ICICLE

Icicle is a library for ZK acceleration using CUDA-enabled GPUs.

Background

Zero Knowledge Proofs (ZKPs) are considered one of the greatest achievements of modern cryptography. Accordingly, ZKPs are expected to disrupt a number of industries and will usher in an era of trustless and privacy preserving services and infrastructure.

If we want ZK hardware today we have FPGAs or GPUs which are relatively inexpensive. However, the biggest selling point of GPUs is the software; we talk in particular about CUDA, which makes it easy to write code running on Nvidia GPUs, taking advantage of their highly parallel architecture. Together with the widespread availability of these devices, if we can get GPUs to work on ZK workloads, then we have made a giant step towards accessible and efficient ZK provers.

Zero Knowledge on GPU

ICICLE is a CUDA implementation of general functions widely used in ZKP. ICICLE currently provides support for MSM, NTT, and ECNTT, with plans to support Hash functions soon.

Supported primitives

• Fields
  • Scalars
  • Points
    • Projective: {x, y, z}
    • Affine: {x, y}
• Curves
  • BLS12-381
  • BLS12-377
  • BN254
  • BW6-671

Build and usage

Prerequisites

• NVCC (version 12.0 or newer)
• cmake 3.18 and above
• follow these instructions

Steps

1. Define or select a curve for your application; we've provided a template for defining a curve
2. Include the curve in curve_config.cuh
3. Now you can build the ICICLE library using nvcc

mkdir -p build
nvcc -o build/<binary_name> ./icicle/curves/index.cu -lib -arch=native

Testing the CUDA code

We are using googletest library for testing. To build and run the test suite for finite field and elliptic curve arithmetic, run from the icicle folder:

mkdir -p build
cmake -S . -B build
cmake --build build
cd build && ctest

NOTE: If you are using cmake versions < 3.24 add -DCUDA_ARCH=<target_cumpute_arch> to the command cmake -S . -B build

Rust Bindings

For convenience, we also provide rust bindings to the ICICLE library for the following primitives:

• MSM
• NTT
  • Forward NTT
  • Inverse NTT
• ECNTT
  • Forward ECNTT
  • Inverse NTT
• Scalar Vector Multiplication
• Point Vector Multiplication

A custom build script is used to compile and link the ICICLE library. The environement variable ARCH_TYPE is used to determine which GPU type the library should be compiled for and it defaults to native when it is not set allowing the compiler to detect the installed GPU type.

NOTE: A GPU must be detectable and therefore installed if the ARCH_TYPE is not set.

Once you have your parameters set, run:

cargo build --release

You'll find a release ready library at target/release/libicicle_utils.rlib.

To benchmark and test the functionality available in RUST, run:

cargo bench
cargo test -- --test-threads=1

The flag --test-threads=1 is needed because currently some tests might interfere with one another inside the GPU.

Example Usage

An example of using the Rust bindings library can be found in our fast-danksharding implementation

Supporting Additional Curves

Supporting additional curves can be done as follows:

Create a JSON file with the curve parameters. The curve is defined by the following parameters:

• curve_name - e.g. bls12_381.
• modulus_p - scalar field modulus (in decimal).
• bit_count_p - number of bits needed to represent modulus_p .
• limb_p - number of (32-bit) limbs needed to represent modulus_p (rounded up).
• ntt_size - log of the maximal size subgroup of the scalar field.
• modulus_q - base field modulus (in decimal).
• bit_count_q - number of bits needed to represent modulus_q .
• limb_q - number of (32-bit) limbs needed to represent modulus_q (rounded up).
• weierstrass_b - b of the curve in Weierstrauss form.
• weierstrass_b_g2_re - real part of the b value in of the g2 curve in Weierstrass form.
• weierstrass_b_g2_im - imaginary part of the b value in of the g2 curve in Weierstrass form.
• gen_x - x coordinate of a generator element for the curve.
• gen_y - y coordinate of a generator element for the curve.
• gen_x_re - real part of the x coordinate of generator element for the g2 curve.
• gen_x_im - imaginary part of the x coordinate of generator element for the g2 curve.
• gen_y_re - real part of the y coordinate of generator element for the g2 curve.
• gen_y_im - imaginary part of the y coordinate of generator element for the g2 curve.
• nonresidue - nonresidue, or i^2, or u^2 - square of the element that generates quadratic extension field of the base field.

Here's an example for BLS12-381.

{
    "curve_name" : "bls12_381", 
    "modulus_p" : 52435875175126190479447740508185965837690552500527637822603658699938581184513,
    "bit_count_p" : 255,
    "limb_p" :  8,
    "ntt_size" : 32,
    "modulus_q" : 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787,
    "bit_count_q" : 381,
    "limb_q" : 12,
    "weierstrass_b" : 4,
    "weierstrass_b_g2_re" : 4,
    "weierstrass_b_g2_im" : 4,
    "gen_x" : 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507,
    "gen_y" : 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569,
    "gen_x_re" : 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160,
    "gen_x_im" : 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758,
    "gen_y_re" : 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905,
    "gen_y_im" : 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582,
    "nonresidue" : -1
}

Save the parameters JSON file under the curve_parameters directory.

Then run the Python script new_curve_script.py from the root folder:

python3 ./curve_parameters/new_curve_script.py ./curve_parameters/bls12_381.json

The script does the following:

• Creates a folder in icicle/curves with the curve name, which contains all of the files needed for the supported operations in cuda.
• Adds the curve's exported operations to icicle/curves/index.cu.
• Creates a file with the curve name in src/curves with the relevant objects for the curve.
• Creates a test file with the curve name in src.

Testing the new curve could be done by running the tests in tests_curve_name (e.g. tests_bls12_381).

Docker

We offer a simple Docker container so you can simply run ICICLE without settig everything up locally.

docker build -t <name_of_your_choice> .
docker run --gpus all -it <name_of_your_choice> /bin/bash

Contributions

Join our Discord Server and find us on the icicle channel. We will be happy to work together to support your use case and talk features, bugs and design.

Development Contributions

If you are changing code, please make sure to change your git hooks path to the repo's hooks directory by running the following command:

git config core.hooksPath ./scripts/hooks

This will ensure our custom hooks are run and will make it easier to follow our coding guidelines.

Hall of Fame

• Robik, for his on-going support and mentorship
• liuxiao, for being a top notch bug smasher

Help & Support

For help and support talk to our devs in our discord channel "ICICLE"

License

ICICLE is distributed under the terms of the MIT License.

See LICENSE-MIT for details.