounds");this._resizeIfNeeded(t)}let i=!1,o="";for(;!i;){let t=Math.floor(a/xa),n=a%xa;if(void 0===e.o.data[t])throw new Error("ERROR");let l=Math.min(2048,e.o.data[t].length-n);const r=new Uint8Array(e.o.data[t].buffer,n,l);let s=r.findIndex((t=>0===t));i=-1!==s,i?(o+=(new TextDecoder).decode(r.slice(0,s)),e.pos=t*xa+n+s+1):(o+=(new TextDecoder).decode(r),e.pos=t*xa+n+r.length),a=e.pos}return o}}const Ga=1024,za=512,Oa=2,Ua=0,Ta=65536,Qa=8192;async function qa(t,e,a){if("string"==typeof t&&(t={type:"file",fileName:t,cacheSize:e||Ta,pageSize:a||Qa}),"file"==t.type)return await La(t.fileName,Ga|za|Oa,t.cacheSize,t.pageSize);if("mem"==t.type)return function(t){const e=t.initialSize||1<<20,a=new Fa;return a.o=t,a.o.data=new Uint8Array(e),a.allocSize=e,a.totalSize=0,a.readOnly=!1,a.pos=0,a}(t);if("bigMem"==t.type)return function(t){const e=t.initialSize||0,a=new Pa;a.o=t;const i=e?Math.floor((e-1)/xa)+1:0;a.o.data=[];for(let t=0;ta)throw new Error("Version not supported");const s=await n.readULE32();let c=[];for(let t=0;t1)throw new Error(t.fileName+": Section Duplicated "+a);t.pos=e[a][0].p,t.readingSection=e[a][0]}async 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")}}),a=e(),i=WebAssembly.compile(a);return Ai=async t=>(await WebAssembly.instantiate(await i,t)).exports}()().then((t=>{xi=t})),vi=64,Bi=[];ii.exports=Ti;var Si=ii.exports.BYTES_MIN=16,Pi=ii.exports.BYTES_MAX=64;ii.exports.BYTES=32;var Gi=ii.exports.KEYBYTES_MIN=16,zi=ii.exports.KEYBYTES_MAX=64;ii.exports.KEYBYTES=32;var Oi=ii.exports.SALTBYTES=16,Ui=ii.exports.PERSONALBYTES=16;function Ti(t,e,a,i,o){if(!(this instanceof Ti))return new Ti(t,e,a,i,o);if(!xi)throw new Error("WASM not loaded. Wait for Blake2b.ready(cb)");t||(t=32),!0!==o&&(Ii(t>=Si,"digestLength must be at least "+Si+", was given "+t),Ii(t<=Pi,"digestLength must be at most "+Pi+", was given "+t),null!=e&&(Ii(e instanceof Uint8Array,"key must be Uint8Array or Buffer"),Ii(e.length>=Gi,"key must be at least "+Gi+", was given "+e.length),Ii(e.length<=zi,"key must be at least "+zi+", was given "+e.length)),null!=a&&(Ii(a instanceof Uint8Array,"salt must be Uint8Array or Buffer"),Ii(a.length===Oi,"salt must be exactly "+Oi+", was given "+a.length)),null!=i&&(Ii(i instanceof Uint8Array,"personal must be Uint8Array or Buffer"),Ii(i.length===Ui,"personal must be exactly "+Ui+", was given "+i.length))),Bi.length||(Bi.push(vi),vi+=216),this.digestLength=t,this.finalized=!1,this.pointer=Bi.pop(),this._memory=new Uint8Array(xi.memory.buffer),this._memory.fill(0,0,64),this._memory[0]=this.digestLength,this._memory[1]=e?e.length:0,this._memory[2]=1,this._memory[3]=1,a&&this._memory.set(a,32),i&&this._memory.set(i,48),this.pointer+216>this._memory.length&&this._realloc(this.pointer+216),xi.blake2b_init(this.pointer,this.digestLength),e&&(this.update(e),this._memory.fill(0,vi,vi+e.length),this._memory[this.pointer+200]=128)}function Qi(){}function qi(t){return(0!=(4294901760&t)?(t&=4294901760,16):0)|(0!=(4278255360&t)?(t&=4278255360,8):0)|(0!=(4042322160&t)?(t&=4042322160,4):0)|(0!=(3435973836&t)?(t&=3435973836,2):0)|0!=(2863311530&t)}function Mi(t,e){const a=new DataView(t.buffer,t.byteOffset,t.byteLength);let i="";for(let t=0;t<4;t++){t>0&&(i+="\n"),i+="\t\t";for(let e=0;e<4;e++)e>0&&(i+=" "),i+=a.getUint32(16*t+4*e).toString(16).padStart(8,"0")}return e&&(i=e+"\n"+i),i}function ki(t,e){if(t.byteLength!=e.byteLength)return!1;for(var a=new Int8Array(t),i=new Int8Array(e),o=0;o!=t.byteLength;o++)if(a[o]!=i[o])return!1;return!0}function Ri(t){const e=t.getPartialHash(),a=ii.exports(64);return a.setPartialHash(e),a}async function Di(t,e,a,i,o){if(t.G1.isZero(e))return!1;if(t.G1.isZero(a))return!1;if(t.G2.isZero(i))return!1;if(t.G2.isZero(o))return!1;return await t.pairingEq(e,o,t.G1.neg(a),i)}function Ni(t){let e=new Uint8Array(t);return void 0!==globalThis.crypto?globalThis.crypto.getRandomValues(e):q.randomFillSync(e),e}async function Vi(t){if(void 0!==globalThis.crypto&&void 0!==globalThis.crypto.subtle){const e=await globalThis.crypto.subtle.digest("SHA-256",t.buffer);return new Uint8Array(e)}return q.createHash("sha256").update(t).digest()}function $i(t,e){return new DataView(t.buffer).getUint32(e,!1)}async function ji(t){for(;!t;)t=await window.prompt("Enter a random text. (Entropy): ","");const e=ii.exports(64);e.update(Ni(64));const a=new TextEncoder;e.update(a.encode(t));const i=e.digest(),o=[];for(let t=0;t<8;t++)o[t]=$i(i,4*t);return new Q(o)}async function Ki(t,e){let a,i;e<32?(a=1<>>0,i=1):(a=4294967296,i=1<>>0);let o=t;for(let t=0;t{a[i]=Wi(t,e[i])})),a}return"bigint"==typeof e||void 0!==e.eq?e.toString(10):e}Ti.prototype._realloc=function(t){xi.memory.grow(Math.max(0,Math.ceil(Math.abs(t-this._memory.length)/65536))),this._memory=new Uint8Array(xi.memory.buffer)},Ti.prototype.update=function(t){return Ii(!1===this.finalized,"Hash instance finalized"),Ii(t instanceof Uint8Array,"input must be Uint8Array or Buffer"),vi+t.length>this._memory.length&&this._realloc(vi+t.length),this._memory.set(t,vi),xi.blake2b_update(this.pointer,vi,vi+t.length),this},Ti.prototype.digest=function(t){if(Ii(!1===this.finalized,"Hash instance finalized"),this.finalized=!0,Bi.push(this.pointer),xi.blake2b_final(this.pointer),!t||"binary"===t)return this._memory.slice(this.pointer+128,this.pointer+128+this.digestLength);if("string"==typeof t)return Fi.toString(this._memory,t,this.pointer+128,this.pointer+128+this.digestLength);Ii(t instanceof Uint8Array&&t.length>=this.digestLength,"input must be Uint8Array or Buffer");for(var e=0;et()),t):t(new Error("WebAssembly not supported"))},Ti.prototype.ready=Ti.ready,Ti.prototype.getPartialHash=function(){return this._memory.slice(this.pointer,this.pointer+216)},Ti.prototype.setPartialHash=function(t){this._memory.set(t,this.pointer)};const Yi=1,Ji=1,Xi=2,to=10,eo=3,ao=17,io=2,oo=3,no=4,lo=5,ro=6,so=7,co=8,uo=9,go=10,fo=11,ho=12,_o=13,po=14,mo=15,wo=16,Lo=17;async function bo(t,e){await Da(t,1),await t.writeULE32(1),await Na(t);const a=await ei(e.q);await Da(t,2);const i=a.q,o=8*(Math.floor((pa.bitLength(i)-1)/64)+1),n=a.r,l=8*(Math.floor((pa.bitLength(n)-1)/64)+1);await t.writeULE32(o),await ja(t,i,o),await t.writeULE32(l),await ja(t,n,l),await t.writeULE32(e.nVars),await t.writeULE32(e.nPublic),await t.writeULE32(e.domainSize),await Ao(t,a,e.vk_alpha_1),await Ao(t,a,e.vk_beta_1),await yo(t,a,e.vk_beta_2),await yo(t,a,e.vk_gamma_2),await Ao(t,a,e.vk_delta_1),await yo(t,a,e.vk_delta_2),await Na(t)}async function Ao(t,e,a){const i=new Uint8Array(2*e.G1.F.n8);e.G1.toRprLEM(i,0,a),await t.write(i)}async function yo(t,e,a){const i=new Uint8Array(2*e.G2.F.n8);e.G2.toRprLEM(i,0,a),await t.write(i)}async function Co(t,e,a){const i=await t.read(2*e.G1.F.n8),o=e.G1.fromRprLEM(i,0);return a?e.G1.toObject(o):o}async function Io(t,e,a){const i=await t.read(2*e.G2.F.n8),o=e.G2.fromRprLEM(i,0);return a?e.G2.toObject(o):o}async function Fo(t,e,a){await Va(t,e,1);const i=await t.readULE32();if(await $a(t),i===Ji)return await async function(t,e,a){const i={protocol:"groth16"};await Va(t,e,2);const o=await t.readULE32();i.n8q=o,i.q=await Ka(t,o);const n=await t.readULE32();return i.n8r=n,i.r=await Ka(t,n),i.curve=await ei(i.q),i.nVars=await t.readULE32(),i.nPublic=await t.readULE32(),i.domainSize=await t.readULE32(),i.power=qi(i.domainSize),i.vk_alpha_1=await Co(t,i.curve,a),i.vk_beta_1=await Co(t,i.curve,a),i.vk_beta_2=await Io(t,i.curve,a),i.vk_gamma_2=await Io(t,i.curve,a),i.vk_delta_1=await Co(t,i.curve,a),i.vk_delta_2=await Io(t,i.curve,a),await $a(t),i}(t,e,a);if(i===Xi)return await async function(t,e,a){const i={protocol:"plonk"};await Va(t,e,2);const o=await t.readULE32();i.n8q=o,i.q=await Ka(t,o);const n=await t.readULE32();return i.n8r=n,i.r=await Ka(t,n),i.curve=await ei(i.q),i.nVars=await t.readULE32(),i.nPublic=await t.readULE32(),i.domainSize=await t.readULE32(),i.power=qi(i.domainSize),i.nAdditions=await t.readULE32(),i.nConstrains=await t.readULE32(),i.k1=await t.read(n),i.k2=await t.read(n),i.Qm=await Co(t,i.curve,a),i.Ql=await Co(t,i.curve,a),i.Qr=await Co(t,i.curve,a),i.Qo=await Co(t,i.curve,a),i.Qc=await Co(t,i.curve,a),i.S1=await Co(t,i.curve,a),i.S2=await Co(t,i.curve,a),i.S3=await Co(t,i.curve,a),i.X_2=await Io(t,i.curve,a),await $a(t),i}(t,e,a);if(i===to)return await async function(t,e,a){const i={protocol:"fflonk"};i.protocolId=to,await Va(t,e,io);const o=await t.readULE32();i.n8q=o,i.q=await Ka(t,o),i.curve=await ei(i.q);const n=await t.readULE32();return i.n8r=n,i.r=await Ka(t,n),i.nVars=await t.readULE32(),i.nPublic=await t.readULE32(),i.domainSize=await t.readULE32(),i.power=qi(i.domainSize),i.nAdditions=await t.readULE32(),i.nConstraints=await t.readULE32(),i.k1=await t.read(n),i.k2=await t.read(n),i.w3=await t.read(n),i.w4=await t.read(n),i.w8=await t.read(n),i.wr=await t.read(n),i.X_2=await Io(t,i.curve,a),i.C0=await Co(t,i.curve,a),await $a(t),i}(t,e,a);throw new Error("Protocol not supported: ")}async function xo(t,e,a){const i={delta:{}};i.deltaAfter=await Co(t,e,a),i.delta.g1_s=await Co(t,e,a),i.delta.g1_sx=await Co(t,e,a),i.delta.g2_spx=await Io(t,e,a),i.transcript=await t.read(64),i.type=await t.readULE32();const o=await t.readULE32(),n=t.pos;let l=0;for(;t.pos-n0){const e=new Uint8Array(i);await t.writeULE32(e.byteLength),await t.write(e)}else await t.writeULE32(0)}async function Bo(t,e,a){await Da(t,10),await t.write(a.csHash),await t.writeULE32(a.contributions.length);for(let i=0;i0;)a.unshift(0),n--;return a}async function qo(t,e){e=e||{};let a,i=32767,o=!1;for(;!o;)try{a=new WebAssembly.Memory({initial:i}),o=!0}catch(t){if(1===i)throw t;console.warn("Could not allocate "+1024*i*64+" bytes. This may cause severe instability. Trying with "+1024*i*64/2+" bytes"),i=Math.floor(i/2)}const n=await WebAssembly.compile(t);let l,r="",s="",c=1,d=0,u=0;const g=await WebAssembly.instantiate(n,{env:{memory:a},runtime:{exceptionHandler:function(t){let e;throw e=1==t?"Signal not found. ":2==t?"Too many signals set. ":3==t?"Signal already set. ":4==t?"Assert Failed. ":5==t?"Not enough memory. ":6==t?"Input signal array access exceeds the size. ":"Unknown error. ",console.error("ERROR: ",t,r),new Error(e+r)},printErrorMessage:function(){r+=h()+"\n"},writeBufferMessage:function(){const t=h();"\n"===t?(console.log(s),s=""):(""!==s&&(s+=" "),s+=t)},showSharedRWMemory:function(){const t=g.exports.getFieldNumLen32(),e=new Uint32Array(t);for(let a=0;a=2&&(d>=1||u>=7)){""!==s&&(s+=" ");const t=pa.fromArray(e,4294967296).toString();s+=t}else console.log(pa.fromArray(e,4294967296))},error:function(t,a,i,o,n,r){let s;throw s=7==t?_(a)+" "+l.getFr(o).toString()+" != "+l.getFr(n).toString()+" "+_(r):9==t?_(a)+" "+l.getFr(o).toString()+" "+_(n):5==t&&e.sym?_(a)+" "+e.sym.labelIdx2Name[n]:_(a)+" "+i+" "+o+" "+n+" "+r,console.log("ERROR: ",t,s),new Error(s)},log:function(t){console.log(l.getFr(t).toString())},logGetSignal:function(t,a){e.logGetSignal&&e.logGetSignal(t,l.getFr(a))},logSetSignal:function(t,a){e.logSetSignal&&e.logSetSignal(t,l.getFr(a))},logStartComponent:function(t){e.logStartComponent&&e.logStartComponent(t)},logFinishComponent:function(t){e.logFinishComponent&&e.logFinishComponent(t)}}});"function"==typeof g.exports.getVersion&&(c=g.exports.getVersion()),"function"==typeof g.exports.getMinorVersion&&(d=g.exports.getMinorVersion()),"function"==typeof g.exports.getPatchVersion&&(u=g.exports.getPatchVersion());const f=e&&(e.sanityCheck||e.logGetSignal||e.logSetSignal||e.logStartComponent||e.logFinishComponent);return l=2===c?new ko(g,f):new Mo(a,g,f),l;function h(){for(var t="",e=g.exports.getMessageChar();0!=e;)t+=String.fromCharCode(e),e=g.exports.getMessageChar();return t}function _(t){const e=new Uint8Array(a.buffer),i=[];for(let a=0;e[t+a]>0;a++)i.push(e[t+a]);return String.fromCharCode.apply(null,i)}}class Mo{constructor(t,e,a){this.memory=t,this.i32=new Uint32Array(t.buffer),this.instance=e,this.n32=(this.instance.exports.getFrLen()>>2)-2;const i=this.instance.exports.getPRawPrime(),o=new Array(this.n32);for(let t=0;t>2)+t];this.prime=pa.fromArray(o,4294967296),this.Fr=new $(this.prime),this.mask32=pa.fromString("FFFFFFFF",16),this.NVars=this.instance.exports.getNVars(),this.n64=Math.floor((this.Fr.bitLength-1)/64)+1,this.R=this.Fr.e(pa.shiftLeft(1,64*this.n64)),this.RInv=this.Fr.inv(this.R),this.sanityCheck=a}circom_version(){return 1}async _doCalculateWitness(t,e){this.instance.exports.init(this.sanityCheck||e?1:0);const a=this.allocInt(),i=this.allocFr();Object.keys(t).forEach((e=>{const o=To(e),n=parseInt(o.slice(0,8),16),l=parseInt(o.slice(8,16),16);try{this.instance.exports.getSignalOffset32(a,0,n,l)}catch(t){throw new Error(`Signal ${e} is not an input of the circuit.`)}const r=this.getInt(a),s=Uo(t[e]);for(let t=0;t>2]}setInt(t,e){this.i32[t>>2]=e}getFr(t){const e=this,a=t>>2;if(2147483648&e.i32[a+1]){const t=new Array(e.n32);for(let i=0;i>2]=o,void(a.i32[1+(t>>2)]=0)}a.i32[t>>2]=0,a.i32[1+(t>>2)]=2147483648;const n=pa.toArray(e,4294967296);for(let e=0;e>2)+e]=i>=0?n[i]:0}}}class ko{constructor(t,e){this.instance=t,this.version=this.instance.exports.getVersion(),this.n32=this.instance.exports.getFieldNumLen32(),this.instance.exports.getRawPrime();const a=new Array(this.n32);for(let t=0;t{const a=To(e),o=parseInt(a.slice(0,8),16),n=parseInt(a.slice(8,16),16),l=Uo(t[e]);for(let t=0;t1)throw new Error(t.fileName+": File has more than one header");t.pos=e[1][0].p;const a=await t.readULE32(),i=await t.read(a),o=pa.fromRprLE(i),n=await ei(o);if(8*n.F1.n64!=a)throw new Error(t.fileName+": Invalid size");const l=await t.readULE32(),r=await t.readULE32();if(t.pos-e[1][0].p!=e[1][0].size)throw new Error("Invalid PTau header size");return{curve:n,power:l,ceremonyPower:r}}function tn(t,e,a,i){const o={tau:{},alpha:{},beta:{}};return o.tau.g1_s=n(),o.tau.g1_sx=n(),o.alpha.g1_s=n(),o.alpha.g1_sx=n(),o.beta.g1_s=n(),o.beta.g1_sx=n(),o.tau.g2_spx=l(),o.alpha.g2_spx=l(),o.beta.g2_spx=l(),o;function n(){let o;return o=i?a.G1.fromRprLEM(t,e):a.G1.fromRprUncompressed(t,e),e+=2*a.G1.F.n8,o}function l(){let o;return o=i?a.G2.fromRprLEM(t,e):a.G2.fromRprUncompressed(t,e),e+=2*a.G2.F.n8,o}}function en(t,e,a,i,o){async function n(i){o?a.G1.toRprLEM(t,e,i):a.G1.toRprUncompressed(t,e,i),e+=2*a.F1.n8}async function l(i){o?a.G2.toRprLEM(t,e,i):a.G2.toRprUncompressed(t,e,i),e+=2*a.F2.n8}return n(i.tau.g1_s),n(i.tau.g1_sx),n(i.alpha.g1_s),n(i.alpha.g1_sx),n(i.beta.g1_s),n(i.beta.g1_sx),l(i.tau.g2_spx),l(i.alpha.g2_spx),l(i.beta.g2_spx),t}async function an(t,e){const a={};a.tauG1=await s(),a.tauG2=await c(),a.alphaG1=await s(),a.betaG1=await s(),a.betaG2=await c(),a.key=await async function(t,e,a){return tn(await t.read(2*e.F1.n8*6+2*e.F2.n8*3),0,e,a)}(t,e,!0),a.partialHash=await t.read(216),a.nextChallenge=await t.read(64),a.type=await t.readULE32();const i=new Uint8Array(2*e.G1.F.n8*6+2*e.G2.F.n8*3);en(i,0,e,a.key,!1);const o=ii.exports(64);o.setPartialHash(a.partialHash),o.update(i),a.responseHash=o.digest();const n=await t.readULE32(),l=t.pos;let r=0;for(;t.pos-l1)throw new Error(t.fileName+": File has more than one contributions section");t.pos=a[7][0].p;const i=await t.readULE32(),o=[];for(let a=0;a0){const e=new Uint8Array(n);await t.writeULE32(e.byteLength),await t.write(e)}else await t.writeULE32(0);async function l(a){e.G1.toRprLEM(i,0,a),await t.write(i)}async function r(a){e.G2.toRprLEM(o,0,a),await t.write(o)}}async function ln(t,e,a){await t.writeULE32(7);const i=t.pos;await t.writeULE64(0),await t.writeULE32(a.length);for(let i=0;i0?u[u.length-1].nextChallenge:rn(c,d,n);const L=await Ra(a,"ptau",1,o?7:2);await Jo(L,c,d);const b=await m.read(64);if(ki(l,w)&&(w=b,u[u.length-1].nextChallenge=w),!ki(b,w))throw new Error("Wrong contribution. this contribution is not based on the previus hash");const A=new ii.exports(64);A.update(b);const y=[];let C;C=await x(m,L,"G1",2,2**d*2-1,[1],"tauG1"),g.tauG1=C[0],C=await x(m,L,"G2",3,2**d,[1],"tauG2"),g.tauG2=C[0],C=await x(m,L,"G1",4,2**d,[0],"alphaG1"),g.alphaG1=C[0],C=await x(m,L,"G1",5,2**d,[0],"betaG1"),g.betaG1=C[0],C=await x(m,L,"G2",6,1,[0],"betaG2"),g.betaG2=C[0],g.partialHash=A.getPartialHash();const I=await m.read(2*c.F1.n8*6+2*c.F2.n8*3);g.key=tn(I,0,c,!1),A.update(new Uint8Array(I));const F=A.digest();if(n&&n.info(Mi(F,"Contribution Response Hash imported: ")),o){const t=new ii.exports(64);t.update(F),await E(t,L,"G1",2,2**d*2-1,"tauG1",n),await E(t,L,"G2",3,2**d,"tauG2",n),await E(t,L,"G1",4,2**d,"alphaTauG1",n),await E(t,L,"G1",5,2**d,"betaTauG1",n),await E(t,L,"G2",6,1,"betaG2",n),g.nextChallenge=t.digest(),n&&n.info(Mi(g.nextChallenge,"Next Challenge Hash: "))}else g.nextChallenge=l;return u.push(g),await ln(L,c,u),await m.close(),await L.close(),await r.close(),g.nextChallenge;async function x(t,e,a,i,l,r,s){return o?await async function(t,e,a,i,o,l,r){const s=c[a],d=s.F.n8,u=2*s.F.n8,g=[];await Da(e,i);const f=Math.floor((1<<24)/u);y[i]=e.pos;for(let a=0;a=a&&e=e&&o1?s[s.length-2]:c;const u=s[s.length-1];if(e&&e.debug("Validating contribution #"+s[s.length-1].id),!await dn(n,u,d,e))return!1;const g=ii.exports(64);g.update(u.responseHash),e&&e.debug("Verifying powers in tau*G1 section");const f=await b(2,"G1","tauG1",2**l*2-1,[0,1],e);if(a=await cn(n,f.R1,f.R2,n.G2.g,u.tauG2),!0!==a)return e&&e.error("tauG1 section. Powers do not match"),!1;if(!n.G1.eq(n.G1.g,f.singularPoints[0]))return e&&e.error("First element of tau*G1 section must be the generator"),!1;if(!n.G1.eq(u.tauG1,f.singularPoints[1]))return e&&e.error("Second element of tau*G1 section does not match the one in the contribution section"),!1;e&&e.debug("Verifying powers in tau*G2 section");const h=await b(3,"G2","tauG2",2**l,[0,1],e);if(a=await cn(n,n.G1.g,u.tauG1,h.R1,h.R2),!0!==a)return e&&e.error("tauG2 section. Powers do not match"),!1;if(!n.G2.eq(n.G2.g,h.singularPoints[0]))return e&&e.error("First element of tau*G2 section must be the generator"),!1;if(!n.G2.eq(u.tauG2,h.singularPoints[1]))return e&&e.error("Second element of tau*G2 section does not match the one in the contribution section"),!1;e&&e.debug("Verifying powers in alpha*tau*G1 section");const _=await b(4,"G1","alphatauG1",2**l,[0],e);if(a=await cn(n,_.R1,_.R2,n.G2.g,u.tauG2),!0!==a)return e&&e.error("alphaTauG1 section. Powers do not match"),!1;if(!n.G1.eq(u.alphaG1,_.singularPoints[0]))return e&&e.error("First element of alpha*tau*G1 section (alpha*G1) does not match the one in the contribution section"),!1;e&&e.debug("Verifying powers in beta*tau*G1 section");const p=await b(5,"G1","betatauG1",2**l,[0],e);if(a=await cn(n,p.R1,p.R2,n.G2.g,u.tauG2),!0!==a)return e&&e.error("betaTauG1 section. Powers do not match"),!1;if(!n.G1.eq(u.betaG1,p.singularPoints[0]))return e&&e.error("First element of beta*tau*G1 section (beta*G1) does not match the one in the contribution section"),!1;const m=await async function(t){const e=n.G2,a=2*e.F.n8,l=new Uint8Array(a);if(!o[6])throw t.error("File has no BetaG2 section"),new Error("File has no BetaG2 section");if(o[6].length>1)throw t.error("File has no BetaG2 section"),new Error("File has more than one GetaG2 section");i.pos=o[6][0].p;const r=await i.read(a),s=e.fromRprLEM(r);return e.toRprUncompressed(l,0,s),g.update(l),s}(e);if(!n.G2.eq(u.betaG2,m))return e&&e.error("betaG2 element in betaG2 section does not match the one in the contribution section"),!1;const w=g.digest();if(l==r&&!ki(w,u.nextChallenge))return e&&e.error("Hash of the values does not match the next challenge of the last contributor in the contributions section"),!1;e&&e.info(Mi(w,"Next challenge hash: ")),L(u,d);for(let t=s.length-2;t>=0;t--){const a=s[t],i=t>0?s[t-1]:c;if(!await dn(n,a,i,e))return!1;L(a,i)}if(e&&e.info("-----------------------------------------------------"),o[12]&&o[13]&&o[14]&&o[15]){let t;if(t=await A("G1",2,12,"tauG1",e),!t)return!1;if(t=await A("G2",3,13,"tauG2",e),!t)return!1;if(t=await A("G1",4,14,"alphaTauG1",e),!t)return!1;if(t=await A("G1",5,15,"betaTauG1",e),!t)return!1}else e&&e.warn('this file does not contain phase2 precalculated values. Please run: \n snarkjs "powersoftau preparephase2" to prepare this file to be used in the phase2 ceremony.');return await i.close(),e&&e.info("Powers of Tau Ok!"),!0;function L(t,a){if(!e)return;e.info("-----------------------------------------------------"),e.info(`Contribution #${t.id}: ${t.name||""}`),e.info(Mi(t.nextChallenge,"Next Challenge: "));const i=new Uint8Array(2*n.G1.F.n8*6+2*n.G2.F.n8*3);en(i,0,n,t.key,!1);const o=ii.exports(64);o.setPartialHash(t.partialHash),o.update(i);const l=o.digest();e.info(Mi(l,"Response Hash:")),e.info(Mi(a.nextChallenge,"Response Hash:")),1==t.type&&(e.info(`Beacon generator: ${Zi(t.beaconHash)}`),e.info(`Beacon iterations Exp: ${t.numIterationsExp}`))}async function b(t,e,a,l,r,s){const c=n[e],d=2*c.F.n8;await Va(i,o,t);const u=[];let f=c.zero,h=c.zero,_=c.zero;for(let t=0;t0){const t=c.fromRprLEM(o,0),e=$i(Ni(4),0);f=c.add(f,c.timesScalar(_,e)),h=c.add(h,c.timesScalar(t,e))}const m=await c.multiExpAffine(o.slice(0,(e-1)*d),p),w=await c.multiExpAffine(o.slice(d),p);f=c.add(f,m),h=c.add(h,w),_=c.fromRprLEM(o,(e-1)*d);for(let a=0;a=t&&i1;)c/=2,d+=1;if(2**d!=s)throw new Error("Invalid file size");o&&o.debug("Power to tau size: "+d);const u=await ji(i),g=await qa(a),f=ii.exports(64);for(let t=0;t{o.debug(e+".g1_s: "+t.G1.toString(p[e].g1_s,16)),o.debug(e+".g1_sx: "+t.G1.toString(p[e].g1_sx,16)),o.debug(e+".g2_sp: "+t.G2.toString(p[e].g2_sp,16)),o.debug(e+".g2_spx: "+t.G2.toString(p[e].g2_spx,16)),o.debug("")}));const m=ii.exports(64);await g.write(_),m.update(_),await gn(n,g,m,t,"G1",2**d*2-1,t.Fr.one,p.tau.prvKey,"COMPRESSED","tauG1",o),await gn(n,g,m,t,"G2",2**d,t.Fr.one,p.tau.prvKey,"COMPRESSED","tauG2",o),await gn(n,g,m,t,"G1",2**d,p.alpha.prvKey,p.tau.prvKey,"COMPRESSED","alphaTauG1",o),await gn(n,g,m,t,"G1",2**d,p.beta.prvKey,p.tau.prvKey,"COMPRESSED","betaTauG1",o),await gn(n,g,m,t,"G2",1,p.beta.prvKey,p.tau.prvKey,"COMPRESSED","betaTauG2",o);const w=new Uint8Array(2*t.F1.n8*6+2*t.F2.n8*3);en(w,0,t,p,!1),await g.write(w),m.update(w);const L=m.digest();o&&o.info(Mi(L,"Contribution Response Hash: ")),await g.close(),await n.close()},beacon:async function(t,e,a,i,o,n){const l=Hi(i);if(0==l.byteLength||2*l.byteLength!=i.length)return n&&n.error("Invalid Beacon Hash. (It must be a valid hexadecimal sequence)"),!1;if(l.length>=256)return n&&n.error("Maximum lenght of beacon hash is 255 bytes"),!1;if((o=parseInt(o))<10||o>63)return n&&n.error("Invalid numIterationsExp. (Must be between 10 and 63)"),!1;await ii.exports.ready();const{fd:r,sections:s}=await ka(t,"ptau",1),{curve:c,power:d,ceremonyPower:u}=await Xo(r,s);if(d!=u)return n&&n.error("This file has been reduced. You cannot contribute into a reduced file."),!1;s[12]&&n&&n.warn("Contributing into a file that has phase2 calculated. You will have to prepare phase2 again.");const g=await on(r,c,s),f={name:a,type:1,numIterationsExp:o,beaconHash:l};let h;h=g.length>0?g[g.length-1].nextChallenge:rn(c,d,n),f.key=await sn(c,h,l,o);const _=new ii.exports(64);_.update(h);const p=await Ra(e,"ptau",1,7);await Jo(p,c,d);const m=[];let w;w=await y(2,"G1",2**d*2-1,c.Fr.e(1),f.key.tau.prvKey,"tauG1",n),f.tauG1=w[1],w=await y(3,"G2",2**d,c.Fr.e(1),f.key.tau.prvKey,"tauG2",n),f.tauG2=w[1],w=await y(4,"G1",2**d,f.key.alpha.prvKey,f.key.tau.prvKey,"alphaTauG1",n),f.alphaG1=w[0],w=await y(5,"G1",2**d,f.key.beta.prvKey,f.key.tau.prvKey,"betaTauG1",n),f.betaG1=w[0],w=await y(6,"G2",1,f.key.beta.prvKey,f.key.tau.prvKey,"betaTauG2",n),f.betaG2=w[0],f.partialHash=_.getPartialHash();const L=new Uint8Array(2*c.F1.n8*6+2*c.F2.n8*3);en(L,0,c,f.key,!1),_.update(new Uint8Array(L));const b=_.digest();n&&n.info(Mi(b,"Contribution Response Hash imported: "));const A=new ii.exports(64);return A.update(b),await C(p,"G1",2,2**d*2-1,"tauG1",n),await C(p,"G2",3,2**d,"tauG2",n),await C(p,"G1",4,2**d,"alphaTauG1",n),await C(p,"G1",5,2**d,"betaTauG1",n),await C(p,"G2",6,1,"betaG2",n),f.nextChallenge=A.digest(),n&&n.info(Mi(f.nextChallenge,"Next Challenge Hash: ")),g.push(f),await ln(p,c,g),await r.close(),await p.close(),b;async function y(t,e,a,i,o,n,l){const d=[];r.pos=s[t][0].p,await Da(p,t),m[t]=p.pos;const u=c[e],g=2*u.F.n8,f=Math.floor((1<<20)/g);let h=i;for(let t=0;t0?d[d.length-1].nextChallenge:rn(r,s,o),u.key=Yo(r,g,f);const h=new ii.exports(64);h.update(g);const _=await Ra(e,"ptau",1,7);await Jo(_,r,s);const p=[];let m;m=await A(2,"G1",2**s*2-1,r.Fr.e(1),u.key.tau.prvKey,"tauG1"),u.tauG1=m[1],m=await A(3,"G2",2**s,r.Fr.e(1),u.key.tau.prvKey,"tauG2"),u.tauG2=m[1],m=await A(4,"G1",2**s,u.key.alpha.prvKey,u.key.tau.prvKey,"alphaTauG1"),u.alphaG1=m[0],m=await A(5,"G1",2**s,u.key.beta.prvKey,u.key.tau.prvKey,"betaTauG1"),u.betaG1=m[0],m=await A(6,"G2",1,u.key.beta.prvKey,u.key.tau.prvKey,"betaTauG2"),u.betaG2=m[0],u.partialHash=h.getPartialHash();const w=new Uint8Array(2*r.F1.n8*6+2*r.F2.n8*3);en(w,0,r,u.key,!1),h.update(new Uint8Array(w));const L=h.digest();o&&o.info(Mi(L,"Contribution Response Hash imported: "));const b=new ii.exports(64);return b.update(L),await y(_,"G1",2,2**s*2-1,"tauG1"),await y(_,"G2",3,2**s,"tauG2"),await y(_,"G1",4,2**s,"alphaTauG1"),await y(_,"G1",5,2**s,"betaTauG1"),await y(_,"G2",6,1,"betaG2"),u.nextChallenge=b.digest(),o&&o.info(Mi(u.nextChallenge,"Next Challenge Hash: ")),d.push(u),await ln(_,r,d),await n.close(),await _.close(),L;async function A(t,e,a,i,s,c){const d=[];n.pos=l[t][0].p,await Da(_,t),p[t]=_.pos;const u=r[e],g=2*u.F.n8,f=Math.floor((1<<20)/g);let m=i;for(let t=0;t=this.length&&(this.length=t+1),!0}getKeys(){const t=new mn;for(let e=0;e1<<20?new mn:[];for(let t=0;t1<<20?new mn:[];for(let t=0;t1<<20?new mn:[];for(let t=0;t{let i="";return Object.keys(a).forEach((o=>{let n=e.varIdx2Name[o];"one"==n&&(n="1");let l=t.curve.Fr.toString(a[o]);"1"==l&&(l=""),"-1"==l&&(l="-"),""!=i&&"-"!=l[0]&&(l="+"+l),""!=i&&(l=" "+l),i=i+l+n})),i},n=`[ ${o(i[0])} ] * [ ${o(i[1])} ] - [ ${o(i[2])} ] = 0`;a&&a.info(n)}},info:async function(t,e){const a=await yn(t);return pa.eq(a.prime,In)?e&&e.info("Curve: bn-128"):pa.eq(a.prime,Cn)?e&&e.info("Curve: bls12-381"):e&&e.info(`Unknown Curve. Prime: ${pa.toString(a.prime)}`),e&&e.info(`# of Wires: ${a.nVars}`),e&&e.info(`# of Constraints: ${a.nConstraints}`),e&&e.info(`# of Private Inputs: ${a.nPrvInputs}`),e&&e.info(`# of Public Inputs: ${a.nPubInputs}`),e&&e.info(`# of Labels: ${a.nLabels}`),e&&e.info(`# of Outputs: ${a.nOutputs}`),a},exportJson:async function(t,e){const a=await yn(t,!0,!0,!0,e),i=a.curve.Fr;return delete a.curve,delete a.F,Wi(i,a)}});async function xn(t){const e={labelIdx2Name:["one"],varIdx2Name:["one"],componentIdx2Name:[]},a=await Ma(t),i=await a.read(a.totalSize),o=new TextDecoder("utf-8").decode(i).split("\n");for(let t=0;t Reading r1cs file");const{fd:i,sections:o}=await ka(t,"r1cs",1),n=await An(i,o,{loadConstraints:!1,loadCustomGates:!1});a&&a.info("> Reading witness file");const{fd:l,sections:r}=await ka(e,"wtns",2),s=await Go(l,r);if(!pa.eq(n.prime,s.q))throw new Error("Curve of the witness does not match the curve of the proving key");const c=await Za(l,r,2);await l.close();const d=(await async function(t){let e;if(pa.eq(t,Ja))e=await ga();else{if(!pa.eq(t,Ya))throw new Error(`Curve not supported: ${pa.toString(t)}`);e=await fa()}return e}(n.prime)).Fr,u=d.n8,g=await Za(i,o,2);a&&(a.info("----------------------------"),a.info(" WITNESS CHECK"),a.info(` Curve: ${n.curve.name}`),a.info(` Vars (wires): ${n.nVars}`),a.info(` Ouputs: ${n.nOutputs}`),a.info(` Public Inputs: ${n.nPubInputs}`),a.info(` Private Inputs: ${n.nPrvInputs}`),a.info(` Labels: ${n.nLabels}`),a.info(` Constraints: ${n.nConstraints}`),a.info(` Custom Gates: ${n.useCustomGates}`),a.info("----------------------------")),a&&a.info("> Checking witness correctness");let f=0,h=!0;for(let t=0;t{const i=function(t){return d.fromRprLE(c.slice(t*u,t*u+u))}(a),o=t[a];e=d.add(e,d.mul(i,o))})),e}function p(){const t={},e=g.slice(f,f+4);f+=4;const a=new DataView(e.buffer).getUint32(0,!0),i=g.slice(f,f+(4+n.n8)*a);f+=(4+n.n8)*a;const o=new DataView(i.buffer);for(let e=0;e=this.length&&(this.length=t+1),!0}getKeys(){const t=new Gn;for(let e=0;eg)return i&&i.error(`circuit too big for this power of tau ceremony. ${_.nConstraints}*2 > 2**${g}`),-1;if(!d[12])return i&&i.error("Powers of tau is not prepared."),-1;const b=_.nOutputs+_.nPubInputs,A=2**L;await Da(p,1),await p.writeULE32(1),await Na(p),await Da(p,2);const y=u.q,C=8*(Math.floor((pa.bitLength(y)-1)/64)+1),I=u.r,F=8*(Math.floor((pa.bitLength(I)-1)/64)+1),x=pa.mod(pa.shl(1,8*F),I),E=u.Fr.e(pa.mod(pa.mul(x,x),I));let v,B,S;await p.writeULE32(C),await ja(p,y,C),await p.writeULE32(F),await ja(p,I,F),await p.writeULE32(_.nVars),await p.writeULE32(b),await p.writeULE32(A),v=await c.read(m,d[4][0].p),await p.write(v),v=await u.G1.batchLEMtoU(v),s.update(v),B=await c.read(m,d[5][0].p),await p.write(B),B=await u.G1.batchLEMtoU(B),s.update(B),S=await c.read(w,d[6][0].p),await p.write(S),S=await u.G2.batchLEMtoU(S),s.update(S);const P=new Uint8Array(m);u.G1.toRprLEM(P,0,u.G1.g);const G=new Uint8Array(w);u.G2.toRprLEM(G,0,u.G2.g);const z=new Uint8Array(m);u.G1.toRprUncompressed(z,0,u.G1.g);const O=new Uint8Array(w);u.G2.toRprUncompressed(O,0,u.G2.g),await p.write(G),await p.write(P),await p.write(G),s.update(O),s.update(z),s.update(O),await Na(p),i&&i.info("Reading r1cs");let U=await Za(f,h,2);const T=new Gn(_.nVars),Q=new Gn(_.nVars),q=new Gn(_.nVars),M=new Gn(_.nVars-b-1),k=new Array(b+1);i&&i.info("Reading tauG1");let R=await Za(c,d,12,(A-1)*m,A*m);i&&i.info("Reading tauG2");let D=await Za(c,d,13,(A-1)*w,A*w);i&&i.info("Reading alphatauG1");let N=await Za(c,d,14,(A-1)*m,A*m);i&&i.info("Reading betatauG1");let V=await Za(c,d,15,(A-1)*m,A*m);await async function(){const t=new Uint8Array(12+u.Fr.n8),e=new DataView(t.buffer),a=new Uint8Array(u.Fr.n8);u.Fr.toRprLE(a,0,u.Fr.e(1));let s=0;function c(){const t=U.slice(s,s+4);s+=4;return new DataView(t.buffer).getUint32(0,!0)}const d=new Gn;for(let t=0;t<_.nConstraints;t++){i&&t%1e4==0&&i.debug(`processing constraints: ${t}/${_.nConstraints}`);const e=c();for(let a=0;a=0?u.Fr.fromRprLE(U.slice(i[3],i[3]+u.Fr.n8),0):u.Fr.fromRprLE(a,0);const n=u.Fr.mul(o,E);u.Fr.toRprLE(t,12,n),g.set(t,h),h+=t.length}await p.write(g),await Na(p)}(),await j(3,"G1",k,"IC"),await async function(){await Da(p,9);const t=new Ge(A*m);if(L(i&&i.debug(`Writing points end ${o}: ${d}/${a.length}`),t)))),r+=n,t++}const c=await Promise.all(l);for(let t=0;t32768?(f=new Ge(_*n),h=new Ge(_*u.Fr.n8)):(f=new Uint8Array(_*n),h=new Uint8Array(_*u.Fr.n8));let p=0,m=0;const w=[R,D,N,V],L=new Uint8Array(u.Fr.n8);u.Fr.toRprLE(L,0,u.Fr.e(1));let b=0;for(let t=0;t=0?h.set(U.slice(e[t][o][2],e[t][o][2]+u.Fr.n8),b*u.Fr.n8):h.set(L,b*u.Fr.n8),b++;if(e.length>1){const t=[];t.push({cmd:"ALLOCSET",var:0,buff:f}),t.push({cmd:"ALLOCSET",var:1,buff:h}),t.push({cmd:"ALLOC",var:2,len:e.length*l}),p=0,m=0;let a=0;for(let i=0;i=0;t--){const e=d.contributions[t];i&&i.info("-------------------------"),i&&i.info(Mi(e.contributionHash,`contribution #${t+1} 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a={protocol:t.protocol,curve:e.name,nPublic:t.nPublic,power:t.power,k1:e.Fr.toObject(t.k1),k2:e.Fr.toObject(t.k2),Qm:e.G1.toObject(t.Qm),Ql:e.G1.toObject(t.Ql),Qr:e.G1.toObject(t.Qr),Qo:e.G1.toObject(t.Qo),Qc:e.G1.toObject(t.Qc),S1:e.G1.toObject(t.S1),S2:e.G1.toObject(t.S2),S3:e.G1.toObject(t.S3),X_2:e.G2.toObject(t.X_2),w:e.Fr.toObject(e.Fr.w[t.power])};return a=Tn(a),a}(o);else{if(!o.protocolId||o.protocolId!==to)throw new Error("zkey file protocol unrecognized");n=await async function(t,e){const a=await ei(t.q);let i={protocol:t.protocol,curve:a.name,nPublic:t.nPublic,power:t.power,k1:a.Fr.toObject(t.k1),k2:a.Fr.toObject(t.k2),w:a.Fr.toObject(a.Fr.w[t.power]),w3:a.Fr.toObject(t.w3),w4:a.Fr.toObject(t.w4),w8:a.Fr.toObject(t.w8),wr:a.Fr.toObject(t.wr),X_2:a.G2.toObject(t.X_2),C0:a.G1.toObject(t.C0)};return Tn(i)}(o)}return await a.close(),e&&e.info("EXPORT VERIFICATION KEY FINISHED"),n}var qn={};const{unstringifyBigInts:Mn,stringifyBigInts:kn}=ma;async function Rn(t,e,a){a&&a.info("FFLONK EXPORT SOLIDITY VERIFIER STARTED");const i=await ai(t.curve);let o=c(t.w3);t.w3_2=d(i.Fr.square(o));let n=c(t.w4);t.w4_2=d(i.Fr.square(n)),t.w4_3=d(i.Fr.mul(i.Fr.square(n),n));let l=c(t.w8),r=i.Fr.one;for(let e=1;e<8;e++)r=i.Fr.mul(r,l),t["w8_"+e]=d(r);let s=e[t.protocol];return a&&a.info("FFLONK EXPORT SOLIDITY VERIFIER FINISHED"),qn.render(s,t);function c(t){const e=Mn(t);return i.Fr.fromObject(e)}function d(t){const e=i.Fr.toObject(t);return kn(e)}}var Dn=Object.freeze({__proto__:null,newZKey:zn,exportBellman:async function(t,e,a){const{fd:i,sections:o}=await ka(t,"zkey",2),n=await Fo(i,o);if("groth16"!=n.protocol)throw new Error("zkey file is not groth16");const l=await ei(n.q),r=2*l.G1.F.n8,s=2*l.G2.F.n8,c=await Eo(i,l,o),d=await qa(e);let u;await w(n.vk_alpha_1),await w(n.vk_beta_1),await L(n.vk_beta_2),await L(n.vk_gamma_2),await w(n.vk_delta_1),await L(n.vk_delta_2),u=await Za(i,o,3),u=await l.G1.batchLEMtoU(u),await b("G1",u);const g=await Za(i,o,9);let f,h,_,p,m;f=await l.G1.fft(g,"affine","jacobian",a),f=await l.G1.batchApplyKey(f,l.Fr.neg(l.Fr.e(2)),l.Fr.w[n.power+1],"jacobian","affine",a),f=f.slice(0,f.byteLength-r),f=await l.G1.batchLEMtoU(f),await b("G1",f),h=await Za(i,o,8),h=await l.G1.batchLEMtoU(h),await b("G1",h),_=await Za(i,o,5),_=await l.G1.batchLEMtoU(_),await b("G1",_),p=await Za(i,o,6),p=await l.G1.batchLEMtoU(p),await b("G1",p),m=await Za(i,o,7),m=await l.G2.batchLEMtoU(m),await b("G2",m),await d.write(c.csHash),await async function(t){const e=new Uint8Array(4);new DataView(e.buffer,e.byteOffset,e.byteLength).setUint32(0,t,!1),await d.write(e)}(c.contributions.length);for(let t=0;tg.contributions.length)return o&&o.error("The impoerted file does not include new contributions"),!1;for(let t=0;t=256)return n&&n.error("Maximum lenght of beacon hash is 255 bytes"),!1;if((o=parseInt(o))<10||o>63)return n&&n.error("Invalid numIterationsExp. 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o,l,r=this.blocks,c=this.byteCount,d=e.length,u=this.blockCount,g=0,f=this.s;g>2]|=e[g]<>2]|=l<>2]|=(192|l>>6)<>2]|=(128|63&l)<=57344?(r[o>>2]|=(224|l>>12)<>2]|=(128|l>>6&63)<>2]|=(128|63&l)<>2]|=(240|l>>18)<>2]|=(128|l>>12&63)<>2]|=(128|l>>6&63)<>2]|=(128|63&l)<=c){for(this.start=o-c,this.block=r[u],o=0;o>=8);a>0;)o.unshift(a),a=255&(t>>=8),++i;return e?o.push(i):o.unshift(i),this.update(o),o.length},B.prototype.encodeString=function(e){var a,i=typeof e;if("string"!==i){if("object"!==i)throw new Error(t);if(null===e)throw new Error(t);if(n&&e.constructor===ArrayBuffer)e=new Uint8Array(e);else if(!(Array.isArray(e)||n&&ArrayBuffer.isView(e)))throw new Error(t);a=!0}var o=0,l=e.length;if(a)o=l;else for(var r=0;r=57344?o+=3:(s=65536+((1023&s)<<10|1023&e.charCodeAt(++r)),o+=4)}return o+=this.encode(8*o),this.update(e),o},B.prototype.bytepad=function(t,e){for(var a=this.encode(e),i=0;i>2]|=this.padding[3&e],this.lastByteIndex===this.byteCount)for(t[0]=t[a],e=1;e>4&15]+l[15&t]+l[t>>12&15]+l[t>>8&15]+l[t>>20&15]+l[t>>16&15]+l[t>>28&15]+l[t>>24&15];r%e==0&&(P(a),n=0)}return o&&(t=a[n],s+=l[t>>4&15]+l[15&t],o>1&&(s+=l[t>>12&15]+l[t>>8&15]),o>2&&(s+=l[t>>20&15]+l[t>>16&15])),s},B.prototype.arrayBuffer=function(){this.finalize();var t,e=this.blockCount,a=this.s,i=this.outputBlocks,o=this.extraBytes,n=0,l=0,r=this.outputBits>>3;t=o?new ArrayBuffer(i+1<<2):new ArrayBuffer(r);for(var s=new Uint32Array(t);l>8&255,s[t+2]=e>>16&255,s[t+3]=e>>24&255;r%a==0&&P(i)}return n&&(t=r<<2,e=i[l],s[t]=255&e,n>1&&(s[t+1]=e>>8&255),n>2&&(s[t+2]=e>>16&255)),s},S.prototype=new B,S.prototype.finalize=function(){return this.encode(this.outputBits,!0),B.prototype.finalize.call(this)};var P=function(t){var e,a,i,o,n,l,r,s,d,u,g,f,h,_,p,m,w,L,b,A,y,C,I,F,x,E,v,B,S,P,G,z,O,U,Q,T,q,M,k,R,D,N,V,$,j,K,H,Z,W,Y,J,X,tt,et,at,it,ot,nt,lt,rt,st,ct,dt;for(i=0;i<48;i+=2)o=t[0]^t[10]^t[20]^t[30]^t[40],n=t[1]^t[11]^t[21]^t[31]^t[41],l=t[2]^t[12]^t[22]^t[32]^t[42],r=t[3]^t[13]^t[23]^t[33]^t[43],s=t[4]^t[14]^t[24]^t[34]^t[44],d=t[5]^t[15]^t[25]^t[35]^t[45],u=t[6]^t[16]^t[26]^t[36]^t[46],g=t[7]^t[17]^t[27]^t[37]^t[47],e=(f=t[8]^t[18]^t[28]^t[38]^t[48])^(l<<1|r>>>31),a=(h=t[9]^t[19]^t[29]^t[39]^t[49])^(r<<1|l>>>31),t[0]^=e,t[1]^=a,t[10]^=e,t[11]^=a,t[20]^=e,t[21]^=a,t[30]^=e,t[31]^=a,t[40]^=e,t[41]^=a,e=o^(s<<1|d>>>31),a=n^(d<<1|s>>>31),t[2]^=e,t[3]^=a,t[12]^=e,t[13]^=a,t[22]^=e,t[23]^=a,t[32]^=e,t[33]^=a,t[42]^=e,t[43]^=a,e=l^(u<<1|g>>>31),a=r^(g<<1|u>>>31),t[4]^=e,t[5]^=a,t[14]^=e,t[15]^=a,t[24]^=e,t[25]^=a,t[34]^=e,t[35]^=a,t[44]^=e,t[45]^=a,e=s^(f<<1|h>>>31),a=d^(h<<1|f>>>31),t[6]^=e,t[7]^=a,t[16]^=e,t[17]^=a,t[26]^=e,t[27]^=a,t[36]^=e,t[37]^=a,t[46]^=e,t[47]^=a,e=u^(o<<1|n>>>31),a=g^(n<<1|o>>>31),t[8]^=e,t[9]^=a,t[18]^=e,t[19]^=a,t[28]^=e,t[29]^=a,t[38]^=e,t[39]^=a,t[48]^=e,t[49]^=a,_=t[0],p=t[1],K=t[11]<<4|t[10]>>>28,H=t[10]<<4|t[11]>>>28,B=t[20]<<3|t[21]>>>29,S=t[21]<<3|t[20]>>>29,rt=t[31]<<9|t[30]>>>23,st=t[30]<<9|t[31]>>>23,N=t[40]<<18|t[41]>>>14,V=t[41]<<18|t[40]>>>14,U=t[2]<<1|t[3]>>>31,Q=t[3]<<1|t[2]>>>31,m=t[13]<<12|t[12]>>>20,w=t[12]<<12|t[13]>>>20,Z=t[22]<<10|t[23]>>>22,W=t[23]<<10|t[22]>>>22,P=t[33]<<13|t[32]>>>19,G=t[32]<<13|t[33]>>>19,ct=t[42]<<2|t[43]>>>30,dt=t[43]<<2|t[42]>>>30,et=t[5]<<30|t[4]>>>2,at=t[4]<<30|t[5]>>>2,T=t[14]<<6|t[15]>>>26,q=t[15]<<6|t[14]>>>26,L=t[25]<<11|t[24]>>>21,b=t[24]<<11|t[25]>>>21,Y=t[34]<<15|t[35]>>>17,J=t[35]<<15|t[34]>>>17,z=t[45]<<29|t[44]>>>3,O=t[44]<<29|t[45]>>>3,F=t[6]<<28|t[7]>>>4,x=t[7]<<28|t[6]>>>4,it=t[17]<<23|t[16]>>>9,ot=t[16]<<23|t[17]>>>9,M=t[26]<<25|t[27]>>>7,k=t[27]<<25|t[26]>>>7,A=t[36]<<21|t[37]>>>11,y=t[37]<<21|t[36]>>>11,X=t[47]<<24|t[46]>>>8,tt=t[46]<<24|t[47]>>>8,$=t[8]<<27|t[9]>>>5,j=t[9]<<27|t[8]>>>5,E=t[18]<<20|t[19]>>>12,v=t[19]<<20|t[18]>>>12,nt=t[29]<<7|t[28]>>>25,lt=t[28]<<7|t[29]>>>25,R=t[38]<<8|t[39]>>>24,D=t[39]<<8|t[38]>>>24,C=t[48]<<14|t[49]>>>18,I=t[49]<<14|t[48]>>>18,t[0]=_^~m&L,t[1]=p^~w&b,t[10]=F^~E&B,t[11]=x^~v&S,t[20]=U^~T&M,t[21]=Q^~q&k,t[30]=$^~K&Z,t[31]=j^~H&W,t[40]=et^~it&nt,t[41]=at^~ot<,t[2]=m^~L&A,t[3]=w^~b&y,t[12]=E^~B&P,t[13]=v^~S&G,t[22]=T^~M&R,t[23]=q^~k&D,t[32]=K^~Z&Y,t[33]=H^~W&J,t[42]=it^~nt&rt,t[43]=ot^~lt&st,t[4]=L^~A&C,t[5]=b^~y&I,t[14]=B^~P&z,t[15]=S^~G&O,t[24]=M^~R&N,t[25]=k^~D&V,t[34]=Z^~Y&X,t[35]=W^~J&tt,t[44]=nt^~rt&ct,t[45]=lt^~st&dt,t[6]=A^~C&_,t[7]=y^~I&p,t[16]=P^~z&F,t[17]=G^~O&x,t[26]=R^~N&U,t[27]=D^~V&Q,t[36]=Y^~X&$,t[37]=J^~tt&j,t[46]=rt^~ct&et,t[47]=st^~dt&at,t[8]=C^~_&m,t[9]=I^~p&w,t[18]=z^~F&E,t[19]=O^~x&v,t[28]=N^~U&T,t[29]=V^~Q&q,t[38]=X^~$&K,t[39]=tt^~j&H,t[48]=ct^~et&it,t[49]=dt^~at&ot,t[0]^=c[i],t[1]^=c[i+1]};if(o)kn.exports=A;else for(C=0;C3*s.domainSize-4&&!d.isZero(e))throw new Error("T Polynomial is not divisible")}a&&a.debug("ifft Tz");const x=await d.ifft(C);for(let t=0;t<4*s.domainSize;t++){const e=x.slice(t*g,(t+1)*g);if(t>3*s.domainSize+5){if(!d.isZero(e))throw new Error("Tz Polynomial is not well calculated")}else F.set(d.add(F.slice(t*g,(t+1)*g),e),t*g)}E=F.slice(0,(3*s.domainSize+6)*g);let v=new Ge((s.domainSize+1)*g);v.set(F.slice(0,s.domainSize*g),0),v.set(U.b[10],s.domainSize*g);let P=new Ge((s.domainSize+1)*g);P.set(F.slice(s.domainSize*g,2*s.domainSize*g),0);const G=d.sub(P.slice(0,g),U.b[10]);P.set(G,0),P.set(U.b[11],s.domainSize*g);let z=new Ge((s.domainSize+6)*g);z.set(F.slice(2*s.domainSize*g,(3*s.domainSize+6)*g),0);const O=d.sub(z.slice(0,g),U.b[11]);function Q(t,e,a,i,o){let n,l;const r=d.mul(t,e),s=d.mul(t,i),c=d.mul(a,e);n=r;let u=d.mul(a,i);return l=d.add(s,c),o&&(l=d.add(l,d.mul(h[o],u))),[n,l]}function T(t,e,a,i,o,n,l,r,s){let c,u;const g=d.mul(t,e),f=d.mul(t,n),_=d.mul(o,e),w=d.mul(o,n),L=d.mul(a,i),b=d.mul(a,r),A=d.mul(l,i),y=d.mul(l,r);c=d.mul(g,L);let C=d.mul(_,L);C=d.add(C,d.mul(f,L)),C=d.add(C,d.mul(g,A)),C=d.add(C,d.mul(g,b));let I=d.mul(w,L);I=d.add(I,d.mul(_,A)),I=d.add(I,d.mul(_,b)),I=d.add(I,d.mul(f,A)),I=d.add(I,d.mul(f,b)),I=d.add(I,d.mul(g,y));let F=d.mul(f,y);F=d.add(F,d.mul(_,y)),F=d.add(F,d.mul(w,b)),F=d.add(F,d.mul(w,A));let x=d.mul(w,y);return u=C,s&&(u=d.add(u,d.mul(h[s],I)),u=d.add(u,d.mul(p[s],F)),u=d.add(u,d.mul(m[s],x))),[c,u]}z.set(O,0),B.T1=await D(v,"multiexp T1"),B.T2=await D(P,"multiexp T2"),B.T3=await D(z,"multiexp T3")}(),await async function(){const t=new Ge(s.domainSize*g);await l.readToBuffer(t,0,s.domainSize*g,r[7][0].p);const e=new Ge(s.domainSize*g);await l.readToBuffer(e,0,s.domainSize*g,r[8][0].p);const i=new Ge(s.domainSize*g);await l.readToBuffer(i,0,s.domainSize*g,r[9][0].p);const o=new Ge(s.domainSize*g);await l.readToBuffer(o,0,s.domainSize*g,r[10][0].p);const n=new Ge(s.domainSize*g);await l.readToBuffer(n,0,s.domainSize*g,r[11][0].p);const c=new Ge(s.domainSize*g);await l.readToBuffer(c,0,s.domainSize*g,r[12][0].p+10*s.domainSize*g);const f=new Uint8Array(2*u.F.n8*3);u.toRprUncompressed(f,0,B.T1),u.toRprUncompressed(f,2*u.F.n8,B.T2),u.toRprUncompressed(f,4*u.F.n8,B.T3),U.xi=M(f),a&&a.debug("xi: "+d.toString(U.xi));B.eval_a=k(C,U.xi),B.eval_b=k(I,U.xi),B.eval_c=k(F,U.xi),B.eval_s1=k(G,U.xi),B.eval_s2=k(z,U.xi),B.eval_t=k(E,U.xi),B.eval_zw=k(x,d.mul(U.xi,d.w[s.power]));const h=d.mul(B.eval_a,B.eval_b);let _=B.eval_a;const p=d.mul(U.beta,U.xi);_=d.add(_,p),_=d.add(_,U.gamma);let m=B.eval_b;m=d.add(m,d.mul(p,s.k1)),m=d.add(m,U.gamma);let w=B.eval_c;w=d.add(w,d.mul(p,s.k2)),w=d.add(w,U.gamma);const L=d.mul(d.mul(d.mul(_,m),w),U.alpha);let b=B.eval_a;b=d.add(b,d.mul(U.beta,B.eval_s1)),b=d.add(b,U.gamma);let A=B.eval_b;A=d.add(A,d.mul(U.beta,B.eval_s2)),A=d.add(A,U.gamma);let y=d.mul(b,A);y=d.mul(y,U.beta),y=d.mul(y,B.eval_zw),y=d.mul(y,U.alpha),U.xim=U.xi;for(let t=0;t=0;o--)i=d.add(d.mul(i,e),t.slice(o*g,(o+1)*g));return i}function R(t,e){const a=t.byteLength/g,i=new Ge(a*g);i.set(d.zero,(a-1)*g),i.set(t.slice((a-1)*g,a*g),(a-2)*g);for(let o=a-3;o>=0;o--)i.set(d.add(t.slice((o+1)*g,(o+2)*g),d.mul(e,i.slice((o+1)*g,(o+2)*g))),o*g);if(!d.eq(t.slice(0,g),d.mul(d.neg(e),i.slice(0,g))))throw new Error("Polinomial does not divide");return i}async function D(t,e){const i=t.byteLength/g,o=O.slice(0,i*c.G1.F.n8*2),n=await c.Fr.batchFromMontgomery(t);let l=await c.G1.multiExpAffine(o,n,a,e);return l=c.G1.toAffine(l),l}async function N(t,e){e=e||[];let a=await d.ifft(t);const i=new Ge(g*s.domainSize*4);i.set(a,0);const o=new Ge(g*(s.domainSize+e.length));o.set(a,0);for(let t=0;ta;){const e=o.shift(),a=o.shift(),i=e[0],n=a[0],l=w++,r=t.zero,s=t.neg(e[1]),c=t.neg(a[1]),d=t.one,u=t.zero;p.push([i,n,l,r,s,c,d,u]),m.push([i,n,e[1],a[1]]),o.push([l,t.one])}for(let t=0;t0?i.toString():a!=t.zero?"k":"0"}function s(e,a,s){const c=r(e),d=r(a);if("0"===c||"0"===d)i(s),l(s);else if("k"===c){l(o(a,e[0],s))}else if("k"===d){l(o(e,a[0],s))}else!function(e,a,i){const o=n(e,1),l=n(a,1),r=n(i,1),s=o.s[0],c=l.s[0],d=r.s[0],u=t.mul(o.coefs[0],l.coefs[0]),g=t.mul(o.coefs[0],l.k),f=t.mul(o.k,l.coefs[0]),h=t.neg(r.coefs[0]),_=t.sub(t.mul(o.k,l.k),r.k);p.push([s,c,d,u,g,f,h,_])}(e,a,s)}for(let e=1;e<=L;e++){const a=e,i=0,o=0,n=t.zero,l=t.one,r=t.zero,s=t.zero,c=t.zero;p.push([a,i,o,n,l,r,s,c])}for(let t=0;tr)return i&&i.error(`circuit too big for this power of tau ceremony. ${p.length} > 2**${r}`),-1;if(!n[12])return i&&i.error("Powers of tau is not prepared."),-1;const C=new Ge(y*u),I=n[12][0].p+(2**A-1)*u;await o.readToBuffer(C,0,y*u,I);const[F,x]=function(){let t=h.two;for(;a(t,[],A);)h.add(t,h.one);let e=h.add(t,h.one);for(;a(e,[t],A);)h.add(e,h.one);return[t,e];function a(t,e,a){const i=2**a;let o=h.one;for(let n=0;n0?2:this.Fr.isZero(e)?0:1}normalizeLinearCombination(t){const e=Object.keys(t);for(let a=0;ao;){const i=l.shift(),o=l.shift(),n=t.nVars++,r=this.fnGetAdditionConstraint(i[0],o[0],n,this.Fr.neg(i[1]),this.Fr.neg(o[1]),this.Fr.zero,this.Fr.one,this.Fr.zero);e.push(r),a.push([i[0],o[0],i[1],o[1]]),l.push([n,this.Fr.one])}for(let t=0;t32768?new Ge(t.length*i.n8):new Uint8Array(t.length*i.n8);for(let e=0;e32768?new Ge(i*o.n8):new Uint8Array(i*o.n8);return n.set(t.coef.slice(),0),new ol(n,e,a)}isEqual(t){const e=this.degree();if(e!==t.degree())return!1;for(let a=0;a32768?new Ge((this.length()+t.length)*this.Fr.n8):new Uint8Array((this.length()+t.length)*this.Fr.n8);e.set(this.coef,0);for(let a=0;athis.coef.byteLength?this.Fr.zero:this.coef.slice(e,e+this.Fr.n8)}setCoef(t,e){if(t>this.length()-1)throw new Error("Coef index is not available");this.coef.set(e,t*this.Fr.n8)}static async to4T(t,e,a,i){a=a||[];let o=await i.ifft(t);const n=4*e>32768?new Ge(4*e*i.n8):new Uint8Array(4*e*i.n8);n.set(o,0);const l=await i.fft(n);if(0===a.length)return[o,l];const r=e+a.length>32768?new Ge((e+a.length)*i.n8):new Uint8Array((e+a.length)*i.n8);r.set(o,0);for(let t=0;t0;t--){const e=t*this.Fr.n8;if(!this.Fr.eq(this.Fr.zero,this.coef.slice(e,e+this.Fr.n8)))return t}return 0}evaluate(t){let e=this.Fr.zero;for(let a=this.degree()+1;a>0;a--){let i=a*this.Fr.n8;const o=this.coef.slice(i-this.Fr.n8,i);e=this.Fr.add(o,this.Fr.mul(e,t))}return e}fastEvaluate(t){const e=this.Fr;let a=this.degree()+1,i=parseInt(a/3),o=a-3*i,n=[],l=[];l[0]=e.one;for(let a=0;a<3;a++){n[a]=e.zero;for(let r=2===a?i+o:i;r>0;r--)n[a]=e.add(this.getCoef(a*i+r-1),e.mul(n[a],t)),0===a&&(l[0]=e.mul(l[0],t))}for(let t=1;t<3;t++)n[0]=e.add(n[0],e.mul(l[t-1],n[t])),l[t]=e.mul(l[t-1],l[0]);return n[0]}add(t,e){let a=!1;t.length()>this.length()&&(a=!0);const i=this.length(),o=t.length();for(let n=0;nthis.length()&&(a=!0);const i=this.length(),o=t.length();for(let n=0;n32768?new Ge(a*e.n8):new Uint8Array(a*e.n8);let o=new ol(i,this.curve,this.logger);o.coef.set(this.coef.slice(0,(a-1)*e.n8),32),this.mulScalar(e.neg(t)),o.add(this),this.coef=o.coef}byXNSubValue(t,e){const a=this.Fr,i=!(this.length()-t-1>=this.degree())?this.length()+t:this.length(),o=i>32768?new Ge(i*a.n8):new Uint8Array(i*a.n8);let n=new ol(o,this.curve,this.logger);n.coef.set(this.coef.slice(0,32*(this.degree()+1)),32*t),this.mulScalar(e),n.add(this),this.coef=n.coef}divBy(t){const e=this.Fr,a=this.degree(),i=t.degree();let o=new ol(this.coef,this.curve,this.logger);this.coef=this.length()>32768?new Ge(this.length()*e.n8):new Uint8Array(this.length()*e.n8);for(let n=a-i;n>=0;n--){this.setCoef(n,e.div(o.getCoef(n+i),t.getCoef(i)));for(let a=0;a<=i;a++)o.setCoef(n+a,e.sub(o.getCoef(n+a),e.mul(this.getCoef(n),t.getCoef(a))))}return o}divByMonic(t,e){const a=this.Fr;let i=this.degree(),o=this.length()>32768?new Ge(this.length()*a.n8):new Uint8Array(this.length()*a.n8),n=new ol(o,this.curve,this.logger),l=[];for(let e=0;e=0&&!(s<0);s-=r){let i=o;l[i]=a.add(this.getCoef(s+t),a.mul(l[i],e)),n.setCoef(s,l[i])}this.coef=n.coef}divByVanishing(t,e){if(this.degree()32768?new Ge(this.length()*a.n8):new Uint8Array(this.length()*a.n8);for(let o=this.length()-1;o>=t;o--){let n=i.getCoef(o);a.eq(a.zero,n)||(i.setCoef(o,a.zero),i.setCoef(o-t,a.add(i.getCoef(o-t),a.mul(e,n))),this.setCoef(o-t,a.add(this.getCoef(o-t),n)))}return i}divByVanishing2(t,e){if(this.degree()32768?new Ge(this.length()*a.n8):new Uint8Array(this.length()*a.n8);let o=this.length()-t,n=Math.floor(o/3),l=o-2*n;console.log(o),console.log(n+" "+l);for(let o=0;o<3;o++){console.log("> Thread "+o);for(let r=0===o?l:n;r>0;r--){let s=r-1;0!==o&&(s+=(o-1)*n+l);let c=s+t,d=i.getCoef(c);a.eq(a.zero,d)||(i.setCoef(c,a.zero),i.setCoef(s,a.add(i.getCoef(s),a.mul(e,d))),this.setCoef(s,a.add(this.getCoef(s),d)),console.log(s+" <-- "+c))}}return this.print(),i}fastDivByVanishing(t){const e=this.Fr;for(let a=0;a32768?new Ge(this.length()*e.n8):new Uint8Array(this.length()*e.n8),this.curve,this.logger),u=this.coef;this.coef=d.coef,d.coef=u;for(let t=0;t0;t--){let a=t-1,o=a*s+c;h[a]=[];for(let l=0;l32768?new Ge(this.length()*this.Fr.n8):new Uint8Array(this.length()*this.Fr.n8);e.set(this.Fr.zero,(this.length()-1)*this.Fr.n8),e.set(this.coef.slice((this.length()-1)*this.Fr.n8,this.length()*this.Fr.n8),(this.length()-2)*this.Fr.n8);for(let a=this.length()-3;a>=0;a--){let i=a*this.Fr.n8;e.set(this.Fr.add(this.coef.slice(i+this.Fr.n8,i+2*this.Fr.n8),this.Fr.mul(t,e.slice(i+this.Fr.n8,i+2*this.Fr.n8))),a*this.Fr.n8)}if(!this.Fr.eq(this.coef.slice(0,this.Fr.n8),this.Fr.mul(this.Fr.neg(t),e.slice(0,this.Fr.n8))))throw new Error("Polynomial does not divide");this.coef=e}divZh(t,e=4){for(let e=0;et*(e-1)-e&&!this.Fr.isZero(o))throw new Error("Polynomial is not divisible")}return this}divByZerofier(t,e){let a=this.Fr;const i=a.inv(e),o=a.neg(i);let n=a.eq(a.one,o),l=a.eq(a.negone,o);if(!n)for(let e=0;ethis.length()-t-1&&!this.Fr.isZero(s))throw new Error("Polynomial is not divisible")}return this}byX(){const t=this.length()+1>32768?new Ge(this.coef.byteLength+this.Fr.n8):new Uint8Array(this.coef.byteLength+this.Fr.n8);t.set(this.Fr.zero,0),t.set(this.coef,this.Fr.n8),this.coef=t}static async expX(t,e,a=!1){const i=t.Fr;if(e<1)throw new Error("Compute a new polynomial to a zero or negative number is not allowed");if(1===e)return await ol.fromEvaluations(t.coef,curve,t.logger);const o=a?t.degree():t.length()-1,n=o*e+1>32768?new Ge((o*e+1)*i.n8):new Uint8Array((o*e+1)*i.n8);n.set(t.getCoef(0),0);for(let a=1;a<=o;a++){const o=a*i.n8,l=t.getCoef(a);n.set(l,o*e)}return new ol(n,t.curve,t.logger)}split(t,e,a){if(t<1)throw new Error(`Polynomials can't be split in ${t} parts`);if(1===t)return[this];if(0!==a.length&&a.length32768?new Ge(l):new Uint8Array(l);o[e]=new ol(r,this.curve,this.logger);const s=e*i,c=n?this.coef.byteLength:(e+1)*i;if(o[e].coef.set(this.coef.slice(s,c),0),n||o[e].coef.set(a[e],i),0!==e){const t=this.Fr.sub(o[e].coef.slice(0,this.Fr.n8),a[e-1]);o[e].coef.set(t,0)}n&&o[e].truncate()}return o}truncate(){const t=this.degree();if(t+132768?new Ge((t+1)*this.Fr.n8):new Uint8Array((t+1)*this.Fr.n8);e.set(this.coef.slice(0,(t+1)*this.Fr.n8),0),this.coef=e}}static lagrangePolynomialInterpolation(t,e,a){const i=a.Fr;let o=n(0);for(let e=1;e32768?new Ge(t.length*i.n8):new Uint8Array(t.length*i.n8);n=new ol(o,a),n.setCoef(0,i.neg(t[e])),n.setCoef(1,i.one)}else n.byXSubValue(t[e]);let l=n.evaluate(t[o]);l=i.inv(l);const r=i.mul(e[o],l);return n.mulScalar(r),n}}static zerofierPolynomial(t,e){const a=e.Fr;let i=t.length+1>32768?new Ge((t.length+1)*a.n8):new Uint8Array((t.length+1)*a.n8),o=new ol(i,e);o.setCoef(0,a.neg(t[0])),o.setCoef(1,a.one);for(let e=1;e=0;a--){const i=this.getCoef(a);t.eq(t.zero,i)||(t.isNegative(i)?e+=" - ":a!==this.degree()&&(e+=" + "),e+=t.toString(i),a>0&&(e+=a>1?"x^"+a:"x"))}console.log(e)}async multiExponentiation(t,e){const a=this.coef.byteLength/this.Fr.n8,i=t.slice(0,a*this.G1.F.n8*2),o=await this.Fr.batchFromMontgomery(this.coef);let n=await this.G1.multiExpAffine(i,o,this.logger,e);return n=this.G1.toAffine(n),n}}class nl{constructor(t,e,a){this.eval=t,this.curve=e,this.Fr=e.Fr,this.logger=a}static async fromPolynomial(t,e,a,i){const o=new Ge(t.length()*e*a.Fr.n8);o.set(t.coef,0);const n=await a.Fr.fft(o);return new nl(n,a,i)}getEvaluation(t){const e=t*this.Fr.n8;if(e+this.Fr.n8>this.eval.byteLength)throw new Error("Evaluations.getEvaluation() out of bounds");return this.eval.slice(e,e+this.Fr.n8)}length(){let t=this.eval.byteLength/this.Fr.n8;if(t!==Math.floor(this.eval.byteLength/this.Fr.n8))throw new Error("Polynomial evaluations buffer has incorrect size");return 0===t&&this.logger.warn("Polynomial has length zero"),t}}class ll{constructor(t,e,a){this.n=t,this.polynomials=Array(t).fill(void 0),this.curve=e,this.Fr=e.Fr,this.G1=e.G1,this.logger=a}addPolynomial(t,e){if(t>this.n-1)throw new Error("CPolynomial:addPolynomial, cannot add a polynomial to a position greater than n-1");this.polynomials[t]=e}degree(){let t=this.polynomials.map(((t,e)=>void 0===t?0:t.degree()*this.n+e));return Math.max(...t)}getPolynomial(){let t=this.polynomials.map((t=>void 0===t?0:t.degree()));const e=this.degree(),a=2**(qi(e-1)+1),i=this.Fr.n8;let o=new ol(new Ge(a*i),this.curve,this.logger);for(let a=0;a0===a.type?t++:e++));let a=new Uint8Array(e*this.Fr.n8+t*this.G1.F.n8*2),i=0;for(let t=0;t{t.polynomials[e]=this.curve.G1.toObject(this.polynomials[e])})),Object.keys(this.evaluations).forEach((e=>{t.evaluations[e]=this.curve.Fr.toObject(this.evaluations[e])})),t}fromObjectProof(t){this.resetProof(),Object.keys(t.polynomials).forEach((e=>{this.polynomials[e]=this.curve.G1.fromObject(t.polynomials[e])})),Object.keys(t.evaluations).forEach((e=>{this.evaluations[e]=this.curve.Fr.fromObject(t.evaluations[e])}))}}const{stringifyBigInts:dl}=ma;async function ul(t,e,a){a&&a.info("FFLONK PROVER STARTED"),a&&a.info("> Reading witness file");const{fd:i,sections:o}=await ka(e,"wtns",2),n=await Bo(i,o);a&&a.info("> Reading zkey file");const{fd:l,sections:r}=await ka(t,"zkey",2),s=await yo(l,r);if(s.protocolId!==Yi)throw new Error("zkey file is not fflonk");if(!pa.eq(s.r,n.q))throw new Error("Curve of the witness does not match the curve of the proving key");if(n.nWitness!==s.nVars-s.nAdditions)throw new Error(`Invalid witness length. Circuit: ${s.nVars}, witness: ${n.nWitness}, ${s.nAdditions}`);const c=s.curve,d=c.Fr,u=c.Fr.n8,g=2*c.G1.F.n8,f=s.domainSize*u;a&&(a.info("----------------------------"),a.info(" FFLONK PROVE SETTINGS"),a.info(` Curve: ${c.name}`),a.info(` Circuit power: ${s.power}`),a.info(` Domain size: ${s.domainSize}`),a.info(` Vars: ${s.nVars}`),a.info(` Public vars: ${s.nPublic}`),a.info(` Constraints: ${s.nConstraints}`),a.info(` Additions: ${s.nAdditions}`),a.info("----------------------------")),a&&a.info("> Reading witness file data");const h=await Za(i,o,2);await i.close(),h.set(d.zero,0);const _=new Ge(s.nAdditions*u);let p={},m={},w={},L={},b={},A={},y=new cl(c,a);a&&a.info(`> Reading Section ${eo}. Additions`),await async function(){a&&a.info("··· Computing additions");const t=await Za(l,r,eo),e=8+2*u;for(let i=0;i Reading Sections ${uo},${go},${fo}. Sigma1, Sigma2 & Sigma 3`),a&&a.info("··· Reading Sigma polynomials "),m.Sigma1=new ol(new Ge(f),c,a),m.Sigma2=new ol(new Ge(f),c,a),m.Sigma3=new ol(new Ge(f),c,a),await l.readToBuffer(m.Sigma1.coef,0,f,r[uo][0].p),await l.readToBuffer(m.Sigma2.coef,0,f,r[go][0].p),await l.readToBuffer(m.Sigma3.coef,0,f,r[fo][0].p),a&&a.info("··· Reading Sigma evaluations"),w.Sigma1=new nl(new Ge(4*f),c,a),w.Sigma2=new nl(new Ge(4*f),c,a),w.Sigma3=new nl(new Ge(4*f),c,a),await l.readToBuffer(w.Sigma1.eval,0,4*f,r[uo][0].p+f),await l.readToBuffer(w.Sigma2.eval,0,4*f,r[go][0].p+f),await l.readToBuffer(w.Sigma3.eval,0,4*f,r[fo][0].p+f),a&&a.info(`> Reading Section ${_o}. Powers of Tau`);const C=new Ge(16*s.domainSize*g);await l.readToBuffer(C,0,(9*s.domainSize+18)*g,r[_o][0].p),globalThis.gc&&globalThis.gc(),a&&a.info(""),a&&a.info("> ROUND 1"),await async function(){b.b=[];for(let t=1;t<=9;t++)b.b[t]=d.random();a&&a.info("> Computing A, B, C wire polynomials");await async function(){a&&a.info("··· Reading data from zkey file");p.A=new Ge(f),p.B=new Ge(f),p.C=new Ge(f);const t=await Za(l,r,ao),e=await Za(l,r,io),i=await Za(l,r,oo);for(let a=0;a=s.domainSize)throw new Error("A Polynomial is not well calculated");if(m.B.degree()>=s.domainSize)throw new Error("B Polynomial is not well calculated");if(m.C.degree()>=s.domainSize)throw new Error("C Polynomial is not well calculated")}(),a&&a.info("> Computing T0 polynomial");await async function(){a&&a.info(`··· Reading sections ${no}, ${lo}, ${ro}, ${so}, ${co}. Q selectors`);w.QL=new nl(new Ge(4*f),c,a),w.QR=new nl(new Ge(4*f),c,a),w.QM=new nl(new Ge(4*f),c,a),w.QO=new nl(new Ge(4*f),c,a),w.QC=new nl(new Ge(4*f),c,a),await l.readToBuffer(w.QL.eval,0,4*f,r[no][0].p+f),await l.readToBuffer(w.QR.eval,0,4*f,r[lo][0].p+f),await l.readToBuffer(w.QM.eval,0,4*f,r[ro][0].p+f),await l.readToBuffer(w.QO.eval,0,4*f,r[so][0].p+f),await l.readToBuffer(w.QC.eval,0,4*f,r[co][0].p+f);const t=await Za(l,r,ho);w.lagrange1=new nl(t,c,a),p.T0=new Ge(4*f),a&&a.info("··· Computing T0 evaluations");for(let t=0;t<4*s.domainSize;t++){a&&0!==t&&t%1e5==0&&a.info(` T0 evaluation ${t}/${4*s.domainSize}`);const e=w.A.getEvaluation(t),i=w.B.getEvaluation(t),o=w.C.getEvaluation(t),n=w.QL.getEvaluation(t),l=w.QR.getEvaluation(t),r=w.QM.getEvaluation(t),c=w.QO.getEvaluation(t),g=w.QC.getEvaluation(t);let f=d.zero;for(let e=0;e=2*s.domainSize-2)throw new Error(`T0 Polynomial is not well calculated (degree is ${m.T0.degree()} and must be less than ${2*s.domainSize+2}`);delete p.T0}(),a&&a.info("> Computing C1 polynomial");await async function(){let t=new ll(4,c,a);if(t.addPolynomial(0,m.A),t.addPolynomial(1,m.B),t.addPolynomial(2,m.C),t.addPolynomial(3,m.T0),m.C1=t.getPolynomial(),m.C1.degree()>=8*s.domainSize-8)throw new Error("C1 Polynomial is not well calculated")}(),a&&a.info("> Computing C1 multi exponentiation");let t=await m.C1.multiExponentiation(C,"C1");return y.addPolynomial("C1",t),0}(),delete m.T0,delete w.QL,delete w.QR,delete w.QM,delete w.QO,delete w.QC,globalThis.gc&&globalThis.gc(),a&&a.info("> ROUND 2"),await async function(){a&&a.info("> Computing challenges beta and gamma");const t=new sl(c);t.addPolCommitment(s.C0);for(let e=0;e Computing Z polynomial");await async function(){a&&a.info("··· Computing Z evaluations");let t=new Ge(f),e=new Ge(f);t.set(d.one,0),e.set(d.one,0);let i=d.one;for(let o=0;o=s.domainSize+3)throw new Error("Z Polynomial is not well calculated");delete p.Z}(),a&&a.info("> Computing T1 polynomial");await async function(){a&&a.info("··· Computing T1 evaluations");p.T1=new Ge(2*f),p.T1z=new Ge(2*f);let t=d.one;for(let e=0;e<2*s.domainSize;e++){a&&0!==e&&e%1e5==0&&a.info(` T1 evaluation ${e}/${4*s.domainSize}`);const i=d.square(t),o=w.Z.getEvaluation(2*e),n=d.add(d.add(d.mul(b.b[7],i),d.mul(b.b[8],t)),b.b[9]),l=w.lagrange1.getEvaluation(s.domainSize+2*e);let r=d.mul(d.sub(o,d.one),l),c=d.mul(n,l);p.T1.set(r,e*u),p.T1z.set(c,e*u),t=d.mul(t,d.w[s.power+1])}a&&a.info("··· Computing T1 ifft");m.T1=await ol.fromEvaluations(p.T1,c,a),m.T1.divByZerofier(s.domainSize,d.one),a&&a.info("··· Computing T1z ifft");if(m.T1z=await ol.fromEvaluations(p.T1z,c,a),m.T1.add(m.T1z),m.T1.degree()>=s.domainSize+2)throw new Error("T1 Polynomial is not well calculated");delete p.T1,delete p.T1z,delete m.T1z}(),a&&a.info("> Computing T2 polynomial");await async function(){a&&a.info("··· Computing T2 evaluations");p.T2=new Ge(4*f),p.T2z=new Ge(4*f);let t=d.one;for(let e=0;e<4*s.domainSize;e++){a&&0!==e&&e%1e5==0&&a.info(` T2 evaluation ${e}/${4*s.domainSize}`);const i=d.square(t),o=d.mul(t,d.w[s.power]),n=d.square(o),l=w.A.getEvaluation(e),r=w.B.getEvaluation(e),c=w.C.getEvaluation(e),g=w.Z.getEvaluation(e),f=w.Z.getEvaluation((4*s.domainSize+4+e)%(4*s.domainSize)),h=d.add(d.add(d.mul(b.b[7],i),d.mul(b.b[8],t)),b.b[9]),_=d.add(d.add(d.mul(b.b[7],n),d.mul(b.b[8],o)),b.b[9]),m=w.Sigma1.getEvaluation(e),L=w.Sigma2.getEvaluation(e),A=w.Sigma3.getEvaluation(e),y=d.mul(b.beta,t);let C=d.add(l,y);C=d.add(C,b.gamma);let I=d.add(r,d.mul(y,s.k1));I=d.add(I,b.gamma);let F=d.add(c,d.mul(y,s.k2));F=d.add(F,b.gamma);let x=d.mul(d.mul(d.mul(C,I),F),g),E=d.mul(d.mul(d.mul(C,I),F),h),v=d.add(l,d.mul(b.beta,m));v=d.add(v,b.gamma);let B=d.add(r,d.mul(b.beta,L));B=d.add(B,b.gamma);let S=d.add(c,d.mul(b.beta,A));S=d.add(S,b.gamma);let P=d.mul(d.mul(d.mul(v,B),S),f),G=d.mul(d.mul(d.mul(v,B),S),_),z=d.sub(x,P),O=d.sub(E,G);p.T2.set(z,e*u),p.T2z.set(O,e*u),t=d.mul(t,d.w[s.power+2])}a&&a.info("··· Computing T2 ifft");m.T2=await ol.fromEvaluations(p.T2,c,a),a&&a.info("··· Computing T2 / ZH");m.T2.divByZerofier(s.domainSize,d.one),a&&a.info("··· Computing T2z ifft");if(m.T2z=await ol.fromEvaluations(p.T2z,c,a),m.T2.add(m.T2z),m.T2.degree()>=3*s.domainSize)throw new Error("T2 Polynomial is not well calculated");delete p.T2,delete p.T2z,delete m.T2z}(),a&&a.info("> Computing C2 polynomial");await async function(){let t=new ll(3,c,a);if(t.addPolynomial(0,m.Z),t.addPolynomial(1,m.T1),t.addPolynomial(2,m.T2),m.C2=t.getPolynomial(),m.C2.degree()>=9*s.domainSize)throw new Error("C2 Polynomial is not well calculated")}(),a&&a.info("> Computing C2 multi exponentiation");let e=await m.C2.multiExponentiation(C,"C2");return y.addPolynomial("C2",e),0}(),delete p.A,delete p.B,delete p.C,delete w.A,delete w.B,delete w.C,delete w.Sigma1,delete w.Sigma2,delete w.Sigma3,delete w.lagrange1,delete w.Z,globalThis.gc&&globalThis.gc(),a&&a.info("> ROUND 3"),await async function(){a&&a.info("> Computing challenge xi");const t=new sl(c);t.addScalar(b.gamma),t.addPolCommitment(y.getPolynomial("C2")),b.xiSeed=t.getChallenge();const e=d.square(b.xiSeed);A.w8=[],A.w8[0]=d.one;for(let t=1;t<8;t++)A.w8[t]=d.mul(A.w8[t-1],s.w8);A.w4=[],A.w4[0]=d.one;for(let t=1;t<4;t++)A.w4[t]=d.mul(A.w4[t-1],s.w4);A.w3=[],A.w3[0]=d.one,A.w3[1]=s.w3,A.w3[2]=d.square(s.w3),A.S0={},A.S0.h0w8=[],A.S0.h0w8[0]=d.mul(e,b.xiSeed);for(let t=1;t<8;t++)A.S0.h0w8[t]=d.mul(A.S0.h0w8[0],A.w8[t]);A.S1={},A.S1.h1w4=[],A.S1.h1w4[0]=d.square(A.S0.h0w8[0]);for(let t=1;t<4;t++)A.S1.h1w4[t]=d.mul(A.S1.h1w4[0],A.w4[t]);A.S2={},A.S2.h2w3=[],A.S2.h2w3[0]=d.mul(A.S1.h1w4[0],e),A.S2.h2w3[1]=d.mul(A.S2.h2w3[0],A.w3[1]),A.S2.h2w3[2]=d.mul(A.S2.h2w3[0],A.w3[2]),A.S2.h3w3=[],A.S2.h3w3[0]=d.mul(A.S2.h2w3[0],s.wr),A.S2.h3w3[1]=d.mul(A.S2.h3w3[0],A.w3[1]),A.S2.h3w3[2]=d.mul(A.S2.h3w3[0],A.w3[2]),b.xi=d.mul(d.square(A.S2.h2w3[0]),A.S2.h2w3[0]),a&&a.info("··· challenges.xi: "+d.toString(b.xi));m.QL=new ol(new Ge(f),c,a),m.QR=new ol(new Ge(f),c,a),m.QM=new ol(new Ge(f),c,a),m.QO=new ol(new Ge(f),c,a),m.QC=new ol(new Ge(f),c,a),await l.readToBuffer(m.QL.coef,0,f,r[no][0].p),await l.readToBuffer(m.QR.coef,0,f,r[lo][0].p),await l.readToBuffer(m.QM.coef,0,f,r[ro][0].p),await l.readToBuffer(m.QO.coef,0,f,r[so][0].p),await l.readToBuffer(m.QC.coef,0,f,r[co][0].p),a&&a.info("··· Computing evaluations");y.addEvaluation("ql",m.QL.evaluate(b.xi)),y.addEvaluation("qr",m.QR.evaluate(b.xi)),y.addEvaluation("qm",m.QM.evaluate(b.xi)),y.addEvaluation("qo",m.QO.evaluate(b.xi)),y.addEvaluation("qc",m.QC.evaluate(b.xi)),y.addEvaluation("s1",m.Sigma1.evaluate(b.xi)),y.addEvaluation("s2",m.Sigma2.evaluate(b.xi)),y.addEvaluation("s3",m.Sigma3.evaluate(b.xi)),y.addEvaluation("a",m.A.evaluate(b.xi)),y.addEvaluation("b",m.B.evaluate(b.xi)),y.addEvaluation("c",m.C.evaluate(b.xi)),y.addEvaluation("z",m.Z.evaluate(b.xi)),b.xiw=d.mul(b.xi,d.w[s.power]),y.addEvaluation("zw",m.Z.evaluate(b.xiw)),y.addEvaluation("t1w",m.T1.evaluate(b.xiw)),y.addEvaluation("t2w",m.T2.evaluate(b.xiw))}(),delete m.A,delete m.B,delete m.C,delete m.Z,delete m.T1,delete m.T2,delete m.Sigma1,delete m.Sigma2,delete m.Sigma3,delete m.QL,delete m.QR,delete m.QM,delete m.QC,delete m.QO,globalThis.gc&&globalThis.gc(),a&&a.info("> ROUND 4"),await async function(){a&&a.info("> Computing challenge alpha");const t=new sl(c);t.addScalar(b.xiSeed),t.addScalar(y.getEvaluation("ql")),t.addScalar(y.getEvaluation("qr")),t.addScalar(y.getEvaluation("qm")),t.addScalar(y.getEvaluation("qo")),t.addScalar(y.getEvaluation("qc")),t.addScalar(y.getEvaluation("s1")),t.addScalar(y.getEvaluation("s2")),t.addScalar(y.getEvaluation("s3")),t.addScalar(y.getEvaluation("a")),t.addScalar(y.getEvaluation("b")),t.addScalar(y.getEvaluation("c")),t.addScalar(y.getEvaluation("z")),t.addScalar(y.getEvaluation("zw")),t.addScalar(y.getEvaluation("t1w")),t.addScalar(y.getEvaluation("t2w")),b.alpha=t.getChallenge(),a&&a.info("··· challenges.alpha: "+d.toString(b.alpha));a&&a.info("> Reading C0 polynomial");m.C0=new ol(new Ge(8*f),c,a),await l.readToBuffer(m.C0.coef,0,8*f,r[po][0].p),a&&a.info("> Computing R0 polynomial");(function(){if(m.R0=ol.lagrangePolynomialInterpolation([A.S0.h0w8[0],A.S0.h0w8[1],A.S0.h0w8[2],A.S0.h0w8[3],A.S0.h0w8[4],A.S0.h0w8[5],A.S0.h0w8[6],A.S0.h0w8[7]],[m.C0.evaluate(A.S0.h0w8[0]),m.C0.evaluate(A.S0.h0w8[1]),m.C0.evaluate(A.S0.h0w8[2]),m.C0.evaluate(A.S0.h0w8[3]),m.C0.evaluate(A.S0.h0w8[4]),m.C0.evaluate(A.S0.h0w8[5]),m.C0.evaluate(A.S0.h0w8[6]),m.C0.evaluate(A.S0.h0w8[7])],c),m.R0.degree()>7)throw new Error("R0 Polynomial is not well calculated")})(),a&&a.info("> Computing R1 polynomial");(function(){if(m.R1=ol.lagrangePolynomialInterpolation([A.S1.h1w4[0],A.S1.h1w4[1],A.S1.h1w4[2],A.S1.h1w4[3]],[m.C1.evaluate(A.S1.h1w4[0]),m.C1.evaluate(A.S1.h1w4[1]),m.C1.evaluate(A.S1.h1w4[2]),m.C1.evaluate(A.S1.h1w4[3])],c),m.R1.degree()>3)throw new Error("R1 Polynomial is not well calculated")})(),a&&a.info("> Computing R2 polynomial");(function(){if(m.R2=ol.lagrangePolynomialInterpolation([A.S2.h2w3[0],A.S2.h2w3[1],A.S2.h2w3[2],A.S2.h3w3[0],A.S2.h3w3[1],A.S2.h3w3[2]],[m.C2.evaluate(A.S2.h2w3[0]),m.C2.evaluate(A.S2.h2w3[1]),m.C2.evaluate(A.S2.h2w3[2]),m.C2.evaluate(A.S2.h3w3[0]),m.C2.evaluate(A.S2.h3w3[1]),m.C2.evaluate(A.S2.h3w3[2])],c),m.R2.degree()>5)throw new Error("R2 Polynomial is not well calculated")})(),a&&a.info("> Computing F polynomial");await async function(){a&&a.info("··· Computing F polynomial");m.F=ol.fromPolynomial(m.C0,c,a),m.F.sub(m.R0),m.F.divByZerofier(8,b.xi);let t=ol.fromPolynomial(m.C1,c,a);t.sub(m.R1),t.mulScalar(b.alpha),t.divByZerofier(4,b.xi);let e=ol.fromPolynomial(m.C2,c,a);if(e.sub(m.R2),e.mulScalar(d.square(b.alpha)),e.divByZerofier(3,b.xi),e.divByZerofier(3,b.xiw),m.F.add(t),m.F.add(e),m.F.degree()>=9*s.domainSize-6)throw new Error("F Polynomial is not well calculated")}(),a&&a.info("> Computing W1 multi exponentiation");let e=await m.F.multiExponentiation(C,"W1");return y.addPolynomial("W1",e),0}(),globalThis.gc&&globalThis.gc(),a&&a.info("> ROUND 5"),await async function(){a&&a.info("> Computing challenge y");const t=new sl(c);t.addScalar(b.alpha),t.addPolCommitment(y.getPolynomial("W1")),b.y=t.getChallenge(),a&&a.info("··· challenges.y: "+d.toString(b.y));a&&a.info("> Computing L polynomial");await async function(){a&&a.info("··· Computing L polynomial");const t=m.R0.evaluate(b.y),e=m.R1.evaluate(b.y),i=m.R2.evaluate(b.y);let o=d.sub(b.y,A.S0.h0w8[0]);for(let t=1;t<8;t++)o=d.mul(o,d.sub(b.y,A.S0.h0w8[t]));let n=d.sub(b.y,A.S1.h1w4[0]);for(let t=1;t<4;t++)n=d.mul(n,d.sub(b.y,A.S1.h1w4[t]));let l=d.sub(b.y,A.S2.h2w3[0]);for(let t=1;t<3;t++)l=d.mul(l,d.sub(b.y,A.S2.h2w3[t]));for(let t=0;t<3;t++)l=d.mul(l,d.sub(b.y,A.S2.h3w3[t]));let r=d.mul(n,l),u=d.mul(b.alpha,d.mul(o,l)),g=d.mul(d.square(b.alpha),d.mul(o,n));L.denH1=n,L.denH2=l,m.L=ol.fromPolynomial(m.C0,c,a),m.L.subScalar(t),m.L.mulScalar(r);let f=ol.fromPolynomial(m.C1,c,a);f.subScalar(e),f.mulScalar(u);let h=ol.fromPolynomial(m.C2,c,a);h.subScalar(i),h.mulScalar(g),m.L.add(f),m.L.add(h),a&&a.info("> Computing ZT polynomial");await async function(){m.ZT=ol.zerofierPolynomial([A.S0.h0w8[0],A.S0.h0w8[1],A.S0.h0w8[2],A.S0.h0w8[3],A.S0.h0w8[4],A.S0.h0w8[5],A.S0.h0w8[6],A.S0.h0w8[7],A.S1.h1w4[0],A.S1.h1w4[1],A.S1.h1w4[2],A.S1.h1w4[3],A.S2.h2w3[0],A.S2.h2w3[1],A.S2.h2w3[2],A.S2.h3w3[0],A.S2.h3w3[1],A.S2.h3w3[2]],c)}();const _=m.ZT.evaluate(b.y);if(m.F.mulScalar(_),m.L.sub(m.F),m.L.degree()>=9*s.domainSize)throw new Error("L Polynomial is not well calculated");delete p.L}(),a&&a.info("> Computing ZTS2 polynomial");await async function(){m.ZTS2=ol.zerofierPolynomial([A.S1.h1w4[0],A.S1.h1w4[1],A.S1.h1w4[2],A.S1.h1w4[3],A.S2.h2w3[0],A.S2.h2w3[1],A.S2.h2w3[2],A.S2.h3w3[0],A.S2.h3w3[1],A.S2.h3w3[2]],c)}();let e=m.ZTS2.evaluate(b.y);e=d.inv(e),m.L.mulScalar(e);const i=ol.fromCoefficientsArray([d.neg(b.y),d.one],c);a&&a.info("> Computing W' = L / ZTS2 polynomial");const o=m.L.divBy(i);if(o.degree()>0)throw new Error(`Degree of L(X)/(ZTS2(y)(X-y)) remainder is ${o.degree()} and should be 0`);if(m.L.degree()>=9*s.domainSize-1)throw new Error("Degree of L(X)/(ZTS2(y)(X-y)) is not correct");a&&a.info("> Computing W' multi exponentiation");let n=await m.L.multiExponentiation(C,"W2");return y.addPolynomial("W2",n),0}(),delete m.C0,delete m.C1,delete m.C2,delete m.R1,delete m.R2,delete m.F,delete m.L,delete m.ZT,delete m.ZTS2,await l.close(),globalThis.gc&&globalThis.gc(),y.addEvaluation("inv",function(){let t=b.xi;for(let e=0;e Reading PTau file");const{fd:o,sections:n}=await ka(e,"ptau",1);if(!n[12])throw new Error("Powers of Tau is not well prepared. Section 12 missing.");i&&i.info("> Getting curve from PTau settings");const{curve:l}=await Wo(o,n);i&&i.info("> Reading r1cs file");const{fd:r,sections:s}=await ka(t,"r1cs",1),c=await wn(r,s,{loadConstraints:!1,loadCustomGates:!0});if(c.prime!==l.r)throw new Error("r1cs curve does not match powers of tau ceremony curve");const d=l.Fr,u=l.Fr.n8,g=2*l.G1.F.n8,f=2*l.G2.F.n8;let h,_={},p={},m={nVars:c.nVars,nPublic:c.nOutputs+c.nPubInputs};const w=new Bn;let L=new Bn;if(i&&i.info("> Processing FFlonk constraints"),await async function(t,e,a){for(let e=0;e computing k1 and k2");const[b,A]=function(){let t=d.two;for(;a(t,[],m.cirPower);)d.add(t,d.one);let e=d.add(t,d.one);for(;a(e,[t],m.cirPower);)d.add(e,d.one);return[t,e];function a(t,e,a){const i=2**a;let o=d.one;for(let n=0;n computing w3");const y=function(){let t=d.e(31624),e=pa.div(3648040478639879203707734290876212514758060733402672390616367364429301415936n,pa.e(3));return d.exp(t,e)}();i&&i.info("> computing w4");const C=d.w[2];i&&i.info("> computing w8");const I=d.w[3];i&&i.info("> computing wr");const F=function(t,e){const a=e.e(467799165886069610036046866799264026481344299079011762026774533774345988080n);return e.exp(a,2**(28-t))}(m.cirPower,l.Fr);return await async function(){i&&i.info("> Writing the zkey file");const t=await Ra(a,"zkey",1,Xi,1<<22,1<<24);i&&i.info(`··· Writing Section ${Hi}. Zkey Header`);await async function(t){await Da(t,Hi),await t.writeULE32(Yi),await Na(t)}(t),i&&i.info(`··· Writing Section ${eo}. Additions`);await async function(t){await Da(t,eo);const e=new Uint8Array(8+2*u),a=new DataView(e.buffer);for(let o=0;o=8*m.domainSize)throw new Error("C0 Polynomial is not well calculated");await Da(t,po),await t.write(_.C0.coef),await Na(t)}(t),globalThis.gc&&globalThis.gc();i&&i.info(`··· Writing Section ${to}. FFlonk Header`);await async function(t){await Da(t,to);const e=l.q,a=8*(Math.floor((pa.bitLength(e)-1)/64)+1);await t.writeULE32(a),await ja(t,e,a);const i=l.r,r=8*(Math.floor((pa.bitLength(i)-1)/64)+1);let s;await t.writeULE32(r),await ja(t,i,r),await t.writeULE32(m.nVars),await t.writeULE32(m.nPublic),await t.writeULE32(m.domainSize),await t.writeULE32(L.length),await t.writeULE32(w.length),await t.write(b),await t.write(A),await t.write(y),await t.write(C),await t.write(I),await t.write(F),s=await o.read(f,n[3][0].p+f),await t.write(s);let c=await _.C0.multiExponentiation(h,"C0");await t.write(c),await Na(t)}(t),globalThis.gc&&globalThis.gc();i&&i.info("> Writing the zkey file finished");await t.close()}(),await r.close(),await o.close(),i&&i.info("FFLONK SETUP FINISHED"),0;async function x(t,e,a,o){await Da(t,e);for(let e=0;e Checking commitments belong to G1"),!function(t,e,a){const i=t.G1;return i.isValid(e.polynomials.C1)&&i.isValid(e.polynomials.C2)&&i.isValid(e.polynomials.W1)&&i.isValid(e.polynomials.W2)&&i.isValid(a.C0)}(o,l,n))return i.error("Proof is not well constructed"),!1;i&&i.info("> Computing challenges");const{challenges:c,roots:d}=function(t,e,a,i,o){const n=t.Fr,l={},r={},s=new sl(t);s.addPolCommitment(a.C0);for(let t=0;t Computing Zero polynomial evaluation Z_H(xi)"),c.zh=s.sub(c.xiN,s.one),c.invzh=s.inv(c.zh),i&&i.info("> Computing Lagrange evaluations");const u=await async function(t,e,a){const i=t.Fr,o=Math.max(1,a.nPublic),n=new Ge(o*i.n8);let l=new Ge(o*i.n8),r=i.one;for(let t=0;t Computing polynomial identities PI(X)");const g=function(t,e,a){const i=t.Fr;let o=i.zero;for(let t=0;t Computing r0(y)");const f=function(t,e,a,i,o,n){const l=o.Fr;n&&n.info("··· Computing C0(h_0ω_8^i) values");let r=[];for(let e=0;e<8;e++){let i=[];i[1]=a.S0.h0w8[e];for(let t=2;t<8;t++)i[t]=l.mul(i[t-1],a.S0.h0w8[e]);r[e]=l.add(t.evaluations.ql,l.mul(t.evaluations.qr,i[1])),r[e]=l.add(r[e],l.mul(t.evaluations.qo,i[2])),r[e]=l.add(r[e],l.mul(t.evaluations.qm,i[3])),r[e]=l.add(r[e],l.mul(t.evaluations.qc,i[4])),r[e]=l.add(r[e],l.mul(t.evaluations.s1,i[5])),r[e]=l.add(r[e],l.mul(t.evaluations.s2,i[6])),r[e]=l.add(r[e],l.mul(t.evaluations.s3,i[7]))}const s=ol.lagrangePolynomialInterpolation([a.S0.h0w8[0],a.S0.h0w8[1],a.S0.h0w8[2],a.S0.h0w8[3],a.S0.h0w8[4],a.S0.h0w8[5],a.S0.h0w8[6],a.S0.h0w8[7]],r,o);if(s.degree()>7)throw new Error("R0 Polynomial is not well calculated");n&&n.info("··· Computing evaluation r0(y)");return s.evaluate(e.y)}(l,c,d,0,o,i);i&&i.info("> Computing r1(y)");const h=function(t,e,a,i,o,n){const l=o.Fr;n&&n.info("··· Computing T0(xi)");let r=l.mul(t.evaluations.ql,t.evaluations.a);r=l.add(r,l.mul(t.evaluations.qr,t.evaluations.b)),r=l.add(r,l.mul(t.evaluations.qm,l.mul(t.evaluations.a,t.evaluations.b))),r=l.add(r,l.mul(t.evaluations.qo,t.evaluations.c)),r=l.add(r,t.evaluations.qc),r=l.add(r,i),r=l.mul(r,e.invzh),n&&n.info("··· Computing C1(h_1ω_4^i) values");let s=[];for(let e=0;e<4;e++){s[e]=t.evaluations.a,s[e]=l.add(s[e],l.mul(a.S1.h1w4[e],t.evaluations.b));const i=l.square(a.S1.h1w4[e]);s[e]=l.add(s[e],l.mul(i,t.evaluations.c)),s[e]=l.add(s[e],l.mul(l.mul(i,a.S1.h1w4[e]),r))}const c=ol.lagrangePolynomialInterpolation([a.S1.h1w4[0],a.S1.h1w4[1],a.S1.h1w4[2],a.S1.h1w4[3]],s,o);if(c.degree()>3)throw new Error("R1 Polynomial is not well calculated");n&&n.info("··· Computing evaluation r1(y)");return c.evaluate(e.y)}(l,c,d,g,o,i);i&&i.info("> Computing r2(y)");const _=function(t,e,a,i,o,n,l){const r=n.Fr;l&&l.info("··· Computing T1(xi)");let s=r.sub(t.evaluations.z,r.one);s=r.mul(s,i),s=r.mul(s,e.invzh),l&&l.info("··· Computing T2(xi)");const c=r.mul(e.beta,e.xi),d=r.add(t.evaluations.a,r.add(c,e.gamma)),u=r.add(t.evaluations.b,r.add(r.mul(c,o.k1),e.gamma)),g=r.add(t.evaluations.c,r.add(r.mul(c,o.k2),e.gamma)),f=r.mul(d,r.mul(u,r.mul(g,t.evaluations.z))),h=r.add(t.evaluations.a,r.add(r.mul(e.beta,t.evaluations.s1),e.gamma)),_=r.add(t.evaluations.b,r.add(r.mul(e.beta,t.evaluations.s2),e.gamma)),p=r.add(t.evaluations.c,r.add(r.mul(e.beta,t.evaluations.s3),e.gamma)),m=r.mul(h,r.mul(_,r.mul(p,t.evaluations.zw)));let w=r.sub(f,m);w=r.mul(w,e.invzh),l&&l.info("··· Computing C2(h_2ω_3^i) values");let L=[];for(let e=0;e<3;e++)L[e]=r.add(t.evaluations.z,r.mul(a.S2.h2w3[e],s)),L[e]=r.add(L[e],r.mul(r.square(a.S2.h2w3[e]),w));l&&l.info("··· Computing C2(h_3ω_3^i) values");for(let e=0;e<3;e++)L[e+3]=r.add(t.evaluations.zw,r.mul(a.S2.h3w3[e],t.evaluations.t1w)),L[e+3]=r.add(L[e+3],r.mul(r.square(a.S2.h3w3[e]),t.evaluations.t2w));l&&l.info("··· Computing r2(xi)");const b=ol.lagrangePolynomialInterpolation([a.S2.h2w3[0],a.S2.h2w3[1],a.S2.h2w3[2],a.S2.h3w3[0],a.S2.h3w3[1],a.S2.h3w3[2]],L,n);if(b.degree()>5)throw new Error("R2 Polynomial is not well calculated");l&&l.info("··· Computing evaluation r2(y)");return b.evaluate(e.y)}(l,c,d,u[1],n,o,i);i&&i.info("> Computing F");const p=function(t,e,a,i,o){const n=t.G1,l=t.Fr;let r=l.sub(i.y,o.S0.h0w8[0]);for(let t=1;t<8;t++)r=l.mul(r,l.sub(i.y,o.S0.h0w8[t]));i.temp=r;let s=l.sub(i.y,o.S1.h1w4[0]);for(let t=1;t<4;t++)s=l.mul(s,l.sub(i.y,o.S1.h1w4[t]));let c=l.sub(i.y,o.S2.h2w3[0]);for(let t=1;t<3;t++)c=l.mul(c,l.sub(i.y,o.S2.h2w3[t]));for(let t=0;t<3;t++)c=l.mul(c,l.sub(i.y,o.S2.h3w3[t]));i.quotient1=l.mul(i.alpha,l.div(r,s)),i.quotient2=l.mul(l.square(i.alpha),l.div(r,c));let d=n.timesFr(e.polynomials.C1,i.quotient1),u=n.timesFr(e.polynomials.C2,i.quotient2);return n.add(a.C0,n.add(d,u))}(o,l,n,c,d);i&&i.info("> Computing E");const m=function(t,e,a,i,o,n,l){const r=t.G1,s=t.Fr;let c=s.mul(n,a.quotient1),d=s.mul(l,a.quotient2);return r.timesFr(r.one,s.add(o,s.add(c,d)))}(o,0,c,0,f,h,_);i&&i.info("> Computing J");const w=function(t,e,a){const i=t.G1;return i.timesFr(e.polynomials.W1,a.temp)}(o,l,c);i&&i.info("> Validate all evaluations with a pairing");const L=await async function(t,e,a,i,o,n,l){const r=t.G1;let s=r.timesFr(e.polynomials.W2,a.y);s=r.add(r.sub(r.sub(o,n),l),s);const c=t.G2.one,d=e.polynomials.W2,u=i.X_2;return await t.pairingEq(r.neg(s),c,d,u)}(o,l,c,n,p,m,w);return i&&(L?i.info("PROOF VERIFIED SUCCESSFULLY"):i.warn("Invalid Proof")),i&&i.info("FFLONK VERIFIER FINISHED"),L},exportSolidityVerifier:qn,exportSolidityCallData:async function(t,e){const a=hl(e),i=hl(t),o=await ai(a.curve),n=o.G1,l=o.Fr;let r="";for(let t=0;t>5,this.byteCount=this.blockCount<<2,this.outputBlocks=a>>5,this.extraBytes=(31&a)>>3;for(var i=0;i<50;++i)this.s[i]=0}function S(t,e,a){B.call(this,t,e,a)}B.prototype.update=function(e){if(this.finalized)throw new Error("finalize already called");var a,i=typeof e;if("string"!==i){if("object"!==i)throw new Error(t);if(null===e)throw new Error(t);if(n&&e.constructor===ArrayBuffer)e=new Uint8Array(e);else if(!(Array.isArray(e)||n&&ArrayBuffer.isView(e)))throw new Error(t);a=!0}for(var o,l,r=this.blocks,c=this.byteCount,d=e.length,u=this.blockCount,g=0,f=this.s;g>2]|=e[g]<>2]|=l<>2]|=(192|l>>6)<>2]|=(128|63&l)<=57344?(r[o>>2]|=(224|l>>12)<>2]|=(128|l>>6&63)<>2]|=(128|63&l)<>2]|=(240|l>>18)<>2]|=(128|l>>12&63)<>2]|=(128|l>>6&63)<>2]|=(128|63&l)<=c){for(this.start=o-c,this.block=r[u],o=0;o>=8);a>0;)o.unshift(a),a=255&(t>>=8),++i;return e?o.push(i):o.unshift(i),this.update(o),o.length},B.prototype.encodeString=function(e){var a,i=typeof e;if("string"!==i){if("object"!==i)throw new Error(t);if(null===e)throw new Error(t);if(n&&e.constructor===ArrayBuffer)e=new Uint8Array(e);else if(!(Array.isArray(e)||n&&ArrayBuffer.isView(e)))throw new Error(t);a=!0}var o=0,l=e.length;if(a)o=l;else for(var r=0;r=57344?o+=3:(s=65536+((1023&s)<<10|1023&e.charCodeAt(++r)),o+=4)}return o+=this.encode(8*o),this.update(e),o},B.prototype.bytepad=function(t,e){for(var a=this.encode(e),i=0;i>2]|=this.padding[3&e],this.lastByteIndex===this.byteCount)for(t[0]=t[a],e=1;e>4&15]+l[15&t]+l[t>>12&15]+l[t>>8&15]+l[t>>20&15]+l[t>>16&15]+l[t>>28&15]+l[t>>24&15];r%e==0&&(P(a),n=0)}return o&&(t=a[n],s+=l[t>>4&15]+l[15&t],o>1&&(s+=l[t>>12&15]+l[t>>8&15]),o>2&&(s+=l[t>>20&15]+l[t>>16&15])),s},B.prototype.arrayBuffer=function(){this.finalize();var t,e=this.blockCount,a=this.s,i=this.outputBlocks,o=this.extraBytes,n=0,l=0,r=this.outputBits>>3;t=o?new ArrayBuffer(i+1<<2):new ArrayBuffer(r);for(var s=new Uint32Array(t);l>8&255,s[t+2]=e>>16&255,s[t+3]=e>>24&255;r%a==0&&P(i)}return n&&(t=r<<2,e=i[l],s[t]=255&e,n>1&&(s[t+1]=e>>8&255),n>2&&(s[t+2]=e>>16&255)),s},S.prototype=new B,S.prototype.finalize=function(){return this.encode(this.outputBits,!0),B.prototype.finalize.call(this)};var P=function(t){var e,a,i,o,n,l,r,s,d,u,g,f,h,_,p,m,w,L,b,A,y,C,I,F,x,E,v,B,S,P,G,z,O,U,T,Q,q,M,k,R,D,N,V,$,j,K,H,Z,W,Y,J,X,tt,et,at,it,ot,nt,lt,rt,st,ct,dt;for(i=0;i<48;i+=2)o=t[0]^t[10]^t[20]^t[30]^t[40],n=t[1]^t[11]^t[21]^t[31]^t[41],l=t[2]^t[12]^t[22]^t[32]^t[42],r=t[3]^t[13]^t[23]^t[33]^t[43],s=t[4]^t[14]^t[24]^t[34]^t[44],d=t[5]^t[15]^t[25]^t[35]^t[45],u=t[6]^t[16]^t[26]^t[36]^t[46],g=t[7]^t[17]^t[27]^t[37]^t[47],e=(f=t[8]^t[18]^t[28]^t[38]^t[48])^(l<<1|r>>>31),a=(h=t[9]^t[19]^t[29]^t[39]^t[49])^(r<<1|l>>>31),t[0]^=e,t[1]^=a,t[10]^=e,t[11]^=a,t[20]^=e,t[21]^=a,t[30]^=e,t[31]^=a,t[40]^=e,t[41]^=a,e=o^(s<<1|d>>>31),a=n^(d<<1|s>>>31),t[2]^=e,t[3]^=a,t[12]^=e,t[13]^=a,t[22]^=e,t[23]^=a,t[32]^=e,t[33]^=a,t[42]^=e,t[43]^=a,e=l^(u<<1|g>>>31),a=r^(g<<1|u>>>31),t[4]^=e,t[5]^=a,t[14]^=e,t[15]^=a,t[24]^=e,t[25]^=a,t[34]^=e,t[35]^=a,t[44]^=e,t[45]^=a,e=s^(f<<1|h>>>31),a=d^(h<<1|f>>>31),t[6]^=e,t[7]^=a,t[16]^=e,t[17]^=a,t[26]^=e,t[27]^=a,t[36]^=e,t[37]^=a,t[46]^=e,t[47]^=a,e=u^(o<<1|n>>>31),a=g^(n<<1|o>>>31),t[8]^=e,t[9]^=a,t[18]^=e,t[19]^=a,t[28]^=e,t[29]^=a,t[38]^=e,t[39]^=a,t[48]^=e,t[49]^=a,_=t[0],p=t[1],K=t[11]<<4|t[10]>>>28,H=t[10]<<4|t[11]>>>28,B=t[20]<<3|t[21]>>>29,S=t[21]<<3|t[20]>>>29,rt=t[31]<<9|t[30]>>>23,st=t[30]<<9|t[31]>>>23,N=t[40]<<18|t[41]>>>14,V=t[41]<<18|t[40]>>>14,U=t[2]<<1|t[3]>>>31,T=t[3]<<1|t[2]>>>31,m=t[13]<<12|t[12]>>>20,w=t[12]<<12|t[13]>>>20,Z=t[22]<<10|t[23]>>>22,W=t[23]<<10|t[22]>>>22,P=t[33]<<13|t[32]>>>19,G=t[32]<<13|t[33]>>>19,ct=t[42]<<2|t[43]>>>30,dt=t[43]<<2|t[42]>>>30,et=t[5]<<30|t[4]>>>2,at=t[4]<<30|t[5]>>>2,Q=t[14]<<6|t[15]>>>26,q=t[15]<<6|t[14]>>>26,L=t[25]<<11|t[24]>>>21,b=t[24]<<11|t[25]>>>21,Y=t[34]<<15|t[35]>>>17,J=t[35]<<15|t[34]>>>17,z=t[45]<<29|t[44]>>>3,O=t[44]<<29|t[45]>>>3,F=t[6]<<28|t[7]>>>4,x=t[7]<<28|t[6]>>>4,it=t[17]<<23|t[16]>>>9,ot=t[16]<<23|t[17]>>>9,M=t[26]<<25|t[27]>>>7,k=t[27]<<25|t[26]>>>7,A=t[36]<<21|t[37]>>>11,y=t[37]<<21|t[36]>>>11,X=t[47]<<24|t[46]>>>8,tt=t[46]<<24|t[47]>>>8,$=t[8]<<27|t[9]>>>5,j=t[9]<<27|t[8]>>>5,E=t[18]<<20|t[19]>>>12,v=t[19]<<20|t[18]>>>12,nt=t[29]<<7|t[28]>>>25,lt=t[28]<<7|t[29]>>>25,R=t[38]<<8|t[39]>>>24,D=t[39]<<8|t[38]>>>24,C=t[48]<<14|t[49]>>>18,I=t[49]<<14|t[48]>>>18,t[0]=_^~m&L,t[1]=p^~w&b,t[10]=F^~E&B,t[11]=x^~v&S,t[20]=U^~Q&M,t[21]=T^~q&k,t[30]=$^~K&Z,t[31]=j^~H&W,t[40]=et^~it&nt,t[41]=at^~ot<,t[2]=m^~L&A,t[3]=w^~b&y,t[12]=E^~B&P,t[13]=v^~S&G,t[22]=Q^~M&R,t[23]=q^~k&D,t[32]=K^~Z&Y,t[33]=H^~W&J,t[42]=it^~nt&rt,t[43]=ot^~lt&st,t[4]=L^~A&C,t[5]=b^~y&I,t[14]=B^~P&z,t[15]=S^~G&O,t[24]=M^~R&N,t[25]=k^~D&V,t[34]=Z^~Y&X,t[35]=W^~J&tt,t[44]=nt^~rt&ct,t[45]=lt^~st&dt,t[6]=A^~C&_,t[7]=y^~I&p,t[16]=P^~z&F,t[17]=G^~O&x,t[26]=R^~N&U,t[27]=D^~V&T,t[36]=Y^~X&$,t[37]=J^~tt&j,t[46]=rt^~ct&et,t[47]=st^~dt&at,t[8]=C^~_&m,t[9]=I^~p&w,t[18]=z^~F&E,t[19]=O^~x&v,t[28]=N^~U&Q,t[29]=V^~T&q,t[38]=X^~$&K,t[39]=tt^~j&H,t[48]=ct^~et&it,t[49]=dt^~at&ot,t[0]^=c[i],t[1]^=c[i+1]};if(o)Nn.exports=A;else for(C=0;C3*s.domainSize-4&&!d.isZero(e))throw new Error("T Polynomial is not divisible")}a&&a.debug("ifft Tz");const x=await d.ifft(C);for(let t=0;t<4*s.domainSize;t++){const e=x.slice(t*g,(t+1)*g);if(t>3*s.domainSize+5){if(!d.isZero(e))throw new Error("Tz Polynomial is not well calculated")}else F.set(d.add(F.slice(t*g,(t+1)*g),e),t*g)}E=F.slice(0,(3*s.domainSize+6)*g);let v=new Ge((s.domainSize+1)*g);v.set(F.slice(0,s.domainSize*g),0),v.set(U.b[10],s.domainSize*g);let P=new Ge((s.domainSize+1)*g);P.set(F.slice(s.domainSize*g,2*s.domainSize*g),0);const G=d.sub(P.slice(0,g),U.b[10]);P.set(G,0),P.set(U.b[11],s.domainSize*g);let z=new Ge((s.domainSize+6)*g);z.set(F.slice(2*s.domainSize*g,(3*s.domainSize+6)*g),0);const O=d.sub(z.slice(0,g),U.b[11]);function T(t,e,a,i,o){let n,l;const r=d.mul(t,e),s=d.mul(t,i),c=d.mul(a,e);n=r;let u=d.mul(a,i);return l=d.add(s,c),o&&(l=d.add(l,d.mul(h[o],u))),[n,l]}function Q(t,e,a,i,o,n,l,r,s){let c,u;const g=d.mul(t,e),f=d.mul(t,n),_=d.mul(o,e),w=d.mul(o,n),L=d.mul(a,i),b=d.mul(a,r),A=d.mul(l,i),y=d.mul(l,r);c=d.mul(g,L);let C=d.mul(_,L);C=d.add(C,d.mul(f,L)),C=d.add(C,d.mul(g,A)),C=d.add(C,d.mul(g,b));let I=d.mul(w,L);I=d.add(I,d.mul(_,A)),I=d.add(I,d.mul(_,b)),I=d.add(I,d.mul(f,A)),I=d.add(I,d.mul(f,b)),I=d.add(I,d.mul(g,y));let F=d.mul(f,y);F=d.add(F,d.mul(_,y)),F=d.add(F,d.mul(w,b)),F=d.add(F,d.mul(w,A));let x=d.mul(w,y);return u=C,s&&(u=d.add(u,d.mul(h[s],I)),u=d.add(u,d.mul(p[s],F)),u=d.add(u,d.mul(m[s],x))),[c,u]}z.set(O,0),B.T1=await D(v,"multiexp T1"),B.T2=await D(P,"multiexp T2"),B.T3=await D(z,"multiexp T3")}(),await async function(){const t=new Ge(s.domainSize*g);await l.readToBuffer(t,0,s.domainSize*g,r[7][0].p);const e=new Ge(s.domainSize*g);await l.readToBuffer(e,0,s.domainSize*g,r[8][0].p);const i=new Ge(s.domainSize*g);await l.readToBuffer(i,0,s.domainSize*g,r[9][0].p);const o=new Ge(s.domainSize*g);await l.readToBuffer(o,0,s.domainSize*g,r[10][0].p);const n=new Ge(s.domainSize*g);await l.readToBuffer(n,0,s.domainSize*g,r[11][0].p);const c=new Ge(s.domainSize*g);await l.readToBuffer(c,0,s.domainSize*g,r[12][0].p+10*s.domainSize*g);const f=new Uint8Array(2*u.F.n8*3);u.toRprUncompressed(f,0,B.T1),u.toRprUncompressed(f,2*u.F.n8,B.T2),u.toRprUncompressed(f,4*u.F.n8,B.T3),U.xi=M(f),a&&a.debug("xi: "+d.toString(U.xi));B.eval_a=k(C,U.xi),B.eval_b=k(I,U.xi),B.eval_c=k(F,U.xi),B.eval_s1=k(G,U.xi),B.eval_s2=k(z,U.xi),B.eval_t=k(E,U.xi),B.eval_zw=k(x,d.mul(U.xi,d.w[s.power]));const h=d.mul(B.eval_a,B.eval_b);let _=B.eval_a;const p=d.mul(U.beta,U.xi);_=d.add(_,p),_=d.add(_,U.gamma);let m=B.eval_b;m=d.add(m,d.mul(p,s.k1)),m=d.add(m,U.gamma);let w=B.eval_c;w=d.add(w,d.mul(p,s.k2)),w=d.add(w,U.gamma);const L=d.mul(d.mul(d.mul(_,m),w),U.alpha);let b=B.eval_a;b=d.add(b,d.mul(U.beta,B.eval_s1)),b=d.add(b,U.gamma);let A=B.eval_b;A=d.add(A,d.mul(U.beta,B.eval_s2)),A=d.add(A,U.gamma);let y=d.mul(b,A);y=d.mul(y,U.beta),y=d.mul(y,B.eval_zw),y=d.mul(y,U.alpha),U.xim=U.xi;for(let t=0;t=0;o--)i=d.add(d.mul(i,e),t.slice(o*g,(o+1)*g));return i}function R(t,e){const a=t.byteLength/g,i=new Ge(a*g);i.set(d.zero,(a-1)*g),i.set(t.slice((a-1)*g,a*g),(a-2)*g);for(let o=a-3;o>=0;o--)i.set(d.add(t.slice((o+1)*g,(o+2)*g),d.mul(e,i.slice((o+1)*g,(o+2)*g))),o*g);if(!d.eq(t.slice(0,g),d.mul(d.neg(e),i.slice(0,g))))throw new Error("Polinomial does not divide");return i}async function D(t,e){const i=t.byteLength/g,o=O.slice(0,i*c.G1.F.n8*2),n=await c.Fr.batchFromMontgomery(t);let l=await c.G1.multiExpAffine(o,n,a,e);return l=c.G1.toAffine(l),l}async function N(t,e){e=e||[];let a=await d.ifft(t);const i=new Ge(g*s.domainSize*4);i.set(a,0);const o=new Ge(g*(s.domainSize+e.length));o.set(a,0);for(let t=0;ta;){const e=o.shift(),a=o.shift(),i=e[0],n=a[0],l=w++,r=t.zero,s=t.neg(e[1]),c=t.neg(a[1]),d=t.one,u=t.zero;p.push([i,n,l,r,s,c,d,u]),m.push([i,n,e[1],a[1]]),o.push([l,t.one])}for(let t=0;t0?i.toString():a!=t.zero?"k":"0"}function s(e,a,s){const c=r(e),d=r(a);if("0"===c||"0"===d)i(s),l(s);else if("k"===c){l(o(a,e[0],s))}else if("k"===d){l(o(e,a[0],s))}else!function(e,a,i){const o=n(e,1),l=n(a,1),r=n(i,1),s=o.s[0],c=l.s[0],d=r.s[0],u=t.mul(o.coefs[0],l.coefs[0]),g=t.mul(o.coefs[0],l.k),f=t.mul(o.k,l.coefs[0]),h=t.neg(r.coefs[0]),_=t.sub(t.mul(o.k,l.k),r.k);p.push([s,c,d,u,g,f,h,_])}(e,a,s)}for(let e=1;e<=L;e++){const a=e,i=0,o=0,n=t.zero,l=t.one,r=t.zero,s=t.zero,c=t.zero;p.push([a,i,o,n,l,r,s,c])}for(let t=0;tr)return i&&i.error(`circuit too big for this power of tau ceremony. ${p.length} > 2**${r}`),-1;if(!n[12])return i&&i.error("Powers of tau is not prepared."),-1;const C=new Ge(y*u),I=n[12][0].p+(2**A-1)*u;await o.readToBuffer(C,0,y*u,I);const[F,x]=function(){let t=h.two;for(;a(t,[],A);)h.add(t,h.one);let e=h.add(t,h.one);for(;a(e,[t],A);)h.add(e,h.one);return[t,e];function a(t,e,a){const i=2**a;let o=h.one;for(let n=0;n0?2:this.Fr.isZero(e)?0:1}normalizeLinearCombination(t){const e=Object.keys(t);for(let a=0;ao;){const i=l.shift(),o=l.shift(),n=t.nVars++,r=this.fnGetAdditionConstraint(i[0],o[0],n,this.Fr.neg(i[1]),this.Fr.neg(o[1]),this.Fr.zero,this.Fr.one,this.Fr.zero);e.push(r),a.push([i[0],o[0],i[1],o[1]]),l.push([n,this.Fr.one])}for(let t=0;t32768?new Ge(t.length*i.n8):new Uint8Array(t.length*i.n8);for(let e=0;e32768?new Ge(i*o.n8):new Uint8Array(i*o.n8);return n.set(t.coef.slice(),0),new rl(n,e,a)}isEqual(t){const e=this.degree();if(e!==t.degree())return!1;for(let a=0;a32768?new Ge((this.length()+t.length)*this.Fr.n8):new Uint8Array((this.length()+t.length)*this.Fr.n8);e.set(this.coef,0);for(let a=0;athis.coef.byteLength?this.Fr.zero:this.coef.slice(e,e+this.Fr.n8)}setCoef(t,e){if(t>this.length()-1)throw new Error("Coef index is not available");this.coef.set(e,t*this.Fr.n8)}static async to4T(t,e,a,i){a=a||[];let o=await i.ifft(t);const n=4*e>32768?new Ge(4*e*i.n8):new Uint8Array(4*e*i.n8);n.set(o,0);const l=await i.fft(n);if(0===a.length)return[o,l];const r=e+a.length>32768?new Ge((e+a.length)*i.n8):new Uint8Array((e+a.length)*i.n8);r.set(o,0);for(let t=0;t0;t--){const e=t*this.Fr.n8;if(!this.Fr.eq(this.Fr.zero,this.coef.slice(e,e+this.Fr.n8)))return t}return 0}evaluate(t){let e=this.Fr.zero;for(let a=this.degree()+1;a>0;a--){let i=a*this.Fr.n8;const o=this.coef.slice(i-this.Fr.n8,i);e=this.Fr.add(o,this.Fr.mul(e,t))}return e}fastEvaluate(t){const e=this.Fr;let a=this.degree()+1,i=parseInt(a/3),o=a-3*i,n=[],l=[];l[0]=e.one;for(let a=0;a<3;a++){n[a]=e.zero;for(let r=2===a?i+o:i;r>0;r--)n[a]=e.add(this.getCoef(a*i+r-1),e.mul(n[a],t)),0===a&&(l[0]=e.mul(l[0],t))}for(let t=1;t<3;t++)n[0]=e.add(n[0],e.mul(l[t-1],n[t])),l[t]=e.mul(l[t-1],l[0]);return n[0]}add(t,e){let a=!1;t.length()>this.length()&&(a=!0);const i=this.length(),o=t.length();for(let n=0;nthis.length()&&(a=!0);const i=this.length(),o=t.length();for(let n=0;n32768?new Ge(a*e.n8):new Uint8Array(a*e.n8);let o=new rl(i,this.curve,this.logger);o.coef.set(this.coef.slice(0,(a-1)*e.n8),32),this.mulScalar(e.neg(t)),o.add(this),this.coef=o.coef}byXNSubValue(t,e){const a=this.Fr,i=!(this.length()-t-1>=this.degree())?this.length()+t:this.length(),o=i>32768?new Ge(i*a.n8):new Uint8Array(i*a.n8);let n=new rl(o,this.curve,this.logger);n.coef.set(this.coef.slice(0,32*(this.degree()+1)),32*t),this.mulScalar(e),n.add(this),this.coef=n.coef}divBy(t){const e=this.Fr,a=this.degree(),i=t.degree();let o=new rl(this.coef,this.curve,this.logger);this.coef=this.length()>32768?new Ge(this.length()*e.n8):new Uint8Array(this.length()*e.n8);for(let n=a-i;n>=0;n--){this.setCoef(n,e.div(o.getCoef(n+i),t.getCoef(i)));for(let a=0;a<=i;a++)o.setCoef(n+a,e.sub(o.getCoef(n+a),e.mul(this.getCoef(n),t.getCoef(a))))}return o}divByMonic(t,e){const a=this.Fr;let i=this.degree(),o=this.length()>32768?new Ge(this.length()*a.n8):new Uint8Array(this.length()*a.n8),n=new rl(o,this.curve,this.logger),l=[];for(let e=0;e=0&&!(s<0);s-=r){let i=o;l[i]=a.add(this.getCoef(s+t),a.mul(l[i],e)),n.setCoef(s,l[i])}this.coef=n.coef}divByVanishing(t,e){if(this.degree()32768?new Ge(this.length()*a.n8):new Uint8Array(this.length()*a.n8);for(let o=this.length()-1;o>=t;o--){let n=i.getCoef(o);a.eq(a.zero,n)||(i.setCoef(o,a.zero),i.setCoef(o-t,a.add(i.getCoef(o-t),a.mul(e,n))),this.setCoef(o-t,a.add(this.getCoef(o-t),n)))}return i}divByVanishing2(t,e){if(this.degree()32768?new Ge(this.length()*a.n8):new Uint8Array(this.length()*a.n8);let o=this.length()-t,n=Math.floor(o/3),l=o-2*n;console.log(o),console.log(n+" "+l);for(let o=0;o<3;o++){console.log("> Thread "+o);for(let r=0===o?l:n;r>0;r--){let s=r-1;0!==o&&(s+=(o-1)*n+l);let c=s+t,d=i.getCoef(c);a.eq(a.zero,d)||(i.setCoef(c,a.zero),i.setCoef(s,a.add(i.getCoef(s),a.mul(e,d))),this.setCoef(s,a.add(this.getCoef(s),d)),console.log(s+" <-- "+c))}}return this.print(),i}fastDivByVanishing(t){const e=this.Fr;for(let a=0;a32768?new Ge(this.length()*e.n8):new Uint8Array(this.length()*e.n8),this.curve,this.logger),u=this.coef;this.coef=d.coef,d.coef=u;for(let t=0;t0;t--){let a=t-1,o=a*s+c;h[a]=[];for(let l=0;l32768?new Ge(this.length()*this.Fr.n8):new Uint8Array(this.length()*this.Fr.n8);e.set(this.Fr.zero,(this.length()-1)*this.Fr.n8),e.set(this.coef.slice((this.length()-1)*this.Fr.n8,this.length()*this.Fr.n8),(this.length()-2)*this.Fr.n8);for(let a=this.length()-3;a>=0;a--){let i=a*this.Fr.n8;e.set(this.Fr.add(this.coef.slice(i+this.Fr.n8,i+2*this.Fr.n8),this.Fr.mul(t,e.slice(i+this.Fr.n8,i+2*this.Fr.n8))),a*this.Fr.n8)}if(!this.Fr.eq(this.coef.slice(0,this.Fr.n8),this.Fr.mul(this.Fr.neg(t),e.slice(0,this.Fr.n8))))throw new Error("Polynomial does not divide");this.coef=e}divZh(t,e=4){for(let e=0;et*(e-1)-e&&!this.Fr.isZero(o))throw new Error("Polynomial is not divisible")}return this}divByZerofier(t,e){let a=this.Fr;const i=a.inv(e),o=a.neg(i);let n=a.eq(a.one,o),l=a.eq(a.negone,o);if(!n)for(let e=0;ethis.length()-t-1&&!this.Fr.isZero(s))throw new Error("Polynomial is not divisible")}return this}byX(){const t=this.length()+1>32768?new Ge(this.coef.byteLength+this.Fr.n8):new Uint8Array(this.coef.byteLength+this.Fr.n8);t.set(this.Fr.zero,0),t.set(this.coef,this.Fr.n8),this.coef=t}static async expX(t,e,a=!1){const i=t.Fr;if(e<1)throw new Error("Compute a new polynomial to a zero or negative number is not allowed");if(1===e)return await rl.fromEvaluations(t.coef,curve,t.logger);const o=a?t.degree():t.length()-1,n=o*e+1>32768?new Ge((o*e+1)*i.n8):new Uint8Array((o*e+1)*i.n8);n.set(t.getCoef(0),0);for(let a=1;a<=o;a++){const o=a*i.n8,l=t.getCoef(a);n.set(l,o*e)}return new rl(n,t.curve,t.logger)}split(t,e,a){if(t<1)throw new Error(`Polynomials can't be split in ${t} parts`);if(1===t)return[this];if(0!==a.length&&a.length32768?new Ge(l):new Uint8Array(l);o[e]=new rl(r,this.curve,this.logger);const s=e*i,c=n?this.coef.byteLength:(e+1)*i;if(o[e].coef.set(this.coef.slice(s,c),0),n||o[e].coef.set(a[e],i),0!==e){const t=this.Fr.sub(o[e].coef.slice(0,this.Fr.n8),a[e-1]);o[e].coef.set(t,0)}n&&o[e].truncate()}return o}truncate(){const t=this.degree();if(t+132768?new Ge((t+1)*this.Fr.n8):new Uint8Array((t+1)*this.Fr.n8);e.set(this.coef.slice(0,(t+1)*this.Fr.n8),0),this.coef=e}}static lagrangePolynomialInterpolation(t,e,a){const i=a.Fr;let o=n(0);for(let e=1;e32768?new Ge(t.length*i.n8):new Uint8Array(t.length*i.n8);n=new rl(o,a),n.setCoef(0,i.neg(t[e])),n.setCoef(1,i.one)}else n.byXSubValue(t[e]);let l=n.evaluate(t[o]);l=i.inv(l);const r=i.mul(e[o],l);return n.mulScalar(r),n}}static zerofierPolynomial(t,e){const a=e.Fr;let i=t.length+1>32768?new Ge((t.length+1)*a.n8):new Uint8Array((t.length+1)*a.n8),o=new rl(i,e);o.setCoef(0,a.neg(t[0])),o.setCoef(1,a.one);for(let e=1;e=0;a--){const i=this.getCoef(a);t.eq(t.zero,i)||(t.isNegative(i)?e+=" - ":a!==this.degree()&&(e+=" + "),e+=t.toString(i),a>0&&(e+=a>1?"x^"+a:"x"))}console.log(e)}async multiExponentiation(t,e){const a=this.coef.byteLength/this.Fr.n8,i=t.slice(0,a*this.G1.F.n8*2),o=await this.Fr.batchFromMontgomery(this.coef);let n=await this.G1.multiExpAffine(i,o,this.logger,e);return n=this.G1.toAffine(n),n}}class sl{constructor(t,e,a){this.eval=t,this.curve=e,this.Fr=e.Fr,this.logger=a}static async fromPolynomial(t,e,a,i){const o=new Ge(t.length()*e*a.Fr.n8);o.set(t.coef,0);const n=await a.Fr.fft(o);return new sl(n,a,i)}getEvaluation(t){const e=t*this.Fr.n8;if(e+this.Fr.n8>this.eval.byteLength)throw new Error("Evaluations.getEvaluation() out of bounds");return this.eval.slice(e,e+this.Fr.n8)}length(){let t=this.eval.byteLength/this.Fr.n8;if(t!==Math.floor(this.eval.byteLength/this.Fr.n8))throw new Error("Polynomial evaluations buffer has incorrect size");return 0===t&&this.logger.warn("Polynomial has length zero"),t}}class cl{constructor(t,e,a){this.n=t,this.polynomials=Array(t).fill(void 0),this.curve=e,this.Fr=e.Fr,this.G1=e.G1,this.logger=a}addPolynomial(t,e){if(t>this.n-1)throw new Error("CPolynomial:addPolynomial, cannot add a polynomial to a position greater than n-1");this.polynomials[t]=e}degree(){let t=this.polynomials.map(((t,e)=>void 0===t?0:t.degree()*this.n+e));return Math.max(...t)}getPolynomial(){let t=this.polynomials.map((t=>void 0===t?0:t.degree()));const e=this.degree(),a=2**(qi(e-1)+1),i=this.Fr.n8;let o=new rl(new Ge(a*i),this.curve,this.logger);for(let a=0;a0===a.type?t++:e++));let a=new Uint8Array(e*this.Fr.n8+t*this.G1.F.n8*2),i=0;for(let t=0;t{t.polynomials[e]=this.curve.G1.toObject(this.polynomials[e])})),Object.keys(this.evaluations).forEach((e=>{t.evaluations[e]=this.curve.Fr.toObject(this.evaluations[e])})),t}fromObjectProof(t){this.resetProof(),Object.keys(t.polynomials).forEach((e=>{this.polynomials[e]=this.curve.G1.fromObject(t.polynomials[e])})),Object.keys(t.evaluations).forEach((e=>{this.evaluations[e]=this.curve.Fr.fromObject(t.evaluations[e])}))}}const{stringifyBigInts:fl}=ma;async function hl(t,e,a){a&&a.info("FFLONK PROVER STARTED"),a&&a.info("> Reading witness file");const{fd:i,sections:o}=await ka(e,"wtns",2),n=await Go(i,o);a&&a.info("> Reading zkey file");const{fd:l,sections:r}=await ka(t,"zkey",2),s=await Fo(l,r);if(s.protocolId!==to)throw new Error("zkey file is not fflonk");if(!pa.eq(s.r,n.q))throw new Error("Curve of the witness does not match the curve of the proving key");if(n.nWitness!==s.nVars-s.nAdditions)throw new Error(`Invalid witness length. Circuit: ${s.nVars}, witness: ${n.nWitness}, ${s.nAdditions}`);const c=s.curve,d=c.Fr,u=c.Fr.n8,g=2*c.G1.F.n8,f=s.domainSize*u;a&&(a.info("----------------------------"),a.info(" FFLONK PROVE SETTINGS"),a.info(` Curve: ${c.name}`),a.info(` Circuit power: ${s.power}`),a.info(` Domain size: ${s.domainSize}`),a.info(` Vars: ${s.nVars}`),a.info(` Public vars: ${s.nPublic}`),a.info(` Constraints: ${s.nConstraints}`),a.info(` Additions: ${s.nAdditions}`),a.info("----------------------------")),a&&a.info("> Reading witness file data");const h=await Za(i,o,2);await i.close(),h.set(d.zero,0);const _=new Ge(s.nAdditions*u);let p={},m={},w={},L={},b={},A={},y=new gl(c,a);a&&a.info(`> Reading Section ${oo}. Additions`),await async function(){a&&a.info("··· Computing additions");const t=await Za(l,r,oo),e=8+2*u;for(let i=0;i Reading Sections ${ho},${_o},${po}. Sigma1, Sigma2 & Sigma 3`),a&&a.info("··· Reading Sigma polynomials "),m.Sigma1=new rl(new Ge(f),c,a),m.Sigma2=new rl(new Ge(f),c,a),m.Sigma3=new rl(new Ge(f),c,a),await l.readToBuffer(m.Sigma1.coef,0,f,r[ho][0].p),await l.readToBuffer(m.Sigma2.coef,0,f,r[_o][0].p),await l.readToBuffer(m.Sigma3.coef,0,f,r[po][0].p),a&&a.info("··· Reading Sigma evaluations"),w.Sigma1=new sl(new Ge(4*f),c,a),w.Sigma2=new sl(new Ge(4*f),c,a),w.Sigma3=new sl(new Ge(4*f),c,a),await l.readToBuffer(w.Sigma1.eval,0,4*f,r[ho][0].p+f),await l.readToBuffer(w.Sigma2.eval,0,4*f,r[_o][0].p+f),await l.readToBuffer(w.Sigma3.eval,0,4*f,r[po][0].p+f),a&&a.info(`> Reading Section ${wo}. Powers of Tau`);const C=new Ge(16*s.domainSize*g);await l.readToBuffer(C,0,(9*s.domainSize+18)*g,r[wo][0].p),globalThis.gc&&globalThis.gc(),a&&a.info(""),a&&a.info("> ROUND 1"),await async function(){b.b=[];for(let t=1;t<=9;t++)b.b[t]=d.random();a&&a.info("> Computing A, B, C wire polynomials");await async function(){a&&a.info("··· Reading data from zkey file");p.A=new Ge(f),p.B=new Ge(f),p.C=new Ge(f);const t=await Za(l,r,no),e=await Za(l,r,lo),i=await Za(l,r,ro);for(let a=0;a=s.domainSize)throw new Error("A Polynomial is not well calculated");if(m.B.degree()>=s.domainSize)throw new Error("B Polynomial is not well calculated");if(m.C.degree()>=s.domainSize)throw new Error("C Polynomial is not well calculated")}(),a&&a.info("> Computing T0 polynomial");await async function(){a&&a.info(`··· Reading sections ${so}, ${co}, ${uo}, ${go}, ${fo}. Q selectors`);w.QL=new sl(new Ge(4*f),c,a),w.QR=new sl(new Ge(4*f),c,a),w.QM=new sl(new Ge(4*f),c,a),w.QO=new sl(new Ge(4*f),c,a),w.QC=new sl(new Ge(4*f),c,a),await l.readToBuffer(w.QL.eval,0,4*f,r[so][0].p+f),await l.readToBuffer(w.QR.eval,0,4*f,r[co][0].p+f),await l.readToBuffer(w.QM.eval,0,4*f,r[uo][0].p+f),await l.readToBuffer(w.QO.eval,0,4*f,r[go][0].p+f),await l.readToBuffer(w.QC.eval,0,4*f,r[fo][0].p+f);const t=await Za(l,r,mo);w.lagrange1=new sl(t,c,a),p.T0=new Ge(4*f),a&&a.info("··· Computing T0 evaluations");for(let t=0;t<4*s.domainSize;t++){a&&0!==t&&t%1e5==0&&a.info(` T0 evaluation ${t}/${4*s.domainSize}`);const e=w.A.getEvaluation(t),i=w.B.getEvaluation(t),o=w.C.getEvaluation(t),n=w.QL.getEvaluation(t),l=w.QR.getEvaluation(t),r=w.QM.getEvaluation(t),c=w.QO.getEvaluation(t),g=w.QC.getEvaluation(t);let f=d.zero;for(let e=0;e=2*s.domainSize-2)throw new Error(`T0 Polynomial is not well calculated (degree is ${m.T0.degree()} and must be less than ${2*s.domainSize+2}`);delete p.T0}(),a&&a.info("> Computing C1 polynomial");await async function(){let t=new cl(4,c,a);if(t.addPolynomial(0,m.A),t.addPolynomial(1,m.B),t.addPolynomial(2,m.C),t.addPolynomial(3,m.T0),m.C1=t.getPolynomial(),m.C1.degree()>=8*s.domainSize-8)throw new Error("C1 Polynomial is not well calculated")}(),a&&a.info("> Computing C1 multi exponentiation");let t=await m.C1.multiExponentiation(C,"C1");return y.addPolynomial("C1",t),0}(),delete m.T0,delete w.QL,delete w.QR,delete w.QM,delete w.QO,delete w.QC,globalThis.gc&&globalThis.gc(),a&&a.info("> ROUND 2"),await async function(){a&&a.info("> Computing challenges beta and gamma");const t=new ul(c);t.addPolCommitment(s.C0);for(let e=0;e Computing Z polynomial");await async function(){a&&a.info("··· Computing Z evaluations");let t=new Ge(f),e=new Ge(f);t.set(d.one,0),e.set(d.one,0);let i=d.one;for(let o=0;o=s.domainSize+3)throw new Error("Z Polynomial is not well calculated");delete p.Z}(),a&&a.info("> Computing T1 polynomial");await async function(){a&&a.info("··· Computing T1 evaluations");p.T1=new Ge(2*f),p.T1z=new Ge(2*f);let t=d.one;for(let e=0;e<2*s.domainSize;e++){a&&0!==e&&e%1e5==0&&a.info(` T1 evaluation ${e}/${4*s.domainSize}`);const i=d.square(t),o=w.Z.getEvaluation(2*e),n=d.add(d.add(d.mul(b.b[7],i),d.mul(b.b[8],t)),b.b[9]),l=w.lagrange1.getEvaluation(s.domainSize+2*e);let r=d.mul(d.sub(o,d.one),l),c=d.mul(n,l);p.T1.set(r,e*u),p.T1z.set(c,e*u),t=d.mul(t,d.w[s.power+1])}a&&a.info("··· Computing T1 ifft");m.T1=await rl.fromEvaluations(p.T1,c,a),m.T1.divByZerofier(s.domainSize,d.one),a&&a.info("··· Computing T1z ifft");if(m.T1z=await rl.fromEvaluations(p.T1z,c,a),m.T1.add(m.T1z),m.T1.degree()>=s.domainSize+2)throw new Error("T1 Polynomial is not well calculated");delete p.T1,delete p.T1z,delete m.T1z}(),a&&a.info("> Computing T2 polynomial");await async function(){a&&a.info("··· Computing T2 evaluations");p.T2=new Ge(4*f),p.T2z=new Ge(4*f);let t=d.one;for(let e=0;e<4*s.domainSize;e++){a&&0!==e&&e%1e5==0&&a.info(` T2 evaluation ${e}/${4*s.domainSize}`);const i=d.square(t),o=d.mul(t,d.w[s.power]),n=d.square(o),l=w.A.getEvaluation(e),r=w.B.getEvaluation(e),c=w.C.getEvaluation(e),g=w.Z.getEvaluation(e),f=w.Z.getEvaluation((4*s.domainSize+4+e)%(4*s.domainSize)),h=d.add(d.add(d.mul(b.b[7],i),d.mul(b.b[8],t)),b.b[9]),_=d.add(d.add(d.mul(b.b[7],n),d.mul(b.b[8],o)),b.b[9]),m=w.Sigma1.getEvaluation(e),L=w.Sigma2.getEvaluation(e),A=w.Sigma3.getEvaluation(e),y=d.mul(b.beta,t);let C=d.add(l,y);C=d.add(C,b.gamma);let I=d.add(r,d.mul(y,s.k1));I=d.add(I,b.gamma);let F=d.add(c,d.mul(y,s.k2));F=d.add(F,b.gamma);let x=d.mul(d.mul(d.mul(C,I),F),g),E=d.mul(d.mul(d.mul(C,I),F),h),v=d.add(l,d.mul(b.beta,m));v=d.add(v,b.gamma);let B=d.add(r,d.mul(b.beta,L));B=d.add(B,b.gamma);let S=d.add(c,d.mul(b.beta,A));S=d.add(S,b.gamma);let P=d.mul(d.mul(d.mul(v,B),S),f),G=d.mul(d.mul(d.mul(v,B),S),_),z=d.sub(x,P),O=d.sub(E,G);p.T2.set(z,e*u),p.T2z.set(O,e*u),t=d.mul(t,d.w[s.power+2])}a&&a.info("··· Computing T2 ifft");m.T2=await rl.fromEvaluations(p.T2,c,a),a&&a.info("··· Computing T2 / ZH");m.T2.divByZerofier(s.domainSize,d.one),a&&a.info("··· Computing T2z ifft");if(m.T2z=await rl.fromEvaluations(p.T2z,c,a),m.T2.add(m.T2z),m.T2.degree()>=3*s.domainSize)throw new Error("T2 Polynomial is not well calculated");delete p.T2,delete p.T2z,delete m.T2z}(),a&&a.info("> Computing C2 polynomial");await async function(){let t=new cl(3,c,a);if(t.addPolynomial(0,m.Z),t.addPolynomial(1,m.T1),t.addPolynomial(2,m.T2),m.C2=t.getPolynomial(),m.C2.degree()>=9*s.domainSize)throw new Error("C2 Polynomial is not well calculated")}(),a&&a.info("> Computing C2 multi exponentiation");let e=await m.C2.multiExponentiation(C,"C2");return y.addPolynomial("C2",e),0}(),delete p.A,delete p.B,delete p.C,delete w.A,delete w.B,delete w.C,delete w.Sigma1,delete w.Sigma2,delete w.Sigma3,delete w.lagrange1,delete w.Z,globalThis.gc&&globalThis.gc(),a&&a.info("> ROUND 3"),await async function(){a&&a.info("> Computing challenge xi");const t=new ul(c);t.addScalar(b.gamma),t.addPolCommitment(y.getPolynomial("C2")),b.xiSeed=t.getChallenge();const e=d.square(b.xiSeed);A.w8=[],A.w8[0]=d.one;for(let t=1;t<8;t++)A.w8[t]=d.mul(A.w8[t-1],s.w8);A.w4=[],A.w4[0]=d.one;for(let t=1;t<4;t++)A.w4[t]=d.mul(A.w4[t-1],s.w4);A.w3=[],A.w3[0]=d.one,A.w3[1]=s.w3,A.w3[2]=d.square(s.w3),A.S0={},A.S0.h0w8=[],A.S0.h0w8[0]=d.mul(e,b.xiSeed);for(let t=1;t<8;t++)A.S0.h0w8[t]=d.mul(A.S0.h0w8[0],A.w8[t]);A.S1={},A.S1.h1w4=[],A.S1.h1w4[0]=d.square(A.S0.h0w8[0]);for(let t=1;t<4;t++)A.S1.h1w4[t]=d.mul(A.S1.h1w4[0],A.w4[t]);A.S2={},A.S2.h2w3=[],A.S2.h2w3[0]=d.mul(A.S1.h1w4[0],e),A.S2.h2w3[1]=d.mul(A.S2.h2w3[0],A.w3[1]),A.S2.h2w3[2]=d.mul(A.S2.h2w3[0],A.w3[2]),A.S2.h3w3=[],A.S2.h3w3[0]=d.mul(A.S2.h2w3[0],s.wr),A.S2.h3w3[1]=d.mul(A.S2.h3w3[0],A.w3[1]),A.S2.h3w3[2]=d.mul(A.S2.h3w3[0],A.w3[2]),b.xi=d.mul(d.square(A.S2.h2w3[0]),A.S2.h2w3[0]),a&&a.info("··· challenges.xi: "+d.toString(b.xi));m.QL=new rl(new Ge(f),c,a),m.QR=new rl(new Ge(f),c,a),m.QM=new rl(new Ge(f),c,a),m.QO=new rl(new Ge(f),c,a),m.QC=new rl(new Ge(f),c,a),await l.readToBuffer(m.QL.coef,0,f,r[so][0].p),await l.readToBuffer(m.QR.coef,0,f,r[co][0].p),await l.readToBuffer(m.QM.coef,0,f,r[uo][0].p),await l.readToBuffer(m.QO.coef,0,f,r[go][0].p),await l.readToBuffer(m.QC.coef,0,f,r[fo][0].p),a&&a.info("··· Computing evaluations");y.addEvaluation("ql",m.QL.evaluate(b.xi)),y.addEvaluation("qr",m.QR.evaluate(b.xi)),y.addEvaluation("qm",m.QM.evaluate(b.xi)),y.addEvaluation("qo",m.QO.evaluate(b.xi)),y.addEvaluation("qc",m.QC.evaluate(b.xi)),y.addEvaluation("s1",m.Sigma1.evaluate(b.xi)),y.addEvaluation("s2",m.Sigma2.evaluate(b.xi)),y.addEvaluation("s3",m.Sigma3.evaluate(b.xi)),y.addEvaluation("a",m.A.evaluate(b.xi)),y.addEvaluation("b",m.B.evaluate(b.xi)),y.addEvaluation("c",m.C.evaluate(b.xi)),y.addEvaluation("z",m.Z.evaluate(b.xi)),b.xiw=d.mul(b.xi,d.w[s.power]),y.addEvaluation("zw",m.Z.evaluate(b.xiw)),y.addEvaluation("t1w",m.T1.evaluate(b.xiw)),y.addEvaluation("t2w",m.T2.evaluate(b.xiw))}(),delete m.A,delete m.B,delete m.C,delete m.Z,delete m.T1,delete m.T2,delete m.Sigma1,delete m.Sigma2,delete m.Sigma3,delete m.QL,delete m.QR,delete m.QM,delete m.QC,delete m.QO,globalThis.gc&&globalThis.gc(),a&&a.info("> ROUND 4"),await async function(){a&&a.info("> Computing challenge alpha");const t=new ul(c);t.addScalar(b.xiSeed),t.addScalar(y.getEvaluation("ql")),t.addScalar(y.getEvaluation("qr")),t.addScalar(y.getEvaluation("qm")),t.addScalar(y.getEvaluation("qo")),t.addScalar(y.getEvaluation("qc")),t.addScalar(y.getEvaluation("s1")),t.addScalar(y.getEvaluation("s2")),t.addScalar(y.getEvaluation("s3")),t.addScalar(y.getEvaluation("a")),t.addScalar(y.getEvaluation("b")),t.addScalar(y.getEvaluation("c")),t.addScalar(y.getEvaluation("z")),t.addScalar(y.getEvaluation("zw")),t.addScalar(y.getEvaluation("t1w")),t.addScalar(y.getEvaluation("t2w")),b.alpha=t.getChallenge(),a&&a.info("··· challenges.alpha: "+d.toString(b.alpha));a&&a.info("> Reading C0 polynomial");m.C0=new rl(new Ge(8*f),c,a),await l.readToBuffer(m.C0.coef,0,8*f,r[Lo][0].p),a&&a.info("> Computing R0 polynomial");(function(){if(m.R0=rl.lagrangePolynomialInterpolation([A.S0.h0w8[0],A.S0.h0w8[1],A.S0.h0w8[2],A.S0.h0w8[3],A.S0.h0w8[4],A.S0.h0w8[5],A.S0.h0w8[6],A.S0.h0w8[7]],[m.C0.evaluate(A.S0.h0w8[0]),m.C0.evaluate(A.S0.h0w8[1]),m.C0.evaluate(A.S0.h0w8[2]),m.C0.evaluate(A.S0.h0w8[3]),m.C0.evaluate(A.S0.h0w8[4]),m.C0.evaluate(A.S0.h0w8[5]),m.C0.evaluate(A.S0.h0w8[6]),m.C0.evaluate(A.S0.h0w8[7])],c),m.R0.degree()>7)throw new Error("R0 Polynomial is not well calculated")})(),a&&a.info("> Computing R1 polynomial");(function(){if(m.R1=rl.lagrangePolynomialInterpolation([A.S1.h1w4[0],A.S1.h1w4[1],A.S1.h1w4[2],A.S1.h1w4[3]],[m.C1.evaluate(A.S1.h1w4[0]),m.C1.evaluate(A.S1.h1w4[1]),m.C1.evaluate(A.S1.h1w4[2]),m.C1.evaluate(A.S1.h1w4[3])],c),m.R1.degree()>3)throw new Error("R1 Polynomial is not well calculated")})(),a&&a.info("> Computing R2 polynomial");(function(){if(m.R2=rl.lagrangePolynomialInterpolation([A.S2.h2w3[0],A.S2.h2w3[1],A.S2.h2w3[2],A.S2.h3w3[0],A.S2.h3w3[1],A.S2.h3w3[2]],[m.C2.evaluate(A.S2.h2w3[0]),m.C2.evaluate(A.S2.h2w3[1]),m.C2.evaluate(A.S2.h2w3[2]),m.C2.evaluate(A.S2.h3w3[0]),m.C2.evaluate(A.S2.h3w3[1]),m.C2.evaluate(A.S2.h3w3[2])],c),m.R2.degree()>5)throw new Error("R2 Polynomial is not well calculated")})(),a&&a.info("> Computing F polynomial");await async function(){a&&a.info("··· Computing F polynomial");m.F=rl.fromPolynomial(m.C0,c,a),m.F.sub(m.R0),m.F.divByZerofier(8,b.xi);let t=rl.fromPolynomial(m.C1,c,a);t.sub(m.R1),t.mulScalar(b.alpha),t.divByZerofier(4,b.xi);let e=rl.fromPolynomial(m.C2,c,a);if(e.sub(m.R2),e.mulScalar(d.square(b.alpha)),e.divByZerofier(3,b.xi),e.divByZerofier(3,b.xiw),m.F.add(t),m.F.add(e),m.F.degree()>=9*s.domainSize-6)throw new Error("F Polynomial is not well calculated")}(),a&&a.info("> Computing W1 multi exponentiation");let e=await m.F.multiExponentiation(C,"W1");return y.addPolynomial("W1",e),0}(),globalThis.gc&&globalThis.gc(),a&&a.info("> ROUND 5"),await async function(){a&&a.info("> Computing challenge y");const t=new ul(c);t.addScalar(b.alpha),t.addPolCommitment(y.getPolynomial("W1")),b.y=t.getChallenge(),a&&a.info("··· challenges.y: "+d.toString(b.y));a&&a.info("> Computing L polynomial");await async function(){a&&a.info("··· Computing L polynomial");const t=m.R0.evaluate(b.y),e=m.R1.evaluate(b.y),i=m.R2.evaluate(b.y);let o=d.sub(b.y,A.S0.h0w8[0]);for(let t=1;t<8;t++)o=d.mul(o,d.sub(b.y,A.S0.h0w8[t]));let n=d.sub(b.y,A.S1.h1w4[0]);for(let t=1;t<4;t++)n=d.mul(n,d.sub(b.y,A.S1.h1w4[t]));let l=d.sub(b.y,A.S2.h2w3[0]);for(let t=1;t<3;t++)l=d.mul(l,d.sub(b.y,A.S2.h2w3[t]));for(let t=0;t<3;t++)l=d.mul(l,d.sub(b.y,A.S2.h3w3[t]));let r=d.mul(n,l),u=d.mul(b.alpha,d.mul(o,l)),g=d.mul(d.square(b.alpha),d.mul(o,n));L.denH1=n,L.denH2=l,m.L=rl.fromPolynomial(m.C0,c,a),m.L.subScalar(t),m.L.mulScalar(r);let f=rl.fromPolynomial(m.C1,c,a);f.subScalar(e),f.mulScalar(u);let h=rl.fromPolynomial(m.C2,c,a);h.subScalar(i),h.mulScalar(g),m.L.add(f),m.L.add(h),a&&a.info("> Computing ZT polynomial");await async function(){m.ZT=rl.zerofierPolynomial([A.S0.h0w8[0],A.S0.h0w8[1],A.S0.h0w8[2],A.S0.h0w8[3],A.S0.h0w8[4],A.S0.h0w8[5],A.S0.h0w8[6],A.S0.h0w8[7],A.S1.h1w4[0],A.S1.h1w4[1],A.S1.h1w4[2],A.S1.h1w4[3],A.S2.h2w3[0],A.S2.h2w3[1],A.S2.h2w3[2],A.S2.h3w3[0],A.S2.h3w3[1],A.S2.h3w3[2]],c)}();const _=m.ZT.evaluate(b.y);if(m.F.mulScalar(_),m.L.sub(m.F),m.L.degree()>=9*s.domainSize)throw new Error("L Polynomial is not well calculated");delete p.L}(),a&&a.info("> Computing ZTS2 polynomial");await async function(){m.ZTS2=rl.zerofierPolynomial([A.S1.h1w4[0],A.S1.h1w4[1],A.S1.h1w4[2],A.S1.h1w4[3],A.S2.h2w3[0],A.S2.h2w3[1],A.S2.h2w3[2],A.S2.h3w3[0],A.S2.h3w3[1],A.S2.h3w3[2]],c)}();let e=m.ZTS2.evaluate(b.y);e=d.inv(e),m.L.mulScalar(e);const i=rl.fromCoefficientsArray([d.neg(b.y),d.one],c);a&&a.info("> Computing W' = L / ZTS2 polynomial");const o=m.L.divBy(i);if(o.degree()>0)throw new Error(`Degree of L(X)/(ZTS2(y)(X-y)) remainder is ${o.degree()} and should be 0`);if(m.L.degree()>=9*s.domainSize-1)throw new Error("Degree of L(X)/(ZTS2(y)(X-y)) is not correct");a&&a.info("> Computing W' multi exponentiation");let n=await m.L.multiExponentiation(C,"W2");return y.addPolynomial("W2",n),0}(),delete m.C0,delete m.C1,delete m.C2,delete m.R1,delete m.R2,delete m.F,delete m.L,delete m.ZT,delete m.ZTS2,await l.close(),globalThis.gc&&globalThis.gc(),y.addEvaluation("inv",function(){let t=b.xi;for(let e=0;e Reading PTau file");const{fd:o,sections:n}=await ka(e,"ptau",1);if(!n[12])throw new Error("Powers of Tau is not well prepared. Section 12 missing.");i&&i.info("> Getting curve from PTau settings");const{curve:l}=await Xo(o,n);i&&i.info("> Reading r1cs file");const{fd:r,sections:s}=await ka(t,"r1cs",1),c=await An(r,s,{loadConstraints:!1,loadCustomGates:!0});if(c.prime!==l.r)throw new Error("r1cs curve does not match powers of tau ceremony curve");const d=l.Fr,u=l.Fr.n8,g=2*l.G1.F.n8,f=2*l.G2.F.n8;let h,_={},p={},m={nVars:c.nVars,nPublic:c.nOutputs+c.nPubInputs};const w=new Gn;let L=new Gn;if(i&&i.info("> Processing FFlonk constraints"),await async function(t,e,a){for(let e=0;e computing k1 and k2");const[b,A]=function(){let t=d.two;for(;a(t,[],m.cirPower);)d.add(t,d.one);let e=d.add(t,d.one);for(;a(e,[t],m.cirPower);)d.add(e,d.one);return[t,e];function a(t,e,a){const i=2**a;let o=d.one;for(let n=0;n computing w3");const y=function(){let t=d.e(31624),e=pa.div(3648040478639879203707734290876212514758060733402672390616367364429301415936n,pa.e(3));return d.exp(t,e)}();i&&i.info("> computing w4");const C=d.w[2];i&&i.info("> computing w8");const I=d.w[3];i&&i.info("> computing wr");const F=function(t,e){const a=e.e(467799165886069610036046866799264026481344299079011762026774533774345988080n);return e.exp(a,2**(28-t))}(m.cirPower,l.Fr);return await async function(){i&&i.info("> Writing the zkey file");const t=await Ra(a,"zkey",1,ao,1<<22,1<<24);i&&i.info(`··· Writing Section ${Yi}. Zkey Header`);await async function(t){await Da(t,Yi),await t.writeULE32(to),await Na(t)}(t),i&&i.info(`··· Writing Section ${oo}. Additions`);await async function(t){await Da(t,oo);const e=new Uint8Array(8+2*u),a=new DataView(e.buffer);for(let o=0;o=8*m.domainSize)throw new Error("C0 Polynomial is not well calculated");await Da(t,Lo),await t.write(_.C0.coef),await Na(t)}(t),globalThis.gc&&globalThis.gc();i&&i.info(`··· Writing Section ${io}. FFlonk Header`);await async function(t){await Da(t,io);const e=l.q,a=8*(Math.floor((pa.bitLength(e)-1)/64)+1);await t.writeULE32(a),await ja(t,e,a);const i=l.r,r=8*(Math.floor((pa.bitLength(i)-1)/64)+1);let s;await t.writeULE32(r),await ja(t,i,r),await t.writeULE32(m.nVars),await t.writeULE32(m.nPublic),await t.writeULE32(m.domainSize),await t.writeULE32(L.length),await t.writeULE32(w.length),await t.write(b),await t.write(A),await t.write(y),await t.write(C),await t.write(I),await t.write(F),s=await o.read(f,n[3][0].p+f),await t.write(s);let c=await _.C0.multiExponentiation(h,"C0");await t.write(c),await Na(t)}(t),globalThis.gc&&globalThis.gc();i&&i.info("> Writing the zkey file finished");await t.close()}(),await r.close(),await o.close(),i&&i.info("FFLONK SETUP FINISHED"),0;async function x(t,e,a,o){await Da(t,e);for(let e=0;e Checking commitments belong to G1"),!function(t,e,a){const i=t.G1;return i.isValid(e.polynomials.C1)&&i.isValid(e.polynomials.C2)&&i.isValid(e.polynomials.W1)&&i.isValid(e.polynomials.W2)&&i.isValid(a.C0)}(o,l,n))return i.error("Proof is not well constructed"),!1;i&&i.info("> Computing challenges");const{challenges:c,roots:d}=function(t,e,a,i,o){const n=t.Fr,l={},r={},s=new ul(t);s.addPolCommitment(a.C0);for(let t=0;t Computing Zero polynomial evaluation Z_H(xi)"),c.zh=s.sub(c.xiN,s.one),c.invzh=s.inv(c.zh),i&&i.info("> Computing Lagrange evaluations");const u=await async function(t,e,a){const i=t.Fr,o=Math.max(1,a.nPublic),n=new Ge(o*i.n8);let l=new Ge(o*i.n8),r=i.one;for(let t=0;t Computing polynomial identities PI(X)");const g=function(t,e,a){const i=t.Fr;let o=i.zero;for(let t=0;t Computing r0(y)");const f=function(t,e,a,i,o,n){const l=o.Fr;n&&n.info("··· Computing C0(h_0ω_8^i) values");let r=[];for(let e=0;e<8;e++){let i=[];i[1]=a.S0.h0w8[e];for(let t=2;t<8;t++)i[t]=l.mul(i[t-1],a.S0.h0w8[e]);r[e]=l.add(t.evaluations.ql,l.mul(t.evaluations.qr,i[1])),r[e]=l.add(r[e],l.mul(t.evaluations.qo,i[2])),r[e]=l.add(r[e],l.mul(t.evaluations.qm,i[3])),r[e]=l.add(r[e],l.mul(t.evaluations.qc,i[4])),r[e]=l.add(r[e],l.mul(t.evaluations.s1,i[5])),r[e]=l.add(r[e],l.mul(t.evaluations.s2,i[6])),r[e]=l.add(r[e],l.mul(t.evaluations.s3,i[7]))}const s=rl.lagrangePolynomialInterpolation([a.S0.h0w8[0],a.S0.h0w8[1],a.S0.h0w8[2],a.S0.h0w8[3],a.S0.h0w8[4],a.S0.h0w8[5],a.S0.h0w8[6],a.S0.h0w8[7]],r,o);if(s.degree()>7)throw new Error("R0 Polynomial is not well calculated");n&&n.info("··· Computing evaluation r0(y)");return s.evaluate(e.y)}(l,c,d,0,o,i);i&&i.info("> Computing r1(y)");const h=function(t,e,a,i,o,n){const l=o.Fr;n&&n.info("··· Computing T0(xi)");let r=l.mul(t.evaluations.ql,t.evaluations.a);r=l.add(r,l.mul(t.evaluations.qr,t.evaluations.b)),r=l.add(r,l.mul(t.evaluations.qm,l.mul(t.evaluations.a,t.evaluations.b))),r=l.add(r,l.mul(t.evaluations.qo,t.evaluations.c)),r=l.add(r,t.evaluations.qc),r=l.add(r,i),r=l.mul(r,e.invzh),n&&n.info("··· Computing C1(h_1ω_4^i) values");let s=[];for(let e=0;e<4;e++){s[e]=t.evaluations.a,s[e]=l.add(s[e],l.mul(a.S1.h1w4[e],t.evaluations.b));const i=l.square(a.S1.h1w4[e]);s[e]=l.add(s[e],l.mul(i,t.evaluations.c)),s[e]=l.add(s[e],l.mul(l.mul(i,a.S1.h1w4[e]),r))}const c=rl.lagrangePolynomialInterpolation([a.S1.h1w4[0],a.S1.h1w4[1],a.S1.h1w4[2],a.S1.h1w4[3]],s,o);if(c.degree()>3)throw new Error("R1 Polynomial is not well calculated");n&&n.info("··· Computing evaluation r1(y)");return c.evaluate(e.y)}(l,c,d,g,o,i);i&&i.info("> Computing r2(y)");const _=function(t,e,a,i,o,n,l){const r=n.Fr;l&&l.info("··· Computing T1(xi)");let s=r.sub(t.evaluations.z,r.one);s=r.mul(s,i),s=r.mul(s,e.invzh),l&&l.info("··· Computing T2(xi)");const c=r.mul(e.beta,e.xi),d=r.add(t.evaluations.a,r.add(c,e.gamma)),u=r.add(t.evaluations.b,r.add(r.mul(c,o.k1),e.gamma)),g=r.add(t.evaluations.c,r.add(r.mul(c,o.k2),e.gamma)),f=r.mul(d,r.mul(u,r.mul(g,t.evaluations.z))),h=r.add(t.evaluations.a,r.add(r.mul(e.beta,t.evaluations.s1),e.gamma)),_=r.add(t.evaluations.b,r.add(r.mul(e.beta,t.evaluations.s2),e.gamma)),p=r.add(t.evaluations.c,r.add(r.mul(e.beta,t.evaluations.s3),e.gamma)),m=r.mul(h,r.mul(_,r.mul(p,t.evaluations.zw)));let w=r.sub(f,m);w=r.mul(w,e.invzh),l&&l.info("··· Computing C2(h_2ω_3^i) values");let L=[];for(let e=0;e<3;e++)L[e]=r.add(t.evaluations.z,r.mul(a.S2.h2w3[e],s)),L[e]=r.add(L[e],r.mul(r.square(a.S2.h2w3[e]),w));l&&l.info("··· Computing C2(h_3ω_3^i) values");for(let e=0;e<3;e++)L[e+3]=r.add(t.evaluations.zw,r.mul(a.S2.h3w3[e],t.evaluations.t1w)),L[e+3]=r.add(L[e+3],r.mul(r.square(a.S2.h3w3[e]),t.evaluations.t2w));l&&l.info("··· Computing r2(xi)");const b=rl.lagrangePolynomialInterpolation([a.S2.h2w3[0],a.S2.h2w3[1],a.S2.h2w3[2],a.S2.h3w3[0],a.S2.h3w3[1],a.S2.h3w3[2]],L,n);if(b.degree()>5)throw new Error("R2 Polynomial is not well calculated");l&&l.info("··· Computing evaluation r2(y)");return b.evaluate(e.y)}(l,c,d,u[1],n,o,i);i&&i.info("> Computing F");const p=function(t,e,a,i,o){const n=t.G1,l=t.Fr;let r=l.sub(i.y,o.S0.h0w8[0]);for(let t=1;t<8;t++)r=l.mul(r,l.sub(i.y,o.S0.h0w8[t]));i.temp=r;let s=l.sub(i.y,o.S1.h1w4[0]);for(let t=1;t<4;t++)s=l.mul(s,l.sub(i.y,o.S1.h1w4[t]));let c=l.sub(i.y,o.S2.h2w3[0]);for(let t=1;t<3;t++)c=l.mul(c,l.sub(i.y,o.S2.h2w3[t]));for(let t=0;t<3;t++)c=l.mul(c,l.sub(i.y,o.S2.h3w3[t]));i.quotient1=l.mul(i.alpha,l.div(r,s)),i.quotient2=l.mul(l.square(i.alpha),l.div(r,c));let d=n.timesFr(e.polynomials.C1,i.quotient1),u=n.timesFr(e.polynomials.C2,i.quotient2);return n.add(a.C0,n.add(d,u))}(o,l,n,c,d);i&&i.info("> Computing E");const m=function(t,e,a,i,o,n,l){const r=t.G1,s=t.Fr;let c=s.mul(n,a.quotient1),d=s.mul(l,a.quotient2);return r.timesFr(r.one,s.add(o,s.add(c,d)))}(o,0,c,0,f,h,_);i&&i.info("> Computing J");const w=function(t,e,a){const i=t.G1;return i.timesFr(e.polynomials.W1,a.temp)}(o,l,c);i&&i.info("> Validate all evaluations with a pairing");const L=await async function(t,e,a,i,o,n,l){const r=t.G1;let s=r.timesFr(e.polynomials.W2,a.y);s=r.add(r.sub(r.sub(o,n),l),s);const c=t.G2.one,d=e.polynomials.W2,u=i.X_2;return await t.pairingEq(r.neg(s),c,d,u)}(o,l,c,n,p,m,w);return i&&(L?i.info("PROOF VERIFIED SUCCESSFULLY"):i.warn("Invalid Proof")),i&&i.info("FFLONK VERIFIER FINISHED"),L},exportSolidityVerifier:Rn,exportSolidityCallData:async function(t,e){const a=ml(e),i=ml(t),o=await ai(a.curve),n=o.G1,l=o.Fr;let r="";for(let t=0;t0) { const firstBase = G.fromRprLEM(bases, 0); - const r = crypto.randomBytes(4).readUInt32BE(0, true); + const r = misc.readUInt32BE(misc.getRandomBytes(4), 0); R1 = G.add(R1, G.timesScalar(lastBase, r)); R2 = G.add(R2, G.timesScalar(firstBase, r)); @@ -408,7 +405,7 @@ export default async function verify(tauFilename, logger) { const seed= new Array(8); for (let i=0; i<8; i++) { - seed[i] = crypto.randomBytes(4).readUInt32BE(0, true); + seed[i] = misc.readUInt32BE(misc.getRandomBytes(4), 0); } for (let p=0; p<= power; p ++) { diff --git a/src/zkey_verify_frominit.js b/src/zkey_verify_frominit.js index d27cc931..56a7fd4e 100644 --- a/src/zkey_verify_frominit.js +++ b/src/zkey_verify_frominit.js @@ -24,7 +24,6 @@ import Blake2b from "blake2b-wasm"; import * as misc from "./misc.js"; import { hashToG2 as hashToG2 } from "./keypair.js"; const sameRatio = misc.sameRatio; -import crypto from "crypto"; import {hashG1, hashPubKey} from "./zkey_utils.js"; import { Scalar, ChaCha, BigBuffer } from "ffjavascript"; @@ -76,7 +75,7 @@ export default async function phase2verifyFromInit(initFileName, pTauFileName, z } if (c.type == 1) { - const rng = misc.rngFromBeaconParams(c.beaconHash, c.numIterationsExp); + const rng = await misc.rngFromBeaconParams(c.beaconHash, c.numIterationsExp); const expected_prvKey = curve.Fr.fromRng(rng); const expected_g1_s = curve.G1.toAffine(curve.G1.fromRng(rng)); const expected_g1_sx = curve.G1.toAffine(curve.G1.timesFr(expected_g1_s, expected_prvKey)); @@ -252,9 +251,7 @@ export default async function phase2verifyFromInit(initFileName, pTauFileName, z const bases1 = await fd1.read(n*sG); const bases2 = await fd2.read(n*sG); - const scalars = new Uint8Array(4*n); - crypto.randomFillSync(scalars); - + const scalars = misc.getRandomBytes(4*n); const r1 = await G.multiExpAffine(bases1, scalars); const r2 = await G.multiExpAffine(bases2, scalars); @@ -285,7 +282,7 @@ export default async function phase2verifyFromInit(initFileName, pTauFileName, z const seed= new Array(8); for (let i=0; i<8; i++) { - seed[i] = crypto.randomBytes(4).readUInt32BE(0, true); + seed[i] = misc.readUInt32BE(misc.getRandomBytes(4), 0); } const rng = new ChaCha(seed); for (let i=0; i { curve = await getCurveFromName("bn128"); -// curve.Fr.s = 10; + // curve.Fr.s = 10; }); after( async () => { await curve.terminate(); From 2eef5d17d578d3bc1c510e9d9b6ba33e6e952b04 Mon Sep 17 00:00:00 2001 From: Blaine Bublitz Date: Thu, 18 May 2023 05:11:20 +0100 Subject: [PATCH 21/48] chore(ci): Add browser testing (#365) --- .github/workflows/tests.yml | 30 + browser_tests/package-lock.json | 1145 ++++++++++++++++++++++++++ browser_tests/package.json | 12 + browser_tests/test/groth16.html | 40 + browser_tests/test/launch-groth16.js | 44 + 5 files changed, 1271 insertions(+) create mode 100644 browser_tests/package-lock.json create mode 100644 browser_tests/package.json create mode 100644 browser_tests/test/groth16.html create mode 100644 browser_tests/test/launch-groth16.js diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml index fde309d2..6b8ba636 100644 --- a/.github/workflows/tests.yml +++ b/.github/workflows/tests.yml @@ -91,3 +91,33 @@ jobs: - name: Run tests run: 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b/browser_tests/test/launch-groth16.js new file mode 100644 index 00000000..fd6323ea --- /dev/null +++ b/browser_tests/test/launch-groth16.js @@ -0,0 +1,44 @@ +import puppeteer from "puppeteer"; +import st from "st"; +import http from "http"; +import url from "url"; + +const projectRoot = new URL("../..", import.meta.url); + +const mount = st({ path: url.fileURLToPath(projectRoot), passthrough: true }); + +const server = http + .createServer((req, res) => { + mount(req, res, () => res.end()); + }) + .listen(1337); + +const browser = await puppeteer.launch({ + headless: "new", + args: [ + // Necessary to have WebCrypto on localhost + "--allow-insecure-localhost", + // Necessary to download the PTAU file from AWS within the tests + "--disable-web-security" + ], +}); +const page = await browser.newPage(); + +page.on("console", (msg) => { + if (msg.type === "assert") { + throw new Error(msg.text()); + } else { + console.log(msg.text()); + } +}); + +page.on("pageerror", (err) => { + throw err; +}); + +await page.exposeFunction("shutdown", async () => { + await browser.close(); + server.close(); +}); + +await page.goto("http://localhost:1337/browser_tests/test/groth16.html"); From e70271b30a6392a34f664e6bececddad284c8854 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Roger=20Taul=C3=A9=20Buxadera?= <55488871+RogerTaule@users.noreply.github.com> Date: Thu, 18 May 2023 17:02:13 +0200 Subject: [PATCH 22/48] Feat lagrange verifier (#368) * update fflonk SC change memory->calldata * Optimizing Lagrange calculation * Fixing Fflonk when having multiple public inputs --------- Co-authored-by: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> --- .../test/smart_contracts.test.js | 10 +- src/fflonk_export_calldata.js | 39 +- src/fflonk_prove.js | 108 +- src/fflonk_verify.js | 154 +-- templates/verifier_fflonk.sol.ejs | 650 +++++++----- test/fflonk/verifier.sol | 939 +++++++++++++----- 6 files changed, 1273 insertions(+), 627 deletions(-) diff --git a/smart_contract_tests/test/smart_contracts.test.js b/smart_contract_tests/test/smart_contracts.test.js index fce30365..a7cee55f 100644 --- a/smart_contract_tests/test/smart_contracts.test.js +++ b/smart_contract_tests/test/smart_contracts.test.js @@ -142,9 +142,8 @@ describe("Smart contracts test suite", function () { // Verifiy the proof in the smart contract const { evaluations, polynomials } = proofJson; - const arrayStrings = Array(24).fill("bytes32"); - const proof = ethers.utils.defaultAbiCoder.encode( - arrayStrings, + + const proof = [ ethers.utils.hexZeroPad(ethers.BigNumber.from(polynomials.C1[0]).toHexString(), 32), ethers.utils.hexZeroPad(ethers.BigNumber.from(polynomials.C1[1]).toHexString(), 32), @@ -170,9 +169,8 @@ describe("Smart contracts test suite", function () { ethers.utils.hexZeroPad(ethers.BigNumber.from(evaluations.t1w).toHexString(), 32), ethers.utils.hexZeroPad(ethers.BigNumber.from(evaluations.t2w).toHexString(), 32), ethers.utils.hexZeroPad(ethers.BigNumber.from(evaluations.inv).toHexString(), 32), - ], - ); + ]; expect(await verifierContract.verifyProof(proof, publicInputs)).to.be.equal(true); }); -}); \ No newline at end of file +}); diff --git a/src/fflonk_export_calldata.js b/src/fflonk_export_calldata.js index 2063fddd..0585e8db 100644 --- a/src/fflonk_export_calldata.js +++ b/src/fflonk_export_calldata.js @@ -29,7 +29,7 @@ function i2hex(i) { function p256(n) { let nstr = n.toString(16); while (nstr.length < 64) nstr = "0" + nstr; - nstr = `"0x${nstr}"`; + nstr = `0x${nstr}`; return nstr; } @@ -47,30 +47,15 @@ export default async function fflonkExportCallData(_pub, _proof) { inputs = inputs + p256(pub[i]); } - const proofBuff = new Uint8Array(G1.F.n8 * 2 * 4 + Fr.n8 * 16); - - G1.toRprUncompressed(proofBuff, 0, G1.e(proof.polynomials.C1)); - G1.toRprUncompressed(proofBuff, G1.F.n8 * 2, G1.e(proof.polynomials.C2)); - G1.toRprUncompressed(proofBuff, G1.F.n8 * 4, G1.e(proof.polynomials.W1)); - G1.toRprUncompressed(proofBuff, G1.F.n8 * 6, G1.e(proof.polynomials.W2)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8, Fr.e(proof.evaluations.ql)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8, Fr.e(proof.evaluations.qr)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 2, Fr.e(proof.evaluations.qm)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 3, Fr.e(proof.evaluations.qo)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 4, Fr.e(proof.evaluations.qc)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 5, Fr.e(proof.evaluations.s1)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 6, Fr.e(proof.evaluations.s2)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 7, Fr.e(proof.evaluations.s3)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 8, Fr.e(proof.evaluations.a)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 9, Fr.e(proof.evaluations.b)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 10, Fr.e(proof.evaluations.c)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 11, Fr.e(proof.evaluations.z)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 12, Fr.e(proof.evaluations.zw)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 13, Fr.e(proof.evaluations.t1w)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 14, Fr.e(proof.evaluations.t2w)); - Fr.toRprBE(proofBuff, G1.F.n8 * 8 + Fr.n8 * 15, Fr.e(proof.evaluations.inv)); - - const proofHex = Array.from(proofBuff).map(i2hex).join(""); - - return `0x${proofHex},[${inputs}]`; + return `[${p256(proof.polynomials.C1[0])}, ${p256(proof.polynomials.C1[1])},` + + `${p256(proof.polynomials.C2[0])},${p256(proof.polynomials.C2[1])},` + + `${p256(proof.polynomials.W1[0])},${p256(proof.polynomials.W1[1])},` + + `${p256(proof.polynomials.W2[0])},${p256(proof.polynomials.W2[1])},` + + `${p256(proof.evaluations.ql)},${p256(proof.evaluations.qr)},${p256(proof.evaluations.qm)},` + + `${p256(proof.evaluations.qo)},${p256(proof.evaluations.qc)},${p256(proof.evaluations.s1)},` + + `${p256(proof.evaluations.s2)},${p256(proof.evaluations.s3)},${p256(proof.evaluations.a)},` + + `${p256(proof.evaluations.b)},${p256(proof.evaluations.c)},${p256(proof.evaluations.z)},` + + `${p256(proof.evaluations.zw)},${p256(proof.evaluations.t1w)},${p256(proof.evaluations.t2w)},` + + `${p256(proof.evaluations.inv)}],` + + `[${inputs}]`; } diff --git a/src/fflonk_prove.js b/src/fflonk_prove.js index b57e2428..c0dbafcd 100644 --- a/src/fflonk_prove.js +++ b/src/fflonk_prove.js @@ -1190,17 +1190,11 @@ export default async function fflonkProve(zkeyFileName, witnessFileName, logger) // toInverse.denH1 & toInverse.denH2 -> Computed in round5, computeL() // · denominator needed in the verifier when computing L_i^{S0}(X), L_i^{S1}(X) and L_i^{S2}(X) - for (let i = 0; i < 8; i++) { - toInverse["LiS0_" + (i + 1)] = computeLiS0(i); - } + computeLiS0(toInverse, roots.S0.h0w8, challenges.y, curve); - for (let i = 0; i < 4; i++) { - toInverse["LiS1_" + (i + 1)] = computeLiS1(i); - } + computeLiS1(toInverse, roots.S1.h1w4, challenges.y, curve); - for (let i = 0; i < 6; i++) { - toInverse["LiS2_" + (i + 1)] = computeLiS2(i); - } + computeLiS2(toInverse, roots.S2.h2w3, roots.S2.h3w3, challenges.y, challenges.xi, challenges.xiw, curve); // · L_i i=1 to num public inputs, needed in step 6 and 7 of the verifier to compute L_1(xi) and PI(xi) const size = Math.max(1, zkey.nPublic); @@ -1208,52 +1202,84 @@ export default async function fflonkProve(zkeyFileName, witnessFileName, logger) let w = Fr.one; for (let i = 0; i < size; i++) { toInverse["Li_" + (i + 1)] = Fr.mul(Fr.e(zkey.domainSize), Fr.sub(challenges.xi, w)); - - w = Fr.mul(w, zkey.w); + w = Fr.mul(w, Fr.w[zkey.power]); } let mulAccumulator = Fr.one; for (const element of Object.values(toInverse)) { - mulAccumulator = Fr.mul(mulAccumulator, element); + if(Array.isArray(element)) { + for (const subElement of element) { + mulAccumulator = Fr.mul(mulAccumulator, subElement); + } + } else { + mulAccumulator = Fr.mul(mulAccumulator, element); + } } return Fr.inv(mulAccumulator); - function computeLiS0(i) { - // Compute L_i^{(S0)}(y) - let idx = i; - let den = Fr.one; - for (let j = 0; j < 7; j++) { - idx = (idx + 1) % 8; - - den = Fr.mul(den, Fr.sub(roots.S0.h0w8[i], roots.S0.h0w8[idx])); + + function computeLiS0(toInverse, roots, x, curve) { + const Fr = curve.Fr; + const len = roots.length; + + const den1 = Fr.mul(Fr.e(len), Fr.exp(roots[0], len - 2)); + + const Li = []; + for (let i = 0; i < len; i++) { + const den2 = roots[((len - 1) * i) % len]; + const den3 = Fr.sub(x, roots[i]); + + toInverse[["LiS0_" + (i + 1)]] = Fr.mul(Fr.mul(den1, den2), den3); } - return den; + + return Li; } - function computeLiS1(i) { - // Compute L_i^{(S1)}(y) - let idx = i; - let den = Fr.one; - for (let j = 0; j < 3; j++) { - idx = (idx + 1) % 4; + function computeLiS1(toInverse, roots, x, curve) { + const Fr = curve.Fr; + const len = roots.length; + + const den1 = Fr.mul(Fr.e(len), Fr.exp(roots[0], len - 2)); + + const Li = []; + for (let i = 0; i < len; i++) { + const den2 = roots[((len - 1) * i) % len]; + const den3 = Fr.sub(x, roots[i]); + + toInverse[["LiS1_" + (i + 1)]] = Fr.mul(Fr.mul(den1, den2), den3); - den = Fr.mul(den, Fr.sub(roots.S1.h1w4[i], roots.S1.h1w4[idx])); } - return den; + + return Li; } - function computeLiS2(i) { - // Compute L_i^{(S1)}(y) - let idx = i; - let den = Fr.one; - for (let j = 0; j < 5; j++) { - idx = (idx + 1) % 6; - - const root1 = i < 3 ? roots.S2.h2w3[i] : roots.S2.h3w3[i - 3]; - const root2 = idx < 3 ? roots.S2.h2w3[idx] : roots.S2.h3w3[idx - 3]; - den = Fr.mul(den, Fr.sub(root1, root2)); + function computeLiS2(toInverse, S2, S2p, value, xi, xiw, curve) { + const Fr = curve.Fr; + + const Li = []; + + const _3h2 = Fr.mul(Fr.e(3), S2[0]); + const xisubxiw = Fr.sub(xi, xiw); + let den1 = Fr.mul(_3h2, xisubxiw); + for (let i = 0; i < 3; i++) { + const den2 = S2[2 * i % 3]; + const den3 = Fr.sub(value, S2[i]); + + toInverse[["LiS2_" + (i + 1)]] = Fr.mul(den1,Fr.mul(den2, den3)); + + } + + const _3h3 = Fr.mul(Fr.e(3), S2p[0]); + const xiwsubxi = Fr.sub(xiw, xi); + den1 = Fr.mul(_3h3, xiwsubxi); + for (let i = 0; i < 3; i++) { + const den2 = S2p[2 * i % 3]; + const den3 = Fr.sub(value, S2p[i]); + + toInverse[["LiS2_" + (i + 1 + 3)]] = Fr.mul(den1,Fr.mul(den2, den3)); } - return den; + + return Li; } } -} \ No newline at end of file +} diff --git a/src/fflonk_verify.js b/src/fflonk_verify.js index e8809836..9c9ec58d 100644 --- a/src/fflonk_verify.js +++ b/src/fflonk_verify.js @@ -21,7 +21,6 @@ import * as curves from "./curves.js"; import { BigBuffer, utils } from "ffjavascript"; import { Proof } from "./proof.js"; import { Keccak256Transcript } from "./Keccak256Transcript.js"; -import { Polynomial } from "./polynomial/polynomial.js"; const { unstringifyBigInts } = utils; @@ -92,7 +91,7 @@ export default async function fflonkVerify(_vk_verifier, _publicSignals, _proof, // STEP 8 - Compute polynomial r0 ∈ F_{<4}[X] if (logger) logger.info("> Computing r0(y)"); - const r0 = computeR0(proof, challenges, roots, pi, curve, logger); + const r0 = computeR0(proof, challenges, roots, curve, logger); // STEP 9 - Compute polynomial r1 ∈ F_{<4}[X] if (logger) logger.info("> Computing r1(y)"); @@ -231,6 +230,7 @@ function computeChallenges(curve, proof, vk, publicSignals, logger) { // Compute xi = xi_seeder^12 challenges.xi = Fr.mul(Fr.square(roots.S2.h2w3[0]), roots.S2.h2w3[0]); + challenges.xiw = Fr.mul(challenges.xi, Fr.w[vk.power]); challenges.xiN = challenges.xi; vk.domainSize = 1; @@ -310,15 +310,17 @@ function calculatePI(curve, publicSignals, lagrangeEvals) { return pi; } -function computeR0(proof, challenges, roots, pi, curve, logger) { +function computeR0(proof, challenges, roots, curve, logger) { const Fr = curve.Fr; + const Li = computeLagrangeLiSi(roots.S0.h0w8, challenges.y, challenges.xi, curve); + // r0(y) = ∑_1^8 C_0(h_0 ω_8^{i-1}) L_i(y). To this end we need to compute // Compute the 8 C0 values - if (logger) logger.info("··· Computing C0(h_0ω_8^i) values"); + if (logger) logger.info("··· Computing r0(y)"); - let c0Values = []; + let res = Fr.zero; for (let i = 0; i < 8; i++) { let coefValues = []; coefValues[1] = roots.S0.h0w8[i]; @@ -326,34 +328,25 @@ function computeR0(proof, challenges, roots, pi, curve, logger) { coefValues[j] = Fr.mul(coefValues[j - 1], roots.S0.h0w8[i]); } - c0Values[i] = Fr.add(proof.evaluations.ql, Fr.mul(proof.evaluations.qr, coefValues[1])); - c0Values[i] = Fr.add(c0Values[i], Fr.mul(proof.evaluations.qo, coefValues[2])); - c0Values[i] = Fr.add(c0Values[i], Fr.mul(proof.evaluations.qm, coefValues[3])); - c0Values[i] = Fr.add(c0Values[i], Fr.mul(proof.evaluations.qc, coefValues[4])); - c0Values[i] = Fr.add(c0Values[i], Fr.mul(proof.evaluations.s1, coefValues[5])); - c0Values[i] = Fr.add(c0Values[i], Fr.mul(proof.evaluations.s2, coefValues[6])); - c0Values[i] = Fr.add(c0Values[i], Fr.mul(proof.evaluations.s3, coefValues[7])); - } - - // Interpolate a polynomial with the points computed previously - const R0 = Polynomial.lagrangePolynomialInterpolation( - [roots.S0.h0w8[0], roots.S0.h0w8[1], roots.S0.h0w8[2], roots.S0.h0w8[3], - roots.S0.h0w8[4], roots.S0.h0w8[5], roots.S0.h0w8[6], roots.S0.h0w8[7]], - c0Values, curve); + let c0 = Fr.add(proof.evaluations.ql, Fr.mul(proof.evaluations.qr, coefValues[1])); + c0 = Fr.add(c0, Fr.mul(proof.evaluations.qo, coefValues[2])); + c0 = Fr.add(c0, Fr.mul(proof.evaluations.qm, coefValues[3])); + c0 = Fr.add(c0, Fr.mul(proof.evaluations.qc, coefValues[4])); + c0 = Fr.add(c0, Fr.mul(proof.evaluations.s1, coefValues[5])); + c0 = Fr.add(c0, Fr.mul(proof.evaluations.s2, coefValues[6])); + c0 = Fr.add(c0, Fr.mul(proof.evaluations.s3, coefValues[7])); - // Check the degree of r1(X) < 4 - if (R0.degree() > 7) { - throw new Error("R0 Polynomial is not well calculated"); + res = Fr.add(res, Fr.mul(c0, Li[i])); } - // Evaluate the polynomial in challenges.y - if (logger) logger.info("··· Computing evaluation r0(y)"); - return R0.evaluate(challenges.y); + return res; } function computeR1(proof, challenges, roots, pi, curve, logger) { const Fr = curve.Fr; + const Li = computeLagrangeLiSi(roots.S1.h1w4, challenges.y, challenges.xi, curve); + // r1(y) = ∑_1^4 C_1(h_1 ω_4^{i-1}) L_i(y). To this end we need to compute // Z1 = {C1(h_1}, C1(h_1 ω_4), C1(h_1 ω_4^2), C1(h_1 ω_4^3)} // where C_1(h_1 ω_4^{i-1}) = eval.a + h_1 ω_4^i eval.b + (h_1 ω_4^i)^2 eval.c + (h_1 ω_4^i)^3 T0(xi), @@ -372,33 +365,25 @@ function computeR1(proof, challenges, roots, pi, curve, logger) { // Compute the 4 C1 values if (logger) logger.info("··· Computing C1(h_1ω_4^i) values"); - let c1Values = []; + let res = Fr.zero; for (let i = 0; i < 4; i++) { - c1Values[i] = proof.evaluations.a; - c1Values[i] = Fr.add(c1Values[i], Fr.mul(roots.S1.h1w4[i], proof.evaluations.b)); + let c1 = proof.evaluations.a; + c1 = Fr.add(c1, Fr.mul(roots.S1.h1w4[i], proof.evaluations.b)); const h1w4Squared = Fr.square(roots.S1.h1w4[i]); - c1Values[i] = Fr.add(c1Values[i], Fr.mul(h1w4Squared, proof.evaluations.c)); - c1Values[i] = Fr.add(c1Values[i], Fr.mul(Fr.mul(h1w4Squared, roots.S1.h1w4[i]), t0)); - } - - // Interpolate a polynomial with the points computed previously - const R1 = Polynomial.lagrangePolynomialInterpolation( - [roots.S1.h1w4[0], roots.S1.h1w4[1], roots.S1.h1w4[2], roots.S1.h1w4[3]], - c1Values, curve); + c1 = Fr.add(c1, Fr.mul(h1w4Squared, proof.evaluations.c)); + c1 = Fr.add(c1, Fr.mul(Fr.mul(h1w4Squared, roots.S1.h1w4[i]), t0)); - // Check the degree of r1(X) < 4 - if (R1.degree() > 3) { - throw new Error("R1 Polynomial is not well calculated"); + res = Fr.add(res, Fr.mul(c1, Li[i])); } - // Evaluate the polynomial in challenges.y - if (logger) logger.info("··· Computing evaluation r1(y)"); - return R1.evaluate(challenges.y); + return res; } function computeR2(proof, challenges, roots, lagrange1, vk, curve, logger) { const Fr = curve.Fr; + const LiS2 = computeLagrangeLiS2([roots.S2.h2w3, roots.S2.h3w3], challenges.y, challenges.xi, challenges.xiw, curve); + // r2(y) = ∑_1^3 C_2(h_2 ω_3^{i-1}) L_i(y) + ∑_1^3 C_2(h_3 ω_3^{i-1}) L_{i+3}(y). To this end we need to compute // Z2 = {[C2(h_2}, C2(h_2 ω_3), C2(h_2 ω_3^2)], [C2(h_3}, C2(h_3 ω_3), C2(h_3 ω_3^2)]} // where C_2(h_2 ω_3^{i-1}) = eval.z + h_2 ω_2^i T1(xi) + (h_2 ω_3^i)^2 T2(xi), @@ -431,33 +416,23 @@ function computeR2(proof, challenges, roots, lagrange1, vk, curve, logger) { // Compute the 6 C2 values if (logger) logger.info("··· Computing C2(h_2ω_3^i) values"); - let c2Values = []; + let res = Fr.zero; for (let i = 0; i < 3; i++) { - c2Values[i] = Fr.add(proof.evaluations.z, Fr.mul(roots.S2.h2w3[i], t1)); - c2Values[i] = Fr.add(c2Values[i], Fr.mul(Fr.square(roots.S2.h2w3[i]), t2)); + let c2 = Fr.add(proof.evaluations.z, Fr.mul(roots.S2.h2w3[i], t1)); + c2 = Fr.add(c2, Fr.mul(Fr.square(roots.S2.h2w3[i]), t2)); + + res = Fr.add(res, Fr.mul(c2, LiS2[i])); } if (logger) logger.info("··· Computing C2(h_3ω_3^i) values"); for (let i = 0; i < 3; i++) { - c2Values[i + 3] = Fr.add(proof.evaluations.zw, Fr.mul(roots.S2.h3w3[i], proof.evaluations.t1w)); - c2Values[i + 3] = Fr.add(c2Values[i + 3], Fr.mul(Fr.square(roots.S2.h3w3[i]), proof.evaluations.t2w)); - } - - // Interpolate a polynomial with the points computed previously - if (logger) logger.info("··· Computing r2(xi)"); - const R2 = Polynomial.lagrangePolynomialInterpolation( - [roots.S2.h2w3[0], roots.S2.h2w3[1], roots.S2.h2w3[2], - roots.S2.h3w3[0], roots.S2.h3w3[1], roots.S2.h3w3[2]], - c2Values, curve); + let c2 = Fr.add(proof.evaluations.zw, Fr.mul(roots.S2.h3w3[i], proof.evaluations.t1w)); + c2 = Fr.add(c2, Fr.mul(Fr.square(roots.S2.h3w3[i]), proof.evaluations.t2w)); - // Check the degree of r2(X) < 6 - if (R2.degree() > 5) { - throw new Error("R2 Polynomial is not well calculated"); + res = Fr.add(res, Fr.mul(c2, LiS2[i + 3])); } - // Evaluate the polynomial in challenges.y - if (logger) logger.info("··· Computing evaluation r2(y)"); - return R2.evaluate(challenges.y); + return res; } function computeF(curve, proof, vk, challenges, roots) { @@ -520,4 +495,59 @@ async function isValidPairing(curve, proof, challenges, vk, F, E, J) { const B2 = vk.X_2; return await curve.pairingEq(G1.neg(A1), A2, B1, B2); -} \ No newline at end of file +} + + +export function computeLagrangeLiSi(roots, x, xi, curve) { + const Fr = curve.Fr; + const len = roots.length; + + const num = Fr.sub(Fr.exp(x, len), xi); + const den1 = Fr.mul(Fr.e(len), Fr.exp(roots[0], len - 2)); + + const Li = []; + for (let i = 0; i < len; i++) { + const den2 = roots[((len - 1) * i) % len]; + const den3 = Fr.sub(x, roots[i]); + + Li[i] = Fr.div(num, Fr.mul(Fr.mul(den1, den2), den3)); + } + + return Li; +} + +export function computeLagrangeLiS2(roots, value, xi0, xi1, curve) { + const Fr = curve.Fr; + + const Li = []; + + const len = roots[0].length; + const n = len * roots.length; + + const num1 = Fr.exp(value, n); + const num2 = Fr.mul(Fr.add(xi0, xi1), Fr.exp(value, len)); + const num3 = Fr.mul(xi0, xi1); + const num = Fr.add(Fr.sub(num1, num2), num3); + + let den1 = Fr.mul(Fr.mul(Fr.e(len), roots[0][0]), Fr.sub(xi0, xi1)); + for (let i = 0; i < len; i++) { + const den2 = roots[0][(len - 1) * i % len]; + const den3 = Fr.sub(value, roots[0][i]); + + const den = Fr.mul(den1,Fr.mul(den2, den3)); + + Li[i] = Fr.div(num, den); + } + + den1 = Fr.mul(Fr.mul(Fr.e(len), roots[1][0]), Fr.sub(xi1, xi0)); + for (let i = 0; i < len; i++) { + const den2 = roots[1][(len - 1) * i % len]; + const den3 = Fr.sub(value, roots[1][i]); + + const den = Fr.mul(den1,Fr.mul(den2, den3)); + + Li[i + len] = Fr.div(num, den); + } + + return Li; +} diff --git a/templates/verifier_fflonk.sol.ejs b/templates/verifier_fflonk.sol.ejs index 3183f694..a87012c3 100644 --- a/templates/verifier_fflonk.sol.ejs +++ b/templates/verifier_fflonk.sol.ejs @@ -70,32 +70,32 @@ contract FflonkVerifier { uint256 constant G2y1 = 8495653923123431417604973247489272438418190587263600148770280649306958101930; uint256 constant G2y2 = 4082367875863433681332203403145435568316851327593401208105741076214120093531; - // Proof data - // Byte offset of every parameter in `bytes memory proof` + // Proof calldata + // Byte offset of every parameter of the calldata // Polynomial commitments - uint16 constant pC1 = 32; // [C1]_1 - uint16 constant pC2 = 96; // [C2]_1 - uint16 constant pW1 = 160; // [W]_1 - uint16 constant pW2 = 224; // [W']_1 + uint16 constant pC1 = 4 + 0; // [C1]_1 + uint16 constant pC2 = 4 + 32*2; // [C2]_1 + uint16 constant pW1 = 4 + 32*4; // [W]_1 + uint16 constant pW2 = 4 + 32*6; // [W']_1 // Opening evaluations - uint16 constant pEval_ql = 288; // q_L(xi) - uint16 constant pEval_qr = 320; // q_R(xi) - uint16 constant pEval_qm = 352; // q_M(xi) - uint16 constant pEval_qo = 384; // q_O(xi) - uint16 constant pEval_qc = 416; // q_C(xi) - uint16 constant pEval_s1 = 448; // S_{sigma_1}(xi) - uint16 constant pEval_s2 = 480; // S_{sigma_2}(xi) - uint16 constant pEval_s3 = 512; // S_{sigma_3}(xi) - uint16 constant pEval_a = 544; // a(xi) - uint16 constant pEval_b = 576; // b(xi) - uint16 constant pEval_c = 608; // c(xi) - uint16 constant pEval_z = 640; // z(xi) - uint16 constant pEval_zw = 672; // z_omega(xi) - uint16 constant pEval_t1w = 704; // T_1(xi omega) - uint16 constant pEval_t2w = 736; // T_2(xi omega) - uint16 constant pEval_inv = 768; // inv(batch) sent by the prover to avoid any inverse calculation to save gas, - // we check the correctness of the inv(batch) by computing batch - // and checking inv(batch) * batch == 1 + uint16 constant pEval_ql = 4 + 32*8; // q_L(xi) + uint16 constant pEval_qr = 4 + 32*9; // q_R(xi) + uint16 constant pEval_qm = 4 + 32*10; // q_M(xi) + uint16 constant pEval_qo = 4 + 32*11; // q_O(xi) + uint16 constant pEval_qc = 4 + 32*12; // q_C(xi) + uint16 constant pEval_s1 = 4 + 32*13; // S_{sigma_1}(xi) + uint16 constant pEval_s2 = 4 + 32*14; // S_{sigma_2}(xi) + uint16 constant pEval_s3 = 4 + 32*15; // S_{sigma_3}(xi) + uint16 constant pEval_a = 4 + 32*16; // a(xi) + uint16 constant pEval_b = 4 + 32*17; // b(xi) + uint16 constant pEval_c = 4 + 32*18; // c(xi) + uint16 constant pEval_z = 4 + 32*19; // z(xi) + uint16 constant pEval_zw = 4 + 32*20; // z_omega(xi) + uint16 constant pEval_t1w = 4 + 32*21; // T_1(xi omega) + uint16 constant pEval_t2w = 4 + 32*22; // T_2(xi omega) + uint16 constant pEval_inv = 4 + 32*23; // inv(batch) sent by the prover to avoid any inverse calculation to save gas, + // we check the correctness of the inv(batch) by computing batch + // and checking inv(batch) * batch == 1 // Memory data // Challenges @@ -152,58 +152,56 @@ contract FflonkVerifier { uint16 constant pLiS1Inv = <%= 224 + 32 * 34 + 64 * 4 %>; // Reserve 4 * 32 bytes to compute r_1(X) uint16 constant pLiS2Inv = <%= 224 + 32 * 38 + 64 * 4 %>; // Reserve 6 * 32 bytes to compute r_2(X) // Lagrange evaluations - <% for (let i = 1; i <= Math.max(nPublic, 1); i++) { - %>uint16 constant pEval_l<%=i%> = <%= 224 + 32 * (43 + i) + 64 * 4 %>; - <% } %> <% let pLastMem = 224 + 32 * (44 + Math.max(nPublic,1)) + 64 * 4 %> - uint16 constant lastMem = <%=pLastMem%>; - - function verifyProof(bytes memory proof, uint256[<%= nPublic %>] calldata pubSignals) public view returns (bool) { + <% for (let i = 1; i <= Math.max(nPublic, 1); i++) { %> + uint16 constant pEval_l<%=i%> = <%= 224 + 32 * (43 + i) + 64 * 4 %>; + <% } %> + <% let pLastMem = 224 + 32 * (44 + Math.max(nPublic,1)) + 64 * 4 %> + uint16 constant lastMem = <%= pLastMem %>; + +<% const inversionArray = ["pZhInv", "pDenH1", "pDenH2", "pLiS0Inv", "add(pLiS0Inv, 32)", "add(pLiS0Inv, 64)", "add(pLiS0Inv, 96)", + "add(pLiS0Inv, 128)", "add(pLiS0Inv, 160)", "add(pLiS0Inv, 192)", "add(pLiS0Inv, 224)", "pLiS1Inv", "add(pLiS1Inv, 32)", + "add(pLiS1Inv, 64)", "add(pLiS1Inv, 96)", "pLiS2Inv", "add(pLiS2Inv, 32)", "add(pLiS2Inv, 64)", "add(pLiS2Inv, 96)", + "add(pLiS2Inv, 128)", "add(pLiS2Inv, 160)"] -%> +<% for (let i=1; i<=Math.max(nPublic, 1); i++) { -%> +<% inversionArray.push(`pEval_l${i}`); -%> +<% } -%> + + function verifyProof(bytes32[24] calldata proof, uint256[<%- Math.max(nPublic, 1) %>] calldata pubSignals) public view returns (bool) { assembly { // Computes the inverse of an array of values // See https://vitalik.ca/general/2018/07/21/starks_part_3.html in section where explain fields operations - // To save the inverse to be computed on chain the prover sends the inverse as an evaluation in proof.eval_inv - function inverseArray(pProof, pVals, n) { + // To save the inverse to be computed on chain the prover sends the inverse as an evaluation in commits.eval_inv + function inverseArray(pMem) { + let pAux := mload(0x40) // Point to the next free position - let pIn := pVals - let lastPIn := add(pVals, mul(n, 32)) // Read n elemnts - let acc := mload(pIn) // Read the first element - pIn := add(pIn, 32) // Point to the second element - - for { } lt(pIn, lastPIn) { - pAux := add(pAux, 32) - pIn := add(pIn, 32) - } - { - mstore(pAux, acc) - acc := mulmod(acc, mload(pIn), q) - } + let acc := mload(add(pMem,<%- inversionArray[0] %>)) // Read the first element + mstore(pAux, acc) + +<% for(let i = 1; i < inversionArray.length; ++i) { -%> + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, <%- inversionArray[i] %>)), q) + mstore(pAux, acc) + +<% } -%> - let inv := mload(add(pProof, pEval_inv)) + let inv := calldataload(pEval_inv) // Before using the inverse sent by the prover the verifier checks inv(batch) * batch === 1 if iszero(eq(1, mulmod(acc, inv, q))) { mstore(0, 0) - return(0, 0x20) + return(0,0x20) } acc := inv - // At this point pAux point to the next free position we substract 1 to point to the last used +<% for(let i = inversionArray.length - 1; i > 0; --i) { -%> pAux := sub(pAux, 32) - // pIn points to the n+1 element, we substract to point to n - pIn := sub(pIn, 32) - lastPIn := pVals // We don't process the first element - for { } gt(pIn, lastPIn) { - pAux := sub(pAux, 32) - pIn := sub(pIn, 32) - } - { - inv := mulmod(acc, mload(pAux), q) - acc := mulmod(acc, mload(pIn), q) - mstore(pIn, inv) - } - // pIn points to first element, we just set it. - mstore(pIn, acc) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, <%- inversionArray[i] %>)), q) + mstore(add(pMem, <%- inversionArray[i] %>), inv) +<% } -%> + + mstore(add(pMem, <%- inversionArray[0] %>), acc) } function checkField(v) { @@ -214,8 +212,8 @@ contract FflonkVerifier { } function checkPointBelongsToBN128Curve(p) { - let x := mload(p) - let y := mload(add(p, 32)) + let x := calldataload(p) + let y := calldataload(add(p, 32)) // Check that the point is on the curve // y^2 = x^3 + 3 @@ -229,58 +227,54 @@ contract FflonkVerifier { } // Validate all the evaluations sent by the prover ∈ F - function checkInput(pProof) { - if iszero(eq(mload(pProof), 768)) { - mstore(0, 0) - return(0, 0x20) - } - + function checkInput() { // Check proof commitments fullfill bn128 curve equation Y^2 = X^3 + 3 - checkPointBelongsToBN128Curve(add(pProof, pC1)) - checkPointBelongsToBN128Curve(add(pProof, pC2)) - checkPointBelongsToBN128Curve(add(pProof, pW1)) - checkPointBelongsToBN128Curve(add(pProof, pW2)) - - checkField(mload(add(pProof, pEval_ql))) - checkField(mload(add(pProof, pEval_qr))) - checkField(mload(add(pProof, pEval_qm))) - checkField(mload(add(pProof, pEval_qo))) - checkField(mload(add(pProof, pEval_qc))) - checkField(mload(add(pProof, pEval_s1))) - checkField(mload(add(pProof, pEval_s2))) - checkField(mload(add(pProof, pEval_s3))) - checkField(mload(add(pProof, pEval_a))) - checkField(mload(add(pProof, pEval_b))) - checkField(mload(add(pProof, pEval_c))) - checkField(mload(add(pProof, pEval_z))) - checkField(mload(add(pProof, pEval_zw))) - checkField(mload(add(pProof, pEval_t1w))) - checkField(mload(add(pProof, pEval_t2w))) - checkField(mload(add(pProof, pEval_inv))) + checkPointBelongsToBN128Curve(pC1) + checkPointBelongsToBN128Curve(pC2) + checkPointBelongsToBN128Curve(pW1) + checkPointBelongsToBN128Curve(pW2) + + checkField(calldataload(pEval_ql)) + checkField(calldataload(pEval_qr)) + checkField(calldataload(pEval_qm)) + checkField(calldataload(pEval_qo)) + checkField(calldataload(pEval_qc)) + checkField(calldataload(pEval_s1)) + checkField(calldataload(pEval_s2)) + checkField(calldataload(pEval_s3)) + checkField(calldataload(pEval_a)) + checkField(calldataload(pEval_b)) + checkField(calldataload(pEval_c)) + checkField(calldataload(pEval_z)) + checkField(calldataload(pEval_zw)) + checkField(calldataload(pEval_t1w)) + checkField(calldataload(pEval_t2w)) + checkField(calldataload(pEval_inv)) // Points are checked in the point operations precompiled smart contracts } - function computeChallenges(pProof, pMem, pPublic) { + function computeChallenges(pMem, pPublic) { // Compute challenge.beta & challenge.gamma mstore(add(pMem, <%= pLastMem %> ), C0x) mstore(add(pMem, <%= pLastMem + 32 %> ), C0y) mstore(add(pMem, <%= pLastMem + 64 %>), calldataload(pPublic)) - <%for (let i=1; imstore(add(pMem, <%= pLastMem + 64 + i * 32 %> ), calldataload(add(pPublic, <%= i * 32 %>))) + <%for (let i=1; i + mstore(add(pMem, <%= pLastMem + 64 + i * 32 %> ), calldataload(add(pPublic, <%= i * 32 %>))) <%}%> + - mstore(add(pMem, <%= pLastMem + nPublic * 32 + 64 %> ), mload(add(pProof, pC1))) - mstore(add(pMem, <%= pLastMem + nPublic * 32 + 96 %> ), mload(add(pProof, add(pC1, 32)))) + mstore(add(pMem, <%= pLastMem + nPublic * 32 + 64 %> ), calldataload(pC1)) + mstore(add(pMem, <%= pLastMem + nPublic * 32 + 96 %> ), calldataload(add(pC1, 32))) mstore(add(pMem, pBeta), mod(keccak256(add(pMem, lastMem), <%= nPublic * 32 + 128 %>), q)) mstore(add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) // Get xiSeed & xiSeed2 mstore(add(pMem, lastMem), mload(add(pMem, pGamma))) - mstore(add(pMem, <%= pLastMem + 32 %>), mload(add(pProof, pC2))) - mstore(add(pMem, <%= pLastMem + 64 %>), mload(add(pProof, add(pC2, 32)))) + mstore(add(pMem, <%= pLastMem + 32 %>), calldataload(pC2)) + mstore(add(pMem, <%= pLastMem + 64 %>), calldataload(add(pC2, 32))) let xiSeed := mod(keccak256(add(pMem, lastMem), 96), q) mstore(add(pMem, pXiSeed), xiSeed) @@ -316,54 +310,153 @@ contract FflonkVerifier { mstore(add(pMem, pXi), xin) // Compute xi^n - <%for ( let i = 0; i < power; i++) { - %>xin:= mulmod(xin, xin, q) + <%for ( let i = 0; i < power; i++) { %> + xin:= mulmod(xin, xin, q) <%}%> + xin:= mod(add(sub(xin, 1), q), q) mstore(add(pMem, pZh), xin) mstore(add(pMem, pZhInv), xin) // We will invert later together with lagrange pols // Compute challenge.alpha mstore(add(pMem, lastMem), xiSeed) - mstore(add(pMem, <%= pLastMem + 32 %>), mload(add(pProof, pEval_ql))) - mstore(add(pMem, <%= pLastMem + 2 * 32 %>), mload(add(pProof, pEval_qr))) - mstore(add(pMem, <%= pLastMem + 3 * 32 %>), mload(add(pProof, pEval_qm))) - mstore(add(pMem, <%= pLastMem + 4 * 32 %>), mload(add(pProof, pEval_qo))) - mstore(add(pMem, <%= pLastMem + 5 * 32 %>), mload(add(pProof, pEval_qc))) - mstore(add(pMem, <%= pLastMem + 6 * 32 %>), mload(add(pProof, pEval_s1))) - mstore(add(pMem, <%= pLastMem + 7 * 32 %>), mload(add(pProof, pEval_s2))) - mstore(add(pMem, <%= pLastMem + 8 * 32 %>), mload(add(pProof, pEval_s3))) - mstore(add(pMem, <%= pLastMem + 9 * 32 %>), mload(add(pProof, pEval_a))) - mstore(add(pMem, <%= pLastMem + 10 * 32 %>), mload(add(pProof, pEval_b))) - mstore(add(pMem, <%= pLastMem + 11 * 32 %>), mload(add(pProof, pEval_c))) - mstore(add(pMem, <%= pLastMem + 12 * 32 %>), mload(add(pProof, pEval_z))) - mstore(add(pMem, <%= pLastMem + 13 * 32 %>), mload(add(pProof, pEval_zw))) - mstore(add(pMem, <%= pLastMem + 14 * 32 %>), mload(add(pProof, pEval_t1w))) - mstore(add(pMem, <%= pLastMem + 15 * 32 %>), mload(add(pProof, pEval_t2w))) + + calldatacopy(add(pMem, <%= pLastMem + 32 %>), pEval_ql, 480) mstore(add(pMem, pAlpha), mod(keccak256(add(pMem, lastMem), 512), q)) // Compute challenge.y mstore(add(pMem, lastMem), mload(add(pMem, pAlpha))) - mstore(add(pMem, <%= pLastMem + 32 %> ), mload(add(pProof, pW1))) - mstore(add(pMem, <%= pLastMem + 64 %> ), mload(add(pProof, add(pW1, 32)))) + mstore(add(pMem, <%= pLastMem + 32 %> ), calldataload(pW1)) + mstore(add(pMem, <%= pLastMem + 64 %> ), calldataload(add(pW1, 32))) mstore(add(pMem, pY), mod(keccak256(add(pMem, lastMem), 96), q)) } - // This function computes allows as to compute (X-X1)·(X-X2)·...·(X-Xn) used in Lagrange interpolation - function calcLagrangeItem(pMem, i, n, pX, pXi) -> result { - let idx := i - let max := add(n, 1) - result := 1 - let X := mload(add(pMem, pX)) - for { let j := 0 } lt(j, n) { j := add(j, 1) } - { - idx := mod(add(idx, 1), max) - result := mulmod(result, addmod(X, mod(sub(q, mload(add(pMem, add(pXi, mul(idx, 32))))), q), q), q) - } + function computeLiS0(pMem) { + let root0 := mload(add(pMem, pH0w8_0)) + let y := mload(add(pMem, pY)) + let den1 := 1 + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + + den1 := mulmod(8, den1, q) + + let den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 0), 8), 32)))) + let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(0, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 1), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(1, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 2), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(2, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 3), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(3, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 4), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(4, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 128)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 5), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(5, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 160)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 6), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(6, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 192)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 7), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(7, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 224)), mulmod(den1, mulmod(den2, den3, q), q)) + + } + + function computeLiS1(pMem) { + let root0 := mload(add(pMem, pH1w4_0)) + let y := mload(add(pMem, pY)) + let den1 := 1 + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + + den1 := mulmod(4, den1, q) + + let den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 0), 4), 32)))) + let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(0, 32))))), q), q) + + mstore(add(pMem, add(pLiS1Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 1), 4), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(1, 32))))), q), q) + + mstore(add(pMem, add(pLiS1Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 2), 4), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(2, 32))))), q), q) + + mstore(add(pMem, add(pLiS1Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 3), 4), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(3, 32))))), q), q) + + mstore(add(pMem, add(pLiS1Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q)) + } + + function computeLiS2(pMem) { + + let y := mload(add(pMem, pY)) + + let den1 := mulmod(mulmod(3,mload(add(pMem, pH2w3_0)),q), addmod(mload(add(pMem, pXi)) ,mod(sub(q, mulmod(mload(add(pMem, pXi)), w1 ,q)), q), q), q) + + let den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 0), 3), 32)))) + let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(0, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 1), 3), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(1, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 2), 3), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(2, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q)) + + den1 := mulmod(mulmod(3,mload(add(pMem, pH3w3_0)),q), addmod(mulmod(mload(add(pMem, pXi)), w1 ,q),mod(sub(q, mload(add(pMem, pXi))), q), q), q) + + den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 0), 3), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(0, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 1), 3), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(1, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 128)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 2), 3), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(2, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 160)), mulmod(den1, mulmod(den2, den3, q), q)) } // Prepare all the denominators that must be inverted, placed them in consecutive memory addresses - function computeInversions(pProof, pMem) { + function computeInversions(pMem) { // 1/ZH(xi) used in steps 8 and 9 of the verifier to multiply by 1/Z_H(xi) // Value computed during computeChallenges function and stores in pMem+pZhInv @@ -385,44 +478,41 @@ contract FflonkVerifier { w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH3w3_2))), q), q), q) mstore(add(pMem, pDenH2), w) + // Denominator needed in the verifier when computing L_i^{S0}(X) + computeLiS0(pMem) + // Denominator needed in the verifier when computing L_i^{S1}(X) - <%for ( let i = 0; i < 8; i++) { - %>mstore(add(pMem, add(pLiS0Inv, <%= i * 32 %>)), calcLagrangeItem(pMem, <%= i %>, 7, add(pH0w8_0, <%= i * 32 %>), pH0w8_0)) - <%}%> - // Denominator needed in the verifier when computing L_i^{S1}(X) - <%for ( let i = 0; i < 4; i++) { - %>mstore(add(pMem, add(pLiS1Inv, <%= i * 32 %>)), calcLagrangeItem(pMem, <%= i %>, 3, add(pH1w4_0, <%= i * 32 %>), pH1w4_0)) - <%}%> + computeLiS1(pMem) + // Denominator needed in the verifier when computing L_i^{S2}(X) - <%for ( let i = 0; i < 6; i++) { - %>mstore(add(pMem, add(pLiS2Inv, <%= i * 32 %>)), calcLagrangeItem(pMem, <%= i %>, 5, add(pH2w3_0, <%= i * 32 %>), pH2w3_0)) - <%}%> + computeLiS2(pMem) + // L_i where i from 1 to num public inputs, needed in step 6 and 7 of the verifier to compute L_1(xi) and PI(xi) w := 1 let xi := mload(add(pMem, pXi)) - <% for (let i=1; i<=Math.max(nPublic, 1); i++) { - %>mstore(add(pMem, pEval_l<%=i%>), mulmod(n, mod(add(sub(xi, w), q), q), q)) - <% if (iw := mulmod(w, w1, q) + <% for (let i=1; i<=Math.max(nPublic, 1); i++) { %> + mstore(add(pMem, pEval_l<%=i%>), mulmod(n, mod(add(sub(xi, w), q), q), q)) + <% if (i + w := mulmod(w, w1, q) <% } } %> + // Execute Montgomery batched inversions of the previous prepared values - inverseArray(pProof, add(pMem, pZhInv), <%= Math.max(nPublic, 1) + 21 %>) - } + inverseArray(pMem) } // Compute Lagrange polynomial evaluation L_i(xi) function computeLagrange(pMem) { let zh := mload(add(pMem, pZh)) let w := 1 <% for (let i=1; i<=Math.max(nPublic, 1); i++) { - if (i===1) { - %>mstore(add(pMem, pEval_l1 ), mulmod(mload(add(pMem, pEval_l1 )), zh, q)) - <% } else { - %>mstore(add(pMem, pEval_l<%=i%>), mulmod(w, mulmod(mload(add(pMem, pEval_l<%=i%>)), zh, q), q)) - <% } - if (iw := mulmod(w, w1, q) - <% } + if (i===1) { %> + mstore(add(pMem, pEval_l1 ), mulmod(mload(add(pMem, pEval_l1 )), zh, q)) + <% } else { %> + mstore(add(pMem, pEval_l<%=i%>), mulmod(w, mulmod(mload(add(pMem, pEval_l<%=i%>)), zh, q), q)) + <% } + if (i + w := mulmod(w, w1, q) + <% } } %> } @@ -430,8 +520,8 @@ contract FflonkVerifier { function computePi(pMem, pPub) { let pi := 0 pi := mod(add(sub(pi, mulmod(mload(add(pMem, pEval_l1)), calldataload(pPub), q)), q), q) - <% for (let i=1; ipi := mod(add(sub(pi, mulmod(mload(add(pMem, pEval_l<%= i + 1 %>)), calldataload(add(pPub, <%= 32 * i %>)), q)), q), q) + <% for (let i=1; i + pi := mod(add(sub(pi, mulmod(mload(add(pMem, pEval_l<%= i + 1 %>)), calldataload(add(pPub, <%= 32 * i %>)), q)), q), q) <% } %> mstore(add(pMem, pPi), pi) } @@ -440,34 +530,46 @@ contract FflonkVerifier { // where x = {h9, h0w8, h0w8^2, h0w8^3, h0w8^4, h0w8^5, h0w8^6, h0w8^7} // and y = {C0(h0), C0(h0w8), C0(h0w8^2), C0(h0w8^3), C0(h0w8^4), C0(h0w8^5), C0(h0w8^6), C0(h0w8^7)} // and computing C0(xi) - function computeR0(pProof, pMem) { + function computeR0(pMem) { + let num := 1 + let y := mload(add(pMem, pY)) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + + num := addmod(num, mod(sub(q, mload(add(pMem, pXi))), q), q) + let res - for { let i := 0 } lt(i, 8) { i := add(i, 1) } - { - // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + - // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 - let h0w80 := mload(add(pMem, add(pH0w8_0, mul(i, 32)))) - - let c0Value := addmod(mload(add(pProof, pEval_ql)), mulmod(mload(add(pProof, pEval_qr)), h0w80, q), q) - let h0w8i := mulmod(h0w80, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_qo)), h0w8i, q), q) - h0w8i := mulmod(h0w8i, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_qm)), h0w8i, q), q) - h0w8i := mulmod(h0w8i, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_qc)), h0w8i, q), q) - h0w8i := mulmod(h0w8i, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_s1)), h0w8i, q), q) - h0w8i := mulmod(h0w8i, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_s2)), h0w8i, q), q) - h0w8i := mulmod(h0w8i, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_s3)), h0w8i, q), q) - - // Compute Lagrange evaluation - let lagrange := calcLagrangeItem(pMem, i, 7, pY, pH0w8_0) - lagrange := mulmod(lagrange, mload(add(pMem, add(pLiS0Inv, mul(i, 32)))), q) - - res := addmod(res, mulmod(c0Value, lagrange, q), q) - } + let h0w80 + let c0Value + let h0w8i +<% for(let i = 0; i < 8; ++i) { -%> + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_<%- i %>)) + c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q) + + res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, <%- i * 32 %>))), q), q), q) + +<% } -%> mstore(add(pMem, pR0), res) } @@ -476,36 +578,45 @@ contract FflonkVerifier { // where x = {h1, h1w4, h1w4^2, h1w4^3} // and y = {C1(h1), C1(h1w4), C1(h1w4^2), C1(h1w4^3)} // and computing T0(xi) - function computeR1(pProof, pMem) { + function computeR1(pMem) { + let num := 1 + let y := mload(add(pMem, pY)) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + + num := addmod(num, mod(sub(q, mload(add(pMem, pXi))), q), q) + let t0 - let evalA := mload(add(pProof, pEval_a)) - let evalB := mload(add(pProof, pEval_b)) - let evalC := mload(add(pProof, pEval_c)) - - t0 := mulmod(mload(add(pProof, pEval_ql)), evalA, q) - t0 := addmod(t0, mulmod(mload(add(pProof, pEval_qr)), evalB, q) ,q) - t0 := addmod(t0, mulmod(mload(add(pProof, pEval_qm)), mulmod(evalA, evalB, q), q) ,q) - t0 := addmod(t0, mulmod(mload(add(pProof, pEval_qo)), evalC, q) ,q) - t0 := addmod(t0, mload(add(pProof, pEval_qc)) ,q) + let evalA := calldataload(pEval_a) + let evalB := calldataload(pEval_b) + let evalC := calldataload(pEval_c) + + t0 := mulmod(calldataload(pEval_ql), evalA, q) + t0 := addmod(t0, mulmod(calldataload(pEval_qr), evalB, q) ,q) + t0 := addmod(t0, mulmod(calldataload(pEval_qm), mulmod(evalA, evalB, q), q) ,q) + t0 := addmod(t0, mulmod(calldataload(pEval_qo), evalC, q) ,q) + t0 := addmod(t0, calldataload(pEval_qc) ,q) t0 := addmod(t0, mload(add(pMem, pPi)), q) t0 := mulmod(t0, mload(add(pMem, pZhInv)), q) let res - for { let i := 0 } lt(i, 4) { i := add(i, 1) } - { - let c1Value := evalA - let h1w4 := mload(add(pMem, add(pH1w4_0, mul(i, 32)))) + let c1Value + let h1w4 + let square +<% for(let i = 0; i < 4; ++i) { -%> + c1Value := evalA + h1w4 := mload(add(pMem, pH1w4_<%-i%>)) - c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) - let square := mulmod(h1w4, h1w4, q) - c1Value := addmod(c1Value, mulmod(square, evalC, q), q) - c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q) + c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) + square := mulmod(h1w4, h1w4, q) + c1Value := addmod(c1Value, mulmod(square, evalC, q), q) + c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q) - let lagrange := calcLagrangeItem(pMem, i, 3, pY, pH1w4_0) - lagrange := mulmod(lagrange, mload(add(pMem, add(pLiS1Inv, mul(i, 32)))), q) + res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(<%- i %>, 32)))), q), q), q) - res := addmod(res, mulmod(c1Value, lagrange, q), q) - } +<% } -%> mstore(add(pMem, pR1), res) } @@ -514,60 +625,93 @@ contract FflonkVerifier { // where x = {[h2, h2w3, h2w3^2], [h3, h3w3, h3w3^2]} // and y = {[C2(h2), C2(h2w3), C2(h2w3^2)], [C2(h3), C2(h3w3), C2(h3w3^2)]} // and computing T1(xi) and T2(xi) - function computeR2(pProof, pMem) { + function computeR2(pMem) { + let y := mload(add(pMem, pY)) + let num := 1 + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + + let num2 := 1 + num2 := mulmod(y, num2, q) + num2 := mulmod(y, num2, q) + num2 := mulmod(y, num2, q) + num2 := mulmod(num2, addmod(mulmod(mload(add(pMem, pXi)), w1 ,q), mload(add(pMem, pXi)), q), q) + + num := addmod(num, mod(sub(q, num2), q), q) + + num2 := mulmod(mulmod(mload(add(pMem, pXi)), w1 ,q), mload(add(pMem, pXi)), q) + + num := addmod(num, num2, q) + let t1 let t2 let betaXi := mulmod(mload(add(pMem, pBeta)), mload(add(pMem, pXi)), q) let gamma := mload(add(pMem, pGamma)) - let evalZ := mload(add(pProof, pEval_z)) - let evalZw := mload(add(pProof, pEval_zw)) - t2 := addmod(mload(add(pProof, pEval_a)), addmod(betaXi, gamma, q) ,q) + t2 := addmod(calldataload( pEval_a), addmod(betaXi, gamma, q) ,q) t2 := mulmod(t2, - addmod(mload(add(pProof, pEval_b)), + addmod(calldataload( pEval_b), addmod(mulmod(betaXi, k1, q), gamma, q) ,q), q) t2 := mulmod(t2, - addmod(mload(add(pProof, pEval_c)), + addmod(calldataload( pEval_c), addmod(mulmod(betaXi, k2, q), gamma, q) ,q), q) - t2 := mulmod(t2, evalZ, q) + t2 := mulmod(t2, calldataload(pEval_z), q) //Let's use t1 as a temporal variable to save one local - t1 := addmod(mload(add(pProof, pEval_a)), addmod(mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), gamma, q) ,q) + t1 := addmod(calldataload(pEval_a), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s1), q), gamma, q) ,q) t1 := mulmod(t1, - addmod(mload(add(pProof, pEval_b)), addmod(mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), gamma, q) ,q), q) + addmod(calldataload(pEval_b), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s2), q), gamma, q) ,q), q) t1 := mulmod(t1, - addmod(mload(add(pProof, pEval_c)), addmod(mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s3)), q), gamma, q) ,q), q) - t1 := mulmod(t1, evalZw, q) + addmod(calldataload(pEval_c), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s3), q), gamma, q) ,q), q) + t1 := mulmod(t1, calldataload(pEval_zw), q) t2:= addmod(t2, mod(sub(q, t1), q), q) t2 := mulmod(t2, mload(add(pMem, pZhInv)), q) // Compute T1(xi) - t1 := sub(evalZ, 1) + t1 := sub(calldataload(pEval_z), 1) t1 := mulmod(t1, mload(add(pMem, pEval_l1)) ,q) t1 := mulmod(t1, mload(add(pMem, pZhInv)) ,q) // Let's use local variable gamma to save the result gamma:=0 - for { let i := 0 } lt(i, 6) { i := add(i, 1) } - { - let hw := mload(add(pMem, add(pH2w3_0, mul(i, 32)))) - - let c2Value - if lt(i, 3) { - c2Value := addmod(evalZ, mulmod(hw, t1, q), q) - c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) - } - if gt(i, 2) { - c2Value := addmod(evalZw, mulmod(hw, mload(add(pProof, pEval_t1w)), q), q) - c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), mload(add(pProof, pEval_t2w)), q), q) - } - - let lagrange := calcLagrangeItem(pMem, i, 5, pY, pH2w3_0) - lagrange := mulmod(lagrange, mload(add(pMem, add(pLiS2Inv, mul(i, 32)))), q) - - gamma := addmod(gamma, mulmod(c2Value, lagrange, q), q) - } + + let hw + let c2Value + + hw := mload(add(pMem, pH2w3_0)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(0, 32)))), q), q), q) + + hw := mload(add(pMem, pH2w3_1)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(1, 32)))), q), q), q) + + hw := mload(add(pMem, pH2w3_2)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(2, 32)))), q), q), q) + + hw := mload(add(pMem, pH3w3_0)) + c2Value := addmod(calldataload(pEval_zw), mulmod(hw, calldataload(pEval_t1w), q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(3, 32)))), q), q), q) + + hw := mload(add(pMem, pH3w3_1)) + c2Value := addmod(calldataload(pEval_zw), mulmod(hw, calldataload(pEval_t1w), q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(4, 32)))), q), q), q) + + hw := mload(add(pMem, pH3w3_2)) + c2Value := addmod(calldataload(pEval_zw), mulmod(hw, calldataload(pEval_t1w), q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(5, 32)))), q), q), q) mstore(add(pMem, pR2), gamma) } @@ -592,8 +736,8 @@ contract FflonkVerifier { function g1_mulAcc(pR, pP, s) { let success let mIn := mload(0x40) - mstore(mIn, mload(pP)) - mstore(add(mIn, 32), mload(add(pP, 32))) + mstore(mIn, calldataload(pP)) + mstore(add(mIn, 32), calldataload(add(pP, 32))) mstore(add(mIn, 64), s) success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64) @@ -640,7 +784,7 @@ contract FflonkVerifier { } } - function computeFEJ(pProof, pMem) { + function computeFEJ(pMem) { // Prepare shared numerator between F, E and J to reuse it let y := mload(add(pMem, pY)) let numerator := addmod(y, mod(sub(q, mload(add(pMem, pH0w8_0))), q), q) @@ -659,18 +803,18 @@ contract FflonkVerifier { // Compute full batched polynomial commitment [F]_1 mstore(add(pMem, pF), C0x) mstore(add(pMem, add(pF, 32)), C0y) - g1_mulAcc(add(pMem, pF), add(pProof, pC1), quotient1) - g1_mulAcc(add(pMem, pF), add(pProof, pC2), quotient2) + g1_mulAcc(add(pMem, pF), pC1, quotient1) + g1_mulAcc(add(pMem, pF), pC2, quotient2) // Compute group-encoded batch evaluation [E]_1 g1_mulAccC(add(pMem, pE), G1x, G1y, addmod(mload(add(pMem, pR0)), addmod(mulmod(quotient1, mload(add(pMem, pR1)),q), mulmod(quotient2, mload(add(pMem, pR2)),q), q), q)) // Compute the full difference [J]_1 - g1_mulAcc(add(pMem, pJ), add(pProof, pW1), numerator) + g1_mulAcc(add(pMem, pJ), pW1, numerator) } // Validate all evaluations with a pairing checking that e([F]_1 - [E]_1 - [J]_1 + y[W2]_1, [1]_2) == e([W']_1, [x]_2) - function checkPairing(pProof, pMem) -> isOk { + function checkPairing(pMem) -> isOk { let mIn := mload(0x40) // First pairing value @@ -681,7 +825,7 @@ contract FflonkVerifier { // F = F - E - J + y·W2 g1_acc(add(pMem, pF), add(pMem, pE)) g1_acc(add(pMem, pF), add(pMem, pJ)) - g1_mulAcc(add(pMem, pF), add(pProof, pW2), mload(add(pMem, pY))) + g1_mulAcc(add(pMem, pF), pW2, mload(add(pMem, pY))) mstore(mIn, mload(add(pMem, pF))) mstore(add(mIn, 32), mload(add(add(pMem, pF), 32))) @@ -694,8 +838,8 @@ contract FflonkVerifier { // Third pairing value // Compute -W2 - mstore(add(mIn, 192), mload(add(pProof, pW2))) - let s := mload(add(add(pProof, pW2), 32)) + mstore(add(mIn, 192), calldataload(pW2)) + let s := calldataload(add(pW2, 32)) s := mod(sub(qf, s), qf) mstore(add(mIn, 224), s) @@ -714,10 +858,10 @@ contract FflonkVerifier { mstore(0x40, add(pMem, lastMem)) // Validate that all evaluations ∈ F - checkInput(proof) + checkInput() // Compute the challenges: beta, gamma, xi, alpha and y ∈ F, h1w4/h2w3/h3w3 roots, xiN and zh(xi) - computeChallenges(proof, pMem, pubSignals) + computeChallenges(pMem, pubSignals) // To divide prime fields the Extended Euclidean Algorithm for computing modular inverses is needed. // The Montgomery batch inversion algorithm allow us to compute n inverses reducing to a single one inversion. @@ -727,7 +871,7 @@ contract FflonkVerifier { // 1) Prepare all the denominators to inverse // 2) Check the inverse sent by the prover it is what it should be // 3) Compute the others inverses using the Montgomery Batched Algorithm using the inverse sent to avoid the inversion operation it does. - computeInversions(proof, pMem) + computeInversions(pMem) // Compute Lagrange polynomial evaluations Li(xi) computeLagrange(pMem) @@ -736,15 +880,15 @@ contract FflonkVerifier { computePi(pMem, pubSignals) // Computes r1(y) and r2(y) - computeR0(proof, pMem) - computeR1(proof, pMem) - computeR2(proof, pMem) + computeR0(pMem) + computeR1(pMem) + computeR2(pMem) // Compute full batched polynomial commitment [F]_1, group-encoded batch evaluation [E]_1 and the full difference [J]_1 - computeFEJ(proof, pMem) + computeFEJ(pMem) // Validate all evaluations - let isValid := checkPairing(proof, pMem) + let isValid := checkPairing(pMem) mstore(0, isValid) return(0, 0x20) diff --git a/test/fflonk/verifier.sol b/test/fflonk/verifier.sol index edc9d866..66738242 100644 --- a/test/fflonk/verifier.sol +++ b/test/fflonk/verifier.sol @@ -70,32 +70,32 @@ contract FflonkVerifier { uint256 constant G2y1 = 8495653923123431417604973247489272438418190587263600148770280649306958101930; uint256 constant G2y2 = 4082367875863433681332203403145435568316851327593401208105741076214120093531; - // Proof data - // Byte offset of every parameter in `bytes memory proof` + // Proof calldata + // Byte offset of every parameter of the calldata // Polynomial commitments - uint16 constant pC1 = 32; // [C1]_1 - uint16 constant pC2 = 96; // [C2]_1 - uint16 constant pW1 = 160; // [W]_1 - uint16 constant pW2 = 224; // [W']_1 + uint16 constant pC1 = 4 + 0; // [C1]_1 + uint16 constant pC2 = 4 + 32*2; // [C2]_1 + uint16 constant pW1 = 4 + 32*4; // [W]_1 + uint16 constant pW2 = 4 + 32*6; // [W']_1 // Opening evaluations - uint16 constant pEval_ql = 288; // q_L(xi) - uint16 constant pEval_qr = 320; // q_R(xi) - uint16 constant pEval_qm = 352; // q_M(xi) - uint16 constant pEval_qo = 384; // q_O(xi) - uint16 constant pEval_qc = 416; // q_C(xi) - uint16 constant pEval_s1 = 448; // S_{sigma_1}(xi) - uint16 constant pEval_s2 = 480; // S_{sigma_2}(xi) - uint16 constant pEval_s3 = 512; // S_{sigma_3}(xi) - uint16 constant pEval_a = 544; // a(xi) - uint16 constant pEval_b = 576; // b(xi) - uint16 constant pEval_c = 608; // c(xi) - uint16 constant pEval_z = 640; // z(xi) - uint16 constant pEval_zw = 672; // z_omega(xi) - uint16 constant pEval_t1w = 704; // T_1(xi omega) - uint16 constant pEval_t2w = 736; // T_2(xi omega) - uint16 constant pEval_inv = 768; // inv(batch) sent by the prover to avoid any inverse calculation to save gas, - // we check the correctness of the inv(batch) by computing batch - // and checking inv(batch) * batch == 1 + uint16 constant pEval_ql = 4 + 32*8; // q_L(xi) + uint16 constant pEval_qr = 4 + 32*9; // q_R(xi) + uint16 constant pEval_qm = 4 + 32*10; // q_M(xi) + uint16 constant pEval_qo = 4 + 32*11; // q_O(xi) + uint16 constant pEval_qc = 4 + 32*12; // q_C(xi) + uint16 constant pEval_s1 = 4 + 32*13; // S_{sigma_1}(xi) + uint16 constant pEval_s2 = 4 + 32*14; // S_{sigma_2}(xi) + uint16 constant pEval_s3 = 4 + 32*15; // S_{sigma_3}(xi) + uint16 constant pEval_a = 4 + 32*16; // a(xi) + uint16 constant pEval_b = 4 + 32*17; // b(xi) + uint16 constant pEval_c = 4 + 32*18; // c(xi) + uint16 constant pEval_z = 4 + 32*19; // z(xi) + uint16 constant pEval_zw = 4 + 32*20; // z_omega(xi) + uint16 constant pEval_t1w = 4 + 32*21; // T_1(xi omega) + uint16 constant pEval_t2w = 4 + 32*22; // T_2(xi omega) + uint16 constant pEval_inv = 4 + 32*23; // inv(batch) sent by the prover to avoid any inverse calculation to save gas, + // we check the correctness of the inv(batch) by computing batch + // and checking inv(batch) * batch == 1 // Memory data // Challenges @@ -152,57 +152,205 @@ contract FflonkVerifier { uint16 constant pLiS1Inv = 1568; // Reserve 4 * 32 bytes to compute r_1(X) uint16 constant pLiS2Inv = 1696; // Reserve 6 * 32 bytes to compute r_2(X) // Lagrange evaluations + uint16 constant pEval_l1 = 1888; - + + uint16 constant lastMem = 1920; + - function verifyProof(bytes memory proof, uint256[1] calldata pubSignals) public view returns (bool) { + function verifyProof(bytes32[24] calldata proof, uint256[1] calldata pubSignals) public view returns (bool) { assembly { // Computes the inverse of an array of values // See https://vitalik.ca/general/2018/07/21/starks_part_3.html in section where explain fields operations - // To save the inverse to be computed on chain the prover sends the inverse as an evaluation in proof.eval_inv - function inverseArray(pProof, pVals, n) { + // To save the inverse to be computed on chain the prover sends the inverse as an evaluation in commits.eval_inv + function inverseArray(pMem) { + let pAux := mload(0x40) // Point to the next free position - let pIn := pVals - let lastPIn := add(pVals, mul(n, 32)) // Read n elemnts - let acc := mload(pIn) // Read the first element - pIn := add(pIn, 32) // Point to the second element - - for { } lt(pIn, lastPIn) { - pAux := add(pAux, 32) - pIn := add(pIn, 32) - } - { - mstore(pAux, acc) - acc := mulmod(acc, mload(pIn), q) - } + let acc := mload(add(pMem,pZhInv)) // Read the first element + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pDenH1)), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pDenH2)), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pLiS0Inv)), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 32))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 64))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 96))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 128))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 160))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 192))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 224))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pLiS1Inv)), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 32))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 64))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 96))), q) + mstore(pAux, acc) - let inv := mload(add(pProof, pEval_inv)) + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pLiS2Inv)), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 32))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 64))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 96))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 128))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 160))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pEval_l1)), q) + mstore(pAux, acc) + + + let inv := calldataload(pEval_inv) // Before using the inverse sent by the prover the verifier checks inv(batch) * batch === 1 if iszero(eq(1, mulmod(acc, inv, q))) { mstore(0, 0) - return(0, 0x20) + return(0,0x20) } acc := inv - // At this point pAux point to the next free position we substract 1 to point to the last used pAux := sub(pAux, 32) - // pIn points to the n+1 element, we substract to point to n - pIn := sub(pIn, 32) - lastPIn := pVals // We don't process the first element - for { } gt(pIn, lastPIn) { - pAux := sub(pAux, 32) - pIn := sub(pIn, 32) - } - { - inv := mulmod(acc, mload(pAux), q) - acc := mulmod(acc, mload(pIn), q) - mstore(pIn, inv) - } - // pIn points to first element, we just set it. - mstore(pIn, acc) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pEval_l1)), q) + mstore(add(pMem, pEval_l1), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 160))), q) + mstore(add(pMem, add(pLiS2Inv, 160)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 128))), q) + mstore(add(pMem, add(pLiS2Inv, 128)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 96))), q) + mstore(add(pMem, add(pLiS2Inv, 96)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 64))), q) + mstore(add(pMem, add(pLiS2Inv, 64)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 32))), q) + mstore(add(pMem, add(pLiS2Inv, 32)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pLiS2Inv)), q) + mstore(add(pMem, pLiS2Inv), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 96))), q) + mstore(add(pMem, add(pLiS1Inv, 96)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 64))), q) + mstore(add(pMem, add(pLiS1Inv, 64)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 32))), q) + mstore(add(pMem, add(pLiS1Inv, 32)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pLiS1Inv)), q) + mstore(add(pMem, pLiS1Inv), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 224))), q) + mstore(add(pMem, add(pLiS0Inv, 224)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 192))), q) + mstore(add(pMem, add(pLiS0Inv, 192)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 160))), q) + mstore(add(pMem, add(pLiS0Inv, 160)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 128))), q) + mstore(add(pMem, add(pLiS0Inv, 128)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 96))), q) + mstore(add(pMem, add(pLiS0Inv, 96)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 64))), q) + mstore(add(pMem, add(pLiS0Inv, 64)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 32))), q) + mstore(add(pMem, add(pLiS0Inv, 32)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pLiS0Inv)), q) + mstore(add(pMem, pLiS0Inv), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pDenH2)), q) + mstore(add(pMem, pDenH2), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pDenH1)), q) + mstore(add(pMem, pDenH1), inv) + + mstore(add(pMem, pZhInv), acc) } function checkField(v) { @@ -213,8 +361,8 @@ contract FflonkVerifier { } function checkPointBelongsToBN128Curve(p) { - let x := mload(p) - let y := mload(add(p, 32)) + let x := calldataload(p) + let y := calldataload(add(p, 32)) // Check that the point is on the curve // y^2 = x^3 + 3 @@ -228,51 +376,52 @@ contract FflonkVerifier { } // Validate all the evaluations sent by the prover ∈ F - function checkInput(pProof) { + function checkInput() { // Check proof commitments fullfill bn128 curve equation Y^2 = X^3 + 3 - checkPointBelongsToBN128Curve(add(pProof, pC1)) - checkPointBelongsToBN128Curve(add(pProof, pC2)) - checkPointBelongsToBN128Curve(add(pProof, pW1)) - checkPointBelongsToBN128Curve(add(pProof, pW2)) - - checkField(mload(add(pProof, pEval_ql))) - checkField(mload(add(pProof, pEval_qr))) - checkField(mload(add(pProof, pEval_qm))) - checkField(mload(add(pProof, pEval_qo))) - checkField(mload(add(pProof, pEval_qc))) - checkField(mload(add(pProof, pEval_s1))) - checkField(mload(add(pProof, pEval_s2))) - checkField(mload(add(pProof, pEval_s3))) - checkField(mload(add(pProof, pEval_a))) - checkField(mload(add(pProof, pEval_b))) - checkField(mload(add(pProof, pEval_c))) - checkField(mload(add(pProof, pEval_z))) - checkField(mload(add(pProof, pEval_zw))) - checkField(mload(add(pProof, pEval_t1w))) - checkField(mload(add(pProof, pEval_t2w))) - checkField(mload(add(pProof, pEval_inv))) + checkPointBelongsToBN128Curve(pC1) + checkPointBelongsToBN128Curve(pC2) + checkPointBelongsToBN128Curve(pW1) + checkPointBelongsToBN128Curve(pW2) + + checkField(calldataload(pEval_ql)) + checkField(calldataload(pEval_qr)) + checkField(calldataload(pEval_qm)) + checkField(calldataload(pEval_qo)) + checkField(calldataload(pEval_qc)) + checkField(calldataload(pEval_s1)) + checkField(calldataload(pEval_s2)) + checkField(calldataload(pEval_s3)) + checkField(calldataload(pEval_a)) + checkField(calldataload(pEval_b)) + checkField(calldataload(pEval_c)) + checkField(calldataload(pEval_z)) + checkField(calldataload(pEval_zw)) + checkField(calldataload(pEval_t1w)) + checkField(calldataload(pEval_t2w)) + checkField(calldataload(pEval_inv)) // Points are checked in the point operations precompiled smart contracts } - function computeChallenges(pProof, pMem, pPublic) { + function computeChallenges(pMem, pPublic) { // Compute challenge.beta & challenge.gamma mstore(add(pMem, 1920 ), C0x) mstore(add(pMem, 1952 ), C0y) mstore(add(pMem, 1984), calldataload(pPublic)) + - mstore(add(pMem, 2016 ), mload(add(pProof, pC1))) - mstore(add(pMem, 2048 ), mload(add(pProof, add(pC1, 32)))) + mstore(add(pMem, 2016 ), calldataload(pC1)) + mstore(add(pMem, 2048 ), calldataload(add(pC1, 32))) mstore(add(pMem, pBeta), mod(keccak256(add(pMem, lastMem), 160), q)) mstore(add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) // Get xiSeed & xiSeed2 mstore(add(pMem, lastMem), mload(add(pMem, pGamma))) - mstore(add(pMem, 1952), mload(add(pProof, pC2))) - mstore(add(pMem, 1984), mload(add(pProof, add(pC2, 32)))) + mstore(add(pMem, 1952), calldataload(pC2)) + mstore(add(pMem, 1984), calldataload(add(pC2, 32))) let xiSeed := mod(keccak256(add(pMem, lastMem), 96), q) mstore(add(pMem, pXiSeed), xiSeed) @@ -308,60 +457,167 @@ contract FflonkVerifier { mstore(add(pMem, pXi), xin) // Compute xi^n + xin:= mulmod(xin, xin, q) + xin:= mulmod(xin, xin, q) + xin:= mulmod(xin, xin, q) + xin:= mulmod(xin, xin, q) + xin:= mulmod(xin, xin, q) + xin:= mulmod(xin, xin, q) + xin:= mulmod(xin, xin, q) + xin:= mulmod(xin, xin, q) + xin:= mod(add(sub(xin, 1), q), q) mstore(add(pMem, pZh), xin) mstore(add(pMem, pZhInv), xin) // We will invert later together with lagrange pols // Compute challenge.alpha mstore(add(pMem, lastMem), xiSeed) - mstore(add(pMem, 1952), mload(add(pProof, pEval_ql))) - mstore(add(pMem, 1984), mload(add(pProof, pEval_qr))) - mstore(add(pMem, 2016), mload(add(pProof, pEval_qm))) - mstore(add(pMem, 2048), mload(add(pProof, pEval_qo))) - mstore(add(pMem, 2080), mload(add(pProof, pEval_qc))) - mstore(add(pMem, 2112), mload(add(pProof, pEval_s1))) - mstore(add(pMem, 2144), mload(add(pProof, pEval_s2))) - mstore(add(pMem, 2176), mload(add(pProof, pEval_s3))) - mstore(add(pMem, 2208), mload(add(pProof, pEval_a))) - mstore(add(pMem, 2240), mload(add(pProof, pEval_b))) - mstore(add(pMem, 2272), mload(add(pProof, pEval_c))) - mstore(add(pMem, 2304), mload(add(pProof, pEval_z))) - mstore(add(pMem, 2336), mload(add(pProof, pEval_zw))) - mstore(add(pMem, 2368), mload(add(pProof, pEval_t1w))) - mstore(add(pMem, 2400), mload(add(pProof, pEval_t2w))) + + calldatacopy(add(pMem, 1952), pEval_ql, 480) mstore(add(pMem, pAlpha), mod(keccak256(add(pMem, lastMem), 512), q)) // Compute challenge.y mstore(add(pMem, lastMem), mload(add(pMem, pAlpha))) - mstore(add(pMem, 1952 ), mload(add(pProof, pW1))) - mstore(add(pMem, 1984 ), mload(add(pProof, add(pW1, 32)))) + mstore(add(pMem, 1952 ), calldataload(pW1)) + mstore(add(pMem, 1984 ), calldataload(add(pW1, 32))) mstore(add(pMem, pY), mod(keccak256(add(pMem, lastMem), 96), q)) } - // This function computes allows as to compute (X-X1)·(X-X2)·...·(X-Xn) used in Lagrange interpolation - function calcLagrangeItem(pMem, i, n, pX, pXi) -> result { - let idx := i - let max := add(n, 1) - result := 1 - let X := mload(add(pMem, pX)) - for { let j := 0 } lt(j, n) { j := add(j, 1) } - { - idx := mod(add(idx, 1), max) - result := mulmod(result, addmod(X, mod(sub(q, mload(add(pMem, add(pXi, mul(idx, 32))))), q), q), q) - } + function computeLiS0(pMem) { + let root0 := mload(add(pMem, pH0w8_0)) + let y := mload(add(pMem, pY)) + let den1 := 1 + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + + den1 := mulmod(8, den1, q) + + let den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 0), 8), 32)))) + let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(0, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 1), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(1, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 2), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(2, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 3), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(3, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 4), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(4, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 128)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 5), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(5, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 160)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 6), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(6, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 192)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 7), 8), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(7, 32))))), q), q) + + mstore(add(pMem, add(pLiS0Inv, 224)), mulmod(den1, mulmod(den2, den3, q), q)) + + } + + function computeLiS1(pMem) { + let root0 := mload(add(pMem, pH1w4_0)) + let y := mload(add(pMem, pY)) + let den1 := 1 + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + + den1 := mulmod(4, den1, q) + + let den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 0), 4), 32)))) + let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(0, 32))))), q), q) + + mstore(add(pMem, add(pLiS1Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 1), 4), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(1, 32))))), q), q) + + mstore(add(pMem, add(pLiS1Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 2), 4), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(2, 32))))), q), q) + + mstore(add(pMem, add(pLiS1Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 3), 4), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(3, 32))))), q), q) + + mstore(add(pMem, add(pLiS1Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q)) + } + + function computeLiS2(pMem) { + + let y := mload(add(pMem, pY)) + + let den1 := mulmod(mulmod(3,mload(add(pMem, pH2w3_0)),q), addmod(mload(add(pMem, pXi)) ,mod(sub(q, mulmod(mload(add(pMem, pXi)), w1 ,q)), q), q), q) + + let den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 0), 3), 32)))) + let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(0, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 1), 3), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(1, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 2), 3), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(2, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q)) + + den1 := mulmod(mulmod(3,mload(add(pMem, pH3w3_0)),q), addmod(mulmod(mload(add(pMem, pXi)), w1 ,q),mod(sub(q, mload(add(pMem, pXi))), q), q), q) + + den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 0), 3), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(0, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 1), 3), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(1, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 128)), mulmod(den1, mulmod(den2, den3, q), q)) + + den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 2), 3), 32)))) + den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(2, 32))))), q), q) + + mstore(add(pMem, add(pLiS2Inv, 160)), mulmod(den1, mulmod(den2, den3, q), q)) } // Prepare all the denominators that must be inverted, placed them in consecutive memory addresses - function computeInversions(pProof, pMem) { + function computeInversions(pMem) { // 1/ZH(xi) used in steps 8 and 9 of the verifier to multiply by 1/Z_H(xi) // Value computed during computeChallenges function and stores in pMem+pZhInv @@ -383,45 +639,32 @@ contract FflonkVerifier { w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH3w3_2))), q), q), q) mstore(add(pMem, pDenH2), w) - // Denominator needed in the verifier when computing L_i^{S1}(X) - mstore(add(pMem, add(pLiS0Inv, 0)), calcLagrangeItem(pMem, 0, 7, add(pH0w8_0, 0), pH0w8_0)) - mstore(add(pMem, add(pLiS0Inv, 32)), calcLagrangeItem(pMem, 1, 7, add(pH0w8_0, 32), pH0w8_0)) - mstore(add(pMem, add(pLiS0Inv, 64)), calcLagrangeItem(pMem, 2, 7, add(pH0w8_0, 64), pH0w8_0)) - mstore(add(pMem, add(pLiS0Inv, 96)), calcLagrangeItem(pMem, 3, 7, add(pH0w8_0, 96), pH0w8_0)) - mstore(add(pMem, add(pLiS0Inv, 128)), calcLagrangeItem(pMem, 4, 7, add(pH0w8_0, 128), pH0w8_0)) - mstore(add(pMem, add(pLiS0Inv, 160)), calcLagrangeItem(pMem, 5, 7, add(pH0w8_0, 160), pH0w8_0)) - mstore(add(pMem, add(pLiS0Inv, 192)), calcLagrangeItem(pMem, 6, 7, add(pH0w8_0, 192), pH0w8_0)) - mstore(add(pMem, add(pLiS0Inv, 224)), calcLagrangeItem(pMem, 7, 7, add(pH0w8_0, 224), pH0w8_0)) + // Denominator needed in the verifier when computing L_i^{S0}(X) + computeLiS0(pMem) // Denominator needed in the verifier when computing L_i^{S1}(X) - mstore(add(pMem, add(pLiS1Inv, 0)), calcLagrangeItem(pMem, 0, 3, add(pH1w4_0, 0), pH1w4_0)) - mstore(add(pMem, add(pLiS1Inv, 32)), calcLagrangeItem(pMem, 1, 3, add(pH1w4_0, 32), pH1w4_0)) - mstore(add(pMem, add(pLiS1Inv, 64)), calcLagrangeItem(pMem, 2, 3, add(pH1w4_0, 64), pH1w4_0)) - mstore(add(pMem, add(pLiS1Inv, 96)), calcLagrangeItem(pMem, 3, 3, add(pH1w4_0, 96), pH1w4_0)) - + computeLiS1(pMem) + // Denominator needed in the verifier when computing L_i^{S2}(X) - mstore(add(pMem, add(pLiS2Inv, 0)), calcLagrangeItem(pMem, 0, 5, add(pH2w3_0, 0), pH2w3_0)) - mstore(add(pMem, add(pLiS2Inv, 32)), calcLagrangeItem(pMem, 1, 5, add(pH2w3_0, 32), pH2w3_0)) - mstore(add(pMem, add(pLiS2Inv, 64)), calcLagrangeItem(pMem, 2, 5, add(pH2w3_0, 64), pH2w3_0)) - mstore(add(pMem, add(pLiS2Inv, 96)), calcLagrangeItem(pMem, 3, 5, add(pH2w3_0, 96), pH2w3_0)) - mstore(add(pMem, add(pLiS2Inv, 128)), calcLagrangeItem(pMem, 4, 5, add(pH2w3_0, 128), pH2w3_0)) - mstore(add(pMem, add(pLiS2Inv, 160)), calcLagrangeItem(pMem, 5, 5, add(pH2w3_0, 160), pH2w3_0)) - + computeLiS2(pMem) + // L_i where i from 1 to num public inputs, needed in step 6 and 7 of the verifier to compute L_1(xi) and PI(xi) w := 1 let xi := mload(add(pMem, pXi)) + mstore(add(pMem, pEval_l1), mulmod(n, mod(add(sub(xi, w), q), q), q)) + // Execute Montgomery batched inversions of the previous prepared values - inverseArray(pProof, add(pMem, pZhInv), 22) - } + inverseArray(pMem) } // Compute Lagrange polynomial evaluation L_i(xi) function computeLagrange(pMem) { let zh := mload(add(pMem, pZh)) let w := 1 - mstore(add(pMem, pEval_l1 ), mulmod(mload(add(pMem, pEval_l1 )), zh, q)) + mstore(add(pMem, pEval_l1 ), mulmod(mload(add(pMem, pEval_l1 )), zh, q)) + } // Compute public input polynomial evaluation PI(xi) @@ -436,34 +679,184 @@ contract FflonkVerifier { // where x = {h9, h0w8, h0w8^2, h0w8^3, h0w8^4, h0w8^5, h0w8^6, h0w8^7} // and y = {C0(h0), C0(h0w8), C0(h0w8^2), C0(h0w8^3), C0(h0w8^4), C0(h0w8^5), C0(h0w8^6), C0(h0w8^7)} // and computing C0(xi) - function computeR0(pProof, pMem) { + function computeR0(pMem) { + let num := 1 + let y := mload(add(pMem, pY)) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + + num := addmod(num, mod(sub(q, mload(add(pMem, pXi))), q), q) + let res - for { let i := 0 } lt(i, 8) { i := add(i, 1) } - { - // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + - // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 - let h0w80 := mload(add(pMem, add(pH0w8_0, mul(i, 32)))) - - let c0Value := addmod(mload(add(pProof, pEval_ql)), mulmod(mload(add(pProof, pEval_qr)), h0w80, q), q) - let h0w8i := mulmod(h0w80, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_qo)), h0w8i, q), q) - h0w8i := mulmod(h0w8i, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_qm)), h0w8i, q), q) - h0w8i := mulmod(h0w8i, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_qc)), h0w8i, q), q) - h0w8i := mulmod(h0w8i, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_s1)), h0w8i, q), q) - h0w8i := mulmod(h0w8i, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_s2)), h0w8i, q), q) - h0w8i := mulmod(h0w8i, h0w80, q) - c0Value := addmod(c0Value, mulmod(mload(add(pProof, pEval_s3)), h0w8i, q), q) - - // Compute Lagrange evaluation - let lagrange := calcLagrangeItem(pMem, i, 7, pY, pH0w8_0) - lagrange := mulmod(lagrange, mload(add(pMem, add(pLiS0Inv, mul(i, 32)))), q) - - res := addmod(res, mulmod(c0Value, lagrange, q), q) - } + let h0w80 + let c0Value + let h0w8i + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_0)) + c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q) + + res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 0))), q), q), q) + + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_1)) + c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q) + + res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 32))), q), q), q) + + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_2)) + c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q) + + res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 64))), q), q), q) + + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_3)) + c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q) + + res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 96))), q), q), q) + + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_4)) + c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q) + + res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 128))), q), q), q) + + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_5)) + c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q) + + res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 160))), q), q), q) + + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_6)) + c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q) + + res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 192))), q), q), q) + + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_7)) + c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q) + + res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 224))), q), q), q) + mstore(add(pMem, pR0), res) } @@ -472,36 +865,73 @@ contract FflonkVerifier { // where x = {h1, h1w4, h1w4^2, h1w4^3} // and y = {C1(h1), C1(h1w4), C1(h1w4^2), C1(h1w4^3)} // and computing T0(xi) - function computeR1(pProof, pMem) { + function computeR1(pMem) { + let num := 1 + let y := mload(add(pMem, pY)) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + + num := addmod(num, mod(sub(q, mload(add(pMem, pXi))), q), q) + let t0 - let evalA := mload(add(pProof, pEval_a)) - let evalB := mload(add(pProof, pEval_b)) - let evalC := mload(add(pProof, pEval_c)) - - t0 := mulmod(mload(add(pProof, pEval_ql)), evalA, q) - t0 := addmod(t0, mulmod(mload(add(pProof, pEval_qr)), evalB, q) ,q) - t0 := addmod(t0, mulmod(mload(add(pProof, pEval_qm)), mulmod(evalA, evalB, q), q) ,q) - t0 := addmod(t0, mulmod(mload(add(pProof, pEval_qo)), evalC, q) ,q) - t0 := addmod(t0, mload(add(pProof, pEval_qc)) ,q) + let evalA := calldataload(pEval_a) + let evalB := calldataload(pEval_b) + let evalC := calldataload(pEval_c) + + t0 := mulmod(calldataload(pEval_ql), evalA, q) + t0 := addmod(t0, mulmod(calldataload(pEval_qr), evalB, q) ,q) + t0 := addmod(t0, mulmod(calldataload(pEval_qm), mulmod(evalA, evalB, q), q) ,q) + t0 := addmod(t0, mulmod(calldataload(pEval_qo), evalC, q) ,q) + t0 := addmod(t0, calldataload(pEval_qc) ,q) t0 := addmod(t0, mload(add(pMem, pPi)), q) t0 := mulmod(t0, mload(add(pMem, pZhInv)), q) let res - for { let i := 0 } lt(i, 4) { i := add(i, 1) } - { - let c1Value := evalA - let h1w4 := mload(add(pMem, add(pH1w4_0, mul(i, 32)))) + let c1Value + let h1w4 + let square + c1Value := evalA + h1w4 := mload(add(pMem, pH1w4_0)) - c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) - let square := mulmod(h1w4, h1w4, q) - c1Value := addmod(c1Value, mulmod(square, evalC, q), q) - c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q) + c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) + square := mulmod(h1w4, h1w4, q) + c1Value := addmod(c1Value, mulmod(square, evalC, q), q) + c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q) - let lagrange := calcLagrangeItem(pMem, i, 3, pY, pH1w4_0) - lagrange := mulmod(lagrange, mload(add(pMem, add(pLiS1Inv, mul(i, 32)))), q) + res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(0, 32)))), q), q), q) + + c1Value := evalA + h1w4 := mload(add(pMem, pH1w4_1)) + + c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) + square := mulmod(h1w4, h1w4, q) + c1Value := addmod(c1Value, mulmod(square, evalC, q), q) + c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q) + + res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(1, 32)))), q), q), q) + + c1Value := evalA + h1w4 := mload(add(pMem, pH1w4_2)) + + c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) + square := mulmod(h1w4, h1w4, q) + c1Value := addmod(c1Value, mulmod(square, evalC, q), q) + c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q) + + res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(2, 32)))), q), q), q) + + c1Value := evalA + h1w4 := mload(add(pMem, pH1w4_3)) + + c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) + square := mulmod(h1w4, h1w4, q) + c1Value := addmod(c1Value, mulmod(square, evalC, q), q) + c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q) + + res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(3, 32)))), q), q), q) - res := addmod(res, mulmod(c1Value, lagrange, q), q) - } mstore(add(pMem, pR1), res) } @@ -510,60 +940,93 @@ contract FflonkVerifier { // where x = {[h2, h2w3, h2w3^2], [h3, h3w3, h3w3^2]} // and y = {[C2(h2), C2(h2w3), C2(h2w3^2)], [C2(h3), C2(h3w3), C2(h3w3^2)]} // and computing T1(xi) and T2(xi) - function computeR2(pProof, pMem) { + function computeR2(pMem) { + let y := mload(add(pMem, pY)) + let num := 1 + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + + let num2 := 1 + num2 := mulmod(y, num2, q) + num2 := mulmod(y, num2, q) + num2 := mulmod(y, num2, q) + num2 := mulmod(num2, addmod(mulmod(mload(add(pMem, pXi)), w1 ,q), mload(add(pMem, pXi)), q), q) + + num := addmod(num, mod(sub(q, num2), q), q) + + num2 := mulmod(mulmod(mload(add(pMem, pXi)), w1 ,q), mload(add(pMem, pXi)), q) + + num := addmod(num, num2, q) + let t1 let t2 let betaXi := mulmod(mload(add(pMem, pBeta)), mload(add(pMem, pXi)), q) let gamma := mload(add(pMem, pGamma)) - let evalZ := mload(add(pProof, pEval_z)) - let evalZw := mload(add(pProof, pEval_zw)) - t2 := addmod(mload(add(pProof, pEval_a)), addmod(betaXi, gamma, q) ,q) + t2 := addmod(calldataload( pEval_a), addmod(betaXi, gamma, q) ,q) t2 := mulmod(t2, - addmod(mload(add(pProof, pEval_b)), + addmod(calldataload( pEval_b), addmod(mulmod(betaXi, k1, q), gamma, q) ,q), q) t2 := mulmod(t2, - addmod(mload(add(pProof, pEval_c)), + addmod(calldataload( pEval_c), addmod(mulmod(betaXi, k2, q), gamma, q) ,q), q) - t2 := mulmod(t2, evalZ, q) + t2 := mulmod(t2, calldataload(pEval_z), q) //Let's use t1 as a temporal variable to save one local - t1 := addmod(mload(add(pProof, pEval_a)), addmod(mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), gamma, q) ,q) + t1 := addmod(calldataload(pEval_a), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s1), q), gamma, q) ,q) t1 := mulmod(t1, - addmod(mload(add(pProof, pEval_b)), addmod(mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), gamma, q) ,q), q) + addmod(calldataload(pEval_b), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s2), q), gamma, q) ,q), q) t1 := mulmod(t1, - addmod(mload(add(pProof, pEval_c)), addmod(mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s3)), q), gamma, q) ,q), q) - t1 := mulmod(t1, evalZw, q) + addmod(calldataload(pEval_c), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s3), q), gamma, q) ,q), q) + t1 := mulmod(t1, calldataload(pEval_z), q) t2:= addmod(t2, mod(sub(q, t1), q), q) t2 := mulmod(t2, mload(add(pMem, pZhInv)), q) // Compute T1(xi) - t1 := sub(evalZ, 1) + t1 := sub(calldataload(pEval_z), 1) t1 := mulmod(t1, mload(add(pMem, pEval_l1)) ,q) t1 := mulmod(t1, mload(add(pMem, pZhInv)) ,q) // Let's use local variable gamma to save the result gamma:=0 - for { let i := 0 } lt(i, 6) { i := add(i, 1) } - { - let hw := mload(add(pMem, add(pH2w3_0, mul(i, 32)))) - - let c2Value - if lt(i, 3) { - c2Value := addmod(evalZ, mulmod(hw, t1, q), q) - c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) - } - if gt(i, 2) { - c2Value := addmod(evalZw, mulmod(hw, mload(add(pProof, pEval_t1w)), q), q) - c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), mload(add(pProof, pEval_t2w)), q), q) - } - - let lagrange := calcLagrangeItem(pMem, i, 5, pY, pH2w3_0) - lagrange := mulmod(lagrange, mload(add(pMem, add(pLiS2Inv, mul(i, 32)))), q) - - gamma := addmod(gamma, mulmod(c2Value, lagrange, q), q) - } + + let hw + let c2Value + + hw := mload(add(pMem, pH2w3_0)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(0, 32)))), q), q), q) + + hw := mload(add(pMem, pH2w3_1)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(1, 32)))), q), q), q) + + hw := mload(add(pMem, pH2w3_2)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(2, 32)))), q), q), q) + + hw := mload(add(pMem, pH3w3_0)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, calldataload(pEval_t1w), q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(3, 32)))), q), q), q) + + hw := mload(add(pMem, pH3w3_1)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, calldataload(pEval_t1w), q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(4, 32)))), q), q), q) + + hw := mload(add(pMem, pH3w3_2)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, calldataload(pEval_t1w), q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q) + gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(5, 32)))), q), q), q) mstore(add(pMem, pR2), gamma) } @@ -588,8 +1051,8 @@ contract FflonkVerifier { function g1_mulAcc(pR, pP, s) { let success let mIn := mload(0x40) - mstore(mIn, mload(pP)) - mstore(add(mIn, 32), mload(add(pP, 32))) + mstore(mIn, calldataload(pP)) + mstore(add(mIn, 32), calldataload(add(pP, 32))) mstore(add(mIn, 64), s) success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64) @@ -636,7 +1099,7 @@ contract FflonkVerifier { } } - function computeFEJ(pProof, pMem) { + function computeFEJ(pMem) { // Prepare shared numerator between F, E and J to reuse it let y := mload(add(pMem, pY)) let numerator := addmod(y, mod(sub(q, mload(add(pMem, pH0w8_0))), q), q) @@ -655,18 +1118,18 @@ contract FflonkVerifier { // Compute full batched polynomial commitment [F]_1 mstore(add(pMem, pF), C0x) mstore(add(pMem, add(pF, 32)), C0y) - g1_mulAcc(add(pMem, pF), add(pProof, pC1), quotient1) - g1_mulAcc(add(pMem, pF), add(pProof, pC2), quotient2) + g1_mulAcc(add(pMem, pF), pC1, quotient1) + g1_mulAcc(add(pMem, pF), pC2, quotient2) // Compute group-encoded batch evaluation [E]_1 g1_mulAccC(add(pMem, pE), G1x, G1y, addmod(mload(add(pMem, pR0)), addmod(mulmod(quotient1, mload(add(pMem, pR1)),q), mulmod(quotient2, mload(add(pMem, pR2)),q), q), q)) // Compute the full difference [J]_1 - g1_mulAcc(add(pMem, pJ), add(pProof, pW1), numerator) + g1_mulAcc(add(pMem, pJ), pW1, numerator) } // Validate all evaluations with a pairing checking that e([F]_1 - [E]_1 - [J]_1 + y[W2]_1, [1]_2) == e([W']_1, [x]_2) - function checkPairing(pProof, pMem) -> isOk { + function checkPairing(pMem) -> isOk { let mIn := mload(0x40) // First pairing value @@ -677,7 +1140,7 @@ contract FflonkVerifier { // F = F - E - J + y·W2 g1_acc(add(pMem, pF), add(pMem, pE)) g1_acc(add(pMem, pF), add(pMem, pJ)) - g1_mulAcc(add(pMem, pF), add(pProof, pW2), mload(add(pMem, pY))) + g1_mulAcc(add(pMem, pF), pW2, mload(add(pMem, pY))) mstore(mIn, mload(add(pMem, pF))) mstore(add(mIn, 32), mload(add(add(pMem, pF), 32))) @@ -690,8 +1153,8 @@ contract FflonkVerifier { // Third pairing value // Compute -W2 - mstore(add(mIn, 192), mload(add(pProof, pW2))) - let s := mload(add(add(pProof, pW2), 32)) + mstore(add(mIn, 192), calldataload(pW2)) + let s := calldataload(add(pW2, 32)) s := mod(sub(qf, s), qf) mstore(add(mIn, 224), s) @@ -710,10 +1173,10 @@ contract FflonkVerifier { mstore(0x40, add(pMem, lastMem)) // Validate that all evaluations ∈ F - checkInput(proof) + checkInput() // Compute the challenges: beta, gamma, xi, alpha and y ∈ F, h1w4/h2w3/h3w3 roots, xiN and zh(xi) - computeChallenges(proof, pMem, pubSignals) + computeChallenges(pMem, pubSignals) // To divide prime fields the Extended Euclidean Algorithm for computing modular inverses is needed. // The Montgomery batch inversion algorithm allow us to compute n inverses reducing to a single one inversion. @@ -723,7 +1186,7 @@ contract FflonkVerifier { // 1) Prepare all the denominators to inverse // 2) Check the inverse sent by the prover it is what it should be // 3) Compute the others inverses using the Montgomery Batched Algorithm using the inverse sent to avoid the inversion operation it does. - computeInversions(proof, pMem) + computeInversions(pMem) // Compute Lagrange polynomial evaluations Li(xi) computeLagrange(pMem) @@ -732,15 +1195,15 @@ contract FflonkVerifier { computePi(pMem, pubSignals) // Computes r1(y) and r2(y) - computeR0(proof, pMem) - computeR1(proof, pMem) - computeR2(proof, pMem) + computeR0(pMem) + computeR1(pMem) + computeR2(pMem) // Compute full batched polynomial commitment [F]_1, group-encoded batch evaluation [E]_1 and the full difference [J]_1 - computeFEJ(proof, pMem) + computeFEJ(pMem) // Validate all evaluations - let isValid := checkPairing(proof, pMem) + let isValid := checkPairing(pMem) mstore(0, isValid) return(0, 0x20) From c8b54e0c0d69cf217cdb398da1ab4b1fef1ad2fb Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Sun, 30 Apr 2023 18:11:28 +0200 Subject: [PATCH 23/48] Plonk refactored with new clsses and working --- package-lock.json | 1889 +--------------------------------- src/plonk.js | 17 + src/plonk_prove.js | 1193 ++++++++++----------- src/polynomial/polynomial.js | 3 +- src/proof.js | 18 +- src/zkey_utils.js | 2 +- 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If not, see . */ +// ZKEY constants +export const ZKEY_PL_NSECTIONS = 13; + +export const ZKEY_PL_HEADER_SECTION = 2; +export const ZKEY_PL_ADDITIONS_SECTION = 3; +export const ZKEY_PL_A_MAP_SECTION = 4; +export const ZKEY_PL_B_MAP_SECTION = 5; +export const ZKEY_PL_C_MAP_SECTION = 6; +export const ZKEY_PL_QM_SECTION = 7; +export const ZKEY_PL_QL_SECTION = 8; +export const ZKEY_PL_QR_SECTION = 9; +export const ZKEY_PL_QO_SECTION = 10; +export const ZKEY_PL_QC_SECTION = 11; +export const ZKEY_PL_SIGMA_SECTION = 12; +export const ZKEY_PL_LAGRANGE_SECTION = 13; +export const ZKEY_PL_PTAU_SECTION = 14; + export {default as setup} from "./plonk_setup.js"; export {default as fullProve} from "./plonk_fullprove.js"; export {default as prove} from "./plonk_prove.js"; diff --git a/src/plonk_prove.js b/src/plonk_prove.js index d12368fa..da5193bf 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -24,17 +24,38 @@ import * as zkeyUtils from "./zkey_utils.js"; import * as wtnsUtils from "./wtns_utils.js"; import { Scalar, utils, BigBuffer } from "ffjavascript"; const {stringifyBigInts} = utils; -import jsSha3 from "js-sha3"; -const { keccak256 } = jsSha3; - +import { Proof } from "./proof.js"; +import { Keccak256Transcript } from "./Keccak256Transcript.js"; +import { MulZ } from "./mul_z.js"; +import { ZKEY_PL_HEADER_SECTION, + ZKEY_PL_ADDITIONS_SECTION, + ZKEY_PL_A_MAP_SECTION, + ZKEY_PL_B_MAP_SECTION, + ZKEY_PL_C_MAP_SECTION, + ZKEY_PL_QM_SECTION, + ZKEY_PL_QL_SECTION, + ZKEY_PL_QR_SECTION, + ZKEY_PL_QO_SECTION, + ZKEY_PL_QC_SECTION, + ZKEY_PL_SIGMA_SECTION, + ZKEY_PL_LAGRANGE_SECTION, + ZKEY_PL_PTAU_SECTION, + } from "./plonk.js"; + import { Polynomial } from "./polynomial/polynomial.js"; + import { Evaluations } from "./polynomial/evaluations.js"; + export default async function plonk16Prove(zkeyFileName, witnessFileName, logger) { const {fd: fdWtns, sections: sectionsWtns} = await binFileUtils.readBinFile(witnessFileName, "wtns", 2, 1<<25, 1<<23); + // Read witness file + if (logger) logger.debug("> Reading witness file"); const wtns = await wtnsUtils.readHeader(fdWtns, sectionsWtns); - const {fd: fdZKey, sections: sectionsZKey} = await binFileUtils.readBinFile(zkeyFileName, "zkey", 2, 1<<25, 1<<23); + // Read zkey file + if (logger) logger.debug("> Reading zkey file"); + const {fd: fdZKey, sections: zkeySections} = await binFileUtils.readBinFile(zkeyFileName, "zkey", 2, 1<<25, 1<<23); - const zkey = await zkeyUtils.readHeader(fdZKey, sectionsZKey); + const zkey = await zkeyUtils.readHeader(fdZKey, zkeySections); if (zkey.protocol != "plonk") { throw new Error("zkey file is not plonk"); } @@ -48,42 +69,65 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } const curve = zkey.curve; + const Fr = curve.Fr; - const G1 = curve.G1; const n8r = curve.Fr.n8; + const sDomain = zkey.domainSize * n8r; + + if (logger) { + logger.info("----------------------------"); + logger.info(" PLONK PROVE SETTINGS"); + logger.info(` Curve: ${curve.name}`); + logger.info(` Circuit power: ${zkey.power}`); + logger.info(` Domain size: ${zkey.domainSize}`); + logger.info(` Vars: ${zkey.nVars}`); + logger.info(` Public vars: ${zkey.nPublic}`); + logger.info(` Constraints: ${zkey.nConstraints}`); + logger.info(` Additions: ${zkey.nAdditions}`); + logger.info("----------------------------"); + } - if (logger) logger.debug("Reading Wtns"); + //Read witness data + if (logger) logger.info("> Reading witness file data"); const buffWitness = await binFileUtils.readSection(fdWtns, sectionsWtns, 2); + // First element in plonk is not used and can be any value. (But always the same). // We set it to zero to go faster in the exponentiations. buffWitness.set(Fr.zero, 0); const buffInternalWitness = new BigBuffer(n8r*zkey.nAdditions); - await calculateAdditions(); + let buffers = {}; + let polynomials = {}; + let evaluations = {}; - let A,B,C,Z; - let A4, B4, C4, Z4; - let pol_a,pol_b,pol_c, pol_z, pol_t, pol_r; - let proof = {}; + let challenges = {}; + let proof = new Proof(curve, logger); + const transcript = new Keccak256Transcript(curve); - const sigmaBuff = new BigBuffer(zkey.domainSize*n8r*4*3); - let o = sectionsZKey[12][0].p + zkey.domainSize*n8r; - await fdZKey.readToBuffer(sigmaBuff, 0 , zkey.domainSize*n8r*4, o); - o += zkey.domainSize*n8r*5; - await fdZKey.readToBuffer(sigmaBuff, zkey.domainSize*n8r*4 , zkey.domainSize*n8r*4, o); - o += zkey.domainSize*n8r*5; - await fdZKey.readToBuffer(sigmaBuff, zkey.domainSize*n8r*8 , zkey.domainSize*n8r*4, o); + if (logger) logger.info(`> Reading Section ${ZKEY_PL_ADDITIONS_SECTION}. Additions`); + await calculateAdditions(); - const pol_s1 = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_s1, 0 , zkey.domainSize*n8r, sectionsZKey[12][0].p); + if (logger) logger.info(`> Reading Section ${ZKEY_PL_SIGMA_SECTION}. Sigma1, Sigma2 & Sigma 3`); + if (logger) logger.info("··· Reading Sigma polynomials "); + polynomials.Sigma1 = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.Sigma2 = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.Sigma3 = new Polynomial(new BigBuffer(sDomain), curve, logger); - const pol_s2 = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_s2, 0 , zkey.domainSize*n8r, sectionsZKey[12][0].p + 5*zkey.domainSize*n8r); + await fdZKey.readToBuffer(polynomials.Sigma1.coef, 0, sDomain, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.Sigma2.coef, 0, sDomain, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 5 * sDomain); + await fdZKey.readToBuffer(polynomials.Sigma3.coef, 0, sDomain, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 10 * sDomain); - const PTau = await binFileUtils.readSection(fdZKey, sectionsZKey, 14); + if (logger) logger.info("··· Reading Sigma evaluations"); + evaluations.Sigma1 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.Sigma2 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.Sigma3 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + await fdZKey.readToBuffer(evaluations.Sigma1.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + sDomain); + await fdZKey.readToBuffer(evaluations.Sigma2.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 6 * sDomain); + await fdZKey.readToBuffer(evaluations.Sigma3.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 11 * sDomain); - const ch = {}; + if (logger) logger.info(`> Reading Section ${ZKEY_PL_PTAU_SECTION}. Powers of Tau`); + const PTau = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_PTAU_SECTION); await round1(); await round2(); @@ -91,14 +135,10 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger await round4(); await round5(); - /////////////////////// // Final adjustments // /////////////////////// - proof.protocol = "plonk"; - proof.curve = curve.name; - await fdZKey.close(); await fdWtns.close(); @@ -109,79 +149,46 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger publicSignals.push(Scalar.fromRprLE(pub)); } - proof.A = G1.toObject(proof.A); - proof.B = G1.toObject(proof.B); - proof.C = G1.toObject(proof.C); - proof.Z = G1.toObject(proof.Z); - - proof.T1 = G1.toObject(proof.T1); - proof.T2 = G1.toObject(proof.T2); - proof.T3 = G1.toObject(proof.T3); - - proof.eval_a = Fr.toObject(proof.eval_a); - proof.eval_b = Fr.toObject(proof.eval_b); - proof.eval_c = Fr.toObject(proof.eval_c); - proof.eval_s1 = Fr.toObject(proof.eval_s1); - proof.eval_s2 = Fr.toObject(proof.eval_s2); - proof.eval_zw = Fr.toObject(proof.eval_zw); - proof.eval_t = Fr.toObject(proof.eval_t); - proof.eval_r = Fr.toObject(proof.eval_r); - - proof.Wxi = G1.toObject(proof.Wxi); - proof.Wxiw = G1.toObject(proof.Wxiw); - - delete proof.eval_t; - - proof = stringifyBigInts(proof); - publicSignals = stringifyBigInts(publicSignals); - - return {proof, publicSignals}; + // Prepare proof + let _proof = proof.toObjectProof(false); + _proof.protocol = "plonk"; + _proof.curve = curve.name; + + return { + proof: stringifyBigInts(_proof), + publicSignals: stringifyBigInts(publicSignals) + }; async function calculateAdditions() { - const additionsBuff = await binFileUtils.readSection(fdZKey, sectionsZKey, 3); - - const sSum = 8+curve.Fr.n8*2; - - for (let i=0; i Computing A, B, C wire polynomials"); + await computeWirePolynomials(); + + // The first output of the prover is ([A]_1, [B]_1, [C]_1) + let commitA = await polynomials.A.multiExponentiation(PTau, "A"); + let commitB = await polynomials.B.multiExponentiation(PTau, "B"); + let commitC = await polynomials.C.multiExponentiation(PTau, "C"); - - proof.A = await expTau(pol_a, "multiexp A"); - proof.B = await expTau(pol_b, "multiexp B"); - proof.C = await expTau(pol_c, "multiexp C"); + proof.addPolynomial("A", commitA); + proof.addPolynomial("B", commitB); + proof.addPolynomial("C", commitC); + + return 0; + } + + async function computeWirePolynomials() { + if (logger) logger.info("··· Reading data from zkey file"); + // Build A, B and C evaluations buffer from zkey and witness files + buffers.A = new BigBuffer(sDomain); + buffers.B = new BigBuffer(sDomain); + buffers.C = new BigBuffer(sDomain); + + const aMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_A_MAP_SECTION); + const bMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_B_MAP_SECTION); + const cMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_C_MAP_SECTION); + + // Compute all witness from signal ids and set them to A,B & C buffers + for (let i = 0; i < zkey.nConstraints; i++) { + const i_sFr = i * n8r; + const offset = i * 4; + + // Compute A value from a signal id + const signalIdA = readUInt32(aMapBuff, offset); + buffers.A.set(getWitness(signalIdA), i_sFr); + + // Compute B value from a signal id + const signalIdB = readUInt32(bMapBuff, offset); + buffers.B.set(getWitness(signalIdB), i_sFr); + + // Compute C value from a signal id + const signalIdC = readUInt32(cMapBuff, offset); + buffers.C.set(getWitness(signalIdC), i_sFr); + } + + buffers.A = await Fr.batchToMontgomery(buffers.A); + buffers.B = await Fr.batchToMontgomery(buffers.B); + buffers.C = await Fr.batchToMontgomery(buffers.C); + + // Compute the coefficients of the wire polynomials a(X), b(X) and c(X) from A,B & C buffers + if (logger) logger.info("··· Computing A ifft"); + polynomials.A = await Polynomial.fromEvaluations(buffers.A, curve, logger); + if (logger) logger.info("··· Computing B ifft"); + polynomials.B = await Polynomial.fromEvaluations(buffers.B, curve, logger); + if (logger) logger.info("··· Computing C ifft"); + polynomials.C = await Polynomial.fromEvaluations(buffers.C, curve, logger); + + // Compute extended evaluations of a(X), b(X) and c(X) polynomials + if (logger) logger.info("··· Computing A fft"); + evaluations.A = await Evaluations.fromPolynomial(polynomials.A, 4, curve, logger); + if (logger) logger.info("··· Computing B fft"); + evaluations.B = await Evaluations.fromPolynomial(polynomials.B, 4, curve, logger); + if (logger) logger.info("··· Computing C fft"); + evaluations.C = await Evaluations.fromPolynomial(polynomials.C, 4, curve, logger); + + // Blind a(X), b(X) and c(X) polynomials coefficients with blinding scalars b + polynomials.A.blindCoefficients([challenges.b[2], challenges.b[1]]); + polynomials.B.blindCoefficients([challenges.b[4], challenges.b[3]]); + polynomials.C.blindCoefficients([challenges.b[6], challenges.b[5]]); + + // // Check degrees + if (polynomials.A.degree() >= zkey.domainSize + 2) { + throw new Error("A Polynomial is not well calculated"); + } + if (polynomials.B.degree() >= zkey.domainSize + 2) { + throw new Error("B Polynomial is not well calculated"); + } + if (polynomials.C.degree() >= zkey.domainSize + 2) { + throw new Error("C Polynomial is not well calculated"); + } } async function round2() { + // STEP 2.1 - Compute permutation challenge beta and gamma ∈ F + // Compute permutation challenge beta + if (logger) logger.debug("> Computing challenges beta and gamma"); + transcript.reset(); + + // TODO Add circuit dependent commitment to the transcript!!!!! + //transcript.addPolCommitment(zkey.?????); - const transcript1 = new Uint8Array(zkey.nPublic*n8r + G1.F.n8*2*3); - for (let i=0; i Computing Z polynomial"); + await computeZ(); + + // The second output of the prover is ([Z]_1) + let commitZ = await polynomials.Z.multiExponentiation(PTau, "Z"); + + proof.addPolynomial("Z", commitZ); + } + async function computeZ() { + if (logger) logger.info("··· Computing Z evaluations"); + + let numArr = new BigBuffer(sDomain); + let denArr = new BigBuffer(sDomain); + + // Set the first values to 1 numArr.set(Fr.one, 0); denArr.set(Fr.one, 0); + // Set initial omega let w = Fr.one; - for (let i=0; i0)&&(Fr.isZero(p.slice(deg*n8r, deg*n8r+n8r)))) deg--; - return deg; - } + let den = Fr.mul(d1, Fr.mul(d2, d3)); - function printPol(P) { - const n=(P.byteLength/n8r); - console.log("["); - for (let i=0; i= zkey.domainSize + 3) { + throw new Error("Z Polynomial is not well calculated"); + } - const Z2 = [ - Fr.zero, - Fr.add(Fr.zero, Fr.mul(Fr.e(-2), Fr.w[2])), - Fr.e(4), - Fr.sub(Fr.zero, Fr.mul(Fr.e(-2), Fr.w[2])), - ]; + delete buffers.Z; + } - const Z3 = [ - Fr.zero, - Fr.add(Fr.e(2), Fr.mul(Fr.e(2), Fr.w[2])), - Fr.e(-8), - Fr.sub(Fr.e(2), Fr.mul(Fr.e(2), Fr.w[2])), - ]; + async function round3() { + if (logger) logger.debug("> Computing challenge alpha"); + // STEP 3.1 - Compute evaluation challenge xi ∈ S + transcript.reset(); + transcript.addPolCommitment(proof.getPolynomial("Z")); + + challenges.alpha = transcript.getChallenge(); + challenges.alpha2 = Fr.square(challenges.alpha); + if (logger) logger.debug("··· challenges.alpha: " + Fr.toString(challenges.alpha)); + + if (logger) logger.info(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + + `, ${ZKEY_PL_QM_SECTION}, ${ZKEY_PL_QO_SECTION}, ${ZKEY_PL_QC_SECTION}. Q selectors`); + // Reserve memory for Q's evaluations + evaluations.QL = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.QR = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.QM = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.QO = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + evaluations.QC = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); + + // Read Q's evaluations from zkey file + await fdZKey.readToBuffer(evaluations.QL.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_QL_SECTION][0].p + sDomain); + await fdZKey.readToBuffer(evaluations.QR.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_QR_SECTION][0].p + sDomain); + await fdZKey.readToBuffer(evaluations.QM.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_QM_SECTION][0].p + sDomain); + await fdZKey.readToBuffer(evaluations.QO.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_QO_SECTION][0].p + sDomain); + await fdZKey.readToBuffer(evaluations.QC.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_QC_SECTION][0].p + sDomain); + + // Read Lagrange polynomials & evaluations from zkey file + evaluations.Lagrange = new Evaluations(new BigBuffer(sDomain * 4 * zkey.nPublic), curve, logger); + + for (let i = 0; i < zkey.nPublic; i++) { + await fdZKey.readToBuffer(evaluations.Lagrange.eval, i * sDomain * 4, sDomain * 4, zkeySections[ZKEY_PL_LAGRANGE_SECTION][0].p + i * 5 * sDomain + sDomain); + } - const T = new BigBuffer(zkey.domainSize*4*n8r); - const Tz = new BigBuffer(zkey.domainSize*4*n8r); + buffers.T = new BigBuffer(sDomain * 4); + buffers.Tz = new BigBuffer(sDomain * 4); let w = Fr.one; for (let i=0; i (zkey.domainSize*3 -4) ) { - if (!Fr.isZero(a)) { - throw new Error("T Polynomial is not divisible"); - } - } - } + // Add the polynomial T1z to T1 to get the final polynomial T1 + polynomials.T.add(polynomials.Tz); - if (logger) logger.debug("ifft Tz"); - const tz = await Fr.ifft(Tz); - for (let i=0; i (zkey.domainSize*3 +5) ) { - if (!Fr.isZero(a)) { - throw new Error("Tz Polynomial is not well calculated"); - } - } else { - t.set( - Fr.add( - t.slice(i*n8r, (i+1)*n8r), - a - ), - i*n8r - ); - } + // Check degree + if (polynomials.T.degree() >= zkey.domainSize * 3 + 6) { + throw new Error("T Polynomial is not well calculated"); } - - pol_t = t.slice(0, (zkey.domainSize * 3 + 6) * n8r); - + // t(x) has degree 3n + 5, we are going to split t(x) into three smaller polynomials: - // t'_low and t'_mid with a degree < n and t'_high with a degree n+5 - // such that t(x) = t'_low(X) + X^n t'_mid(X) + X^{2n} t'_hi(X) + // T1' and T2' with a degree < n and T3' with a degree n+5 + // such that t(x) = T1'(X) + X^n T2'(X) + X^{2n} T3'(X) // To randomize the parts we use blinding scalars b_10 and b_11 in a way that doesn't change t(X): - // t_low(X) = t'_low(X) + b_10 X^n - // t_mid(X) = t'_mid(X) - b_10 + b_11 X^n - // t_high(X) = t'_high(X) - b_11 + // T1(X) = T1'(X) + b_10 X^n + // T2(X) = T2'(X) - b_10 + b_11 X^n + // T3(X) = T3'(X) - b_11 // such that - // t(X) = t_low(X) + X^n t_mid(X) + X^2n t_high(X) + // t(X) = T1(X) + X^n T2(X) + X^2n T3(X) + + polynomials.T1 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); + polynomials.T2 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); + polynomials.T3 = new Polynomial(new BigBuffer((zkey.domainSize + 6) * n8r), curve, logger); + + polynomials.T1.coef.set(polynomials.T.coef.slice(0, sDomain), 0); + polynomials.T2.coef.set(polynomials.T.coef.slice(sDomain, sDomain * 2), 0); + polynomials.T3.coef.set(polynomials.T.coef.slice(sDomain * 2, sDomain * 3 + 6 * n8r), 0); - // compute t_low(X) - let polTLow = new BigBuffer((zkey.domainSize + 1) * n8r); - polTLow.set(t.slice(0, zkey.domainSize * n8r), 0); // Add blinding scalar b_10 as a new coefficient n - polTLow.set(ch.b[10], zkey.domainSize * n8r); + polynomials.T1.setCoef(zkey.domainSize, challenges.b[10]); // compute t_mid(X) - let polTMid = new BigBuffer((zkey.domainSize + 1) * n8r); - polTMid.set(t.slice(zkey.domainSize * n8r, zkey.domainSize * 2 * n8r), 0); // Subtract blinding scalar b_10 to the lowest coefficient of t_mid - const lowestMid = Fr.sub(polTMid.slice(0, n8r), ch.b[10]); - polTMid.set(lowestMid, 0); - // Add blinding scalar b_11 as a new coefficient n - polTMid.set(ch.b[11], zkey.domainSize * n8r); + const lowestMid = Fr.sub(polynomials.T2.getCoef(0), challenges.b[10]); + polynomials.T2.setCoef(0, lowestMid); + polynomials.T2.setCoef(zkey.domainSize, challenges.b[11]); // compute t_high(X) - let polTHigh = new BigBuffer((zkey.domainSize + 6) * n8r); - polTHigh.set(t.slice(zkey.domainSize * 2 * n8r, (zkey.domainSize * 3 + 6) * n8r), 0); //Subtract blinding scalar b_11 to the lowest coefficient of t_high - const lowestHigh = Fr.sub(polTHigh.slice(0, n8r), ch.b[11]); - polTHigh.set(lowestHigh, 0); - - proof.T1 = await expTau(polTLow, "multiexp T1"); - proof.T2 = await expTau(polTMid, "multiexp T2"); - proof.T3 = await expTau(polTHigh, "multiexp T3"); - - function mul2(a,b, ap, bp, p) { - let r, rz; - - - const a_b = Fr.mul(a,b); - const a_bp = Fr.mul(a,bp); - const ap_b = Fr.mul(ap,b); - const ap_bp = Fr.mul(ap,bp); - - r = a_b; + const lowestHigh = Fr.sub(polynomials.T3.getCoef(0), challenges.b[11]); + polynomials.T3.setCoef(0, lowestHigh); - let a0 = Fr.add(a_bp, ap_b); - - let a1 = ap_bp; - - rz = a0; - if (p) { - rz = Fr.add(rz, Fr.mul(Z1[p], a1)); - } - - return [r, rz]; - } - - function mul4(a,b,c,d, ap, bp, cp, dp, p) { - let r, rz; - - - const a_b = Fr.mul(a,b); - const a_bp = Fr.mul(a,bp); - const ap_b = Fr.mul(ap,b); - const ap_bp = Fr.mul(ap,bp); - - const c_d = Fr.mul(c,d); - const c_dp = Fr.mul(c,dp); - const cp_d = Fr.mul(cp,d); - const cp_dp = Fr.mul(cp,dp); - - r = Fr.mul(a_b, c_d); - - let a0 = Fr.mul(ap_b, c_d); - a0 = Fr.add(a0, Fr.mul(a_bp, c_d)); - a0 = Fr.add(a0, Fr.mul(a_b, cp_d)); - a0 = Fr.add(a0, Fr.mul(a_b, c_dp)); - - let a1 = Fr.mul(ap_bp, c_d); - a1 = Fr.add(a1, Fr.mul(ap_b, cp_d)); - a1 = Fr.add(a1, Fr.mul(ap_b, c_dp)); - a1 = Fr.add(a1, Fr.mul(a_bp, cp_d)); - a1 = Fr.add(a1, Fr.mul(a_bp, c_dp)); - a1 = Fr.add(a1, Fr.mul(a_b, cp_dp)); - - let a2 = Fr.mul(a_bp, cp_dp); - a2 = Fr.add(a2, Fr.mul(ap_b, cp_dp)); - a2 = Fr.add(a2, Fr.mul(ap_bp, c_dp)); - a2 = Fr.add(a2, Fr.mul(ap_bp, cp_d)); - - let a3 = Fr.mul(ap_bp, cp_dp); - - rz = a0; - if (p) { - rz = Fr.add(rz, Fr.mul(Z1[p], a1)); - rz = Fr.add(rz, Fr.mul(Z2[p], a2)); - rz = Fr.add(rz, Fr.mul(Z3[p], a3)); - } + // The third output of the prover is ([T1]_1, [T2]_1, [T3]_1) + let commitT1 = await polynomials.T1.multiExponentiation(PTau, "T1"); + let commitT2 = await polynomials.T2.multiExponentiation(PTau, "T2"); + let commitT3 = await polynomials.T3.multiExponentiation(PTau, "T3"); - return [r, rz]; - } + proof.addPolynomial("T1", commitT1); + proof.addPolynomial("T2", commitT2); + proof.addPolynomial("T3", commitT3); } async function round4() { - const pol_qm = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_qm, 0 , zkey.domainSize*n8r, sectionsZKey[7][0].p); - - const pol_ql = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_ql, 0 , zkey.domainSize*n8r, sectionsZKey[8][0].p); - - const pol_qr = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_qr, 0 , zkey.domainSize*n8r, sectionsZKey[9][0].p); - - const pol_qo = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_qo, 0 , zkey.domainSize*n8r, sectionsZKey[10][0].p); - - const pol_qc = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_qc, 0 , zkey.domainSize*n8r, sectionsZKey[11][0].p); - - const pol_s3 = new BigBuffer(zkey.domainSize*n8r); - await fdZKey.readToBuffer(pol_s3, 0 , zkey.domainSize*n8r, sectionsZKey[12][0].p + 10*zkey.domainSize*n8r); - - const transcript4 = new Uint8Array(G1.F.n8*2*3); - G1.toRprUncompressed(transcript4, 0, proof.T1); - G1.toRprUncompressed(transcript4, G1.F.n8*2, proof.T2); - G1.toRprUncompressed(transcript4, G1.F.n8*4, proof.T3); - ch.xi = hashToFr(transcript4); - - if (logger) logger.debug("xi: " + Fr.toString(ch.xi)); - - proof.eval_a = evalPol(pol_a, ch.xi); - proof.eval_b = evalPol(pol_b, ch.xi); - proof.eval_c = evalPol(pol_c, ch.xi); - proof.eval_s1 = evalPol(pol_s1, ch.xi); - proof.eval_s2 = evalPol(pol_s2, ch.xi); - proof.eval_t = evalPol(pol_t, ch.xi); - proof.eval_zw = evalPol(pol_z, Fr.mul(ch.xi, Fr.w[zkey.power])); - - const coef_ab = Fr.mul(proof.eval_a, proof.eval_b); + if (logger) logger.debug("> Computing challenge xi"); + // STEP 3.1 - Compute evaluation challenge xi ∈ S + transcript.reset(); + transcript.addPolCommitment(proof.getPolynomial("T1")); + transcript.addPolCommitment(proof.getPolynomial("T2")); + transcript.addPolCommitment(proof.getPolynomial("T3")); + + challenges.xi = transcript.getChallenge(); + challenges.xiw = Fr.mul(challenges.xi, Fr.w[zkey.power]); + if (logger) logger.debug("··· challenges.xi: " + Fr.toString(challenges.xi)); + + // Reserve memory for Q's polynomials + polynomials.QL = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.QR = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.QM = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.QO = new Polynomial(new BigBuffer(sDomain), curve, logger); + polynomials.QC = new Polynomial(new BigBuffer(sDomain), curve, logger); + + // Read Q's evaluations from zkey file + await fdZKey.readToBuffer(polynomials.QL.coef, 0, sDomain, zkeySections[ZKEY_PL_QL_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.QR.coef, 0, sDomain, zkeySections[ZKEY_PL_QR_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.QM.coef, 0, sDomain, zkeySections[ZKEY_PL_QM_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.QO.coef, 0, sDomain, zkeySections[ZKEY_PL_QO_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.QC.coef, 0, sDomain, zkeySections[ZKEY_PL_QC_SECTION][0].p); + + proof.addEvaluation("eval_a", polynomials.A.evaluate(challenges.xi)); + proof.addEvaluation("eval_b", polynomials.B.evaluate(challenges.xi)); + proof.addEvaluation("eval_c", polynomials.C.evaluate(challenges.xi)); + proof.addEvaluation("eval_s1", polynomials.Sigma1.evaluate(challenges.xi)); + proof.addEvaluation("eval_s2", polynomials.Sigma2.evaluate(challenges.xi)); + proof.addEvaluation("eval_t", polynomials.T.evaluate(challenges.xi)); + proof.addEvaluation("eval_zw", polynomials.Z.evaluate(challenges.xiw)); + + const coef_ab = Fr.mul(proof.evaluations.eval_a, proof.evaluations.eval_b); - let e2a = proof.eval_a; - const betaxi = Fr.mul(ch.beta, ch.xi); + let e2a = proof.evaluations.eval_a; + const betaxi = Fr.mul(challenges.beta, challenges.xi); e2a = Fr.add( e2a, betaxi); - e2a = Fr.add( e2a, ch.gamma); + e2a = Fr.add( e2a, challenges.gamma); - let e2b = proof.eval_b; + let e2b = proof.evaluations.eval_b; e2b = Fr.add( e2b, Fr.mul(betaxi, zkey.k1)); - e2b = Fr.add( e2b, ch.gamma); + e2b = Fr.add( e2b, challenges.gamma); - let e2c = proof.eval_c; + let e2c = proof.evaluations.eval_c; e2c = Fr.add( e2c, Fr.mul(betaxi, zkey.k2)); - e2c = Fr.add( e2c, ch.gamma); + e2c = Fr.add( e2c, challenges.gamma); - const e2 = Fr.mul(Fr.mul(Fr.mul(e2a, e2b), e2c), ch.alpha); + const e2 = Fr.mul(Fr.mul(Fr.mul(e2a, e2b), e2c), challenges.alpha); - let e3a = proof.eval_a; - e3a = Fr.add( e3a, Fr.mul(ch.beta, proof.eval_s1)); - e3a = Fr.add( e3a, ch.gamma); + let e3a = proof.evaluations.eval_a; + e3a = Fr.add( e3a, Fr.mul(challenges.beta, proof.evaluations.eval_s1)); + e3a = Fr.add( e3a, challenges.gamma); - let e3b = proof.eval_b; - e3b = Fr.add( e3b, Fr.mul(ch.beta, proof.eval_s2)); - e3b = Fr.add( e3b, ch.gamma); + let e3b = proof.evaluations.eval_b; + e3b = Fr.add( e3b, Fr.mul(challenges.beta, proof.evaluations.eval_s2)); + e3b = Fr.add( e3b, challenges.gamma); let e3 = Fr.mul(e3a, e3b); - e3 = Fr.mul(e3, ch.beta); - e3 = Fr.mul(e3, proof.eval_zw); - e3 = Fr.mul(e3, ch.alpha); + e3 = Fr.mul(e3, challenges.beta); + e3 = Fr.mul(e3, proof.evaluations.eval_zw); + e3 = Fr.mul(e3, challenges.alpha); - ch.xim= ch.xi; - for (let i=0; i Computing challenge v"); + + transcript.reset(); + transcript.addScalar(proof.getEvaluation("eval_a")); + transcript.addScalar(proof.getEvaluation("eval_b")); + transcript.addScalar(proof.getEvaluation("eval_c")); + transcript.addScalar(proof.getEvaluation("eval_s1")); + transcript.addScalar(proof.getEvaluation("eval_s2")); + transcript.addScalar(proof.getEvaluation("eval_zw")); + transcript.addScalar(proof.getEvaluation("eval_r")); + + challenges.v = []; + challenges.v[1] = transcript.getChallenge(); + if (logger) logger.debug("··· challenges.v: " + Fr.toString(challenges.v)); + + for (let i=2; i<=6; i++ ) challenges.v[i] = Fr.mul(challenges.v[i-1], challenges.v[1]); - let pol_wxi = new BigBuffer((zkey.domainSize+6)*n8r); - - const xi2m = Fr.mul(ch.xim, ch.xim); - - for (let i = 0; i < zkey.domainSize + 6; i++) { - let w = Fr.zero; - - const polTHigh = pol_t.slice((zkey.domainSize * 2 + i) * n8r, (zkey.domainSize * 2 + i + 1) * n8r); - w = Fr.add(w, Fr.mul(xi2m, polTHigh)); - - if (i < zkey.domainSize + 3) { - w = Fr.add(w, Fr.mul(ch.v[1], pol_r.slice(i * n8r, (i + 1) * n8r))); - } - - if (i < zkey.domainSize + 2) { - w = Fr.add(w, Fr.mul(ch.v[2], pol_a.slice(i * n8r, (i + 1) * n8r))); - w = Fr.add(w, Fr.mul(ch.v[3], pol_b.slice(i * n8r, (i + 1) * n8r))); - w = Fr.add(w, Fr.mul(ch.v[4], pol_c.slice(i * n8r, (i + 1) * n8r))); - } - - if (i < zkey.domainSize) { - const polTLow = pol_t.slice(i * n8r, (i + 1) * n8r); - w = Fr.add(w, polTLow); - - const polTMid = pol_t.slice((zkey.domainSize + i) * n8r, (zkey.domainSize + i + 1) * n8r); - w = Fr.add(w, Fr.mul(ch.xim, polTMid)); - - w = Fr.add(w, Fr.mul(ch.v[5], pol_s1.slice(i * n8r, (i + 1) * n8r))); - w = Fr.add(w, Fr.mul(ch.v[6], pol_s2.slice(i * n8r, (i + 1) * n8r))); - } - - // b_10 and b_11 blinding scalars were applied on round 3 to randomize the polynomials t_low, t_mid, t_high - // Subtract blinding scalar b_10 and b_11 to the lowest coefficient - if (i === 0) { - w = Fr.sub(w, Fr.mul(xi2m, ch.b[11])); - w = Fr.sub(w, Fr.mul(ch.xim, ch.b[10])); - } - - // Add blinding scalars b_10 and b_11 to the coefficient n - if (i === zkey.domainSize) { - w = Fr.add(w, ch.b[10]); - w = Fr.add(w, Fr.mul(ch.xim, ch.b[11])); - } - - pol_wxi.set(w, i * n8r); - } - - let w0 = pol_wxi.slice(0, n8r); - w0 = Fr.sub(w0, proof.eval_t); - w0 = Fr.sub(w0, Fr.mul(ch.v[1], proof.eval_r)); - w0 = Fr.sub(w0, Fr.mul(ch.v[2], proof.eval_a)); - w0 = Fr.sub(w0, Fr.mul(ch.v[3], proof.eval_b)); - w0 = Fr.sub(w0, Fr.mul(ch.v[4], proof.eval_c)); - w0 = Fr.sub(w0, Fr.mul(ch.v[5], proof.eval_s1)); - w0 = Fr.sub(w0, Fr.mul(ch.v[6], proof.eval_s2)); - pol_wxi.set(w0, 0); - - pol_wxi= divPol1(pol_wxi, ch.xi); - - proof.Wxi = await expTau(pol_wxi, "multiexp Wxi"); - - let pol_wxiw = new BigBuffer((zkey.domainSize+3)*n8r); - for (let i=0; i=0; i--) { - res = Fr.add(Fr.mul(res, x), P.slice(i*n8r, (i+1)*n8r)); - } - return res; - } - - function divPol1(P, d) { - const n = P.byteLength/n8r; - const res = new BigBuffer(n*n8r); - res.set(Fr.zero, (n-1) *n8r); - res.set(P.slice((n-1)*n8r, n*n8r), (n-2)*n8r); - for (let i=n-3; i>=0; i--) { - res.set( - Fr.add( - P.slice((i+1)*n8r, (i+2)*n8r), - Fr.mul( - d, - res.slice((i+1)*n8r, (i+2)*n8r) - ) - ), - i*n8r - ); - } - if (!Fr.eq( - P.slice(0, n8r), - Fr.mul( - Fr.neg(d), - res.slice(0, n8r) - ) - )) { - throw new Error("Polinomial does not divide"); - } - return res; - } - - async function expTau(b, name) { - const n = b.byteLength/n8r; - const PTauN = PTau.slice(0, n*curve.G1.F.n8*2); - const bm = await curve.Fr.batchFromMontgomery(b); - let res = await curve.G1.multiExpAffine(PTauN, bm, logger, name); - res = curve.G1.toAffine(res); - return res; - } - - - async function to4T(A, pz) { - pz = pz || []; - let a = await Fr.ifft(A); - const a4 = new BigBuffer(n8r*zkey.domainSize*4); - a4.set(a, 0); - - const a1 = new BigBuffer(n8r*(zkey.domainSize + pz.length)); - a1.set(a, 0); - for (let i= 0; i { - res.polynomials[key] = this.curve.G1.toObject(this.polynomials[key]); + const value = this.curve.G1.toObject(this.polynomials[key]); + if(splitFields) { + res.polynomials[key] = value; + } else { + res[key] = value; + } }); Object.keys(this.evaluations).forEach(key => { - res.evaluations[key] = this.curve.Fr.toObject(this.evaluations[key]); + const value = this.curve.Fr.toObject(this.evaluations[key]); + if(splitFields) { + res.polynomials[key] = value; + } else { + res[key] = value; + } }); return res; diff --git a/src/zkey_utils.js b/src/zkey_utils.js index 54bbddbc..5ceb4c71 100644 --- a/src/zkey_utils.js +++ b/src/zkey_utils.js @@ -279,7 +279,7 @@ async function readHeaderPlonk(fd, sections, toObject) { zkey.domainSize = await fd.readULE32(); zkey.power = log2(zkey.domainSize); zkey.nAdditions = await fd.readULE32(); - zkey.nConstrains = await fd.readULE32(); + zkey.nConstraints = await fd.readULE32(); zkey.k1 = await fd.read(n8r); zkey.k2 = await fd.read(n8r); From 3b6349d3bbb109e56ddc4dba7ee0ad7861e09a19 Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Mon, 1 May 2023 09:21:19 +0200 Subject: [PATCH 24/48] change logger.in -> logger.debug --- src/plonk_prove.js | 98 ++++++++++++++++++++++++++-------------------- 1 file changed, 55 insertions(+), 43 deletions(-) diff --git a/src/plonk_prove.js b/src/plonk_prove.js index da5193bf..777a7770 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -75,20 +75,20 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger const sDomain = zkey.domainSize * n8r; if (logger) { - logger.info("----------------------------"); - logger.info(" PLONK PROVE SETTINGS"); - logger.info(` Curve: ${curve.name}`); - logger.info(` Circuit power: ${zkey.power}`); - logger.info(` Domain size: ${zkey.domainSize}`); - logger.info(` Vars: ${zkey.nVars}`); - logger.info(` Public vars: ${zkey.nPublic}`); - logger.info(` Constraints: ${zkey.nConstraints}`); - logger.info(` Additions: ${zkey.nAdditions}`); - logger.info("----------------------------"); + logger.debug("----------------------------"); + logger.debug(" PLONK PROVE SETTINGS"); + logger.debug(` Curve: ${curve.name}`); + logger.debug(` Circuit power: ${zkey.power}`); + logger.debug(` Domain size: ${zkey.domainSize}`); + logger.debug(` Vars: ${zkey.nVars}`); + logger.debug(` Public vars: ${zkey.nPublic}`); + logger.debug(` Constraints: ${zkey.nConstraints}`); + logger.debug(` Additions: ${zkey.nAdditions}`); + logger.debug("----------------------------"); } //Read witness data - if (logger) logger.info("> Reading witness file data"); + if (logger) logger.debug("> Reading witness file data"); const buffWitness = await binFileUtils.readSection(fdWtns, sectionsWtns, 2); // First element in plonk is not used and can be any value. (But always the same). @@ -104,11 +104,11 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger let proof = new Proof(curve, logger); const transcript = new Keccak256Transcript(curve); - if (logger) logger.info(`> Reading Section ${ZKEY_PL_ADDITIONS_SECTION}. Additions`); + if (logger) logger.debug(`> Reading Section ${ZKEY_PL_ADDITIONS_SECTION}. Additions`); await calculateAdditions(); - if (logger) logger.info(`> Reading Section ${ZKEY_PL_SIGMA_SECTION}. Sigma1, Sigma2 & Sigma 3`); - if (logger) logger.info("··· Reading Sigma polynomials "); + if (logger) logger.debug(`> Reading Section ${ZKEY_PL_SIGMA_SECTION}. Sigma1, Sigma2 & Sigma 3`); + if (logger) logger.debug("··· Reading Sigma polynomials "); polynomials.Sigma1 = new Polynomial(new BigBuffer(sDomain), curve, logger); polynomials.Sigma2 = new Polynomial(new BigBuffer(sDomain), curve, logger); polynomials.Sigma3 = new Polynomial(new BigBuffer(sDomain), curve, logger); @@ -117,7 +117,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger await fdZKey.readToBuffer(polynomials.Sigma2.coef, 0, sDomain, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 5 * sDomain); await fdZKey.readToBuffer(polynomials.Sigma3.coef, 0, sDomain, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 10 * sDomain); - if (logger) logger.info("··· Reading Sigma evaluations"); + if (logger) logger.debug("··· Reading Sigma evaluations"); evaluations.Sigma1 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); evaluations.Sigma2 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); evaluations.Sigma3 = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); @@ -126,13 +126,23 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger await fdZKey.readToBuffer(evaluations.Sigma2.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 6 * sDomain); await fdZKey.readToBuffer(evaluations.Sigma3.eval, 0, sDomain * 4, zkeySections[ZKEY_PL_SIGMA_SECTION][0].p + 11 * sDomain); - if (logger) logger.info(`> Reading Section ${ZKEY_PL_PTAU_SECTION}. Powers of Tau`); + if (logger) logger.debug(`> Reading Section ${ZKEY_PL_PTAU_SECTION}. Powers of Tau`); const PTau = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_PTAU_SECTION); + if (logger) logger.debug(""); + if (logger) logger.debug("> ROUND 1"); await round1(); + + if (logger) logger.debug("> ROUND 2"); await round2(); + + if (logger) logger.debug("> ROUND 3"); await round3(); + + if (logger) logger.debug("> ROUND 4"); await round4(); + + if (logger) logger.debug("> ROUND 5"); await round5(); /////////////////////// @@ -154,13 +164,15 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger _proof.protocol = "plonk"; _proof.curve = curve.name; + if (logger) logger.debug("PLONK PROVER FINISHED"); + return { proof: stringifyBigInts(_proof), publicSignals: stringifyBigInts(publicSignals) }; async function calculateAdditions() { - if (logger) logger.info("··· Computing additions"); + if (logger) logger.debug("··· Computing additions"); const additionsBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_ADDITIONS_SECTION); // sizes: wireId_x = 4 bytes (32 bits), factor_x = field size bits @@ -168,7 +180,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger const sSum = 8 + n8r * 2; for (let i = 0; i < zkey.nAdditions; i++) { - if (logger && (0 !== i) && (i % 100000 === 0)) logger.info(` addition ${i}/${zkey.nAdditions}`); + if (logger && (0 !== i) && (i % 100000 === 0)) logger.debug(` addition ${i}/${zkey.nAdditions}`); // Read addition values let offset = i * sSum; @@ -214,7 +226,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } // STEP 1.2 - Compute wire polynomials a(X), b(X) and c(X) - if (logger) logger.info("> Computing A, B, C wire polynomials"); + if (logger) logger.debug("> Computing A, B, C wire polynomials"); await computeWirePolynomials(); // The first output of the prover is ([A]_1, [B]_1, [C]_1) @@ -230,7 +242,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } async function computeWirePolynomials() { - if (logger) logger.info("··· Reading data from zkey file"); + if (logger) logger.debug("··· Reading data from zkey file"); // Build A, B and C evaluations buffer from zkey and witness files buffers.A = new BigBuffer(sDomain); buffers.B = new BigBuffer(sDomain); @@ -263,19 +275,19 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger buffers.C = await Fr.batchToMontgomery(buffers.C); // Compute the coefficients of the wire polynomials a(X), b(X) and c(X) from A,B & C buffers - if (logger) logger.info("··· Computing A ifft"); + if (logger) logger.debug("··· Computing A ifft"); polynomials.A = await Polynomial.fromEvaluations(buffers.A, curve, logger); - if (logger) logger.info("··· Computing B ifft"); + if (logger) logger.debug("··· Computing B ifft"); polynomials.B = await Polynomial.fromEvaluations(buffers.B, curve, logger); - if (logger) logger.info("··· Computing C ifft"); + if (logger) logger.debug("··· Computing C ifft"); polynomials.C = await Polynomial.fromEvaluations(buffers.C, curve, logger); // Compute extended evaluations of a(X), b(X) and c(X) polynomials - if (logger) logger.info("··· Computing A fft"); + if (logger) logger.debug("··· Computing A fft"); evaluations.A = await Evaluations.fromPolynomial(polynomials.A, 4, curve, logger); - if (logger) logger.info("··· Computing B fft"); + if (logger) logger.debug("··· Computing B fft"); evaluations.B = await Evaluations.fromPolynomial(polynomials.B, 4, curve, logger); - if (logger) logger.info("··· Computing C fft"); + if (logger) logger.debug("··· Computing C fft"); evaluations.C = await Evaluations.fromPolynomial(polynomials.C, 4, curve, logger); // Blind a(X), b(X) and c(X) polynomials coefficients with blinding scalars b @@ -324,7 +336,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger if (logger) logger.debug("··· challenges.gamma: " + Fr.toString(challenges.gamma)); // STEP 2.2 - Compute permutation polynomial z(X) - if (logger) logger.info("> Computing Z polynomial"); + if (logger) logger.debug("> Computing Z polynomial"); await computeZ(); // The second output of the prover is ([Z]_1) @@ -334,7 +346,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } async function computeZ() { - if (logger) logger.info("··· Computing Z evaluations"); + if (logger) logger.debug("··· Computing Z evaluations"); let numArr = new BigBuffer(sDomain); let denArr = new BigBuffer(sDomain); @@ -411,11 +423,11 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } // Compute polynomial coefficients z(X) from buffers.Z - if (logger) logger.info("··· Computing Z ifft"); + if (logger) logger.debug("··· Computing Z ifft"); polynomials.Z = await Polynomial.fromEvaluations(buffers.Z, curve, logger); // Compute extended evaluations of z(X) polynomial - if (logger) logger.info("··· Computing Z fft"); + if (logger) logger.debug("··· Computing Z fft"); evaluations.Z = await Evaluations.fromPolynomial(polynomials.Z, 4, curve, logger); // Blind z(X) polynomial coefficients with blinding scalars b @@ -439,7 +451,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger challenges.alpha2 = Fr.square(challenges.alpha); if (logger) logger.debug("··· challenges.alpha: " + Fr.toString(challenges.alpha)); - if (logger) logger.info(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + + if (logger) logger.debug(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + `, ${ZKEY_PL_QM_SECTION}, ${ZKEY_PL_QO_SECTION}, ${ZKEY_PL_QC_SECTION}. Q selectors`); // Reserve memory for Q's evaluations evaluations.QL = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); @@ -467,7 +479,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger let w = Fr.one; for (let i=0; i Date: Tue, 2 May 2023 15:52:07 +0200 Subject: [PATCH 25/48] update protocol to last version --- src/plonk_prove.js | 245 ++++++++++++++++++++++++++------------------ src/plonk_verify.js | 230 ++++++++++++++++++----------------------- 2 files changed, 244 insertions(+), 231 deletions(-) diff --git a/src/plonk_prove.js b/src/plonk_prove.js index 777a7770..94e54074 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -129,6 +129,13 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger if (logger) logger.debug(`> Reading Section ${ZKEY_PL_PTAU_SECTION}. Powers of Tau`); const PTau = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_PTAU_SECTION); + let publicSignals = []; + + for (let i=1; i<= zkey.nPublic; i++) { + const pub = buffWitness.slice(i*Fr.n8, i*Fr.n8+Fr.n8); + publicSignals.push(Scalar.fromRprLE(pub)); + } + if (logger) logger.debug(""); if (logger) logger.debug("> ROUND 1"); await round1(); @@ -152,13 +159,6 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger await fdZKey.close(); await fdWtns.close(); - let publicSignals = []; - - for (let i=1; i<= zkey.nPublic; i++) { - const pub = buffWitness.slice(i*Fr.n8, i*Fr.n8+Fr.n8); - publicSignals.push(Scalar.fromRprLE(pub)); - } - // Prepare proof let _proof = proof.toObjectProof(false); _proof.protocol = "plonk"; @@ -222,7 +222,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger async function round1() { challenges.b = []; for (let i=1; i<=11; i++) { - challenges.b[i] = curve.Fr.one;//curve.Fr.random(); + challenges.b[i] = curve.Fr.random(); } // STEP 1.2 - Compute wire polynomials a(X), b(X) and c(X) @@ -327,13 +327,13 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger transcript.addPolCommitment(proof.getPolynomial("C")); challenges.beta = transcript.getChallenge(); - if (logger) logger.debug("··· challenges.beta: " + Fr.toString(challenges.beta)); + if (logger) logger.debug("··· challenges.beta: " + Fr.toString(challenges.beta, 16)); // Compute permutation challenge gamma transcript.reset(); transcript.addScalar(challenges.beta); challenges.gamma = transcript.getChallenge(); - if (logger) logger.debug("··· challenges.gamma: " + Fr.toString(challenges.gamma)); + if (logger) logger.debug("··· challenges.gamma: " + Fr.toString(challenges.gamma, 16)); // STEP 2.2 - Compute permutation polynomial z(X) if (logger) logger.debug("> Computing Z polynomial"); @@ -449,7 +449,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger challenges.alpha = transcript.getChallenge(); challenges.alpha2 = Fr.square(challenges.alpha); - if (logger) logger.debug("··· challenges.alpha: " + Fr.toString(challenges.alpha)); + if (logger) logger.debug("··· challenges.alpha: " + Fr.toString(challenges.alpha, 16)); if (logger) logger.debug(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + `, ${ZKEY_PL_QM_SECTION}, ${ZKEY_PL_QO_SECTION}, ${ZKEY_PL_QC_SECTION}. Q selectors`); @@ -637,7 +637,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger const lowestHigh = Fr.sub(polynomials.T3.getCoef(0), challenges.b[11]); polynomials.T3.setCoef(0, lowestHigh); - // The third output of the prover is ([T1]_1, [T2]_1, [T3]_1) + // Third output of the prover is ([T1]_1, [T2]_1, [T3]_1) let commitT1 = await polynomials.T1.multiExponentiation(PTau, "T1"); let commitT2 = await polynomials.T2.multiExponentiation(PTau, "T2"); let commitT3 = await polynomials.T3.multiExponentiation(PTau, "T3"); @@ -649,6 +649,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger async function round4() { if (logger) logger.debug("> Computing challenge xi"); + // STEP 3.1 - Compute evaluation challenge xi ∈ S transcript.reset(); transcript.addPolCommitment(proof.getPolynomial("T1")); @@ -657,8 +658,55 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger challenges.xi = transcript.getChallenge(); challenges.xiw = Fr.mul(challenges.xi, Fr.w[zkey.power]); - if (logger) logger.debug("··· challenges.xi: " + Fr.toString(challenges.xi)); + + if (logger) logger.debug("··· challenges.xi: " + Fr.toString(challenges.xi, 16)); + + // Fourth output of the prover is ( a(xi), b(xi), c(xi), s1(xi), s2(xi), z(xiw) ) + proof.addEvaluation("eval_a", polynomials.A.evaluate(challenges.xi)); + proof.addEvaluation("eval_b", polynomials.B.evaluate(challenges.xi)); + proof.addEvaluation("eval_c", polynomials.C.evaluate(challenges.xi)); + proof.addEvaluation("eval_s1", polynomials.Sigma1.evaluate(challenges.xi)); + proof.addEvaluation("eval_s2", polynomials.Sigma2.evaluate(challenges.xi)); + proof.addEvaluation("eval_zw", polynomials.Z.evaluate(challenges.xiw)); + } + + async function round5() { + if (logger) logger.debug("> Computing challenge v"); + transcript.reset(); + transcript.addScalar(proof.getEvaluation("eval_a")); + transcript.addScalar(proof.getEvaluation("eval_b")); + transcript.addScalar(proof.getEvaluation("eval_c")); + transcript.addScalar(proof.getEvaluation("eval_s1")); + transcript.addScalar(proof.getEvaluation("eval_s2")); + transcript.addScalar(proof.getEvaluation("eval_zw")); + + challenges.v = []; + challenges.v[1] = transcript.getChallenge(); + if (logger) logger.debug("··· challenges.v: " + Fr.toString(challenges.v[1], 16)); + + for (let i = 2; i < 6; i++) { + challenges.v[i] = Fr.mul(challenges.v[i - 1], challenges.v[1]); + } + + await computeR(); + + computeWxi(); + + // Compute opening proof polynomial Wxiω(X) + computeWxiw(); + + // Fifth output of the prover is ([Wxi]_1, [Wxiw]_1) + let commitWxi = await polynomials.Wxi.multiExponentiation(PTau, "Wxi"); + let commitWxiw = await polynomials.Wxiw.multiExponentiation(PTau, "Wxiw"); + + proof.addPolynomial("Wxi", commitWxi); + proof.addPolynomial("Wxiw", commitWxiw); + } + + async function computeR() { + const Fr = curve.Fr; + // Reserve memory for Q's polynomials polynomials.QL = new Polynomial(new BigBuffer(sDomain), curve, logger); polynomials.QR = new Polynomial(new BigBuffer(sDomain), curve, logger); @@ -671,129 +719,126 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger await fdZKey.readToBuffer(polynomials.QR.coef, 0, sDomain, zkeySections[ZKEY_PL_QR_SECTION][0].p); await fdZKey.readToBuffer(polynomials.QM.coef, 0, sDomain, zkeySections[ZKEY_PL_QM_SECTION][0].p); await fdZKey.readToBuffer(polynomials.QO.coef, 0, sDomain, zkeySections[ZKEY_PL_QO_SECTION][0].p); - await fdZKey.readToBuffer(polynomials.QC.coef, 0, sDomain, zkeySections[ZKEY_PL_QC_SECTION][0].p); + await fdZKey.readToBuffer(polynomials.QC.coef, 0, sDomain, zkeySections[ZKEY_PL_QC_SECTION][0].p); + + challenges.xin = challenges.xi; + for (let i = 0; i < zkey.power; i++) { + challenges.xin = Fr.square(challenges.xin); + } - proof.addEvaluation("eval_a", polynomials.A.evaluate(challenges.xi)); - proof.addEvaluation("eval_b", polynomials.B.evaluate(challenges.xi)); - proof.addEvaluation("eval_c", polynomials.C.evaluate(challenges.xi)); - proof.addEvaluation("eval_s1", polynomials.Sigma1.evaluate(challenges.xi)); - proof.addEvaluation("eval_s2", polynomials.Sigma2.evaluate(challenges.xi)); - proof.addEvaluation("eval_t", polynomials.T.evaluate(challenges.xi)); - proof.addEvaluation("eval_zw", polynomials.Z.evaluate(challenges.xiw)); + challenges.zh = Fr.sub(challenges.xin, Fr.one); + + const L = []; + + const n = Fr.e(zkey.domainSize); + let w = Fr.one; + for (let i = 1; i <= Math.max(1, zkey.nPublic); i++) { + L[i] = Fr.div(Fr.mul(w, challenges.zh), Fr.mul(n, Fr.sub(challenges.xi, w))); + w = Fr.mul(w, Fr.w[zkey.power]); + } + + const eval_l1 = Fr.div( + Fr.sub(challenges.xin, Fr.one), + Fr.mul(n, Fr.sub(challenges.xi, Fr.one)) + ); + + if (logger) { + logger.debug("Lagrange Evaluations: "); + for (let i=1; i Computing challenge v"); + let r0 = Fr.sub(eval_pi, Fr.mul(e3, Fr.add(proof.evaluations.eval_c, challenges.gamma))); + r0 = Fr.sub(r0, e4); - transcript.reset(); - transcript.addScalar(proof.getEvaluation("eval_a")); - transcript.addScalar(proof.getEvaluation("eval_b")); - transcript.addScalar(proof.getEvaluation("eval_c")); - transcript.addScalar(proof.getEvaluation("eval_s1")); - transcript.addScalar(proof.getEvaluation("eval_s2")); - transcript.addScalar(proof.getEvaluation("eval_zw")); - transcript.addScalar(proof.getEvaluation("eval_r")); + logger.debug("r0: " + Fr.toString(r0, 16)); - challenges.v = []; - challenges.v[1] = transcript.getChallenge(); - if (logger) logger.debug("··· challenges.v: " + Fr.toString(challenges.v[1])); + polynomials.R.addScalar(r0); + } - for (let i=2; i<=6; i++ ) { - challenges.v[i] = Fr.mul(challenges.v[i-1], challenges.v[1]); - } - + function computeWxi() { polynomials.Wxi = new Polynomial(new BigBuffer(sDomain + 6 * n8r), curve, logger); - polynomials.Wxi.add(polynomials.T1); - polynomials.Wxi.add(polynomials.T2, challenges.xim); - polynomials.Wxi.add(polynomials.T3, Fr.square(challenges.xim)); - polynomials.Wxi.add(polynomials.R, challenges.v[1]); - polynomials.Wxi.add(polynomials.A, challenges.v[2]); - polynomials.Wxi.add(polynomials.B, challenges.v[3]); - polynomials.Wxi.add(polynomials.C, challenges.v[4]); - polynomials.Wxi.add(polynomials.Sigma1, challenges.v[5]); - polynomials.Wxi.add(polynomials.Sigma2, challenges.v[6]); - - polynomials.Wxi.subScalar(proof.evaluations.eval_t); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[1], proof.evaluations.eval_r)); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[2], proof.evaluations.eval_a)); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[3], proof.evaluations.eval_b)); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[4], proof.evaluations.eval_c)); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[5], proof.evaluations.eval_s1)); - polynomials.Wxi.subScalar(Fr.mul(challenges.v[6], proof.evaluations.eval_s2)); + polynomials.Wxi.add(polynomials.R); + polynomials.Wxi.add(polynomials.A, challenges.v[1]); + polynomials.Wxi.add(polynomials.B, challenges.v[2]); + polynomials.Wxi.add(polynomials.C, challenges.v[3]); + polynomials.Wxi.add(polynomials.Sigma1, challenges.v[4]); + polynomials.Wxi.add(polynomials.Sigma2, challenges.v[5]); + + polynomials.Wxi.subScalar(Fr.mul(challenges.v[1], proof.evaluations.eval_a)); + polynomials.Wxi.subScalar(Fr.mul(challenges.v[2], proof.evaluations.eval_b)); + polynomials.Wxi.subScalar(Fr.mul(challenges.v[3], proof.evaluations.eval_c)); + polynomials.Wxi.subScalar(Fr.mul(challenges.v[4], proof.evaluations.eval_s1)); + polynomials.Wxi.subScalar(Fr.mul(challenges.v[5], proof.evaluations.eval_s2)); polynomials.Wxi.divByZerofier(1, challenges.xi); + } - // Compute opening proof polynomial Wxiω(X) + async function computeWxiw() { polynomials.Wxiw = Polynomial.fromPolynomial(polynomials.Z, curve, logger); polynomials.Wxiw.subScalar(proof.evaluations.eval_zw); polynomials.Wxiw.divByZerofier(1, challenges.xiw); - - // The fifth output of the prover is ([Wxi]_1, [Wxiw]_1) - let commitWxi = await polynomials.Wxi.multiExponentiation(PTau, "Wxi"); - let commitWxiw = await polynomials.Wxiw.multiExponentiation(PTau, "Wxiw"); - - proof.addPolynomial("Wxi", commitWxi); - proof.addPolynomial("Wxiw", commitWxiw); } -} \ No newline at end of file +} diff --git a/src/plonk_verify.js b/src/plonk_verify.js index 2859fccf..27196607 100644 --- a/src/plonk_verify.js +++ b/src/plonk_verify.js @@ -26,9 +26,10 @@ import jsSha3 from "js-sha3"; const { keccak256 } = jsSha3; + export default async function plonkVerify(_vk_verifier, _publicSignals, _proof, logger) { let vk_verifier = unstringifyBigInts(_vk_verifier); - let proof = unstringifyBigInts(_proof); + _proof = unstringifyBigInts(_proof); let publicSignals = unstringifyBigInts(_publicSignals); const curve = await curves.getCurveFromName(vk_verifier.curve); @@ -36,31 +37,35 @@ export default async function plonkVerify(_vk_verifier, _publicSignals, _proof, const Fr = curve.Fr; const G1 = curve.G1; - proof = fromObjectProof(curve,proof); + if (logger) logger.info("PLONK VERIFIER STARTED"); + + let proof = fromObjectProof(curve,_proof); vk_verifier = fromObjectVk(curve, vk_verifier); + if (!isWellConstructed(curve, proof)) { logger.error("Proof is not well constructed"); return false; } + if (publicSignals.length != vk_verifier.nPublic) { logger.error("Invalid number of public inputs"); return false; } - const challanges = calculateChallanges(curve, proof, publicSignals); + const challenges = calculatechallenges(curve, proof, publicSignals); if (logger) { - logger.debug("beta: " + Fr.toString(challanges.beta, 16)); - logger.debug("gamma: " + Fr.toString(challanges.gamma, 16)); - logger.debug("alpha: " + Fr.toString(challanges.alpha, 16)); - logger.debug("xi: " + Fr.toString(challanges.xi, 16)); - logger.debug("v1: " + Fr.toString(challanges.v[1], 16)); - logger.debug("v6: " + Fr.toString(challanges.v[6], 16)); - logger.debug("u: " + Fr.toString(challanges.u, 16)); + logger.debug("beta: " + Fr.toString(challenges.beta, 16)); + logger.debug("gamma: " + Fr.toString(challenges.gamma, 16)); + logger.debug("alpha: " + Fr.toString(challenges.alpha, 16)); + logger.debug("xi: " + Fr.toString(challenges.xi, 16)); + for(let i=1;i<6;i++) { + if (logger) logger.debug("v: " + Fr.toString(challenges.v[i], 16)); + } + logger.debug("u: " + Fr.toString(challenges.u, 16)); } - const L = calculateLagrangeEvaluations(curve, challanges, vk_verifier); + const L = calculateLagrangeEvaluations(curve, challenges, vk_verifier); if (logger) { - logger.debug("Lagrange Evaluations: "); for (let i=1; i Date: Tue, 2 May 2023 17:46:21 +0200 Subject: [PATCH 26/48] Refactor Fiat-Shamir adding preprocessed circuit dependent values --- src/plonk_prove.js | 163 ++++++++++++++++++++++++++++---------------- src/plonk_verify.js | 106 +++++++++++++++------------- 2 files changed, 162 insertions(+), 107 deletions(-) diff --git a/src/plonk_prove.js b/src/plonk_prove.js index 94e54074..833a45df 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -28,21 +28,21 @@ import { Proof } from "./proof.js"; import { Keccak256Transcript } from "./Keccak256Transcript.js"; import { MulZ } from "./mul_z.js"; import { ZKEY_PL_HEADER_SECTION, - ZKEY_PL_ADDITIONS_SECTION, - ZKEY_PL_A_MAP_SECTION, - ZKEY_PL_B_MAP_SECTION, - ZKEY_PL_C_MAP_SECTION, - ZKEY_PL_QM_SECTION, - ZKEY_PL_QL_SECTION, - ZKEY_PL_QR_SECTION, - ZKEY_PL_QO_SECTION, - ZKEY_PL_QC_SECTION, - ZKEY_PL_SIGMA_SECTION, - ZKEY_PL_LAGRANGE_SECTION, - ZKEY_PL_PTAU_SECTION, - } from "./plonk.js"; - import { Polynomial } from "./polynomial/polynomial.js"; - import { Evaluations } from "./polynomial/evaluations.js"; + ZKEY_PL_ADDITIONS_SECTION, + ZKEY_PL_A_MAP_SECTION, + ZKEY_PL_B_MAP_SECTION, + ZKEY_PL_C_MAP_SECTION, + ZKEY_PL_QM_SECTION, + ZKEY_PL_QL_SECTION, + ZKEY_PL_QR_SECTION, + ZKEY_PL_QO_SECTION, + ZKEY_PL_QC_SECTION, + ZKEY_PL_SIGMA_SECTION, + ZKEY_PL_LAGRANGE_SECTION, + ZKEY_PL_PTAU_SECTION, +} from "./plonk.js"; +import { Polynomial } from "./polynomial/polynomial.js"; +import { Evaluations } from "./polynomial/evaluations.js"; export default async function plonk16Prove(zkeyFileName, witnessFileName, logger) { const {fd: fdWtns, sections: sectionsWtns} = await binFileUtils.readBinFile(witnessFileName, "wtns", 2, 1<<25, 1<<23); @@ -220,6 +220,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger } async function round1() { + // STEP 1.1 - Generate random blinding scalars (b1, ..., b11) ∈ F challenges.b = []; for (let i=1; i<=11; i++) { challenges.b[i] = curve.Fr.random(); @@ -229,11 +230,13 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger if (logger) logger.debug("> Computing A, B, C wire polynomials"); await computeWirePolynomials(); - // The first output of the prover is ([A]_1, [B]_1, [C]_1) + // STEP 1.3 - Compute [a]_1, [b]_1, [c]_1 + if (logger) logger.debug("> Computing A, B, C MSM"); let commitA = await polynomials.A.multiExponentiation(PTau, "A"); let commitB = await polynomials.B.multiExponentiation(PTau, "B"); let commitC = await polynomials.C.multiExponentiation(PTau, "C"); + // First output of the prover is ([A]_1, [B]_1, [C]_1) proof.addPolynomial("A", commitA); proof.addPolynomial("B", commitB); proof.addPolynomial("C", commitC); @@ -243,11 +246,13 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger async function computeWirePolynomials() { if (logger) logger.debug("··· Reading data from zkey file"); + // Build A, B and C evaluations buffer from zkey and witness files buffers.A = new BigBuffer(sDomain); buffers.B = new BigBuffer(sDomain); buffers.C = new BigBuffer(sDomain); + // Read zkey file to the buffers const aMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_A_MAP_SECTION); const bMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_B_MAP_SECTION); const cMapBuff = await binFileUtils.readSection(fdZKey, zkeySections, ZKEY_PL_C_MAP_SECTION); @@ -295,7 +300,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger polynomials.B.blindCoefficients([challenges.b[4], challenges.b[3]]); polynomials.C.blindCoefficients([challenges.b[6], challenges.b[5]]); - // // Check degrees + // Check degrees if (polynomials.A.degree() >= zkey.domainSize + 2) { throw new Error("A Polynomial is not well calculated"); } @@ -313,8 +318,14 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger if (logger) logger.debug("> Computing challenges beta and gamma"); transcript.reset(); - // TODO Add circuit dependent commitment to the transcript!!!!! - //transcript.addPolCommitment(zkey.?????); + transcript.addPolCommitment(zkey.Qm); + transcript.addPolCommitment(zkey.Ql); + transcript.addPolCommitment(zkey.Qr); + transcript.addPolCommitment(zkey.Qo); + transcript.addPolCommitment(zkey.Ql); + transcript.addPolCommitment(zkey.S1); + transcript.addPolCommitment(zkey.S2); + transcript.addPolCommitment(zkey.S3); // Add A to the transcript for (let i = 0; i < zkey.nPublic; i++) { @@ -339,9 +350,11 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger if (logger) logger.debug("> Computing Z polynomial"); await computeZ(); - // The second output of the prover is ([Z]_1) + // STEP 2.3 - Compute permutation [z]_1 + if (logger) logger.debug("> Computing Z MSM"); let commitZ = await polynomials.Z.multiExponentiation(PTau, "Z"); + // Second output of the prover is ([Z]_1) proof.addPolynomial("Z", commitZ); } @@ -443,16 +456,37 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger async function round3() { if (logger) logger.debug("> Computing challenge alpha"); - // STEP 3.1 - Compute evaluation challenge xi ∈ S + + // STEP 3.1 - Compute evaluation challenge alpha ∈ F transcript.reset(); + transcript.addScalar(challenges.beta); + transcript.addScalar(challenges.gamma); transcript.addPolCommitment(proof.getPolynomial("Z")); challenges.alpha = transcript.getChallenge(); challenges.alpha2 = Fr.square(challenges.alpha); if (logger) logger.debug("··· challenges.alpha: " + Fr.toString(challenges.alpha, 16)); - if (logger) logger.debug(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + - `, ${ZKEY_PL_QM_SECTION}, ${ZKEY_PL_QO_SECTION}, ${ZKEY_PL_QC_SECTION}. Q selectors`); + // Compute quotient polynomial T(X) + if (logger) logger.debug("> Computing T polynomial"); + await computeT(); + + // Compute [T1]_1, [T2]_1, [T3]_1 + if (logger) logger.debug("> Computing T MSM"); + let commitT1 = await polynomials.T1.multiExponentiation(PTau, "T1"); + let commitT2 = await polynomials.T2.multiExponentiation(PTau, "T2"); + let commitT3 = await polynomials.T3.multiExponentiation(PTau, "T3"); + + // Third output of the prover is ([T1]_1, [T2]_1, [T3]_1) + proof.addPolynomial("T1", commitT1); + proof.addPolynomial("T2", commitT2); + proof.addPolynomial("T3", commitT3); + } + + async function computeT() { + if (logger) + logger.debug(`··· Reading sections ${ZKEY_PL_QL_SECTION}, ${ZKEY_PL_QR_SECTION}` + + `, ${ZKEY_PL_QM_SECTION}, ${ZKEY_PL_QO_SECTION}, ${ZKEY_PL_QC_SECTION}. Q selectors`); // Reserve memory for Q's evaluations evaluations.QL = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); evaluations.QR = new Evaluations(new BigBuffer(sDomain * 4), curve, logger); @@ -477,9 +511,12 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger buffers.T = new BigBuffer(sDomain * 4); buffers.Tz = new BigBuffer(sDomain * 4); + if (logger) logger.debug("··· Computing T evaluations"); + let w = Fr.one; - for (let i=0; i= zkey.domainSize * 3 + 6) { throw new Error("T Polynomial is not well calculated"); } - + // t(x) has degree 3n + 5, we are going to split t(x) into three smaller polynomials: // T1' and T2' with a degree < n and T3' with a degree n+5 // such that t(x) = T1'(X) + X^n T2'(X) + X^{2n} T3'(X) @@ -614,7 +659,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger // T3(X) = T3'(X) - b_11 // such that // t(X) = T1(X) + X^n T2(X) + X^2n T3(X) - + logger.debug("··· Computing T1, T2, T3 polynomials"); polynomials.T1 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); polynomials.T2 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); polynomials.T3 = new Polynomial(new BigBuffer((zkey.domainSize + 6) * n8r), curve, logger); @@ -636,22 +681,14 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger //Subtract blinding scalar b_11 to the lowest coefficient of t_high const lowestHigh = Fr.sub(polynomials.T3.getCoef(0), challenges.b[11]); polynomials.T3.setCoef(0, lowestHigh); - - // Third output of the prover is ([T1]_1, [T2]_1, [T3]_1) - let commitT1 = await polynomials.T1.multiExponentiation(PTau, "T1"); - let commitT2 = await polynomials.T2.multiExponentiation(PTau, "T2"); - let commitT3 = await polynomials.T3.multiExponentiation(PTau, "T3"); - - proof.addPolynomial("T1", commitT1); - proof.addPolynomial("T2", commitT2); - proof.addPolynomial("T3", commitT3); } async function round4() { if (logger) logger.debug("> Computing challenge xi"); - // STEP 3.1 - Compute evaluation challenge xi ∈ S + // STEP 4.1 - Compute evaluation challenge xi ∈ F transcript.reset(); + transcript.addScalar(challenges.alpha); transcript.addPolCommitment(proof.getPolynomial("T1")); transcript.addPolCommitment(proof.getPolynomial("T2")); transcript.addPolCommitment(proof.getPolynomial("T3")); @@ -672,8 +709,10 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger async function round5() { if (logger) logger.debug("> Computing challenge v"); - + + // STEP 5.1 - Compute evaluation challenge v ∈ F transcript.reset(); + transcript.addScalar(challenges.xi); transcript.addScalar(proof.getEvaluation("eval_a")); transcript.addScalar(proof.getEvaluation("eval_b")); transcript.addScalar(proof.getEvaluation("eval_c")); @@ -689,17 +728,23 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger challenges.v[i] = Fr.mul(challenges.v[i - 1], challenges.v[1]); } + // STEP 5.2 Compute linearisation polynomial r(X) + if (logger) logger.debug("> Computing linearisation polynomial R(X)"); await computeR(); + //STEP 5.3 Compute opening proof polynomial Wxi(X) + if (logger) logger.debug("> Computing opening proof polynomial Wxi(X) polynomial"); computeWxi(); - // Compute opening proof polynomial Wxiω(X) + //STEP 5.4 Compute opening proof polynomial Wxiw(X) + if (logger) logger.debug("> Computing opening proof polynomial Wxiw(X) polynomial"); computeWxiw(); - // Fifth output of the prover is ([Wxi]_1, [Wxiw]_1) + if (logger) logger.debug("> Computing Wxi, Wxiw MSM"); let commitWxi = await polynomials.Wxi.multiExponentiation(PTau, "Wxi"); let commitWxiw = await polynomials.Wxiw.multiExponentiation(PTau, "Wxiw"); + // Fifth output of the prover is ([Wxi]_1, [Wxiw]_1) proof.addPolynomial("Wxi", commitWxi); proof.addPolynomial("Wxiw", commitWxiw); } diff --git a/src/plonk_verify.js b/src/plonk_verify.js index 27196607..212782d0 100644 --- a/src/plonk_verify.js +++ b/src/plonk_verify.js @@ -18,12 +18,10 @@ */ /* Implementation of this paper: https://eprint.iacr.org/2019/953.pdf */ -import { Scalar } from "ffjavascript"; import * as curves from "./curves.js"; import { utils } from "ffjavascript"; const {unstringifyBigInts} = utils; -import jsSha3 from "js-sha3"; -const { keccak256 } = jsSha3; +import { Keccak256Transcript } from "./Keccak256Transcript.js"; @@ -51,7 +49,8 @@ export default async function plonkVerify(_vk_verifier, _publicSignals, _proof, logger.error("Invalid number of public inputs"); return false; } - const challenges = calculatechallenges(curve, proof, publicSignals); + const challenges = calculatechallenges(curve, proof, publicSignals, vk_verifier); + if (logger) { logger.debug("beta: " + Fr.toString(challenges.beta, 16)); logger.debug("gamma: " + Fr.toString(challenges.gamma, 16)); @@ -169,53 +168,69 @@ function isWellConstructed(curve, proof) { return true; } -function calculatechallenges(curve, proof, publicSignals) { - const G1 = curve.G1; +function calculatechallenges(curve, proof, publicSignals, vk) { const Fr = curve.Fr; - const n8r = curve.Fr.n8; const res = {}; - - const transcript1 = new Uint8Array(publicSignals.length*n8r + G1.F.n8*2*3); - for (let i=0; i Date: Fri, 12 May 2023 07:00:49 +0000 Subject: [PATCH 27/48] fix errors. working --- src/plonk_prove.js | 4 ++-- src/proof.js | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/src/plonk_prove.js b/src/plonk_prove.js index 833a45df..ab48a4c6 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -659,7 +659,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger // T3(X) = T3'(X) - b_11 // such that // t(X) = T1(X) + X^n T2(X) + X^2n T3(X) - logger.debug("··· Computing T1, T2, T3 polynomials"); + if (logger) logger.debug("··· Computing T1, T2, T3 polynomials"); polynomials.T1 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); polynomials.T2 = new Polynomial(new BigBuffer((zkey.domainSize + 1) * n8r), curve, logger); polynomials.T3 = new Polynomial(new BigBuffer((zkey.domainSize + 6) * n8r), curve, logger); @@ -856,7 +856,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger let r0 = Fr.sub(eval_pi, Fr.mul(e3, Fr.add(proof.evaluations.eval_c, challenges.gamma))); r0 = Fr.sub(r0, e4); - logger.debug("r0: " + Fr.toString(r0, 16)); + if (logger) logger.debug("r0: " + Fr.toString(r0, 16)); polynomials.R.addScalar(r0); } diff --git a/src/proof.js b/src/proof.js index d8ca1f21..ba7d96d1 100644 --- a/src/proof.js +++ b/src/proof.js @@ -73,7 +73,7 @@ export class Proof { Object.keys(this.evaluations).forEach(key => { const value = this.curve.Fr.toObject(this.evaluations[key]); if(splitFields) { - res.polynomials[key] = value; + res.evaluations[key] = value; } else { res[key] = value; } From 2485bb4c8dfb401cc59fa30ede7c130d1f2b0947 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Fri, 12 May 2023 07:01:48 +0000 Subject: [PATCH 28/48] wip --- src/plonk_prove.js | 2 +- src/plonk_verify.js | 2 +- templates/verifier_plonk.sol.ejs | 433 ++++++++++---------- test/plonk_circuit/circuit.zkey | Bin 14916 -> 14748 bytes test/plonk_circuit/proof.json | 49 ++- test/plonk_circuit/verification_key.json | 35 +- test/plonk_circuit/verifier.sol | 477 ++++++++++++----------- 7 files changed, 526 insertions(+), 472 deletions(-) diff --git a/src/plonk_prove.js b/src/plonk_prove.js index ab48a4c6..6c3409f7 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -322,7 +322,7 @@ export default async function plonk16Prove(zkeyFileName, witnessFileName, logger transcript.addPolCommitment(zkey.Ql); transcript.addPolCommitment(zkey.Qr); transcript.addPolCommitment(zkey.Qo); - transcript.addPolCommitment(zkey.Ql); + transcript.addPolCommitment(zkey.Qc); transcript.addPolCommitment(zkey.S1); transcript.addPolCommitment(zkey.S2); transcript.addPolCommitment(zkey.S3); diff --git a/src/plonk_verify.js b/src/plonk_verify.js index 212782d0..31692b76 100644 --- a/src/plonk_verify.js +++ b/src/plonk_verify.js @@ -178,7 +178,7 @@ function calculatechallenges(curve, proof, publicSignals, vk) { transcript.addPolCommitment(vk.Ql); transcript.addPolCommitment(vk.Qr); transcript.addPolCommitment(vk.Qo); - transcript.addPolCommitment(vk.Ql); + transcript.addPolCommitment(vk.Qc); transcript.addPolCommitment(vk.S1); transcript.addPolCommitment(vk.S2); transcript.addPolCommitment(vk.S3); diff --git a/templates/verifier_plonk.sol.ejs b/templates/verifier_plonk.sol.ejs index c6d8452e..6485cc0c 100644 --- a/templates/verifier_plonk.sol.ejs +++ b/templates/verifier_plonk.sol.ejs @@ -75,7 +75,6 @@ contract PlonkVerifier { uint16 constant pEval_s1 = 704; uint16 constant pEval_s2 = 736; uint16 constant pEval_zw = 768; - uint16 constant pEval_r = 800; uint16 constant pAlpha = 0; uint16 constant pBeta = 32; @@ -90,16 +89,18 @@ contract PlonkVerifier { uint16 constant pV5 = 320; uint16 constant pV6 = 352; uint16 constant pU = 384; - uint16 constant pPl = 416; - uint16 constant pEval_t = 448; - uint16 constant pA1 = 480; - uint16 constant pB1 = 544; - uint16 constant pZh = 608; - uint16 constant pZhInv = 640; + uint16 constant pPI = 416; + uint16 constant pEval_r0 = 448; + uint16 constant pD = 480; + uint16 constant pF = 544; + uint16 constant pE = 608; + uint16 constant pTmp = 672; + uint16 constant pZh = 736; + uint16 constant pZhInv = 768; <% for (let i=1; i<=Math.max(nPublic, 1); i++) { %> - uint16 constant pEval_l<%=i%> = <%=640+i*32%>; + uint16 constant pEval_l<%=i%> = <%=768+i*32%>; <% } %> - <% let pLastMem = 672+32*Math.max(nPublic,1) %> + <% let pLastMem = 800+32*Math.max(nPublic,1) %> uint16 constant lastMem = <%=pLastMem%>; @@ -193,7 +194,6 @@ contract PlonkVerifier { checkField(mload(add(pProof, pEval_s1))) checkField(mload(add(pProof, pEval_s2))) checkField(mload(add(pProof, pEval_zw))) - checkField(mload(add(pProof, pEval_r))) // Points are checked in the point operations precompiled smart contracts } @@ -203,23 +203,69 @@ contract PlonkVerifier { let a let b + // Challenges.beta + mstore( add(pMem, <%=pLastMem%> ), Qmx) + mstore( add(pMem, <%=pLastMem + 32%> ), Qmy) + mstore( add(pMem, <%=pLastMem + 64%> ), Qlx) + mstore( add(pMem, <%=pLastMem + 96%> ), Qly) + mstore( add(pMem, <%=pLastMem + 128%> ), Qrx) + mstore( add(pMem, <%=pLastMem + 160%> ), Qry) + mstore( add(pMem, <%=pLastMem + 192%> ), Qox) + mstore( add(pMem, <%=pLastMem + 224%> ), Qoy) + mstore( add(pMem, <%=pLastMem + 256%> ), Qcx) + mstore( add(pMem, <%=pLastMem + 288%> ), Qcy) + mstore( add(pMem, <%=pLastMem + 320%> ), S1x) + mstore( add(pMem, <%=pLastMem + 352%> ), S1x) + mstore( add(pMem, <%=pLastMem + 384%> ), S2x) + mstore( add(pMem, <%=pLastMem + 416%> ), S2x) + mstore( add(pMem, <%=pLastMem + 448%> ), S3x) + mstore( add(pMem, <%=pLastMem + 480%> ), S3x) + <%for (let i=0; i - mstore( add(pMem, <%=pLastMem + i*32%> ), mload( add( pPublic, <%=i*32 + 32%>))) + mstore( add(pMem, <%=pLastMem + 512 + i*32%> ), mload( add( pPublic, <%=i*32 + 32%>))) <%}%> - mstore( add(pMem, <%=pLastMem + nPublic*32 +0%> ), mload( add( pProof, pA))) - mstore( add(pMem, <%=pLastMem + nPublic*32 +32%> ), mload( add( pProof, add(pA,32)))) - mstore( add(pMem, <%=pLastMem + nPublic*32 +64%> ), mload( add( pProof, add(pA,64)))) - mstore( add(pMem, <%=pLastMem + nPublic*32 +96%> ), mload( add( pProof, add(pA,96)))) - mstore( add(pMem, <%=pLastMem + nPublic*32 +128%> ), mload( add( pProof, add(pA,128)))) - mstore( add(pMem, <%=pLastMem + nPublic*32 +160%> ), mload( add( pProof, add(pA,160)))) - - b := mod(keccak256(add(pMem, lastMem), <%= 192 + 32*nPublic %>), q) - mstore( add(pMem, pBeta), b) - mstore( add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) - mstore( add(pMem, pAlpha), mod(keccak256(add(pProof, pZ), 64), q)) - - a := mod(keccak256(add(pProof, pT1), 192), q) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +0%> ), mload( add( pProof, pA))) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +32%> ), mload( add( pProof, add(pA,32)))) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +64%> ), mload( add( pProof, pB))) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +96%> ), mload( add( pProof, add(pB, 32)))) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +128%> ), mload( add( pProof, pC))) + mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +160%> ), mload( add( pProof, add(pC, 32)))) + + b := mod(keccak256(add(pMem, lastMem), <%= 704 + 32*nPublic %>), q) + mstore(add(pMem, pBeta), b) + + // Challenges.gamma + mstore(add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) + + // Challenges.alpha + mstore(add(pMem, <%=pLastMem%>), mload(add(pMem, pBeta))) + mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pMem, pGamma))) + mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, pZ))) + mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, add(pZ, 32)))) + a := mod(keccak256(add(pMem, lastMem), 128), q) + mstore(add(pMem, pAlpha), a) + + mstore(add(pMem, <%=pLastMem%>), mload(add(pMem, pAlpha))) + mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pProof, pT1))) + mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, add(pT1, 32)))) + mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, pT2))) + mstore(add(pMem, <%=pLastMem + 128%>), mload(add(pProof, add(pT2, 32)))) + mstore(add(pMem, <%=pLastMem + 160%>), mload(add(pProof, pT3))) + mstore(add(pMem, <%=pLastMem + 192%>), mload(add(pProof, add(pT3, 32)))) + a := mod(keccak256(add(pMem, lastMem), 224), q) mstore( add(pMem, pXi), a) + + mstore(add(pMem, <%=pLastMem%>), a) + mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pProof, pEval_a))) + mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, pEval_b))) + mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, pEval_c))) + mstore(add(pMem, <%=pLastMem + 128%>), mload(add(pProof, pEval_s1))) + mstore(add(pMem, <%=pLastMem + 160%>), mload(add(pProof, pEval_s2))) + mstore(add(pMem, <%=pLastMem + 192%>), mload(add(pProof, pEval_zw))) + let v1 := mod(keccak256(add(pMem, lastMem), 224), q) + mstore(add(pMem, pV1), v1) + + // Compute betaxi mstore( add(pMem, pBetaXi), mulmod(b, a, q)) <%for (let i=0; i a:= mulmod(a, a, q) @@ -228,9 +274,7 @@ contract PlonkVerifier { a:= mod(add(sub(a, 1),q), q) mstore( add(pMem, pZh), a) mstore( add(pMem, pZhInv), a) // We will invert later together with lagrange pols - - let v1 := mod(keccak256(add(pProof, pEval_a), 224), q) - mstore( add(pMem, pV1), v1) + a := mulmod(v1, v1, q) mstore( add(pMem, pV2), a) a := mulmod(a, v1, q) @@ -307,7 +351,7 @@ contract PlonkVerifier { } - function calculatePl(pMem, pPub) { + function calculatePI(pMem, pPub) { let pl := 0 <% for (let i=0; i @@ -327,88 +371,43 @@ contract PlonkVerifier { ) <% } %> - mstore(add(pMem, pPl), pl) + mstore(add(pMem, pPI), pl) } - function calculateT(pProof, pMem) { - let t - let t1 - let t2 - t := addmod( - mload(add(pProof, pEval_r)), - mload(add(pMem, pPl)), - q - ) - - t1 := mulmod( - mload(add(pProof, pEval_s1)), - mload(add(pMem, pBeta)), - q - ) + function calculateR0(pProof, pMem) { + let alpha2 := mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q) + let e1 := mload(add(pMem, pPI)) - t1 := addmod( - t1, - mload(add(pProof, pEval_a)), - q - ) - - t1 := addmod( - t1, - mload(add(pMem, pGamma)), - q - ) + let e2 := mulmod(mload(add(pMem, pEval_l1)), alpha2, q) - t2 := mulmod( - mload(add(pProof, pEval_s2)), - mload(add(pMem, pBeta)), - q - ) + let e3a := addmod( + mload(add(pProof, pEval_a)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), + q) + e3a := addmod(e3a, mload(add(pMem, pGamma)), q) - t2 := addmod( - t2, + let e3b := addmod( mload(add(pProof, pEval_b)), - q - ) - - t2 := addmod( - t2, - mload(add(pMem, pGamma)), - q - ) - - t1 := mulmod(t1, t2, q) - - t2 := addmod( + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), + q) + e3b := addmod(e3b, mload(add(pMem, pGamma)), q) + + let e3c := addmod( mload(add(pProof, pEval_c)), mload(add(pMem, pGamma)), - q - ) + q) - t1 := mulmod(t1, t2, q) - t1 := mulmod(t1, mload(add(pProof, pEval_zw)), q) - t1 := mulmod(t1, mload(add(pMem, pAlpha)), q) - - t2 := mulmod( - mload(add(pMem, pEval_l1)), - mload(add(pMem, pAlpha)), - q - ) - - t2 := mulmod( - t2, - mload(add(pMem, pAlpha)), - q - ) + let e3 := mulmod(mulmod(e3a, e3b, q), e3c, q) - t1 := addmod(t1, t2, q) - - t := mod(sub(add(t, q), t1), q) - t := mulmod(t, mload(add(pMem, pZhInv)), q) + e3 := mulmod(e3, mload(add(pProof, pEval_zw)), q) + e3 := mulmod(e3, mload(add(pMem, pAlpha)), q) + + let r0 := mod(sub(e1, e2), q) + r0 := mod(sub(r0, e3), q) - mstore( add(pMem, pEval_t) , t) - + mstore(add(pMem, pEval_r0) , r0) } function g1_set(pR, pP) { @@ -497,119 +496,146 @@ contract PlonkVerifier { } } + function calculateD(pProof, pMem) { + let p:= add(pMem, pD) + let mIn := mload(0x40) + + g1_mulSetC(p, Qmx, Qmy, mulmod(mload(add(pProof, pEval_a)), mload(add(pProof, pEval_b)), q)) + g1_mulAccC(p, Qlx, Qly, mload(add(pProof, pEval_a))) + g1_mulAccC(p, Qrx, Qry, mload(add(pProof, pEval_b))) + g1_mulAccC(p, Qox, Qoy, mload(add(pProof, pEval_c))) + g1_mulAccC(p, Qcx, Qcy, 1) - function calculateA1(pProof, pMem) { - let p := add(pMem, pA1) - g1_set(p, add(pProof, pWxi)) - g1_mulAcc(p, add(pProof, pWxiw), mload(add(pMem, pU))) - } - + let val1 := addmod( + addmod(mload(add(pProof, pEval_a)), mload(add(pMem, pBetaXi)), q), + mload(add(pMem, pGamma)), + q) + + let val2 := addmod( + addmod( + mload(add(pProof, pEval_b)), + mulmod(mload(add(pMem, pBetaXi)), k1, q), + q), + mload(add(pMem, pGamma)), + q) + + let val3 := addmod( + addmod( + mload(add(pProof, pEval_c)), + mulmod(mload(add(pMem, pBetaXi)), k2, q), + q), + mload(add(pMem, pGamma)), + q) + + let d2a := mulmod( + mulmod(mulmod(val1, val2, q), val3, q), + mload(add(pMem, pAlpha)), + q + ) + + let d2b := mulmod( + mload(add(pMem, pEval_l1)), + mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q), + q + ) + + // We'll use pF to save d2 + g1_mulAcc( + add(pMem, pF), + add(pProof, pZ), + addmod(addmod(d2a, d2b, q), mload(add(pMem, pU)), q)) - function calculateB1(pProof, pMem) { - let s - let s1 - let p := add(pMem, pB1) - - // Calculate D - s := mulmod( mload(add(pProof, pEval_a)), mload(add(pMem, pV1)), q) - g1_mulSetC(p, Qlx, Qly, s) + val1 := addmod( + addmod( + mload(add(pProof, pEval_a)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), + q), + mload(add(pMem, pGamma)), + q) - s := mulmod( s, mload(add(pProof, pEval_b)), q) - g1_mulAccC(p, Qmx, Qmy, s) + val2 := addmod( + addmod( + mload(add(pProof, pEval_b)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), + q), + mload(add(pMem, pGamma)), + q) + + val3 := mulmod( + mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pBeta)), q), + mload(add(pProof, pEval_zw)), q) + - s := mulmod( mload(add(pProof, pEval_b)), mload(add(pMem, pV1)), q) - g1_mulAccC(p, Qrx, Qry, s) - - s := mulmod( mload(add(pProof, pEval_c)), mload(add(pMem, pV1)), q) - g1_mulAccC(p, Qox, Qoy, s) - - s :=mload(add(pMem, pV1)) - g1_mulAccC(p, Qcx, Qcy, s) - - s := addmod(mload(add(pProof, pEval_a)), mload(add(pMem, pBetaXi)), q) - s := addmod(s, mload(add(pMem, pGamma)), q) - s1 := mulmod(k1, mload(add(pMem, pBetaXi)), q) - s1 := addmod(s1, mload(add(pProof, pEval_b)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s1 := mulmod(k2, mload(add(pMem, pBetaXi)), q) - s1 := addmod(s1, mload(add(pProof, pEval_c)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s := mulmod(s, mload(add(pMem, pAlpha)), q) - s := mulmod(s, mload(add(pMem, pV1)), q) - s1 := mulmod(mload(add(pMem, pEval_l1)), mload(add(pMem, pAlpha)), q) - s1 := mulmod(s1, mload(add(pMem, pAlpha)), q) - s1 := mulmod(s1, mload(add(pMem, pV1)), q) - s := addmod(s, s1, q) - s := addmod(s, mload(add(pMem, pU)), q) - g1_mulAcc(p, add(pProof, pZ), s) - - s := mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q) - s := addmod(s, mload(add(pProof, pEval_a)), q) - s := addmod(s, mload(add(pMem, pGamma)), q) - s1 := mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q) - s1 := addmod(s1, mload(add(pProof, pEval_b)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s := mulmod(s, mload(add(pMem, pAlpha)), q) - s := mulmod(s, mload(add(pMem, pV1)), q) - s := mulmod(s, mload(add(pMem, pBeta)), q) - s := mulmod(s, mload(add(pProof, pEval_zw)), q) - s := mod(sub(q, s), q) - g1_mulAccC(p, S3x, S3y, s) - - - // calculate F - g1_acc(p , add(pProof, pT1)) - - s := mload(add(pMem, pXin)) - g1_mulAcc(p, add(pProof, pT2), s) - - s := mulmod(s, s, q) - g1_mulAcc(p, add(pProof, pT3), s) - - g1_mulAcc(p, add(pProof, pA), mload(add(pMem, pV2))) - g1_mulAcc(p, add(pProof, pB), mload(add(pMem, pV3))) - g1_mulAcc(p, add(pProof, pC), mload(add(pMem, pV4))) - g1_mulAccC(p, S1x, S1y, mload(add(pMem, pV5))) - g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV6))) - - // calculate E - s := mload(add(pMem, pEval_t)) - s := addmod(s, mulmod(mload(add(pProof, pEval_r)), mload(add(pMem, pV1)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_a)), mload(add(pMem, pV2)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_b)), mload(add(pMem, pV3)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_c)), mload(add(pMem, pV4)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s1)), mload(add(pMem, pV5)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s2)), mload(add(pMem, pV6)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_zw)), mload(add(pMem, pU)), q), q) - s := mod(sub(q, s), q) - g1_mulAccC(p, G1x, G1y, s) - - - // Last part of B - s := mload(add(pMem, pXi)) - g1_mulAcc(p, add(pProof, pWxi), s) + // We'll use pE to save d3 + g1_mulAccC( + add(pMem, pE), + S3x, + S3y, + mulmod(mulmod(val1, val2, q), val3, q)) - s := mulmod(mload(add(pMem, pU)), mload(add(pMem, pXi)), q) - s := mulmod(s, w1, q) - g1_mulAcc(p, add(pProof, pWxiw), s) + // We'll use pTmp to save d4 + g1_set(add(pMem, pTmp), add(pProof, pT1)) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT2), add(pMem, pXin)) + let xin2 := mulmod(add(pMem, pXin), add(pMem, pXin), q) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) + + g1_mulAcc(mIn, add(pMem, pTmp), add(pMem, pZh)) + + mstore(add(add(pMem, pE), 32), mod(sub(qf, mload(add(add(pMem, pE), 32))), qf)) + mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) + g1_acc(add(pMem, pD), add(pMem, pF)) + g1_acc(add(pMem, pD), add(pMem, pE)) + g1_acc(add(pMem, pD), add(pMem, mIn)) } - function checkPairing(pMem) -> isOk { + function calculateF(pProof, pMem) { + let p := add(pMem, pF) + + g1_set(p, add(pMem, pD)) + g1_mulAcc(p, add(pProof, pA), mload(add(pMem, pV1))) + g1_mulAcc(p, add(pProof, pB), mload(add(pMem, pV2))) + g1_mulAcc(p, add(pProof, pC), mload(add(pMem, pV3))) + g1_mulAccC(p, S1x, S1y, mload(add(pMem, pV4))) + g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV5))) + } + + function calculateE(pProof, pMem) { + let s := mod(sub(q, mload(add(pMem, pEval_r0))), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_a)), mload(add(pMem, pV1)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_b)), mload(add(pMem, pV2)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_c)), mload(add(pMem, pV3)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_s1)), mload(add(pMem, pV4)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_s2)), mload(add(pMem, pV5)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_zw)), mload(add(pMem, pU)), q), q) + g1_mulAccC(add(pMem, pE), G1x, G1y, s) + } + + function checkPairing(pProof, pMem) -> isOk { let mIn := mload(0x40) - mstore(mIn, mload(add(pMem, pA1))) - mstore(add(mIn,32), mload(add(add(pMem, pA1), 32))) + + // A1 + g1_mulAcc(mIn, add(pProof, pWxiw), add(pMem, pU)) + g1_acc(mIn, add(pProof, pWxi)) + mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) + + // [X]_2 mstore(add(mIn,64), X2x2) mstore(add(mIn,96), X2x1) mstore(add(mIn,128), X2y2) mstore(add(mIn,160), X2y1) - mstore(add(mIn,192), mload(add(pMem, pB1))) - let s := mload(add(add(pMem, pB1), 32)) - s := mod(sub(qf, s), qf) - mstore(add(mIn,224), s) + + // B1 + g1_mulAcc(add(mIn, 192), add(pMem, pWxi), mload(add(pMem, pXi))) + let s := mulmod(mload(mload(add(pMem, pU))), mload(mload(add(pMem, pXi))), q) + s := mulmod(s, w1, q) + g1_mulAcc(add(mIn, 256), add(pProof, pWxiw), s) + g1_acc(add(mIn, 192), add(mIn, 256)) + g1_acc(add(mIn, 192), add(pMem, pF)) + g1_acc(add(mIn, 192), add(pMem, pE)) + + // [1]_2 mstore(add(mIn,256), G2x2) mstore(add(mIn,288), G2x1) mstore(add(mIn,320), G2y2) @@ -617,7 +643,7 @@ contract PlonkVerifier { let success := staticcall(sub(gas(), 2000), 8, mIn, 384, mIn, 0x20) - isOk := and(success, mload(mIn)) + isOk := and(success, mload(mIn)) } let pMem := mload(0x40) @@ -626,11 +652,12 @@ contract PlonkVerifier { checkInput(proof) calculateChallanges(proof, pMem, pubSignals) calculateLagrange(pMem) - calculatePl(pMem, pubSignals) - calculateT(proof, pMem) - calculateA1(proof, pMem) - calculateB1(proof, pMem) - let isValid := checkPairing(pMem) + calculatePI(pMem, pubSignals) + calculateR0(proof, pMem) + calculateD(proof, pMem) + calculateF(proof, pMem) + calculateE(proof, pMem) + let isValid := checkPairing(proof, pMem) mstore(0x40, sub(pMem, lastMem)) mstore(0, isValid) diff --git a/test/plonk_circuit/circuit.zkey b/test/plonk_circuit/circuit.zkey index f282380ed6c4f6944cf60a20445b7b3abe758c50..8e804de9702db2b723d45915fb4f79b523483f19 100644 GIT binary patch delta 6952 zcmb_hRal(OlE&RFI5WTuZowj0g8#T%aCaLZf#8EXgA?3c27+5~2pZg-paFtg7IOAn z>|X4-*?yjC`}*s*x~r?Jy1NJR#Z|@A*8CG90s;cw6Cpp*zXQrshWx(^&)<>$o1W`Y zpXlG|zuP=j{SC-*r^JN+yAlOPgD6CYY(wS>G9YoqnMevSPbodN(eL7o8LHDrd?YQW z>!FP20sso`6Zaw)atpn^!`pV171lUD1~Kvlp!Zonvu;lkKOnPO~XImR=~K)_o( 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[ - "14505892627896587350473010034286107819685493071925324450974954770526434593332", - "6186416458036711799535608999371759388592544992468951288703737883955685292858", + "15230464306286391636550107373893393844263753443858456494056755797915359962735", + "4295923307603640725029862081489021526166422259641176323643637657103650618753", "1" ], "Z": [ - "12081441476366171431338238830264497598570062548451685935024863321326757767785", - "9387897371969025065284991899948083393556628309133379383594080265474146141157", + "11004047411656828660428328961973286292047311564838972190990878440058680688901", + "15436256766327825842224680700992331794957429153268020624016727514510742018077", "1" ], "T1": [ - "11697295649838930633765261378756086756478619706964809367863062927042238692921", - "14968409908681220375122607622180081440264275996476655054223469087507417759789", + "21351603608071808295830607650880557871325148899242110976740167133549418528603", + "2645708186332646685572914154670045342238946773079254998870890373729236802677", "1" ], "T2": [ - "2953189016956047791736757973461484048315463397915849932374528729412270696527", - "8620891985757406277592771106070049395916563323571640384543833813728271133486", + "18718055159322028716891056460848640315600372124708181482177956090488976138766", + "14545564657670478509737277771736582695733692748073867042597808406303105978491", "1" ], "T3": [ - "16223333010830689480143912693604648201451508158843567126275050570081980855643", - "14438863974133388343515803834890541076773695198795082356970685950267401738910", + "17300643912187364232525793334678321814907265220556429696382901135492186928813", + "13687463097807270467456771887349938731995528743034200574450167125019408139064", "1" ], - "eval_a": "14339139182789381237229239915123261853915681686933828385685851702630204504663", - "eval_b": "14868966654115759140239472823375151970328635256589988386102968278787868240414", - "eval_c": "564057494214488102817009147593706678326690684832103817838290432546546599925", - "eval_s1": "19371496695515240161592963759911623294871060124201355865755153108252682382360", - "eval_s2": "2579612056529355211259943592521042166985820548059386261162331074609979969098", - "eval_zw": "19685091872602775677986598924926591283988441651361153034121001539751878867815", - "eval_r": "17019396159933864043409418821108145005876806528173417875530903213264996917828", "Wxi": [ - "4789447887245439838828293816801085734534480786500369542683260813915807895018", - "5743534347322910212791948378800524709212623490686788228035168007519506810508", + "13971416223242651542366715728368906359640038706276531500429531708796073258277", + "10421443948033763642149912846113365572165014601716715331224624947552460520043", "1" ], "Wxiw": [ - "19379972490037320589254794886333437175961689166573424007077500138714809349682", - "12523908414418029668596495120104904066342410136497532239942511327769729048404", + "17765787784457670830871593390874368837165912572092183824115141625095019062878", + "1923706056001260011656416104295967740181091112784478760912734896662208628583", "1" ], + "eval_a": "10799560112054680901137226204213873700826592739080369812528079446253216295813", + "eval_b": "7877313129049829225962721657498993624288591252629781090410265210156591091645", + "eval_c": "19262479669546615646866494950794050991978938609429436242634904528122872883540", + "eval_s1": "9943707996031584540773781677363098084929121111061462884057666436801558016467", + "eval_s2": "20442292478151764537886021535271741908528859398849641563695916267470568099112", + "eval_zw": "2514741082646163896220326677313738849736483859214666037715057616704431674465", "protocol": "plonk", "curve": "bn128" } \ No newline at end of file diff --git a/test/plonk_circuit/verification_key.json b/test/plonk_circuit/verification_key.json index 63321622..419cf6c4 100644 --- a/test/plonk_circuit/verification_key.json +++ b/test/plonk_circuit/verification_key.json @@ -6,43 +6,43 @@ "k1": "2", "k2": "3", "Qm": [ - "4574976860925876233715815557145957880705707179788243092345689458042383890488", - "4280641572679440220740870768701934042005081764212788702122100316880968332003", + "17953645607507459900286185560951810786731058999325781923205502055353263497291", + "19385486967908870028674938916390954985705306268782601788969000107603897770767", "1" ], "Ql": [ - "965658296392348546197801330054212493203716810675203464920320569299615906620", - "2656007013467620250344837426700774817845582578535592475523934494973414078961", + "11940858774017579942566450477449012460918017239896733829055270107468309760540", + "947254594125514574342968640034741130676940992205538578216940265903584710169", "1" ], "Qr": [ - "9466120146806803512081752933000124200435544680867502413168004293837549973279", - "21718061423910769411439185483074527939398926867139106591112998426662463026765", + "16057511199156614460548645536725007313348939819318943470685206502402956172907", + "10506209454111335156976278630909826596572196999531725341452203577193363727183", "1" ], "Qo": [ - "14232475876760437187555678371073865360567175818750566973123447255794615727867", - "12884948380030714721172201264029036846611910042838904312559968631894569296588", + "17157624048880737579826278328189066542171805404376573481770268188483838847757", + "18514386016535062016800932564037101304017747936838789635283796814642720512673", "1" ], "Qc": [ - "14611255151810715369553599153356422265550902840832241273629187752840438096443", - "9099095607583972457036848580058361056377035074964862926640921566382822995435", + "9425204922382128984212419080680000340238602060329517997301340801336513664736", + "9167308630107900718125273932943677561306913176994118892249570126249686869364", "1" ], "S1": [ - "14533465958261944855196820716374074689704505288368818447966063234824080424576", - "12453353674569653145950160230568106433424266373528956571501497772329286407421", + "10782085188530267881189340256496934831907742532399561656521702603135823217637", + "12403008688044971496101927450821599344745023222457894394078671019783662128471", "1" ], "S2": [ - "19581287390493194877650947725652399954855738146667446650367315521331119724530", - "13292535777423157488265774466403939589622049710743071078999542362804505686482", + "9279525915934333912510150900730589708299616165652915633005823194068751444534", + "17339946533833948904498037980944354287085405669808936769308277491115888828896", "1" ], "S3": [ - "7628615832235497959754170049702774596960536866278288444040861507702299255530", - "6061093738111279431632848690609155827426019335581022466737969401920480256170", + "10636394165993966883449775646752541022226109588433686577933510456646304718904", + "18335534742276222998450555199564351867006746787413781617417650248398260441193", "1" ], "X_2": [ @@ -58,5 +58,6 @@ "1", "0" ] - ] + ], + "w": "19540430494807482326159819597004422086093766032135589407132600596362845576832" } \ No newline at end of file diff --git a/test/plonk_circuit/verifier.sol b/test/plonk_circuit/verifier.sol index 9e2a122d..5b02324a 100644 --- a/test/plonk_circuit/verifier.sol +++ b/test/plonk_circuit/verifier.sol @@ -27,22 +27,22 @@ contract PlonkVerifier { uint16 constant nPublic = 2; uint16 constant nLagrange = 2; - uint256 constant Qmx = 4574976860925876233715815557145957880705707179788243092345689458042383890488; - uint256 constant Qmy = 4280641572679440220740870768701934042005081764212788702122100316880968332003; - uint256 constant Qlx = 965658296392348546197801330054212493203716810675203464920320569299615906620; - uint256 constant Qly = 2656007013467620250344837426700774817845582578535592475523934494973414078961; - uint256 constant Qrx = 9466120146806803512081752933000124200435544680867502413168004293837549973279; - uint256 constant Qry = 21718061423910769411439185483074527939398926867139106591112998426662463026765; - uint256 constant Qox = 14232475876760437187555678371073865360567175818750566973123447255794615727867; - uint256 constant Qoy = 12884948380030714721172201264029036846611910042838904312559968631894569296588; - uint256 constant Qcx = 14611255151810715369553599153356422265550902840832241273629187752840438096443; - uint256 constant Qcy = 9099095607583972457036848580058361056377035074964862926640921566382822995435; - uint256 constant S1x = 14533465958261944855196820716374074689704505288368818447966063234824080424576; - uint256 constant S1y = 12453353674569653145950160230568106433424266373528956571501497772329286407421; - uint256 constant S2x = 19581287390493194877650947725652399954855738146667446650367315521331119724530; - uint256 constant S2y = 13292535777423157488265774466403939589622049710743071078999542362804505686482; - uint256 constant S3x = 7628615832235497959754170049702774596960536866278288444040861507702299255530; - uint256 constant S3y = 6061093738111279431632848690609155827426019335581022466737969401920480256170; + uint256 constant Qmx = 17953645607507459900286185560951810786731058999325781923205502055353263497291; + uint256 constant Qmy = 19385486967908870028674938916390954985705306268782601788969000107603897770767; + uint256 constant Qlx = 11940858774017579942566450477449012460918017239896733829055270107468309760540; + uint256 constant Qly = 947254594125514574342968640034741130676940992205538578216940265903584710169; + uint256 constant Qrx = 16057511199156614460548645536725007313348939819318943470685206502402956172907; + uint256 constant Qry = 10506209454111335156976278630909826596572196999531725341452203577193363727183; + uint256 constant Qox = 17157624048880737579826278328189066542171805404376573481770268188483838847757; + uint256 constant Qoy = 18514386016535062016800932564037101304017747936838789635283796814642720512673; + uint256 constant Qcx = 9425204922382128984212419080680000340238602060329517997301340801336513664736; + uint256 constant Qcy = 9167308630107900718125273932943677561306913176994118892249570126249686869364; + uint256 constant S1x = 10782085188530267881189340256496934831907742532399561656521702603135823217637; + uint256 constant S1y = 12403008688044971496101927450821599344745023222457894394078671019783662128471; + uint256 constant S2x = 9279525915934333912510150900730589708299616165652915633005823194068751444534; + uint256 constant S2y = 17339946533833948904498037980944354287085405669808936769308277491115888828896; + uint256 constant S3x = 10636394165993966883449775646752541022226109588433686577933510456646304718904; + uint256 constant S3y = 18335534742276222998450555199564351867006746787413781617417650248398260441193; uint256 constant k1 = 2; uint256 constant k2 = 3; uint256 constant X2x1 = 18029695676650738226693292988307914797657423701064905010927197838374790804409; @@ -75,7 +75,6 @@ contract PlonkVerifier { uint16 constant pEval_s1 = 704; uint16 constant pEval_s2 = 736; uint16 constant pEval_zw = 768; - uint16 constant pEval_r = 800; uint16 constant pAlpha = 0; uint16 constant pBeta = 32; @@ -90,20 +89,22 @@ contract PlonkVerifier { uint16 constant pV5 = 320; uint16 constant pV6 = 352; uint16 constant pU = 384; - uint16 constant pPl = 416; - uint16 constant pEval_t = 448; - uint16 constant pA1 = 480; - uint16 constant pB1 = 544; - uint16 constant pZh = 608; - uint16 constant pZhInv = 640; + uint16 constant pPI = 416; + uint16 constant pEval_r0 = 448; + uint16 constant pD = 480; + uint16 constant pF = 544; + uint16 constant pE = 608; + uint16 constant pTmp = 672; + uint16 constant pZh = 736; + uint16 constant pZhInv = 768; - uint16 constant pEval_l1 = 672; + uint16 constant pEval_l1 = 800; - uint16 constant pEval_l2 = 704; + uint16 constant pEval_l2 = 832; - uint16 constant lastMem = 736; + uint16 constant lastMem = 864; function verifyProof(bytes memory proof, uint[] memory pubSignals) public view returns (bool) { assembly { @@ -195,7 +196,6 @@ contract PlonkVerifier { checkField(mload(add(pProof, pEval_s1))) checkField(mload(add(pProof, pEval_s2))) checkField(mload(add(pProof, pEval_zw))) - checkField(mload(add(pProof, pEval_r))) // Points are checked in the point operations precompiled smart contracts } @@ -205,25 +205,71 @@ contract PlonkVerifier { let a let b - - mstore( add(pMem, 736 ), mload( add( pPublic, 32))) - - mstore( add(pMem, 768 ), mload( add( pPublic, 64))) - - mstore( add(pMem, 800 ), mload( add( pProof, pA))) - mstore( add(pMem, 832 ), mload( add( pProof, add(pA,32)))) - mstore( add(pMem, 864 ), mload( add( pProof, add(pA,64)))) - mstore( add(pMem, 896 ), mload( add( pProof, add(pA,96)))) - mstore( add(pMem, 928 ), mload( add( pProof, add(pA,128)))) - mstore( add(pMem, 960 ), mload( add( pProof, add(pA,160)))) - - b := mod(keccak256(add(pMem, lastMem), 256), q) - mstore( add(pMem, pBeta), b) - mstore( add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) - mstore( add(pMem, pAlpha), mod(keccak256(add(pProof, pZ), 64), q)) - - a := mod(keccak256(add(pProof, pT1), 192), q) + // Challenges.beta + mstore( add(pMem, 864 ), Qmx) + mstore( add(pMem, 896 ), Qmy) + mstore( add(pMem, 928 ), Qlx) + mstore( add(pMem, 960 ), Qly) + mstore( add(pMem, 992 ), Qrx) + mstore( add(pMem, 1024 ), Qry) + mstore( add(pMem, 1056 ), Qox) + mstore( add(pMem, 1088 ), Qoy) + mstore( add(pMem, 1120 ), Qcx) + mstore( add(pMem, 1152 ), Qcy) + mstore( add(pMem, 1184 ), S1x) + mstore( add(pMem, 1216 ), S1x) + mstore( add(pMem, 1248 ), S2x) + mstore( add(pMem, 1280 ), S2x) + mstore( add(pMem, 1312 ), S3x) + mstore( add(pMem, 1344 ), S3x) + + + mstore( add(pMem, 1376 ), mload( add( pPublic, 32))) + + mstore( add(pMem, 1408 ), mload( add( pPublic, 64))) + + mstore( add(pMem, 1440 ), mload( add( pProof, pA))) + mstore( add(pMem, 1472 ), mload( add( pProof, add(pA,32)))) + mstore( add(pMem, 1504 ), mload( add( pProof, pB))) + mstore( add(pMem, 1536 ), mload( add( pProof, add(pB, 32)))) + mstore( add(pMem, 1568 ), mload( add( pProof, pC))) + mstore( add(pMem, 1600 ), mload( add( pProof, add(pC, 32)))) + + b := mod(keccak256(add(pMem, lastMem), 768), q) + mstore(add(pMem, pBeta), b) + + // Challenges.gamma + mstore(add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) + + // Challenges.alpha + mstore(add(pMem, 864), mload(add(pMem, pBeta))) + mstore(add(pMem, 896), mload(add(pMem, pGamma))) + mstore(add(pMem, 928), mload(add(pProof, pZ))) + mstore(add(pMem, 960), mload(add(pProof, add(pZ, 32)))) + a := mod(keccak256(add(pMem, lastMem), 128), q) + mstore(add(pMem, pAlpha), a) + + mstore(add(pMem, 864), mload(add(pMem, pAlpha))) + mstore(add(pMem, 896), mload(add(pProof, pT1))) + mstore(add(pMem, 928), mload(add(pProof, add(pT1, 32)))) + mstore(add(pMem, 960), mload(add(pProof, pT2))) + mstore(add(pMem, 992), mload(add(pProof, add(pT2, 32)))) + mstore(add(pMem, 1024), mload(add(pProof, pT3))) + mstore(add(pMem, 1056), mload(add(pProof, add(pT3, 32)))) + a := mod(keccak256(add(pMem, lastMem), 224), q) mstore( add(pMem, pXi), a) + + mstore(add(pMem, 864), a) + mstore(add(pMem, 896), mload(add(pProof, pEval_a))) + mstore(add(pMem, 928), mload(add(pProof, pEval_b))) + mstore(add(pMem, 960), mload(add(pProof, pEval_c))) + mstore(add(pMem, 992), mload(add(pProof, pEval_s1))) + mstore(add(pMem, 1024), mload(add(pProof, pEval_s2))) + mstore(add(pMem, 1056), mload(add(pProof, pEval_zw))) + let v1 := mod(keccak256(add(pMem, lastMem), 224), q) + mstore(add(pMem, pV1), v1) + + // Compute betaxi mstore( add(pMem, pBetaXi), mulmod(b, a, q)) a:= mulmod(a, a, q) @@ -236,9 +282,7 @@ contract PlonkVerifier { a:= mod(add(sub(a, 1),q), q) mstore( add(pMem, pZh), a) mstore( add(pMem, pZhInv), a) // We will invert later together with lagrange pols - - let v1 := mod(keccak256(add(pProof, pEval_a), 224), q) - mstore( add(pMem, pV1), v1) + a := mulmod(v1, v1, q) mstore( add(pMem, pV2), a) a := mulmod(a, v1, q) @@ -337,7 +381,7 @@ contract PlonkVerifier { } - function calculatePl(pMem, pPub) { + function calculatePI(pMem, pPub) { let pl := 0 @@ -372,88 +416,43 @@ contract PlonkVerifier { ) - mstore(add(pMem, pPl), pl) + mstore(add(pMem, pPI), pl) } - function calculateT(pProof, pMem) { - let t - let t1 - let t2 - t := addmod( - mload(add(pProof, pEval_r)), - mload(add(pMem, pPl)), - q - ) - - t1 := mulmod( - mload(add(pProof, pEval_s1)), - mload(add(pMem, pBeta)), - q - ) + function calculateR0(pProof, pMem) { + let alpha2 := mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q) + let e1 := mload(add(pMem, pPI)) - t1 := addmod( - t1, - mload(add(pProof, pEval_a)), - q - ) - - t1 := addmod( - t1, - mload(add(pMem, pGamma)), - q - ) + let e2 := mulmod(mload(add(pMem, pEval_l1)), alpha2, q) - t2 := mulmod( - mload(add(pProof, pEval_s2)), - mload(add(pMem, pBeta)), - q - ) + let e3a := addmod( + mload(add(pProof, pEval_a)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), + q) + e3a := addmod(e3a, mload(add(pMem, pGamma)), q) - t2 := addmod( - t2, + let e3b := addmod( mload(add(pProof, pEval_b)), - q - ) - - t2 := addmod( - t2, - mload(add(pMem, pGamma)), - q - ) - - t1 := mulmod(t1, t2, q) - - t2 := addmod( + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), + q) + e3b := addmod(e3b, mload(add(pMem, pGamma)), q) + + let e3c := addmod( mload(add(pProof, pEval_c)), mload(add(pMem, pGamma)), - q - ) + q) - t1 := mulmod(t1, t2, q) - t1 := mulmod(t1, mload(add(pProof, pEval_zw)), q) - t1 := mulmod(t1, mload(add(pMem, pAlpha)), q) - - t2 := mulmod( - mload(add(pMem, pEval_l1)), - mload(add(pMem, pAlpha)), - q - ) - - t2 := mulmod( - t2, - mload(add(pMem, pAlpha)), - q - ) + let e3 := mulmod(mulmod(e3a, e3b, q), e3c, q) - t1 := addmod(t1, t2, q) - - t := mod(sub(add(t, q), t1), q) - t := mulmod(t, mload(add(pMem, pZhInv)), q) + e3 := mulmod(e3, mload(add(pProof, pEval_zw)), q) + e3 := mulmod(e3, mload(add(pMem, pAlpha)), q) + + let r0 := mod(sub(e1, e2), q) + r0 := mod(sub(r0, e3), q) - mstore( add(pMem, pEval_t) , t) - + mstore(add(pMem, pEval_r0) , r0) } function g1_set(pR, pP) { @@ -542,119 +541,146 @@ contract PlonkVerifier { } } + function calculateD(pProof, pMem) { + let p:= add(pMem, pD) + let mIn := mload(0x40) + + g1_mulSetC(p, Qmx, Qmy, mulmod(mload(add(pProof, pEval_a)), mload(add(pProof, pEval_b)), q)) + g1_mulAccC(p, Qlx, Qly, mload(add(pProof, pEval_a))) + g1_mulAccC(p, Qrx, Qry, mload(add(pProof, pEval_b))) + g1_mulAccC(p, Qox, Qoy, mload(add(pProof, pEval_c))) + g1_mulAccC(p, Qcx, Qcy, 1) + + let val1 := addmod( + addmod(mload(add(pProof, pEval_a)), mload(add(pMem, pBetaXi)), q), + mload(add(pMem, pGamma)), + q) + + let val2 := addmod( + addmod( + mload(add(pProof, pEval_b)), + mulmod(mload(add(pMem, pBetaXi)), k1, q), + q), + mload(add(pMem, pGamma)), + q) + + let val3 := addmod( + addmod( + mload(add(pProof, pEval_c)), + mulmod(mload(add(pMem, pBetaXi)), k2, q), + q), + mload(add(pMem, pGamma)), + q) + + let d2a := mulmod( + mulmod(mulmod(val1, val2, q), val3, q), + mload(add(pMem, pAlpha)), + q + ) + + let d2b := mulmod( + mload(add(pMem, pEval_l1)), + mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q), + q + ) + + // We'll use pF to save d2 + g1_mulAcc( + add(pMem, pF), + add(pProof, pZ), + addmod(addmod(d2a, d2b, q), mload(add(pMem, pU)), q)) + + val1 := addmod( + addmod( + mload(add(pProof, pEval_a)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), + q), + mload(add(pMem, pGamma)), + q) - function calculateA1(pProof, pMem) { - let p := add(pMem, pA1) - g1_set(p, add(pProof, pWxi)) - g1_mulAcc(p, add(pProof, pWxiw), mload(add(pMem, pU))) + val2 := addmod( + addmod( + mload(add(pProof, pEval_b)), + mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), + q), + mload(add(pMem, pGamma)), + q) + + val3 := mulmod( + mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pBeta)), q), + mload(add(pProof, pEval_zw)), q) + + + // We'll use pE to save d3 + g1_mulAccC( + add(pMem, pE), + S3x, + S3y, + mulmod(mulmod(val1, val2, q), val3, q)) + + + // We'll use pTmp to save d4 + g1_set(add(pMem, pTmp), add(pProof, pT1)) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT2), add(pMem, pXin)) + let xin2 := mulmod(add(pMem, pXin), add(pMem, pXin), q) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) + g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) + + g1_mulAcc(mIn, add(pMem, pTmp), add(pMem, pZh)) + + mstore(add(add(pMem, pE), 32), mod(sub(qf, mload(add(add(pMem, pE), 32))), qf)) + mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) + g1_acc(add(pMem, pD), add(pMem, pF)) + g1_acc(add(pMem, pD), add(pMem, pE)) + g1_acc(add(pMem, pD), add(pMem, mIn)) } + function calculateF(pProof, pMem) { + let p := add(pMem, pF) + + g1_set(p, add(pMem, pD)) + g1_mulAcc(p, add(pProof, pA), mload(add(pMem, pV1))) + g1_mulAcc(p, add(pProof, pB), mload(add(pMem, pV2))) + g1_mulAcc(p, add(pProof, pC), mload(add(pMem, pV3))) + g1_mulAccC(p, S1x, S1y, mload(add(pMem, pV4))) + g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV5))) + } - function calculateB1(pProof, pMem) { - let s - let s1 - let p := add(pMem, pB1) - - // Calculate D - s := mulmod( mload(add(pProof, pEval_a)), mload(add(pMem, pV1)), q) - g1_mulSetC(p, Qlx, Qly, s) - - s := mulmod( s, mload(add(pProof, pEval_b)), q) - g1_mulAccC(p, Qmx, Qmy, s) - - s := mulmod( mload(add(pProof, pEval_b)), mload(add(pMem, pV1)), q) - g1_mulAccC(p, Qrx, Qry, s) - - s := mulmod( mload(add(pProof, pEval_c)), mload(add(pMem, pV1)), q) - g1_mulAccC(p, Qox, Qoy, s) - - s :=mload(add(pMem, pV1)) - g1_mulAccC(p, Qcx, Qcy, s) - - s := addmod(mload(add(pProof, pEval_a)), mload(add(pMem, pBetaXi)), q) - s := addmod(s, mload(add(pMem, pGamma)), q) - s1 := mulmod(k1, mload(add(pMem, pBetaXi)), q) - s1 := addmod(s1, mload(add(pProof, pEval_b)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s1 := mulmod(k2, mload(add(pMem, pBetaXi)), q) - s1 := addmod(s1, mload(add(pProof, pEval_c)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s := mulmod(s, mload(add(pMem, pAlpha)), q) - s := mulmod(s, mload(add(pMem, pV1)), q) - s1 := mulmod(mload(add(pMem, pEval_l1)), mload(add(pMem, pAlpha)), q) - s1 := mulmod(s1, mload(add(pMem, pAlpha)), q) - s1 := mulmod(s1, mload(add(pMem, pV1)), q) - s := addmod(s, s1, q) - s := addmod(s, mload(add(pMem, pU)), q) - g1_mulAcc(p, add(pProof, pZ), s) - - s := mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q) - s := addmod(s, mload(add(pProof, pEval_a)), q) - s := addmod(s, mload(add(pMem, pGamma)), q) - s1 := mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q) - s1 := addmod(s1, mload(add(pProof, pEval_b)), q) - s1 := addmod(s1, mload(add(pMem, pGamma)), q) - s := mulmod(s, s1, q) - s := mulmod(s, mload(add(pMem, pAlpha)), q) - s := mulmod(s, mload(add(pMem, pV1)), q) - s := mulmod(s, mload(add(pMem, pBeta)), q) - s := mulmod(s, mload(add(pProof, pEval_zw)), q) - s := mod(sub(q, s), q) - g1_mulAccC(p, S3x, S3y, s) - - - // calculate F - g1_acc(p , add(pProof, pT1)) - - s := mload(add(pMem, pXin)) - g1_mulAcc(p, add(pProof, pT2), s) - - s := mulmod(s, s, q) - g1_mulAcc(p, add(pProof, pT3), s) - - g1_mulAcc(p, add(pProof, pA), mload(add(pMem, pV2))) - g1_mulAcc(p, add(pProof, pB), mload(add(pMem, pV3))) - g1_mulAcc(p, add(pProof, pC), mload(add(pMem, pV4))) - g1_mulAccC(p, S1x, S1y, mload(add(pMem, pV5))) - g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV6))) - - // calculate E - s := mload(add(pMem, pEval_t)) - s := addmod(s, mulmod(mload(add(pProof, pEval_r)), mload(add(pMem, pV1)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_a)), mload(add(pMem, pV2)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_b)), mload(add(pMem, pV3)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_c)), mload(add(pMem, pV4)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s1)), mload(add(pMem, pV5)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s2)), mload(add(pMem, pV6)), q), q) + function calculateE(pProof, pMem) { + let s := mod(sub(q, mload(add(pMem, pEval_r0))), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_a)), mload(add(pMem, pV1)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_b)), mload(add(pMem, pV2)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_c)), mload(add(pMem, pV3)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_s1)), mload(add(pMem, pV4)), q), q) + s := addmod(s, mulmod(mload(add(pProof, pEval_s2)), mload(add(pMem, pV5)), q), q) s := addmod(s, mulmod(mload(add(pProof, pEval_zw)), mload(add(pMem, pU)), q), q) - s := mod(sub(q, s), q) - g1_mulAccC(p, G1x, G1y, s) - - - // Last part of B - s := mload(add(pMem, pXi)) - g1_mulAcc(p, add(pProof, pWxi), s) - - s := mulmod(mload(add(pMem, pU)), mload(add(pMem, pXi)), q) - s := mulmod(s, w1, q) - g1_mulAcc(p, add(pProof, pWxiw), s) - + g1_mulAccC(add(pMem, pE), G1x, G1y, s) } - function checkPairing(pMem) -> isOk { + function checkPairing(pProof, pMem) -> isOk { let mIn := mload(0x40) - mstore(mIn, mload(add(pMem, pA1))) - mstore(add(mIn,32), mload(add(add(pMem, pA1), 32))) + + // A1 + g1_mulAcc(mIn, add(pProof, pWxiw), add(pMem, pU)) + g1_acc(mIn, add(pProof, pWxi)) + mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) + + // [X]_2 mstore(add(mIn,64), X2x2) mstore(add(mIn,96), X2x1) mstore(add(mIn,128), X2y2) mstore(add(mIn,160), X2y1) - mstore(add(mIn,192), mload(add(pMem, pB1))) - let s := mload(add(add(pMem, pB1), 32)) - s := mod(sub(qf, s), qf) - mstore(add(mIn,224), s) + + // B1 + g1_mulAcc(add(mIn, 192), add(pMem, pWxi), mload(add(pMem, pXi))) + let s := mulmod(mload(mload(add(pMem, pU))), mload(mload(add(pMem, pXi))), q) + s := mulmod(s, w1, q) + g1_mulAcc(add(mIn, 256), add(pProof, pWxiw), s) + g1_acc(add(mIn, 192), add(mIn, 256)) + g1_acc(add(mIn, 192), add(pMem, pF)) + g1_acc(add(mIn, 192), add(pMem, pE)) + + // [1]_2 mstore(add(mIn,256), G2x2) mstore(add(mIn,288), G2x1) mstore(add(mIn,320), G2y2) @@ -662,7 +688,7 @@ contract PlonkVerifier { let success := staticcall(sub(gas(), 2000), 8, mIn, 384, mIn, 0x20) - isOk := and(success, mload(mIn)) + isOk := and(success, mload(mIn)) } let pMem := mload(0x40) @@ -671,11 +697,12 @@ contract PlonkVerifier { checkInput(proof) calculateChallanges(proof, pMem, pubSignals) calculateLagrange(pMem) - calculatePl(pMem, pubSignals) - calculateT(proof, pMem) - calculateA1(proof, pMem) - calculateB1(proof, pMem) - let isValid := checkPairing(pMem) + calculatePI(pMem, pubSignals) + calculateR0(proof, pMem) + calculateD(proof, pMem) + calculateF(proof, pMem) + calculateE(proof, pMem) + let isValid := checkPairing(proof, pMem) mstore(0x40, sub(pMem, lastMem)) mstore(0, isValid) From 9237714eaa53b8d8e125ec4ef9e4c48ceaae8104 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Sat, 13 May 2023 06:08:33 +0200 Subject: [PATCH 29/48] add debug function --- templates/verifier_plonk.sol.ejs | 29 +++++++++++++++++++++++++---- 1 file changed, 25 insertions(+), 4 deletions(-) diff --git a/templates/verifier_plonk.sol.ejs b/templates/verifier_plonk.sol.ejs index 6485cc0c..b4f301e2 100644 --- a/templates/verifier_plonk.sol.ejs +++ b/templates/verifier_plonk.sol.ejs @@ -21,6 +21,8 @@ pragma solidity >=0.7.0 <0.9.0; +import "hardhat/console.sol"; + contract PlonkVerifier { uint32 constant n = <%=2**power%>; @@ -104,7 +106,7 @@ contract PlonkVerifier { uint16 constant lastMem = <%=pLastMem%>; - function verifyProof(bytes memory proof, uint[] memory pubSignals) public view returns (bool) { + function verifyProof(bytes memory proof, uint[] memory pubSignals) public /*view*/ returns (bool) { assembly { ///////// // Computes the inverse using the extended euclidean algorithm @@ -658,11 +660,30 @@ contract PlonkVerifier { calculateF(proof, pMem) calculateE(proof, pMem) let isValid := checkPairing(proof, pMem) - - mstore(0x40, sub(pMem, lastMem)) + + sstore(0, mload(add(pMem, pGamma))) + } + + bytes32 value = debug(); + console.logBytes32(value); + + assembly { + mstore(0, true) + return(0,0x20) + } + } + + function debug() public view returns (bytes32 result) { + assembly { + result := sload(0) + } + } +} + + /*mstore(0x40, sub(pMem, lastMem)) mstore(0, isValid) return(0,0x20) } } -} +}/* From 9b094328b1df7b16992694d9137aaaa4d322ddc7 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Wed, 17 May 2023 11:25:22 +0200 Subject: [PATCH 30/48] Plonk smart contracte refactored. --- src/plonk_exportsoliditycalldata.js | 39 +- templates/verifier_plonk.sol.ejs | 571 ++++++++++++++-------------- 2 files changed, 312 insertions(+), 298 deletions(-) diff --git a/src/plonk_exportsoliditycalldata.js b/src/plonk_exportsoliditycalldata.js index 48d437fd..d1bcce37 100644 --- a/src/plonk_exportsoliditycalldata.js +++ b/src/plonk_exportsoliditycalldata.js @@ -46,27 +46,20 @@ export default async function plonkExportSolidityCallData(_proof, _pub) { inputs = inputs + p256(pub[i]); } - const proofBuff = new Uint8Array(G1.F.n8*2*9 + Fr.n8*7); - G1.toRprUncompressed(proofBuff, 0, G1.e(proof.A)); - G1.toRprUncompressed(proofBuff, G1.F.n8*2, G1.e(proof.B)); - G1.toRprUncompressed(proofBuff, G1.F.n8*4, G1.e(proof.C)); - G1.toRprUncompressed(proofBuff, G1.F.n8*6, G1.e(proof.Z)); - G1.toRprUncompressed(proofBuff, G1.F.n8*8, G1.e(proof.T1)); - G1.toRprUncompressed(proofBuff, G1.F.n8*10, G1.e(proof.T2)); - G1.toRprUncompressed(proofBuff, G1.F.n8*12, G1.e(proof.T3)); - G1.toRprUncompressed(proofBuff, G1.F.n8*14, G1.e(proof.Wxi)); - G1.toRprUncompressed(proofBuff, G1.F.n8*16, G1.e(proof.Wxiw)); - Fr.toRprBE(proofBuff, G1.F.n8*18 , Fr.e(proof.eval_a)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8, Fr.e(proof.eval_b)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8*2, Fr.e(proof.eval_c)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8*3, Fr.e(proof.eval_s1)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8*4, Fr.e(proof.eval_s2)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8*5, Fr.e(proof.eval_zw)); - Fr.toRprBE(proofBuff, G1.F.n8*18 + Fr.n8*6, Fr.e(proof.eval_r)); - - const proofHex = Array.from(proofBuff).map(i2hex).join(""); - - const S="0x"+proofHex+",["+inputs+"]"; - - return S; + return `[${p256(proof.A[0])}, ${p256(proof.A[1])},` + + `${p256(proof.B[0])},${p256(proof.B[1])},` + + `${p256(proof.C[0])},${p256(proof.C[1])},` + + `${p256(proof.Z[0])},${p256(proof.Z[1])},` + + `${p256(proof.T1[0])},${p256(proof.T1[1])},` + + `${p256(proof.T2[0])},${p256(proof.T2[1])},` + + `${p256(proof.T3[0])},${p256(proof.T3[1])},` + + `${p256(proof.Wxi[0])},${p256(proof.Wxi[1])},` + + `${p256(proof.Wxiw[0])},${p256(proof.Wxiw[1])},` + + `${p256(proof.eval_a)},` + + `${p256(proof.eval_b)},` + + `${p256(proof.eval_c)},` + + `${p256(proof.eval_s1)},` + + `${p256(proof.eval_s2)},` + + `${p256(proof.eval_zw)}]` + + `[${inputs}]`; } diff --git a/templates/verifier_plonk.sol.ejs b/templates/verifier_plonk.sol.ejs index b4f301e2..25f38eb1 100644 --- a/templates/verifier_plonk.sol.ejs +++ b/templates/verifier_plonk.sol.ejs @@ -24,81 +24,95 @@ pragma solidity >=0.7.0 <0.9.0; import "hardhat/console.sol"; contract PlonkVerifier { - - uint32 constant n = <%=2**power%>; - uint16 constant nPublic = <%=nPublic%>; - uint16 constant nLagrange = <%=Math.max(nPublic, 1)%>; - - uint256 constant Qmx = <%=Qm[0]%>; - uint256 constant Qmy = <%=Qm[0] == "0" ? "0" : Qm[1]%>; - uint256 constant Qlx = <%=Ql[0]%>; - uint256 constant Qly = <%=Ql[0] == "0" ? "0" : Ql[1]%>; - uint256 constant Qrx = <%=Qr[0]%>; - uint256 constant Qry = <%=Qr[0] == "0" ? "0" : Qr[1]%>; - uint256 constant Qox = <%=Qo[0]%>; - uint256 constant Qoy = <%=Qo[0] == "0" ? "0" : Qo[1]%>; - uint256 constant Qcx = <%=Qc[0]%>; - uint256 constant Qcy = <%=Qc[0] == "0" ? "0" : Qc[1]%>; - uint256 constant S1x = <%=S1[0]%>; - uint256 constant S1y = <%=S1[0] == "0" ? "0" : S1[1]%>; - uint256 constant S2x = <%=S2[0]%>; - uint256 constant S2y = <%=S2[0] == "0" ? "0" : S2[1]%>; - uint256 constant S3x = <%=S3[0]%>; - uint256 constant S3y = <%=S3[0] == "0" ? "0" : S3[1]%>; - uint256 constant k1 = 2; - uint256 constant k2 = 3; - uint256 constant X2x1 = <%=X_2[0][0]%>; - uint256 constant X2x2 = <%=X_2[0][1]%>; - uint256 constant X2y1 = <%=X_2[1][0]%>; - uint256 constant X2y2 = <%=X_2[1][1]%>; - - uint256 constant q = 21888242871839275222246405745257275088548364400416034343698204186575808495617; - uint256 constant qf = 21888242871839275222246405745257275088696311157297823662689037894645226208583; + // Omega uint256 constant w1 = <%=w%>; + // Scalar field size + uint256 constant q = 21888242871839275222246405745257275088548364400416034343698204186575808495617; + // Base field size + uint256 constant qf = 21888242871839275222246405745257275088696311157297823662689037894645226208583; + // [1]_1 uint256 constant G1x = 1; uint256 constant G1y = 2; + // [1]_2 uint256 constant G2x1 = 10857046999023057135944570762232829481370756359578518086990519993285655852781; uint256 constant G2x2 = 11559732032986387107991004021392285783925812861821192530917403151452391805634; uint256 constant G2y1 = 8495653923123431417604973247489272438418190587263600148770280649306958101930; uint256 constant G2y2 = 4082367875863433681332203403145435568316851327593401208105741076214120093531; - uint16 constant pA = 32; - uint16 constant pB = 96; - uint16 constant pC = 160; - uint16 constant pZ = 224; - uint16 constant pT1 = 288; - uint16 constant pT2 = 352; - uint16 constant pT3 = 416; - uint16 constant pWxi = 480; - uint16 constant pWxiw = 544; - uint16 constant pEval_a = 608; - uint16 constant pEval_b = 640; - uint16 constant pEval_c = 672; - uint16 constant pEval_s1 = 704; - uint16 constant pEval_s2 = 736; - uint16 constant pEval_zw = 768; - uint16 constant pAlpha = 0; - uint16 constant pBeta = 32; - uint16 constant pGamma = 64; - uint16 constant pXi = 96; - uint16 constant pXin = 128; + // Verification Key data + uint32 constant n = <%=2**power%>; + uint16 constant nPublic = <%=nPublic%>; + uint16 constant nLagrange = <%=Math.max(nPublic, 1)%>; + + uint256 constant Qmx = <%=Qm[0]%>; + uint256 constant Qmy = <%=Qm[0] == "0" ? "0" : Qm[1]%>; + uint256 constant Qlx = <%=Ql[0]%>; + uint256 constant Qly = <%=Ql[0] == "0" ? "0" : Ql[1]%>; + uint256 constant Qrx = <%=Qr[0]%>; + uint256 constant Qry = <%=Qr[0] == "0" ? "0" : Qr[1]%>; + uint256 constant Qox = <%=Qo[0]%>; + uint256 constant Qoy = <%=Qo[0] == "0" ? "0" : Qo[1]%>; + uint256 constant Qcx = <%=Qc[0]%>; + uint256 constant Qcy = <%=Qc[0] == "0" ? "0" : Qc[1]%>; + uint256 constant S1x = <%=S1[0]%>; + uint256 constant S1y = <%=S1[0] == "0" ? "0" : S1[1]%>; + uint256 constant S2x = <%=S2[0]%>; + uint256 constant S2y = <%=S2[0] == "0" ? "0" : S2[1]%>; + uint256 constant S3x = <%=S3[0]%>; + uint256 constant S3y = <%=S3[0] == "0" ? "0" : S3[1]%>; + uint256 constant k1 = <%=k1%>; + uint256 constant k2 = <%=k2%>; + uint256 constant X2x1 = <%=X_2[0][0]%>; + uint256 constant X2x2 = <%=X_2[0][1]%>; + uint256 constant X2y1 = <%=X_2[1][0]%>; + uint256 constant X2y2 = <%=X_2[1][1]%>; + + // Proof calldata + // Byte offset of every parameter of the calldata + // Polynomial commitments + uint16 constant pA = 4 + 0; + uint16 constant pB = 4 + 64; + uint16 constant pC = 4 + 128; + uint16 constant pZ = 4 + 192; + uint16 constant pT1 = 4 + 256; + uint16 constant pT2 = 4 + 320; + uint16 constant pT3 = 4 + 384; + uint16 constant pWxi = 4 + 448; + uint16 constant pWxiw = 4 + 512; + // Opening evaluations + uint16 constant pEval_a = 4 + 576; + uint16 constant pEval_b = 4 + 608; + uint16 constant pEval_c = 4 + 640; + uint16 constant pEval_s1 = 4 + 672; + uint16 constant pEval_s2 = 4 + 704; + uint16 constant pEval_zw = 4 + 736; + + // Memory data + // Challenges + uint16 constant pAlpha = 0; + uint16 constant pBeta = 32; + uint16 constant pGamma = 64; + uint16 constant pXi = 96; + uint16 constant pXin = 128; uint16 constant pBetaXi = 160; - uint16 constant pV1 = 192; - uint16 constant pV2 = 224; - uint16 constant pV3 = 256; - uint16 constant pV4 = 288; - uint16 constant pV5 = 320; - uint16 constant pV6 = 352; - uint16 constant pU = 384; - uint16 constant pPI = 416; - uint16 constant pEval_r0 = 448; - uint16 constant pD = 480; - uint16 constant pF = 544; - uint16 constant pE = 608; - uint16 constant pTmp = 672; - uint16 constant pZh = 736; - uint16 constant pZhInv = 768; + uint16 constant pV1 = 192; + uint16 constant pV2 = 224; + uint16 constant pV3 = 256; + uint16 constant pV4 = 288; + uint16 constant pV5 = 320; + uint16 constant pU = 352; + + uint16 constant pPI = 384; + uint16 constant pEval_r0 = 416; + uint16 constant pD = 448; + uint16 constant pF = 512; + uint16 constant pE = 576; + uint16 constant pTmp = 640; + uint16 constant pAlpha2 = 704; + uint16 constant pZh = 736; + uint16 constant pZhInv = 768; + <% for (let i=1; i<=Math.max(nPublic, 1); i++) { %> uint16 constant pEval_l<%=i%> = <%=768+i*32%>; <% } %> @@ -106,7 +120,7 @@ contract PlonkVerifier { uint16 constant lastMem = <%=pLastMem%>; - function verifyProof(bytes memory proof, uint[] memory pubSignals) public /*view*/ returns (bool) { + function verifyProof(uint256[24] calldata _proof, uint256[<%=nPublic%>] calldata _pubSignals) public view returns (bool) { assembly { ///////// // Computes the inverse using the extended euclidean algorithm @@ -185,114 +199,123 @@ contract PlonkVerifier { } } - function checkInput(pProof) { - if iszero(eq(mload(pProof), 800 )) { - mstore(0, 0) - return(0,0x20) - } - checkField(mload(add(pProof, pEval_a))) - checkField(mload(add(pProof, pEval_b))) - checkField(mload(add(pProof, pEval_c))) - checkField(mload(add(pProof, pEval_s1))) - checkField(mload(add(pProof, pEval_s2))) - checkField(mload(add(pProof, pEval_zw))) - - // Points are checked in the point operations precompiled smart contracts + function checkInput() { + checkField(calldataload(pEval_a)) + checkField(calldataload(pEval_b)) + checkField(calldataload(pEval_c)) + checkField(calldataload(pEval_s1)) + checkField(calldataload(pEval_s2)) + checkField(calldataload(pEval_zw)) } - function calculateChallanges(pProof, pMem, pPublic) { - - let a - let b - - // Challenges.beta - mstore( add(pMem, <%=pLastMem%> ), Qmx) - mstore( add(pMem, <%=pLastMem + 32%> ), Qmy) - mstore( add(pMem, <%=pLastMem + 64%> ), Qlx) - mstore( add(pMem, <%=pLastMem + 96%> ), Qly) - mstore( add(pMem, <%=pLastMem + 128%> ), Qrx) - mstore( add(pMem, <%=pLastMem + 160%> ), Qry) - mstore( add(pMem, <%=pLastMem + 192%> ), Qox) - mstore( add(pMem, <%=pLastMem + 224%> ), Qoy) - mstore( add(pMem, <%=pLastMem + 256%> ), Qcx) - mstore( add(pMem, <%=pLastMem + 288%> ), Qcy) - mstore( add(pMem, <%=pLastMem + 320%> ), S1x) - mstore( add(pMem, <%=pLastMem + 352%> ), S1x) - mstore( add(pMem, <%=pLastMem + 384%> ), S2x) - mstore( add(pMem, <%=pLastMem + 416%> ), S2x) - mstore( add(pMem, <%=pLastMem + 448%> ), S3x) - mstore( add(pMem, <%=pLastMem + 480%> ), S3x) + function calculateChallenges(pMem, pPublic) { + let beta + let aux + + let mIn := mload(0x40) // Pointer to the next free memory position + + // Compute challenge.beta & challenge.gamma + mstore(mIn, Qmx) + mstore(add(mIn, 32), Qmy) + mstore(add(mIn, 64), Qlx) + mstore(add(mIn, 96), Qly) + mstore(add(mIn, 128), Qrx) + mstore(add(mIn, 160), Qry) + mstore(add(mIn, 192), Qox) + mstore(add(mIn, 224), Qoy) + mstore(add(mIn, 256), Qcx) + mstore(add(mIn, 288), Qcy) + mstore(add(mIn, 320), S1x) + mstore(add(mIn, 352), S1y) + mstore(add(mIn, 384), S2x) + mstore(add(mIn, 416), S2y) + mstore(add(mIn, 448), S3x) + mstore(add(mIn, 480), S3y) <%for (let i=0; i - mstore( add(pMem, <%=pLastMem + 512 + i*32%> ), mload( add( pPublic, <%=i*32 + 32%>))) + mstore(add(mIn, <%= 512 + i*32 %>), calldataload(add(pPublic, <%=i*32%>))) <%}%> - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +0%> ), mload( add( pProof, pA))) - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +32%> ), mload( add( pProof, add(pA,32)))) - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +64%> ), mload( add( pProof, pB))) - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +96%> ), mload( add( pProof, add(pB, 32)))) - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +128%> ), mload( add( pProof, pC))) - mstore( add(pMem, <%=pLastMem + 512 + nPublic*32 +160%> ), mload( add( pProof, add(pC, 32)))) + mstore(add(mIn, <%= 512 + nPublic*32 + 0 %> ), calldataload(pA)) + mstore(add(mIn, <%= 512 + nPublic*32 + 32 %> ), calldataload(add(pA, 32))) + mstore(add(mIn, <%= 512 + nPublic*32 + 64 %> ), calldataload(pB)) + mstore(add(mIn, <%= 512 + nPublic*32 + 96 %> ), calldataload(add(pB, 32))) + mstore(add(mIn, <%= 512 + nPublic*32 + 128 %> ), calldataload(pC)) + mstore(add(mIn, <%= 512 + nPublic*32 + 160 %> ), calldataload(add(pC, 32))) - b := mod(keccak256(add(pMem, lastMem), <%= 704 + 32*nPublic %>), q) - mstore(add(pMem, pBeta), b) + beta := mod(keccak256(mIn, <%= 704 + 32 * nPublic %>), q) + mstore(add(pMem, pBeta), beta) - // Challenges.gamma + // challenges.gamma mstore(add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q)) - // Challenges.alpha - mstore(add(pMem, <%=pLastMem%>), mload(add(pMem, pBeta))) - mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pMem, pGamma))) - mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, pZ))) - mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, add(pZ, 32)))) - a := mod(keccak256(add(pMem, lastMem), 128), q) - mstore(add(pMem, pAlpha), a) - - mstore(add(pMem, <%=pLastMem%>), mload(add(pMem, pAlpha))) - mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pProof, pT1))) - mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, add(pT1, 32)))) - mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, pT2))) - mstore(add(pMem, <%=pLastMem + 128%>), mload(add(pProof, add(pT2, 32)))) - mstore(add(pMem, <%=pLastMem + 160%>), mload(add(pProof, pT3))) - mstore(add(pMem, <%=pLastMem + 192%>), mload(add(pProof, add(pT3, 32)))) - a := mod(keccak256(add(pMem, lastMem), 224), q) - mstore( add(pMem, pXi), a) - - mstore(add(pMem, <%=pLastMem%>), a) - mstore(add(pMem, <%=pLastMem + 32%>), mload(add(pProof, pEval_a))) - mstore(add(pMem, <%=pLastMem + 64%>), mload(add(pProof, pEval_b))) - mstore(add(pMem, <%=pLastMem + 96%>), mload(add(pProof, pEval_c))) - mstore(add(pMem, <%=pLastMem + 128%>), mload(add(pProof, pEval_s1))) - mstore(add(pMem, <%=pLastMem + 160%>), mload(add(pProof, pEval_s2))) - mstore(add(pMem, <%=pLastMem + 192%>), mload(add(pProof, pEval_zw))) - let v1 := mod(keccak256(add(pMem, lastMem), 224), q) + // challenges.alpha + mstore(mIn, mload(add(pMem, pBeta))) + mstore(add(mIn, 32), mload(add(pMem, pGamma))) + mstore(add(mIn, 64), calldataload(pZ)) + mstore(add(mIn, 96), calldataload(add(pZ, 32))) + + aux := mod(keccak256(mIn, 128), q) + mstore(add(pMem, pAlpha), aux) + mstore(add(pMem, pAlpha2), mulmod(aux, aux, q)) + + // challenges.xi + mstore(mIn, aux) + mstore(add(mIn, 32), calldataload(pT1)) + mstore(add(mIn, 64), calldataload(add(pT1, 32))) + mstore(add(mIn, 96), calldataload(pT2)) + mstore(add(mIn, 128), calldataload(add(pT2, 32))) + mstore(add(mIn, 160), calldataload(pT3)) + mstore(add(mIn, 192), calldataload(add(pT3, 32))) + + aux := mod(keccak256(mIn, 224), q) + mstore( add(pMem, pXi), aux) + + // challenges.v + mstore(mIn, aux) + mstore(add(mIn, 32), calldataload(pEval_a)) + mstore(add(mIn, 64), calldataload(pEval_b)) + mstore(add(mIn, 96), calldataload(pEval_c)) + mstore(add(mIn, 128), calldataload(pEval_s1)) + mstore(add(mIn, 160), calldataload(pEval_s2)) + mstore(add(mIn, 192), calldataload(pEval_zw)) + + let v1 := mod(keccak256(mIn, 224), q) mstore(add(pMem, pV1), v1) - // Compute betaxi - mstore( add(pMem, pBetaXi), mulmod(b, a, q)) + // challenges.beta * challenges.xi + mstore(add(pMem, pBetaXi), mulmod(beta, aux, q)) + + // challenges.xi^n <%for (let i=0; i - a:= mulmod(a, a, q) + aux:= mulmod(aux, aux, q) <%}%> - mstore( add(pMem, pXin), a) - a:= mod(add(sub(a, 1),q), q) - mstore( add(pMem, pZh), a) - mstore( add(pMem, pZhInv), a) // We will invert later together with lagrange pols + mstore(add(pMem, pXin), aux) + + // Zh + aux:= mod(add(sub(aux, 1), q), q) + mstore(add(pMem, pZh), aux) + mstore(add(pMem, pZhInv), aux) // We will invert later together with lagrange pols - a := mulmod(v1, v1, q) - mstore( add(pMem, pV2), a) - a := mulmod(a, v1, q) - mstore( add(pMem, pV3), a) - a := mulmod(a, v1, q) - mstore( add(pMem, pV4), a) - a := mulmod(a, v1, q) - mstore( add(pMem, pV5), a) - a := mulmod(a, v1, q) - mstore( add(pMem, pV6), a) - - mstore( add(pMem, pU), mod(keccak256(add(pProof, pWxi), 128), q)) + // challenges.v^2, challenges.v^3, challenges.v^4, challenges.v^5 + aux := mulmod(v1, v1, q) + mstore(add(pMem, pV2), aux) + aux := mulmod(aux, v1, q) + mstore(add(pMem, pV3), aux) + aux := mulmod(aux, v1, q) + mstore(add(pMem, pV4), aux) + aux := mulmod(aux, v1, q) + mstore(add(pMem, pV5), aux) + + // challenges.u + mstore(mIn, calldataload(pWxi)) + mstore(add(mIn, 32), calldataload(add(pWxi, 32))) + mstore(add(mIn, 64), calldataload(pWxiw)) + mstore(add(mIn, 96), calldataload(add(pWxiw, 32))) + + mstore(add(pMem, pU), mod(keccak256(mIn, 128), q)) } function calculateLagrange(pMem) { - let w := 1 <% for (let i=1; i<=Math.max(nPublic, 1); i++) { %> mstore( @@ -363,7 +386,7 @@ contract PlonkVerifier { pl, mulmod( mload(add(pMem, pEval_l<%=i+1%>)), - mload(add(pPub, <%=32+i*32%>)), + calldataload(add(pPub, <%=i*32%>)), q ) ), @@ -374,40 +397,36 @@ contract PlonkVerifier { <% } %> mstore(add(pMem, pPI), pl) - - } - function calculateR0(pProof, pMem) { - let alpha2 := mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q) + function calculateR0(pMem) { let e1 := mload(add(pMem, pPI)) - let e2 := mulmod(mload(add(pMem, pEval_l1)), alpha2, q) + let e2 := mulmod(mload(add(pMem, pEval_l1)), mload(add(pMem, pAlpha2)), q) let e3a := addmod( - mload(add(pProof, pEval_a)), - mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), + calldataload(pEval_a), + mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s1), q), q) e3a := addmod(e3a, mload(add(pMem, pGamma)), q) let e3b := addmod( - mload(add(pProof, pEval_b)), - mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), + calldataload(pEval_b), + mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s2), q), q) e3b := addmod(e3b, mload(add(pMem, pGamma)), q) let e3c := addmod( - mload(add(pProof, pEval_c)), + calldataload(pEval_c), mload(add(pMem, pGamma)), q) let e3 := mulmod(mulmod(e3a, e3b, q), e3c, q) - - e3 := mulmod(e3, mload(add(pProof, pEval_zw)), q) + e3 := mulmod(e3, calldataload(pEval_zw), q) e3 := mulmod(e3, mload(add(pMem, pAlpha)), q) - let r0 := mod(sub(e1, e2), q) - r0 := mod(sub(r0, e3), q) + let r0 := addmod(e1, mod(sub(q, e2), q), q) + r0 := addmod(r0, mod(sub(q, e3), q), q) mstore(add(pMem, pEval_r0) , r0) } @@ -415,6 +434,16 @@ contract PlonkVerifier { function g1_set(pR, pP) { mstore(pR, mload(pP)) mstore(add(pR, 32), mload(add(pP,32))) + } + + function g1_setC(pR, x, y) { + mstore(pR, x) + mstore(add(pR, 32), y) + } + + function g1_calldataSet(pR, pP) { + mstore(pR, calldataload(pP)) + mstore(add(pR, 32), calldataload(add(pP, 32))) } function g1_acc(pR, pP) { @@ -498,36 +527,38 @@ contract PlonkVerifier { } } - function calculateD(pProof, pMem) { - let p:= add(pMem, pD) + function g1_mulSet(pR, pP, s) { + g1_mulSetC(pR, mload(pP), mload(add(pP, 32)), s) + } + + function calculateD(pMem) { + let _pD:= add(pMem, pD) + let gamma := mload(add(pMem, pGamma)) let mIn := mload(0x40) + mstore(0x40, add(mIn, 256)) // d1, d2, d3 & d4 (4*64 bytes) - g1_mulSetC(p, Qmx, Qmy, mulmod(mload(add(pProof, pEval_a)), mload(add(pProof, pEval_b)), q)) - g1_mulAccC(p, Qlx, Qly, mload(add(pProof, pEval_a))) - g1_mulAccC(p, Qrx, Qry, mload(add(pProof, pEval_b))) - g1_mulAccC(p, Qox, Qoy, mload(add(pProof, pEval_c))) - g1_mulAccC(p, Qcx, Qcy, 1) + g1_setC(_pD, Qcx, Qcy) + g1_mulAccC(_pD, Qmx, Qmy, mulmod(calldataload(pEval_a), calldataload(pEval_b), q)) + g1_mulAccC(_pD, Qlx, Qly, calldataload(pEval_a)) + g1_mulAccC(_pD, Qrx, Qry, calldataload(pEval_b)) + g1_mulAccC(_pD, Qox, Qoy, calldataload(pEval_c)) + let betaxi := mload(add(pMem, pBetaXi)) let val1 := addmod( - addmod(mload(add(pProof, pEval_a)), mload(add(pMem, pBetaXi)), q), - mload(add(pMem, pGamma)), - q) + addmod(calldataload(pEval_a), betaxi, q), + gamma, q) let val2 := addmod( addmod( - mload(add(pProof, pEval_b)), - mulmod(mload(add(pMem, pBetaXi)), k1, q), - q), - mload(add(pMem, pGamma)), - q) + calldataload(pEval_b), + mulmod(betaxi, k1, q), + q), gamma, q) let val3 := addmod( addmod( - mload(add(pProof, pEval_c)), - mulmod(mload(add(pMem, pBetaXi)), k2, q), - q), - mload(add(pMem, pGamma)), - q) + calldataload(pEval_c), + mulmod(betaxi, k2, q), + q), gamma, q) let d2a := mulmod( mulmod(mulmod(val1, val2, q), val3, q), @@ -537,89 +568,96 @@ contract PlonkVerifier { let d2b := mulmod( mload(add(pMem, pEval_l1)), - mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q), + mload(add(pMem, pAlpha2)), q ) - // We'll use pF to save d2 - g1_mulAcc( - add(pMem, pF), - add(pProof, pZ), + // We'll use mIn to save d2 + g1_calldataSet(add(mIn, 192), pZ) + g1_mulSet( + mIn, + add(mIn, 192), addmod(addmod(d2a, d2b, q), mload(add(pMem, pU)), q)) - + + val1 := addmod( addmod( - mload(add(pProof, pEval_a)), - mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s1)), q), - q), - mload(add(pMem, pGamma)), - q) + calldataload(pEval_a), + mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s1), q), + q), gamma, q) val2 := addmod( addmod( - mload(add(pProof, pEval_b)), - mulmod(mload(add(pMem, pBeta)), mload(add(pProof, pEval_s2)), q), - q), - mload(add(pMem, pGamma)), - q) + calldataload(pEval_b), + mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s2), q), + q), gamma, q) val3 := mulmod( mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pBeta)), q), - mload(add(pProof, pEval_zw)), q) + calldataload(pEval_zw), q) - // We'll use pE to save d3 - g1_mulAccC( - add(pMem, pE), + // We'll use mIn + 64 to save d3 + g1_mulSetC( + add(mIn, 64), S3x, S3y, mulmod(mulmod(val1, val2, q), val3, q)) + // We'll use mIn + 128 to save d4 + g1_calldataSet(add(mIn, 128), pT1) - // We'll use pTmp to save d4 - g1_set(add(pMem, pTmp), add(pProof, pT1)) - g1_mulAcc(add(pMem, pTmp), add(pProof, pT2), add(pMem, pXin)) - let xin2 := mulmod(add(pMem, pXin), add(pMem, pXin), q) - g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) - g1_mulAcc(add(pMem, pTmp), add(pProof, pT3), xin2) + g1_mulAccC(add(mIn, 128), calldataload(pT2), calldataload(add(pT2, 32)), mload(add(pMem, pXin))) + let xin2 := mulmod(mload(add(pMem, pXin)), mload(add(pMem, pXin)), q) + g1_mulAccC(add(mIn, 128), calldataload(pT3), calldataload(add(pT3, 32)) , xin2) - g1_mulAcc(mIn, add(pMem, pTmp), add(pMem, pZh)) + g1_mulSetC(add(mIn, 128), mload(add(mIn, 128)), mload(add(mIn, 160)), mload(add(pMem, pZh))) - mstore(add(add(pMem, pE), 32), mod(sub(qf, mload(add(add(pMem, pE), 32))), qf)) - mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) - g1_acc(add(pMem, pD), add(pMem, pF)) - g1_acc(add(pMem, pD), add(pMem, pE)) - g1_acc(add(pMem, pD), add(pMem, mIn)) + mstore(add(add(mIn, 64), 32), mod(sub(qf, mload(add(add(mIn, 64), 32))), qf)) + mstore(add(mIn, 160), mod(sub(qf, mload(add(mIn, 160))), qf)) + g1_acc(_pD, mIn) + g1_acc(_pD, add(mIn, 64)) + g1_acc(_pD, add(mIn, 128)) } - function calculateF(pProof, pMem) { + function calculateF(pMem) { let p := add(pMem, pF) g1_set(p, add(pMem, pD)) - g1_mulAcc(p, add(pProof, pA), mload(add(pMem, pV1))) - g1_mulAcc(p, add(pProof, pB), mload(add(pMem, pV2))) - g1_mulAcc(p, add(pProof, pC), mload(add(pMem, pV3))) + g1_mulAccC(p, calldataload(pA), calldataload(add(pA, 32)), mload(add(pMem, pV1))) + g1_mulAccC(p, calldataload(pB), calldataload(add(pB, 32)), mload(add(pMem, pV2))) + g1_mulAccC(p, calldataload(pC), calldataload(add(pC, 32)), mload(add(pMem, pV3))) g1_mulAccC(p, S1x, S1y, mload(add(pMem, pV4))) - g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV5))) + g1_mulAccC(p, S2x, S2y, mload(add(pMem, pV5))) } - function calculateE(pProof, pMem) { + function calculateE(pMem) { let s := mod(sub(q, mload(add(pMem, pEval_r0))), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_a)), mload(add(pMem, pV1)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_b)), mload(add(pMem, pV2)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_c)), mload(add(pMem, pV3)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s1)), mload(add(pMem, pV4)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_s2)), mload(add(pMem, pV5)), q), q) - s := addmod(s, mulmod(mload(add(pProof, pEval_zw)), mload(add(pMem, pU)), q), q) - g1_mulAccC(add(pMem, pE), G1x, G1y, s) + + s := addmod(s, mulmod(calldataload(pEval_a), mload(add(pMem, pV1)), q), q) + s := addmod(s, mulmod(calldataload(pEval_b), mload(add(pMem, pV2)), q), q) + s := addmod(s, mulmod(calldataload(pEval_c), mload(add(pMem, pV3)), q), q) + s := addmod(s, mulmod(calldataload(pEval_s1), mload(add(pMem, pV4)), q), q) + s := addmod(s, mulmod(calldataload(pEval_s2), mload(add(pMem, pV5)), q), q) + s := addmod(s, mulmod(calldataload(pEval_zw), mload(add(pMem, pU)), q), q) + + g1_mulSetC(add(pMem, pE), G1x, G1y, s) } - function checkPairing(pProof, pMem) -> isOk { + function checkPairing(pMem) -> isOk { let mIn := mload(0x40) - + mstore(0x40, add(mIn, 576)) // [0..383] = pairing data, [384..447] = pWxi, [448..512] = pWxiw + + let _pWxi := add(mIn, 384) + let _pWxiw := add(mIn, 448) + let _aux := add(mIn, 512) + + g1_calldataSet(_pWxi, pWxi) + g1_calldataSet(_pWxiw, pWxiw) + // A1 - g1_mulAcc(mIn, add(pProof, pWxiw), add(pMem, pU)) - g1_acc(mIn, add(pProof, pWxi)) + g1_mulSet(mIn, _pWxiw, mload(add(pMem, pU))) + g1_acc(mIn, _pWxi) mstore(add(mIn, 32), mod(sub(qf, mload(add(mIn, 32))), qf)) // [X]_2 @@ -629,12 +667,14 @@ contract PlonkVerifier { mstore(add(mIn,160), X2y1) // B1 - g1_mulAcc(add(mIn, 192), add(pMem, pWxi), mload(add(pMem, pXi))) - let s := mulmod(mload(mload(add(pMem, pU))), mload(mload(add(pMem, pXi))), q) + g1_mulSet(add(mIn, 192), _pWxi, mload(add(pMem, pXi))) + + let s := mulmod(mload(add(pMem, pU)), mload(add(pMem, pXi)), q) s := mulmod(s, w1, q) - g1_mulAcc(add(mIn, 256), add(pProof, pWxiw), s) - g1_acc(add(mIn, 192), add(mIn, 256)) + g1_mulSet(_aux, _pWxiw, s) + g1_acc(add(mIn, 192), _aux) g1_acc(add(mIn, 192), add(pMem, pF)) + mstore(add(pMem, add(pE, 32)), mod(sub(qf, mload(add(pMem, add(pE, 32)))), qf)) g1_acc(add(mIn, 192), add(pMem, pE)) // [1]_2 @@ -645,45 +685,26 @@ contract PlonkVerifier { let success := staticcall(sub(gas(), 2000), 8, mIn, 384, mIn, 0x20) - isOk := and(success, mload(mIn)) + isOk := and(success, mload(mIn)) } let pMem := mload(0x40) mstore(0x40, add(pMem, lastMem)) - checkInput(proof) - calculateChallanges(proof, pMem, pubSignals) + checkInput() + calculateChallenges(pMem, _pubSignals) calculateLagrange(pMem) - calculatePI(pMem, pubSignals) - calculateR0(proof, pMem) - calculateD(proof, pMem) - calculateF(proof, pMem) - calculateE(proof, pMem) - let isValid := checkPairing(proof, pMem) + calculatePI(pMem, _pubSignals) + calculateR0(pMem) + calculateD(pMem) + calculateF(pMem) + calculateE(pMem) + let isValid := checkPairing(pMem) - sstore(0, mload(add(pMem, pGamma))) - } - - bytes32 value = debug(); - console.logBytes32(value); - - assembly { - mstore(0, true) - return(0,0x20) - } - } - - function debug() public view returns (bytes32 result) { - assembly { - result := sload(0) - } - } -} - - /*mstore(0x40, sub(pMem, lastMem)) + mstore(0x40, sub(pMem, lastMem)) mstore(0, isValid) return(0,0x20) } } -}/* +} From 46dfbd38be895e4005309d70b09cb9e421434373 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Wed, 17 May 2023 11:28:19 +0200 Subject: [PATCH 31/48] Added cricuits tests with +1 inputs --- test/circuit2/circuit.circom | 17 + test/circuit2/circuit.r1cs | Bin 0 -> 164180 bytes test/circuit2/circuit.zkey | Bin 0 -> 4160728 bytes test/circuit2/circuit_js/circuit.wasm | Bin 0 -> 38826 bytes test/circuit2/circuit_js/generate_witness.cjs | 20 ++ .../circuit_js/witness_calculator.cjs | 337 ++++++++++++++++++ test/circuit2/input.json | 5 + test/circuit2/witness.wtns | Bin 0 -> 32204 bytes 8 files changed, 379 insertions(+) create mode 100644 test/circuit2/circuit.circom create mode 100644 test/circuit2/circuit.r1cs create mode 100644 test/circuit2/circuit.zkey create mode 100644 test/circuit2/circuit_js/circuit.wasm create mode 100644 test/circuit2/circuit_js/generate_witness.cjs create mode 100644 test/circuit2/circuit_js/witness_calculator.cjs create mode 100644 test/circuit2/input.json create mode 100644 test/circuit2/witness.wtns diff --git a/test/circuit2/circuit.circom b/test/circuit2/circuit.circom new file mode 100644 index 00000000..98763ffe --- /dev/null +++ b/test/circuit2/circuit.circom @@ -0,0 +1,17 @@ +template Multiplier(n) { + signal input a; + signal input b; + signal input c; + signal output d; + + signal int[n]; + + int[0] <== a * a + b * 2 + c + 3; + for (var i = 1; i < n; i++) { + int[i] <== int[i-1] * int[i-1] + b + 4; + } + + d <== int[n-1]; +} + +component main {public [a, b, c]} = Multiplier(1000); diff --git a/test/circuit2/circuit.r1cs b/test/circuit2/circuit.r1cs new file mode 100644 index 0000000000000000000000000000000000000000..d8fca25b9da83ab4f53c22d3e7b50761bfaab417 GIT binary patch literal 164180 zcmb{1bC8^Q!}alOY}>YN+qP}n6Yj>gZQHi(WMV9`$Qn<2_vEejuRG^dov!LR)6?Ji zU7zVn)gAlB1DJ~p+4S2e!P!r5%?G)MBr=xeHP;V^bf(Mrgq;up#1Ax>6_FK z3ffhs`ko9+as>CR+B*BEF0lXW7C8UYHU3u@`s0(IJ1fk82YlA0bf3Fs;I#<&Ki7pN zZA$mKYqGX*q)q8uw(z7)>0Gu5q)q8uwuq!n>0Gu*q)q8uw#cMS>0Gubq)q8uwy2~{ z>0GvGq)q8uw&0GuLq)q8uwwR<%>0Gv0q)q8uw%DXi>0Gurq)q8uwz#BC>0GvW zq)q8uw)mt?>0Gu1q)q8uwuGcj>0Gu%q)q8uw#1}O>0GuXq)q8uwxpy@>0GvCq)q8u 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smart_contract_tests/package-lock.json | 22 ++--- smart_contract_tests/package.json | 2 +- 4 files changed, 105 insertions(+), 29 deletions(-) diff --git a/package-lock.json b/package-lock.json index e53a88b3..8d7a8924 100644 --- a/package-lock.json +++ b/package-lock.json @@ -15,7 +15,7 @@ "circom_runtime": "0.1.22", "ejs": "^3.1.6", "fastfile": "0.0.20", - "ffjavascript": "0.2.57", + "ffjavascript": "0.2.59", "js-sha3": "^0.8.0", "logplease": "^1.2.15", "r1csfile": "0.0.45" @@ -736,6 +736,24 @@ "calcwit": "calcwit.js" } }, + "node_modules/circom_runtime/node_modules/ffjavascript": { + "version": "0.2.57", + "resolved": "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.57.tgz", + "integrity": "sha512-V+vxZ/zPNcthrWmqfe/1YGgqdkTamJeXiED0tsk7B84g40DKlrTdx47IqZuiygqAVG6zMw4qYuvXftIJWsmfKQ==", + "dependencies": { + "wasmbuilder": "0.0.16", + "wasmcurves": "0.2.0", + "web-worker": "^1.2.0" + } + }, + "node_modules/circom_runtime/node_modules/wasmcurves": { + "version": "0.2.0", + "resolved": "https://registry.npmjs.org/wasmcurves/-/wasmcurves-0.2.0.tgz", + "integrity": "sha512-3e2rbxdujOwaod657gxgmdhZNn+i1qKdHO3Y/bK+8E7bV8ttV/fu5FO4/WLBACF375cK0QDLOP+65Na63qYuWA==", + "dependencies": { + "wasmbuilder": "0.0.16" + } + }, "node_modules/cliui": { "version": "7.0.4", "resolved": "https://registry.npmjs.org/cliui/-/cliui-7.0.4.tgz", @@ -1092,12 +1110,12 @@ } }, "node_modules/ffjavascript": { - "version": "0.2.57", - "resolved": "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.57.tgz", - "integrity": "sha512-V+vxZ/zPNcthrWmqfe/1YGgqdkTamJeXiED0tsk7B84g40DKlrTdx47IqZuiygqAVG6zMw4qYuvXftIJWsmfKQ==", + "version": "0.2.59", + "resolved": "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.59.tgz", + "integrity": "sha512-QssOEUv+wilz9Sg7Zaj6KWAm7QceOAEsFuEBTltUsDo1cjn11rA/LGYvzFBPbzNfxRlZxwgJ7uxpCQcdDlrNfw==", "dependencies": { "wasmbuilder": "0.0.16", - "wasmcurves": "0.2.0", + "wasmcurves": "0.2.1", "web-worker": "^1.2.0" } }, @@ -2015,6 +2033,24 @@ "ffjavascript": "0.2.57" } }, + "node_modules/r1csfile/node_modules/ffjavascript": { + "version": "0.2.57", + "resolved": "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.57.tgz", + "integrity": "sha512-V+vxZ/zPNcthrWmqfe/1YGgqdkTamJeXiED0tsk7B84g40DKlrTdx47IqZuiygqAVG6zMw4qYuvXftIJWsmfKQ==", + "dependencies": { + "wasmbuilder": "0.0.16", + "wasmcurves": "0.2.0", + "web-worker": "^1.2.0" + } + }, + "node_modules/r1csfile/node_modules/wasmcurves": { + "version": "0.2.0", + "resolved": "https://registry.npmjs.org/wasmcurves/-/wasmcurves-0.2.0.tgz", + "integrity": "sha512-3e2rbxdujOwaod657gxgmdhZNn+i1qKdHO3Y/bK+8E7bV8ttV/fu5FO4/WLBACF375cK0QDLOP+65Na63qYuWA==", + "dependencies": { + "wasmbuilder": "0.0.16" + } + }, "node_modules/randombytes": { "version": "2.1.0", "resolved": "https://registry.npmjs.org/randombytes/-/randombytes-2.1.0.tgz", @@ -2452,9 +2488,9 @@ "integrity": "sha512-Qx3lEFqaVvp1cEYW7Bfi+ebRJrOiwz2Ieu7ZG2l7YyeSJIok/reEQCQCuicj/Y32ITIJuGIM9xZQppGx5LrQdA==" }, "node_modules/wasmcurves": { - "version": "0.2.0", - "resolved": "https://registry.npmjs.org/wasmcurves/-/wasmcurves-0.2.0.tgz", - "integrity": "sha512-3e2rbxdujOwaod657gxgmdhZNn+i1qKdHO3Y/bK+8E7bV8ttV/fu5FO4/WLBACF375cK0QDLOP+65Na63qYuWA==", + "version": "0.2.1", + "resolved": "https://registry.npmjs.org/wasmcurves/-/wasmcurves-0.2.1.tgz", + "integrity": "sha512-9ciO7bUE5bgpbOcdK7IO3enrSVIKHwrQmPibok4GLJWaCA7Wyqc9PRYnu5HbiFv9NDFNqVKPtU5R6Is5KujBLg==", "dependencies": { "wasmbuilder": "0.0.16" } @@ -3113,6 +3149,26 @@ "integrity": "sha512-V/XYZWBhbZY8SotkaGH4FbiDYAZ8a1Md++MBiKPDOuWS/NIJB+Q+XIiTC8zKMgoDaa9cd2OiTvsC9J6te7twNg==", "requires": { "ffjavascript": "0.2.57" + }, + "dependencies": { + "ffjavascript": { + "version": "0.2.57", + "resolved": "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.57.tgz", + "integrity": "sha512-V+vxZ/zPNcthrWmqfe/1YGgqdkTamJeXiED0tsk7B84g40DKlrTdx47IqZuiygqAVG6zMw4qYuvXftIJWsmfKQ==", + "requires": { + "wasmbuilder": "0.0.16", + "wasmcurves": "0.2.0", + "web-worker": "^1.2.0" + } + }, + "wasmcurves": { + "version": "0.2.0", + "resolved": "https://registry.npmjs.org/wasmcurves/-/wasmcurves-0.2.0.tgz", + "integrity": "sha512-3e2rbxdujOwaod657gxgmdhZNn+i1qKdHO3Y/bK+8E7bV8ttV/fu5FO4/WLBACF375cK0QDLOP+65Na63qYuWA==", + "requires": { + "wasmbuilder": "0.0.16" + } + } } }, "cliui": { @@ -3385,12 +3441,12 @@ } }, "ffjavascript": { - "version": "0.2.57", - "resolved": "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.57.tgz", - "integrity": "sha512-V+vxZ/zPNcthrWmqfe/1YGgqdkTamJeXiED0tsk7B84g40DKlrTdx47IqZuiygqAVG6zMw4qYuvXftIJWsmfKQ==", + "version": "0.2.59", + "resolved": "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.59.tgz", + "integrity": "sha512-QssOEUv+wilz9Sg7Zaj6KWAm7QceOAEsFuEBTltUsDo1cjn11rA/LGYvzFBPbzNfxRlZxwgJ7uxpCQcdDlrNfw==", "requires": { "wasmbuilder": "0.0.16", - "wasmcurves": "0.2.0", + "wasmcurves": "0.2.1", "web-worker": "^1.2.0" } }, @@ -4065,6 +4121,26 @@ "@iden3/binfileutils": "0.0.11", "fastfile": "0.0.20", "ffjavascript": "0.2.57" + }, + "dependencies": { + "ffjavascript": { + "version": "0.2.57", + "resolved": "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.57.tgz", + "integrity": "sha512-V+vxZ/zPNcthrWmqfe/1YGgqdkTamJeXiED0tsk7B84g40DKlrTdx47IqZuiygqAVG6zMw4qYuvXftIJWsmfKQ==", + "requires": { + "wasmbuilder": "0.0.16", + "wasmcurves": "0.2.0", + "web-worker": "^1.2.0" + } + }, + "wasmcurves": { + "version": "0.2.0", + "resolved": "https://registry.npmjs.org/wasmcurves/-/wasmcurves-0.2.0.tgz", + "integrity": "sha512-3e2rbxdujOwaod657gxgmdhZNn+i1qKdHO3Y/bK+8E7bV8ttV/fu5FO4/WLBACF375cK0QDLOP+65Na63qYuWA==", + "requires": { + "wasmbuilder": "0.0.16" + } + } } }, "randombytes": { @@ -4372,9 +4448,9 @@ "integrity": "sha512-Qx3lEFqaVvp1cEYW7Bfi+ebRJrOiwz2Ieu7ZG2l7YyeSJIok/reEQCQCuicj/Y32ITIJuGIM9xZQppGx5LrQdA==" }, "wasmcurves": { - "version": "0.2.0", - "resolved": "https://registry.npmjs.org/wasmcurves/-/wasmcurves-0.2.0.tgz", - "integrity": "sha512-3e2rbxdujOwaod657gxgmdhZNn+i1qKdHO3Y/bK+8E7bV8ttV/fu5FO4/WLBACF375cK0QDLOP+65Na63qYuWA==", + "version": "0.2.1", + "resolved": "https://registry.npmjs.org/wasmcurves/-/wasmcurves-0.2.1.tgz", + "integrity": "sha512-9ciO7bUE5bgpbOcdK7IO3enrSVIKHwrQmPibok4GLJWaCA7Wyqc9PRYnu5HbiFv9NDFNqVKPtU5R6Is5KujBLg==", "requires": { "wasmbuilder": "0.0.16" } @@ -4468,4 +4544,4 @@ "dev": true } } -} \ No newline at end of file +} diff --git a/package.json b/package.json index 1cde4e05..3d1ef78e 100644 --- a/package.json +++ b/package.json @@ -45,7 +45,7 @@ "circom_runtime": "0.1.22", "ejs": "^3.1.6", "fastfile": "0.0.20", - "ffjavascript": "0.2.57", + "ffjavascript": "0.2.59", "js-sha3": "^0.8.0", "logplease": "^1.2.15", "r1csfile": "0.0.45" diff --git a/smart_contract_tests/package-lock.json b/smart_contract_tests/package-lock.json index 3f17c9e8..46a83e14 100644 --- a/smart_contract_tests/package-lock.json +++ b/smart_contract_tests/package-lock.json @@ -11,14 +11,14 @@ "chai": "^4.3.7", "ethereum-waffle": "^4.0.10", "ethers": "^5.7.2", - "ffjavascript": "0.2.57", + "ffjavascript": "0.2.59", "hardhat": "^2.14.0", "mocha": "^10.2.0", "snarkjs": "file:.." } }, "..": { - "version": "0.6.10", + "version": "0.6.11", "dev": true, "license": "GPL-3.0", "dependencies": { @@ -28,7 +28,7 @@ "circom_runtime": "0.1.22", "ejs": "^3.1.6", "fastfile": "0.0.20", - "ffjavascript": "0.2.57", + "ffjavascript": "0.2.59", "js-sha3": "^0.8.0", "logplease": "^1.2.15", "r1csfile": "0.0.45" @@ -3608,13 +3608,13 @@ "dev": true }, "node_modules/ffjavascript": { - "version": "0.2.57", - "resolved": "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.57.tgz", - "integrity": "sha512-V+vxZ/zPNcthrWmqfe/1YGgqdkTamJeXiED0tsk7B84g40DKlrTdx47IqZuiygqAVG6zMw4qYuvXftIJWsmfKQ==", + "version": "0.2.59", + "resolved": "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.59.tgz", + "integrity": "sha512-QssOEUv+wilz9Sg7Zaj6KWAm7QceOAEsFuEBTltUsDo1cjn11rA/LGYvzFBPbzNfxRlZxwgJ7uxpCQcdDlrNfw==", "dev": true, "dependencies": { "wasmbuilder": "0.0.16", - "wasmcurves": "0.2.0", + "wasmcurves": "0.2.1", "web-worker": "^1.2.0" } }, @@ -7376,9 +7376,9 @@ "dev": true }, "node_modules/wasmcurves": { - "version": "0.2.0", - "resolved": "https://registry.npmjs.org/wasmcurves/-/wasmcurves-0.2.0.tgz", - "integrity": "sha512-3e2rbxdujOwaod657gxgmdhZNn+i1qKdHO3Y/bK+8E7bV8ttV/fu5FO4/WLBACF375cK0QDLOP+65Na63qYuWA==", + "version": "0.2.1", + "resolved": "https://registry.npmjs.org/wasmcurves/-/wasmcurves-0.2.1.tgz", + "integrity": "sha512-9ciO7bUE5bgpbOcdK7IO3enrSVIKHwrQmPibok4GLJWaCA7Wyqc9PRYnu5HbiFv9NDFNqVKPtU5R6Is5KujBLg==", "dev": true, "dependencies": { "wasmbuilder": "0.0.16" @@ -7629,4 +7629,4 @@ } } } -} \ No newline at end of file +} diff --git a/smart_contract_tests/package.json b/smart_contract_tests/package.json index 80ef8e98..0c734c06 100644 --- a/smart_contract_tests/package.json +++ b/smart_contract_tests/package.json @@ -11,7 +11,7 @@ "chai": "^4.3.7", "ethereum-waffle": "^4.0.10", "ethers": "^5.7.2", - "ffjavascript": "0.2.57", + "ffjavascript": "0.2.59", "hardhat": "^2.14.0", "mocha": "^10.2.0", "snarkjs": "file:.." From bdcfff733cdc42fe0648249f6c7bc74d1e158db0 Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Sat, 6 May 2023 07:04:53 +0200 Subject: [PATCH 34/48] Add check functions in js and sc --- src/fflonk_verify.js | 49 ++++++++++++++++++++++++++++-- src/groth16_verify.js | 28 +++++++++++++++++ src/plonk_verify.js | 42 +++++++++++++++++++++++-- templates/verifier_groth16.sol.ejs | 47 ++++++++++++++++++++++++++++ templates/verifier_plonk.sol.ejs | 37 ++++++++++++++++++++-- 5 files changed, 196 insertions(+), 7 deletions(-) diff --git a/src/fflonk_verify.js b/src/fflonk_verify.js index 9c9ec58d..23d1250c 100644 --- a/src/fflonk_verify.js +++ b/src/fflonk_verify.js @@ -61,15 +61,23 @@ export default async function fflonkVerify(_vk_verifier, _publicSignals, _proof, // STEP 1 - Validate that all polynomial commitments ∈ G_1 if (logger) logger.info("> Checking commitments belong to G1"); if (!commitmentsBelongToG1(curve, proof, vk)) { - logger.error("Proof is not well constructed"); + if (logger) logger.error("Proof commitments are not valid"); return false; } - // TODO // STEP 2 - Validate that all evaluations ∈ F + if (logger) logger.info("> Checking evaluations belong to F"); + if (!evaluationsAreValid(curve, proof)) { + if (logger) logger.error("Proof evaluations are not valid."); + return false; + } - // TODO // STEP 3 - Validate that w_i ∈ F for i ∈ [l] + if (logger) logger.info("> Checking public inputs belong to F"); + if (!publicInputsAreValid(curve, publicSignals)) { + if (logger) logger.error("Public inputs are not valid."); + return false; + } // STEP 4 - Compute the challenges: beta, gamma, xi, alpha and y ∈ F // as in prover description, from the common preprocessed inputs, public inputs and elements of π_SNARK @@ -151,6 +159,41 @@ function commitmentsBelongToG1(curve, proof, vk) { && G1.isValid(vk.C0); } +function checkValueBelongToField(curve, value) { + return Scalar.lt(value, curve.r); +} + +function checkEvaluationIsValid(curve, evaluation) { + return checkValueBelongToField(curve, Scalar.fromRprLE(evaluation)); +} + +function evaluationsAreValid(curve, proof) { + return checkEvaluationIsValid(curve, proof.evaluations.ql) + && checkEvaluationIsValid(curve, proof.evaluations.qr) + && checkEvaluationIsValid(curve, proof.evaluations.qm) + && checkEvaluationIsValid(curve, proof.evaluations.qo) + && checkEvaluationIsValid(curve, proof.evaluations.qc) + && checkEvaluationIsValid(curve, proof.evaluations.s1) + && checkEvaluationIsValid(curve, proof.evaluations.s2) + && checkEvaluationIsValid(curve, proof.evaluations.s3) + && checkEvaluationIsValid(curve, proof.evaluations.a) + && checkEvaluationIsValid(curve, proof.evaluations.b) + && checkEvaluationIsValid(curve, proof.evaluations.c) + && checkEvaluationIsValid(curve, proof.evaluations.z) + && checkEvaluationIsValid(curve, proof.evaluations.zw) + && checkEvaluationIsValid(curve, proof.evaluations.t1w) + && checkEvaluationIsValid(curve, proof.evaluations.t2w); +} + +function publicInputsAreValid(curve, publicInputs) { + for(let i = 0; i < publicInputs.length; i++) { + if(!checkValueBelongToField(curve, publicInputs[i])) { + return false; + } + } + return true; +} + function computeChallenges(curve, proof, vk, publicSignals, logger) { const Fr = curve.Fr; diff --git a/src/groth16_verify.js b/src/groth16_verify.js index f4936fa7..d2101a45 100644 --- a/src/groth16_verify.js +++ b/src/groth16_verify.js @@ -41,6 +41,11 @@ export default async function groth16Verify(_vk_verifier, _publicSignals, _proof const IC = new Uint8Array(curve.G1.F.n8*2 * publicSignals.length); const w = new Uint8Array(curve.Fr.n8 * publicSignals.length); + if (!publicInputsAreValid(curve, publicSignals)) { + if (logger) logger.error("Public inputs are not valid."); + return false; + } + for (let i=0; i, @@ -238,9 +268,26 @@ contract Verifier { proof.B = Pairing.G2Point([b[0][0], b[0][1]], [b[1][0], b[1][1]]); proof.C = Pairing.G1Point(c[0], c[1]); uint[] memory inputValues = new uint[](input.length); + + // Check public inputs belong to field for(uint i = 0; i < input.length; i++){ inputValues[i] = input[i]; + checkField(inputValues[i]); } + + // Check G1 points coordinates belong to field + checkField(a[0]); + checkField(a[1]); + checkField(b[0][0]); + checkField(b[0][1]); + checkField(b[1][0]); + checkField(b[1][1]); + checkField(c[0]); + checkField(c[1]); + + checkPointBelongsToBN128Curve(proof.A); + checkPointBelongsToBN128Curve(proof.C); + if (verify(inputValues, proof) == 0) { return true; } else { diff --git a/templates/verifier_plonk.sol.ejs b/templates/verifier_plonk.sol.ejs index c6d8452e..af188d05 100644 --- a/templates/verifier_plonk.sol.ejs +++ b/templates/verifier_plonk.sol.ejs @@ -182,11 +182,46 @@ contract PlonkVerifier { } } + function checkPointBelongsToBN128Curve(p) { + let x := mload(p) + let y := mload(add(p, 32)) + + // Check that the point is on the curve + // y^2 = x^3 + 3 + let x3_3 := addmod(mulmod(x, mulmod(x, x, qf), qf), 3, qf) + let y2 := mulmod(y, y, qf) + + if iszero(eq(x3_3, y2)) { + mstore(0, 0) + return(0, 0x20) + } + } + function checkInput(pProof) { if iszero(eq(mload(pProof), 800 )) { mstore(0, 0) return(0,0x20) } + + checkField(mload(add(pProof, pA))) + checkField(mload(add(pProof, add(pA, 32)))) + checkField(mload(add(pProof, pB))) + checkField(mload(add(pProof, add(pB, 32)))) + checkField(mload(add(pProof, pC))) + checkField(mload(add(pProof, add(pC, 32)))) + checkField(mload(add(pProof, pZ))) + checkField(mload(add(pProof, add(pZ, 32)))) + checkField(mload(add(pProof, pT1))) + checkField(mload(add(pProof, add(pT1, 32)))) + checkField(mload(add(pProof, pT2))) + checkField(mload(add(pProof, add(pT2, 32)))) + checkField(mload(add(pProof, pT3))) + checkField(mload(add(pProof, add(pT3, 32)))) + checkField(mload(add(pProof, pWxi))) + checkField(mload(add(pProof, add(pWxi, 32)))) + checkField(mload(add(pProof, pWxiw))) + checkField(mload(add(pProof, add(pWxiw, 32)))) + checkField(mload(add(pProof, pEval_a))) checkField(mload(add(pProof, pEval_b))) checkField(mload(add(pProof, pEval_c))) @@ -194,8 +229,6 @@ contract PlonkVerifier { checkField(mload(add(pProof, pEval_s2))) checkField(mload(add(pProof, pEval_zw))) checkField(mload(add(pProof, pEval_r))) - - // Points are checked in the point operations precompiled smart contracts } function calculateChallanges(pProof, pMem, pPublic) { From fe202484c0c2d89e0532945bcc88b7381cc150f7 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Thu, 11 May 2023 09:11:04 +0200 Subject: [PATCH 35/48] refactor groth16 smart contract to assembly code --- .vscode/launch.json | 91 ++++++ templates/verifier_groth16.sol.ejs | 452 +++++++++++------------------ 2 files changed, 255 insertions(+), 288 deletions(-) diff --git a/.vscode/launch.json b/.vscode/launch.json index dd59ba47..1074b58f 100644 --- a/.vscode/launch.json +++ b/.vscode/launch.json @@ -12,6 +12,97 @@ "/**" ], "type": "node" + }, + { + "type": "node", + "request": "launch", + "name": "groth16 setup", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "groth16", "setup", + "test/groth16/circuit.r1cs", + "test/plonk_circuit/powersOfTau15_final.ptau", + "test/groth16/circuit.zkey" + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 prove", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "groth16", "prove", + "test/groth16/circuit.zkey", + "test/groth16/witness.wtns", + "test/groth16/proof.json", + "test/groth16/public.json", + "-v" + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 export vk", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "zkev", + "test/groth16/circuit.zkey", + "test/groth16/verification_key.json", + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 verify", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "groth16", "verify", + "test/groth16/verification_key.json", + "test/groth16/public.json", + "test/groth16/proof.json", + "-v" + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 solidity verifier", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "zkesv", + "test/groth16/circuit.zkey", + "test/groth16/verifier.sol", + ] + }, + + { + "type": "node", + "request": "launch", + "name": "groth16 solidity calldata", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "zkesc", + "test/groth16/public.json", + "test/groth16/proof.json", + ] }, { "type": "node", diff --git a/templates/verifier_groth16.sol.ejs b/templates/verifier_groth16.sol.ejs index eba018e7..12503206 100644 --- a/templates/verifier_groth16.sol.ejs +++ b/templates/verifier_groth16.sol.ejs @@ -1,297 +1,173 @@ -// -// Copyright 2017 Christian Reitwiessner -// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: -// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. -// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. -// -// 2019 OKIMS -// ported to solidity 0.6 -// fixed linter warnings -// added requiere error messages -// -// // SPDX-License-Identifier: GPL-3.0 -pragma solidity ^0.6.11; -library Pairing { - struct G1Point { - uint X; - uint Y; - } - // Encoding of field elements is: X[0] * z + X[1] - struct G2Point { - uint[2] X; - uint[2] Y; - } - /// @return the generator of G1 - function P1() internal pure returns (G1Point memory) { - return G1Point(1, 2); - } - /// @return the generator of G2 - function P2() internal pure returns (G2Point memory) { - // Original code point - return G2Point( - [11559732032986387107991004021392285783925812861821192530917403151452391805634, - 10857046999023057135944570762232829481370756359578518086990519993285655852781], - [4082367875863433681332203403145435568316851327593401208105741076214120093531, - 8495653923123431417604973247489272438418190587263600148770280649306958101930] - ); - /* - // Changed by Jordi point - return G2Point( - [10857046999023057135944570762232829481370756359578518086990519993285655852781, - 11559732032986387107991004021392285783925812861821192530917403151452391805634], - [8495653923123431417604973247489272438418190587263600148770280649306958101930, - 4082367875863433681332203403145435568316851327593401208105741076214120093531] - ); + Copyright 2021 0KIMS association. + + This file is generated with [snarkJS](https://github.com/iden3/snarkjs). + + snarkJS is a free software: you can redistribute it and/or modify it + under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + snarkJS is distributed in the hope that it will be useful, but WITHOUT + ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public + License for more details. + + You should have received a copy of the GNU General Public License + along with snarkJS. If not, see . */ - } - /// @return r the negation of p, i.e. p.addition(p.negate()) should be zero. - function negate(G1Point memory p) internal pure returns (G1Point memory r) { - // The prime q in the base field F_q for G1 - uint q = 21888242871839275222246405745257275088696311157297823662689037894645226208583; - if (p.X == 0 && p.Y == 0) - return G1Point(0, 0); - return G1Point(p.X, q - (p.Y % q)); - } - /// @return r the sum of two points of G1 - function addition(G1Point memory p1, G1Point memory p2) internal view returns (G1Point memory r) { - uint[4] memory input; - input[0] = p1.X; - input[1] = p1.Y; - input[2] = p2.X; - input[3] = p2.Y; - bool success; - // solium-disable-next-line security/no-inline-assembly - assembly { - success := staticcall(sub(gas(), 2000), 6, input, 0xc0, r, 0x60) - // Use "invalid" to make gas estimation work - switch success case 0 { invalid() } - } - require(success,"pairing-add-failed"); - } - /// @return r the product of a point on G1 and a scalar, i.e. - /// p == p.scalar_mul(1) and p.addition(p) == p.scalar_mul(2) for all points p. - function scalar_mul(G1Point memory p, uint s) internal view returns (G1Point memory r) { - uint[3] memory input; - input[0] = p.X; - input[1] = p.Y; - input[2] = s; - bool success; - // solium-disable-next-line security/no-inline-assembly - assembly { - success := staticcall(sub(gas(), 2000), 7, input, 0x80, r, 0x60) - // Use "invalid" to make gas estimation work - switch success case 0 { invalid() } - } - require (success,"pairing-mul-failed"); - } - /// @return the result of computing the pairing check - /// e(p1[0], p2[0]) * .... * e(p1[n], p2[n]) == 1 - /// For example pairing([P1(), P1().negate()], [P2(), P2()]) should - /// return true. - function pairing(G1Point[] memory p1, G2Point[] memory p2) internal view returns (bool) { - require(p1.length == p2.length,"pairing-lengths-failed"); - uint elements = p1.length; - uint inputSize = elements * 6; - uint[] memory input = new uint[](inputSize); - for (uint i = 0; i < elements; i++) - { - input[i * 6 + 0] = p1[i].X; - input[i * 6 + 1] = p1[i].Y; - input[i * 6 + 2] = p2[i].X[0]; - input[i * 6 + 3] = p2[i].X[1]; - input[i * 6 + 4] = p2[i].Y[0]; - input[i * 6 + 5] = p2[i].Y[1]; - } - uint[1] memory out; - bool success; - // solium-disable-next-line security/no-inline-assembly - assembly { - success := staticcall(sub(gas(), 2000), 8, add(input, 0x20), mul(inputSize, 0x20), out, 0x20) - // Use "invalid" to make gas estimation work - switch success case 0 { invalid() } - } - require(success,"pairing-opcode-failed"); - return out[0] != 0; - } - /// Convenience method for a pairing check for two pairs. - function pairingProd2(G1Point memory a1, G2Point memory a2, G1Point memory b1, G2Point memory b2) internal view returns (bool) { - G1Point[] memory p1 = new G1Point[](2); - G2Point[] memory p2 = new G2Point[](2); - p1[0] = a1; - p1[1] = b1; - p2[0] = a2; - p2[1] = b2; - return pairing(p1, p2); - } - /// Convenience method for a pairing check for three pairs. - function pairingProd3( - G1Point memory a1, G2Point memory a2, - G1Point memory b1, G2Point memory b2, - G1Point memory c1, G2Point memory c2 - ) internal view returns (bool) { - G1Point[] memory p1 = new G1Point[](3); - G2Point[] memory p2 = new G2Point[](3); - p1[0] = a1; - p1[1] = b1; - p1[2] = c1; - p2[0] = a2; - p2[1] = b2; - p2[2] = c2; - return pairing(p1, p2); - } - /// Convenience method for a pairing check for four pairs. - function pairingProd4( - G1Point memory a1, G2Point memory a2, - G1Point memory b1, G2Point memory b2, - G1Point memory c1, G2Point memory c2, - G1Point memory d1, G2Point memory d2 - ) internal view returns (bool) { - G1Point[] memory p1 = new G1Point[](4); - G2Point[] memory p2 = new G2Point[](4); - p1[0] = a1; - p1[1] = b1; - p1[2] = c1; - p1[3] = d1; - p2[0] = a2; - p2[1] = b2; - p2[2] = c2; - p2[3] = d2; - return pairing(p1, p2); - } -} -contract Verifier { - uint256 constant p_bn128 = 21888242871839275222246405745257275088548364400416034343698204186575808495617; - uint256 constant q_bn128 = 21888242871839275222246405745257275088696311157297823662689037894645226208583; - - using Pairing for *; - struct VerifyingKey { - Pairing.G1Point alfa1; - Pairing.G2Point beta2; - Pairing.G2Point gamma2; - Pairing.G2Point delta2; - Pairing.G1Point[] IC; - } - struct Proof { - Pairing.G1Point A; - Pairing.G2Point B; - Pairing.G1Point C; - } - - function checkField(uint v) internal pure returns (uint) { + +pragma solidity >=0.7.0 <0.9.0; + +import "hardhat/console.sol"; + +contract Groth16Verifier { + // Scalar field size + uint256 constant r = 21888242871839275222246405745257275088548364400416034343698204186575808495617; + // Base field size + uint256 constant q = 21888242871839275222246405745257275088696311157297823662689037894645226208583; + + // Verification Key data + uint256 constant alphax = <%= vk_alpha_1[0] %>; + uint256 constant alphay = <%= vk_alpha_1[1] %>; + uint256 constant betax1 = <%= vk_beta_2[0][1] %>; + uint256 constant betax2 = <%= vk_beta_2[0][0] %>; + uint256 constant betay1 = <%= vk_beta_2[1][1] %>; + uint256 constant betay2 = <%= vk_beta_2[1][0] %>; + uint256 constant gammax1 = <%= vk_gamma_2[0][1] %>; + uint256 constant gammax2 = <%= vk_gamma_2[0][0] %>; + uint256 constant gammay1 = <%= vk_gamma_2[1][1] %>; + uint256 constant gammay2 = <%= vk_gamma_2[1][0] %>; + uint256 constant deltax1 = <%= vk_delta_2[0][1] %>; + uint256 constant deltax2 = <%= vk_delta_2[0][0] %>; + uint256 constant deltay1 = <%= vk_delta_2[1][1] %>; + uint256 constant deltay2 = <%= vk_delta_2[1][0] %>; + + <% for (let i=0; i + uint256 constant IC<%=i%>x = <%=IC[i][0]%>; + uint256 constant IC<%=i%>y = <%=IC[i][1]%>; + <% } %> + + // Proof calldata + // Byte offset of every parameter of the calldata + uint16 constant pA = <%=4 + 0%>; // [A]_1 + uint16 constant pB = <%=4 + 32*2%>; // [B]_2 + uint16 constant pC = <%=4 + 32*6%>; // [C]_1 + + // Memory data + uint16 constant pVk = 0; + uint16 constant pPairing = 128; + + uint16 constant pLastMem = 896; + + function verifyProof(bytes32[8] calldata _proof, bytes32[<%=IC.length-1%>] calldata _pubSignals) public view returns (bool) { assembly { - if iszero(lt(v, p_bn128)) { - mstore(0, 0) - return(0, 0x20) + function checkField(v) { + if iszero(lt(v, q)) { + mstore(0, 0) + return(0, 0x20) + } } - } - } + + // G1 function to multiply a G1 value(x,y) to value in an address + function g1_mulAccC(pR, x, y, s) { + let success + let mIn := mload(0x40) + mstore(mIn, x) + mstore(add(mIn, 32), y) + mstore(add(mIn, 64), s) - function checkPointBelongsToBN128Curve(Pairing.G1Point memory p) internal pure returns (uint) { - assembly { - let x := mload(p) - let y := mload(add(p,0x20)) + success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } - // Check that the point is on the curve - // y^2 = x^3 + 3 - let x3_3 := addmod(mulmod(x, mulmod(x, x, q_bn128), q_bn128), 3, q_bn128) - let y2 := mulmod(y, y, q_bn128) + mstore(add(mIn, 64), mload(pR)) + mstore(add(mIn, 96), mload(add(pR, 32))) - if iszero(eq(x3_3, y2)) { - mstore(0, 0) - return(0, 0x20) + success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } } - } - } - - function verifyingKey() internal pure returns (VerifyingKey memory vk) { - vk.alfa1 = Pairing.G1Point( - <%=vk_alpha_1[0]%>, - <%=vk_alpha_1[1]%> - ); - - vk.beta2 = Pairing.G2Point( - [<%=vk_beta_2[0][1]%>, - <%=vk_beta_2[0][0]%>], - [<%=vk_beta_2[1][1]%>, - <%=vk_beta_2[1][0]%>] - ); - vk.gamma2 = Pairing.G2Point( - [<%=vk_gamma_2[0][1]%>, - <%=vk_gamma_2[0][0]%>], - [<%=vk_gamma_2[1][1]%>, - <%=vk_gamma_2[1][0]%>] - ); - vk.delta2 = Pairing.G2Point( - [<%=vk_delta_2[0][1]%>, - <%=vk_delta_2[0][0]%>], - [<%=vk_delta_2[1][1]%>, - <%=vk_delta_2[1][0]%>] - ); - vk.IC = new Pairing.G1Point[](<%=IC.length%>); - <% for (let i=0; i - vk.IC[<%=i%>] = Pairing.G1Point( - <%=IC[i][0]%>, - <%=IC[i][1]%> - ); - <% } %> - } - function verify(uint[] memory input, Proof memory proof) internal view returns (uint) { - uint256 snark_scalar_field = 21888242871839275222246405745257275088548364400416034343698204186575808495617; - VerifyingKey memory vk = verifyingKey(); - require(input.length + 1 == vk.IC.length,"verifier-bad-input"); - // Compute the linear combination vk_x - Pairing.G1Point memory vk_x = Pairing.G1Point(0, 0); - for (uint i = 0; i < input.length; i++) { - require(input[i] < snark_scalar_field,"verifier-gte-snark-scalar-field"); - vk_x = Pairing.addition(vk_x, Pairing.scalar_mul(vk.IC[i + 1], input[i])); - } - vk_x = Pairing.addition(vk_x, vk.IC[0]); - if (!Pairing.pairingProd4( - Pairing.negate(proof.A), proof.B, - vk.alfa1, vk.beta2, - vk_x, vk.gamma2, - proof.C, vk.delta2 - )) return 1; - return 0; - } - /// @return r bool true if proof is valid - function verifyProof( - uint[2] memory a, - uint[2][2] memory b, - uint[2] memory c, - uint[<%=IC.length-1%>] memory input - ) public view returns (bool r) { - Proof memory proof; - proof.A = Pairing.G1Point(a[0], a[1]); - proof.B = Pairing.G2Point([b[0][0], b[0][1]], [b[1][0], b[1][1]]); - proof.C = Pairing.G1Point(c[0], c[1]); - uint[] memory inputValues = new uint[](input.length); - - // Check public inputs belong to field - for(uint i = 0; i < input.length; i++){ - inputValues[i] = input[i]; - checkField(inputValues[i]); - } - - // Check G1 points coordinates belong to field - checkField(a[0]); - checkField(a[1]); - checkField(b[0][0]); - checkField(b[0][1]); - checkField(b[1][0]); - checkField(b[1][1]); - checkField(c[0]); - checkField(c[1]); - - checkPointBelongsToBN128Curve(proof.A); - checkPointBelongsToBN128Curve(proof.C); - - if (verify(inputValues, proof) == 0) { - return true; - } else { - return false; - } - } -} + + function checkPairing(proof, pubSignals, pMem) -> isOk { + let _pPairing := add(pMem, pPairing) + let _pVk := add(pMem, pVk) + + mstore(_pVk, IC0x) + mstore(add(_pVk, 32), IC0y) + + // Compute the linear combination vk_x + <% for (let i = 1; i <= nPublic; i++) { %> + g1_mulAccC(_pVk, IC<%=i%>x, IC<%=i%>y, calldataload(add(pubSignals, <%=(i-1)*32%>))) + <% } %> + + // -A + mstore(_pPairing, calldataload(pA)) + mstore(add(_pPairing, 32), mod(sub(q, calldataload(add(pA, 32))), q)) + + // B + mstore(add(_pPairing, 64), calldataload(pB)) + mstore(add(_pPairing, 96), calldataload(add(pB, 32))) + mstore(add(_pPairing, 128), calldataload(add(pB, 64))) + mstore(add(_pPairing, 160), calldataload(add(pB, 96))) + + // alpha1 + mstore(add(_pPairing, 192), alphax) + mstore(add(_pPairing, 224), alphay) + + // beta2 + mstore(add(_pPairing, 256), betax1) + mstore(add(_pPairing, 288), betax2) + mstore(add(_pPairing, 320), betay1) + mstore(add(_pPairing, 352), betay2) + + // vk_x + mstore(add(_pPairing, 384), mload(add(pMem, pVk))) + mstore(add(_pPairing, 416), mload(add(pMem, add(pVk, 32)))) + + + // gamma2 + mstore(add(_pPairing, 448), gammax1) + mstore(add(_pPairing, 480), gammax2) + mstore(add(_pPairing, 512), gammay1) + mstore(add(_pPairing, 544), gammay2) + + // C + mstore(add(_pPairing, 576), calldataload(pC)) + mstore(add(_pPairing, 608), calldataload(add(pC, 32))) + + // delta2 + mstore(add(_pPairing, 640), deltax1) + mstore(add(_pPairing, 672), deltax2) + mstore(add(_pPairing, 704), deltay1) + mstore(add(_pPairing, 736), deltay2) + + + let success := staticcall(sub(gas(), 2000), 8, _pPairing, 768, _pPairing, 0x20) + + isOk := and(success, mload(_pPairing)) + } + + let pMem := mload(0x40) + mstore(0x40, add(pMem, pLastMem)) + + // Validate that all evaluations ∈ F + <% for (let i=0; i + checkField(calldataload(add(_pubSignals, <%=i*32%>))) + <% } %> + + // Validate all evaluations + let isValid := checkPairing(_proof, _pubSignals, pMem) + + mstore(0, isValid) + return(0, 0x20) + } + } + } From f87687923c08297ff781cab41c518657901a8a4f Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Thu, 11 May 2023 09:31:56 +0200 Subject: [PATCH 36/48] fix calldata types and test passing --- smart_contract_tests/test/smart_contracts.test.js | 2 +- templates/verifier_groth16.sol.ejs | 12 +++--------- 2 files changed, 4 insertions(+), 10 deletions(-) diff --git a/smart_contract_tests/test/smart_contracts.test.js b/smart_contract_tests/test/smart_contracts.test.js index a7cee55f..c5636656 100644 --- a/smart_contract_tests/test/smart_contracts.test.js +++ b/smart_contract_tests/test/smart_contracts.test.js @@ -54,7 +54,7 @@ describe("Smart contracts test suite", function () { await run("compile"); // Deploy mock groth16 verifier - const VerifierFactory = await ethers.getContractFactory("Verifier"); + const VerifierFactory = await ethers.getContractFactory("Groth16Verifier"); verifierContract = await VerifierFactory.deploy(); // Verifiy the proof in the smart contract diff --git a/templates/verifier_groth16.sol.ejs b/templates/verifier_groth16.sol.ejs index 12503206..7c9687ac 100644 --- a/templates/verifier_groth16.sol.ejs +++ b/templates/verifier_groth16.sol.ejs @@ -48,12 +48,6 @@ contract Groth16Verifier { uint256 constant IC<%=i%>x = <%=IC[i][0]%>; uint256 constant IC<%=i%>y = <%=IC[i][1]%>; <% } %> - - // Proof calldata - // Byte offset of every parameter of the calldata - uint16 constant pA = <%=4 + 0%>; // [A]_1 - uint16 constant pB = <%=4 + 32*2%>; // [B]_2 - uint16 constant pC = <%=4 + 32*6%>; // [C]_1 // Memory data uint16 constant pVk = 0; @@ -61,7 +55,7 @@ contract Groth16Verifier { uint16 constant pLastMem = 896; - function verifyProof(bytes32[8] calldata _proof, bytes32[<%=IC.length-1%>] calldata _pubSignals) public view returns (bool) { + function verifyProof(uint[2] calldata _pA, uint[2][2] calldata _pB, uint[2] calldata _pC, uint[<%=IC.length-1%>] calldata _pubSignals) public view returns (bool) { assembly { function checkField(v) { if iszero(lt(v, q)) { @@ -96,7 +90,7 @@ contract Groth16Verifier { } } - function checkPairing(proof, pubSignals, pMem) -> isOk { + function checkPairing(pA, pB, pC, pubSignals, pMem) -> isOk { let _pPairing := add(pMem, pPairing) let _pVk := add(pMem, pVk) @@ -164,7 +158,7 @@ contract Groth16Verifier { <% } %> // Validate all evaluations - let isValid := checkPairing(_proof, _pubSignals, pMem) + let isValid := checkPairing(_pA, _pB, _pC, _pubSignals, pMem) mstore(0, isValid) return(0, 0x20) From ee8b9e3349a9fb0763755d09b7f810d92d4b2fc2 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Sat, 13 May 2023 06:09:20 +0200 Subject: [PATCH 37/48] remove console.log import --- templates/verifier_groth16.sol.ejs | 2 -- 1 file changed, 2 deletions(-) diff --git a/templates/verifier_groth16.sol.ejs b/templates/verifier_groth16.sol.ejs index 7c9687ac..32c260ed 100644 --- a/templates/verifier_groth16.sol.ejs +++ b/templates/verifier_groth16.sol.ejs @@ -20,8 +20,6 @@ pragma solidity >=0.7.0 <0.9.0; -import "hardhat/console.sol"; - contract Groth16Verifier { // Scalar field size uint256 constant r = 21888242871839275222246405745257275088548364400416034343698204186575808495617; From fd9b765a60caa3084d5ba59a8bb0b72d53bfe656 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Thu, 18 May 2023 17:46:50 +0200 Subject: [PATCH 38/48] add scalar import --- src/fflonk_verify.js | 1 + 1 file changed, 1 insertion(+) diff --git a/src/fflonk_verify.js b/src/fflonk_verify.js index 23d1250c..03201664 100644 --- a/src/fflonk_verify.js +++ b/src/fflonk_verify.js @@ -21,6 +21,7 @@ import * as curves from "./curves.js"; import { BigBuffer, utils } from "ffjavascript"; import { Proof } from "./proof.js"; import { Keccak256Transcript } from "./Keccak256Transcript.js"; +import { Scalar } from "ffjavascript"; const { unstringifyBigInts } = utils; From 0cdacdf8e858690a3d148240859fb4292d57b555 Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Sat, 6 May 2023 07:04:53 +0200 Subject: [PATCH 39/48] Add check functions in js and sc --- src/fflonk_verify.js | 49 ++++++++++++++++++++++++++++-- src/groth16_verify.js | 28 +++++++++++++++++ src/plonk_verify.js | 2 +- templates/verifier_groth16.sol.ejs | 47 ++++++++++++++++++++++++++++ templates/verifier_plonk.sol.ejs | 4 +-- 5 files changed, 123 insertions(+), 7 deletions(-) diff --git a/src/fflonk_verify.js b/src/fflonk_verify.js index 9c9ec58d..23d1250c 100644 --- a/src/fflonk_verify.js +++ b/src/fflonk_verify.js @@ -61,15 +61,23 @@ export default async function fflonkVerify(_vk_verifier, _publicSignals, _proof, // STEP 1 - Validate that all polynomial commitments ∈ G_1 if (logger) logger.info("> Checking commitments belong to G1"); if (!commitmentsBelongToG1(curve, proof, vk)) { - logger.error("Proof is not well constructed"); + if (logger) logger.error("Proof commitments are not valid"); return false; } - // TODO // STEP 2 - Validate that all evaluations ∈ F + if (logger) logger.info("> Checking evaluations belong to F"); + if (!evaluationsAreValid(curve, proof)) { + if (logger) logger.error("Proof evaluations are not valid."); + return false; + } - // TODO // STEP 3 - Validate that w_i ∈ F for i ∈ [l] + if (logger) logger.info("> Checking public inputs belong to F"); + if (!publicInputsAreValid(curve, publicSignals)) { + if (logger) logger.error("Public inputs are not valid."); + return false; + } // STEP 4 - Compute the challenges: beta, gamma, xi, alpha and y ∈ F // as in prover description, from the common preprocessed inputs, public inputs and elements of π_SNARK @@ -151,6 +159,41 @@ function commitmentsBelongToG1(curve, proof, vk) { && G1.isValid(vk.C0); } +function checkValueBelongToField(curve, value) { + return Scalar.lt(value, curve.r); +} + +function checkEvaluationIsValid(curve, evaluation) { + return checkValueBelongToField(curve, Scalar.fromRprLE(evaluation)); +} + +function evaluationsAreValid(curve, proof) { + return checkEvaluationIsValid(curve, proof.evaluations.ql) + && checkEvaluationIsValid(curve, proof.evaluations.qr) + && checkEvaluationIsValid(curve, proof.evaluations.qm) + && checkEvaluationIsValid(curve, proof.evaluations.qo) + && checkEvaluationIsValid(curve, proof.evaluations.qc) + && checkEvaluationIsValid(curve, proof.evaluations.s1) + && checkEvaluationIsValid(curve, proof.evaluations.s2) + && checkEvaluationIsValid(curve, proof.evaluations.s3) + && checkEvaluationIsValid(curve, proof.evaluations.a) + && checkEvaluationIsValid(curve, proof.evaluations.b) + && checkEvaluationIsValid(curve, proof.evaluations.c) + && checkEvaluationIsValid(curve, proof.evaluations.z) + && checkEvaluationIsValid(curve, proof.evaluations.zw) + && checkEvaluationIsValid(curve, proof.evaluations.t1w) + && checkEvaluationIsValid(curve, proof.evaluations.t2w); +} + +function publicInputsAreValid(curve, publicInputs) { + for(let i = 0; i < publicInputs.length; i++) { + if(!checkValueBelongToField(curve, publicInputs[i])) { + return false; + } + } + return true; +} + function computeChallenges(curve, proof, vk, publicSignals, logger) { const Fr = curve.Fr; diff --git a/src/groth16_verify.js b/src/groth16_verify.js index f4936fa7..d2101a45 100644 --- a/src/groth16_verify.js +++ b/src/groth16_verify.js @@ -41,6 +41,11 @@ export default async function groth16Verify(_vk_verifier, _publicSignals, _proof const IC = new Uint8Array(curve.G1.F.n8*2 * publicSignals.length); const w = new Uint8Array(curve.Fr.n8 * publicSignals.length); + if (!publicInputsAreValid(curve, publicSignals)) { + if (logger) logger.error("Public inputs are not valid."); + return false; + } + for (let i=0; i, @@ -238,9 +268,26 @@ contract Verifier { proof.B = Pairing.G2Point([b[0][0], b[0][1]], [b[1][0], b[1][1]]); proof.C = Pairing.G1Point(c[0], c[1]); uint[] memory inputValues = new uint[](input.length); + + // Check public inputs belong to field for(uint i = 0; i < input.length; i++){ inputValues[i] = input[i]; + checkField(inputValues[i]); } + + // Check G1 points coordinates belong to field + checkField(a[0]); + checkField(a[1]); + checkField(b[0][0]); + checkField(b[0][1]); + checkField(b[1][0]); + checkField(b[1][1]); + checkField(c[0]); + checkField(c[1]); + + checkPointBelongsToBN128Curve(proof.A); + checkPointBelongsToBN128Curve(proof.C); + if (verify(inputValues, proof) == 0) { return true; } else { diff --git a/templates/verifier_plonk.sol.ejs b/templates/verifier_plonk.sol.ejs index 25f38eb1..36e2d275 100644 --- a/templates/verifier_plonk.sol.ejs +++ b/templates/verifier_plonk.sol.ejs @@ -21,8 +21,6 @@ pragma solidity >=0.7.0 <0.9.0; -import "hardhat/console.sol"; - contract PlonkVerifier { // Omega uint256 constant w1 = <%=w%>; @@ -707,4 +705,4 @@ contract PlonkVerifier { } } -} +} \ No newline at end of file From 62a3b9e28527a4cb6848812949c1b2a8e95ce642 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Thu, 11 May 2023 09:11:04 +0200 Subject: [PATCH 40/48] refactor groth16 smart contract to assembly code --- .vscode/launch.json | 91 ++++++ templates/verifier_groth16.sol.ejs | 452 +++++++++++------------------ 2 files changed, 255 insertions(+), 288 deletions(-) diff --git a/.vscode/launch.json b/.vscode/launch.json index dd59ba47..1074b58f 100644 --- a/.vscode/launch.json +++ b/.vscode/launch.json @@ -12,6 +12,97 @@ "/**" ], "type": "node" + }, + { + "type": "node", + "request": "launch", + "name": "groth16 setup", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "groth16", "setup", + "test/groth16/circuit.r1cs", + "test/plonk_circuit/powersOfTau15_final.ptau", + "test/groth16/circuit.zkey" + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 prove", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "groth16", "prove", + "test/groth16/circuit.zkey", + "test/groth16/witness.wtns", + "test/groth16/proof.json", + "test/groth16/public.json", + "-v" + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 export vk", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "zkev", + "test/groth16/circuit.zkey", + "test/groth16/verification_key.json", + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 verify", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "groth16", "verify", + "test/groth16/verification_key.json", + "test/groth16/public.json", + "test/groth16/proof.json", + "-v" + ] + }, + { + "type": "node", + "request": "launch", + "name": "groth16 solidity verifier", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "zkesv", + "test/groth16/circuit.zkey", + "test/groth16/verifier.sol", + ] + }, + + { + "type": "node", + "request": "launch", + "name": "groth16 solidity calldata", + "skipFiles": [ + "/**" + ], + "program": "cli.js", + "args": [ + "zkesc", + "test/groth16/public.json", + "test/groth16/proof.json", + ] }, { "type": "node", diff --git a/templates/verifier_groth16.sol.ejs b/templates/verifier_groth16.sol.ejs index eba018e7..12503206 100644 --- a/templates/verifier_groth16.sol.ejs +++ b/templates/verifier_groth16.sol.ejs @@ -1,297 +1,173 @@ -// -// Copyright 2017 Christian Reitwiessner -// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: -// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. -// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. -// -// 2019 OKIMS -// ported to solidity 0.6 -// fixed linter warnings -// added requiere error messages -// -// // SPDX-License-Identifier: GPL-3.0 -pragma solidity ^0.6.11; -library Pairing { - struct G1Point { - uint X; - uint Y; - } - // Encoding of field elements is: X[0] * z + X[1] - struct G2Point { - uint[2] X; - uint[2] Y; - } - /// @return the generator of G1 - function P1() internal pure returns (G1Point memory) { - return G1Point(1, 2); - } - /// @return the generator of G2 - function P2() internal pure returns (G2Point memory) { - // Original code point - return G2Point( - [11559732032986387107991004021392285783925812861821192530917403151452391805634, - 10857046999023057135944570762232829481370756359578518086990519993285655852781], - [4082367875863433681332203403145435568316851327593401208105741076214120093531, - 8495653923123431417604973247489272438418190587263600148770280649306958101930] - ); - /* - // Changed by Jordi point - return G2Point( - [10857046999023057135944570762232829481370756359578518086990519993285655852781, - 11559732032986387107991004021392285783925812861821192530917403151452391805634], - [8495653923123431417604973247489272438418190587263600148770280649306958101930, - 4082367875863433681332203403145435568316851327593401208105741076214120093531] - ); + Copyright 2021 0KIMS association. + + This file is generated with [snarkJS](https://github.com/iden3/snarkjs). + + snarkJS is a free software: you can redistribute it and/or modify it + under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + snarkJS is distributed in the hope that it will be useful, but WITHOUT + ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public + License for more details. + + You should have received a copy of the GNU General Public License + along with snarkJS. If not, see . */ - } - /// @return r the negation of p, i.e. p.addition(p.negate()) should be zero. - function negate(G1Point memory p) internal pure returns (G1Point memory r) { - // The prime q in the base field F_q for G1 - uint q = 21888242871839275222246405745257275088696311157297823662689037894645226208583; - if (p.X == 0 && p.Y == 0) - return G1Point(0, 0); - return G1Point(p.X, q - (p.Y % q)); - } - /// @return r the sum of two points of G1 - function addition(G1Point memory p1, G1Point memory p2) internal view returns (G1Point memory r) { - uint[4] memory input; - input[0] = p1.X; - input[1] = p1.Y; - input[2] = p2.X; - input[3] = p2.Y; - bool success; - // solium-disable-next-line security/no-inline-assembly - assembly { - success := staticcall(sub(gas(), 2000), 6, input, 0xc0, r, 0x60) - // Use "invalid" to make gas estimation work - switch success case 0 { invalid() } - } - require(success,"pairing-add-failed"); - } - /// @return r the product of a point on G1 and a scalar, i.e. - /// p == p.scalar_mul(1) and p.addition(p) == p.scalar_mul(2) for all points p. - function scalar_mul(G1Point memory p, uint s) internal view returns (G1Point memory r) { - uint[3] memory input; - input[0] = p.X; - input[1] = p.Y; - input[2] = s; - bool success; - // solium-disable-next-line security/no-inline-assembly - assembly { - success := staticcall(sub(gas(), 2000), 7, input, 0x80, r, 0x60) - // Use "invalid" to make gas estimation work - switch success case 0 { invalid() } - } - require (success,"pairing-mul-failed"); - } - /// @return the result of computing the pairing check - /// e(p1[0], p2[0]) * .... * e(p1[n], p2[n]) == 1 - /// For example pairing([P1(), P1().negate()], [P2(), P2()]) should - /// return true. - function pairing(G1Point[] memory p1, G2Point[] memory p2) internal view returns (bool) { - require(p1.length == p2.length,"pairing-lengths-failed"); - uint elements = p1.length; - uint inputSize = elements * 6; - uint[] memory input = new uint[](inputSize); - for (uint i = 0; i < elements; i++) - { - input[i * 6 + 0] = p1[i].X; - input[i * 6 + 1] = p1[i].Y; - input[i * 6 + 2] = p2[i].X[0]; - input[i * 6 + 3] = p2[i].X[1]; - input[i * 6 + 4] = p2[i].Y[0]; - input[i * 6 + 5] = p2[i].Y[1]; - } - uint[1] memory out; - bool success; - // solium-disable-next-line security/no-inline-assembly - assembly { - success := staticcall(sub(gas(), 2000), 8, add(input, 0x20), mul(inputSize, 0x20), out, 0x20) - // Use "invalid" to make gas estimation work - switch success case 0 { invalid() } - } - require(success,"pairing-opcode-failed"); - return out[0] != 0; - } - /// Convenience method for a pairing check for two pairs. - function pairingProd2(G1Point memory a1, G2Point memory a2, G1Point memory b1, G2Point memory b2) internal view returns (bool) { - G1Point[] memory p1 = new G1Point[](2); - G2Point[] memory p2 = new G2Point[](2); - p1[0] = a1; - p1[1] = b1; - p2[0] = a2; - p2[1] = b2; - return pairing(p1, p2); - } - /// Convenience method for a pairing check for three pairs. - function pairingProd3( - G1Point memory a1, G2Point memory a2, - G1Point memory b1, G2Point memory b2, - G1Point memory c1, G2Point memory c2 - ) internal view returns (bool) { - G1Point[] memory p1 = new G1Point[](3); - G2Point[] memory p2 = new G2Point[](3); - p1[0] = a1; - p1[1] = b1; - p1[2] = c1; - p2[0] = a2; - p2[1] = b2; - p2[2] = c2; - return pairing(p1, p2); - } - /// Convenience method for a pairing check for four pairs. - function pairingProd4( - G1Point memory a1, G2Point memory a2, - G1Point memory b1, G2Point memory b2, - G1Point memory c1, G2Point memory c2, - G1Point memory d1, G2Point memory d2 - ) internal view returns (bool) { - G1Point[] memory p1 = new G1Point[](4); - G2Point[] memory p2 = new G2Point[](4); - p1[0] = a1; - p1[1] = b1; - p1[2] = c1; - p1[3] = d1; - p2[0] = a2; - p2[1] = b2; - p2[2] = c2; - p2[3] = d2; - return pairing(p1, p2); - } -} -contract Verifier { - uint256 constant p_bn128 = 21888242871839275222246405745257275088548364400416034343698204186575808495617; - uint256 constant q_bn128 = 21888242871839275222246405745257275088696311157297823662689037894645226208583; - - using Pairing for *; - struct VerifyingKey { - Pairing.G1Point alfa1; - Pairing.G2Point beta2; - Pairing.G2Point gamma2; - Pairing.G2Point delta2; - Pairing.G1Point[] IC; - } - struct Proof { - Pairing.G1Point A; - Pairing.G2Point B; - Pairing.G1Point C; - } - - function checkField(uint v) internal pure returns (uint) { + +pragma solidity >=0.7.0 <0.9.0; + +import "hardhat/console.sol"; + +contract Groth16Verifier { + // Scalar field size + uint256 constant r = 21888242871839275222246405745257275088548364400416034343698204186575808495617; + // Base field size + uint256 constant q = 21888242871839275222246405745257275088696311157297823662689037894645226208583; + + // Verification Key data + uint256 constant alphax = <%= vk_alpha_1[0] %>; + uint256 constant alphay = <%= vk_alpha_1[1] %>; + uint256 constant betax1 = <%= vk_beta_2[0][1] %>; + uint256 constant betax2 = <%= vk_beta_2[0][0] %>; + uint256 constant betay1 = <%= vk_beta_2[1][1] %>; + uint256 constant betay2 = <%= vk_beta_2[1][0] %>; + uint256 constant gammax1 = <%= vk_gamma_2[0][1] %>; + uint256 constant gammax2 = <%= vk_gamma_2[0][0] %>; + uint256 constant gammay1 = <%= vk_gamma_2[1][1] %>; + uint256 constant gammay2 = <%= vk_gamma_2[1][0] %>; + uint256 constant deltax1 = <%= vk_delta_2[0][1] %>; + uint256 constant deltax2 = <%= vk_delta_2[0][0] %>; + uint256 constant deltay1 = <%= vk_delta_2[1][1] %>; + uint256 constant deltay2 = <%= vk_delta_2[1][0] %>; + + <% for (let i=0; i + uint256 constant IC<%=i%>x = <%=IC[i][0]%>; + uint256 constant IC<%=i%>y = <%=IC[i][1]%>; + <% } %> + + // Proof calldata + // Byte offset of every parameter of the calldata + uint16 constant pA = <%=4 + 0%>; // [A]_1 + uint16 constant pB = <%=4 + 32*2%>; // [B]_2 + uint16 constant pC = <%=4 + 32*6%>; // [C]_1 + + // Memory data + uint16 constant pVk = 0; + uint16 constant pPairing = 128; + + uint16 constant pLastMem = 896; + + function verifyProof(bytes32[8] calldata _proof, bytes32[<%=IC.length-1%>] calldata _pubSignals) public view returns (bool) { assembly { - if iszero(lt(v, p_bn128)) { - mstore(0, 0) - return(0, 0x20) + function checkField(v) { + if iszero(lt(v, q)) { + mstore(0, 0) + return(0, 0x20) + } } - } - } + + // G1 function to multiply a G1 value(x,y) to value in an address + function g1_mulAccC(pR, x, y, s) { + let success + let mIn := mload(0x40) + mstore(mIn, x) + mstore(add(mIn, 32), y) + mstore(add(mIn, 64), s) - function checkPointBelongsToBN128Curve(Pairing.G1Point memory p) internal pure returns (uint) { - assembly { - let x := mload(p) - let y := mload(add(p,0x20)) + success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } - // Check that the point is on the curve - // y^2 = x^3 + 3 - let x3_3 := addmod(mulmod(x, mulmod(x, x, q_bn128), q_bn128), 3, q_bn128) - let y2 := mulmod(y, y, q_bn128) + mstore(add(mIn, 64), mload(pR)) + mstore(add(mIn, 96), mload(add(pR, 32))) - if iszero(eq(x3_3, y2)) { - mstore(0, 0) - return(0, 0x20) + success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } } - } - } - - function verifyingKey() internal pure returns (VerifyingKey memory vk) { - vk.alfa1 = Pairing.G1Point( - <%=vk_alpha_1[0]%>, - <%=vk_alpha_1[1]%> - ); - - vk.beta2 = Pairing.G2Point( - [<%=vk_beta_2[0][1]%>, - <%=vk_beta_2[0][0]%>], - [<%=vk_beta_2[1][1]%>, - <%=vk_beta_2[1][0]%>] - ); - vk.gamma2 = Pairing.G2Point( - [<%=vk_gamma_2[0][1]%>, - <%=vk_gamma_2[0][0]%>], - [<%=vk_gamma_2[1][1]%>, - <%=vk_gamma_2[1][0]%>] - ); - vk.delta2 = Pairing.G2Point( - [<%=vk_delta_2[0][1]%>, - <%=vk_delta_2[0][0]%>], - [<%=vk_delta_2[1][1]%>, - <%=vk_delta_2[1][0]%>] - ); - vk.IC = new Pairing.G1Point[](<%=IC.length%>); - <% for (let i=0; i - vk.IC[<%=i%>] = Pairing.G1Point( - <%=IC[i][0]%>, - <%=IC[i][1]%> - ); - <% } %> - } - function verify(uint[] memory input, Proof memory proof) internal view returns (uint) { - uint256 snark_scalar_field = 21888242871839275222246405745257275088548364400416034343698204186575808495617; - VerifyingKey memory vk = verifyingKey(); - require(input.length + 1 == vk.IC.length,"verifier-bad-input"); - // Compute the linear combination vk_x - Pairing.G1Point memory vk_x = Pairing.G1Point(0, 0); - for (uint i = 0; i < input.length; i++) { - require(input[i] < snark_scalar_field,"verifier-gte-snark-scalar-field"); - vk_x = Pairing.addition(vk_x, Pairing.scalar_mul(vk.IC[i + 1], input[i])); - } - vk_x = Pairing.addition(vk_x, vk.IC[0]); - if (!Pairing.pairingProd4( - Pairing.negate(proof.A), proof.B, - vk.alfa1, vk.beta2, - vk_x, vk.gamma2, - proof.C, vk.delta2 - )) return 1; - return 0; - } - /// @return r bool true if proof is valid - function verifyProof( - uint[2] memory a, - uint[2][2] memory b, - uint[2] memory c, - uint[<%=IC.length-1%>] memory input - ) public view returns (bool r) { - Proof memory proof; - proof.A = Pairing.G1Point(a[0], a[1]); - proof.B = Pairing.G2Point([b[0][0], b[0][1]], [b[1][0], b[1][1]]); - proof.C = Pairing.G1Point(c[0], c[1]); - uint[] memory inputValues = new uint[](input.length); - - // Check public inputs belong to field - for(uint i = 0; i < input.length; i++){ - inputValues[i] = input[i]; - checkField(inputValues[i]); - } - - // Check G1 points coordinates belong to field - checkField(a[0]); - checkField(a[1]); - checkField(b[0][0]); - checkField(b[0][1]); - checkField(b[1][0]); - checkField(b[1][1]); - checkField(c[0]); - checkField(c[1]); - - checkPointBelongsToBN128Curve(proof.A); - checkPointBelongsToBN128Curve(proof.C); - - if (verify(inputValues, proof) == 0) { - return true; - } else { - return false; - } - } -} + + function checkPairing(proof, pubSignals, pMem) -> isOk { + let _pPairing := add(pMem, pPairing) + let _pVk := add(pMem, pVk) + + mstore(_pVk, IC0x) + mstore(add(_pVk, 32), IC0y) + + // Compute the linear combination vk_x + <% for (let i = 1; i <= nPublic; i++) { %> + g1_mulAccC(_pVk, IC<%=i%>x, IC<%=i%>y, calldataload(add(pubSignals, <%=(i-1)*32%>))) + <% } %> + + // -A + mstore(_pPairing, calldataload(pA)) + mstore(add(_pPairing, 32), mod(sub(q, calldataload(add(pA, 32))), q)) + + // B + mstore(add(_pPairing, 64), calldataload(pB)) + mstore(add(_pPairing, 96), calldataload(add(pB, 32))) + mstore(add(_pPairing, 128), calldataload(add(pB, 64))) + mstore(add(_pPairing, 160), calldataload(add(pB, 96))) + + // alpha1 + mstore(add(_pPairing, 192), alphax) + mstore(add(_pPairing, 224), alphay) + + // beta2 + mstore(add(_pPairing, 256), betax1) + mstore(add(_pPairing, 288), betax2) + mstore(add(_pPairing, 320), betay1) + mstore(add(_pPairing, 352), betay2) + + // vk_x + mstore(add(_pPairing, 384), mload(add(pMem, pVk))) + mstore(add(_pPairing, 416), mload(add(pMem, add(pVk, 32)))) + + + // gamma2 + mstore(add(_pPairing, 448), gammax1) + mstore(add(_pPairing, 480), gammax2) + mstore(add(_pPairing, 512), gammay1) + mstore(add(_pPairing, 544), gammay2) + + // C + mstore(add(_pPairing, 576), calldataload(pC)) + mstore(add(_pPairing, 608), calldataload(add(pC, 32))) + + // delta2 + mstore(add(_pPairing, 640), deltax1) + mstore(add(_pPairing, 672), deltax2) + mstore(add(_pPairing, 704), deltay1) + mstore(add(_pPairing, 736), deltay2) + + + let success := staticcall(sub(gas(), 2000), 8, _pPairing, 768, _pPairing, 0x20) + + isOk := and(success, mload(_pPairing)) + } + + let pMem := mload(0x40) + mstore(0x40, add(pMem, pLastMem)) + + // Validate that all evaluations ∈ F + <% for (let i=0; i + checkField(calldataload(add(_pubSignals, <%=i*32%>))) + <% } %> + + // Validate all evaluations + let isValid := checkPairing(_proof, _pubSignals, pMem) + + mstore(0, isValid) + return(0, 0x20) + } + } + } From d5a179ca1cbafaabe6076290bd48f2c8add388bd Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Thu, 11 May 2023 09:31:56 +0200 Subject: [PATCH 41/48] fix calldata types and test passing --- smart_contract_tests/test/smart_contracts.test.js | 2 +- templates/verifier_groth16.sol.ejs | 12 +++--------- 2 files changed, 4 insertions(+), 10 deletions(-) diff --git a/smart_contract_tests/test/smart_contracts.test.js b/smart_contract_tests/test/smart_contracts.test.js index 0e2a475b..ec0bc7cb 100644 --- a/smart_contract_tests/test/smart_contracts.test.js +++ b/smart_contract_tests/test/smart_contracts.test.js @@ -94,7 +94,7 @@ describe("Smart contracts test suite", function () { await run("compile"); // Deploy mock groth16 verifier - const VerifierFactory = await ethers.getContractFactory("Verifier"); + const VerifierFactory = await ethers.getContractFactory("Groth16Verifier"); verifierContract = await VerifierFactory.deploy(); return await verifierContract.verifyProof(proofA, proofB, proofC, publicInputs); diff --git a/templates/verifier_groth16.sol.ejs b/templates/verifier_groth16.sol.ejs index 12503206..7c9687ac 100644 --- a/templates/verifier_groth16.sol.ejs +++ b/templates/verifier_groth16.sol.ejs @@ -48,12 +48,6 @@ contract Groth16Verifier { uint256 constant IC<%=i%>x = <%=IC[i][0]%>; uint256 constant IC<%=i%>y = <%=IC[i][1]%>; <% } %> - - // Proof calldata - // Byte offset of every parameter of the calldata - uint16 constant pA = <%=4 + 0%>; // [A]_1 - uint16 constant pB = <%=4 + 32*2%>; // [B]_2 - uint16 constant pC = <%=4 + 32*6%>; // [C]_1 // Memory data uint16 constant pVk = 0; @@ -61,7 +55,7 @@ contract Groth16Verifier { uint16 constant pLastMem = 896; - function verifyProof(bytes32[8] calldata _proof, bytes32[<%=IC.length-1%>] calldata _pubSignals) public view returns (bool) { + function verifyProof(uint[2] calldata _pA, uint[2][2] calldata _pB, uint[2] calldata _pC, uint[<%=IC.length-1%>] calldata _pubSignals) public view returns (bool) { assembly { function checkField(v) { if iszero(lt(v, q)) { @@ -96,7 +90,7 @@ contract Groth16Verifier { } } - function checkPairing(proof, pubSignals, pMem) -> isOk { + function checkPairing(pA, pB, pC, pubSignals, pMem) -> isOk { let _pPairing := add(pMem, pPairing) let _pVk := add(pMem, pVk) @@ -164,7 +158,7 @@ contract Groth16Verifier { <% } %> // Validate all evaluations - let isValid := checkPairing(_proof, _pubSignals, pMem) + let isValid := checkPairing(_pA, _pB, _pC, _pubSignals, pMem) mstore(0, isValid) return(0, 0x20) From 5f41773b409a64b2baa638b070059d1e87125095 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Sat, 13 May 2023 06:09:20 +0200 Subject: [PATCH 42/48] remove console.log import --- templates/verifier_groth16.sol.ejs | 2 -- 1 file changed, 2 deletions(-) diff --git a/templates/verifier_groth16.sol.ejs b/templates/verifier_groth16.sol.ejs index 7c9687ac..32c260ed 100644 --- a/templates/verifier_groth16.sol.ejs +++ b/templates/verifier_groth16.sol.ejs @@ -20,8 +20,6 @@ pragma solidity >=0.7.0 <0.9.0; -import "hardhat/console.sol"; - contract Groth16Verifier { // Scalar field size uint256 constant r = 21888242871839275222246405745257275088548364400416034343698204186575808495617; From cfac623ac98101078fc010e450d82d10bac9bd60 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Thu, 18 May 2023 17:46:50 +0200 Subject: [PATCH 43/48] add scalar import --- src/fflonk_verify.js | 1 + 1 file changed, 1 insertion(+) diff --git a/src/fflonk_verify.js b/src/fflonk_verify.js index 23d1250c..03201664 100644 --- a/src/fflonk_verify.js +++ b/src/fflonk_verify.js @@ -21,6 +21,7 @@ import * as curves from "./curves.js"; import { BigBuffer, utils } from "ffjavascript"; import { Proof } from "./proof.js"; import { Keccak256Transcript } from "./Keccak256Transcript.js"; +import { Scalar } from "ffjavascript"; const { unstringifyBigInts } = utils; From 03f344b6294867383bd6d92a49de7ab68e357b5c Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Thu, 18 May 2023 18:12:43 +0200 Subject: [PATCH 44/48] remove hardhat import --- templates/verifier_plonk.sol.ejs | 2 -- 1 file changed, 2 deletions(-) diff --git a/templates/verifier_plonk.sol.ejs b/templates/verifier_plonk.sol.ejs index da3f145b..36e2d275 100644 --- a/templates/verifier_plonk.sol.ejs +++ b/templates/verifier_plonk.sol.ejs @@ -21,8 +21,6 @@ pragma solidity >=0.7.0 <0.9.0; -import "hardhat/console.sol"; - contract PlonkVerifier { // Omega uint256 constant w1 = <%=w%>; From 88e3304fbe6d26d92e3a054949476c55b13dfbb5 Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Fri, 21 Apr 2023 05:56:57 +0200 Subject: [PATCH 45/48] Add num additions to r1cs info --- src/r1cs_info.js | 72 +++++++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 71 insertions(+), 1 deletion(-) diff --git a/src/r1cs_info.js b/src/r1cs_info.js index f144fb2f..58769ba5 100644 --- a/src/r1cs_info.js +++ b/src/r1cs_info.js @@ -18,15 +18,28 @@ */ import { Scalar } from "ffjavascript"; -import { readR1cs } from "r1csfile"; +import { readR1cs, readR1csFd } from "r1csfile"; + +import { + getFFlonkAdditionConstraint, + getFFlonkConstantConstraint, + getFFlonkMultiplicationConstraint +} from "./plonk_equation.js"; +import {r1csConstraintProcessor} from "./r1cs_constraint_processor.js"; +import * as binFileUtils from "@iden3/binfileutils"; + +import {readBinFile} from "@iden3/binfileutils"; const bls12381r = Scalar.e("73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001", 16); const bn128r = Scalar.e("21888242871839275222246405745257275088548364400416034343698204186575808495617"); + export default async function r1csInfo(r1csName, logger) { const cir = await readR1cs(r1csName); + const {nAdditions: additions} = await countConstraints(cir.F, r1csName, logger); + if (Scalar.eq(cir.prime, bn128r)) { if (logger) logger.info("Curve: bn-128"); } else if (Scalar.eq(cir.prime, bls12381r)) { @@ -36,6 +49,7 @@ export default async function r1csInfo(r1csName, logger) { } if (logger) logger.info(`# of Wires: ${cir.nVars}`); if (logger) logger.info(`# of Constraints: ${cir.nConstraints}`); + if (logger) logger.info(`# of Additions: ${additions}`); if (logger) logger.info(`# of Private Inputs: ${cir.nPrvInputs}`); if (logger) logger.info(`# of Public Inputs: ${cir.nPubInputs}`); if (logger) logger.info(`# of Labels: ${cir.nLabels}`); @@ -43,3 +57,59 @@ export default async function r1csInfo(r1csName, logger) { return cir; } + +async function countConstraints(Fr, r1csFilename, logger) { + const {fd: fdR1cs, sections: sectionsR1cs} = await readBinFile(r1csFilename, "r1cs", 1, 1 << 22, 1 << 24); + const r1cs = await readR1csFd(fdR1cs, sectionsR1cs, {loadConstraints: false, loadCustomGates: true}); + + // Add all constraints from r1cs file + const r1csProcessor = new r1csConstraintProcessor(Fr, getFFlonkConstantConstraint, getFFlonkAdditionConstraint, getFFlonkMultiplicationConstraint, logger); + + const bR1cs = await binFileUtils.readSection(fdR1cs, sectionsR1cs, 2); + let bR1csPos = 0; + let settings = { + nVars: 0 + }; + + let nConstraints = 0; + let nAdditions = 0; + + for (let i = 0; i < r1cs.nConstraints; i++) { + const [constraints, additions] = r1csProcessor.processR1csConstraint(settings, ...readConstraint()); + + nConstraints += constraints.length; + nAdditions += additions.length; + } + + await fdR1cs.close(); + + return {nConstraints, nAdditions}; + + function readConstraint() { + const c = []; + c[0] = readLC(); + c[1] = readLC(); + c[2] = readLC(); + return c; + } + + function readLC() { + const lc = {}; + + const buffUL32 = bR1cs.slice(bR1csPos, bR1csPos + 4); + bR1csPos += 4; + const buffUL32V = new DataView(buffUL32.buffer); + const nIdx = buffUL32V.getUint32(0, true); + + const buff = bR1cs.slice(bR1csPos, bR1csPos + (4 + r1cs.n8) * nIdx); + bR1csPos += (4 + r1cs.n8) * nIdx; + const buffV = new DataView(buff.buffer); + for (let i = 0; i < nIdx; i++) { + const idx = buffV.getUint32(i * (4 + r1cs.n8), true); + const val = r1cs.F.fromRprLE(buff, i * (4 + r1cs.n8) + 4); + lc[idx] = val; + } + return lc; + } +} + From 5d2b9c15041aa8373184b8767816e1ed266e6882 Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Fri, 21 Apr 2023 04:44:23 +0000 Subject: [PATCH 46/48] add checkAddtions as optional flag --- cli.js | 7 +++--- src/r1cs_info.js | 56 ++++++++++++++++++++++++++++++------------------ 2 files changed, 39 insertions(+), 24 deletions(-) diff --git a/cli.js b/cli.js index 4f9ce292..4eec155e 100755 --- a/cli.js +++ b/cli.js @@ -137,6 +137,7 @@ const commands = [ cmd: "r1cs info [circuit.r1cs]", description: "Print statistiscs of a circuit", alias: ["ri", "info -r|r1cs:circuit.r1cs"], + options: "-checkadditions|ca", action: r1csInfo }, { @@ -389,11 +390,11 @@ function changeExt(fileName, newExt) { // r1cs export circomJSON [circuit.r1cs] [circuit.json] async function r1csInfo(params, options) { const r1csName = params[0] || "circuit.r1cs"; + let checkAdditions = false; - if (options.verbose) Logger.setLogLevel("DEBUG"); - - await r1cs.info(r1csName, logger); + if (options.checkadditions) checkAdditions = true; + await r1cs.info(r1csName, checkAdditions, logger); return 0; } diff --git a/src/r1cs_info.js b/src/r1cs_info.js index 58769ba5..6e160bbf 100644 --- a/src/r1cs_info.js +++ b/src/r1cs_info.js @@ -18,49 +18,61 @@ */ import { Scalar } from "ffjavascript"; -import { readR1cs, readR1csFd } from "r1csfile"; +import { readR1cs, readR1csFd } from "r1csfile"; import { getFFlonkAdditionConstraint, getFFlonkConstantConstraint, getFFlonkMultiplicationConstraint } from "./plonk_equation.js"; -import {r1csConstraintProcessor} from "./r1cs_constraint_processor.js"; +import { r1csConstraintProcessor } from "./r1cs_constraint_processor.js"; import * as binFileUtils from "@iden3/binfileutils"; -import {readBinFile} from "@iden3/binfileutils"; +import { readBinFile } from "@iden3/binfileutils"; const bls12381r = Scalar.e("73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001", 16); const bn128r = Scalar.e("21888242871839275222246405745257275088548364400416034343698204186575808495617"); -export default async function r1csInfo(r1csName, logger) { +export default async function r1csInfo(r1csName, checkAdditions, logger) { + const cir = await readR1cs(r1csName, false); - const cir = await readR1cs(r1csName); - - const {nAdditions: additions} = await countConstraints(cir.F, r1csName, logger); + let nConstraints, nAdditions; + if (checkAdditions) { + ({ nConstraints, nAdditions } = await countConstraints(cir.F, r1csName, logger)); + } + let curve; if (Scalar.eq(cir.prime, bn128r)) { - if (logger) logger.info("Curve: bn-128"); + curve = "Curve: bn-128"; } else if (Scalar.eq(cir.prime, bls12381r)) { - if (logger) logger.info("Curve: bls12-381"); + curve = "Curve: bls12-381"; } else { - if (logger) logger.info(`Unknown Curve. Prime: ${Scalar.toString(cir.prime)}`); + curve = `Unknown. Prime: ${Scalar.toString(cir.prime)}`; + } + + if (logger) { + logger.info("----------------------------"); + logger.info(" R1CS INFO"); + + logger.info(` Curve: ${curve}`); + logger.info(` # of Wires: ${cir.nVars}`); + logger.info(` # of Constraints: ${cir.nConstraints}`); + if (checkAdditions) logger.info(`# of Additions: ${nAdditions}`); + logger.info(` # of Private Inputs: ${cir.nPrvInputs}`); + logger.info(` # of Public Inputs: ${cir.nPubInputs}`); + logger.info(` # of Labels: ${cir.nLabels}`); + logger.info(` # of Outputs: ${cir.nOutputs}`); + + logger.info("----------------------------"); } - if (logger) logger.info(`# of Wires: ${cir.nVars}`); - if (logger) logger.info(`# of Constraints: ${cir.nConstraints}`); - if (logger) logger.info(`# of Additions: ${additions}`); - if (logger) logger.info(`# of Private Inputs: ${cir.nPrvInputs}`); - if (logger) logger.info(`# of Public Inputs: ${cir.nPubInputs}`); - if (logger) logger.info(`# of Labels: ${cir.nLabels}`); - if (logger) logger.info(`# of Outputs: ${cir.nOutputs}`); return cir; } async function countConstraints(Fr, r1csFilename, logger) { - const {fd: fdR1cs, sections: sectionsR1cs} = await readBinFile(r1csFilename, "r1cs", 1, 1 << 22, 1 << 24); - const r1cs = await readR1csFd(fdR1cs, sectionsR1cs, {loadConstraints: false, loadCustomGates: true}); + const { fd: fdR1cs, sections: sectionsR1cs } = await readBinFile(r1csFilename, "r1cs", 1, 1 << 22, 1 << 24); + const r1cs = await readR1csFd(fdR1cs, sectionsR1cs, { loadConstraints: false, loadCustomGates: true }); // Add all constraints from r1cs file const r1csProcessor = new r1csConstraintProcessor(Fr, getFFlonkConstantConstraint, getFFlonkAdditionConstraint, getFFlonkMultiplicationConstraint, logger); @@ -75,15 +87,17 @@ async function countConstraints(Fr, r1csFilename, logger) { let nAdditions = 0; for (let i = 0; i < r1cs.nConstraints; i++) { + if (i !== 0 && i % 100000 === 0) { + if (logger) logger.info(`Processed ${i}/${r1cs.nConstraints} constraints`); + } const [constraints, additions] = r1csProcessor.processR1csConstraint(settings, ...readConstraint()); - nConstraints += constraints.length; nAdditions += additions.length; } await fdR1cs.close(); - return {nConstraints, nAdditions}; + return { nConstraints, nAdditions }; function readConstraint() { const c = []; From f20470dc799b779b424c7c125f6f8cd5a998ac34 Mon Sep 17 00:00:00 2001 From: Xavi Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Fri, 21 Apr 2023 04:52:09 +0000 Subject: [PATCH 47/48] add total constraints in info --- src/r1cs_info.js | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/src/r1cs_info.js b/src/r1cs_info.js index 6e160bbf..106c9a77 100644 --- a/src/r1cs_info.js +++ b/src/r1cs_info.js @@ -58,7 +58,10 @@ export default async function r1csInfo(r1csName, checkAdditions, logger) { logger.info(` Curve: ${curve}`); logger.info(` # of Wires: ${cir.nVars}`); logger.info(` # of Constraints: ${cir.nConstraints}`); - if (checkAdditions) logger.info(`# of Additions: ${nAdditions}`); + if (checkAdditions) { + logger.info(` # of Additions: ${nAdditions}`); + logger.info(` # total constraints: ${cir.nConstraints + nAdditions}`); + } logger.info(` # of Private Inputs: ${cir.nPrvInputs}`); logger.info(` # of Public Inputs: ${cir.nPubInputs}`); logger.info(` # of Labels: ${cir.nLabels}`); From 3f81e1af6fa89b77b9397ac91530634db330b734 Mon Sep 17 00:00:00 2001 From: Xavier Pinsach <10213118+xavi-pinsach@users.noreply.github.com> Date: Thu, 18 May 2023 19:22:18 +0200 Subject: [PATCH 48/48] remove circular dependency --- src/plonk.js | 18 +----------------- src/plonk_constants.js | 16 ++++++++++++++++ src/plonk_prove.js | 2 +- 3 files changed, 18 insertions(+), 18 deletions(-) create mode 100644 src/plonk_constants.js diff --git a/src/plonk.js b/src/plonk.js index ecf7240f..c7f4b92b 100644 --- a/src/plonk.js +++ b/src/plonk.js @@ -17,25 +17,9 @@ along with snarkJS. If not, see . */ -// ZKEY constants -export const ZKEY_PL_NSECTIONS = 13; - -export const ZKEY_PL_HEADER_SECTION = 2; -export const ZKEY_PL_ADDITIONS_SECTION = 3; -export const ZKEY_PL_A_MAP_SECTION = 4; -export const ZKEY_PL_B_MAP_SECTION = 5; -export const ZKEY_PL_C_MAP_SECTION = 6; -export const ZKEY_PL_QM_SECTION = 7; -export const ZKEY_PL_QL_SECTION = 8; -export const ZKEY_PL_QR_SECTION = 9; -export const ZKEY_PL_QO_SECTION = 10; -export const ZKEY_PL_QC_SECTION = 11; -export const ZKEY_PL_SIGMA_SECTION = 12; -export const ZKEY_PL_LAGRANGE_SECTION = 13; -export const ZKEY_PL_PTAU_SECTION = 14; - export {default as setup} from "./plonk_setup.js"; export {default as fullProve} from "./plonk_fullprove.js"; export {default as prove} from "./plonk_prove.js"; export {default as verify} from "./plonk_verify.js"; export {default as exportSolidityCallData} from "./plonk_exportsoliditycalldata.js"; + diff --git a/src/plonk_constants.js b/src/plonk_constants.js new file mode 100644 index 00000000..d9492fec --- /dev/null +++ b/src/plonk_constants.js @@ -0,0 +1,16 @@ +// ZKEY constants +export const ZKEY_PL_NSECTIONS = 13; + +export const ZKEY_PL_HEADER_SECTION = 2; +export const ZKEY_PL_ADDITIONS_SECTION = 3; +export const ZKEY_PL_A_MAP_SECTION = 4; +export const ZKEY_PL_B_MAP_SECTION = 5; +export const ZKEY_PL_C_MAP_SECTION = 6; +export const ZKEY_PL_QM_SECTION = 7; +export const ZKEY_PL_QL_SECTION = 8; +export const ZKEY_PL_QR_SECTION = 9; +export const ZKEY_PL_QO_SECTION = 10; +export const ZKEY_PL_QC_SECTION = 11; +export const ZKEY_PL_SIGMA_SECTION = 12; +export const ZKEY_PL_LAGRANGE_SECTION = 13; +export const ZKEY_PL_PTAU_SECTION = 14; \ No newline at end of file diff --git a/src/plonk_prove.js b/src/plonk_prove.js index 6c3409f7..efb016fe 100644 --- a/src/plonk_prove.js +++ b/src/plonk_prove.js @@ -40,7 +40,7 @@ import { ZKEY_PL_HEADER_SECTION, ZKEY_PL_SIGMA_SECTION, ZKEY_PL_LAGRANGE_SECTION, ZKEY_PL_PTAU_SECTION, -} from "./plonk.js"; +} from "./plonk_constants.js"; import { Polynomial } from "./polynomial/polynomial.js"; import { Evaluations } from "./polynomial/evaluations.js";
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a/test/circuit2/circuit_js/generate_witness.cjs b/test/circuit2/circuit_js/generate_witness.cjs new file mode 100644 index 00000000..08214fbf --- /dev/null +++ b/test/circuit2/circuit_js/generate_witness.cjs @@ -0,0 +1,20 @@ +const wc = require("./witness_calculator.cjs"); +const { readFileSync, writeFile } = require("fs"); + +if (process.argv.length != 5) { + console.log("Usage: node generate_witness.js "); +} else { + const input = JSON.parse(readFileSync(process.argv[3], "utf8")); + + const buffer = readFileSync(process.argv[2]); + wc(buffer).then(async witnessCalculator => { + // const w= await witnessCalculator.calculateWitness(input,0); + // for (let i=0; i< w.length; i++){ + // console.log(w[i]); + // } + const buff= await witnessCalculator.calculateWTNSBin(input,0); + writeFile(process.argv[4], buff, function(err) { + if (err) throw err; + }); + }); +} diff --git a/test/circuit2/circuit_js/witness_calculator.cjs b/test/circuit2/circuit_js/witness_calculator.cjs new file mode 100644 index 00000000..20e6e20a --- /dev/null +++ b/test/circuit2/circuit_js/witness_calculator.cjs @@ -0,0 +1,337 @@ +module.exports = async function builder(code, options) { + + options = options || {}; + + let wasmModule; + try { + wasmModule = await WebAssembly.compile(code); + } catch (err) { + console.log(err); + console.log("\nTry to run circom --c in order to generate c++ code instead\n"); + throw new Error(err); + } + + let wc; + + let errStr = ""; + let msgStr = ""; + + const instance = await WebAssembly.instantiate(wasmModule, { + runtime: { + exceptionHandler : function(code) { + let err; + if (code == 1) { + err = "Signal not found.\n"; + } else if (code == 2) { + err = "Too many signals set.\n"; + } else if (code == 3) { + err = "Signal already set.\n"; + } else if (code == 4) { + err = "Assert Failed.\n"; + } else if (code == 5) { + err = "Not enough memory.\n"; + } else if (code == 6) { + err = "Input signal array access exceeds the size.\n"; + } else { + err = "Unknown error.\n"; + } + throw new Error(err + errStr); + }, + printErrorMessage : function() { + errStr += getMessage() + "\n"; + // console.error(getMessage()); + }, + writeBufferMessage : function() { + const msg = getMessage(); + // Any calls to `log()` will always end with a `\n`, so that's when we print and reset + if (msg === "\n") { + console.log(msgStr); + msgStr = ""; + } else { + // If we've buffered other content, put a space in between the items + if (msgStr !== "") { + msgStr += " " + } + // Then append the message to the message we are creating + msgStr += msg; + } + }, + showSharedRWMemory : function() { + printSharedRWMemory (); + } + + } + }); + + const sanityCheck = + options +// options && +// ( +// options.sanityCheck || +// options.logGetSignal || +// options.logSetSignal || +// options.logStartComponent || +// options.logFinishComponent +// ); + + + wc = new WitnessCalculator(instance, sanityCheck); + return wc; + + function getMessage() { + var message = ""; + var c = instance.exports.getMessageChar(); + while ( c != 0 ) { + message += String.fromCharCode(c); + c = instance.exports.getMessageChar(); + } + return message; + } + + function printSharedRWMemory () { + const shared_rw_memory_size = instance.exports.getFieldNumLen32(); + const arr = new Uint32Array(shared_rw_memory_size); + for (let j=0; j { + const h = fnvHash(k); + const hMSB = parseInt(h.slice(0,8), 16); + const hLSB = parseInt(h.slice(8,16), 16); + const fArr = flatArray(input[k]); + let signalSize = this.instance.exports.getInputSignalSize(hMSB, hLSB); + if (signalSize < 0){ + throw new Error(`Signal ${k} not found\n`); + } + if (fArr.length < signalSize) { + throw new Error(`Not enough values for input signal ${k}\n`); + } + if (fArr.length > signalSize) { + throw new Error(`Too many values for input signal ${k}\n`); + } + for (let i=0; i0) { + res.unshift(0); + i--; + } + } + return res; +} + +function fromArray32(arr) { //returns a BigInt + var res = BigInt(0); + const radix = 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a/test/circuit2/circuit_js/generate_witness.cjs b/test/circuit2/circuit_js/generate_witness.cjs new file mode 100644 index 00000000..08214fbf --- /dev/null +++ b/test/circuit2/circuit_js/generate_witness.cjs @@ -0,0 +1,20 @@ +const wc = require("./witness_calculator.cjs"); +const { readFileSync, writeFile } = require("fs"); + +if (process.argv.length != 5) { + console.log("Usage: node generate_witness.js "); +} else { + const input = JSON.parse(readFileSync(process.argv[3], "utf8")); + + const buffer = readFileSync(process.argv[2]); + wc(buffer).then(async witnessCalculator => { + // const w= await witnessCalculator.calculateWitness(input,0); + // for (let i=0; i< w.length; i++){ + // console.log(w[i]); + // } + const buff= await witnessCalculator.calculateWTNSBin(input,0); + writeFile(process.argv[4], buff, function(err) { + if (err) throw err; + }); + }); +} diff --git a/test/circuit2/circuit_js/witness_calculator.cjs b/test/circuit2/circuit_js/witness_calculator.cjs new file mode 100644 index 00000000..20e6e20a --- /dev/null +++ b/test/circuit2/circuit_js/witness_calculator.cjs @@ -0,0 +1,337 @@ +module.exports = async function builder(code, options) { + + options = options || {}; + + let wasmModule; + try { + wasmModule = await WebAssembly.compile(code); + } catch (err) { + console.log(err); + console.log("\nTry to run circom --c in order to generate c++ code instead\n"); + throw new Error(err); + } + + let wc; + + let errStr = ""; + let msgStr = ""; + + const instance = await WebAssembly.instantiate(wasmModule, { + runtime: { + exceptionHandler : function(code) { + let err; + if (code == 1) { + err = "Signal not found.\n"; + } else if (code == 2) { + err = "Too many signals set.\n"; + } else if (code == 3) { + err = "Signal already set.\n"; + } else if (code == 4) { + err = "Assert Failed.\n"; + } else if (code == 5) { + err = "Not enough memory.\n"; + } else if (code == 6) { + err = "Input signal array access exceeds the size.\n"; + } else { + err = "Unknown error.\n"; + } + throw new Error(err + errStr); + }, + printErrorMessage : function() { + errStr += getMessage() + "\n"; + // console.error(getMessage()); + }, + writeBufferMessage : function() { + const msg = getMessage(); + // Any calls to `log()` will always end with a `\n`, so that's when we print and reset + if (msg === "\n") { + console.log(msgStr); + msgStr = ""; + } else { + // If we've buffered other content, put a space in between the items + if (msgStr !== "") { + msgStr += " " + } + // Then append the message to the message we are creating + msgStr += msg; + } + }, + showSharedRWMemory : function() { + printSharedRWMemory (); + } + + } + }); + + const sanityCheck = + options +// options && +// ( +// options.sanityCheck || +// options.logGetSignal || +// options.logSetSignal || +// options.logStartComponent || +// options.logFinishComponent +// ); + + + wc = new WitnessCalculator(instance, sanityCheck); + return wc; + + function getMessage() { + var message = ""; + var c = instance.exports.getMessageChar(); + while ( c != 0 ) { + message += String.fromCharCode(c); + c = instance.exports.getMessageChar(); + } + return message; + } + + function printSharedRWMemory () { + const shared_rw_memory_size = instance.exports.getFieldNumLen32(); + const arr = new Uint32Array(shared_rw_memory_size); + for (let j=0; j { + const h = fnvHash(k); + const hMSB = parseInt(h.slice(0,8), 16); + const hLSB = parseInt(h.slice(8,16), 16); + const fArr = flatArray(input[k]); + let signalSize = this.instance.exports.getInputSignalSize(hMSB, hLSB); + if (signalSize < 0){ + throw new Error(`Signal ${k} not found\n`); + } + if (fArr.length < signalSize) { + throw new Error(`Not enough values for input signal ${k}\n`); + } + if (fArr.length > signalSize) { + throw new Error(`Too many values for input signal ${k}\n`); + } + for (let i=0; i0) { + res.unshift(0); + i--; + } + } + return res; +} + +function fromArray32(arr) { //returns a BigInt + var res = BigInt(0); + const radix = 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