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/* Copyright (c) 2024, Google Inc.
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
#include <openssl/mlkem.h>
#include <assert.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <openssl/base.h>
#include <openssl/bytestring.h>
#include <openssl/mem.h>
#include <openssl/rand.h>
#include "../internal.h"
#include "../keccak/internal.h"
#include "./internal.h"
// See
// https://csrc.nist.gov/pubs/fips/203/final
static void prf(uint8_t *out, size_t out_len, const uint8_t in[33]) {
BORINGSSL_keccak(out, out_len, in, 33, boringssl_shake256);
}
// Section 4.1
static void hash_h(uint8_t out[32], const uint8_t *in, size_t len) {
BORINGSSL_keccak(out, 32, in, len, boringssl_sha3_256);
}
static void hash_g(uint8_t out[64], const uint8_t *in, size_t len) {
BORINGSSL_keccak(out, 64, in, len, boringssl_sha3_512);
}
// This is called `J` in the spec.
static void kdf(uint8_t out[MLKEM_SHARED_SECRET_BYTES],
const uint8_t failure_secret[32], const uint8_t *ciphertext,
size_t ciphertext_len) {
struct BORINGSSL_keccak_st st;
BORINGSSL_keccak_init(&st, boringssl_shake256);
BORINGSSL_keccak_absorb(&st, failure_secret, 32);
BORINGSSL_keccak_absorb(&st, ciphertext, ciphertext_len);
BORINGSSL_keccak_squeeze(&st, out, MLKEM_SHARED_SECRET_BYTES);
}
// Constants that are common across all sizes.
#define DEGREE 256
static const size_t kBarrettMultiplier = 5039;
static const unsigned kBarrettShift = 24;
static const uint16_t kPrime = 3329;
static const int kLog2Prime = 12;
static const uint16_t kHalfPrime = (/*kPrime=*/3329 - 1) / 2;
// kInverseDegree is 128^-1 mod 3329; 128 because kPrime does not have a 512th
// root of unity.
static const uint16_t kInverseDegree = 3303;
// Rank-specific constants.
#define RANK768 3
static const int kDU768 = 10;
static const int kDV768 = 4;
#define RANK1024 4
static const int kDU1024 = 11;
static const int kDV1024 = 5;
constexpr size_t encoded_vector_size(int rank) {
return (kLog2Prime * DEGREE / 8) * static_cast<size_t>(rank);
}
constexpr size_t encoded_public_key_size(int rank) {
return encoded_vector_size(rank) + /*sizeof(rho)=*/32;
}
static_assert(encoded_public_key_size(RANK768) == MLKEM768_PUBLIC_KEY_BYTES,
"");
static_assert(encoded_public_key_size(RANK1024) == MLKEM1024_PUBLIC_KEY_BYTES,
"");
constexpr size_t compressed_vector_size(int rank) {
// `if constexpr` isn't available in C++17.
return (rank == RANK768 ? kDU768 : kDU1024) * static_cast<size_t>(rank) *
DEGREE / 8;
}
constexpr size_t ciphertext_size(int rank) {
return compressed_vector_size(rank) +
(rank == RANK768 ? kDV768 : kDV1024) * DEGREE / 8;
}
static_assert(ciphertext_size(RANK768) == MLKEM768_CIPHERTEXT_BYTES, "");
static_assert(ciphertext_size(RANK1024) == MLKEM1024_CIPHERTEXT_BYTES, "");
typedef struct scalar {
// On every function entry and exit, 0 <= c < kPrime.
uint16_t c[DEGREE];
} scalar;
template <int RANK>
struct vector {
scalar v[RANK];
};
template <int RANK>
struct matrix {
scalar v[RANK][RANK];
};
// This bit of Python will be referenced in some of the following comments:
//
// p = 3329
//
// def bitreverse(i):
// ret = 0
// for n in range(7):
// bit = i & 1
// ret <<= 1
// ret |= bit
// i >>= 1
// return ret
// kNTTRoots = [pow(17, bitreverse(i), p) for i in range(128)]
static const uint16_t kNTTRoots[128] = {
1, 1729, 2580, 3289, 2642, 630, 1897, 848, 1062, 1919, 193, 797,
2786, 3260, 569, 1746, 296, 2447, 1339, 1476, 3046, 56, 2240, 1333,
1426, 2094, 535, 2882, 2393, 2879, 1974, 821, 289, 331, 3253, 1756,
1197, 2304, 2277, 2055, 650, 1977, 2513, 632, 2865, 33, 1320, 1915,
2319, 1435, 807, 452, 1438, 2868, 1534, 2402, 2647, 2617, 1481, 648,
2474, 3110, 1227, 910, 17, 2761, 583, 2649, 1637, 723, 2288, 1100,
1409, 2662, 3281, 233, 756, 2156, 3015, 3050, 1703, 1651, 2789, 1789,
1847, 952, 1461, 2687, 939, 2308, 2437, 2388, 733, 2337, 268, 641,
1584, 2298, 2037, 3220, 375, 2549, 2090, 1645, 1063, 319, 2773, 757,
2099, 561, 2466, 2594, 2804, 1092, 403, 1026, 1143, 2150, 2775, 886,
1722, 1212, 1874, 1029, 2110, 2935, 885, 2154,
};
// kInverseNTTRoots = [pow(17, -bitreverse(i), p) for i in range(128)]
static const uint16_t kInverseNTTRoots[128] = {
1, 1600, 40, 749, 2481, 1432, 2699, 687, 1583, 2760, 69, 543,
2532, 3136, 1410, 2267, 2508, 1355, 450, 936, 447, 2794, 1235, 1903,
1996, 1089, 3273, 283, 1853, 1990, 882, 3033, 2419, 2102, 219, 855,
2681, 1848, 712, 682, 927, 1795, 461, 1891, 2877, 2522, 1894, 1010,
1414, 2009, 3296, 464, 2697, 816, 1352, 2679, 1274, 1052, 1025, 2132,
1573, 76, 2998, 3040, 1175, 2444, 394, 1219, 2300, 1455, 2117, 1607,
2443, 554, 1179, 2186, 2303, 2926, 2237, 525, 735, 863, 2768, 1230,
2572, 556, 3010, 2266, 1684, 1239, 780, 2954, 109, 1292, 1031, 1745,
2688, 3061, 992, 2596, 941, 892, 1021, 2390, 642, 1868, 2377, 1482,
1540, 540, 1678, 1626, 279, 314, 1173, 2573, 3096, 48, 667, 1920,
2229, 1041, 2606, 1692, 680, 2746, 568, 3312,
};
// kModRoots = [pow(17, 2*bitreverse(i) + 1, p) for i in range(128)]
static const uint16_t kModRoots[128] = {
17, 3312, 2761, 568, 583, 2746, 2649, 680, 1637, 1692, 723, 2606,
2288, 1041, 1100, 2229, 1409, 1920, 2662, 667, 3281, 48, 233, 3096,
756, 2573, 2156, 1173, 3015, 314, 3050, 279, 1703, 1626, 1651, 1678,
2789, 540, 1789, 1540, 1847, 1482, 952, 2377, 1461, 1868, 2687, 642,
939, 2390, 2308, 1021, 2437, 892, 2388, 941, 733, 2596, 2337, 992,
268, 3061, 641, 2688, 1584, 1745, 2298, 1031, 2037, 1292, 3220, 109,
375, 2954, 2549, 780, 2090, 1239, 1645, 1684, 1063, 2266, 319, 3010,
2773, 556, 757, 2572, 2099, 1230, 561, 2768, 2466, 863, 2594, 735,
2804, 525, 1092, 2237, 403, 2926, 1026, 2303, 1143, 2186, 2150, 1179,
2775, 554, 886, 2443, 1722, 1607, 1212, 2117, 1874, 1455, 1029, 2300,
2110, 1219, 2935, 394, 885, 2444, 2154, 1175,
};
// reduce_once reduces 0 <= x < 2*kPrime, mod kPrime.
static uint16_t reduce_once(uint16_t x) {
assert(x < 2 * kPrime);
const uint16_t subtracted = x - kPrime;
uint16_t mask = 0u - (subtracted >> 15);
// On Aarch64, omitting a |value_barrier_u16| results in a 2x speedup of
// ML-KEM overall and Clang still produces constant-time code using `csel`. On
// other platforms & compilers on godbolt that we care about, this code also
// produces constant-time output.
return (mask & x) | (~mask & subtracted);
}
// constant time reduce x mod kPrime using Barrett reduction. x must be less
// than kPrime + 2×kPrime².
static uint16_t reduce(uint32_t x) {
assert(x < kPrime + 2u * kPrime * kPrime);
uint64_t product = (uint64_t)x * kBarrettMultiplier;
uint32_t quotient = (uint32_t)(product >> kBarrettShift);
uint32_t remainder = x - quotient * kPrime;
return reduce_once(remainder);
}
static void scalar_zero(scalar *out) { OPENSSL_memset(out, 0, sizeof(*out)); }
template <int RANK>
static void vector_zero(vector<RANK> *out) {
OPENSSL_memset(out->v, 0, sizeof(scalar) * RANK);
}
// In place number theoretic transform of a given scalar.
// Note that MLKEM's kPrime 3329 does not have a 512th root of unity, so this
// transform leaves off the last iteration of the usual FFT code, with the 128
// relevant roots of unity being stored in |kNTTRoots|. This means the output
// should be seen as 128 elements in GF(3329^2), with the coefficients of the
// elements being consecutive entries in |s->c|.
static void scalar_ntt(scalar *s) {
int offset = DEGREE;
// `int` is used here because using `size_t` throughout caused a ~5% slowdown
// with Clang 14 on Aarch64.
for (int step = 1; step < DEGREE / 2; step <<= 1) {
offset >>= 1;
int k = 0;
for (int i = 0; i < step; i++) {
const uint32_t step_root = kNTTRoots[i + step];
for (int j = k; j < k + offset; j++) {
uint16_t odd = reduce(step_root * s->c[j + offset]);
uint16_t even = s->c[j];
s->c[j] = reduce_once(odd + even);
s->c[j + offset] = reduce_once(even - odd + kPrime);
}
k += 2 * offset;
}
}
}
template <int RANK>
static void vector_ntt(vector<RANK> *a) {
for (int i = 0; i < RANK; i++) {
scalar_ntt(&a->v[i]);
}
}
// In place inverse number theoretic transform of a given scalar, with pairs of
// entries of s->v being interpreted as elements of GF(3329^2). Just as with the
// number theoretic transform, this leaves off the first step of the normal iFFT
// to account for the fact that 3329 does not have a 512th root of unity, using
// the precomputed 128 roots of unity stored in |kInverseNTTRoots|.
static void scalar_inverse_ntt(scalar *s) {
int step = DEGREE / 2;
// `int` is used here because using `size_t` throughout caused a ~5% slowdown
// with Clang 14 on Aarch64.
for (int offset = 2; offset < DEGREE; offset <<= 1) {
step >>= 1;
int k = 0;
for (int i = 0; i < step; i++) {
uint32_t step_root = kInverseNTTRoots[i + step];
for (int j = k; j < k + offset; j++) {
uint16_t odd = s->c[j + offset];
uint16_t even = s->c[j];
s->c[j] = reduce_once(odd + even);
s->c[j + offset] = reduce(step_root * (even - odd + kPrime));
}
k += 2 * offset;
}
}
for (int i = 0; i < DEGREE; i++) {
s->c[i] = reduce(s->c[i] * kInverseDegree);
}
}
template <int RANK>
static void vector_inverse_ntt(vector<RANK> *a) {
for (int i = 0; i < RANK; i++) {
scalar_inverse_ntt(&a->v[i]);
}
}
static void scalar_add(scalar *lhs, const scalar *rhs) {
for (int i = 0; i < DEGREE; i++) {
lhs->c[i] = reduce_once(lhs->c[i] + rhs->c[i]);
}
}
static void scalar_sub(scalar *lhs, const scalar *rhs) {
for (int i = 0; i < DEGREE; i++) {
lhs->c[i] = reduce_once(lhs->c[i] - rhs->c[i] + kPrime);
}
}
// Multiplying two scalars in the number theoretically transformed state. Since
// 3329 does not have a 512th root of unity, this means we have to interpret
// the 2*ith and (2*i+1)th entries of the scalar as elements of GF(3329)[X]/(X^2
// - 17^(2*bitreverse(i)+1)) The value of 17^(2*bitreverse(i)+1) mod 3329 is
// stored in the precomputed |kModRoots| table. Note that our Barrett transform
// only allows us to multipy two reduced numbers together, so we need some
// intermediate reduction steps, even if an uint64_t could hold 3 multiplied
// numbers.
static void scalar_mult(scalar *out, const scalar *lhs, const scalar *rhs) {
for (int i = 0; i < DEGREE / 2; i++) {
uint32_t real_real = (uint32_t)lhs->c[2 * i] * rhs->c[2 * i];
uint32_t img_img = (uint32_t)lhs->c[2 * i + 1] * rhs->c[2 * i + 1];
uint32_t real_img = (uint32_t)lhs->c[2 * i] * rhs->c[2 * i + 1];
uint32_t img_real = (uint32_t)lhs->c[2 * i + 1] * rhs->c[2 * i];
out->c[2 * i] =
reduce(real_real + (uint32_t)reduce(img_img) * kModRoots[i]);
out->c[2 * i + 1] = reduce(img_real + real_img);
}
}
template <int RANK>
static void vector_add(vector<RANK> *lhs, const vector<RANK> *rhs) {
for (int i = 0; i < RANK; i++) {
scalar_add(&lhs->v[i], &rhs->v[i]);
}
}
template <int RANK>
static void matrix_mult(vector<RANK> *out, const matrix<RANK> *m,
const vector<RANK> *a) {
vector_zero(out);
for (int i = 0; i < RANK; i++) {
for (int j = 0; j < RANK; j++) {
scalar product;
scalar_mult(&product, &m->v[i][j], &a->v[j]);
scalar_add(&out->v[i], &product);
}
}
}
template <int RANK>
static void matrix_mult_transpose(vector<RANK> *out, const matrix<RANK> *m,
const vector<RANK> *a) {
vector_zero(out);
for (int i = 0; i < RANK; i++) {
for (int j = 0; j < RANK; j++) {
scalar product;
scalar_mult(&product, &m->v[j][i], &a->v[j]);
scalar_add(&out->v[i], &product);
}
}
}
template <int RANK>
static void scalar_inner_product(scalar *out, const vector<RANK> *lhs,
const vector<RANK> *rhs) {
scalar_zero(out);
for (int i = 0; i < RANK; i++) {
scalar product;
scalar_mult(&product, &lhs->v[i], &rhs->v[i]);
scalar_add(out, &product);
}
}
// Algorithm 6 from the spec. Rejection samples a Keccak stream to get
// uniformly distributed elements. This is used for matrix expansion and only
// operates on public inputs.
static void scalar_from_keccak_vartime(scalar *out,
struct BORINGSSL_keccak_st *keccak_ctx) {
assert(keccak_ctx->squeeze_offset == 0);
assert(keccak_ctx->rate_bytes == 168);
static_assert(168 % 3 == 0, "block and coefficient boundaries do not align");
int done = 0;
while (done < DEGREE) {
uint8_t block[168];
BORINGSSL_keccak_squeeze(keccak_ctx, block, sizeof(block));
for (size_t i = 0; i < sizeof(block) && done < DEGREE; i += 3) {
uint16_t d1 = block[i] + 256 * (block[i + 1] % 16);
uint16_t d2 = block[i + 1] / 16 + 16 * block[i + 2];
if (d1 < kPrime) {
out->c[done++] = d1;
}
if (d2 < kPrime && done < DEGREE) {
out->c[done++] = d2;
}
}
}
}
// Algorithm 7 from the spec, with eta fixed to two and the PRF call
// included. Creates binominally distributed elements by sampling 2*|eta| bits,
// and setting the coefficient to the count of the first bits minus the count of
// the second bits, resulting in a centered binomial distribution. Since eta is
// two this gives -2/2 with a probability of 1/16, -1/1 with probability 1/4,
// and 0 with probability 3/8.
static void scalar_centered_binomial_distribution_eta_2_with_prf(
scalar *out, const uint8_t input[33]) {
uint8_t entropy[128];
static_assert(sizeof(entropy) == 2 * /*kEta=*/2 * DEGREE / 8, "");
prf(entropy, sizeof(entropy), input);
for (int i = 0; i < DEGREE; i += 2) {
uint8_t byte = entropy[i / 2];
uint16_t value = kPrime;
value += (byte & 1) + ((byte >> 1) & 1);
value -= ((byte >> 2) & 1) + ((byte >> 3) & 1);
out->c[i] = reduce_once(value);
byte >>= 4;
value = kPrime;
value += (byte & 1) + ((byte >> 1) & 1);
value -= ((byte >> 2) & 1) + ((byte >> 3) & 1);
out->c[i + 1] = reduce_once(value);
}
}
// Generates a secret vector by using
// |scalar_centered_binomial_distribution_eta_2_with_prf|, using the given seed
// appending and incrementing |counter| for entry of the vector.
template <int RANK>
static void vector_generate_secret_eta_2(vector<RANK> *out, uint8_t *counter,
const uint8_t seed[32]) {
uint8_t input[33];
OPENSSL_memcpy(input, seed, 32);
for (int i = 0; i < RANK; i++) {
input[32] = (*counter)++;
scalar_centered_binomial_distribution_eta_2_with_prf(&out->v[i], input);
}
}
// Expands the matrix of a seed for key generation and for encaps-CPA.
template <int RANK>
static void matrix_expand(matrix<RANK> *out, const uint8_t rho[32]) {
uint8_t input[34];
OPENSSL_memcpy(input, rho, 32);
for (int i = 0; i < RANK; i++) {
for (int j = 0; j < RANK; j++) {
input[32] = i;
input[33] = j;
struct BORINGSSL_keccak_st keccak_ctx;
BORINGSSL_keccak_init(&keccak_ctx, boringssl_shake128);
BORINGSSL_keccak_absorb(&keccak_ctx, input, sizeof(input));
scalar_from_keccak_vartime(&out->v[i][j], &keccak_ctx);
}
}
}
static const uint8_t kMasks[8] = {0x01, 0x03, 0x07, 0x0f,
0x1f, 0x3f, 0x7f, 0xff};
static void scalar_encode(uint8_t *out, const scalar *s, int bits) {
assert(bits <= (int)sizeof(*s->c) * 8 && bits != 1);
uint8_t out_byte = 0;
int out_byte_bits = 0;
for (int i = 0; i < DEGREE; i++) {
uint16_t element = s->c[i];
int element_bits_done = 0;
while (element_bits_done < bits) {
int chunk_bits = bits - element_bits_done;
int out_bits_remaining = 8 - out_byte_bits;
if (chunk_bits >= out_bits_remaining) {
chunk_bits = out_bits_remaining;
out_byte |= (element & kMasks[chunk_bits - 1]) << out_byte_bits;
*out = out_byte;
out++;
out_byte_bits = 0;
out_byte = 0;
} else {
out_byte |= (element & kMasks[chunk_bits - 1]) << out_byte_bits;
out_byte_bits += chunk_bits;
}
element_bits_done += chunk_bits;
element >>= chunk_bits;
}
}
if (out_byte_bits > 0) {
*out = out_byte;
}
}
// scalar_encode_1 is |scalar_encode| specialised for |bits| == 1.
static void scalar_encode_1(uint8_t out[32], const scalar *s) {
for (int i = 0; i < DEGREE; i += 8) {
uint8_t out_byte = 0;
for (int j = 0; j < 8; j++) {
out_byte |= (s->c[i + j] & 1) << j;
}
*out = out_byte;
out++;
}
}
// Encodes an entire vector into 32*|RANK|*|bits| bytes. Note that since 256
// (DEGREE) is divisible by 8, the individual vector entries will always fill a
// whole number of bytes, so we do not need to worry about bit packing here.
template <int RANK>
static void vector_encode(uint8_t *out, const vector<RANK> *a, int bits) {
for (int i = 0; i < RANK; i++) {
scalar_encode(out + i * bits * DEGREE / 8, &a->v[i], bits);
}
}
// scalar_decode parses |DEGREE * bits| bits from |in| into |DEGREE| values in
// |out|. It returns one on success and zero if any parsed value is >=
// |kPrime|.
static int scalar_decode(scalar *out, const uint8_t *in, int bits) {
assert(bits <= (int)sizeof(*out->c) * 8 && bits != 1);
uint8_t in_byte = 0;
int in_byte_bits_left = 0;
for (int i = 0; i < DEGREE; i++) {
uint16_t element = 0;
int element_bits_done = 0;
while (element_bits_done < bits) {
if (in_byte_bits_left == 0) {
in_byte = *in;
in++;
in_byte_bits_left = 8;
}
int chunk_bits = bits - element_bits_done;
if (chunk_bits > in_byte_bits_left) {
chunk_bits = in_byte_bits_left;
}
element |= (in_byte & kMasks[chunk_bits - 1]) << element_bits_done;
in_byte_bits_left -= chunk_bits;
in_byte >>= chunk_bits;
element_bits_done += chunk_bits;
}
if (element >= kPrime) {
return 0;
}
out->c[i] = element;
}
return 1;
}
// scalar_decode_1 is |scalar_decode| specialised for |bits| == 1.
static void scalar_decode_1(scalar *out, const uint8_t in[32]) {
for (int i = 0; i < DEGREE; i += 8) {
uint8_t in_byte = *in;
in++;
for (int j = 0; j < 8; j++) {
out->c[i + j] = in_byte & 1;
in_byte >>= 1;
}
}
}
// Decodes 32*|RANK|*|bits| bytes from |in| into |out|. It returns one on
// success or zero if any parsed value is >= |kPrime|.
template <int RANK>
static int vector_decode(vector<RANK> *out, const uint8_t *in, int bits) {
for (int i = 0; i < RANK; i++) {
if (!scalar_decode(&out->v[i], in + i * bits * DEGREE / 8, bits)) {
return 0;
}
}
return 1;
}
// Compresses (lossily) an input |x| mod 3329 into |bits| many bits by grouping
// numbers close to each other together. The formula used is
// round(2^|bits|/kPrime*x) mod 2^|bits|.
// Uses Barrett reduction to achieve constant time. Since we need both the
// remainder (for rounding) and the quotient (as the result), we cannot use
// |reduce| here, but need to do the Barrett reduction directly.
static uint16_t compress(uint16_t x, int bits) {
uint32_t shifted = (uint32_t)x << bits;
uint64_t product = (uint64_t)shifted * kBarrettMultiplier;
uint32_t quotient = (uint32_t)(product >> kBarrettShift);
uint32_t remainder = shifted - quotient * kPrime;
// Adjust the quotient to round correctly:
// 0 <= remainder <= kHalfPrime round to 0
// kHalfPrime < remainder <= kPrime + kHalfPrime round to 1
// kPrime + kHalfPrime < remainder < 2 * kPrime round to 2
assert(remainder < 2u * kPrime);
quotient += 1 & constant_time_lt_w(kHalfPrime, remainder);
quotient += 1 & constant_time_lt_w(kPrime + kHalfPrime, remainder);
return quotient & ((1 << bits) - 1);
}
// Decompresses |x| by using an equi-distant representative. The formula is
// round(kPrime/2^|bits|*x). Note that 2^|bits| being the divisor allows us to
// implement this logic using only bit operations.
static uint16_t decompress(uint16_t x, int bits) {
uint32_t product = (uint32_t)x * kPrime;
uint32_t power = 1 << bits;
// This is |product| % power, since |power| is a power of 2.
uint32_t remainder = product & (power - 1);
// This is |product| / power, since |power| is a power of 2.
uint32_t lower = product >> bits;
// The rounding logic works since the first half of numbers mod |power| have a
// 0 as first bit, and the second half has a 1 as first bit, since |power| is
// a power of 2. As a 12 bit number, |remainder| is always positive, so we
// will shift in 0s for a right shift.
return lower + (remainder >> (bits - 1));
}
static void scalar_compress(scalar *s, int bits) {
for (int i = 0; i < DEGREE; i++) {
s->c[i] = compress(s->c[i], bits);
}
}
static void scalar_decompress(scalar *s, int bits) {
for (int i = 0; i < DEGREE; i++) {
s->c[i] = decompress(s->c[i], bits);
}
}
template <int RANK>
static void vector_compress(vector<RANK> *a, int bits) {
for (int i = 0; i < RANK; i++) {
scalar_compress(&a->v[i], bits);
}
}
template <int RANK>
static void vector_decompress(vector<RANK> *a, int bits) {
for (int i = 0; i < RANK; i++) {
scalar_decompress(&a->v[i], bits);
}
}
template <int RANK>
struct public_key {
vector<RANK> t;
uint8_t rho[32];
uint8_t public_key_hash[32];
matrix<RANK> m;
};
static struct public_key<RANK768> *public_key_768_from_external(
const struct MLKEM768_public_key *external) {
static_assert(sizeof(struct MLKEM768_public_key) >=
sizeof(struct public_key<RANK768>),
"MLKEM public key is too small");
static_assert(alignof(struct MLKEM768_public_key) >=
alignof(struct public_key<RANK768>),
"MLKEM public key alignment incorrect");
return (struct public_key<RANK768> *)external;
}
static struct public_key<RANK1024> *
public_key_1024_from_external(const struct MLKEM1024_public_key *external) {
static_assert(sizeof(struct MLKEM1024_public_key) >=
sizeof(struct public_key<RANK1024>),
"MLKEM1024 public key is too small");
static_assert(alignof(struct MLKEM1024_public_key) >=
alignof(struct public_key<RANK1024>),
"MLKEM1024 public key alignment incorrect");
return (struct public_key<RANK1024> *)external;
}
template <int RANK>
struct private_key {
struct public_key<RANK> pub;
vector<RANK> s;
uint8_t fo_failure_secret[32];
};
static struct private_key<RANK768> *private_key_768_from_external(
const struct MLKEM768_private_key *external) {
static_assert(sizeof(struct MLKEM768_private_key) >=
sizeof(struct private_key<RANK768>),
"MLKEM private key too small");
static_assert(alignof(struct MLKEM768_private_key) >=
alignof(struct private_key<RANK768>),
"MLKEM private key alignment incorrect");
return (struct private_key<RANK768> *)external;
}
static struct private_key<RANK1024> *
private_key_1024_from_external(const struct MLKEM1024_private_key *external) {
static_assert(sizeof(struct MLKEM1024_private_key) >=
sizeof(struct private_key<RANK1024>),
"MLKEM1024 private key too small");
static_assert(alignof(struct MLKEM1024_private_key) >=
alignof(struct private_key<RANK1024>),
"MLKEM1024 private key alignment incorrect");
return (struct private_key<RANK1024> *)external;
}
void MLKEM768_generate_key(uint8_t out_encoded_public_key[MLKEM768_PUBLIC_KEY_BYTES],
uint8_t optional_out_seed[MLKEM_SEED_BYTES],
struct MLKEM768_private_key *out_private_key) {
uint8_t seed[MLKEM_SEED_BYTES];
RAND_bytes(seed, sizeof(seed));
if (optional_out_seed) {
OPENSSL_memcpy(optional_out_seed, seed, sizeof(seed));
}
MLKEM768_generate_key_external_seed(out_encoded_public_key, out_private_key,
seed);
}
int MLKEM768_private_key_from_seed(struct MLKEM768_private_key *out_private_key,
const uint8_t *seed, size_t seed_len) {
if (seed_len != MLKEM_SEED_BYTES) {
return 0;
}
uint8_t public_key_bytes[MLKEM768_PUBLIC_KEY_BYTES];
MLKEM768_generate_key_external_seed(public_key_bytes, out_private_key, seed);
return 1;
}
void MLKEM1024_generate_key(
uint8_t out_encoded_public_key[MLKEM1024_PUBLIC_KEY_BYTES],
uint8_t optional_out_seed[MLKEM_SEED_BYTES],
struct MLKEM1024_private_key *out_private_key) {
uint8_t seed[MLKEM_SEED_BYTES];
RAND_bytes(seed, sizeof(seed));
if (optional_out_seed) {
OPENSSL_memcpy(optional_out_seed, seed, sizeof(seed));
}
MLKEM1024_generate_key_external_seed(out_encoded_public_key, out_private_key,
seed);
}
int MLKEM1024_private_key_from_seed(
struct MLKEM1024_private_key *out_private_key, const uint8_t *seed,
size_t seed_len) {
if (seed_len != MLKEM_SEED_BYTES) {
return 0;
}
uint8_t public_key_bytes[MLKEM1024_PUBLIC_KEY_BYTES];
MLKEM1024_generate_key_external_seed(public_key_bytes, out_private_key, seed);
return 1;
}
template <int RANK>
static int mlkem_marshal_public_key(CBB *out,
const struct public_key<RANK> *pub) {
uint8_t *vector_output;
if (!CBB_add_space(out, &vector_output, encoded_vector_size(RANK))) {
return 0;
}
vector_encode(vector_output, &pub->t, kLog2Prime);
if (!CBB_add_bytes(out, pub->rho, sizeof(pub->rho))) {
return 0;
}
return 1;
}
template <int RANK>
void mlkem_generate_key_external_seed(uint8_t *out_encoded_public_key,
private_key<RANK> *priv,
const uint8_t seed[MLKEM_SEED_BYTES]) {
uint8_t augmented_seed[33];
OPENSSL_memcpy(augmented_seed, seed, 32);
augmented_seed[32] = RANK;
uint8_t hashed[64];
hash_g(hashed, augmented_seed, sizeof(augmented_seed));
const uint8_t *const rho = hashed;
const uint8_t *const sigma = hashed + 32;
OPENSSL_memcpy(priv->pub.rho, hashed, sizeof(priv->pub.rho));
matrix_expand(&priv->pub.m, rho);
uint8_t counter = 0;
vector_generate_secret_eta_2(&priv->s, &counter, sigma);
vector_ntt(&priv->s);
vector<RANK> error;
vector_generate_secret_eta_2(&error, &counter, sigma);
vector_ntt(&error);
matrix_mult_transpose(&priv->pub.t, &priv->pub.m, &priv->s);
vector_add(&priv->pub.t, &error);
CBB cbb;
CBB_init_fixed(&cbb, out_encoded_public_key, encoded_public_key_size(RANK));
if (!mlkem_marshal_public_key(&cbb, &priv->pub)) {
abort();
}
hash_h(priv->pub.public_key_hash, out_encoded_public_key,
encoded_public_key_size(RANK));
OPENSSL_memcpy(priv->fo_failure_secret, seed + 32, 32);
}
void MLKEM768_generate_key_external_seed(
uint8_t out_encoded_public_key[MLKEM768_PUBLIC_KEY_BYTES],
struct MLKEM768_private_key *out_private_key,
const uint8_t seed[MLKEM_SEED_BYTES]) {
private_key<RANK768> *priv = private_key_768_from_external(out_private_key);
mlkem_generate_key_external_seed(out_encoded_public_key, priv, seed);
}
void MLKEM1024_generate_key_external_seed(
uint8_t out_encoded_public_key[MLKEM1024_PUBLIC_KEY_BYTES],
struct MLKEM1024_private_key *out_private_key,
const uint8_t seed[MLKEM_SEED_BYTES]) {
private_key<RANK1024> *priv = private_key_1024_from_external(out_private_key);
mlkem_generate_key_external_seed(out_encoded_public_key, priv, seed);
}
void MLKEM768_public_from_private(
struct MLKEM768_public_key *out_public_key,
const struct MLKEM768_private_key *private_key) {
struct public_key<RANK768> *const pub =
public_key_768_from_external(out_public_key);
const struct ::private_key<RANK768> *const priv =
private_key_768_from_external(private_key);
*pub = priv->pub;
}
void MLKEM1024_public_from_private(
struct MLKEM1024_public_key *out_public_key,
const struct MLKEM1024_private_key *private_key) {
struct public_key<RANK1024> *const pub =
public_key_1024_from_external(out_public_key);
const struct ::private_key<RANK1024> *const priv =
private_key_1024_from_external(private_key);
*pub = priv->pub;
}
// Encrypts a message with given randomness to
// the ciphertext in |out|. Without applying the Fujisaki-Okamoto transform this
// would not result in a CCA secure scheme, since lattice schemes are vulnerable
// to decryption failure oracles.
template <int RANK>
static void encrypt_cpa(uint8_t *out, const struct public_key<RANK> *pub,
const uint8_t message[32],
const uint8_t randomness[32]) {
constexpr int du = RANK == RANK768 ? kDU768 : kDU1024;
constexpr int dv = RANK == RANK768 ? kDV768 : kDV1024;
uint8_t counter = 0;
vector<RANK> secret;
vector_generate_secret_eta_2(&secret, &counter, randomness);
vector_ntt(&secret);
vector<RANK> error;
vector_generate_secret_eta_2(&error, &counter, randomness);
uint8_t input[33];
OPENSSL_memcpy(input, randomness, 32);
input[32] = counter;
scalar scalar_error;
scalar_centered_binomial_distribution_eta_2_with_prf(&scalar_error, input);
vector<RANK> u;
matrix_mult(&u, &pub->m, &secret);
vector_inverse_ntt(&u);
vector_add(&u, &error);
scalar v;
scalar_inner_product(&v, &pub->t, &secret);
scalar_inverse_ntt(&v);
scalar_add(&v, &scalar_error);
scalar expanded_message;
scalar_decode_1(&expanded_message, message);
scalar_decompress(&expanded_message, 1);
scalar_add(&v, &expanded_message);
vector_compress(&u, du);
vector_encode(out, &u, du);
scalar_compress(&v, dv);
scalar_encode(out + compressed_vector_size(RANK), &v, dv);
}
// Calls |MLKEM768_encap_external_entropy| with random bytes from |RAND_bytes|
void MLKEM768_encap(uint8_t out_ciphertext[MLKEM768_CIPHERTEXT_BYTES],
uint8_t out_shared_secret[MLKEM_SHARED_SECRET_BYTES],
const struct MLKEM768_public_key *public_key) {
uint8_t entropy[MLKEM_ENCAP_ENTROPY];
RAND_bytes(entropy, MLKEM_ENCAP_ENTROPY);
MLKEM768_encap_external_entropy(out_ciphertext, out_shared_secret, public_key,
entropy);
}
void MLKEM1024_encap(uint8_t out_ciphertext[MLKEM1024_CIPHERTEXT_BYTES],
uint8_t out_shared_secret[MLKEM_SHARED_SECRET_BYTES],
const struct MLKEM1024_public_key *public_key) {
uint8_t entropy[MLKEM_ENCAP_ENTROPY];
RAND_bytes(entropy, MLKEM_ENCAP_ENTROPY);
MLKEM1024_encap_external_entropy(out_ciphertext, out_shared_secret,
public_key, entropy);
}
// See section 6.2.
template <int RANK>
static void mlkem_encap_external_entropy(
uint8_t *out_ciphertext,
uint8_t out_shared_secret[MLKEM_SHARED_SECRET_BYTES],
const struct public_key<RANK> *pub,
const uint8_t entropy[MLKEM_ENCAP_ENTROPY]) {
uint8_t input[64];
OPENSSL_memcpy(input, entropy, MLKEM_ENCAP_ENTROPY);
OPENSSL_memcpy(input + MLKEM_ENCAP_ENTROPY, pub->public_key_hash,
sizeof(input) - MLKEM_ENCAP_ENTROPY);
uint8_t key_and_randomness[64];
hash_g(key_and_randomness, input, sizeof(input));
encrypt_cpa(out_ciphertext, pub, entropy, key_and_randomness + 32);
static_assert(MLKEM_SHARED_SECRET_BYTES == 32, "");
memcpy(out_shared_secret, key_and_randomness, 32);
}
void MLKEM768_encap_external_entropy(
uint8_t out_ciphertext[MLKEM768_CIPHERTEXT_BYTES],
uint8_t out_shared_secret[MLKEM_SHARED_SECRET_BYTES],
const struct MLKEM768_public_key *public_key,
const uint8_t entropy[MLKEM_ENCAP_ENTROPY]) {
const struct ::public_key<RANK768> *pub =
public_key_768_from_external(public_key);
mlkem_encap_external_entropy(out_ciphertext, out_shared_secret, pub, entropy);
}
void MLKEM1024_encap_external_entropy(
uint8_t out_ciphertext[MLKEM1024_CIPHERTEXT_BYTES],
uint8_t out_shared_secret[MLKEM_SHARED_SECRET_BYTES],
const struct MLKEM1024_public_key *public_key,
const uint8_t entropy[MLKEM_ENCAP_ENTROPY]) {
const struct ::public_key<RANK1024> *pub =
public_key_1024_from_external(public_key);
mlkem_encap_external_entropy(out_ciphertext, out_shared_secret, pub, entropy);
}
template <int RANK>
static void decrypt_cpa(uint8_t out[32], const struct private_key<RANK> *priv,
const uint8_t ciphertext[MLKEM768_CIPHERTEXT_BYTES]) {
constexpr int du = RANK == RANK768 ? kDU768 : kDU1024;
constexpr int dv = RANK == RANK768 ? kDV768 : kDV1024;
vector<RANK> u;
vector_decode(&u, ciphertext, du);
vector_decompress(&u, du);
vector_ntt(&u);
scalar v;
scalar_decode(&v, ciphertext + compressed_vector_size(RANK), dv);
scalar_decompress(&v, dv);
scalar mask;
scalar_inner_product(&mask, &priv->s, &u);
scalar_inverse_ntt(&mask);
scalar_sub(&v, &mask);
scalar_compress(&v, 1);
scalar_encode_1(out, &v);
}
// See section 6.3
template <int RANK>
static void mlkem_decap(uint8_t out_shared_secret[MLKEM_SHARED_SECRET_BYTES],
const uint8_t *ciphertext,
const struct private_key<RANK> *priv) {
uint8_t decrypted[64];
decrypt_cpa(decrypted, priv, ciphertext);
OPENSSL_memcpy(decrypted + 32, priv->pub.public_key_hash,
sizeof(decrypted) - 32);
uint8_t key_and_randomness[64];
hash_g(key_and_randomness, decrypted, sizeof(decrypted));
constexpr size_t ciphertext_len = ciphertext_size(RANK);
uint8_t expected_ciphertext[MLKEM1024_CIPHERTEXT_BYTES];
static_assert(ciphertext_len <= sizeof(expected_ciphertext), "");
encrypt_cpa(expected_ciphertext, &priv->pub, decrypted,
key_and_randomness + 32);
uint8_t failure_key[32];
kdf(failure_key, priv->fo_failure_secret, ciphertext, ciphertext_len);
uint8_t mask = constant_time_eq_int_8(
CRYPTO_memcmp(ciphertext, expected_ciphertext, ciphertext_len), 0);
for (int i = 0; i < MLKEM_SHARED_SECRET_BYTES; i++) {
out_shared_secret[i] =
constant_time_select_8(mask, key_and_randomness[i], failure_key[i]);
}
}
int MLKEM768_decap(uint8_t out_shared_secret[MLKEM_SHARED_SECRET_BYTES],
const uint8_t *ciphertext, size_t ciphertext_len,
const struct MLKEM768_private_key *private_key) {
if (ciphertext_len != MLKEM768_CIPHERTEXT_BYTES) {
RAND_bytes(out_shared_secret, MLKEM_SHARED_SECRET_BYTES);
return 0;
}
const struct ::private_key<RANK768> *priv =
private_key_768_from_external(private_key);
mlkem_decap(out_shared_secret, ciphertext, priv);
return 1;
}
int MLKEM1024_decap(uint8_t out_shared_secret[MLKEM_SHARED_SECRET_BYTES],
const uint8_t *ciphertext, size_t ciphertext_len,
const struct MLKEM1024_private_key *private_key) {
if (ciphertext_len != MLKEM1024_CIPHERTEXT_BYTES) {
RAND_bytes(out_shared_secret, MLKEM_SHARED_SECRET_BYTES);
return 0;
}
const struct ::private_key<RANK1024> *priv =
private_key_1024_from_external(private_key);
mlkem_decap(out_shared_secret, ciphertext, priv);
return 1;
}
int MLKEM768_marshal_public_key(CBB *out,
const struct MLKEM768_public_key *public_key) {
return mlkem_marshal_public_key(out,
public_key_768_from_external(public_key));
}
int MLKEM1024_marshal_public_key(
CBB *out, const struct MLKEM1024_public_key *public_key) {
return mlkem_marshal_public_key(out,
public_key_1024_from_external(public_key));
}
// mlkem_parse_public_key_no_hash parses |in| into |pub| but doesn't calculate
// the value of |pub->public_key_hash|.
template <int RANK>
static int mlkem_parse_public_key_no_hash(struct public_key<RANK> *pub,
CBS *in) {
CBS t_bytes;
if (!CBS_get_bytes(in, &t_bytes, encoded_vector_size(RANK)) ||
!vector_decode(&pub->t, CBS_data(&t_bytes), kLog2Prime) ||
!CBS_copy_bytes(in, pub->rho, sizeof(pub->rho))) {
return 0;
}
matrix_expand(&pub->m, pub->rho);
return 1;
}
template <int RANK>
static int mlkem_parse_public_key(struct public_key<RANK> *pub, CBS *in) {
CBS orig_in = *in;
if (!mlkem_parse_public_key_no_hash(pub, in) || //
CBS_len(in) != 0) {
return 0;
}
hash_h(pub->public_key_hash, CBS_data(&orig_in), CBS_len(&orig_in));
return 1;
}
int MLKEM768_parse_public_key(struct MLKEM768_public_key *public_key, CBS *in) {
struct ::public_key<RANK768> *pub = public_key_768_from_external(public_key);
return mlkem_parse_public_key(pub, in);
}
int MLKEM1024_parse_public_key(struct MLKEM1024_public_key *public_key,
CBS *in) {
struct ::public_key<RANK1024> *pub =
public_key_1024_from_external(public_key);
return mlkem_parse_public_key(pub, in);
}
template <int RANK>
static int mlkem_marshal_private_key(CBB *out,
const struct private_key<RANK> *priv) {
uint8_t *s_output;
if (!CBB_add_space(out, &s_output, encoded_vector_size(RANK))) {
return 0;
}
vector_encode(s_output, &priv->s, kLog2Prime);
if (!mlkem_marshal_public_key(out, &priv->pub) ||
!CBB_add_bytes(out, priv->pub.public_key_hash,
sizeof(priv->pub.public_key_hash)) ||
!CBB_add_bytes(out, priv->fo_failure_secret,
sizeof(priv->fo_failure_secret))) {
return 0;
}
return 1;
}
int MLKEM768_marshal_private_key(
CBB *out, const struct MLKEM768_private_key *private_key) {
const struct ::private_key<RANK768> *const priv =
private_key_768_from_external(private_key);
return mlkem_marshal_private_key(out, priv);
}
int MLKEM1024_marshal_private_key(
CBB *out, const struct MLKEM1024_private_key *private_key) {
const struct ::private_key<RANK1024> *const priv =
private_key_1024_from_external(private_key);
return mlkem_marshal_private_key(out, priv);
}
template <int RANK>
static int mlkem_parse_private_key(struct private_key<RANK> *priv, CBS *in) {
CBS s_bytes;
if (!CBS_get_bytes(in, &s_bytes, encoded_vector_size(RANK)) ||
!vector_decode(&priv->s, CBS_data(&s_bytes), kLog2Prime) ||
!mlkem_parse_public_key_no_hash(&priv->pub, in) ||
!CBS_copy_bytes(in, priv->pub.public_key_hash,
sizeof(priv->pub.public_key_hash)) ||
!CBS_copy_bytes(in, priv->fo_failure_secret,
sizeof(priv->fo_failure_secret)) ||
CBS_len(in) != 0) {
return 0;
}
return 1;
}
int MLKEM768_parse_private_key(struct MLKEM768_private_key *out_private_key,
CBS *in) {
struct private_key<RANK768> *const priv =
private_key_768_from_external(out_private_key);
return mlkem_parse_private_key(priv, in);
}
int MLKEM1024_parse_private_key(struct MLKEM1024_private_key *out_private_key,
CBS *in) {
struct private_key<RANK1024> *const priv =
private_key_1024_from_external(out_private_key);
return mlkem_parse_private_key(priv, in);
}