scrypt.c

/*-
 * Copyright 2009 Colin Percival, 2011 ArtForz
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * This file was originally written by Colin Percival as part of the Tarsnap
 * online backup system.
 */

#include "scrypt.h"
#include <stdlib.h>
#include <stdint.h>
#include <string.h>

static __inline uint32_t
be32dec(const void *pp)
{
	const uint8_t *p = (uint8_t const *)pp;

	return ((uint32_t)(p[3]) + ((uint32_t)(p[2]) << 8) +
	    ((uint32_t)(p[1]) << 16) + ((uint32_t)(p[0]) << 24));
}

static __inline void
be32enc(void *pp, uint32_t x)
{
	uint8_t * p = (uint8_t *)pp;

	p[3] = x & 0xff;
	p[2] = (x >> 8) & 0xff;
	p[1] = (x >> 16) & 0xff;
	p[0] = (x >> 24) & 0xff;
}

static __inline uint32_t
le32dec(const void *pp)
{
	const uint8_t *p = (uint8_t const *)pp;

	return ((uint32_t)(p[0]) + ((uint32_t)(p[1]) << 8) +
	    ((uint32_t)(p[2]) << 16) + ((uint32_t)(p[3]) << 24));
}

static __inline void
le32enc(void *pp, uint32_t x)
{
	uint8_t * p = (uint8_t *)pp;

	p[0] = x & 0xff;
	p[1] = (x >> 8) & 0xff;
	p[2] = (x >> 16) & 0xff;
	p[3] = (x >> 24) & 0xff;
}


typedef struct SHA256Context {
	uint32_t state[8];
	uint32_t count[2];
	unsigned char buf[64];
} SHA256_CTX;

typedef struct HMAC_SHA256Context {
	SHA256_CTX ictx;
	SHA256_CTX octx;
} HMAC_SHA256_CTX;

/*
 * Encode a length len/4 vector of (uint32_t) into a length len vector of
 * (unsigned char) in big-endian form.  Assumes len is a multiple of 4.
 */
static void
be32enc_vect(unsigned char *dst, const uint32_t *src, size_t len)
{
	size_t i;

	for (i = 0; i < len / 4; i++)
		be32enc(dst + i * 4, src[i]);
}

/*
 * Decode a big-endian length len vector of (unsigned char) into a length
 * len/4 vector of (uint32_t).  Assumes len is a multiple of 4.
 */
static void
be32dec_vect(uint32_t *dst, const unsigned char *src, size_t len)
{
	size_t i;

	for (i = 0; i < len / 4; i++)
		dst[i] = be32dec(src + i * 4);
}

/* Elementary functions used by SHA256 */
#define Ch(x, y, z)	((x & (y ^ z)) ^ z)
#define Maj(x, y, z)	((x & (y | z)) | (y & z))
#define SHR(x, n)	(x >> n)
#define ROTR(x, n)	((x >> n) | (x << (32 - n)))
#define S0(x)		(ROTR(x, 2) ^ ROTR(x, 13) ^ ROTR(x, 22))
#define S1(x)		(ROTR(x, 6) ^ ROTR(x, 11) ^ ROTR(x, 25))
#define s0(x)		(ROTR(x, 7) ^ ROTR(x, 18) ^ SHR(x, 3))
#define s1(x)		(ROTR(x, 17) ^ ROTR(x, 19) ^ SHR(x, 10))

/* SHA256 round function */
#define RND(a, b, c, d, e, f, g, h, k)			\
	t0 = h + S1(e) + Ch(e, f, g) + k;		\
	t1 = S0(a) + Maj(a, b, c);			\
	d += t0;					\
	h  = t0 + t1;

/* Adjusted round function for rotating state */
#define RNDr(S, W, i, k)			\
	RND(S[(64 - i) % 8], S[(65 - i) % 8],	\
	    S[(66 - i) % 8], S[(67 - i) % 8],	\
	    S[(68 - i) % 8], S[(69 - i) % 8],	\
	    S[(70 - i) % 8], S[(71 - i) % 8],	\
	    W[i] + k)

/*
 * SHA256 block compression function.  The 256-bit state is transformed via
 * the 512-bit input block to produce a new state.
 */
static void
SHA256_Transform(uint32_t * state, const unsigned char block[64])
{
	uint32_t W[64];
	uint32_t S[8];
	uint32_t t0, t1;
	int i;

	/* 1. Prepare message schedule W. */
	be32dec_vect(W, block, 64);
	for (i = 16; i < 64; i++)
		W[i] = s1(W[i - 2]) + W[i - 7] + s0(W[i - 15]) + W[i - 16];

	/* 2. Initialize working variables. */
	memcpy(S, state, 32);

	/* 3. Mix. */
	RNDr(S, W, 0, 0x428a2f98);
	RNDr(S, W, 1, 0x71374491);
	RNDr(S, W, 2, 0xb5c0fbcf);
	RNDr(S, W, 3, 0xe9b5dba5);
	RNDr(S, W, 4, 0x3956c25b);
	RNDr(S, W, 5, 0x59f111f1);
	RNDr(S, W, 6, 0x923f82a4);
	RNDr(S, W, 7, 0xab1c5ed5);
	RNDr(S, W, 8, 0xd807aa98);
	RNDr(S, W, 9, 0x12835b01);
	RNDr(S, W, 10, 0x243185be);
	RNDr(S, W, 11, 0x550c7dc3);
	RNDr(S, W, 12, 0x72be5d74);
	RNDr(S, W, 13, 0x80deb1fe);
	RNDr(S, W, 14, 0x9bdc06a7);
	RNDr(S, W, 15, 0xc19bf174);
	RNDr(S, W, 16, 0xe49b69c1);
	RNDr(S, W, 17, 0xefbe4786);
	RNDr(S, W, 18, 0x0fc19dc6);
	RNDr(S, W, 19, 0x240ca1cc);
	RNDr(S, W, 20, 0x2de92c6f);
	RNDr(S, W, 21, 0x4a7484aa);
	RNDr(S, W, 22, 0x5cb0a9dc);
	RNDr(S, W, 23, 0x76f988da);
	RNDr(S, W, 24, 0x983e5152);
	RNDr(S, W, 25, 0xa831c66d);
	RNDr(S, W, 26, 0xb00327c8);
	RNDr(S, W, 27, 0xbf597fc7);
	RNDr(S, W, 28, 0xc6e00bf3);
	RNDr(S, W, 29, 0xd5a79147);
	RNDr(S, W, 30, 0x06ca6351);
	RNDr(S, W, 31, 0x14292967);
	RNDr(S, W, 32, 0x27b70a85);
	RNDr(S, W, 33, 0x2e1b2138);
	RNDr(S, W, 34, 0x4d2c6dfc);
	RNDr(S, W, 35, 0x53380d13);
	RNDr(S, W, 36, 0x650a7354);
	RNDr(S, W, 37, 0x766a0abb);
	RNDr(S, W, 38, 0x81c2c92e);
	RNDr(S, W, 39, 0x92722c85);
	RNDr(S, W, 40, 0xa2bfe8a1);
	RNDr(S, W, 41, 0xa81a664b);
	RNDr(S, W, 42, 0xc24b8b70);
	RNDr(S, W, 43, 0xc76c51a3);
	RNDr(S, W, 44, 0xd192e819);
	RNDr(S, W, 45, 0xd6990624);
	RNDr(S, W, 46, 0xf40e3585);
	RNDr(S, W, 47, 0x106aa070);
	RNDr(S, W, 48, 0x19a4c116);
	RNDr(S, W, 49, 0x1e376c08);
	RNDr(S, W, 50, 0x2748774c);
	RNDr(S, W, 51, 0x34b0bcb5);
	RNDr(S, W, 52, 0x391c0cb3);
	RNDr(S, W, 53, 0x4ed8aa4a);
	RNDr(S, W, 54, 0x5b9cca4f);
	RNDr(S, W, 55, 0x682e6ff3);
	RNDr(S, W, 56, 0x748f82ee);
	RNDr(S, W, 57, 0x78a5636f);
	RNDr(S, W, 58, 0x84c87814);
	RNDr(S, W, 59, 0x8cc70208);
	RNDr(S, W, 60, 0x90befffa);
	RNDr(S, W, 61, 0xa4506ceb);
	RNDr(S, W, 62, 0xbef9a3f7);
	RNDr(S, W, 63, 0xc67178f2);

	/* 4. Mix local working variables into global state */
	for (i = 0; i < 8; i++)
		state[i] += S[i];

	/* Clean the stack. */
	memset(W, 0, 256);
	memset(S, 0, 32);
	t0 = t1 = 0;
}

static unsigned char PAD[64] = {
	0x80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
};

/* SHA-256 initialization.  Begins a SHA-256 operation. */
static void
SHA256_Init(SHA256_CTX * ctx)
{

	/* Zero bits processed so far */
	ctx->count[0] = ctx->count[1] = 0;

	/* Magic initialization constants */
	ctx->state[0] = 0x6A09E667;
	ctx->state[1] = 0xBB67AE85;
	ctx->state[2] = 0x3C6EF372;
	ctx->state[3] = 0xA54FF53A;
	ctx->state[4] = 0x510E527F;
	ctx->state[5] = 0x9B05688C;
	ctx->state[6] = 0x1F83D9AB;
	ctx->state[7] = 0x5BE0CD19;
}

/* Add bytes into the hash */
static void
SHA256_Update(SHA256_CTX * ctx, const void *in, size_t len)
{
	uint32_t bitlen[2];
	uint32_t r;
	const unsigned char *src = in;

	/* Number of bytes left in the buffer from previous updates */
	r = (ctx->count[1] >> 3) & 0x3f;

	/* Convert the length into a number of bits */
	bitlen[1] = ((uint32_t)len) << 3;
	bitlen[0] = (uint32_t)(len >> 29);

	/* Update number of bits */
	if ((ctx->count[1] += bitlen[1]) < bitlen[1])
		ctx->count[0]++;
	ctx->count[0] += bitlen[0];

	/* Handle the case where we don't need to perform any transforms */
	if (len < 64 - r) {
		memcpy(&ctx->buf[r], src, len);
		return;
	}

	/* Finish the current block */
	memcpy(&ctx->buf[r], src, 64 - r);
	SHA256_Transform(ctx->state, ctx->buf);
	src += 64 - r;
	len -= 64 - r;

	/* Perform complete blocks */
	while (len >= 64) {
		SHA256_Transform(ctx->state, src);
		src += 64;
		len -= 64;
	}

	/* Copy left over data into buffer */
	memcpy(ctx->buf, src, len);
}

/* Add padding and terminating bit-count. */
static void
SHA256_Pad(SHA256_CTX * ctx)
{
	unsigned char len[8];
	uint32_t r, plen;

	/*
	 * Convert length to a vector of bytes -- we do this now rather
	 * than later because the length will change after we pad.
	 */
	be32enc_vect(len, ctx->count, 8);

	/* Add 1--64 bytes so that the resulting length is 56 mod 64 */
	r = (ctx->count[1] >> 3) & 0x3f;
	plen = (r < 56) ? (56 - r) : (120 - r);
	SHA256_Update(ctx, PAD, (size_t)plen);

	/* Add the terminating bit-count */
	SHA256_Update(ctx, len, 8);
}

/*
 * SHA-256 finalization.  Pads the input data, exports the hash value,
 * and clears the context state.
 */
static void
SHA256_Final(unsigned char digest[32], SHA256_CTX * ctx)
{

	/* Add padding */
	SHA256_Pad(ctx);

	/* Write the hash */
	be32enc_vect(digest, ctx->state, 32);

	/* Clear the context state */
	memset((void *)ctx, 0, sizeof(*ctx));
}

/* Initialize an HMAC-SHA256 operation with the given key. */
static void
HMAC_SHA256_Init(HMAC_SHA256_CTX * ctx, const void * _K, size_t Klen)
{
	unsigned char pad[64];
	unsigned char khash[32];
	const unsigned char * K = _K;
	size_t i;

	/* If Klen > 64, the key is really SHA256(K). */
	if (Klen > 64) {
		SHA256_Init(&ctx->ictx);
		SHA256_Update(&ctx->ictx, K, Klen);
		SHA256_Final(khash, &ctx->ictx);
		K = khash;
		Klen = 32;
	}

	/* Inner SHA256 operation is SHA256(K xor [block of 0x36] || data). */
	SHA256_Init(&ctx->ictx);
	memset(pad, 0x36, 64);
	for (i = 0; i < Klen; i++)
		pad[i] ^= K[i];
	SHA256_Update(&ctx->ictx, pad, 64);

	/* Outer SHA256 operation is SHA256(K xor [block of 0x5c] || hash). */
	SHA256_Init(&ctx->octx);
	memset(pad, 0x5c, 64);
	for (i = 0; i < Klen; i++)
		pad[i] ^= K[i];
	SHA256_Update(&ctx->octx, pad, 64);

	/* Clean the stack. */
	memset(khash, 0, 32);
}

/* Add bytes to the HMAC-SHA256 operation. */
static void
HMAC_SHA256_Update(HMAC_SHA256_CTX * ctx, const void *in, size_t len)
{

	/* Feed data to the inner SHA256 operation. */
	SHA256_Update(&ctx->ictx, in, len);
}

/* Finish an HMAC-SHA256 operation. */
static void
HMAC_SHA256_Final(unsigned char digest[32], HMAC_SHA256_CTX * ctx)
{
	unsigned char ihash[32];

	/* Finish the inner SHA256 operation. */
	SHA256_Final(ihash, &ctx->ictx);

	/* Feed the inner hash to the outer SHA256 operation. */
	SHA256_Update(&ctx->octx, ihash, 32);

	/* Finish the outer SHA256 operation. */
	SHA256_Final(digest, &ctx->octx);

	/* Clean the stack. */
	memset(ihash, 0, 32);
}

/**
 * PBKDF2_SHA256(passwd, passwdlen, salt, saltlen, c, buf, dkLen):
 * Compute PBKDF2(passwd, salt, c, dkLen) using HMAC-SHA256 as the PRF, and
 * write the output to buf.  The value dkLen must be at most 32 * (2^32 - 1).
 */
static void
PBKDF2_SHA256(const uint8_t * passwd, size_t passwdlen, const uint8_t * salt,
    size_t saltlen, uint64_t c, uint8_t * buf, size_t dkLen)
{
	HMAC_SHA256_CTX PShctx, hctx;
	size_t i;
	uint8_t ivec[4];
	uint8_t U[32];
	uint8_t T[32];
	uint64_t j;
	int k;
	size_t clen;

	/* Compute HMAC state after processing P and S. */
	HMAC_SHA256_Init(&PShctx, passwd, passwdlen);
	HMAC_SHA256_Update(&PShctx, salt, saltlen);

	/* Iterate through the blocks. */
	for (i = 0; i * 32 < dkLen; i++) {
		/* Generate INT(i + 1). */
		be32enc(ivec, (uint32_t)(i + 1));

		/* Compute U_1 = PRF(P, S || INT(i)). */
		memcpy(&hctx, &PShctx, sizeof(HMAC_SHA256_CTX));
		HMAC_SHA256_Update(&hctx, ivec, 4);
		HMAC_SHA256_Final(U, &hctx);

		/* T_i = U_1 ... */
		memcpy(T, U, 32);

		for (j = 2; j <= c; j++) {
			/* Compute U_j. */
			HMAC_SHA256_Init(&hctx, passwd, passwdlen);
			HMAC_SHA256_Update(&hctx, U, 32);
			HMAC_SHA256_Final(U, &hctx);

			/* ... xor U_j ... */
			for (k = 0; k < 32; k++)
				T[k] ^= U[k];
		}

		/* Copy as many bytes as necessary into buf. */
		clen = dkLen - i * 32;
		if (clen > 32)
			clen = 32;
		memcpy(&buf[i * 32], T, clen);
	}

	/* Clean PShctx, since we never called _Final on it. */
	memset(&PShctx, 0, sizeof(HMAC_SHA256_CTX));
}


static void blkcpy(void *, void *, size_t);
static void blkxor(void *, void *, size_t);
static void salsa20_8(uint32_t[16]);
static void blockmix_salsa8(uint32_t *, uint32_t *, uint32_t *, size_t);
static uint64_t integerify(void *, size_t);
static void smix(uint8_t *, size_t, uint64_t, uint32_t *, uint32_t *);

static void
blkcpy(void * dest, void * src, size_t len)
{
	size_t * D = dest;
	size_t * S = src;
	size_t L = len / sizeof(size_t);
	size_t i;

	for (i = 0; i < L; i++)
		D[i] = S[i];
}

static void
blkxor(void * dest, void * src, size_t len)
{
	size_t * D = dest;
	size_t * S = src;
	size_t L = len / sizeof(size_t);
	size_t i;

	for (i = 0; i < L; i++)
		D[i] ^= S[i];
}

/**
 * salsa20_8(B):
 * Apply the salsa20/8 core to the provided block.
 */
static void
salsa20_8(uint32_t B[16])
{
	uint32_t x[16];
	size_t i;

	blkcpy(x, B, 64);
	for (i = 0; i < 8; i += 2) {
#define R(a,b) (((a) << (b)) | ((a) >> (32 - (b))))
		/* Operate on columns. */
		x[ 4] ^= R(x[ 0]+x[12], 7);  x[ 8] ^= R(x[ 4]+x[ 0], 9);
		x[12] ^= R(x[ 8]+x[ 4],13);  x[ 0] ^= R(x[12]+x[ 8],18);

		x[ 9] ^= R(x[ 5]+x[ 1], 7);  x[13] ^= R(x[ 9]+x[ 5], 9);
		x[ 1] ^= R(x[13]+x[ 9],13);  x[ 5] ^= R(x[ 1]+x[13],18);

		x[14] ^= R(x[10]+x[ 6], 7);  x[ 2] ^= R(x[14]+x[10], 9);
		x[ 6] ^= R(x[ 2]+x[14],13);  x[10] ^= R(x[ 6]+x[ 2],18);

		x[ 3] ^= R(x[15]+x[11], 7);  x[ 7] ^= R(x[ 3]+x[15], 9);
		x[11] ^= R(x[ 7]+x[ 3],13);  x[15] ^= R(x[11]+x[ 7],18);

		/* Operate on rows. */
		x[ 1] ^= R(x[ 0]+x[ 3], 7);  x[ 2] ^= R(x[ 1]+x[ 0], 9);
		x[ 3] ^= R(x[ 2]+x[ 1],13);  x[ 0] ^= R(x[ 3]+x[ 2],18);

		x[ 6] ^= R(x[ 5]+x[ 4], 7);  x[ 7] ^= R(x[ 6]+x[ 5], 9);
		x[ 4] ^= R(x[ 7]+x[ 6],13);  x[ 5] ^= R(x[ 4]+x[ 7],18);

		x[11] ^= R(x[10]+x[ 9], 7);  x[ 8] ^= R(x[11]+x[10], 9);
		x[ 9] ^= R(x[ 8]+x[11],13);  x[10] ^= R(x[ 9]+x[ 8],18);

		x[12] ^= R(x[15]+x[14], 7);  x[13] ^= R(x[12]+x[15], 9);
		x[14] ^= R(x[13]+x[12],13);  x[15] ^= R(x[14]+x[13],18);
#undef R
	}
	for (i = 0; i < 16; i++)
		B[i] += x[i];
}

/**
 * blockmix_salsa8(Bin, Bout, X, r):
 * Compute Bout = BlockMix_{salsa20/8, r}(Bin).  The input Bin must be 128r
 * bytes in length; the output Bout must also be the same size.  The
 * temporary space X must be 64 bytes.
 */
static void
blockmix_salsa8(uint32_t * Bin, uint32_t * Bout, uint32_t * X, size_t r)
{
	size_t i;

	/* 1: X <-- B_{2r - 1} */
	blkcpy(X, &Bin[(2 * r - 1) * 16], 64);

	/* 2: for i = 0 to 2r - 1 do */
	for (i = 0; i < 2 * r; i += 2) {
		/* 3: X <-- H(X \xor B_i) */
		blkxor(X, &Bin[i * 16], 64);
		salsa20_8(X);

		/* 4: Y_i <-- X */
		/* 6: B' <-- (Y_0, Y_2 ... Y_{2r-2}, Y_1, Y_3 ... Y_{2r-1}) */
		blkcpy(&Bout[i * 8], X, 64);

		/* 3: X <-- H(X \xor B_i) */
		blkxor(X, &Bin[i * 16 + 16], 64);
		salsa20_8(X);

		/* 4: Y_i <-- X */
		/* 6: B' <-- (Y_0, Y_2 ... Y_{2r-2}, Y_1, Y_3 ... Y_{2r-1}) */
		blkcpy(&Bout[i * 8 + r * 16], X, 64);
	}
}

/**
 * integerify(B, r):
 * Return the result of parsing B_{2r-1} as a little-endian integer.
 */
static uint64_t
integerify(void * B, size_t r)
{
	uint32_t * X = (void *)((uintptr_t)(B) + (2 * r - 1) * 64);

	return (((uint64_t)(X[1]) << 32) + X[0]);
}

/**
 * smix(B, r, N, V, XY):
 * Compute B = SMix_r(B, N).  The input B must be 128r bytes in length;
 * the temporary storage V must be 128rN bytes in length; the temporary
 * storage XY must be 256r + 64 bytes in length.  The value N must be a
 * power of 2 greater than 1.  The arrays B, V, and XY must be aligned to a
 * multiple of 64 bytes.
 */
static void
smix(uint8_t * B, size_t r, uint64_t N, uint32_t * V, uint32_t * XY)
{
	uint32_t * X = XY;
	uint32_t * Y = &XY[32 * r];
	uint32_t * Z = &XY[64 * r];
	uint64_t i;
	uint64_t j;
	size_t k;

	/* 1: X <-- B */
	for (k = 0; k < 32 * r; k++)
		X[k] = le32dec(&B[4 * k]);

	/* 2: for i = 0 to N - 1 do */
	for (i = 0; i < N; i += 2) {
		/* 3: V_i <-- X */
		blkcpy(&V[i * (32 * r)], X, 128 * r);

		/* 4: X <-- H(X) */
		blockmix_salsa8(X, Y, Z, r);

		/* 3: V_i <-- X */
		blkcpy(&V[(i + 1) * (32 * r)], Y, 128 * r);

		/* 4: X <-- H(X) */
		blockmix_salsa8(Y, X, Z, r);
	}

	/* 6: for i = 0 to N - 1 do */
	for (i = 0; i < N; i += 2) {
		/* 7: j <-- Integerify(X) mod N */
		j = integerify(X, r) & (N - 1);

		/* 8: X <-- H(X \xor V_j) */
		blkxor(X, &V[j * (32 * r)], 128 * r);
		blockmix_salsa8(X, Y, Z, r);

		/* 7: j <-- Integerify(X) mod N */
		j = integerify(Y, r) & (N - 1);

		/* 8: X <-- H(X \xor V_j) */
		blkxor(Y, &V[j * (32 * r)], 128 * r);
		blockmix_salsa8(Y, X, Z, r);
	}

	/* 10: B' <-- X */
	for (k = 0; k < 32 * r; k++)
		le32enc(&B[4 * k], X[k]);
}

/* cpu and memory intensive function to transform a 80 byte buffer into a 32 byte output
   scratchpad size needs to be at least 63 + (128 * r * p) + (256 * r + 64) + (128 * r * N) bytes
 */
void scrypt_1024_1_1_256_sp(const char* input, char* output, char* scratchpad)
{
	uint8_t * B;
	uint32_t * V;
	uint32_t * XY;
	uint32_t i;

	const uint32_t N = 1024;
	const uint32_t r = 1;
	const uint32_t p = 1;

	B = (uint8_t *)(((uintptr_t)(scratchpad) + 63) & ~ (uintptr_t)(63));
	XY = (uint32_t *)(B + (128 * r * p));
	V = (uint32_t *)(B + (128 * r * p) + (256 * r + 64));

	/* 1: (B_0 ... B_{p-1}) <-- PBKDF2(P, S, 1, p * MFLen) */
	PBKDF2_SHA256((const uint8_t*)input, 80, (const uint8_t*)input, 80, 1, B, p * 128 * r);

	/* 2: for i = 0 to p - 1 do */
	for (i = 0; i < p; i++) {
		/* 3: B_i <-- MF(B_i, N) */
		smix(&B[i * 128 * r], r, N, V, XY);
	}

	/* 5: DK <-- PBKDF2(P, B, 1, dkLen) */
	PBKDF2_SHA256((const uint8_t*)input, 80, B, p * 128 * r, 1, (uint8_t*)output, 32);
}

void scrypt_1024_1_1_256(const char* input, char* output)
{
	char scratchpad[131583];
	scrypt_1024_1_1_256_sp(input, output, scratchpad);
}