xref: /aosp_15_r20/external/boringssl/src/crypto/dilithium/dilithium.c (revision 8fb009dc861624b67b6cdb62ea21f0f22d0c584b)

/* Copyright (c) 2023, Google LLC
 *
 * 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. */

#define OPENSSL_UNSTABLE_EXPERIMENTAL_DILITHIUM
#include <openssl/experimental/dilithium.h>

#include <assert.h>
#include <stdlib.h>

#include <openssl/bytestring.h>
#include <openssl/rand.h>

#include "../internal.h"
#include "../keccak/internal.h"
#include "./internal.h"

#define DEGREE 256
#define K 6
#define L 5
#define ETA 4
#define TAU 49
#define BETA 196
#define OMEGA 55

#define RHO_BYTES 32
#define SIGMA_BYTES 64
#define K_BYTES 32
#define TR_BYTES 64
#define MU_BYTES 64
#define RHO_PRIME_BYTES 64
#define LAMBDA_BITS 192
#define LAMBDA_BYTES (LAMBDA_BITS / 8)

// 2^23 - 2^13 + 1
static const uint32_t kPrime = 8380417;
// Inverse of -kPrime modulo 2^32
static const uint32_t kPrimeNegInverse = 4236238847;
static const int kDroppedBits = 13;
static const uint32_t kHalfPrime = (8380417 - 1) / 2;
static const uint32_t kGamma1 = 1 << 19;
static const uint32_t kGamma2 = (8380417 - 1) / 32;
// 256^-1 mod kPrime, in Montgomery form.
static const uint32_t kInverseDegreeMontgomery = 41978;

typedef struct scalar {
  uint32_t c[DEGREE];
} scalar;

typedef struct vectork {
  scalar v[K];
} vectork;

typedef struct vectorl {
  scalar v[L];
} vectorl;

typedef struct matrix {
  scalar v[K][L];
} matrix;

/* Arithmetic */

// This bit of Python will be referenced in some of the following comments:
//
// q = 8380417
// # Inverse of -q modulo 2^32
// q_neg_inverse = 4236238847
// # 2^64 modulo q
// montgomery_square = 2365951
//
// def bitreverse(i):
//     ret = 0
//     for n in range(8):
//         bit = i & 1
//         ret <<= 1
//         ret |= bit
//         i >>= 1
//     return ret
//
// def montgomery_reduce(x):
//     a = (x * q_neg_inverse) % 2**32
//     b = x + a * q
//     assert b & 0xFFFF_FFFF == 0
//     c = b >> 32
//     assert c < q
//     return c
//
// def montgomery_transform(x):
//     return montgomery_reduce(x * montgomery_square)

// kNTTRootsMontgomery = [
//   montgomery_transform(pow(1753, bitreverse(i), q)) for i in range(256)
// ]
static const uint32_t kNTTRootsMontgomery[256] = {
    4193792, 25847,   5771523, 7861508, 237124,  7602457, 7504169, 466468,
    1826347, 2353451, 8021166, 6288512, 3119733, 5495562, 3111497, 2680103,
    2725464, 1024112, 7300517, 3585928, 7830929, 7260833, 2619752, 6271868,
    6262231, 4520680, 6980856, 5102745, 1757237, 8360995, 4010497, 280005,
    2706023, 95776,   3077325, 3530437, 6718724, 4788269, 5842901, 3915439,
    4519302, 5336701, 3574422, 5512770, 3539968, 8079950, 2348700, 7841118,
    6681150, 6736599, 3505694, 4558682, 3507263, 6239768, 6779997, 3699596,
    811944,  531354,  954230,  3881043, 3900724, 5823537, 2071892, 5582638,
    4450022, 6851714, 4702672, 5339162, 6927966, 3475950, 2176455, 6795196,
    7122806, 1939314, 4296819, 7380215, 5190273, 5223087, 4747489, 126922,
    3412210, 7396998, 2147896, 2715295, 5412772, 4686924, 7969390, 5903370,
    7709315, 7151892, 8357436, 7072248, 7998430, 1349076, 1852771, 6949987,
    5037034, 264944,  508951,  3097992, 44288,   7280319, 904516,  3958618,
    4656075, 8371839, 1653064, 5130689, 2389356, 8169440, 759969,  7063561,
    189548,  4827145, 3159746, 6529015, 5971092, 8202977, 1315589, 1341330,
    1285669, 6795489, 7567685, 6940675, 5361315, 4499357, 4751448, 3839961,
    2091667, 3407706, 2316500, 3817976, 5037939, 2244091, 5933984, 4817955,
    266997,  2434439, 7144689, 3513181, 4860065, 4621053, 7183191, 5187039,
    900702,  1859098, 909542,  819034,  495491,  6767243, 8337157, 7857917,
    7725090, 5257975, 2031748, 3207046, 4823422, 7855319, 7611795, 4784579,
    342297,  286988,  5942594, 4108315, 3437287, 5038140, 1735879, 203044,
    2842341, 2691481, 5790267, 1265009, 4055324, 1247620, 2486353, 1595974,
    4613401, 1250494, 2635921, 4832145, 5386378, 1869119, 1903435, 7329447,
    7047359, 1237275, 5062207, 6950192, 7929317, 1312455, 3306115, 6417775,
    7100756, 1917081, 5834105, 7005614, 1500165, 777191,  2235880, 3406031,
    7838005, 5548557, 6709241, 6533464, 5796124, 4656147, 594136,  4603424,
    6366809, 2432395, 2454455, 8215696, 1957272, 3369112, 185531,  7173032,
    5196991, 162844,  1616392, 3014001, 810149,  1652634, 4686184, 6581310,
    5341501, 3523897, 3866901, 269760,  2213111, 7404533, 1717735, 472078,
    7953734, 1723600, 6577327, 1910376, 6712985, 7276084, 8119771, 4546524,
    5441381, 6144432, 7959518, 6094090, 183443,  7403526, 1612842, 4834730,
    7826001, 3919660, 8332111, 7018208, 3937738, 1400424, 7534263, 1976782};

// Reduces x mod kPrime in constant time, where 0 <= x < 2*kPrime.
static uint32_t reduce_once(uint32_t x) {
  declassify_assert(x < 2 * kPrime);
  // return x < kPrime ? x : x - kPrime;
  return constant_time_select_int(constant_time_lt_w(x, kPrime), x, x - kPrime);
}

// Returns the absolute value in constant time.
static uint32_t abs_signed(uint32_t x) {
  // return is_positive(x) ? x : -x;
  // Note: MSVC doesn't like applying the unary minus operator to unsigned types
  // (warning C4146), so we write the negation as a bitwise not plus one
  // (assuming two's complement representation).
  return constant_time_select_int(constant_time_lt_w(x, 0x80000000), x, ~x + 1);
}

// Returns the absolute value modulo kPrime.
static uint32_t abs_mod_prime(uint32_t x) {
  declassify_assert(x < kPrime);
  // return x > kHalfPrime ? kPrime - x : x;
  return constant_time_select_int(constant_time_lt_w(kHalfPrime, x), kPrime - x,
                                  x);
}

// Returns the maximum of two values in constant time.
static uint32_t maximum(uint32_t x, uint32_t y) {
  // return x < y ? y : x;
  return constant_time_select_int(constant_time_lt_w(x, y), y, x);
}

static void scalar_add(scalar *out, const scalar *lhs, const scalar *rhs) {
  for (int i = 0; i < DEGREE; i++) {
    out->c[i] = reduce_once(lhs->c[i] + rhs->c[i]);
  }
}

static void scalar_sub(scalar *out, const scalar *lhs, const scalar *rhs) {
  for (int i = 0; i < DEGREE; i++) {
    out->c[i] = reduce_once(kPrime + lhs->c[i] - rhs->c[i]);
  }
}

static uint32_t reduce_montgomery(uint64_t x) {
  uint64_t a = (uint32_t)x * kPrimeNegInverse;
  uint64_t b = x + a * kPrime;
  declassify_assert((b & 0xffffffff) == 0);
  uint32_t c = b >> 32;
  return reduce_once(c);
}

// Multiply two scalars in the number theoretically transformed state.
static void scalar_mult(scalar *out, const scalar *lhs, const scalar *rhs) {
  for (int i = 0; i < DEGREE; i++) {
    out->c[i] = reduce_montgomery((uint64_t)lhs->c[i] * (uint64_t)rhs->c[i]);
  }
}

// In place number theoretic transform of a given scalar.
//
// FIPS 204, Algorithm 35 (`NTT`).
static void scalar_ntt(scalar *s) {
  // Step: 1, 2, 4, 8, ..., 128
  // Offset: 128, 64, 32, 16, ..., 1
  int offset = DEGREE;
  for (int step = 1; step < DEGREE; step <<= 1) {
    offset >>= 1;
    int k = 0;
    for (int i = 0; i < step; i++) {
      assert(k == 2 * offset * i);
      const uint32_t step_root = kNTTRootsMontgomery[step + i];
      for (int j = k; j < k + offset; j++) {
        uint32_t even = s->c[j];
        uint32_t odd =
            reduce_montgomery((uint64_t)step_root * (uint64_t)s->c[j + offset]);
        s->c[j] = reduce_once(odd + even);
        s->c[j + offset] = reduce_once(kPrime + even - odd);
      }
      k += 2 * offset;
    }
  }
}

// In place inverse number theoretic transform of a given scalar.
//
// FIPS 204, Algorithm 36 (`NTT^-1`).
static void scalar_inverse_ntt(scalar *s) {
  // Step: 128, 64, 32, 16, ..., 1
  // Offset: 1, 2, 4, 8, ..., 128
  int step = DEGREE;
  for (int offset = 1; offset < DEGREE; offset <<= 1) {
    step >>= 1;
    int k = 0;
    for (int i = 0; i < step; i++) {
      assert(k == 2 * offset * i);
      const uint32_t step_root =
          kPrime - kNTTRootsMontgomery[step + (step - 1 - i)];
      for (int j = k; j < k + offset; j++) {
        uint32_t even = s->c[j];
        uint32_t odd = s->c[j + offset];
        s->c[j] = reduce_once(odd + even);
        s->c[j + offset] = reduce_montgomery((uint64_t)step_root *
                                             (uint64_t)(kPrime + even - odd));
      }
      k += 2 * offset;
    }
  }
  for (int i = 0; i < DEGREE; i++) {
    s->c[i] = reduce_montgomery((uint64_t)s->c[i] *
                                (uint64_t)kInverseDegreeMontgomery);
  }
}

static void vectork_zero(vectork *out) { OPENSSL_memset(out, 0, sizeof(*out)); }

static void vectork_add(vectork *out, const vectork *lhs, const vectork *rhs) {
  for (int i = 0; i < K; i++) {
    scalar_add(&out->v[i], &lhs->v[i], &rhs->v[i]);
  }
}

static void vectork_sub(vectork *out, const vectork *lhs, const vectork *rhs) {
  for (int i = 0; i < K; i++) {
    scalar_sub(&out->v[i], &lhs->v[i], &rhs->v[i]);
  }
}

static void vectork_mult_scalar(vectork *out, const vectork *lhs,
                                const scalar *rhs) {
  for (int i = 0; i < K; i++) {
    scalar_mult(&out->v[i], &lhs->v[i], rhs);
  }
}

static void vectork_ntt(vectork *a) {
  for (int i = 0; i < K; i++) {
    scalar_ntt(&a->v[i]);
  }
}

static void vectork_inverse_ntt(vectork *a) {
  for (int i = 0; i < K; i++) {
    scalar_inverse_ntt(&a->v[i]);
  }
}

static void vectorl_add(vectorl *out, const vectorl *lhs, const vectorl *rhs) {
  for (int i = 0; i < L; i++) {
    scalar_add(&out->v[i], &lhs->v[i], &rhs->v[i]);
  }
}

static void vectorl_mult_scalar(vectorl *out, const vectorl *lhs,
                                const scalar *rhs) {
  for (int i = 0; i < L; i++) {
    scalar_mult(&out->v[i], &lhs->v[i], rhs);
  }
}

static void vectorl_ntt(vectorl *a) {
  for (int i = 0; i < L; i++) {
    scalar_ntt(&a->v[i]);
  }
}

static void vectorl_inverse_ntt(vectorl *a) {
  for (int i = 0; i < L; i++) {
    scalar_inverse_ntt(&a->v[i]);
  }
}

static void matrix_mult(vectork *out, const matrix *m, const vectorl *a) {
  vectork_zero(out);
  for (int i = 0; i < K; i++) {
    for (int j = 0; j < L; j++) {
      scalar product;
      scalar_mult(&product, &m->v[i][j], &a->v[j]);
      scalar_add(&out->v[i], &out->v[i], &product);
    }
  }
}

/* Rounding & hints */

// FIPS 204, Algorithm 29 (`Power2Round`).
static void power2_round(uint32_t *r1, uint32_t *r0, uint32_t r) {
  *r1 = r >> kDroppedBits;
  *r0 = r - (*r1 << kDroppedBits);

  uint32_t r0_adjusted = reduce_once(kPrime + *r0 - (1 << kDroppedBits));
  uint32_t r1_adjusted = *r1 + 1;

  // Mask is set iff r0 > 2^(dropped_bits - 1).
  crypto_word_t mask =
      constant_time_lt_w((uint32_t)(1 << (kDroppedBits - 1)), *r0);
  // r0 = mask ? r0_adjusted : r0
  *r0 = constant_time_select_int(mask, r0_adjusted, *r0);
  // r1 = mask ? r1_adjusted : r1
  *r1 = constant_time_select_int(mask, r1_adjusted, *r1);
}

// Scale back previously rounded value.
static void scale_power2_round(uint32_t *out, uint32_t r1) {
  // Pre-condition: 0 <= r1 <= 2^10 - 1
  *out = r1 << kDroppedBits;
  // Post-condition: 0 <= out <= 2^23 - 2^13 = kPrime - 1
  assert(*out < kPrime);
}

// FIPS 204, Algorithm 31 (`HighBits`).
static uint32_t high_bits(uint32_t x) {
  // Reference description (given 0 <= x < q):
  //
  // ```
  // int32_t r0 = x mod+- (2 * kGamma2);
  // if (x - r0 == q - 1) {
  //   return 0;
  // } else {
  //   return (x - r0) / (2 * kGamma2);
  // }
  // ```
  //
  // Below is the formula taken from the reference implementation.
  //
  // Here, kGamma2 == 2^18 - 2^8
  // This returns ((ceil(x / 2^7) * (2^10 + 1) + 2^21) / 2^22) mod 2^4
  uint32_t r1 = (x + 127) >> 7;
  r1 = (r1 * 1025 + (1 << 21)) >> 22;
  r1 &= 15;
  return r1;
}

// FIPS 204, Algorithm 30 (`Decompose`).
static void decompose(uint32_t *r1, int32_t *r0, uint32_t r) {
  *r1 = high_bits(r);

  *r0 = r;
  *r0 -= *r1 * 2 * (int32_t)kGamma2;
  *r0 -= (((int32_t)kHalfPrime - *r0) >> 31) & (int32_t)kPrime;
}

// FIPS 204, Algorithm 32 (`LowBits`).
static int32_t low_bits(uint32_t x) {
  uint32_t r1;
  int32_t r0;
  decompose(&r1, &r0, x);
  return r0;
}

// FIPS 204, Algorithm 33 (`MakeHint`).
static int32_t make_hint(uint32_t ct0, uint32_t cs2, uint32_t w) {
  uint32_t r_plus_z = reduce_once(kPrime + w - cs2);
  uint32_t r = reduce_once(r_plus_z + ct0);
  return high_bits(r) != high_bits(r_plus_z);
}

// FIPS 204, Algorithm 34 (`UseHint`).
static uint32_t use_hint_vartime(uint32_t h, uint32_t r) {
  uint32_t r1;
  int32_t r0;
  decompose(&r1, &r0, r);

  if (h) {
    if (r0 > 0) {
      return (r1 + 1) & 15;
    } else {
      return (r1 - 1) & 15;
    }
  } else {
    return r1;
  }
}

static void scalar_power2_round(scalar *s1, scalar *s0, const scalar *s) {
  for (int i = 0; i < DEGREE; i++) {
    power2_round(&s1->c[i], &s0->c[i], s->c[i]);
  }
}

static void scalar_scale_power2_round(scalar *out, const scalar *in) {
  for (int i = 0; i < DEGREE; i++) {
    scale_power2_round(&out->c[i], in->c[i]);
  }
}

static void scalar_high_bits(scalar *out, const scalar *in) {
  for (int i = 0; i < DEGREE; i++) {
    out->c[i] = high_bits(in->c[i]);
  }
}

static void scalar_low_bits(scalar *out, const scalar *in) {
  for (int i = 0; i < DEGREE; i++) {
    out->c[i] = low_bits(in->c[i]);
  }
}

static void scalar_max(uint32_t *max, const scalar *s) {
  for (int i = 0; i < DEGREE; i++) {
    uint32_t abs = abs_mod_prime(s->c[i]);
    *max = maximum(*max, abs);
  }
}

static void scalar_max_signed(uint32_t *max, const scalar *s) {
  for (int i = 0; i < DEGREE; i++) {
    uint32_t abs = abs_signed(s->c[i]);
    *max = maximum(*max, abs);
  }
}

static void scalar_make_hint(scalar *out, const scalar *ct0, const scalar *cs2,
                             const scalar *w) {
  for (int i = 0; i < DEGREE; i++) {
    out->c[i] = make_hint(ct0->c[i], cs2->c[i], w->c[i]);
  }
}

static void scalar_use_hint_vartime(scalar *out, const scalar *h,
                                    const scalar *r) {
  for (int i = 0; i < DEGREE; i++) {
    out->c[i] = use_hint_vartime(h->c[i], r->c[i]);
  }
}

static void vectork_power2_round(vectork *t1, vectork *t0, const vectork *t) {
  for (int i = 0; i < K; i++) {
    scalar_power2_round(&t1->v[i], &t0->v[i], &t->v[i]);
  }
}

static void vectork_scale_power2_round(vectork *out, const vectork *in) {
  for (int i = 0; i < K; i++) {
    scalar_scale_power2_round(&out->v[i], &in->v[i]);
  }
}

static void vectork_high_bits(vectork *out, const vectork *in) {
  for (int i = 0; i < K; i++) {
    scalar_high_bits(&out->v[i], &in->v[i]);
  }
}

static void vectork_low_bits(vectork *out, const vectork *in) {
  for (int i = 0; i < K; i++) {
    scalar_low_bits(&out->v[i], &in->v[i]);
  }
}

static uint32_t vectork_max(const vectork *a) {
  uint32_t max = 0;
  for (int i = 0; i < K; i++) {
    scalar_max(&max, &a->v[i]);
  }
  return max;
}

static uint32_t vectork_max_signed(const vectork *a) {
  uint32_t max = 0;
  for (int i = 0; i < K; i++) {
    scalar_max_signed(&max, &a->v[i]);
  }
  return max;
}

// The input vector contains only zeroes and ones.
static size_t vectork_count_ones(const vectork *a) {
  size_t count = 0;
  for (int i = 0; i < K; i++) {
    for (int j = 0; j < DEGREE; j++) {
      count += a->v[i].c[j];
    }
  }
  return count;
}

static void vectork_make_hint(vectork *out, const vectork *ct0,
                              const vectork *cs2, const vectork *w) {
  for (int i = 0; i < K; i++) {
    scalar_make_hint(&out->v[i], &ct0->v[i], &cs2->v[i], &w->v[i]);
  }
}

static void vectork_use_hint_vartime(vectork *out, const vectork *h,
                                     const vectork *r) {
  for (int i = 0; i < K; i++) {
    scalar_use_hint_vartime(&out->v[i], &h->v[i], &r->v[i]);
  }
}

static uint32_t vectorl_max(const vectorl *a) {
  uint32_t max = 0;
  for (int i = 0; i < L; i++) {
    scalar_max(&max, &a->v[i]);
  }
  return max;
}

/* Bit packing */

static const uint8_t kMasks[8] = {0x01, 0x03, 0x07, 0x0f,
                                  0x1f, 0x3f, 0x7f, 0xff};

// FIPS 204, Algorithm 10 (`SimpleBitPack`).
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++) {
    uint32_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;
  }
}

// FIPS 204, Algorithm 11 (`BitPack`).
static void scalar_encode_signed(uint8_t *out, const scalar *s, int bits,
                                 uint32_t max) {
  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++) {
    uint32_t element = reduce_once(kPrime + max - s->c[i]);
    declassify_assert(element <= 2 * max);
    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;
  }
}

// FIPS 204, Algorithm 12 (`SimpleBitUnpack`).
static void 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++) {
    uint32_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;
    }

    out->c[i] = element;
  }
}

// FIPS 204, Algorithm 13 (`BitUnpack`).
static int scalar_decode_signed(scalar *out, const uint8_t *in, int bits,
                                uint32_t max) {
  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++) {
    uint32_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;
    }

    // This may be only out of range in cases of invalid input, in which case it
    // is okay to leak the value. This function is also called with secret
    // input during signing, in |scalar_sample_mask|. However, in that case
    // (and in any case when |max| is a power of two), this case is impossible.
    if (constant_time_declassify_int(element > 2 * max)) {
      return 0;
    }
    out->c[i] = reduce_once(kPrime + max - element);
  }

  return 1;
}

/* Expansion functions */

// FIPS 204, Algorithm 24 (`RejNTTPoly`).
//
// 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, const uint8_t derived_seed[RHO_BYTES + 2]) {
  struct BORINGSSL_keccak_st keccak_ctx;
  BORINGSSL_keccak_init(&keccak_ctx, boringssl_shake128);
  BORINGSSL_keccak_absorb(&keccak_ctx, derived_seed, RHO_BYTES + 2);
  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) {
      // FIPS 204, Algorithm 8 (`CoeffFromThreeBytes`).
      uint32_t value = (uint32_t)block[i] | ((uint32_t)block[i + 1] << 8) |
                       (((uint32_t)block[i + 2] & 0x7f) << 16);
      if (value < kPrime) {
        out->c[done++] = value;
      }
    }
  }
}

// FIPS 204, Algorithm 25 (`RejBoundedPoly`).
static void scalar_uniform_eta_4(scalar *out,
                                 const uint8_t derived_seed[SIGMA_BYTES + 2]) {
  static_assert(ETA == 4, "This implementation is specialized for ETA == 4");

  struct BORINGSSL_keccak_st keccak_ctx;
  BORINGSSL_keccak_init(&keccak_ctx, boringssl_shake256);
  BORINGSSL_keccak_absorb(&keccak_ctx, derived_seed, SIGMA_BYTES + 2);
  assert(keccak_ctx.squeeze_offset == 0);
  assert(keccak_ctx.rate_bytes == 136);

  int done = 0;
  while (done < DEGREE) {
    uint8_t block[136];
    BORINGSSL_keccak_squeeze(&keccak_ctx, block, sizeof(block));
    for (size_t i = 0; i < sizeof(block) && done < DEGREE; ++i) {
      uint32_t t0 = block[i] & 0x0F;
      uint32_t t1 = block[i] >> 4;
      // FIPS 204, Algorithm 9 (`CoefFromHalfByte`). Although both the input and
      // output here are secret, it is OK to leak when we rejected a byte.
      // Individual bytes of the SHAKE-256 stream are (indistiguishable from)
      // independent of each other and the original seed, so leaking information
      // about the rejected bytes does not reveal the input or output.
      if (constant_time_declassify_int(t0 < 9)) {
        out->c[done++] = reduce_once(kPrime + ETA - t0);
      }
      if (done < DEGREE && constant_time_declassify_int(t1 < 9)) {
        out->c[done++] = reduce_once(kPrime + ETA - t1);
      }
    }
  }
}

// FIPS 204, Algorithm 28 (`ExpandMask`).
static void scalar_sample_mask(
    scalar *out, const uint8_t derived_seed[RHO_PRIME_BYTES + 2]) {
  uint8_t buf[640];
  BORINGSSL_keccak(buf, sizeof(buf), derived_seed, RHO_PRIME_BYTES + 2,
                   boringssl_shake256);

  // Note: Decoding 20 bits into (-2^19, 2^19] cannot fail.
  scalar_decode_signed(out, buf, 20, 1 << 19);
}

// FIPS 204, Algorithm 23 (`SampleInBall`).
static void scalar_sample_in_ball_vartime(scalar *out, const uint8_t *seed,
                                          int len) {
  assert(len == 32);

  struct BORINGSSL_keccak_st keccak_ctx;
  BORINGSSL_keccak_init(&keccak_ctx, boringssl_shake256);
  BORINGSSL_keccak_absorb(&keccak_ctx, seed, len);
  assert(keccak_ctx.squeeze_offset == 0);
  assert(keccak_ctx.rate_bytes == 136);

  uint8_t block[136];
  BORINGSSL_keccak_squeeze(&keccak_ctx, block, sizeof(block));

  uint64_t signs = CRYPTO_load_u64_le(block);
  int offset = 8;
  // SampleInBall implements a Fisher–Yates shuffle, which unavoidably leaks
  // where the zeros are by memory access pattern. Although this leak happens
  // before bad signatures are rejected, this is safe. See
  // https://boringssl-review.googlesource.com/c/boringssl/+/67747/comment/8d8f01ac_70af3f21/
  CONSTTIME_DECLASSIFY(block + offset, sizeof(block) - offset);

  OPENSSL_memset(out, 0, sizeof(*out));
  for (size_t i = DEGREE - TAU; i < DEGREE; i++) {
    size_t byte;
    for (;;) {
      if (offset == 136) {
        BORINGSSL_keccak_squeeze(&keccak_ctx, block, sizeof(block));
        // See above.
        CONSTTIME_DECLASSIFY(block, sizeof(block));
        offset = 0;
      }

      byte = block[offset++];
      if (byte <= i) {
        break;
      }
    }

    out->c[i] = out->c[byte];
    out->c[byte] = reduce_once(kPrime + 1 - 2 * (signs & 1));
    signs >>= 1;
  }
}

// FIPS 204, Algorithm 26 (`ExpandA`).
static void matrix_expand(matrix *out, const uint8_t rho[RHO_BYTES]) {
  static_assert(K <= 0x100, "K must fit in 8 bits");
  static_assert(L <= 0x100, "L must fit in 8 bits");

  uint8_t derived_seed[RHO_BYTES + 2];
  OPENSSL_memcpy(derived_seed, rho, RHO_BYTES);
  for (int i = 0; i < K; i++) {
    for (int j = 0; j < L; j++) {
      derived_seed[RHO_BYTES + 1] = i;
      derived_seed[RHO_BYTES] = j;
      scalar_from_keccak_vartime(&out->v[i][j], derived_seed);
    }
  }
}

// FIPS 204, Algorithm 27 (`ExpandS`).
static void vector_expand_short(vectorl *s1, vectork *s2,
                                const uint8_t sigma[SIGMA_BYTES]) {
  static_assert(K <= 0x100, "K must fit in 8 bits");
  static_assert(L <= 0x100, "L must fit in 8 bits");
  static_assert(K + L <= 0x100, "K+L must fit in 8 bits");

  uint8_t derived_seed[SIGMA_BYTES + 2];
  OPENSSL_memcpy(derived_seed, sigma, SIGMA_BYTES);
  derived_seed[SIGMA_BYTES] = 0;
  derived_seed[SIGMA_BYTES + 1] = 0;
  for (int i = 0; i < L; i++) {
    scalar_uniform_eta_4(&s1->v[i], derived_seed);
    ++derived_seed[SIGMA_BYTES];
  }
  for (int i = 0; i < K; i++) {
    scalar_uniform_eta_4(&s2->v[i], derived_seed);
    ++derived_seed[SIGMA_BYTES];
  }
}

// FIPS 204, Algorithm 28 (`ExpandMask`).
static void vectorl_expand_mask(vectorl *out,
                                const uint8_t seed[RHO_PRIME_BYTES],
                                size_t kappa) {
  assert(kappa + L <= 0x10000);

  uint8_t derived_seed[RHO_PRIME_BYTES + 2];
  OPENSSL_memcpy(derived_seed, seed, RHO_PRIME_BYTES);
  for (int i = 0; i < L; i++) {
    size_t index = kappa + i;
    derived_seed[RHO_PRIME_BYTES] = index & 0xFF;
    derived_seed[RHO_PRIME_BYTES + 1] = (index >> 8) & 0xFF;
    scalar_sample_mask(&out->v[i], derived_seed);
  }
}

/* Encoding */

// FIPS 204, Algorithm 10 (`SimpleBitPack`).
//
// Encodes an entire vector into 32*K*|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.
static void vectork_encode(uint8_t *out, const vectork *a, int bits) {
  for (int i = 0; i < K; i++) {
    scalar_encode(out + i * bits * DEGREE / 8, &a->v[i], bits);
  }
}

// FIPS 204, Algorithm 12 (`SimpleBitUnpack`).
static void vectork_decode(vectork *out, const uint8_t *in, int bits) {
  for (int i = 0; i < K; i++) {
    scalar_decode(&out->v[i], in + i * bits * DEGREE / 8, bits);
  }
}

static void vectork_encode_signed(uint8_t *out, const vectork *a, int bits,
                                  uint32_t max) {
  for (int i = 0; i < K; i++) {
    scalar_encode_signed(out + i * bits * DEGREE / 8, &a->v[i], bits, max);
  }
}

static int vectork_decode_signed(vectork *out, const uint8_t *in, int bits,
                                 uint32_t max) {
  for (int i = 0; i < K; i++) {
    if (!scalar_decode_signed(&out->v[i], in + i * bits * DEGREE / 8, bits,
                              max)) {
      return 0;
    }
  }
  return 1;
}

// FIPS 204, Algorithm 11 (`BitPack`).
//
// Encodes an entire vector into 32*L*|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.
static void vectorl_encode_signed(uint8_t *out, const vectorl *a, int bits,
                                  uint32_t max) {
  for (int i = 0; i < L; i++) {
    scalar_encode_signed(out + i * bits * DEGREE / 8, &a->v[i], bits, max);
  }
}

static int vectorl_decode_signed(vectorl *out, const uint8_t *in, int bits,
                                 uint32_t max) {
  for (int i = 0; i < L; i++) {
    if (!scalar_decode_signed(&out->v[i], in + i * bits * DEGREE / 8, bits,
                              max)) {
      return 0;
    }
  }
  return 1;
}

// FIPS 204, Algorithm 22 (`w1Encode`).
//
// The output must point to an array of 128*K bytes.
static void w1_encode(uint8_t *out, const vectork *w1) {
  vectork_encode(out, w1, 4);
}

// FIPS 204, Algorithm 14 (`HintBitPack`).
static void hint_bit_pack(uint8_t *out, const vectork *h) {
  OPENSSL_memset(out, 0, OMEGA + K);
  int index = 0;
  for (int i = 0; i < K; i++) {
    for (int j = 0; j < DEGREE; j++) {
      if (h->v[i].c[j]) {
        out[index++] = j;
      }
    }
    out[OMEGA + i] = index;
  }
}

// FIPS 204, Algorithm 15 (`HintBitUnpack`).
static int hint_bit_unpack(vectork *h, const uint8_t *in) {
  vectork_zero(h);
  int index = 0;
  for (int i = 0; i < K; i++) {
    int limit = in[OMEGA + i];
    if (limit < index || limit > OMEGA) {
      return 0;
    }

    int last = -1;
    while (index < limit) {
      int byte = in[index++];
      if (last >= 0 && byte <= last) {
        return 0;
      }
      last = byte;
      h->v[i].c[byte] = 1;
    }
  }
  for (; index < OMEGA; index++) {
    if (in[index] != 0) {
      return 0;
    }
  }
  return 1;
}

struct public_key {
  uint8_t rho[RHO_BYTES];
  vectork t1;
  // Pre-cached value(s).
  uint8_t public_key_hash[TR_BYTES];
};

struct private_key {
  uint8_t rho[RHO_BYTES];
  uint8_t k[K_BYTES];
  uint8_t public_key_hash[TR_BYTES];
  vectorl s1;
  vectork s2;
  vectork t0;
};

struct signature {
  uint8_t c_tilde[2 * LAMBDA_BYTES];
  vectorl z;
  vectork h;
};

// FIPS 204, Algorithm 16 (`pkEncode`).
static int dilithium_marshal_public_key(CBB *out,
                                        const struct public_key *pub) {
  if (!CBB_add_bytes(out, pub->rho, sizeof(pub->rho))) {
    return 0;
  }

  uint8_t *vectork_output;
  if (!CBB_add_space(out, &vectork_output, 320 * K)) {
    return 0;
  }
  vectork_encode(vectork_output, &pub->t1, 10);

  return 1;
}

// FIPS 204, Algorithm 17 (`pkDecode`).
static int dilithium_parse_public_key(struct public_key *pub, CBS *in) {
  if (!CBS_copy_bytes(in, pub->rho, sizeof(pub->rho))) {
    return 0;
  }

  CBS t1_bytes;
  if (!CBS_get_bytes(in, &t1_bytes, 320 * K)) {
    return 0;
  }
  vectork_decode(&pub->t1, CBS_data(&t1_bytes), 10);

  return 1;
}

// FIPS 204, Algorithm 18 (`skEncode`).
static int dilithium_marshal_private_key(CBB *out,
                                         const struct private_key *priv) {
  if (!CBB_add_bytes(out, priv->rho, sizeof(priv->rho)) ||
      !CBB_add_bytes(out, priv->k, sizeof(priv->k)) ||
      !CBB_add_bytes(out, priv->public_key_hash,
                     sizeof(priv->public_key_hash))) {
    return 0;
  }

  uint8_t *vectorl_output;
  if (!CBB_add_space(out, &vectorl_output, 128 * L)) {
    return 0;
  }
  vectorl_encode_signed(vectorl_output, &priv->s1, 4, ETA);

  uint8_t *vectork_output;
  if (!CBB_add_space(out, &vectork_output, 128 * K)) {
    return 0;
  }
  vectork_encode_signed(vectork_output, &priv->s2, 4, ETA);

  if (!CBB_add_space(out, &vectork_output, 416 * K)) {
    return 0;
  }
  vectork_encode_signed(vectork_output, &priv->t0, 13, 1 << 12);

  return 1;
}

// FIPS 204, Algorithm 19 (`skDecode`).
static int dilithium_parse_private_key(struct private_key *priv, CBS *in) {
  CBS s1_bytes;
  CBS s2_bytes;
  CBS t0_bytes;
  if (!CBS_copy_bytes(in, priv->rho, sizeof(priv->rho)) ||
      !CBS_copy_bytes(in, priv->k, sizeof(priv->k)) ||
      !CBS_copy_bytes(in, priv->public_key_hash,
                      sizeof(priv->public_key_hash)) ||
      !CBS_get_bytes(in, &s1_bytes, 128 * L) ||
      !vectorl_decode_signed(&priv->s1, CBS_data(&s1_bytes), 4, ETA) ||
      !CBS_get_bytes(in, &s2_bytes, 128 * K) ||
      !vectork_decode_signed(&priv->s2, CBS_data(&s2_bytes), 4, ETA) ||
      !CBS_get_bytes(in, &t0_bytes, 416 * K) ||
      // Note: Decoding 13 bits into (-2^12, 2^12] cannot fail.
      !vectork_decode_signed(&priv->t0, CBS_data(&t0_bytes), 13, 1 << 12)) {
    return 0;
  }

  return 1;
}

// FIPS 204, Algorithm 20 (`sigEncode`).
static int dilithium_marshal_signature(CBB *out, const struct signature *sign) {
  if (!CBB_add_bytes(out, sign->c_tilde, sizeof(sign->c_tilde))) {
    return 0;
  }

  uint8_t *vectorl_output;
  if (!CBB_add_space(out, &vectorl_output, 640 * L)) {
    return 0;
  }
  vectorl_encode_signed(vectorl_output, &sign->z, 20, 1 << 19);

  uint8_t *hint_output;
  if (!CBB_add_space(out, &hint_output, OMEGA + K)) {
    return 0;
  }
  hint_bit_pack(hint_output, &sign->h);

  return 1;
}

// FIPS 204, Algorithm 21 (`sigDecode`).
static int dilithium_parse_signature(struct signature *sign, CBS *in) {
  CBS z_bytes;
  CBS hint_bytes;
  if (!CBS_copy_bytes(in, sign->c_tilde, sizeof(sign->c_tilde)) ||
      !CBS_get_bytes(in, &z_bytes, 640 * L) ||
      // Note: Decoding 20 bits into (-2^19, 2^19] cannot fail.
      !vectorl_decode_signed(&sign->z, CBS_data(&z_bytes), 20, 1 << 19) ||
      !CBS_get_bytes(in, &hint_bytes, OMEGA + K) ||
      !hint_bit_unpack(&sign->h, CBS_data(&hint_bytes))) {
    return 0;
  };

  return 1;
}

static struct private_key *private_key_from_external(
    const struct DILITHIUM_private_key *external) {
  static_assert(
      sizeof(struct DILITHIUM_private_key) == sizeof(struct private_key),
      "Kyber private key size incorrect");
  static_assert(
      alignof(struct DILITHIUM_private_key) == alignof(struct private_key),
      "Kyber private key align incorrect");
  return (struct private_key *)external;
}

static struct public_key *public_key_from_external(
    const struct DILITHIUM_public_key *external) {
  static_assert(
      sizeof(struct DILITHIUM_public_key) == sizeof(struct public_key),
      "Dilithium public key size incorrect");
  static_assert(
      alignof(struct DILITHIUM_public_key) == alignof(struct public_key),
      "Dilithium public key align incorrect");
  return (struct public_key *)external;
}

/* API */

// Calls |DILITHIUM_generate_key_external_entropy| with random bytes from
// |RAND_bytes|. Returns 1 on success and 0 on failure.
int DILITHIUM_generate_key(
    uint8_t out_encoded_public_key[DILITHIUM_PUBLIC_KEY_BYTES],
    struct DILITHIUM_private_key *out_private_key) {
  uint8_t entropy[DILITHIUM_GENERATE_KEY_ENTROPY];
  RAND_bytes(entropy, sizeof(entropy));
  return DILITHIUM_generate_key_external_entropy(out_encoded_public_key,
                                                 out_private_key, entropy);
}

// FIPS 204, Algorithm 1 (`ML-DSA.KeyGen`). Returns 1 on success and 0 on
// failure.
int DILITHIUM_generate_key_external_entropy(
    uint8_t out_encoded_public_key[DILITHIUM_PUBLIC_KEY_BYTES],
    struct DILITHIUM_private_key *out_private_key,
    const uint8_t entropy[DILITHIUM_GENERATE_KEY_ENTROPY]) {
  int ret = 0;

  // Intermediate values, allocated on the heap to allow use when there is a
  // limited amount of stack.
  struct values_st {
    struct public_key pub;
    matrix a_ntt;
    vectorl s1_ntt;
    vectork t;
  };
  struct values_st *values = OPENSSL_malloc(sizeof(*values));
  if (values == NULL) {
    goto err;
  }

  struct private_key *priv = private_key_from_external(out_private_key);

  uint8_t expanded_seed[RHO_BYTES + SIGMA_BYTES + K_BYTES];
  BORINGSSL_keccak(expanded_seed, sizeof(expanded_seed), entropy,
                   DILITHIUM_GENERATE_KEY_ENTROPY, boringssl_shake256);
  const uint8_t *const rho = expanded_seed;
  const uint8_t *const sigma = expanded_seed + RHO_BYTES;
  const uint8_t *const k = expanded_seed + RHO_BYTES + SIGMA_BYTES;
  // rho is public.
  CONSTTIME_DECLASSIFY(rho, RHO_BYTES);
  OPENSSL_memcpy(values->pub.rho, rho, sizeof(values->pub.rho));
  OPENSSL_memcpy(priv->rho, rho, sizeof(priv->rho));
  OPENSSL_memcpy(priv->k, k, sizeof(priv->k));

  matrix_expand(&values->a_ntt, rho);
  vector_expand_short(&priv->s1, &priv->s2, sigma);

  OPENSSL_memcpy(&values->s1_ntt, &priv->s1, sizeof(values->s1_ntt));
  vectorl_ntt(&values->s1_ntt);

  matrix_mult(&values->t, &values->a_ntt, &values->s1_ntt);
  vectork_inverse_ntt(&values->t);
  vectork_add(&values->t, &values->t, &priv->s2);

  vectork_power2_round(&values->pub.t1, &priv->t0, &values->t);
  // t1 is public.
  CONSTTIME_DECLASSIFY(&values->pub.t1, sizeof(values->pub.t1));

  CBB cbb;
  CBB_init_fixed(&cbb, out_encoded_public_key, DILITHIUM_PUBLIC_KEY_BYTES);
  if (!dilithium_marshal_public_key(&cbb, &values->pub)) {
    goto err;
  }

  BORINGSSL_keccak(priv->public_key_hash, sizeof(priv->public_key_hash),
                   out_encoded_public_key, DILITHIUM_PUBLIC_KEY_BYTES,
                   boringssl_shake256);

  ret = 1;
err:
  OPENSSL_free(values);
  return ret;
}

int DILITHIUM_public_from_private(
    struct DILITHIUM_public_key *out_public_key,
    const struct DILITHIUM_private_key *private_key) {
  int ret = 0;

  // Intermediate values, allocated on the heap to allow use when there is a
  // limited amount of stack.
  struct values_st {
    matrix a_ntt;
    vectorl s1_ntt;
    vectork t;
    vectork t0;
  };
  struct values_st *values = OPENSSL_malloc(sizeof(*values));
  if (values == NULL) {
    goto err;
  }

  const struct private_key *priv = private_key_from_external(private_key);
  struct public_key *pub = public_key_from_external(out_public_key);

  OPENSSL_memcpy(pub->rho, priv->rho, sizeof(pub->rho));
  OPENSSL_memcpy(pub->public_key_hash, priv->public_key_hash,
                 sizeof(pub->public_key_hash));

  matrix_expand(&values->a_ntt, priv->rho);

  OPENSSL_memcpy(&values->s1_ntt, &priv->s1, sizeof(values->s1_ntt));
  vectorl_ntt(&values->s1_ntt);

  matrix_mult(&values->t, &values->a_ntt, &values->s1_ntt);
  vectork_inverse_ntt(&values->t);
  vectork_add(&values->t, &values->t, &priv->s2);

  vectork_power2_round(&pub->t1, &values->t0, &values->t);

  ret = 1;
err:
  OPENSSL_free(values);
  return ret;
}

// FIPS 204, Algorithm 2 (`ML-DSA.Sign`). Returns 1 on success and 0 on failure.
static int dilithium_sign_with_randomizer(
    uint8_t out_encoded_signature[DILITHIUM_SIGNATURE_BYTES],
    const struct DILITHIUM_private_key *private_key, const uint8_t *msg,
    size_t msg_len,
    const uint8_t randomizer[DILITHIUM_SIGNATURE_RANDOMIZER_BYTES]) {
  int ret = 0;

  const struct private_key *priv = private_key_from_external(private_key);

  uint8_t mu[MU_BYTES];
  struct BORINGSSL_keccak_st keccak_ctx;
  BORINGSSL_keccak_init(&keccak_ctx, boringssl_shake256);
  BORINGSSL_keccak_absorb(&keccak_ctx, priv->public_key_hash,
                          sizeof(priv->public_key_hash));
  BORINGSSL_keccak_absorb(&keccak_ctx, msg, msg_len);
  BORINGSSL_keccak_squeeze(&keccak_ctx, mu, MU_BYTES);

  uint8_t rho_prime[RHO_PRIME_BYTES];
  BORINGSSL_keccak_init(&keccak_ctx, boringssl_shake256);
  BORINGSSL_keccak_absorb(&keccak_ctx, priv->k, sizeof(priv->k));
  BORINGSSL_keccak_absorb(&keccak_ctx, randomizer,
                          DILITHIUM_SIGNATURE_RANDOMIZER_BYTES);
  BORINGSSL_keccak_absorb(&keccak_ctx, mu, MU_BYTES);
  BORINGSSL_keccak_squeeze(&keccak_ctx, rho_prime, RHO_PRIME_BYTES);

  // Intermediate values, allocated on the heap to allow use when there is a
  // limited amount of stack.
  struct values_st {
    struct signature sign;
    vectorl s1_ntt;
    vectork s2_ntt;
    vectork t0_ntt;
    matrix a_ntt;
    vectorl y;
    vectorl y_ntt;
    vectork w;
    vectork w1;
    vectorl cs1;
    vectork cs2;
    vectork r0;
    vectork ct0;
  };
  struct values_st *values = OPENSSL_malloc(sizeof(*values));
  if (values == NULL) {
    goto err;
  }
  OPENSSL_memcpy(&values->s1_ntt, &priv->s1, sizeof(values->s1_ntt));
  vectorl_ntt(&values->s1_ntt);

  OPENSSL_memcpy(&values->s2_ntt, &priv->s2, sizeof(values->s2_ntt));
  vectork_ntt(&values->s2_ntt);

  OPENSSL_memcpy(&values->t0_ntt, &priv->t0, sizeof(values->t0_ntt));
  vectork_ntt(&values->t0_ntt);

  matrix_expand(&values->a_ntt, priv->rho);

  for (size_t kappa = 0;; kappa += L) {
    // TODO(bbe): y only lives long enough to compute y_ntt.
    // consider using another vectorl to save memory.
    vectorl_expand_mask(&values->y, rho_prime, kappa);

    OPENSSL_memcpy(&values->y_ntt, &values->y, sizeof(values->y_ntt));
    vectorl_ntt(&values->y_ntt);

    // TODO(bbe): w only lives long enough to compute y_ntt.
    // consider using another vectork to save memory.
    matrix_mult(&values->w, &values->a_ntt, &values->y_ntt);
    vectork_inverse_ntt(&values->w);

    vectork_high_bits(&values->w1, &values->w);
    uint8_t w1_encoded[128 * K];
    w1_encode(w1_encoded, &values->w1);

    BORINGSSL_keccak_init(&keccak_ctx, boringssl_shake256);
    BORINGSSL_keccak_absorb(&keccak_ctx, mu, MU_BYTES);
    BORINGSSL_keccak_absorb(&keccak_ctx, w1_encoded, 128 * K);
    BORINGSSL_keccak_squeeze(&keccak_ctx, values->sign.c_tilde,
                             2 * LAMBDA_BYTES);

    scalar c_ntt;
    scalar_sample_in_ball_vartime(&c_ntt, values->sign.c_tilde, 32);
    scalar_ntt(&c_ntt);

    vectorl_mult_scalar(&values->cs1, &values->s1_ntt, &c_ntt);
    vectorl_inverse_ntt(&values->cs1);
    vectork_mult_scalar(&values->cs2, &values->s2_ntt, &c_ntt);
    vectork_inverse_ntt(&values->cs2);

    vectorl_add(&values->sign.z, &values->y, &values->cs1);

    vectork_sub(&values->r0, &values->w, &values->cs2);
    vectork_low_bits(&values->r0, &values->r0);

    // Leaking the fact that a signature was rejected is fine as the next
    // attempt at a signature will be (indistinguishable from) independent of
    // this one. Note, however, that we additionally leak which of the two
    // branches rejected the signature. Section 5.5 of
    // https://pq-crystals.org/dilithium/data/dilithium-specification-round3.pdf
    // describes this leak as OK. Note we leak less than what is described by
    // the paper; we do not reveal which coefficient violated the bound, and we
    // hide which of the |z_max| or |r0_max| bound failed. See also
    // https://boringssl-review.googlesource.com/c/boringssl/+/67747/comment/2bbab0fa_d241d35a/
    uint32_t z_max = vectorl_max(&values->sign.z);
    uint32_t r0_max = vectork_max_signed(&values->r0);
    if (constant_time_declassify_w(
            constant_time_ge_w(z_max, kGamma1 - BETA) |
            constant_time_ge_w(r0_max, kGamma2 - BETA))) {
      continue;
    }

    vectork_mult_scalar(&values->ct0, &values->t0_ntt, &c_ntt);
    vectork_inverse_ntt(&values->ct0);
    vectork_make_hint(&values->sign.h, &values->ct0, &values->cs2, &values->w);

    // See above.
    uint32_t ct0_max = vectork_max(&values->ct0);
    size_t h_ones = vectork_count_ones(&values->sign.h);
    if (constant_time_declassify_w(constant_time_ge_w(ct0_max, kGamma2) |
                                   constant_time_lt_w(OMEGA, h_ones))) {
      continue;
    }

    // Although computed with the private key, the signature is public.
    CONSTTIME_DECLASSIFY(values->sign.c_tilde, sizeof(values->sign.c_tilde));
    CONSTTIME_DECLASSIFY(&values->sign.z, sizeof(values->sign.z));
    CONSTTIME_DECLASSIFY(&values->sign.h, sizeof(values->sign.h));

    CBB cbb;
    CBB_init_fixed(&cbb, out_encoded_signature, DILITHIUM_SIGNATURE_BYTES);
    if (!dilithium_marshal_signature(&cbb, &values->sign)) {
      goto err;
    }

    BSSL_CHECK(CBB_len(&cbb) == DILITHIUM_SIGNATURE_BYTES);
    ret = 1;
    break;
  }

err:
  OPENSSL_free(values);
  return ret;
}

// Dilithium signature in deterministic mode. Returns 1 on success and 0 on
// failure.
int DILITHIUM_sign_deterministic(
    uint8_t out_encoded_signature[DILITHIUM_SIGNATURE_BYTES],
    const struct DILITHIUM_private_key *private_key, const uint8_t *msg,
    size_t msg_len) {
  uint8_t randomizer[DILITHIUM_SIGNATURE_RANDOMIZER_BYTES];
  OPENSSL_memset(randomizer, 0, sizeof(randomizer));
  return dilithium_sign_with_randomizer(out_encoded_signature, private_key, msg,
                                        msg_len, randomizer);
}

// Dilithium signature in randomized mode, filling the random bytes with
// |RAND_bytes|. Returns 1 on success and 0 on failure.
int DILITHIUM_sign(uint8_t out_encoded_signature[DILITHIUM_SIGNATURE_BYTES],
                   const struct DILITHIUM_private_key *private_key,
                   const uint8_t *msg, size_t msg_len) {
  uint8_t randomizer[DILITHIUM_SIGNATURE_RANDOMIZER_BYTES];
  RAND_bytes(randomizer, sizeof(randomizer));
  return dilithium_sign_with_randomizer(out_encoded_signature, private_key, msg,
                                        msg_len, randomizer);
}

// FIPS 204, Algorithm 3 (`ML-DSA.Verify`).
int DILITHIUM_verify(const struct DILITHIUM_public_key *public_key,
                     const uint8_t encoded_signature[DILITHIUM_SIGNATURE_BYTES],
                     const uint8_t *msg, size_t msg_len) {
  int ret = 0;

  // Intermediate values, allocated on the heap to allow use when there is a
  // limited amount of stack.
  struct values_st {
    struct signature sign;
    matrix a_ntt;
    vectorl z_ntt;
    vectork az_ntt;
    vectork t1_ntt;
    vectork ct1_ntt;
    vectork w_approx;
    vectork w1;
  };
  struct values_st *values = OPENSSL_malloc(sizeof(*values));
  if (values == NULL) {
    goto err;
  }

  const struct public_key *pub = public_key_from_external(public_key);

  CBS cbs;
  CBS_init(&cbs, encoded_signature, DILITHIUM_SIGNATURE_BYTES);
  if (!dilithium_parse_signature(&values->sign, &cbs)) {
    goto err;
  }

  matrix_expand(&values->a_ntt, pub->rho);

  uint8_t mu[MU_BYTES];
  struct BORINGSSL_keccak_st keccak_ctx;
  BORINGSSL_keccak_init(&keccak_ctx, boringssl_shake256);
  BORINGSSL_keccak_absorb(&keccak_ctx, pub->public_key_hash,
                          sizeof(pub->public_key_hash));
  BORINGSSL_keccak_absorb(&keccak_ctx, msg, msg_len);
  BORINGSSL_keccak_squeeze(&keccak_ctx, mu, MU_BYTES);

  scalar c_ntt;
  scalar_sample_in_ball_vartime(&c_ntt, values->sign.c_tilde, 32);
  scalar_ntt(&c_ntt);

  OPENSSL_memcpy(&values->z_ntt, &values->sign.z, sizeof(values->z_ntt));
  vectorl_ntt(&values->z_ntt);

  matrix_mult(&values->az_ntt, &values->a_ntt, &values->z_ntt);

  vectork_scale_power2_round(&values->t1_ntt, &pub->t1);
  vectork_ntt(&values->t1_ntt);

  vectork_mult_scalar(&values->ct1_ntt, &values->t1_ntt, &c_ntt);

  vectork_sub(&values->w_approx, &values->az_ntt, &values->ct1_ntt);
  vectork_inverse_ntt(&values->w_approx);

  vectork_use_hint_vartime(&values->w1, &values->sign.h, &values->w_approx);
  uint8_t w1_encoded[128 * K];
  w1_encode(w1_encoded, &values->w1);

  uint8_t c_tilde[2 * LAMBDA_BYTES];
  BORINGSSL_keccak_init(&keccak_ctx, boringssl_shake256);
  BORINGSSL_keccak_absorb(&keccak_ctx, mu, MU_BYTES);
  BORINGSSL_keccak_absorb(&keccak_ctx, w1_encoded, 128 * K);
  BORINGSSL_keccak_squeeze(&keccak_ctx, c_tilde, 2 * LAMBDA_BYTES);

  uint32_t z_max = vectorl_max(&values->sign.z);
  size_t h_ones = vectork_count_ones(&values->sign.h);
  if (z_max < kGamma1 - BETA && h_ones <= OMEGA &&
      OPENSSL_memcmp(c_tilde, values->sign.c_tilde, 2 * LAMBDA_BYTES) == 0) {
    ret = 1;
  }

err:
  OPENSSL_free(values);
  return ret;
}

/* Serialization of keys. */

int DILITHIUM_marshal_public_key(
    CBB *out, const struct DILITHIUM_public_key *public_key) {
  return dilithium_marshal_public_key(out,
                                      public_key_from_external(public_key));
}

int DILITHIUM_parse_public_key(struct DILITHIUM_public_key *public_key,
                               CBS *in) {
  struct public_key *pub = public_key_from_external(public_key);
  CBS orig_in = *in;
  if (!dilithium_parse_public_key(pub, in) || CBS_len(in) != 0) {
    return 0;
  }

  // Compute pre-cached values.
  BORINGSSL_keccak(pub->public_key_hash, sizeof(pub->public_key_hash),
                   CBS_data(&orig_in), CBS_len(&orig_in), boringssl_shake256);
  return 1;
}

int DILITHIUM_marshal_private_key(
    CBB *out, const struct DILITHIUM_private_key *private_key) {
  return dilithium_marshal_private_key(out,
                                       private_key_from_external(private_key));
}

int DILITHIUM_parse_private_key(struct DILITHIUM_private_key *private_key,
                                CBS *in) {
  struct private_key *priv = private_key_from_external(private_key);
  return dilithium_parse_private_key(priv, in) && CBS_len(in) == 0;
}