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Diffstat (limited to 'src/3p/monocypher/monocypher.c')
| -rw-r--r-- | src/3p/monocypher/monocypher.c | 2958 |
1 files changed, 2958 insertions, 0 deletions
diff --git a/src/3p/monocypher/monocypher.c b/src/3p/monocypher/monocypher.c new file mode 100644 index 0000000..bd73306 --- /dev/null +++ b/src/3p/monocypher/monocypher.c @@ -0,0 +1,2958 @@ +// Monocypher version 3.1.3 +// +// This file is dual-licensed. Choose whichever licence you want from +// the two licences listed below. +// +// The first licence is a regular 2-clause BSD licence. The second licence +// is the CC-0 from Creative Commons. It is intended to release Monocypher +// to the public domain. The BSD licence serves as a fallback option. +// +// SPDX-License-Identifier: BSD-2-Clause OR CC0-1.0 +// +// ------------------------------------------------------------------------ +// +// Copyright (c) 2017-2020, Loup Vaillant +// 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 COPYRIGHT HOLDERS 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 COPYRIGHT +// HOLDER 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. +// +// ------------------------------------------------------------------------ +// +// Written in 2017-2020 by Loup Vaillant +// +// To the extent possible under law, the author(s) have dedicated all copyright +// and related neighboring rights to this software to the public domain +// worldwide. This software is distributed without any warranty. +// +// You should have received a copy of the CC0 Public Domain Dedication along +// with this software. If not, see +// <https://creativecommons.org/publicdomain/zero/1.0/> + +#include "monocypher.h" + +#ifdef MONOCYPHER_CPP_NAMESPACE +namespace MONOCYPHER_CPP_NAMESPACE { +#endif + +///////////////// +/// Utilities /// +///////////////// +#define FOR_T(type, i, start, end) for (type i = (start); i < (end); i++) +#define FOR(i, start, end) FOR_T(size_t, i, start, end) +#define COPY(dst, src, size) FOR(i__, 0, size) (dst)[i__] = (src)[i__] +#define ZERO(buf, size) FOR(i__, 0, size) (buf)[i__] = 0 +#define WIPE_CTX(ctx) crypto_wipe(ctx , sizeof(*(ctx))) +#define WIPE_BUFFER(buffer) crypto_wipe(buffer, sizeof(buffer)) +#define MIN(a, b) ((a) <= (b) ? (a) : (b)) +#define MAX(a, b) ((a) >= (b) ? (a) : (b)) + +typedef int8_t i8; +typedef uint8_t u8; +typedef int16_t i16; +typedef uint32_t u32; +typedef int32_t i32; +typedef int64_t i64; +typedef uint64_t u64; + +static const u8 zero[128] = {0}; + +// returns the smallest positive integer y such that +// (x + y) % pow_2 == 0 +// Basically, it's how many bytes we need to add to "align" x. +// Only works when pow_2 is a power of 2. +// Note: we use ~x+1 instead of -x to avoid compiler warnings +static size_t align(size_t x, size_t pow_2) +{ + return (~x + 1) & (pow_2 - 1); +} + +static u32 load24_le(const u8 s[3]) +{ + return (u32)s[0] + | ((u32)s[1] << 8) + | ((u32)s[2] << 16); +} + +static u32 load32_le(const u8 s[4]) +{ + return (u32)s[0] + | ((u32)s[1] << 8) + | ((u32)s[2] << 16) + | ((u32)s[3] << 24); +} + +static u64 load64_le(const u8 s[8]) +{ + return load32_le(s) | ((u64)load32_le(s+4) << 32); +} + +static void store32_le(u8 out[4], u32 in) +{ + out[0] = in & 0xff; + out[1] = (in >> 8) & 0xff; + out[2] = (in >> 16) & 0xff; + out[3] = (in >> 24) & 0xff; +} + +static void store64_le(u8 out[8], u64 in) +{ + store32_le(out , (u32)in ); + store32_le(out + 4, in >> 32); +} + +static void load32_le_buf (u32 *dst, const u8 *src, size_t size) { + FOR(i, 0, size) { dst[i] = load32_le(src + i*4); } +} +static void load64_le_buf (u64 *dst, const u8 *src, size_t size) { + FOR(i, 0, size) { dst[i] = load64_le(src + i*8); } +} +static void store32_le_buf(u8 *dst, const u32 *src, size_t size) { + FOR(i, 0, size) { store32_le(dst + i*4, src[i]); } +} +static void store64_le_buf(u8 *dst, const u64 *src, size_t size) { + FOR(i, 0, size) { store64_le(dst + i*8, src[i]); } +} + +static u64 rotr64(u64 x, u64 n) { return (x >> n) ^ (x << (64 - n)); } +static u32 rotl32(u32 x, u32 n) { return (x << n) ^ (x >> (32 - n)); } + +static int neq0(u64 diff) +{ // constant time comparison to zero + // return diff != 0 ? -1 : 0 + u64 half = (diff >> 32) | ((u32)diff); + return (1 & ((half - 1) >> 32)) - 1; +} + +static u64 x16(const u8 a[16], const u8 b[16]) +{ + return (load64_le(a + 0) ^ load64_le(b + 0)) + | (load64_le(a + 8) ^ load64_le(b + 8)); +} +static u64 x32(const u8 a[32],const u8 b[32]){return x16(a,b)| x16(a+16, b+16);} +static u64 x64(const u8 a[64],const u8 b[64]){return x32(a,b)| x32(a+32, b+32);} +int crypto_verify16(const u8 a[16], const u8 b[16]){ return neq0(x16(a, b)); } +int crypto_verify32(const u8 a[32], const u8 b[32]){ return neq0(x32(a, b)); } +int crypto_verify64(const u8 a[64], const u8 b[64]){ return neq0(x64(a, b)); } + +void crypto_wipe(void *secret, size_t size) +{ + volatile u8 *v_secret = (u8*)secret; + ZERO(v_secret, size); +} + +///////////////// +/// Chacha 20 /// +///////////////// +#define QUARTERROUND(a, b, c, d) \ + a += b; d = rotl32(d ^ a, 16); \ + c += d; b = rotl32(b ^ c, 12); \ + a += b; d = rotl32(d ^ a, 8); \ + c += d; b = rotl32(b ^ c, 7) + +static void chacha20_rounds(u32 out[16], const u32 in[16]) +{ + // The temporary variables make Chacha20 10% faster. + u32 t0 = in[ 0]; u32 t1 = in[ 1]; u32 t2 = in[ 2]; u32 t3 = in[ 3]; + u32 t4 = in[ 4]; u32 t5 = in[ 5]; u32 t6 = in[ 6]; u32 t7 = in[ 7]; + u32 t8 = in[ 8]; u32 t9 = in[ 9]; u32 t10 = in[10]; u32 t11 = in[11]; + u32 t12 = in[12]; u32 t13 = in[13]; u32 t14 = in[14]; u32 t15 = in[15]; + + FOR (i, 0, 10) { // 20 rounds, 2 rounds per loop. + QUARTERROUND(t0, t4, t8 , t12); // column 0 + QUARTERROUND(t1, t5, t9 , t13); // column 1 + QUARTERROUND(t2, t6, t10, t14); // column 2 + QUARTERROUND(t3, t7, t11, t15); // column 3 + QUARTERROUND(t0, t5, t10, t15); // diagonal 0 + QUARTERROUND(t1, t6, t11, t12); // diagonal 1 + QUARTERROUND(t2, t7, t8 , t13); // diagonal 2 + QUARTERROUND(t3, t4, t9 , t14); // diagonal 3 + } + out[ 0] = t0; out[ 1] = t1; out[ 2] = t2; out[ 3] = t3; + out[ 4] = t4; out[ 5] = t5; out[ 6] = t6; out[ 7] = t7; + out[ 8] = t8; out[ 9] = t9; out[10] = t10; out[11] = t11; + out[12] = t12; out[13] = t13; out[14] = t14; out[15] = t15; +} + +const u8 *chacha20_constant = (const u8*)"expand 32-byte k"; // 16 bytes + +void crypto_hchacha20(u8 out[32], const u8 key[32], const u8 in [16]) +{ + u32 block[16]; + load32_le_buf(block , chacha20_constant, 4); + load32_le_buf(block + 4, key , 8); + load32_le_buf(block + 12, in , 4); + + chacha20_rounds(block, block); + + // prevent reversal of the rounds by revealing only half of the buffer. + store32_le_buf(out , block , 4); // constant + store32_le_buf(out+16, block+12, 4); // counter and nonce + WIPE_BUFFER(block); +} + +u64 crypto_chacha20_ctr(u8 *cipher_text, const u8 *plain_text, + size_t text_size, const u8 key[32], const u8 nonce[8], + u64 ctr) +{ + u32 input[16]; + load32_le_buf(input , chacha20_constant, 4); + load32_le_buf(input + 4, key , 8); + load32_le_buf(input + 14, nonce , 2); + input[12] = (u32) ctr; + input[13] = (u32)(ctr >> 32); + + // Whole blocks + u32 pool[16]; + size_t nb_blocks = text_size >> 6; + FOR (i, 0, nb_blocks) { + chacha20_rounds(pool, input); + if (plain_text != 0) { + FOR (j, 0, 16) { + u32 p = pool[j] + input[j]; + store32_le(cipher_text, p ^ load32_le(plain_text)); + cipher_text += 4; + plain_text += 4; + } + } else { + FOR (j, 0, 16) { + u32 p = pool[j] + input[j]; + store32_le(cipher_text, p); + cipher_text += 4; + } + } + input[12]++; + if (input[12] == 0) { + input[13]++; + } + } + text_size &= 63; + + // Last (incomplete) block + if (text_size > 0) { + if (plain_text == 0) { + plain_text = zero; + } + chacha20_rounds(pool, input); + u8 tmp[64]; + FOR (i, 0, 16) { + store32_le(tmp + i*4, pool[i] + input[i]); + } + FOR (i, 0, text_size) { + cipher_text[i] = tmp[i] ^ plain_text[i]; + } + WIPE_BUFFER(tmp); + } + ctr = input[12] + ((u64)input[13] << 32) + (text_size > 0); + + WIPE_BUFFER(pool); + WIPE_BUFFER(input); + return ctr; +} + +u32 crypto_ietf_chacha20_ctr(u8 *cipher_text, const u8 *plain_text, + size_t text_size, + const u8 key[32], const u8 nonce[12], u32 ctr) +{ + u64 big_ctr = ctr + ((u64)load32_le(nonce) << 32); + return (u32)crypto_chacha20_ctr(cipher_text, plain_text, text_size, + key, nonce + 4, big_ctr); +} + +u64 crypto_xchacha20_ctr(u8 *cipher_text, const u8 *plain_text, + size_t text_size, + const u8 key[32], const u8 nonce[24], u64 ctr) +{ + u8 sub_key[32]; + crypto_hchacha20(sub_key, key, nonce); + ctr = crypto_chacha20_ctr(cipher_text, plain_text, text_size, + sub_key, nonce+16, ctr); + WIPE_BUFFER(sub_key); + return ctr; +} + +void crypto_chacha20(u8 *cipher_text, const u8 *plain_text, size_t text_size, + const u8 key[32], const u8 nonce[8]) +{ + crypto_chacha20_ctr(cipher_text, plain_text, text_size, key, nonce, 0); + +} +void crypto_ietf_chacha20(u8 *cipher_text, const u8 *plain_text, + size_t text_size, + const u8 key[32], const u8 nonce[12]) +{ + crypto_ietf_chacha20_ctr(cipher_text, plain_text, text_size, key, nonce, 0); +} + +void crypto_xchacha20(u8 *cipher_text, const u8 *plain_text, size_t text_size, + const u8 key[32], const u8 nonce[24]) +{ + crypto_xchacha20_ctr(cipher_text, plain_text, text_size, key, nonce, 0); +} + +///////////////// +/// Poly 1305 /// +///////////////// + +// h = (h + c) * r +// preconditions: +// ctx->h <= 4_ffffffff_ffffffff_ffffffff_ffffffff +// ctx->r <= 0ffffffc_0ffffffc_0ffffffc_0fffffff +// end <= 1 +// Postcondition: +// ctx->h <= 4_ffffffff_ffffffff_ffffffff_ffffffff +static void poly_block(crypto_poly1305_ctx *ctx, const u8 in[16], unsigned end) +{ + u32 s[4]; + load32_le_buf(s, in, 4); + + // s = h + c, without carry propagation + const u64 s0 = ctx->h[0] + (u64)s[0]; // s0 <= 1_fffffffe + const u64 s1 = ctx->h[1] + (u64)s[1]; // s1 <= 1_fffffffe + const u64 s2 = ctx->h[2] + (u64)s[2]; // s2 <= 1_fffffffe + const u64 s3 = ctx->h[3] + (u64)s[3]; // s3 <= 1_fffffffe + const u32 s4 = ctx->h[4] + end; // s4 <= 5 + + // Local all the things! + const u32 r0 = ctx->r[0]; // r0 <= 0fffffff + const u32 r1 = ctx->r[1]; // r1 <= 0ffffffc + const u32 r2 = ctx->r[2]; // r2 <= 0ffffffc + const u32 r3 = ctx->r[3]; // r3 <= 0ffffffc + const u32 rr0 = (r0 >> 2) * 5; // rr0 <= 13fffffb // lose 2 bits... + const u32 rr1 = (r1 >> 2) + r1; // rr1 <= 13fffffb // rr1 == (r1 >> 2) * 5 + const u32 rr2 = (r2 >> 2) + r2; // rr2 <= 13fffffb // rr1 == (r2 >> 2) * 5 + const u32 rr3 = (r3 >> 2) + r3; // rr3 <= 13fffffb // rr1 == (r3 >> 2) * 5 + + // (h + c) * r, without carry propagation + const u64 x0 = s0*r0+ s1*rr3+ s2*rr2+ s3*rr1+ s4*rr0; // <= 97ffffe007fffff8 + const u64 x1 = s0*r1+ s1*r0 + s2*rr3+ s3*rr2+ s4*rr1; // <= 8fffffe20ffffff6 + const u64 x2 = s0*r2+ s1*r1 + s2*r0 + s3*rr3+ s4*rr2; // <= 87ffffe417fffff4 + const u64 x3 = s0*r3+ s1*r2 + s2*r1 + s3*r0 + s4*rr3; // <= 7fffffe61ffffff2 + const u32 x4 = s4 * (r0 & 3); // ...recover 2 bits // <= f + + // partial reduction modulo 2^130 - 5 + const u32 u5 = x4 + (x3 >> 32); // u5 <= 7ffffff5 + const u64 u0 = (u5 >> 2) * 5 + (x0 & 0xffffffff); + const u64 u1 = (u0 >> 32) + (x1 & 0xffffffff) + (x0 >> 32); + const u64 u2 = (u1 >> 32) + (x2 & 0xffffffff) + (x1 >> 32); + const u64 u3 = (u2 >> 32) + (x3 & 0xffffffff) + (x2 >> 32); + const u64 u4 = (u3 >> 32) + (u5 & 3); + + // Update the hash + ctx->h[0] = (u32)u0; // u0 <= 1_9ffffff0 + ctx->h[1] = (u32)u1; // u1 <= 1_97ffffe0 + ctx->h[2] = (u32)u2; // u2 <= 1_8fffffe2 + ctx->h[3] = (u32)u3; // u3 <= 1_87ffffe4 + ctx->h[4] = (u32)u4; // u4 <= 4 +} + +void crypto_poly1305_init(crypto_poly1305_ctx *ctx, const u8 key[32]) +{ + ZERO(ctx->h, 5); // Initial hash is zero + ctx->c_idx = 0; + // load r and pad (r has some of its bits cleared) + load32_le_buf(ctx->r , key , 4); + load32_le_buf(ctx->pad, key+16, 4); + FOR (i, 0, 1) { ctx->r[i] &= 0x0fffffff; } + FOR (i, 1, 4) { ctx->r[i] &= 0x0ffffffc; } +} + +void crypto_poly1305_update(crypto_poly1305_ctx *ctx, + const u8 *message, size_t message_size) +{ + // Align ourselves with block boundaries + size_t aligned = MIN(align(ctx->c_idx, 16), message_size); + FOR (i, 0, aligned) { + ctx->c[ctx->c_idx] = *message; + ctx->c_idx++; + message++; + message_size--; + } + + // If block is complete, process it + if (ctx->c_idx == 16) { + poly_block(ctx, ctx->c, 1); + ctx->c_idx = 0; + } + + // Process the message block by block + size_t nb_blocks = message_size >> 4; + FOR (i, 0, nb_blocks) { + poly_block(ctx, message, 1); + message += 16; + } + message_size &= 15; + + // remaining bytes (we never complete a block here) + FOR (i, 0, message_size) { + ctx->c[ctx->c_idx] = message[i]; + ctx->c_idx++; + } +} + +void crypto_poly1305_final(crypto_poly1305_ctx *ctx, u8 mac[16]) +{ + // Process the last block (if any) + // We move the final 1 according to remaining input length + // (this will add less than 2^130 to the last input block) + if (ctx->c_idx != 0) { + ZERO(ctx->c + ctx->c_idx, 16 - ctx->c_idx); + ctx->c[ctx->c_idx] = 1; + poly_block(ctx, ctx->c, 0); + } + + // check if we should subtract 2^130-5 by performing the + // corresponding carry propagation. + u64 c = 5; + FOR (i, 0, 4) { + c += ctx->h[i]; + c >>= 32; + } + c += ctx->h[4]; + c = (c >> 2) * 5; // shift the carry back to the beginning + // c now indicates how many times we should subtract 2^130-5 (0 or 1) + FOR (i, 0, 4) { + c += (u64)ctx->h[i] + ctx->pad[i]; + store32_le(mac + i*4, (u32)c); + c = c >> 32; + } + WIPE_CTX(ctx); +} + +void crypto_poly1305(u8 mac[16], const u8 *message, + size_t message_size, const u8 key[32]) +{ + crypto_poly1305_ctx ctx; + crypto_poly1305_init (&ctx, key); + crypto_poly1305_update(&ctx, message, message_size); + crypto_poly1305_final (&ctx, mac); +} + +//////////////// +/// BLAKE2 b /// +//////////////// +static const u64 iv[8] = { + 0x6a09e667f3bcc908, 0xbb67ae8584caa73b, + 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1, + 0x510e527fade682d1, 0x9b05688c2b3e6c1f, + 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179, +}; + +static void blake2b_compress(crypto_blake2b_ctx *ctx, int is_last_block) +{ + static const u8 sigma[12][16] = { + { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }, + { 14, 10, 4, 8, 9, 15, 13, 6, 1, 12, 0, 2, 11, 7, 5, 3 }, + { 11, 8, 12, 0, 5, 2, 15, 13, 10, 14, 3, 6, 7, 1, 9, 4 }, + { 7, 9, 3, 1, 13, 12, 11, 14, 2, 6, 5, 10, 4, 0, 15, 8 }, + { 9, 0, 5, 7, 2, 4, 10, 15, 14, 1, 11, 12, 6, 8, 3, 13 }, + { 2, 12, 6, 10, 0, 11, 8, 3, 4, 13, 7, 5, 15, 14, 1, 9 }, + { 12, 5, 1, 15, 14, 13, 4, 10, 0, 7, 6, 3, 9, 2, 8, 11 }, + { 13, 11, 7, 14, 12, 1, 3, 9, 5, 0, 15, 4, 8, 6, 2, 10 }, + { 6, 15, 14, 9, 11, 3, 0, 8, 12, 2, 13, 7, 1, 4, 10, 5 }, + { 10, 2, 8, 4, 7, 6, 1, 5, 15, 11, 9, 14, 3, 12, 13, 0 }, + { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }, + { 14, 10, 4, 8, 9, 15, 13, 6, 1, 12, 0, 2, 11, 7, 5, 3 }, + }; + + // increment input offset + u64 *x = ctx->input_offset; + size_t y = ctx->input_idx; + x[0] += y; + if (x[0] < y) { + x[1]++; + } + + // init work vector + u64 v0 = ctx->hash[0]; u64 v8 = iv[0]; + u64 v1 = ctx->hash[1]; u64 v9 = iv[1]; + u64 v2 = ctx->hash[2]; u64 v10 = iv[2]; + u64 v3 = ctx->hash[3]; u64 v11 = iv[3]; + u64 v4 = ctx->hash[4]; u64 v12 = iv[4] ^ ctx->input_offset[0]; + u64 v5 = ctx->hash[5]; u64 v13 = iv[5] ^ ctx->input_offset[1]; + u64 v6 = ctx->hash[6]; u64 v14 = iv[6] ^ (u64)~(is_last_block - 1); + u64 v7 = ctx->hash[7]; u64 v15 = iv[7]; + + // mangle work vector + u64 *input = ctx->input; +#define BLAKE2_G(a, b, c, d, x, y) \ + a += b + x; d = rotr64(d ^ a, 32); \ + c += d; b = rotr64(b ^ c, 24); \ + a += b + y; d = rotr64(d ^ a, 16); \ + c += d; b = rotr64(b ^ c, 63) +#define BLAKE2_ROUND(i) \ + BLAKE2_G(v0, v4, v8 , v12, input[sigma[i][ 0]], input[sigma[i][ 1]]); \ + BLAKE2_G(v1, v5, v9 , v13, input[sigma[i][ 2]], input[sigma[i][ 3]]); \ + BLAKE2_G(v2, v6, v10, v14, input[sigma[i][ 4]], input[sigma[i][ 5]]); \ + BLAKE2_G(v3, v7, v11, v15, input[sigma[i][ 6]], input[sigma[i][ 7]]); \ + BLAKE2_G(v0, v5, v10, v15, input[sigma[i][ 8]], input[sigma[i][ 9]]); \ + BLAKE2_G(v1, v6, v11, v12, input[sigma[i][10]], input[sigma[i][11]]); \ + BLAKE2_G(v2, v7, v8 , v13, input[sigma[i][12]], input[sigma[i][13]]); \ + BLAKE2_G(v3, v4, v9 , v14, input[sigma[i][14]], input[sigma[i][15]]) + +#ifdef BLAKE2_NO_UNROLLING + FOR (i, 0, 12) { + BLAKE2_ROUND(i); + } +#else + BLAKE2_ROUND(0); BLAKE2_ROUND(1); BLAKE2_ROUND(2); BLAKE2_ROUND(3); + BLAKE2_ROUND(4); BLAKE2_ROUND(5); BLAKE2_ROUND(6); BLAKE2_ROUND(7); + BLAKE2_ROUND(8); BLAKE2_ROUND(9); BLAKE2_ROUND(10); BLAKE2_ROUND(11); +#endif + + // update hash + ctx->hash[0] ^= v0 ^ v8; ctx->hash[1] ^= v1 ^ v9; + ctx->hash[2] ^= v2 ^ v10; ctx->hash[3] ^= v3 ^ v11; + ctx->hash[4] ^= v4 ^ v12; ctx->hash[5] ^= v5 ^ v13; + ctx->hash[6] ^= v6 ^ v14; ctx->hash[7] ^= v7 ^ v15; +} + +static void blake2b_set_input(crypto_blake2b_ctx *ctx, u8 input, size_t index) +{ + if (index == 0) { + ZERO(ctx->input, 16); + } + size_t word = index >> 3; + size_t byte = index & 7; + ctx->input[word] |= (u64)input << (byte << 3); +} + +void crypto_blake2b_general_init(crypto_blake2b_ctx *ctx, size_t hash_size, + const u8 *key, size_t key_size) +{ + // initial hash + COPY(ctx->hash, iv, 8); + ctx->hash[0] ^= 0x01010000 ^ (key_size << 8) ^ hash_size; + + ctx->input_offset[0] = 0; // beginning of the input, no offset + ctx->input_offset[1] = 0; // beginning of the input, no offset + ctx->hash_size = hash_size; // remember the hash size we want + ctx->input_idx = 0; + + // if there is a key, the first block is that key (padded with zeroes) + if (key_size > 0) { + u8 key_block[128] = {0}; + COPY(key_block, key, key_size); + // same as calling crypto_blake2b_update(ctx, key_block , 128) + load64_le_buf(ctx->input, key_block, 16); + ctx->input_idx = 128; + } +} + +void crypto_blake2b_init(crypto_blake2b_ctx *ctx) +{ + crypto_blake2b_general_init(ctx, 64, 0, 0); +} + +void crypto_blake2b_update(crypto_blake2b_ctx *ctx, + const u8 *message, size_t message_size) +{ + // Align ourselves with block boundaries + // The block that may result is not compressed yet + size_t aligned = MIN(align(ctx->input_idx, 128), message_size); + FOR (i, 0, aligned) { + blake2b_set_input(ctx, *message, ctx->input_idx); + ctx->input_idx++; + message++; + message_size--; + } + + // Process the message block by block + // The last block is not compressed yet. + size_t nb_blocks = message_size >> 7; + FOR (i, 0, nb_blocks) { + if (ctx->input_idx == 128) { + blake2b_compress(ctx, 0); + } + load64_le_buf(ctx->input, message, 16); + message += 128; + ctx->input_idx = 128; + } + message_size &= 127; + + // Fill remaining bytes (not the whole buffer) + // The last block is never fully filled + FOR (i, 0, message_size) { + if (ctx->input_idx == 128) { + blake2b_compress(ctx, 0); + ctx->input_idx = 0; + } + blake2b_set_input(ctx, message[i], ctx->input_idx); + ctx->input_idx++; + } +} + +void crypto_blake2b_final(crypto_blake2b_ctx *ctx, u8 *hash) +{ + // Pad the end of the block with zeroes + FOR (i, ctx->input_idx, 128) { + blake2b_set_input(ctx, 0, i); + } + blake2b_compress(ctx, 1); // compress the last block + size_t nb_words = ctx->hash_size >> 3; + store64_le_buf(hash, ctx->hash, nb_words); + FOR (i, nb_words << 3, ctx->hash_size) { + hash[i] = (ctx->hash[i >> 3] >> (8 * (i & 7))) & 0xff; + } + WIPE_CTX(ctx); +} + +void crypto_blake2b_general(u8 *hash , size_t hash_size, + const u8 *key , size_t key_size, + const u8 *message, size_t message_size) +{ + crypto_blake2b_ctx ctx; + crypto_blake2b_general_init(&ctx, hash_size, key, key_size); + crypto_blake2b_update(&ctx, message, message_size); + crypto_blake2b_final(&ctx, hash); +} + +void crypto_blake2b(u8 hash[64], const u8 *message, size_t message_size) +{ + crypto_blake2b_general(hash, 64, 0, 0, message, message_size); +} + +static void blake2b_vtable_init(void *ctx) { + crypto_blake2b_init(&((crypto_sign_ctx*)ctx)->hash); +} +static void blake2b_vtable_update(void *ctx, const u8 *m, size_t s) { + crypto_blake2b_update(&((crypto_sign_ctx*)ctx)->hash, m, s); +} +static void blake2b_vtable_final(void *ctx, u8 *h) { + crypto_blake2b_final(&((crypto_sign_ctx*)ctx)->hash, h); +} +const crypto_sign_vtable crypto_blake2b_vtable = { + crypto_blake2b, + blake2b_vtable_init, + blake2b_vtable_update, + blake2b_vtable_final, + sizeof(crypto_sign_ctx), +}; + +//////////////// +/// Argon2 i /// +//////////////// +// references to R, Z, Q etc. come from the spec + +// Argon2 operates on 1024 byte blocks. +typedef struct { u64 a[128]; } block; + +static void wipe_block(block *b) +{ + volatile u64* a = b->a; + ZERO(a, 128); +} + +// updates a BLAKE2 hash with a 32 bit word, little endian. +static void blake_update_32(crypto_blake2b_ctx *ctx, u32 input) +{ + u8 buf[4]; + store32_le(buf, input); + crypto_blake2b_update(ctx, buf, 4); + WIPE_BUFFER(buf); +} + +static void load_block(block *b, const u8 bytes[1024]) +{ + load64_le_buf(b->a, bytes, 128); +} + +static void store_block(u8 bytes[1024], const block *b) +{ + store64_le_buf(bytes, b->a, 128); +} + +static void copy_block(block *o,const block*in){FOR(i,0,128)o->a[i] = in->a[i];} +static void xor_block(block *o,const block*in){FOR(i,0,128)o->a[i]^= in->a[i];} + +// Hash with a virtually unlimited digest size. +// Doesn't extract more entropy than the base hash function. +// Mainly used for filling a whole kilobyte block with pseudo-random bytes. +// (One could use a stream cipher with a seed hash as the key, but +// this would introduce another dependency —and point of failure.) +static void extended_hash(u8 *digest, u32 digest_size, + const u8 *input , u32 input_size) +{ + crypto_blake2b_ctx ctx; + crypto_blake2b_general_init(&ctx, MIN(digest_size, 64), 0, 0); + blake_update_32 (&ctx, digest_size); + crypto_blake2b_update (&ctx, input, input_size); + crypto_blake2b_final (&ctx, digest); + + if (digest_size > 64) { + // the conversion to u64 avoids integer overflow on + // ludicrously big hash sizes. + u32 r = (u32)(((u64)digest_size + 31) >> 5) - 2; + u32 i = 1; + u32 in = 0; + u32 out = 32; + while (i < r) { + // Input and output overlap. This is intentional + crypto_blake2b(digest + out, digest + in, 64); + i += 1; + in += 32; + out += 32; + } + crypto_blake2b_general(digest + out, digest_size - (32 * r), + 0, 0, // no key + digest + in , 64); + } +} + +#define LSB(x) ((x) & 0xffffffff) +#define G(a, b, c, d) \ + a += b + 2 * LSB(a) * LSB(b); d ^= a; d = rotr64(d, 32); \ + c += d + 2 * LSB(c) * LSB(d); b ^= c; b = rotr64(b, 24); \ + a += b + 2 * LSB(a) * LSB(b); d ^= a; d = rotr64(d, 16); \ + c += d + 2 * LSB(c) * LSB(d); b ^= c; b = rotr64(b, 63) +#define ROUND(v0, v1, v2, v3, v4, v5, v6, v7, \ + v8, v9, v10, v11, v12, v13, v14, v15) \ + G(v0, v4, v8, v12); G(v1, v5, v9, v13); \ + G(v2, v6, v10, v14); G(v3, v7, v11, v15); \ + G(v0, v5, v10, v15); G(v1, v6, v11, v12); \ + G(v2, v7, v8, v13); G(v3, v4, v9, v14) + +// Core of the compression function G. Computes Z from R in place. +static void g_rounds(block *work_block) +{ + // column rounds (work_block = Q) + for (int i = 0; i < 128; i += 16) { + ROUND(work_block->a[i ], work_block->a[i + 1], + work_block->a[i + 2], work_block->a[i + 3], + work_block->a[i + 4], work_block->a[i + 5], + work_block->a[i + 6], work_block->a[i + 7], + work_block->a[i + 8], work_block->a[i + 9], + work_block->a[i + 10], work_block->a[i + 11], + work_block->a[i + 12], work_block->a[i + 13], + work_block->a[i + 14], work_block->a[i + 15]); + } + // row rounds (work_block = Z) + for (int i = 0; i < 16; i += 2) { + ROUND(work_block->a[i ], work_block->a[i + 1], + work_block->a[i + 16], work_block->a[i + 17], + work_block->a[i + 32], work_block->a[i + 33], + work_block->a[i + 48], work_block->a[i + 49], + work_block->a[i + 64], work_block->a[i + 65], + work_block->a[i + 80], work_block->a[i + 81], + work_block->a[i + 96], work_block->a[i + 97], + work_block->a[i + 112], work_block->a[i + 113]); + } +} + +// Argon2i uses a kind of stream cipher to determine which reference +// block it will take to synthesise the next block. This context hold +// that stream's state. (It's very similar to Chacha20. The block b +// is analogous to Chacha's own pool) +typedef struct { + block b; + u32 pass_number; + u32 slice_number; + u32 nb_blocks; + u32 nb_iterations; + u32 ctr; + u32 offset; +} gidx_ctx; + +// The block in the context will determine array indices. To avoid +// timing attacks, it only depends on public information. No looking +// at a previous block to seed the next. This makes offline attacks +// easier, but timing attacks are the bigger threat in many settings. +static void gidx_refresh(gidx_ctx *ctx) +{ + // seed the beginning of the block... + ctx->b.a[0] = ctx->pass_number; + ctx->b.a[1] = 0; // lane number (we have only one) + ctx->b.a[2] = ctx->slice_number; + ctx->b.a[3] = ctx->nb_blocks; + ctx->b.a[4] = ctx->nb_iterations; + ctx->b.a[5] = 1; // type: Argon2i + ctx->b.a[6] = ctx->ctr; + ZERO(ctx->b.a + 7, 121); // ...then zero the rest out + + // Shuffle the block thus: ctx->b = G((G(ctx->b, zero)), zero) + // (G "square" function), to get cheap pseudo-random numbers. + block tmp; + copy_block(&tmp, &ctx->b); + g_rounds (&ctx->b); + xor_block (&ctx->b, &tmp); + copy_block(&tmp, &ctx->b); + g_rounds (&ctx->b); + xor_block (&ctx->b, &tmp); + wipe_block(&tmp); +} + +static void gidx_init(gidx_ctx *ctx, + u32 pass_number, u32 slice_number, + u32 nb_blocks, u32 nb_iterations) +{ + ctx->pass_number = pass_number; + ctx->slice_number = slice_number; + ctx->nb_blocks = nb_blocks; + ctx->nb_iterations = nb_iterations; + ctx->ctr = 0; + + // Offset from the beginning of the segment. For the first slice + // of the first pass, we start at the *third* block, so the offset + // starts at 2, not 0. + if (pass_number != 0 || slice_number != 0) { + ctx->offset = 0; + } else { + ctx->offset = 2; + ctx->ctr++; // Compensates for missed lazy creation + gidx_refresh(ctx); // at the start of gidx_next() + } +} + +static u32 gidx_next(gidx_ctx *ctx) +{ + // lazily creates the offset block we need + if ((ctx->offset & 127) == 0) { + ctx->ctr++; + gidx_refresh(ctx); + } + u32 index = ctx->offset & 127; // save index for current call + u32 offset = ctx->offset; // save offset for current call + ctx->offset++; // update offset for next call + + // Computes the area size. + // Pass 0 : all already finished segments plus already constructed + // blocks in this segment + // Pass 1+: 3 last segments plus already constructed + // blocks in this segment. THE SPEC SUGGESTS OTHERWISE. + // I CONFORM TO THE REFERENCE IMPLEMENTATION. + int first_pass = ctx->pass_number == 0; + u32 slice_size = ctx->nb_blocks >> 2; + u32 nb_segments = first_pass ? ctx->slice_number : 3; + u32 area_size = nb_segments * slice_size + offset - 1; + + // Computes the starting position of the reference area. + // CONTRARY TO WHAT THE SPEC SUGGESTS, IT STARTS AT THE + // NEXT SEGMENT, NOT THE NEXT BLOCK. + u32 next_slice = ((ctx->slice_number + 1) & 3) * slice_size; + u32 start_pos = first_pass ? 0 : next_slice; + + // Generate offset from J1 (no need for J2, there's only one lane) + u64 j1 = ctx->b.a[index] & 0xffffffff; // pseudo-random number + u64 x = (j1 * j1) >> 32; + u64 y = (area_size * x) >> 32; + u64 z = (area_size - 1) - y; + u64 ref = start_pos + z; // ref < 2 * nb_blocks + return (u32)(ref < ctx->nb_blocks ? ref : ref - ctx->nb_blocks); +} + +// Main algorithm +void crypto_argon2i_general(u8 *hash, u32 hash_size, + void *work_area, u32 nb_blocks, + u32 nb_iterations, + const u8 *password, u32 password_size, + const u8 *salt, u32 salt_size, + const u8 *key, u32 key_size, + const u8 *ad, u32 ad_size) +{ + // work area seen as blocks (must be suitably aligned) + block *blocks = (block*)work_area; + { + crypto_blake2b_ctx ctx; + crypto_blake2b_init(&ctx); + + blake_update_32 (&ctx, 1 ); // p: number of threads + blake_update_32 (&ctx, hash_size ); + blake_update_32 (&ctx, nb_blocks ); + blake_update_32 (&ctx, nb_iterations); + blake_update_32 (&ctx, 0x13 ); // v: version number + blake_update_32 (&ctx, 1 ); // y: Argon2i + blake_update_32 (&ctx, password_size); + crypto_blake2b_update(&ctx, password, password_size); + blake_update_32 (&ctx, salt_size); + crypto_blake2b_update(&ctx, salt, salt_size); + blake_update_32 (&ctx, key_size); + crypto_blake2b_update(&ctx, key, key_size); + blake_update_32 (&ctx, ad_size); + crypto_blake2b_update(&ctx, ad, ad_size); + + u8 initial_hash[72]; // 64 bytes plus 2 words for future hashes + crypto_blake2b_final(&ctx, initial_hash); + + // fill first 2 blocks + u8 hash_area[1024]; + store32_le(initial_hash + 64, 0); // first additional word + store32_le(initial_hash + 68, 0); // second additional word + extended_hash(hash_area, 1024, initial_hash, 72); + load_block(blocks, hash_area); + + store32_le(initial_hash + 64, 1); // slight modification + extended_hash(hash_area, 1024, initial_hash, 72); + load_block(blocks + 1, hash_area); + + WIPE_BUFFER(initial_hash); + WIPE_BUFFER(hash_area); + } + + // Actual number of blocks + nb_blocks -= nb_blocks & 3; // round down to 4 p (p == 1 thread) + const u32 segment_size = nb_blocks >> 2; + + // fill (then re-fill) the rest of the blocks + block tmp; + gidx_ctx ctx; // public information, no need to wipe + FOR_T (u32, pass_number, 0, nb_iterations) { + int first_pass = pass_number == 0; + + FOR_T (u32, segment, 0, 4) { + gidx_init(&ctx, pass_number, segment, nb_blocks, nb_iterations); + + // On the first segment of the first pass, + // blocks 0 and 1 are already filled. + // We use the offset to skip them. + u32 start_offset = first_pass && segment == 0 ? 2 : 0; + u32 segment_start = segment * segment_size + start_offset; + u32 segment_end = (segment + 1) * segment_size; + FOR_T (u32, current_block, segment_start, segment_end) { + block *reference = blocks + gidx_next(&ctx); + block *current = blocks + current_block; + block *previous = current_block == 0 + ? blocks + nb_blocks - 1 + : blocks + current_block - 1; + // Apply compression function G, + // And copy it (or XOR it) to the current block. + copy_block(&tmp, previous); + xor_block (&tmp, reference); + if (first_pass) { copy_block(current, &tmp); } + else { xor_block (current, &tmp); } + g_rounds (&tmp); + xor_block (current, &tmp); + } + } + } + wipe_block(&tmp); + u8 final_block[1024]; + store_block(final_block, blocks + (nb_blocks - 1)); + + // wipe work area + volatile u64 *p = (u64*)work_area; + ZERO(p, 128 * nb_blocks); + + // hash the very last block with H' into the output hash + extended_hash(hash, hash_size, final_block, 1024); + WIPE_BUFFER(final_block); +} + +void crypto_argon2i(u8 *hash, u32 hash_size, + void *work_area, u32 nb_blocks, u32 nb_iterations, + const u8 *password, u32 password_size, + const u8 *salt, u32 salt_size) +{ + crypto_argon2i_general(hash, hash_size, work_area, nb_blocks, nb_iterations, + password, password_size, salt , salt_size, 0,0,0,0); +} + +//////////////////////////////////// +/// Arithmetic modulo 2^255 - 19 /// +//////////////////////////////////// +// Originally taken from SUPERCOP's ref10 implementation. +// A bit bigger than TweetNaCl, over 4 times faster. + +// field element +typedef i32 fe[10]; + +// field constants +// +// fe_one : 1 +// sqrtm1 : sqrt(-1) +// d : -121665 / 121666 +// D2 : 2 * -121665 / 121666 +// lop_x, lop_y: low order point in Edwards coordinates +// ufactor : -sqrt(-1) * 2 +// A2 : 486662^2 (A squared) +static const fe fe_one = {1}; +static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, + -272473, -25146209, -2005654, 326686, 11406482,}; +static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729, + -8787816, -6275908, -3247719, -18696448, -12055116,}; +static const fe D2 = {-21827239, -5839606, -30745221, 13898782, 229458, + 15978800, -12551817, -6495438, 29715968, 9444199,}; +static const fe lop_x = {21352778, 5345713, 4660180, -8347857, 24143090, + 14568123, 30185756, -12247770, -33528939, 8345319,}; +static const fe lop_y = {-6952922, -1265500, 6862341, -7057498, -4037696, + -5447722, 31680899, -15325402, -19365852, 1569102,}; +static const fe ufactor = {-1917299, 15887451, -18755900, -7000830, -24778944, + 544946, -16816446, 4011309, -653372, 10741468,}; +static const fe A2 = {12721188, 3529, 0, 0, 0, 0, 0, 0, 0, 0,}; + +static void fe_0(fe h) { ZERO(h , 10); } +static void fe_1(fe h) { h[0] = 1; ZERO(h+1, 9); } + +static void fe_copy(fe h,const fe f ){FOR(i,0,10) h[i] = f[i]; } +static void fe_neg (fe h,const fe f ){FOR(i,0,10) h[i] = -f[i]; } +static void fe_add (fe h,const fe f,const fe g){FOR(i,0,10) h[i] = f[i] + g[i];} +static void fe_sub (fe h,const fe f,const fe g){FOR(i,0,10) h[i] = f[i] - g[i];} + +static void fe_cswap(fe f, fe g, int b) +{ + i32 mask = -b; // -1 = 0xffffffff + FOR (i, 0, 10) { + i32 x = (f[i] ^ g[i]) & mask; + f[i] = f[i] ^ x; + g[i] = g[i] ^ x; + } +} + +static void fe_ccopy(fe f, const fe g, int b) +{ + i32 mask = -b; // -1 = 0xffffffff + FOR (i, 0, 10) { + i32 x = (f[i] ^ g[i]) & mask; + f[i] = f[i] ^ x; + } +} + + +// Signed carry propagation +// ------------------------ +// +// Let t be a number. It can be uniquely decomposed thus: +// +// t = h*2^26 + l +// such that -2^25 <= l < 2^25 +// +// Let c = (t + 2^25) / 2^26 (rounded down) +// c = (h*2^26 + l + 2^25) / 2^26 (rounded down) +// c = h + (l + 2^25) / 2^26 (rounded down) +// c = h (exactly) +// Because 0 <= l + 2^25 < 2^26 +// +// Let u = t - c*2^26 +// u = h*2^26 + l - h*2^26 +// u = l +// Therefore, -2^25 <= u < 2^25 +// +// Additionally, if |t| < x, then |h| < x/2^26 (rounded down) +// +// Notations: +// - In C, 1<<25 means 2^25. +// - In C, x>>25 means floor(x / (2^25)). +// - All of the above applies with 25 & 24 as well as 26 & 25. +// +// +// Note on negative right shifts +// ----------------------------- +// +// In C, x >> n, where x is a negative integer, is implementation +// defined. In practice, all platforms do arithmetic shift, which is +// equivalent to division by 2^26, rounded down. Some compilers, like +// GCC, even guarantee it. +// +// If we ever stumble upon a platform that does not propagate the sign +// bit (we won't), visible failures will show at the slightest test, and +// the signed shifts can be replaced by the following: +// +// typedef struct { i64 x:39; } s25; +// typedef struct { i64 x:38; } s26; +// i64 shift25(i64 x) { s25 s; s.x = ((u64)x)>>25; return s.x; } +// i64 shift26(i64 x) { s26 s; s.x = ((u64)x)>>26; return s.x; } +// +// Current compilers cannot optimise this, causing a 30% drop in +// performance. Fairly expensive for something that never happens. +// +// +// Precondition +// ------------ +// +// |t0| < 2^63 +// |t1|..|t9| < 2^62 +// +// Algorithm +// --------- +// c = t0 + 2^25 / 2^26 -- |c| <= 2^36 +// t0 -= c * 2^26 -- |t0| <= 2^25 +// t1 += c -- |t1| <= 2^63 +// +// c = t4 + 2^25 / 2^26 -- |c| <= 2^36 +// t4 -= c * 2^26 -- |t4| <= 2^25 +// t5 += c -- |t5| <= 2^63 +// +// c = t1 + 2^24 / 2^25 -- |c| <= 2^38 +// t1 -= c * 2^25 -- |t1| <= 2^24 +// t2 += c -- |t2| <= 2^63 +// +// c = t5 + 2^24 / 2^25 -- |c| <= 2^38 +// t5 -= c * 2^25 -- |t5| <= 2^24 +// t6 += c -- |t6| <= 2^63 +// +// c = t2 + 2^25 / 2^26 -- |c| <= 2^37 +// t2 -= c * 2^26 -- |t2| <= 2^25 < 1.1 * 2^25 (final t2) +// t3 += c -- |t3| <= 2^63 +// +// c = t6 + 2^25 / 2^26 -- |c| <= 2^37 +// t6 -= c * 2^26 -- |t6| <= 2^25 < 1.1 * 2^25 (final t6) +// t7 += c -- |t7| <= 2^63 +// +// c = t3 + 2^24 / 2^25 -- |c| <= 2^38 +// t3 -= c * 2^25 -- |t3| <= 2^24 < 1.1 * 2^24 (final t3) +// t4 += c -- |t4| <= 2^25 + 2^38 < 2^39 +// +// c = t7 + 2^24 / 2^25 -- |c| <= 2^38 +// t7 -= c * 2^25 -- |t7| <= 2^24 < 1.1 * 2^24 (final t7) +// t8 += c -- |t8| <= 2^63 +// +// c = t4 + 2^25 / 2^26 -- |c| <= 2^13 +// t4 -= c * 2^26 -- |t4| <= 2^25 < 1.1 * 2^25 (final t4) +// t5 += c -- |t5| <= 2^24 + 2^13 < 1.1 * 2^24 (final t5) +// +// c = t8 + 2^25 / 2^26 -- |c| <= 2^37 +// t8 -= c * 2^26 -- |t8| <= 2^25 < 1.1 * 2^25 (final t8) +// t9 += c -- |t9| <= 2^63 +// +// c = t9 + 2^24 / 2^25 -- |c| <= 2^38 +// t9 -= c * 2^25 -- |t9| <= 2^24 < 1.1 * 2^24 (final t9) +// t0 += c * 19 -- |t0| <= 2^25 + 2^38*19 < 2^44 +// +// c = t0 + 2^25 / 2^26 -- |c| <= 2^18 +// t0 -= c * 2^26 -- |t0| <= 2^25 < 1.1 * 2^25 (final t0) +// t1 += c -- |t1| <= 2^24 + 2^18 < 1.1 * 2^24 (final t1) +// +// Postcondition +// ------------- +// |t0|, |t2|, |t4|, |t6|, |t8| < 1.1 * 2^25 +// |t1|, |t3|, |t5|, |t7|, |t9| < 1.1 * 2^24 +#define FE_CARRY \ + i64 c; \ + c = (t0 + ((i64)1<<25)) >> 26; t0 -= c * ((i64)1 << 26); t1 += c; \ + c = (t4 + ((i64)1<<25)) >> 26; t4 -= c * ((i64)1 << 26); t5 += c; \ + c = (t1 + ((i64)1<<24)) >> 25; t1 -= c * ((i64)1 << 25); t2 += c; \ + c = (t5 + ((i64)1<<24)) >> 25; t5 -= c * ((i64)1 << 25); t6 += c; \ + c = (t2 + ((i64)1<<25)) >> 26; t2 -= c * ((i64)1 << 26); t3 += c; \ + c = (t6 + ((i64)1<<25)) >> 26; t6 -= c * ((i64)1 << 26); t7 += c; \ + c = (t3 + ((i64)1<<24)) >> 25; t3 -= c * ((i64)1 << 25); t4 += c; \ + c = (t7 + ((i64)1<<24)) >> 25; t7 -= c * ((i64)1 << 25); t8 += c; \ + c = (t4 + ((i64)1<<25)) >> 26; t4 -= c * ((i64)1 << 26); t5 += c; \ + c = (t8 + ((i64)1<<25)) >> 26; t8 -= c * ((i64)1 << 26); t9 += c; \ + c = (t9 + ((i64)1<<24)) >> 25; t9 -= c * ((i64)1 << 25); t0 += c * 19; \ + c = (t0 + ((i64)1<<25)) >> 26; t0 -= c * ((i64)1 << 26); t1 += c; \ + h[0]=(i32)t0; h[1]=(i32)t1; h[2]=(i32)t2; h[3]=(i32)t3; h[4]=(i32)t4; \ + h[5]=(i32)t5; h[6]=(i32)t6; h[7]=(i32)t7; h[8]=(i32)t8; h[9]=(i32)t9 + +// Decodes a field element from a byte buffer. +// mask specifies how many bits we ignore. +// Traditionally we ignore 1. It's useful for EdDSA, +// which uses that bit to denote the sign of x. +// Elligator however uses positive representatives, +// which means ignoring 2 bits instead. +static void fe_frombytes_mask(fe h, const u8 s[32], unsigned nb_mask) +{ + i32 mask = 0xffffff >> nb_mask; + i64 t0 = load32_le(s); // t0 < 2^32 + i64 t1 = load24_le(s + 4) << 6; // t1 < 2^30 + i64 t2 = load24_le(s + 7) << 5; // t2 < 2^29 + i64 t3 = load24_le(s + 10) << 3; // t3 < 2^27 + i64 t4 = load24_le(s + 13) << 2; // t4 < 2^26 + i64 t5 = load32_le(s + 16); // t5 < 2^32 + i64 t6 = load24_le(s + 20) << 7; // t6 < 2^31 + i64 t7 = load24_le(s + 23) << 5; // t7 < 2^29 + i64 t8 = load24_le(s + 26) << 4; // t8 < 2^28 + i64 t9 = (load24_le(s + 29) & mask) << 2; // t9 < 2^25 + FE_CARRY; // Carry precondition OK +} + +static void fe_frombytes(fe h, const u8 s[32]) +{ + fe_frombytes_mask(h, s, 1); +} + + +// Precondition +// |h[0]|, |h[2]|, |h[4]|, |h[6]|, |h[8]| < 1.1 * 2^25 +// |h[1]|, |h[3]|, |h[5]|, |h[7]|, |h[9]| < 1.1 * 2^24 +// +// Therefore, |h| < 2^255-19 +// There are two possibilities: +// +// - If h is positive, all we need to do is reduce its individual +// limbs down to their tight positive range. +// - If h is negative, we also need to add 2^255-19 to it. +// Or just remove 19 and chop off any excess bit. +static void fe_tobytes(u8 s[32], const fe h) +{ + i32 t[10]; + COPY(t, h, 10); + i32 q = (19 * t[9] + (((i32) 1) << 24)) >> 25; + // |t9| < 1.1 * 2^24 + // -1.1 * 2^24 < t9 < 1.1 * 2^24 + // -21 * 2^24 < 19 * t9 < 21 * 2^24 + // -2^29 < 19 * t9 + 2^24 < 2^29 + // -2^29 / 2^25 < (19 * t9 + 2^24) / 2^25 < 2^29 / 2^25 + // -16 < (19 * t9 + 2^24) / 2^25 < 16 + FOR (i, 0, 5) { + q += t[2*i ]; q >>= 26; // q = 0 or -1 + q += t[2*i+1]; q >>= 25; // q = 0 or -1 + } + // q = 0 iff h >= 0 + // q = -1 iff h < 0 + // Adding q * 19 to h reduces h to its proper range. + q *= 19; // Shift carry back to the beginning + FOR (i, 0, 5) { + t[i*2 ] += q; q = t[i*2 ] >> 26; t[i*2 ] -= q * ((i32)1 << 26); + t[i*2+1] += q; q = t[i*2+1] >> 25; t[i*2+1] -= q * ((i32)1 << 25); + } + // h is now fully reduced, and q represents the excess bit. + + store32_le(s + 0, ((u32)t[0] >> 0) | ((u32)t[1] << 26)); + store32_le(s + 4, ((u32)t[1] >> 6) | ((u32)t[2] << 19)); + store32_le(s + 8, ((u32)t[2] >> 13) | ((u32)t[3] << 13)); + store32_le(s + 12, ((u32)t[3] >> 19) | ((u32)t[4] << 6)); + store32_le(s + 16, ((u32)t[5] >> 0) | ((u32)t[6] << 25)); + store32_le(s + 20, ((u32)t[6] >> 7) | ((u32)t[7] << 19)); + store32_le(s + 24, ((u32)t[7] >> 13) | ((u32)t[8] << 12)); + store32_le(s + 28, ((u32)t[8] >> 20) | ((u32)t[9] << 6)); + + WIPE_BUFFER(t); +} + +// Precondition +// ------------- +// |f0|, |f2|, |f4|, |f6|, |f8| < 1.65 * 2^26 +// |f1|, |f3|, |f5|, |f7|, |f9| < 1.65 * 2^25 +// +// |g0|, |g2|, |g4|, |g6|, |g8| < 1.65 * 2^26 +// |g1|, |g3|, |g5|, |g7|, |g9| < 1.65 * 2^25 +static void fe_mul_small(fe h, const fe f, i32 g) +{ + i64 t0 = f[0] * (i64) g; i64 t1 = f[1] * (i64) g; + i64 t2 = f[2] * (i64) g; i64 t3 = f[3] * (i64) g; + i64 t4 = f[4] * (i64) g; i64 t5 = f[5] * (i64) g; + i64 t6 = f[6] * (i64) g; i64 t7 = f[7] * (i64) g; + i64 t8 = f[8] * (i64) g; i64 t9 = f[9] * (i64) g; + // |t0|, |t2|, |t4|, |t6|, |t8| < 1.65 * 2^26 * 2^31 < 2^58 + // |t1|, |t3|, |t5|, |t7|, |t9| < 1.65 * 2^25 * 2^31 < 2^57 + + FE_CARRY; // Carry precondition OK +} + +// Precondition +// ------------- +// |f0|, |f2|, |f4|, |f6|, |f8| < 1.65 * 2^26 +// |f1|, |f3|, |f5|, |f7|, |f9| < 1.65 * 2^25 +// +// |g0|, |g2|, |g4|, |g6|, |g8| < 1.65 * 2^26 +// |g1|, |g3|, |g5|, |g7|, |g9| < 1.65 * 2^25 +static void fe_mul(fe h, const fe f, const fe g) +{ + // Everything is unrolled and put in temporary variables. + // We could roll the loop, but that would make curve25519 twice as slow. + i32 f0 = f[0]; i32 f1 = f[1]; i32 f2 = f[2]; i32 f3 = f[3]; i32 f4 = f[4]; + i32 f5 = f[5]; i32 f6 = f[6]; i32 f7 = f[7]; i32 f8 = f[8]; i32 f9 = f[9]; + i32 g0 = g[0]; i32 g1 = g[1]; i32 g2 = g[2]; i32 g3 = g[3]; i32 g4 = g[4]; + i32 g5 = g[5]; i32 g6 = g[6]; i32 g7 = g[7]; i32 g8 = g[8]; i32 g9 = g[9]; + i32 F1 = f1*2; i32 F3 = f3*2; i32 F5 = f5*2; i32 F7 = f7*2; i32 F9 = f9*2; + i32 G1 = g1*19; i32 G2 = g2*19; i32 G3 = g3*19; + i32 G4 = g4*19; i32 G5 = g5*19; i32 G6 = g6*19; + i32 G7 = g7*19; i32 G8 = g8*19; i32 G9 = g9*19; + // |F1|, |F3|, |F5|, |F7|, |F9| < 1.65 * 2^26 + // |G0|, |G2|, |G4|, |G6|, |G8| < 2^31 + // |G1|, |G3|, |G5|, |G7|, |G9| < 2^30 + + i64 t0 = f0*(i64)g0 + F1*(i64)G9 + f2*(i64)G8 + F3*(i64)G7 + f4*(i64)G6 + + F5*(i64)G5 + f6*(i64)G4 + F7*(i64)G3 + f8*(i64)G2 + F9*(i64)G1; + i64 t1 = f0*(i64)g1 + f1*(i64)g0 + f2*(i64)G9 + f3*(i64)G8 + f4*(i64)G7 + + f5*(i64)G6 + f6*(i64)G5 + f7*(i64)G4 + f8*(i64)G3 + f9*(i64)G2; + i64 t2 = f0*(i64)g2 + F1*(i64)g1 + f2*(i64)g0 + F3*(i64)G9 + f4*(i64)G8 + + F5*(i64)G7 + f6*(i64)G6 + F7*(i64)G5 + f8*(i64)G4 + F9*(i64)G3; + i64 t3 = f0*(i64)g3 + f1*(i64)g2 + f2*(i64)g1 + f3*(i64)g0 + f4*(i64)G9 + + f5*(i64)G8 + f6*(i64)G7 + f7*(i64)G6 + f8*(i64)G5 + f9*(i64)G4; + i64 t4 = f0*(i64)g4 + F1*(i64)g3 + f2*(i64)g2 + F3*(i64)g1 + f4*(i64)g0 + + F5*(i64)G9 + f6*(i64)G8 + F7*(i64)G7 + f8*(i64)G6 + F9*(i64)G5; + i64 t5 = f0*(i64)g5 + f1*(i64)g4 + f2*(i64)g3 + f3*(i64)g2 + f4*(i64)g1 + + f5*(i64)g0 + f6*(i64)G9 + f7*(i64)G8 + f8*(i64)G7 + f9*(i64)G6; + i64 t6 = f0*(i64)g6 + F1*(i64)g5 + f2*(i64)g4 + F3*(i64)g3 + f4*(i64)g2 + + F5*(i64)g1 + f6*(i64)g0 + F7*(i64)G9 + f8*(i64)G8 + F9*(i64)G7; + i64 t7 = f0*(i64)g7 + f1*(i64)g6 + f2*(i64)g5 + f3*(i64)g4 + f4*(i64)g3 + + f5*(i64)g2 + f6*(i64)g1 + f7*(i64)g0 + f8*(i64)G9 + f9*(i64)G8; + i64 t8 = f0*(i64)g8 + F1*(i64)g7 + f2*(i64)g6 + F3*(i64)g5 + f4*(i64)g4 + + F5*(i64)g3 + f6*(i64)g2 + F7*(i64)g1 + f8*(i64)g0 + F9*(i64)G9; + i64 t9 = f0*(i64)g9 + f1*(i64)g8 + f2*(i64)g7 + f3*(i64)g6 + f4*(i64)g5 + + f5*(i64)g4 + f6*(i64)g3 + f7*(i64)g2 + f8*(i64)g1 + f9*(i64)g0; + // t0 < 0.67 * 2^61 + // t1 < 0.41 * 2^61 + // t2 < 0.52 * 2^61 + // t3 < 0.32 * 2^61 + // t4 < 0.38 * 2^61 + // t5 < 0.22 * 2^61 + // t6 < 0.23 * 2^61 + // t7 < 0.13 * 2^61 + // t8 < 0.09 * 2^61 + // t9 < 0.03 * 2^61 + + FE_CARRY; // Everything below 2^62, Carry precondition OK +} + +// Precondition +// ------------- +// |f0|, |f2|, |f4|, |f6|, |f8| < 1.65 * 2^26 +// |f1|, |f3|, |f5|, |f7|, |f9| < 1.65 * 2^25 +// +// Note: we could use fe_mul() for this, but this is significantly faster +static void fe_sq(fe h, const fe f) +{ + i32 f0 = f[0]; i32 f1 = f[1]; i32 f2 = f[2]; i32 f3 = f[3]; i32 f4 = f[4]; + i32 f5 = f[5]; i32 f6 = f[6]; i32 f7 = f[7]; i32 f8 = f[8]; i32 f9 = f[9]; + i32 f0_2 = f0*2; i32 f1_2 = f1*2; i32 f2_2 = f2*2; i32 f3_2 = f3*2; + i32 f4_2 = f4*2; i32 f5_2 = f5*2; i32 f6_2 = f6*2; i32 f7_2 = f7*2; + i32 f5_38 = f5*38; i32 f6_19 = f6*19; i32 f7_38 = f7*38; + i32 f8_19 = f8*19; i32 f9_38 = f9*38; + // |f0_2| , |f2_2| , |f4_2| , |f6_2| , |f8_2| < 1.65 * 2^27 + // |f1_2| , |f3_2| , |f5_2| , |f7_2| , |f9_2| < 1.65 * 2^26 + // |f5_38|, |f6_19|, |f7_38|, |f8_19|, |f9_38| < 2^31 + + i64 t0 = f0 *(i64)f0 + f1_2*(i64)f9_38 + f2_2*(i64)f8_19 + + f3_2*(i64)f7_38 + f4_2*(i64)f6_19 + f5 *(i64)f5_38; + i64 t1 = f0_2*(i64)f1 + f2 *(i64)f9_38 + f3_2*(i64)f8_19 + + f4 *(i64)f7_38 + f5_2*(i64)f6_19; + i64 t2 = f0_2*(i64)f2 + f1_2*(i64)f1 + f3_2*(i64)f9_38 + + f4_2*(i64)f8_19 + f5_2*(i64)f7_38 + f6 *(i64)f6_19; + i64 t3 = f0_2*(i64)f3 + f1_2*(i64)f2 + f4 *(i64)f9_38 + + f5_2*(i64)f8_19 + f6 *(i64)f7_38; + i64 t4 = f0_2*(i64)f4 + f1_2*(i64)f3_2 + f2 *(i64)f2 + + f5_2*(i64)f9_38 + f6_2*(i64)f8_19 + f7 *(i64)f7_38; + i64 t5 = f0_2*(i64)f5 + f1_2*(i64)f4 + f2_2*(i64)f3 + + f6 *(i64)f9_38 + f7_2*(i64)f8_19; + i64 t6 = f0_2*(i64)f6 + f1_2*(i64)f5_2 + f2_2*(i64)f4 + + f3_2*(i64)f3 + f7_2*(i64)f9_38 + f8 *(i64)f8_19; + i64 t7 = f0_2*(i64)f7 + f1_2*(i64)f6 + f2_2*(i64)f5 + + f3_2*(i64)f4 + f8 *(i64)f9_38; + i64 t8 = f0_2*(i64)f8 + f1_2*(i64)f7_2 + f2_2*(i64)f6 + + f3_2*(i64)f5_2 + f4 *(i64)f4 + f9 *(i64)f9_38; + i64 t9 = f0_2*(i64)f9 + f1_2*(i64)f8 + f2_2*(i64)f7 + + f3_2*(i64)f6 + f4 *(i64)f5_2; + // t0 < 0.67 * 2^61 + // t1 < 0.41 * 2^61 + // t2 < 0.52 * 2^61 + // t3 < 0.32 * 2^61 + // t4 < 0.38 * 2^61 + // t5 < 0.22 * 2^61 + // t6 < 0.23 * 2^61 + // t7 < 0.13 * 2^61 + // t8 < 0.09 * 2^61 + // t9 < 0.03 * 2^61 + + FE_CARRY; +} + +// Parity check. Returns 0 if even, 1 if odd +static int fe_isodd(const fe f) +{ + u8 s[32]; + fe_tobytes(s, f); + u8 isodd = s[0] & 1; + WIPE_BUFFER(s); + return isodd; +} + +// Returns 1 if equal, 0 if not equal +static int fe_isequal(const fe f, const fe g) +{ + u8 fs[32]; + u8 gs[32]; + fe_tobytes(fs, f); + fe_tobytes(gs, g); + int isdifferent = crypto_verify32(fs, gs); + WIPE_BUFFER(fs); + WIPE_BUFFER(gs); + return 1 + isdifferent; +} + +// Inverse square root. +// Returns true if x is a square, false otherwise. +// After the call: +// isr = sqrt(1/x) if x is a non-zero square. +// isr = sqrt(sqrt(-1)/x) if x is not a square. +// isr = 0 if x is zero. +// We do not guarantee the sign of the square root. +// +// Notes: +// Let quartic = x^((p-1)/4) +// +// x^((p-1)/2) = chi(x) +// quartic^2 = chi(x) +// quartic = sqrt(chi(x)) +// quartic = 1 or -1 or sqrt(-1) or -sqrt(-1) +// +// Note that x is a square if quartic is 1 or -1 +// There are 4 cases to consider: +// +// if quartic = 1 (x is a square) +// then x^((p-1)/4) = 1 +// x^((p-5)/4) * x = 1 +// x^((p-5)/4) = 1/x +// x^((p-5)/8) = sqrt(1/x) or -sqrt(1/x) +// +// if quartic = -1 (x is a square) +// then x^((p-1)/4) = -1 +// x^((p-5)/4) * x = -1 +// x^((p-5)/4) = -1/x +// x^((p-5)/8) = sqrt(-1) / sqrt(x) +// x^((p-5)/8) * sqrt(-1) = sqrt(-1)^2 / sqrt(x) +// x^((p-5)/8) * sqrt(-1) = -1/sqrt(x) +// x^((p-5)/8) * sqrt(-1) = -sqrt(1/x) or sqrt(1/x) +// +// if quartic = sqrt(-1) (x is not a square) +// then x^((p-1)/4) = sqrt(-1) +// x^((p-5)/4) * x = sqrt(-1) +// x^((p-5)/4) = sqrt(-1)/x +// x^((p-5)/8) = sqrt(sqrt(-1)/x) or -sqrt(sqrt(-1)/x) +// +// Note that the product of two non-squares is always a square: +// For any non-squares a and b, chi(a) = -1 and chi(b) = -1. +// Since chi(x) = x^((p-1)/2), chi(a)*chi(b) = chi(a*b) = 1. +// Therefore a*b is a square. +// +// Since sqrt(-1) and x are both non-squares, their product is a +// square, and we can compute their square root. +// +// if quartic = -sqrt(-1) (x is not a square) +// then x^((p-1)/4) = -sqrt(-1) +// x^((p-5)/4) * x = -sqrt(-1) +// x^((p-5)/4) = -sqrt(-1)/x +// x^((p-5)/8) = sqrt(-sqrt(-1)/x) +// x^((p-5)/8) = sqrt( sqrt(-1)/x) * sqrt(-1) +// x^((p-5)/8) * sqrt(-1) = sqrt( sqrt(-1)/x) * sqrt(-1)^2 +// x^((p-5)/8) * sqrt(-1) = sqrt( sqrt(-1)/x) * -1 +// x^((p-5)/8) * sqrt(-1) = -sqrt(sqrt(-1)/x) or sqrt(sqrt(-1)/x) +static int invsqrt(fe isr, const fe x) +{ + fe t0, t1, t2; + + // t0 = x^((p-5)/8) + // Can be achieved with a simple double & add ladder, + // but it would be slower. + fe_sq(t0, x); + fe_sq(t1,t0); fe_sq(t1, t1); fe_mul(t1, x, t1); + fe_mul(t0, t0, t1); + fe_sq(t0, t0); fe_mul(t0, t1, t0); + fe_sq(t1, t0); FOR (i, 1, 5) fe_sq(t1, t1); fe_mul(t0, t1, t0); + fe_sq(t1, t0); FOR (i, 1, 10) fe_sq(t1, t1); fe_mul(t1, t1, t0); + fe_sq(t2, t1); FOR (i, 1, 20) fe_sq(t2, t2); fe_mul(t1, t2, t1); + fe_sq(t1, t1); FOR (i, 1, 10) fe_sq(t1, t1); fe_mul(t0, t1, t0); + fe_sq(t1, t0); FOR (i, 1, 50) fe_sq(t1, t1); fe_mul(t1, t1, t0); + fe_sq(t2, t1); FOR (i, 1, 100) fe_sq(t2, t2); fe_mul(t1, t2, t1); + fe_sq(t1, t1); FOR (i, 1, 50) fe_sq(t1, t1); fe_mul(t0, t1, t0); + fe_sq(t0, t0); FOR (i, 1, 2) fe_sq(t0, t0); fe_mul(t0, t0, x); + + // quartic = x^((p-1)/4) + i32 *quartic = t1; + fe_sq (quartic, t0); + fe_mul(quartic, quartic, x); + + i32 *check = t2; + fe_0 (check); int z0 = fe_isequal(x , check); + fe_1 (check); int p1 = fe_isequal(quartic, check); + fe_neg(check, check ); int m1 = fe_isequal(quartic, check); + fe_neg(check, sqrtm1); int ms = fe_isequal(quartic, check); + + // if quartic == -1 or sqrt(-1) + // then isr = x^((p-1)/4) * sqrt(-1) + // else isr = x^((p-1)/4) + fe_mul(isr, t0, sqrtm1); + fe_ccopy(isr, t0, 1 - (m1 | ms)); + + WIPE_BUFFER(t0); + WIPE_BUFFER(t1); + WIPE_BUFFER(t2); + return p1 | m1 | z0; +} + +// Inverse in terms of inverse square root. +// Requires two additional squarings to get rid of the sign. +// +// 1/x = x * (+invsqrt(x^2))^2 +// = x * (-invsqrt(x^2))^2 +// +// A fully optimised exponentiation by p-1 would save 6 field +// multiplications, but it would require more code. +static void fe_invert(fe out, const fe x) +{ + fe tmp; + fe_sq(tmp, x); + invsqrt(tmp, tmp); + fe_sq(tmp, tmp); + fe_mul(out, tmp, x); + WIPE_BUFFER(tmp); +} + +// trim a scalar for scalar multiplication +static void trim_scalar(u8 scalar[32]) +{ + scalar[ 0] &= 248; + scalar[31] &= 127; + scalar[31] |= 64; +} + +// get bit from scalar at position i +static int scalar_bit(const u8 s[32], int i) +{ + if (i < 0) { return 0; } // handle -1 for sliding windows + return (s[i>>3] >> (i&7)) & 1; +} + +/////////////// +/// X-25519 /// Taken from SUPERCOP's ref10 implementation. +/////////////// +static void scalarmult(u8 q[32], const u8 scalar[32], const u8 p[32], + int nb_bits) +{ + // computes the scalar product + fe x1; + fe_frombytes(x1, p); + + // computes the actual scalar product (the result is in x2 and z2) + fe x2, z2, x3, z3, t0, t1; + // Montgomery ladder + // In projective coordinates, to avoid divisions: x = X / Z + // We don't care about the y coordinate, it's only 1 bit of information + fe_1(x2); fe_0(z2); // "zero" point + fe_copy(x3, x1); fe_1(z3); // "one" point + int swap = 0; + for (int pos = nb_bits-1; pos >= 0; --pos) { + // constant time conditional swap before ladder step + int b = scalar_bit(scalar, pos); + swap ^= b; // xor trick avoids swapping at the end of the loop + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + swap = b; // anticipates one last swap after the loop + + // Montgomery ladder step: replaces (P2, P3) by (P2*2, P2+P3) + // with differential addition + fe_sub(t0, x3, z3); + fe_sub(t1, x2, z2); + fe_add(x2, x2, z2); + fe_add(z2, x3, z3); + fe_mul(z3, t0, x2); + fe_mul(z2, z2, t1); + fe_sq (t0, t1 ); + fe_sq (t1, x2 ); + fe_add(x3, z3, z2); + fe_sub(z2, z3, z2); + fe_mul(x2, t1, t0); + fe_sub(t1, t1, t0); + fe_sq (z2, z2 ); + fe_mul_small(z3, t1, 121666); + fe_sq (x3, x3 ); + fe_add(t0, t0, z3); + fe_mul(z3, x1, z2); + fe_mul(z2, t1, t0); + } + // last swap is necessary to compensate for the xor trick + // Note: after this swap, P3 == P2 + P1. + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + + // normalises the coordinates: x == X / Z + fe_invert(z2, z2); + fe_mul(x2, x2, z2); + fe_tobytes(q, x2); + + WIPE_BUFFER(x1); + WIPE_BUFFER(x2); WIPE_BUFFER(z2); WIPE_BUFFER(t0); + WIPE_BUFFER(x3); WIPE_BUFFER(z3); WIPE_BUFFER(t1); +} + +void crypto_x25519(u8 raw_shared_secret[32], + const u8 your_secret_key [32], + const u8 their_public_key [32]) +{ + // restrict the possible scalar values + u8 e[32]; + COPY(e, your_secret_key, 32); + trim_scalar(e); + scalarmult(raw_shared_secret, e, their_public_key, 255); + WIPE_BUFFER(e); +} + +void crypto_x25519_public_key(u8 public_key[32], + const u8 secret_key[32]) +{ + static const u8 base_point[32] = {9}; + crypto_x25519(public_key, secret_key, base_point); +} + +/////////////////////////// +/// Arithmetic modulo L /// +/////////////////////////// +static const u32 L[8] = {0x5cf5d3ed, 0x5812631a, 0xa2f79cd6, 0x14def9de, + 0x00000000, 0x00000000, 0x00000000, 0x10000000,}; + +// p = a*b + p +static void multiply(u32 p[16], const u32 a[8], const u32 b[8]) +{ + FOR (i, 0, 8) { + u64 carry = 0; + FOR (j, 0, 8) { + carry += p[i+j] + (u64)a[i] * b[j]; + p[i+j] = (u32)carry; + carry >>= 32; + } + p[i+8] = (u32)carry; + } +} + +static int is_above_l(const u32 x[8]) +{ + // We work with L directly, in a 2's complement encoding + // (-L == ~L + 1) + u64 carry = 1; + FOR (i, 0, 8) { + carry += (u64)x[i] + (~L[i] & 0xffffffff); + carry >>= 32; + } + return (int)carry; // carry is either 0 or 1 +} + +// Final reduction modulo L, by conditionally removing L. +// if x < l , then r = x +// if l <= x 2*l, then r = x-l +// otherwise the result will be wrong +static void remove_l(u32 r[8], const u32 x[8]) +{ + u64 carry = is_above_l(x); + u32 mask = ~(u32)carry + 1; // carry == 0 or 1 + FOR (i, 0, 8) { + carry += (u64)x[i] + (~L[i] & mask); + r[i] = (u32)carry; + carry >>= 32; + } +} + +// Full reduction modulo L (Barrett reduction) +static void mod_l(u8 reduced[32], const u32 x[16]) +{ + static const u32 r[9] = {0x0a2c131b,0xed9ce5a3,0x086329a7,0x2106215d, + 0xffffffeb,0xffffffff,0xffffffff,0xffffffff,0xf,}; + // xr = x * r + u32 xr[25] = {0}; + FOR (i, 0, 9) { + u64 carry = 0; + FOR (j, 0, 16) { + carry += xr[i+j] + (u64)r[i] * x[j]; + xr[i+j] = (u32)carry; + carry >>= 32; + } + xr[i+16] = (u32)carry; + } + // xr = floor(xr / 2^512) * L + // Since the result is guaranteed to be below 2*L, + // it is enough to only compute the first 256 bits. + // The division is performed by saying xr[i+16]. (16 * 32 = 512) + ZERO(xr, 8); + FOR (i, 0, 8) { + u64 carry = 0; + FOR (j, 0, 8-i) { + carry += xr[i+j] + (u64)xr[i+16] * L[j]; + xr[i+j] = (u32)carry; + carry >>= 32; + } + } + // xr = x - xr + u64 carry = 1; + FOR (i, 0, 8) { + carry += (u64)x[i] + (~xr[i] & 0xffffffff); + xr[i] = (u32)carry; + carry >>= 32; + } + // Final reduction modulo L (conditional subtraction) + remove_l(xr, xr); + store32_le_buf(reduced, xr, 8); + + WIPE_BUFFER(xr); +} + +static void reduce(u8 r[64]) +{ + u32 x[16]; + load32_le_buf(x, r, 16); + mod_l(r, x); + WIPE_BUFFER(x); +} + +// r = (a * b) + c +static void mul_add(u8 r[32], const u8 a[32], const u8 b[32], const u8 c[32]) +{ + u32 A[8]; load32_le_buf(A, a, 8); + u32 B[8]; load32_le_buf(B, b, 8); + u32 p[16]; load32_le_buf(p, c, 8); ZERO(p + 8, 8); + multiply(p, A, B); + mod_l(r, p); + WIPE_BUFFER(p); + WIPE_BUFFER(A); + WIPE_BUFFER(B); +} + +/////////////// +/// Ed25519 /// +/////////////// + +// Point (group element, ge) in a twisted Edwards curve, +// in extended projective coordinates. +// ge : x = X/Z, y = Y/Z, T = XY/Z +// ge_cached : Yp = X+Y, Ym = X-Y, T2 = T*D2 +// ge_precomp: Z = 1 +typedef struct { fe X; fe Y; fe Z; fe T; } ge; +typedef struct { fe Yp; fe Ym; fe Z; fe T2; } ge_cached; +typedef struct { fe Yp; fe Ym; fe T2; } ge_precomp; + +static void ge_zero(ge *p) +{ + fe_0(p->X); + fe_1(p->Y); + fe_1(p->Z); + fe_0(p->T); +} + +static void ge_tobytes(u8 s[32], const ge *h) +{ + fe recip, x, y; + fe_invert(recip, h->Z); + fe_mul(x, h->X, recip); + fe_mul(y, h->Y, recip); + fe_tobytes(s, y); + s[31] ^= fe_isodd(x) << 7; + + WIPE_BUFFER(recip); + WIPE_BUFFER(x); + WIPE_BUFFER(y); +} + +// h = -s, where s is a point encoded in 32 bytes +// +// Variable time! Inputs must not be secret! +// => Use only to *check* signatures. +// +// From the specifications: +// The encoding of s contains y and the sign of x +// x = sqrt((y^2 - 1) / (d*y^2 + 1)) +// In extended coordinates: +// X = x, Y = y, Z = 1, T = x*y +// +// Note that num * den is a square iff num / den is a square +// If num * den is not a square, the point was not on the curve. +// From the above: +// Let num = y^2 - 1 +// Let den = d*y^2 + 1 +// x = sqrt((y^2 - 1) / (d*y^2 + 1)) +// x = sqrt(num / den) +// x = sqrt(num^2 / (num * den)) +// x = num * sqrt(1 / (num * den)) +// +// Therefore, we can just compute: +// num = y^2 - 1 +// den = d*y^2 + 1 +// isr = invsqrt(num * den) // abort if not square +// x = num * isr +// Finally, negate x if its sign is not as specified. +static int ge_frombytes_neg_vartime(ge *h, const u8 s[32]) +{ + fe_frombytes(h->Y, s); + fe_1(h->Z); + fe_sq (h->T, h->Y); // t = y^2 + fe_mul(h->X, h->T, d ); // x = d*y^2 + fe_sub(h->T, h->T, h->Z); // t = y^2 - 1 + fe_add(h->X, h->X, h->Z); // x = d*y^2 + 1 + fe_mul(h->X, h->T, h->X); // x = (y^2 - 1) * (d*y^2 + 1) + int is_square = invsqrt(h->X, h->X); + if (!is_square) { + return -1; // Not on the curve, abort + } + fe_mul(h->X, h->T, h->X); // x = sqrt((y^2 - 1) / (d*y^2 + 1)) + if (fe_isodd(h->X) == (s[31] >> 7)) { + fe_neg(h->X, h->X); + } + fe_mul(h->T, h->X, h->Y); + return 0; +} + +static void ge_cache(ge_cached *c, const ge *p) +{ + fe_add (c->Yp, p->Y, p->X); + fe_sub (c->Ym, p->Y, p->X); + fe_copy(c->Z , p->Z ); + fe_mul (c->T2, p->T, D2 ); +} + +// Internal buffers are not wiped! Inputs must not be secret! +// => Use only to *check* signatures. +static void ge_add(ge *s, const ge *p, const ge_cached *q) +{ + fe a, b; + fe_add(a , p->Y, p->X ); + fe_sub(b , p->Y, p->X ); + fe_mul(a , a , q->Yp); + fe_mul(b , b , q->Ym); + fe_add(s->Y, a , b ); + fe_sub(s->X, a , b ); + + fe_add(s->Z, p->Z, p->Z ); + fe_mul(s->Z, s->Z, q->Z ); + fe_mul(s->T, p->T, q->T2); + fe_add(a , s->Z, s->T ); + fe_sub(b , s->Z, s->T ); + + fe_mul(s->T, s->X, s->Y); + fe_mul(s->X, s->X, b ); + fe_mul(s->Y, s->Y, a ); + fe_mul(s->Z, a , b ); +} + +// Internal buffers are not wiped! Inputs must not be secret! +// => Use only to *check* signatures. +static void ge_sub(ge *s, const ge *p, const ge_cached *q) +{ + ge_cached neg; + fe_copy(neg.Ym, q->Yp); + fe_copy(neg.Yp, q->Ym); + fe_copy(neg.Z , q->Z ); + fe_neg (neg.T2, q->T2); + ge_add(s, p, &neg); +} + +static void ge_madd(ge *s, const ge *p, const ge_precomp *q, fe a, fe b) +{ + fe_add(a , p->Y, p->X ); + fe_sub(b , p->Y, p->X ); + fe_mul(a , a , q->Yp); + fe_mul(b , b , q->Ym); + fe_add(s->Y, a , b ); + fe_sub(s->X, a , b ); + + fe_add(s->Z, p->Z, p->Z ); + fe_mul(s->T, p->T, q->T2); + fe_add(a , s->Z, s->T ); + fe_sub(b , s->Z, s->T ); + + fe_mul(s->T, s->X, s->Y); + fe_mul(s->X, s->X, b ); + fe_mul(s->Y, s->Y, a ); + fe_mul(s->Z, a , b ); +} + +// Internal buffers are not wiped! Inputs must not be secret! +// => Use only to *check* signatures. +static void ge_msub(ge *s, const ge *p, const ge_precomp *q, fe a, fe b) +{ + ge_precomp neg; + fe_copy(neg.Ym, q->Yp); + fe_copy(neg.Yp, q->Ym); + fe_neg (neg.T2, q->T2); + ge_madd(s, p, &neg, a, b); +} + +static void ge_double(ge *s, const ge *p, ge *q) +{ + fe_sq (q->X, p->X); + fe_sq (q->Y, p->Y); + fe_sq (q->Z, p->Z); // qZ = pZ^2 + fe_mul_small(q->Z, q->Z, 2); // qZ = pZ^2 * 2 + fe_add(q->T, p->X, p->Y); + fe_sq (s->T, q->T); + fe_add(q->T, q->Y, q->X); + fe_sub(q->Y, q->Y, q->X); + fe_sub(q->X, s->T, q->T); + fe_sub(q->Z, q->Z, q->Y); + + fe_mul(s->X, q->X , q->Z); + fe_mul(s->Y, q->T , q->Y); + fe_mul(s->Z, q->Y , q->Z); + fe_mul(s->T, q->X , q->T); +} + +// 5-bit signed window in cached format (Niels coordinates, Z=1) +static const ge_precomp b_window[8] = { + {{25967493,-14356035,29566456,3660896,-12694345, + 4014787,27544626,-11754271,-6079156,2047605,}, + {-12545711,934262,-2722910,3049990,-727428, + 9406986,12720692,5043384,19500929,-15469378,}, + {-8738181,4489570,9688441,-14785194,10184609, + -12363380,29287919,11864899,-24514362,-4438546,},}, + {{15636291,-9688557,24204773,-7912398,616977, + -16685262,27787600,-14772189,28944400,-1550024,}, + {16568933,4717097,-11556148,-1102322,15682896, + -11807043,16354577,-11775962,7689662,11199574,}, + {30464156,-5976125,-11779434,-15670865,23220365, + 15915852,7512774,10017326,-17749093,-9920357,},}, + {{10861363,11473154,27284546,1981175,-30064349, + 12577861,32867885,14515107,-15438304,10819380,}, + {4708026,6336745,20377586,9066809,-11272109, + 6594696,-25653668,12483688,-12668491,5581306,}, + {19563160,16186464,-29386857,4097519,10237984, + -4348115,28542350,13850243,-23678021,-15815942,},}, + {{5153746,9909285,1723747,-2777874,30523605, + 5516873,19480852,5230134,-23952439,-15175766,}, + {-30269007,-3463509,7665486,10083793,28475525, + 1649722,20654025,16520125,30598449,7715701,}, + {28881845,14381568,9657904,3680757,-20181635, + 7843316,-31400660,1370708,29794553,-1409300,},}, + {{-22518993,-6692182,14201702,-8745502,-23510406, + 8844726,18474211,-1361450,-13062696,13821877,}, + {-6455177,-7839871,3374702,-4740862,-27098617, + -10571707,31655028,-7212327,18853322,-14220951,}, + {4566830,-12963868,-28974889,-12240689,-7602672, + -2830569,-8514358,-10431137,2207753,-3209784,},}, + {{-25154831,-4185821,29681144,7868801,-6854661, + -9423865,-12437364,-663000,-31111463,-16132436,}, + {25576264,-2703214,7349804,-11814844,16472782, + 9300885,3844789,15725684,171356,6466918,}, + {23103977,13316479,9739013,-16149481,817875, + -15038942,8965339,-14088058,-30714912,16193877,},}, + {{-33521811,3180713,-2394130,14003687,-16903474, + -16270840,17238398,4729455,-18074513,9256800,}, + {-25182317,-4174131,32336398,5036987,-21236817, + 11360617,22616405,9761698,-19827198,630305,}, + {-13720693,2639453,-24237460,-7406481,9494427, + -5774029,-6554551,-15960994,-2449256,-14291300,},}, + {{-3151181,-5046075,9282714,6866145,-31907062, + -863023,-18940575,15033784,25105118,-7894876,}, + {-24326370,15950226,-31801215,-14592823,-11662737, + -5090925,1573892,-2625887,2198790,-15804619,}, + {-3099351,10324967,-2241613,7453183,-5446979, + -2735503,-13812022,-16236442,-32461234,-12290683,},}, +}; + +// Incremental sliding windows (left to right) +// Based on Roberto Maria Avanzi[2005] +typedef struct { + i16 next_index; // position of the next signed digit + i8 next_digit; // next signed digit (odd number below 2^window_width) + u8 next_check; // point at which we must check for a new window +} slide_ctx; + +static void slide_init(slide_ctx *ctx, const u8 scalar[32]) +{ + // scalar is guaranteed to be below L, either because we checked (s), + // or because we reduced it modulo L (h_ram). L is under 2^253, so + // so bits 253 to 255 are guaranteed to be zero. No need to test them. + // + // Note however that L is very close to 2^252, so bit 252 is almost + // always zero. If we were to start at bit 251, the tests wouldn't + // catch the off-by-one error (constructing one that does would be + // prohibitively expensive). + // + // We should still check bit 252, though. + int i = 252; + while (i > 0 && scalar_bit(scalar, i) == 0) { + i--; + } + ctx->next_check = (u8)(i + 1); + ctx->next_index = -1; + ctx->next_digit = -1; +} + +static int slide_step(slide_ctx *ctx, int width, int i, const u8 scalar[32]) +{ + if (i == ctx->next_check) { + if (scalar_bit(scalar, i) == scalar_bit(scalar, i - 1)) { + ctx->next_check--; + } else { + // compute digit of next window + int w = MIN(width, i + 1); + int v = -(scalar_bit(scalar, i) << (w-1)); + FOR_T (int, j, 0, w-1) { + v += scalar_bit(scalar, i-(w-1)+j) << j; + } + v += scalar_bit(scalar, i-w); + int lsb = v & (~v + 1); // smallest bit of v + int s = ( ((lsb & 0xAA) != 0) // log2(lsb) + | (((lsb & 0xCC) != 0) << 1) + | (((lsb & 0xF0) != 0) << 2)); + ctx->next_index = (i16)(i-(w-1)+s); + ctx->next_digit = (i8) (v >> s ); + ctx->next_check -= (u8) w; + } + } + return i == ctx->next_index ? ctx->next_digit: 0; +} + +#define P_W_WIDTH 3 // Affects the size of the stack +#define B_W_WIDTH 5 // Affects the size of the binary +#define P_W_SIZE (1<<(P_W_WIDTH-2)) + +// P = [b]B + [p]P, where B is the base point +// +// Variable time! Internal buffers are not wiped! Inputs must not be secret! +// => Use only to *check* signatures. +static void ge_double_scalarmult_vartime(ge *P, const u8 p[32], const u8 b[32]) +{ + // cache P window for addition + ge_cached cP[P_W_SIZE]; + { + ge P2, tmp; + ge_double(&P2, P, &tmp); + ge_cache(&cP[0], P); + FOR (i, 1, P_W_SIZE) { + ge_add(&tmp, &P2, &cP[i-1]); + ge_cache(&cP[i], &tmp); + } + } + + // Merged double and add ladder, fused with sliding + slide_ctx p_slide; slide_init(&p_slide, p); + slide_ctx b_slide; slide_init(&b_slide, b); + int i = MAX(p_slide.next_check, b_slide.next_check); + ge *sum = P; + ge_zero(sum); + while (i >= 0) { + ge tmp; + ge_double(sum, sum, &tmp); + int p_digit = slide_step(&p_slide, P_W_WIDTH, i, p); + int b_digit = slide_step(&b_slide, B_W_WIDTH, i, b); + if (p_digit > 0) { ge_add(sum, sum, &cP[ p_digit / 2]); } + if (p_digit < 0) { ge_sub(sum, sum, &cP[-p_digit / 2]); } + fe t1, t2; + if (b_digit > 0) { ge_madd(sum, sum, b_window + b_digit/2, t1, t2); } + if (b_digit < 0) { ge_msub(sum, sum, b_window + -b_digit/2, t1, t2); } + i--; + } +} + +// 5-bit signed comb in cached format (Niels coordinates, Z=1) +static const ge_precomp b_comb_low[8] = { + {{-6816601,-2324159,-22559413,124364,18015490, + 8373481,19993724,1979872,-18549925,9085059,}, + {10306321,403248,14839893,9633706,8463310, + -8354981,-14305673,14668847,26301366,2818560,}, + {-22701500,-3210264,-13831292,-2927732,-16326337, + -14016360,12940910,177905,12165515,-2397893,},}, + {{-12282262,-7022066,9920413,-3064358,-32147467, + 2927790,22392436,-14852487,2719975,16402117,}, + {-7236961,-4729776,2685954,-6525055,-24242706, + -15940211,-6238521,14082855,10047669,12228189,}, + {-30495588,-12893761,-11161261,3539405,-11502464, + 16491580,-27286798,-15030530,-7272871,-15934455,},}, + {{17650926,582297,-860412,-187745,-12072900, + -10683391,-20352381,15557840,-31072141,-5019061,}, + {-6283632,-2259834,-4674247,-4598977,-4089240, + 12435688,-31278303,1060251,6256175,10480726,}, + {-13871026,2026300,-21928428,-2741605,-2406664, + -8034988,7355518,15733500,-23379862,7489131,},}, + {{6883359,695140,23196907,9644202,-33430614, + 11354760,-20134606,6388313,-8263585,-8491918,}, + {-7716174,-13605463,-13646110,14757414,-19430591, + -14967316,10359532,-11059670,-21935259,12082603,}, + {-11253345,-15943946,10046784,5414629,24840771, + 8086951,-6694742,9868723,15842692,-16224787,},}, + {{9639399,11810955,-24007778,-9320054,3912937, + -9856959,996125,-8727907,-8919186,-14097242,}, + {7248867,14468564,25228636,-8795035,14346339, + 8224790,6388427,-7181107,6468218,-8720783,}, + {15513115,15439095,7342322,-10157390,18005294, + -7265713,2186239,4884640,10826567,7135781,},}, + {{-14204238,5297536,-5862318,-6004934,28095835, + 4236101,-14203318,1958636,-16816875,3837147,}, + {-5511166,-13176782,-29588215,12339465,15325758, + -15945770,-8813185,11075932,-19608050,-3776283,}, + {11728032,9603156,-4637821,-5304487,-7827751, + 2724948,31236191,-16760175,-7268616,14799772,},}, + {{-28842672,4840636,-12047946,-9101456,-1445464, + 381905,-30977094,-16523389,1290540,12798615,}, + {27246947,-10320914,14792098,-14518944,5302070, + -8746152,-3403974,-4149637,-27061213,10749585,}, + {25572375,-6270368,-15353037,16037944,1146292, + 32198,23487090,9585613,24714571,-1418265,},}, + {{19844825,282124,-17583147,11004019,-32004269, + -2716035,6105106,-1711007,-21010044,14338445,}, + {8027505,8191102,-18504907,-12335737,25173494, + -5923905,15446145,7483684,-30440441,10009108,}, + {-14134701,-4174411,10246585,-14677495,33553567, + -14012935,23366126,15080531,-7969992,7663473,},}, +}; + +static const ge_precomp b_comb_high[8] = { + {{33055887,-4431773,-521787,6654165,951411, + -6266464,-5158124,6995613,-5397442,-6985227,}, + {4014062,6967095,-11977872,3960002,8001989, + 5130302,-2154812,-1899602,-31954493,-16173976,}, + {16271757,-9212948,23792794,731486,-25808309, + -3546396,6964344,-4767590,10976593,10050757,},}, + {{2533007,-4288439,-24467768,-12387405,-13450051, + 14542280,12876301,13893535,15067764,8594792,}, + {20073501,-11623621,3165391,-13119866,13188608, + -11540496,-10751437,-13482671,29588810,2197295,}, + {-1084082,11831693,6031797,14062724,14748428, + -8159962,-20721760,11742548,31368706,13161200,},}, + {{2050412,-6457589,15321215,5273360,25484180, + 124590,-18187548,-7097255,-6691621,-14604792,}, + {9938196,2162889,-6158074,-1711248,4278932, + -2598531,-22865792,-7168500,-24323168,11746309,}, + {-22691768,-14268164,5965485,9383325,20443693, + 5854192,28250679,-1381811,-10837134,13717818,},}, + {{-8495530,16382250,9548884,-4971523,-4491811, + -3902147,6182256,-12832479,26628081,10395408,}, + {27329048,-15853735,7715764,8717446,-9215518, + -14633480,28982250,-5668414,4227628,242148,}, + {-13279943,-7986904,-7100016,8764468,-27276630, + 3096719,29678419,-9141299,3906709,11265498,},}, + {{11918285,15686328,-17757323,-11217300,-27548967, + 4853165,-27168827,6807359,6871949,-1075745,}, + {-29002610,13984323,-27111812,-2713442,28107359, + -13266203,6155126,15104658,3538727,-7513788,}, + {14103158,11233913,-33165269,9279850,31014152, + 4335090,-1827936,4590951,13960841,12787712,},}, + {{1469134,-16738009,33411928,13942824,8092558, + -8778224,-11165065,1437842,22521552,-2792954,}, + {31352705,-4807352,-25327300,3962447,12541566, + -9399651,-27425693,7964818,-23829869,5541287,}, + {-25732021,-6864887,23848984,3039395,-9147354, + 6022816,-27421653,10590137,25309915,-1584678,},}, + {{-22951376,5048948,31139401,-190316,-19542447, + -626310,-17486305,-16511925,-18851313,-12985140,}, + {-9684890,14681754,30487568,7717771,-10829709, + 9630497,30290549,-10531496,-27798994,-13812825,}, + {5827835,16097107,-24501327,12094619,7413972, + 11447087,28057551,-1793987,-14056981,4359312,},}, + {{26323183,2342588,-21887793,-1623758,-6062284, + 2107090,-28724907,9036464,-19618351,-13055189,}, + {-29697200,14829398,-4596333,14220089,-30022969, + 2955645,12094100,-13693652,-5941445,7047569,}, + {-3201977,14413268,-12058324,-16417589,-9035655, + -7224648,9258160,1399236,30397584,-5684634,},}, +}; + +static void lookup_add(ge *p, ge_precomp *tmp_c, fe tmp_a, fe tmp_b, + const ge_precomp comb[8], const u8 scalar[32], int i) +{ + u8 teeth = (u8)((scalar_bit(scalar, i) ) + + (scalar_bit(scalar, i + 32) << 1) + + (scalar_bit(scalar, i + 64) << 2) + + (scalar_bit(scalar, i + 96) << 3)); + u8 high = teeth >> 3; + u8 index = (teeth ^ (high - 1)) & 7; + FOR (j, 0, 8) { + i32 select = 1 & (((j ^ index) - 1) >> 8); + fe_ccopy(tmp_c->Yp, comb[j].Yp, select); + fe_ccopy(tmp_c->Ym, comb[j].Ym, select); + fe_ccopy(tmp_c->T2, comb[j].T2, select); + } + fe_neg(tmp_a, tmp_c->T2); + fe_cswap(tmp_c->T2, tmp_a , high ^ 1); + fe_cswap(tmp_c->Yp, tmp_c->Ym, high ^ 1); + ge_madd(p, p, tmp_c, tmp_a, tmp_b); +} + +// p = [scalar]B, where B is the base point +static void ge_scalarmult_base(ge *p, const u8 scalar[32]) +{ + // twin 4-bits signed combs, from Mike Hamburg's + // Fast and compact elliptic-curve cryptography (2012) + // 1 / 2 modulo L + static const u8 half_mod_L[32] = { + 247,233,122,46,141,49,9,44,107,206,123,81,239,124,111,10, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8, }; + // (2^256 - 1) / 2 modulo L + static const u8 half_ones[32] = { + 142,74,204,70,186,24,118,107,184,231,190,57,250,173,119,99, + 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,7, }; + + // All bits set form: 1 means 1, 0 means -1 + u8 s_scalar[32]; + mul_add(s_scalar, scalar, half_mod_L, half_ones); + + // Double and add ladder + fe tmp_a, tmp_b; // temporaries for addition + ge_precomp tmp_c; // temporary for comb lookup + ge tmp_d; // temporary for doubling + fe_1(tmp_c.Yp); + fe_1(tmp_c.Ym); + fe_0(tmp_c.T2); + + // Save a double on the first iteration + ge_zero(p); + lookup_add(p, &tmp_c, tmp_a, tmp_b, b_comb_low , s_scalar, 31); + lookup_add(p, &tmp_c, tmp_a, tmp_b, b_comb_high, s_scalar, 31+128); + // Regular double & add for the rest + for (int i = 30; i >= 0; i--) { + ge_double(p, p, &tmp_d); + lookup_add(p, &tmp_c, tmp_a, tmp_b, b_comb_low , s_scalar, i); + lookup_add(p, &tmp_c, tmp_a, tmp_b, b_comb_high, s_scalar, i+128); + } + // Note: we could save one addition at the end if we assumed the + // scalar fit in 252 bits. Which it does in practice if it is + // selected at random. However, non-random, non-hashed scalars + // *can* overflow 252 bits in practice. Better account for that + // than leaving that kind of subtle corner case. + + WIPE_BUFFER(tmp_a); WIPE_CTX(&tmp_d); + WIPE_BUFFER(tmp_b); WIPE_CTX(&tmp_c); + WIPE_BUFFER(s_scalar); +} + +void crypto_sign_public_key_custom_hash(u8 public_key[32], + const u8 secret_key[32], + const crypto_sign_vtable *hash) +{ + u8 a[64]; + hash->hash(a, secret_key, 32); + trim_scalar(a); + ge A; + ge_scalarmult_base(&A, a); + ge_tobytes(public_key, &A); + WIPE_BUFFER(a); + WIPE_CTX(&A); +} + +void crypto_sign_public_key(u8 public_key[32], const u8 secret_key[32]) +{ + crypto_sign_public_key_custom_hash(public_key, secret_key, + &crypto_blake2b_vtable); +} + +void crypto_sign_init_first_pass_custom_hash(crypto_sign_ctx_abstract *ctx, + const u8 secret_key[32], + const u8 public_key[32], + const crypto_sign_vtable *hash) +{ + ctx->hash = hash; // set vtable + u8 *a = ctx->buf; + u8 *prefix = ctx->buf + 32; + ctx->hash->hash(a, secret_key, 32); + trim_scalar(a); + + if (public_key == 0) { + crypto_sign_public_key_custom_hash(ctx->pk, secret_key, ctx->hash); + } else { + COPY(ctx->pk, public_key, 32); + } + + // Deterministic part of EdDSA: Construct a nonce by hashing the message + // instead of generating a random number. + // An actual random number would work just fine, and would save us + // the trouble of hashing the message twice. If we did that + // however, the user could fuck it up and reuse the nonce. + ctx->hash->init (ctx); + ctx->hash->update(ctx, prefix , 32); +} + +void crypto_sign_init_first_pass(crypto_sign_ctx_abstract *ctx, + const u8 secret_key[32], + const u8 public_key[32]) +{ + crypto_sign_init_first_pass_custom_hash(ctx, secret_key, public_key, + &crypto_blake2b_vtable); +} + +void crypto_sign_update(crypto_sign_ctx_abstract *ctx, + const u8 *msg, size_t msg_size) +{ + ctx->hash->update(ctx, msg, msg_size); +} + +void crypto_sign_init_second_pass(crypto_sign_ctx_abstract *ctx) +{ + u8 *r = ctx->buf + 32; + u8 *half_sig = ctx->buf + 64; + ctx->hash->final(ctx, r); + reduce(r); + + // first half of the signature = "random" nonce times the base point + ge R; + ge_scalarmult_base(&R, r); + ge_tobytes(half_sig, &R); + WIPE_CTX(&R); + + // Hash R, the public key, and the message together. + // It cannot be done in parallel with the first hash. + ctx->hash->init (ctx); + ctx->hash->update(ctx, half_sig, 32); + ctx->hash->update(ctx, ctx->pk , 32); +} + +void crypto_sign_final(crypto_sign_ctx_abstract *ctx, u8 signature[64]) +{ + u8 *a = ctx->buf; + u8 *r = ctx->buf + 32; + u8 *half_sig = ctx->buf + 64; + u8 h_ram[64]; + ctx->hash->final(ctx, h_ram); + reduce(h_ram); + COPY(signature, half_sig, 32); + mul_add(signature + 32, h_ram, a, r); // s = h_ram * a + r + WIPE_BUFFER(h_ram); + crypto_wipe(ctx, ctx->hash->ctx_size); +} + +void crypto_sign(u8 signature[64], + const u8 secret_key[32], + const u8 public_key[32], + const u8 *message, size_t message_size) +{ + crypto_sign_ctx ctx; + crypto_sign_ctx_abstract *actx = (crypto_sign_ctx_abstract*)&ctx; + crypto_sign_init_first_pass (actx, secret_key, public_key); + crypto_sign_update (actx, message, message_size); + crypto_sign_init_second_pass(actx); + crypto_sign_update (actx, message, message_size); + crypto_sign_final (actx, signature); +} + +void crypto_check_init_custom_hash(crypto_check_ctx_abstract *ctx, + const u8 signature[64], + const u8 public_key[32], + const crypto_sign_vtable *hash) +{ + ctx->hash = hash; // set vtable + COPY(ctx->buf, signature , 64); + COPY(ctx->pk , public_key, 32); + ctx->hash->init (ctx); + ctx->hash->update(ctx, signature , 32); + ctx->hash->update(ctx, public_key, 32); +} + +void crypto_check_init(crypto_check_ctx_abstract *ctx, const u8 signature[64], + const u8 public_key[32]) +{ + crypto_check_init_custom_hash(ctx, signature, public_key, + &crypto_blake2b_vtable); +} + +void crypto_check_update(crypto_check_ctx_abstract *ctx, + const u8 *msg, size_t msg_size) +{ + ctx->hash->update(ctx, msg, msg_size); +} + +int crypto_check_final(crypto_check_ctx_abstract *ctx) +{ + u8 *s = ctx->buf + 32; // s + u8 h_ram[64]; + u32 s32[8]; // s (different encoding) + ge A; + + ctx->hash->final(ctx, h_ram); + reduce(h_ram); + load32_le_buf(s32, s, 8); + if (ge_frombytes_neg_vartime(&A, ctx->pk) || // A = -pk + is_above_l(s32)) { // prevent s malleability + return -1; + } + ge_double_scalarmult_vartime(&A, h_ram, s); // A = [s]B - [h_ram]pk + ge_tobytes(ctx->pk, &A); // R_check = A + return crypto_verify32(ctx->buf, ctx->pk); // R == R_check ? OK : fail +} + +int crypto_check(const u8 signature[64], const u8 public_key[32], + const u8 *message, size_t message_size) +{ + crypto_check_ctx ctx; + crypto_check_ctx_abstract *actx = (crypto_check_ctx_abstract*)&ctx; + crypto_check_init (actx, signature, public_key); + crypto_check_update(actx, message, message_size); + return crypto_check_final(actx); +} + +/////////////////////// +/// EdDSA to X25519 /// +/////////////////////// +void crypto_from_eddsa_private(u8 x25519[32], const u8 eddsa[32]) +{ + u8 a[64]; + crypto_blake2b(a, eddsa, 32); + COPY(x25519, a, 32); + WIPE_BUFFER(a); +} + +void crypto_from_eddsa_public(u8 x25519[32], const u8 eddsa[32]) +{ + fe t1, t2; + fe_frombytes(t2, eddsa); + fe_add(t1, fe_one, t2); + fe_sub(t2, fe_one, t2); + fe_invert(t2, t2); + fe_mul(t1, t1, t2); + fe_tobytes(x25519, t1); + WIPE_BUFFER(t1); + WIPE_BUFFER(t2); +} + +///////////////////////////////////////////// +/// Dirty ephemeral public key generation /// +///////////////////////////////////////////// + +// Those functions generates a public key, *without* clearing the +// cofactor. Sending that key over the network leaks 3 bits of the +// private key. Use only to generate ephemeral keys that will be hidden +// with crypto_curve_to_hidden(). +// +// The public key is otherwise compatible with crypto_x25519() and +// crypto_key_exchange() (those properly clear the cofactor). +// +// Note that the distribution of the resulting public keys is almost +// uniform. Flipping the sign of the v coordinate (not provided by this +// function), covers the entire key space almost perfectly, where +// "almost" means a 2^-128 bias (undetectable). This uniformity is +// needed to ensure the proper randomness of the resulting +// representatives (once we apply crypto_curve_to_hidden()). +// +// Recall that Curve25519 has order C = 2^255 + e, with e < 2^128 (not +// to be confused with the prime order of the main subgroup, L, which is +// 8 times less than that). +// +// Generating all points would require us to multiply a point of order C +// (the base point plus any point of order 8) by all scalars from 0 to +// C-1. Clamping limits us to scalars between 2^254 and 2^255 - 1. But +// by negating the resulting point at random, we also cover scalars from +// -2^255 + 1 to -2^254 (which modulo C is congruent to e+1 to 2^254 + e). +// +// In practice: +// - Scalars from 0 to e + 1 are never generated +// - Scalars from 2^255 to 2^255 + e are never generated +// - Scalars from 2^254 + 1 to 2^254 + e are generated twice +// +// Since e < 2^128, detecting this bias requires observing over 2^100 +// representatives from a given source (this will never happen), *and* +// recovering enough of the private key to determine that they do, or do +// not, belong to the biased set (this practically requires solving +// discrete logarithm, which is conjecturally intractable). +// +// In practice, this means the bias is impossible to detect. + +// s + (x*L) % 8*L +// Guaranteed to fit in 256 bits iff s fits in 255 bits. +// L < 2^253 +// x%8 < 2^3 +// L * (x%8) < 2^255 +// s < 2^255 +// s + L * (x%8) < 2^256 +static void add_xl(u8 s[32], u8 x) +{ + u64 mod8 = x & 7; + u64 carry = 0; + FOR (i , 0, 8) { + carry = carry + load32_le(s + 4*i) + L[i] * mod8; + store32_le(s + 4*i, (u32)carry); + carry >>= 32; + } +} + +// "Small" dirty ephemeral key. +// Use if you need to shrink the size of the binary, and can afford to +// slow down by a factor of two (compared to the fast version) +// +// This version works by decoupling the cofactor from the main factor. +// +// - The trimmed scalar determines the main factor +// - The clamped bits of the scalar determine the cofactor. +// +// Cofactor and main factor are combined into a single scalar, which is +// then multiplied by a point of order 8*L (unlike the base point, which +// has prime order). That "dirty" base point is the addition of the +// regular base point (9), and a point of order 8. +void crypto_x25519_dirty_small(u8 public_key[32], const u8 secret_key[32]) +{ + // Base point of order 8*L + // Raw scalar multiplication with it does not clear the cofactor, + // and the resulting public key will reveal 3 bits of the scalar. + // + // The low order component of this base point has been chosen + // to yield the same results as crypto_x25519_dirty_fast(). + static const u8 dirty_base_point[32] = { + 0xd8, 0x86, 0x1a, 0xa2, 0x78, 0x7a, 0xd9, 0x26, 0x8b, 0x74, 0x74, 0xb6, + 0x82, 0xe3, 0xbe, 0xc3, 0xce, 0x36, 0x9a, 0x1e, 0x5e, 0x31, 0x47, 0xa2, + 0x6d, 0x37, 0x7c, 0xfd, 0x20, 0xb5, 0xdf, 0x75, + }; + // separate the main factor & the cofactor of the scalar + u8 scalar[32]; + COPY(scalar, secret_key, 32); + trim_scalar(scalar); + + // Separate the main factor and the cofactor + // + // The scalar is trimmed, so its cofactor is cleared. The three + // least significant bits however still have a main factor. We must + // remove it for X25519 compatibility. + // + // cofactor = lsb * L (modulo 8*L) + // combined = scalar + cofactor (modulo 8*L) + add_xl(scalar, secret_key[0]); + scalarmult(public_key, scalar, dirty_base_point, 256); + WIPE_BUFFER(scalar); +} + +// Select low order point +// We're computing the [cofactor]lop scalar multiplication, where: +// +// cofactor = tweak & 7. +// lop = (lop_x, lop_y) +// lop_x = sqrt((sqrt(d + 1) + 1) / d) +// lop_y = -lop_x * sqrtm1 +// +// The low order point has order 8. There are 4 such points. We've +// chosen the one whose both coordinates are positive (below p/2). +// The 8 low order points are as follows: +// +// [0]lop = ( 0 , 1 ) +// [1]lop = ( lop_x , lop_y) +// [2]lop = ( sqrt(-1), -0 ) +// [3]lop = ( lop_x , -lop_y) +// [4]lop = (-0 , -1 ) +// [5]lop = (-lop_x , -lop_y) +// [6]lop = (-sqrt(-1), 0 ) +// [7]lop = (-lop_x , lop_y) +// +// The x coordinate is either 0, sqrt(-1), lop_x, or their opposite. +// The y coordinate is either 0, -1 , lop_y, or their opposite. +// The pattern for both is the same, except for a rotation of 2 (modulo 8) +// +// This helper function captures the pattern, and we can use it thus: +// +// select_lop(x, lop_x, sqrtm1, cofactor); +// select_lop(y, lop_y, fe_one, cofactor + 2); +// +// This is faster than an actual scalar multiplication, +// and requires less code than naive constant time look up. +static void select_lop(fe out, const fe x, const fe k, u8 cofactor) +{ + fe tmp; + fe_0(out); + fe_ccopy(out, k , (cofactor >> 1) & 1); // bit 1 + fe_ccopy(out, x , (cofactor >> 0) & 1); // bit 0 + fe_neg (tmp, out); + fe_ccopy(out, tmp, (cofactor >> 2) & 1); // bit 2 + WIPE_BUFFER(tmp); +} + +// "Fast" dirty ephemeral key +// We use this one by default. +// +// This version works by performing a regular scalar multiplication, +// then add a low order point. The scalar multiplication is done in +// Edwards space for more speed (*2 compared to the "small" version). +// The cost is a bigger binary for programs that don't also sign messages. +void crypto_x25519_dirty_fast(u8 public_key[32], const u8 secret_key[32]) +{ + // Compute clean scalar multiplication + u8 scalar[32]; + ge pk; + COPY(scalar, secret_key, 32); + trim_scalar(scalar); + ge_scalarmult_base(&pk, scalar); + + // Compute low order point + fe t1, t2; + select_lop(t1, lop_x, sqrtm1, secret_key[0]); + select_lop(t2, lop_y, fe_one, secret_key[0] + 2); + ge_precomp low_order_point; + fe_add(low_order_point.Yp, t2, t1); + fe_sub(low_order_point.Ym, t2, t1); + fe_mul(low_order_point.T2, t2, t1); + fe_mul(low_order_point.T2, low_order_point.T2, D2); + + // Add low order point to the public key + ge_madd(&pk, &pk, &low_order_point, t1, t2); + + // Convert to Montgomery u coordinate (we ignore the sign) + fe_add(t1, pk.Z, pk.Y); + fe_sub(t2, pk.Z, pk.Y); + fe_invert(t2, t2); + fe_mul(t1, t1, t2); + + fe_tobytes(public_key, t1); + + WIPE_BUFFER(t1); WIPE_CTX(&pk); + WIPE_BUFFER(t2); WIPE_CTX(&low_order_point); + WIPE_BUFFER(scalar); +} + +/////////////////// +/// Elligator 2 /// +/////////////////// +static const fe A = {486662}; + +// Elligator direct map +// +// Computes the point corresponding to a representative, encoded in 32 +// bytes (little Endian). Since positive representatives fits in 254 +// bits, The two most significant bits are ignored. +// +// From the paper: +// w = -A / (fe(1) + non_square * r^2) +// e = chi(w^3 + A*w^2 + w) +// u = e*w - (fe(1)-e)*(A//2) +// v = -e * sqrt(u^3 + A*u^2 + u) +// +// We ignore v because we don't need it for X25519 (the Montgomery +// ladder only uses u). +// +// Note that e is either 0, 1 or -1 +// if e = 0 u = 0 and v = 0 +// if e = 1 u = w +// if e = -1 u = -w - A = w * non_square * r^2 +// +// Let r1 = non_square * r^2 +// Let r2 = 1 + r1 +// Note that r2 cannot be zero, -1/non_square is not a square. +// We can (tediously) verify that: +// w^3 + A*w^2 + w = (A^2*r1 - r2^2) * A / r2^3 +// Therefore: +// chi(w^3 + A*w^2 + w) = chi((A^2*r1 - r2^2) * (A / r2^3)) +// chi(w^3 + A*w^2 + w) = chi((A^2*r1 - r2^2) * (A / r2^3)) * 1 +// chi(w^3 + A*w^2 + w) = chi((A^2*r1 - r2^2) * (A / r2^3)) * chi(r2^6) +// chi(w^3 + A*w^2 + w) = chi((A^2*r1 - r2^2) * (A / r2^3) * r2^6) +// chi(w^3 + A*w^2 + w) = chi((A^2*r1 - r2^2) * A * r2^3) +// Corollary: +// e = 1 if (A^2*r1 - r2^2) * A * r2^3) is a non-zero square +// e = -1 if (A^2*r1 - r2^2) * A * r2^3) is not a square +// Note that w^3 + A*w^2 + w (and therefore e) can never be zero: +// w^3 + A*w^2 + w = w * (w^2 + A*w + 1) +// w^3 + A*w^2 + w = w * (w^2 + A*w + A^2/4 - A^2/4 + 1) +// w^3 + A*w^2 + w = w * (w + A/2)^2 - A^2/4 + 1) +// which is zero only if: +// w = 0 (impossible) +// (w + A/2)^2 = A^2/4 - 1 (impossible, because A^2/4-1 is not a square) +// +// Let isr = invsqrt((A^2*r1 - r2^2) * A * r2^3) +// isr = sqrt(1 / ((A^2*r1 - r2^2) * A * r2^3)) if e = 1 +// isr = sqrt(sqrt(-1) / ((A^2*r1 - r2^2) * A * r2^3)) if e = -1 +// +// if e = 1 +// let u1 = -A * (A^2*r1 - r2^2) * A * r2^2 * isr^2 +// u1 = w +// u1 = u +// +// if e = -1 +// let ufactor = -non_square * sqrt(-1) * r^2 +// let vfactor = sqrt(ufactor) +// let u2 = -A * (A^2*r1 - r2^2) * A * r2^2 * isr^2 * ufactor +// u2 = w * -1 * -non_square * r^2 +// u2 = w * non_square * r^2 +// u2 = u +void crypto_hidden_to_curve(uint8_t curve[32], const uint8_t hidden[32]) +{ + fe r, u, t1, t2, t3; + fe_frombytes_mask(r, hidden, 2); // r is encoded in 254 bits. + fe_sq(r, r); + fe_add(t1, r, r); + fe_add(u, t1, fe_one); + fe_sq (t2, u); + fe_mul(t3, A2, t1); + fe_sub(t3, t3, t2); + fe_mul(t3, t3, A); + fe_mul(t1, t2, u); + fe_mul(t1, t3, t1); + int is_square = invsqrt(t1, t1); + fe_mul(u, r, ufactor); + fe_ccopy(u, fe_one, is_square); + fe_sq (t1, t1); + fe_mul(u, u, A); + fe_mul(u, u, t3); + fe_mul(u, u, t2); + fe_mul(u, u, t1); + fe_neg(u, u); + fe_tobytes(curve, u); + + WIPE_BUFFER(t1); WIPE_BUFFER(r); + WIPE_BUFFER(t2); WIPE_BUFFER(u); + WIPE_BUFFER(t3); +} + +// Elligator inverse map +// +// Computes the representative of a point, if possible. If not, it does +// nothing and returns -1. Note that the success of the operation +// depends only on the point (more precisely its u coordinate). The +// tweak parameter is used only upon success +// +// The tweak should be a random byte. Beyond that, its contents are an +// implementation detail. Currently, the tweak comprises: +// - Bit 1 : sign of the v coordinate (0 if positive, 1 if negative) +// - Bit 2-5: not used +// - Bits 6-7: random padding +// +// From the paper: +// Let sq = -non_square * u * (u+A) +// if sq is not a square, or u = -A, there is no mapping +// Assuming there is a mapping: +// if v is positive: r = sqrt(-u / (non_square * (u+A))) +// if v is negative: r = sqrt(-(u+A) / (non_square * u )) +// +// We compute isr = invsqrt(-non_square * u * (u+A)) +// if it wasn't a square, abort. +// else, isr = sqrt(-1 / (non_square * u * (u+A)) +// +// If v is positive, we return isr * u: +// isr * u = sqrt(-1 / (non_square * u * (u+A)) * u +// isr * u = sqrt(-u / (non_square * (u+A)) +// +// If v is negative, we return isr * (u+A): +// isr * (u+A) = sqrt(-1 / (non_square * u * (u+A)) * (u+A) +// isr * (u+A) = sqrt(-(u+A) / (non_square * u) +int crypto_curve_to_hidden(u8 hidden[32], const u8 public_key[32], u8 tweak) +{ + fe t1, t2, t3; + fe_frombytes(t1, public_key); // t1 = u + + fe_add(t2, t1, A); // t2 = u + A + fe_mul(t3, t1, t2); + fe_mul_small(t3, t3, -2); + int is_square = invsqrt(t3, t3); // t3 = sqrt(-1 / non_square * u * (u+A)) + if (is_square) { + // The only variable time bit. This ultimately reveals how many + // tries it took us to find a representable key. + // This does not affect security as long as we try keys at random. + + fe_ccopy (t1, t2, tweak & 1); // multiply by u if v is positive, + fe_mul (t3, t1, t3); // multiply by u+A otherwise + fe_mul_small(t1, t3, 2); + fe_neg (t2, t3); + fe_ccopy (t3, t2, fe_isodd(t1)); + fe_tobytes(hidden, t3); + + // Pad with two random bits + hidden[31] |= tweak & 0xc0; + } + + WIPE_BUFFER(t1); + WIPE_BUFFER(t2); + WIPE_BUFFER(t3); + return is_square - 1; +} + +void crypto_hidden_key_pair(u8 hidden[32], u8 secret_key[32], u8 seed[32]) +{ + u8 pk [32]; // public key + u8 buf[64]; // seed + representative + COPY(buf + 32, seed, 32); + do { + crypto_chacha20(buf, 0, 64, buf+32, zero); + crypto_x25519_dirty_fast(pk, buf); // or the "small" version + } while(crypto_curve_to_hidden(buf+32, pk, buf[32])); + // Note that the return value of crypto_curve_to_hidden() is + // independent from its tweak parameter. + // Therefore, buf[32] is not actually reused. Either we loop one + // more time and buf[32] is used for the new seed, or we succeeded, + // and buf[32] becomes the tweak parameter. + + crypto_wipe(seed, 32); + COPY(hidden , buf + 32, 32); + COPY(secret_key, buf , 32); + WIPE_BUFFER(buf); + WIPE_BUFFER(pk); +} + +//////////////////// +/// Key exchange /// +//////////////////// +void crypto_key_exchange(u8 shared_key[32], + const u8 your_secret_key [32], + const u8 their_public_key[32]) +{ + crypto_x25519(shared_key, your_secret_key, their_public_key); + crypto_hchacha20(shared_key, shared_key, zero); +} + +/////////////////////// +/// Scalar division /// +/////////////////////// + +// Montgomery reduction. +// Divides x by (2^256), and reduces the result modulo L +// +// Precondition: +// x < L * 2^256 +// Constants: +// r = 2^256 (makes division by r trivial) +// k = (r * (1/r) - 1) // L (1/r is computed modulo L ) +// Algorithm: +// s = (x * k) % r +// t = x + s*L (t is always a multiple of r) +// u = (t/r) % L (u is always below 2*L, conditional subtraction is enough) +static void redc(u32 u[8], u32 x[16]) +{ + static const u32 k[8] = { 0x12547e1b, 0xd2b51da3, 0xfdba84ff, 0xb1a206f2, + 0xffa36bea, 0x14e75438, 0x6fe91836, 0x9db6c6f2, }; + + // s = x * k (modulo 2^256) + // This is cheaper than the full multiplication. + u32 s[8] = {0}; + FOR (i, 0, 8) { + u64 carry = 0; + FOR (j, 0, 8-i) { + carry += s[i+j] + (u64)x[i] * k[j]; + s[i+j] = (u32)carry; + carry >>= 32; + } + } + u32 t[16] = {0}; + multiply(t, s, L); + + // t = t + x + u64 carry = 0; + FOR (i, 0, 16) { + carry += (u64)t[i] + x[i]; + t[i] = (u32)carry; + carry >>= 32; + } + + // u = (t / 2^256) % L + // Note that t / 2^256 is always below 2*L, + // So a constant time conditional subtraction is enough + remove_l(u, t+8); + + WIPE_BUFFER(s); + WIPE_BUFFER(t); +} + +void crypto_x25519_inverse(u8 blind_salt [32], const u8 private_key[32], + const u8 curve_point[32]) +{ + static const u8 Lm2[32] = { // L - 2 + 0xeb, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, + 0xde, 0xf9, 0xde, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, }; + // 1 in Montgomery form + u32 m_inv [8] = {0x8d98951d, 0xd6ec3174, 0x737dcf70, 0xc6ef5bf4, + 0xfffffffe, 0xffffffff, 0xffffffff, 0x0fffffff,}; + + u8 scalar[32]; + COPY(scalar, private_key, 32); + trim_scalar(scalar); + + // Convert the scalar in Montgomery form + // m_scl = scalar * 2^256 (modulo L) + u32 m_scl[8]; + { + u32 tmp[16]; + ZERO(tmp, 8); + load32_le_buf(tmp+8, scalar, 8); + mod_l(scalar, tmp); + load32_le_buf(m_scl, scalar, 8); + WIPE_BUFFER(tmp); // Wipe ASAP to save stack space + } + + // Compute the inverse + u32 product[16]; + for (int i = 252; i >= 0; i--) { + ZERO(product, 16); + multiply(product, m_inv, m_inv); + redc(m_inv, product); + if (scalar_bit(Lm2, i)) { + ZERO(product, 16); + multiply(product, m_inv, m_scl); + redc(m_inv, product); + } + } + // Convert the inverse *out* of Montgomery form + // scalar = m_inv / 2^256 (modulo L) + COPY(product, m_inv, 8); + ZERO(product + 8, 8); + redc(m_inv, product); + store32_le_buf(scalar, m_inv, 8); // the *inverse* of the scalar + + // Clear the cofactor of scalar: + // cleared = scalar * (3*L + 1) (modulo 8*L) + // cleared = scalar + scalar * 3 * L (modulo 8*L) + // Note that (scalar * 3) is reduced modulo 8, so we only need the + // first byte. + add_xl(scalar, scalar[0] * 3); + + // Recall that 8*L < 2^256. However it is also very close to + // 2^255. If we spanned the ladder over 255 bits, random tests + // wouldn't catch the off-by-one error. + scalarmult(blind_salt, scalar, curve_point, 256); + + WIPE_BUFFER(scalar); WIPE_BUFFER(m_scl); + WIPE_BUFFER(product); WIPE_BUFFER(m_inv); +} + +//////////////////////////////// +/// Authenticated encryption /// +//////////////////////////////// +static void lock_auth(u8 mac[16], const u8 auth_key[32], + const u8 *ad , size_t ad_size, + const u8 *cipher_text, size_t text_size) +{ + u8 sizes[16]; // Not secret, not wiped + store64_le(sizes + 0, ad_size); + store64_le(sizes + 8, text_size); + crypto_poly1305_ctx poly_ctx; // auto wiped... + crypto_poly1305_init (&poly_ctx, auth_key); + crypto_poly1305_update(&poly_ctx, ad , ad_size); + crypto_poly1305_update(&poly_ctx, zero , align(ad_size, 16)); + crypto_poly1305_update(&poly_ctx, cipher_text, text_size); + crypto_poly1305_update(&poly_ctx, zero , align(text_size, 16)); + crypto_poly1305_update(&poly_ctx, sizes , 16); + crypto_poly1305_final (&poly_ctx, mac); // ...here +} + +void crypto_lock_aead(u8 mac[16], u8 *cipher_text, + const u8 key[32], const u8 nonce[24], + const u8 *ad , size_t ad_size, + const u8 *plain_text, size_t text_size) +{ + u8 sub_key[32]; + u8 auth_key[64]; // "Wasting" the whole Chacha block is faster + crypto_hchacha20(sub_key, key, nonce); + crypto_chacha20(auth_key, 0, 64, sub_key, nonce + 16); + crypto_chacha20_ctr(cipher_text, plain_text, text_size, + sub_key, nonce + 16, 1); + lock_auth(mac, auth_key, ad, ad_size, cipher_text, text_size); + WIPE_BUFFER(sub_key); + WIPE_BUFFER(auth_key); +} + +int crypto_unlock_aead(u8 *plain_text, const u8 key[32], const u8 nonce[24], + const u8 mac[16], + const u8 *ad , size_t ad_size, + const u8 *cipher_text, size_t text_size) +{ + u8 sub_key[32]; + u8 auth_key[64]; // "Wasting" the whole Chacha block is faster + crypto_hchacha20(sub_key, key, nonce); + crypto_chacha20(auth_key, 0, 64, sub_key, nonce + 16); + u8 real_mac[16]; + lock_auth(real_mac, auth_key, ad, ad_size, cipher_text, text_size); + WIPE_BUFFER(auth_key); + int mismatch = crypto_verify16(mac, real_mac); + if (!mismatch) { + crypto_chacha20_ctr(plain_text, cipher_text, text_size, + sub_key, nonce + 16, 1); + } + WIPE_BUFFER(sub_key); + WIPE_BUFFER(real_mac); + return mismatch; +} + +void crypto_lock(u8 mac[16], u8 *cipher_text, + const u8 key[32], const u8 nonce[24], + const u8 *plain_text, size_t text_size) +{ + crypto_lock_aead(mac, cipher_text, key, nonce, 0, 0, plain_text, text_size); +} + +int crypto_unlock(u8 *plain_text, + const u8 key[32], const u8 nonce[24], const u8 mac[16], + const u8 *cipher_text, size_t text_size) +{ + return crypto_unlock_aead(plain_text, key, nonce, mac, 0, 0, + cipher_text, text_size); +} + +#ifdef MONOCYPHER_CPP_NAMESPACE +} +#endif |