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ardupilot/libraries/AP_CheckFirmware/monocypher.cpp

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// Monocypher version 3.1.2
//
// 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"
// we don't need Argon2
#define MONOCYPHER_ARGON2_ENABLE 0
// we want the bootloader to be as small as possible
#define BLAKE2_NO_UNROLLING 1
/////////////////
/// Utilities ///
/////////////////
#define FOR_T(type, i0, start, end) for (type i0 = (start); i0 < (end); i0++)
#define FOR(i1, start, end) FOR_T(size_t, i1, start, end)
#define COPY(dst, src, size) FOR(i2, 0, size) (dst)[i2] = (src)[i2]
#define ZERO(buf, size) FOR(i3, 0, size) (buf)[i3] = 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;
}
static void chacha20_init_key(u32 block[16], const u8 key[32])
{
load32_le_buf(block , (const u8*)"expand 32-byte k", 4); // constant
load32_le_buf(block+4, key , 8); // key
}
void crypto_hchacha20(u8 out[32], const u8 key[32], const u8 in [16])
{
u32 block[16];
chacha20_init_key(block, key);
// input
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];
chacha20_init_key(input, key);
input[12] = (u32) ctr;
input[13] = (u32)(ctr >> 32);
load32_le_buf(input+14, nonce, 2);
// 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->c <= 1_ffffffff_ffffffff_ffffffff_ffffffff
// ctx->r <= 0ffffffc_0ffffffc_0ffffffc_0fffffff
// Postcondition:
// ctx->h <= 4_ffffffff_ffffffff_ffffffff_ffffffff
static void poly_block(crypto_poly1305_ctx *ctx)
{
// s = h + c, without carry propagation
const u64 s0 = ctx->h[0] + (u64)ctx->c[0]; // s0 <= 1_fffffffe
const u64 s1 = ctx->h[1] + (u64)ctx->c[1]; // s1 <= 1_fffffffe
const u64 s2 = ctx->h[2] + (u64)ctx->c[2]; // s2 <= 1_fffffffe
const u64 s3 = ctx->h[3] + (u64)ctx->c[3]; // s3 <= 1_fffffffe
const u32 s4 = ctx->h[4] + ctx->c[4]; // 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
}
// (re-)initialises the input counter and input buffer
static void poly_clear_c(crypto_poly1305_ctx *ctx)
{
ZERO(ctx->c, 4);
ctx->c_idx = 0;
}
static void poly_take_input(crypto_poly1305_ctx *ctx, u8 input)
{
size_t word = ctx->c_idx >> 2;
size_t byte = ctx->c_idx & 3;
ctx->c[word] |= (u32)input << (byte * 8);
ctx->c_idx++;
}
static void poly_update(crypto_poly1305_ctx *ctx,
const u8 *message, size_t message_size)
{
FOR (i, 0, message_size) {
poly_take_input(ctx, message[i]);
if (ctx->c_idx == 16) {
poly_block(ctx);
poly_clear_c(ctx);
}
}
}
void crypto_poly1305_init(crypto_poly1305_ctx *ctx, const u8 key[32])
{
// Initial hash is zero
ZERO(ctx->h, 5);
// add 2^130 to every input block
ctx->c[4] = 1;
poly_clear_c(ctx);
// 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)
{
if (message_size == 0) {
return;
}
// Align ourselves with block boundaries
size_t aligned = MIN(align(ctx->c_idx, 16), message_size);
poly_update(ctx, message, aligned);
message += aligned;
message_size -= aligned;
// Process the message block by block
size_t nb_blocks = message_size >> 4;
FOR (i, 0, nb_blocks) {
load32_le_buf(ctx->c, message, 4);
poly_block(ctx);
message += 16;
}
if (nb_blocks > 0) {
poly_clear_c(ctx);
}
message_size &= 15;
// remaining bytes
poly_update(ctx, message, message_size);
}
void crypto_poly1305_final(crypto_poly1305_ctx *ctx, u8 mac[16])
{
// Process the last block (if any)
if (ctx->c_idx != 0) {
// move the final 1 according to remaining input length
// (We may add less than 2^130 to the last input block)
ctx->c[4] = 0;
poly_take_input(ctx, 1);
// one last hash update
poly_block(ctx);
}
// 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,
};
// increment the input offset
static void blake2b_incr(crypto_blake2b_ctx *ctx)
{
u64 *x = ctx->input_offset;
size_t y = ctx->input_idx;
x[0] += y;
if (x[0] < y) {
x[1]++;
}
}
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 },
};
// 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);
}
static void blake2b_end_block(crypto_blake2b_ctx *ctx)
{
if (ctx->input_idx == 128) { // If buffer is full,
blake2b_incr(ctx); // update the input offset
blake2b_compress(ctx, 0); // and compress the (not last) block
ctx->input_idx = 0;
}
}
static void blake2b_update(crypto_blake2b_ctx *ctx,
const u8 *message, size_t message_size)
{
FOR (i, 0, message_size) {
blake2b_end_block(ctx);
blake2b_set_input(ctx, message[i], ctx->input_idx);
ctx->input_idx++;
}
}
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)
{
if (message_size == 0) {
return;
}
// Align ourselves with block boundaries
size_t aligned = MIN(align(ctx->input_idx, 128), message_size);
blake2b_update(ctx, message, aligned);
message += aligned;
message_size -= aligned;
// Process the message block by block
FOR (i, 0, message_size >> 7) { // number of blocks
blake2b_end_block(ctx);
load64_le_buf(ctx->input, message, 16);
message += 128;
ctx->input_idx = 128;
}
message_size &= 127;
// remaining bytes
blake2b_update(ctx, message, message_size);
}
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_incr(ctx); // update the input offset
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),
};
#if MONOCYPHER_ARGON2_ENABLE
////////////////
/// 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]);
}
}
// The compression function G (copy version for the first pass)
static void g_copy(block *result, const block *x, const block *y, block* tmp)
{
copy_block(tmp , x ); // tmp = X
xor_block (tmp , y ); // tmp = X ^ Y = R
copy_block(result, tmp); // result = R (only difference with g_xor)
g_rounds (tmp); // tmp = Z
xor_block (result, tmp); // result = R ^ Z
}
// The compression function G (xor version for subsequent passes)
static void g_xor(block *result, const block *x, const block *y, block *tmp)
{
copy_block(tmp , x ); // tmp = X
xor_block (tmp , y ); // tmp = X ^ Y = R
xor_block (result, tmp); // result = R ^ old (only difference with g_copy)
g_rounds (tmp); // tmp = Z
xor_block (result, tmp); // result = R ^ old ^ Z
}
// Unary version of the compression function.
// The missing argument is implied zero.
// Does the transformation in place.
static void unary_g(block *work_block, block *tmp)
{
// work_block == R
copy_block(tmp, work_block); // tmp = R
g_rounds (work_block); // work_block = Z
xor_block (work_block, tmp); // work_block = Z ^ R
}
// 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;
unary_g(&ctx->b, &tmp);
unary_g(&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
block tmp_block;
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(&tmp_block, hash_area);
copy_block(blocks, &tmp_block);
store32_le(initial_hash + 64, 1); // slight modification
extended_hash(hash_area, 1024, initial_hash, 72);
load_block(&tmp_block, hash_area);
copy_block(blocks + 1, &tmp_block);
WIPE_BUFFER(initial_hash);
WIPE_BUFFER(hash_area);
wipe_block(&tmp_block);
}
// 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) {
u32 reference_block = gidx_next(&ctx);
u32 previous_block = current_block == 0
? nb_blocks - 1
: current_block - 1;
block *c = blocks + current_block;
block *p = blocks + previous_block;
block *r = blocks + reference_block;
if (first_pass) { g_copy(c, p, r, &tmp); }
else { g_xor (c, p, r, &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);
}
#endif // MONOCYPHER_ARGON2_ENABLE
////////////////////////////////////
/// 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
static void fe_frombytes(fe h, const u8 s[32])
{
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) & 0x7fffff) << 2; // t9 < 2^25
FE_CARRY; // Carry recondition OK
}
// 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;
}
// h = 2 * (f^2)
//
// Precondition
// -------------
// |f0|, |f2|, |f4|, |f6|, |f8| < 1.65 * 2^26
// |f1|, |f3|, |f5|, |f7|, |f9| < 1.65 * 2^25
//
// Note: we could implement fe_sq2() by copying fe_sq(), multiplying
// each limb by 2, *then* perform the carry. This saves one carry.
// However, doing so with the stated preconditions does not work (t2
// would overflow). There are 3 ways to solve this:
//
// 1. Show that t2 actually never overflows (it really does not).
// 2. Accept an additional carry, at a small lost of performance.
// 3. Make sure the input of fe_sq2() is freshly carried.
//
// SUPERCOP ref10 relies on (1).
// Monocypher chose (2) and (3), mostly to save code.
static void fe_sq2(fe h, const fe f)
{
fe_sq(h, f);
fe_mul_small(h, h, 2);
}
// This could be simplified, but it would be slower
static void fe_pow22523(fe out, const fe z)
{
fe t0, t1, t2;
fe_sq(t0, z);
fe_sq(t1,t0); fe_sq(t1, t1); fe_mul(t1, z, 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(out, t0, z);
WIPE_BUFFER(t0);
WIPE_BUFFER(t1);
WIPE_BUFFER(t2);
}
// Inverting means multiplying by 2^255 - 21
// 2^255 - 21 = (2^252 - 3) * 8 + 3
// So we reuse the multiplication chain of fe_pow22523
static void fe_invert(fe out, const fe z)
{
fe tmp;
fe_pow22523(tmp, z);
// tmp2^8 * z^3
fe_sq(tmp, tmp); // 0
fe_sq(tmp, tmp); fe_mul(tmp, tmp, z); // 1
fe_sq(tmp, tmp); fe_mul(out, tmp, z); // 1
WIPE_BUFFER(tmp);
}
// 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 non zero square, false otherwise.
// After the call:
// isr = sqrt(1/x) if x is 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 check, quartic;
fe_copy(check, x);
fe_pow22523(isr, check);
fe_sq (quartic, isr);
fe_mul(quartic, quartic, 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);
fe_mul(check, isr, sqrtm1);
fe_ccopy(isr, check, m1 | ms);
WIPE_BUFFER(quartic);
WIPE_BUFFER(check);
return p1 | m1;
}
// 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];
carry >>= 32;
}
return carry;
}
// 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];
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_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 );
}
static void ge_msub(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->Ym);
fe_mul(b , b , q->Yp);
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_sub(a , s->Z, s->T );
fe_add(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 );
}
static void ge_double(ge *s, const ge *p, ge *q)
{
fe_sq (q->X, p->X);
fe_sq (q->Y, p->Y);
fe_sq2(q->Z, p->Z);
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--;
}
}
// R_check = s[B] - h_ram[pk], where B is the base point
//
// Variable time! Internal buffers are not wiped! Inputs must not be secret!
// => Use only to *check* signatures.
static int ge_r_check(u8 R_check[32], u8 s[32], u8 h_ram[32], u8 pk[32])
{
ge A; // not secret, not wiped
u32 s32[8]; // not secret, not wiped
load32_le_buf(s32, s, 8);
if (ge_frombytes_vartime(&A, pk) || // A = pk
is_above_l(s32)) { // prevent s malleability
return -1;
}
fe_neg(A.X, A.X);
fe_neg(A.T, A.T); // A = -pk
ge_double_scalarmult_vartime(&A, h_ram, s); // A = [s]B - [h_ram]pk
ge_tobytes(R_check, &A); // R_check = A
return 0;
}
// 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 bit. 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 h_ram[64];
ctx->hash->final(ctx, h_ram);
reduce(h_ram);
u8 *R = ctx->buf; // R
u8 *s = ctx->buf + 32; // s
u8 *R_check = ctx->pk; // overwrite ctx->pk to save stack space
if (ge_r_check(R_check, s, h_ram, ctx->pk)) {
return -1;
}
return crypto_verify32(R, R_check); // 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.
static const u8 dirty_base_point[32] = {
0x34, 0xfc, 0x6c, 0xb7, 0xc8, 0xde, 0x58, 0x97, 0x77, 0x70, 0xd9, 0x52,
0x16, 0xcc, 0xdc, 0x6c, 0x85, 0x90, 0xbe, 0xcd, 0x91, 0x9c, 0x07, 0x59,
0x94, 0x14, 0x56, 0x3b, 0x4b, 0xa4, 0x47, 0x0f, };
// 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.
//
// We exploit the fact that 5*L = 1 (modulo 8)
// cofactor = lsb * 5 * L (modulo 8*L)
// combined = scalar + cofactor (modulo 8*L)
// combined = scalar + (lsb * 5 * L) (modulo 8*L)
add_xl(scalar, secret_key[0] * 5);
scalarmult(public_key, scalar, dirty_base_point, 256);
WIPE_BUFFER(scalar);
}
// "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])
{
u8 scalar[32];
ge pk;
COPY(scalar, secret_key, 32);
trim_scalar(scalar);
ge_scalarmult_base(&pk, 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
// Notes:
// - A (single) Montgomery ladder would be twice as slow.
// - An actual scalar multiplication would hurt performance.
// - A full table lookup would take more code.
u8 cofactor = secret_key[0] & 7;
int a = (cofactor >> 2) & 1;
int b = (cofactor >> 1) & 1;
int c = (cofactor >> 0) & 1;
fe t1, t2, t3;
fe_0(t1);
fe_ccopy(t1, sqrtm1, b);
fe_ccopy(t1, lop_x , c);
fe_neg (t3, t1);
fe_ccopy(t1, t3, a);
fe_1(t2);
fe_0(t3);
fe_ccopy(t2, t3 , b);
fe_ccopy(t2, lop_y, c);
fe_neg (t3, t2);
fe_ccopy(t2, t3, a^b);
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_BUFFER(scalar);
WIPE_BUFFER(t2); WIPE_CTX(&pk);
WIPE_BUFFER(t3); WIPE_CTX(&low_order_point);
}
///////////////////
/// 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])
{
// Representatives are encoded in 254 bits.
// The two most significant ones are random padding that must be ignored.
u8 clamped[32];
COPY(clamped, hidden, 32);
clamped[31] &= 0x3f;
fe r, u, t1, t2, t3;
fe_frombytes(r, clamped);
fe_sq2(t1, 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_sq(u, r);
fe_mul(u, u, 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); WIPE_BUFFER(clamped);
}
// 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+A) / u)
// if v is negative: r = sqrt(-u / (u+A))
//
// We compute isr = invsqrt(-non_square * u * (u+A))
// if it wasn't a non-zero square, abort.
// else, isr = sqrt(-1 / (non_square * u * (u+A))
//
// This causes us to abort if u is zero, even though we shouldn't. This
// never happens in practice, because (i) a random point in the curve has
// a negligible chance of being zero, and (ii) scalar multiplication with
// a trimmed scalar *never* yields zero.
//
// Since:
// isr * (u+A) = sqrt(-1 / (non_square * u * (u+A)) * (u+A)
// isr * (u+A) = sqrt(-(u+A) / (non_square * u * (u+A))
// and:
// isr = u = sqrt(-1 / (non_square * u * (u+A)) * u
// isr = u = sqrt(-u / (non_square * u * (u+A))
// Therefore:
// if v is positive: r = isr * (u+A)
// if v is negative: r = isr * 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);
fe_add(t2, t1, A);
fe_mul(t3, t1, t2);
fe_mul_small(t3, t3, -2);
int is_square = invsqrt(t3, t3);
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.
WIPE_BUFFER(t1);
WIPE_BUFFER(t2);
WIPE_BUFFER(t3);
return -1;
}
fe_ccopy (t1, t2, tweak & 1);
fe_mul (t3, t1, t3);
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 0;
}
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,};
static const u32 l[8] = { 0x5cf5d3ed, 0x5812631a, 0xa2f79cd6, 0x14def9de,
0x00000000, 0x00000000, 0x00000000, 0x10000000,};
// 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
// We work with L directly, in a 2's complement encoding
// (-L == ~L + 1)
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
}
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);
if (crypto_verify16(mac, real_mac)) {
WIPE_BUFFER(sub_key);
WIPE_BUFFER(real_mac);
return -1;
}
crypto_chacha20_ctr(plain_text, cipher_text, text_size,
sub_key, nonce + 16, 1);
WIPE_BUFFER(sub_key);
WIPE_BUFFER(real_mac);
return 0;
}
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);
}
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