third_party/fiat/curve25519.c

// The MIT License (MIT)
//
// Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file).
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.

// Some of this code is taken from the ref10 version of Ed25519 in SUPERCOP
// 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as
// public domain but parts have been replaced with code generated by Fiat
// (https://github.com/mit-plv/fiat-crypto), which is MIT licensed.
//
// The field functions are shared by Ed25519 and X25519 where possible.

#include <openssl/curve25519.h>

#include <assert.h>
#include <string.h>

#include <openssl/cpu.h>
#include <openssl/mem.h>
#include <openssl/rand.h>
#include <openssl/sha.h>

#include "internal.h"
#include "../../crypto/internal.h"


static const int64_t kBottom25Bits = INT64_C(0x1ffffff);
static const int64_t kBottom26Bits = INT64_C(0x3ffffff);

static uint64_t load_3(const uint8_t *in) {
  uint64_t result;
  result = (uint64_t)in[0];
  result |= ((uint64_t)in[1]) << 8;
  result |= ((uint64_t)in[2]) << 16;
  return result;
}

static uint64_t load_4(const uint8_t *in) {
  uint64_t result;
  result = (uint64_t)in[0];
  result |= ((uint64_t)in[1]) << 8;
  result |= ((uint64_t)in[2]) << 16;
  result |= ((uint64_t)in[3]) << 24;
  return result;
}

#define assert_fe(f) do { \
  for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \
    assert(f[_assert_fe_i] < 1.125*(1<<(26-(_assert_fe_i&1)))); \
  } \
} while (0)

#define assert_fe_loose(f) do { \
  for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \
    assert(f[_assert_fe_i] < 3.375*(1<<(26-(_assert_fe_i&1)))); \
  } \
} while (0)

static void fe_frombytes_impl(uint32_t h[10], const uint8_t *s) {
  // Ignores top bit of s.
  uint32_t a0 = load_4(s);
  uint32_t a1 = load_4(s+4);
  uint32_t a2 = load_4(s+8);
  uint32_t a3 = load_4(s+12);
  uint32_t a4 = load_4(s+16);
  uint32_t a5 = load_4(s+20);
  uint32_t a6 = load_4(s+24);
  uint32_t a7 = load_4(s+28);
  h[0] = a0&((1<<26)-1);                    // 26 used, 32-26 left.   26
  h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); // (32-26) + 19 =  6+19 = 25
  h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); // (32-19) + 13 = 13+13 = 26
  h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); // (32-13) +  6 = 19+ 6 = 25
  h[4] = (a3>> 6);                          // (32- 6)              = 26
  h[5] = a4&((1<<25)-1);                    //                        25
  h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); // (32-25) + 19 =  7+19 = 26
  h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); // (32-19) + 12 = 13+12 = 25
  h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); // (32-12) +  6 = 20+ 6 = 26
  h[9] = (a7>> 6)&((1<<25)-1); //                                     25
  assert_fe(h);
}

static void fe_frombytes(fe *h, const uint8_t *s) {
  fe_frombytes_impl(h->v, s);
}

// Preconditions:
//  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
//
// Write p=2^255-19; q=floor(h/p).
// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
//
// Proof:
//   Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
//   Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
//
//   Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
//   Then 0<y<1.
//
//   Write r=h-pq.
//   Have 0<=r<=p-1=2^255-20.
//   Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
//
//   Write x=r+19(2^-255)r+y.
//   Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
//
//   Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
//   so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
static void fe_tobytes_impl(uint8_t *s, const uint32_t h[10]) {
  assert_fe_loose(h);
  int32_t h0 = h[0];
  int32_t h1 = h[1];
  int32_t h2 = h[2];
  int32_t h3 = h[3];
  int32_t h4 = h[4];
  int32_t h5 = h[5];
  int32_t h6 = h[6];
  int32_t h7 = h[7];
  int32_t h8 = h[8];
  int32_t h9 = h[9];
  int32_t q;

  q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
  q = (h0 + q) >> 26;
  q = (h1 + q) >> 25;
  q = (h2 + q) >> 26;
  q = (h3 + q) >> 25;
  q = (h4 + q) >> 26;
  q = (h5 + q) >> 25;
  q = (h6 + q) >> 26;
  q = (h7 + q) >> 25;
  q = (h8 + q) >> 26;
  q = (h9 + q) >> 25;

  // Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
  h0 += 19 * q;
  // Goal: Output h-2^255 q, which is between 0 and 2^255-20.

  h1 += h0 >> 26; h0 &= kBottom26Bits;
  h2 += h1 >> 25; h1 &= kBottom25Bits;
  h3 += h2 >> 26; h2 &= kBottom26Bits;
  h4 += h3 >> 25; h3 &= kBottom25Bits;
  h5 += h4 >> 26; h4 &= kBottom26Bits;
  h6 += h5 >> 25; h5 &= kBottom25Bits;
  h7 += h6 >> 26; h6 &= kBottom26Bits;
  h8 += h7 >> 25; h7 &= kBottom25Bits;
  h9 += h8 >> 26; h8 &= kBottom26Bits;
                  h9 &= kBottom25Bits;
                  // h10 = carry9

  // Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
  // Have h0+...+2^230 h9 between 0 and 2^255-1;
  // evidently 2^255 h10-2^255 q = 0.
  // Goal: Output h0+...+2^230 h9.

  s[0] = h0 >> 0;
  s[1] = h0 >> 8;
  s[2] = h0 >> 16;
  s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
  s[4] = h1 >> 6;
  s[5] = h1 >> 14;
  s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
  s[7] = h2 >> 5;
  s[8] = h2 >> 13;
  s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
  s[10] = h3 >> 3;
  s[11] = h3 >> 11;
  s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
  s[13] = h4 >> 2;
  s[14] = h4 >> 10;
  s[15] = h4 >> 18;
  s[16] = h5 >> 0;
  s[17] = h5 >> 8;
  s[18] = h5 >> 16;
  s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
  s[20] = h6 >> 7;
  s[21] = h6 >> 15;
  s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
  s[23] = h7 >> 5;
  s[24] = h7 >> 13;
  s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
  s[26] = h8 >> 4;
  s[27] = h8 >> 12;
  s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
  s[29] = h9 >> 2;
  s[30] = h9 >> 10;
  s[31] = h9 >> 18;
}

static void fe_tobytes(uint8_t *s, const fe *h) {
  fe_tobytes_impl(s, h->v);
}

static void fe_loose_tobytes(uint8_t *s, const fe_loose *h) {
  fe_tobytes_impl(s, h->v);
}

// h = f
static void fe_copy(fe *h, const fe *f) {
  OPENSSL_memmove(h, f, sizeof(uint32_t) * 10);
}

static void fe_copy_lt(fe_loose *h, const fe *f) {
  OPENSSL_memmove(h, f, sizeof(uint32_t) * 10);
}
#if !defined(OPENSSL_SMALL)
static void fe_copy_ll(fe_loose *h, const fe_loose *f) {
  OPENSSL_memmove(h, f, sizeof(uint32_t) * 10);
}
#endif // !defined(OPENSSL_SMALL)

// h = 0
static void fe_0(fe *h) {
  OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
}

static void fe_loose_0(fe_loose *h) {
  OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
}

// h = 1
static void fe_1(fe *h) {
  OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
  h->v[0] = 1;
}

static void fe_loose_1(fe_loose *h) {
  OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
  h->v[0] = 1;
}

static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
  { const uint32_t x20 = in1[9];
  { const uint32_t x21 = in1[8];
  { const uint32_t x19 = in1[7];
  { const uint32_t x17 = in1[6];
  { const uint32_t x15 = in1[5];
  { const uint32_t x13 = in1[4];
  { const uint32_t x11 = in1[3];
  { const uint32_t x9 = in1[2];
  { const uint32_t x7 = in1[1];
  { const uint32_t x5 = in1[0];
  { const uint32_t x38 = in2[9];
  { const uint32_t x39 = in2[8];
  { const uint32_t x37 = in2[7];
  { const uint32_t x35 = in2[6];
  { const uint32_t x33 = in2[5];
  { const uint32_t x31 = in2[4];
  { const uint32_t x29 = in2[3];
  { const uint32_t x27 = in2[2];
  { const uint32_t x25 = in2[1];
  { const uint32_t x23 = in2[0];
  out[0] = (x5 + x23);
  out[1] = (x7 + x25);
  out[2] = (x9 + x27);
  out[3] = (x11 + x29);
  out[4] = (x13 + x31);
  out[5] = (x15 + x33);
  out[6] = (x17 + x35);
  out[7] = (x19 + x37);
  out[8] = (x21 + x39);
  out[9] = (x20 + x38);
  }}}}}}}}}}}}}}}}}}}}
}

// h = f + g
// Can overlap h with f or g.
//
// Preconditions:
//    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
//    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
//
// Postconditions:
//    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
static void fe_add(fe_loose *h, const fe *f, const fe *g) {
  assert_fe(f->v);
  assert_fe(g->v);
  fe_add_impl(h->v, f->v, g->v);
  assert_fe_loose(h->v);
}

static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
  { const uint32_t x20 = in1[9];
  { const uint32_t x21 = in1[8];
  { const uint32_t x19 = in1[7];
  { const uint32_t x17 = in1[6];
  { const uint32_t x15 = in1[5];
  { const uint32_t x13 = in1[4];
  { const uint32_t x11 = in1[3];
  { const uint32_t x9 = in1[2];
  { const uint32_t x7 = in1[1];
  { const uint32_t x5 = in1[0];
  { const uint32_t x38 = in2[9];
  { const uint32_t x39 = in2[8];
  { const uint32_t x37 = in2[7];
  { const uint32_t x35 = in2[6];
  { const uint32_t x33 = in2[5];
  { const uint32_t x31 = in2[4];
  { const uint32_t x29 = in2[3];
  { const uint32_t x27 = in2[2];
  { const uint32_t x25 = in2[1];
  { const uint32_t x23 = in2[0];
  out[0] = ((0x7ffffda + x5) - x23);
  out[1] = ((0x3fffffe + x7) - x25);
  out[2] = ((0x7fffffe + x9) - x27);
  out[3] = ((0x3fffffe + x11) - x29);
  out[4] = ((0x7fffffe + x13) - x31);
  out[5] = ((0x3fffffe + x15) - x33);
  out[6] = ((0x7fffffe + x17) - x35);
  out[7] = ((0x3fffffe + x19) - x37);
  out[8] = ((0x7fffffe + x21) - x39);
  out[9] = ((0x3fffffe + x20) - x38);
  }}}}}}}}}}}}}}}}}}}}
}

// h = f - g
// Can overlap h with f or g.
//
// Preconditions:
//    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
//    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
//
// Postconditions:
//    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
static void fe_sub(fe_loose *h, const fe *f, const fe *g) {
  assert_fe(f->v);
  assert_fe(g->v);
  fe_sub_impl(h->v, f->v, g->v);
  assert_fe_loose(h->v);
}

static void fe_carry_impl(uint32_t out[10], const uint32_t in1[10]) {
  { const uint32_t x17 = in1[9];
  { const uint32_t x18 = in1[8];
  { const uint32_t x16 = in1[7];
  { const uint32_t x14 = in1[6];
  { const uint32_t x12 = in1[5];
  { const uint32_t x10 = in1[4];
  { const uint32_t x8 = in1[3];
  { const uint32_t x6 = in1[2];
  { const uint32_t x4 = in1[1];
  { const uint32_t x2 = in1[0];
  { uint32_t x19 = (x2 >> 0x1a);
  { uint32_t x20 = (x2 & 0x3ffffff);
  { uint32_t x21 = (x19 + x4);
  { uint32_t x22 = (x21 >> 0x19);
  { uint32_t x23 = (x21 & 0x1ffffff);
  { uint32_t x24 = (x22 + x6);
  { uint32_t x25 = (x24 >> 0x1a);
  { uint32_t x26 = (x24 & 0x3ffffff);
  { uint32_t x27 = (x25 + x8);
  { uint32_t x28 = (x27 >> 0x19);
  { uint32_t x29 = (x27 & 0x1ffffff);
  { uint32_t x30 = (x28 + x10);
  { uint32_t x31 = (x30 >> 0x1a);
  { uint32_t x32 = (x30 & 0x3ffffff);
  { uint32_t x33 = (x31 + x12);
  { uint32_t x34 = (x33 >> 0x19);
  { uint32_t x35 = (x33 & 0x1ffffff);
  { uint32_t x36 = (x34 + x14);
  { uint32_t x37 = (x36 >> 0x1a);
  { uint32_t x38 = (x36 & 0x3ffffff);
  { uint32_t x39 = (x37 + x16);
  { uint32_t x40 = (x39 >> 0x19);
  { uint32_t x41 = (x39 & 0x1ffffff);
  { uint32_t x42 = (x40 + x18);
  { uint32_t x43 = (x42 >> 0x1a);
  { uint32_t x44 = (x42 & 0x3ffffff);
  { uint32_t x45 = (x43 + x17);
  { uint32_t x46 = (x45 >> 0x19);
  { uint32_t x47 = (x45 & 0x1ffffff);
  { uint32_t x48 = (x20 + (0x13 * x46));
  { uint32_t x49 = (x48 >> 0x1a);
  { uint32_t x50 = (x48 & 0x3ffffff);
  { uint32_t x51 = (x49 + x23);
  { uint32_t x52 = (x51 >> 0x19);
  { uint32_t x53 = (x51 & 0x1ffffff);
  out[0] = x50;
  out[1] = x53;
  out[2] = (x52 + x26);
  out[3] = x29;
  out[4] = x32;
  out[5] = x35;
  out[6] = x38;
  out[7] = x41;
  out[8] = x44;
  out[9] = x47;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
}

static void fe_carry(fe *h, const fe_loose* f) {
  assert_fe_loose(f->v);
  fe_carry_impl(h->v, f->v);
  assert_fe(h->v);
}

static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
  assert_fe_loose(in1);
  assert_fe_loose(in2);
  { const uint32_t x20 = in1[9];
  { const uint32_t x21 = in1[8];
  { const uint32_t x19 = in1[7];
  { const uint32_t x17 = in1[6];
  { const uint32_t x15 = in1[5];
  { const uint32_t x13 = in1[4];
  { const uint32_t x11 = in1[3];
  { const uint32_t x9 = in1[2];
  { const uint32_t x7 = in1[1];
  { const uint32_t x5 = in1[0];
  { const uint32_t x38 = in2[9];
  { const uint32_t x39 = in2[8];
  { const uint32_t x37 = in2[7];
  { const uint32_t x35 = in2[6];
  { const uint32_t x33 = in2[5];
  { const uint32_t x31 = in2[4];
  { const uint32_t x29 = in2[3];
  { const uint32_t x27 = in2[2];
  { const uint32_t x25 = in2[1];
  { const uint32_t x23 = in2[0];
  { uint64_t x40 = ((uint64_t)x23 * x5);
  { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
  { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
  { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
  { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
  { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
  { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
  { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
  { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
  { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
  { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
  { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
  { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
  { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
  { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
  { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
  { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
  { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
  { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
  { uint64_t x59 = (x48 + (x58 << 0x4));
  { uint64_t x60 = (x59 + (x58 << 0x1));
  { uint64_t x61 = (x60 + x58);
  { uint64_t x62 = (x47 + (x57 << 0x4));
  { uint64_t x63 = (x62 + (x57 << 0x1));
  { uint64_t x64 = (x63 + x57);
  { uint64_t x65 = (x46 + (x56 << 0x4));
  { uint64_t x66 = (x65 + (x56 << 0x1));
  { uint64_t x67 = (x66 + x56);
  { uint64_t x68 = (x45 + (x55 << 0x4));
  { uint64_t x69 = (x68 + (x55 << 0x1));
  { uint64_t x70 = (x69 + x55);
  { uint64_t x71 = (x44 + (x54 << 0x4));
  { uint64_t x72 = (x71 + (x54 << 0x1));
  { uint64_t x73 = (x72 + x54);
  { uint64_t x74 = (x43 + (x53 << 0x4));
  { uint64_t x75 = (x74 + (x53 << 0x1));
  { uint64_t x76 = (x75 + x53);
  { uint64_t x77 = (x42 + (x52 << 0x4));
  { uint64_t x78 = (x77 + (x52 << 0x1));
  { uint64_t x79 = (x78 + x52);
  { uint64_t x80 = (x41 + (x51 << 0x4));
  { uint64_t x81 = (x80 + (x51 << 0x1));
  { uint64_t x82 = (x81 + x51);
  { uint64_t x83 = (x40 + (x50 << 0x4));
  { uint64_t x84 = (x83 + (x50 << 0x1));
  { uint64_t x85 = (x84 + x50);
  { uint64_t x86 = (x85 >> 0x1a);
  { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
  { uint64_t x88 = (x86 + x82);
  { uint64_t x89 = (x88 >> 0x19);
  { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
  { uint64_t x91 = (x89 + x79);
  { uint64_t x92 = (x91 >> 0x1a);
  { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
  { uint64_t x94 = (x92 + x76);
  { uint64_t x95 = (x94 >> 0x19);
  { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
  { uint64_t x97 = (x95 + x73);
  { uint64_t x98 = (x97 >> 0x1a);
  { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
  { uint64_t x100 = (x98 + x70);
  { uint64_t x101 = (x100 >> 0x19);
  { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
  { uint64_t x103 = (x101 + x67);
  { uint64_t x104 = (x103 >> 0x1a);
  { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
  { uint64_t x106 = (x104 + x64);
  { uint64_t x107 = (x106 >> 0x19);
  { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
  { uint64_t x109 = (x107 + x61);
  { uint64_t x110 = (x109 >> 0x1a);
  { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
  { uint64_t x112 = (x110 + x49);
  { uint64_t x113 = (x112 >> 0x19);
  { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
  { uint64_t x115 = (x87 + (0x13 * x113));
  { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
  { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
  { uint32_t x118 = (x116 + x90);
  { uint32_t x119 = (x118 >> 0x19);
  { uint32_t x120 = (x118 & 0x1ffffff);
  out[0] = x117;
  out[1] = x120;
  out[2] = (x119 + x93);
  out[3] = x96;
  out[4] = x99;
  out[5] = x102;
  out[6] = x105;
  out[7] = x108;
  out[8] = x111;
  out[9] = x114;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
  assert_fe(out);
}

static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_llt(fe_loose *h, const fe_loose *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_ttt(fe *h, const fe *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_ttl(fe *h, const fe *f, const fe_loose *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10]) {
  assert_fe_loose(in1);
  { const uint32_t x17 = in1[9];
  { const uint32_t x18 = in1[8];
  { const uint32_t x16 = in1[7];
  { const uint32_t x14 = in1[6];
  { const uint32_t x12 = in1[5];
  { const uint32_t x10 = in1[4];
  { const uint32_t x8 = in1[3];
  { const uint32_t x6 = in1[2];
  { const uint32_t x4 = in1[1];
  { const uint32_t x2 = in1[0];
  { uint64_t x19 = ((uint64_t)x2 * x2);
  { uint64_t x20 = ((uint64_t)(0x2 * x2) * x4);
  { uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6)));
  { uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8)));
  { uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10));
  { uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12)));
  { uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12)));
  { uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16)));
  { uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12))))));
  { uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17)));
  { uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17)))));
  { uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17)));
  { uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17))))));
  { uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17)));
  { uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17)));
  { uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17)));
  { uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17));
  { uint64_t x36 = ((uint64_t)(0x2 * x18) * x17);
  { uint64_t x37 = ((uint64_t)(0x2 * x17) * x17);
  { uint64_t x38 = (x27 + (x37 << 0x4));
  { uint64_t x39 = (x38 + (x37 << 0x1));
  { uint64_t x40 = (x39 + x37);
  { uint64_t x41 = (x26 + (x36 << 0x4));
  { uint64_t x42 = (x41 + (x36 << 0x1));
  { uint64_t x43 = (x42 + x36);
  { uint64_t x44 = (x25 + (x35 << 0x4));
  { uint64_t x45 = (x44 + (x35 << 0x1));
  { uint64_t x46 = (x45 + x35);
  { uint64_t x47 = (x24 + (x34 << 0x4));
  { uint64_t x48 = (x47 + (x34 << 0x1));
  { uint64_t x49 = (x48 + x34);
  { uint64_t x50 = (x23 + (x33 << 0x4));
  { uint64_t x51 = (x50 + (x33 << 0x1));
  { uint64_t x52 = (x51 + x33);
  { uint64_t x53 = (x22 + (x32 << 0x4));
  { uint64_t x54 = (x53 + (x32 << 0x1));
  { uint64_t x55 = (x54 + x32);
  { uint64_t x56 = (x21 + (x31 << 0x4));
  { uint64_t x57 = (x56 + (x31 << 0x1));
  { uint64_t x58 = (x57 + x31);
  { uint64_t x59 = (x20 + (x30 << 0x4));
  { uint64_t x60 = (x59 + (x30 << 0x1));
  { uint64_t x61 = (x60 + x30);
  { uint64_t x62 = (x19 + (x29 << 0x4));
  { uint64_t x63 = (x62 + (x29 << 0x1));
  { uint64_t x64 = (x63 + x29);
  { uint64_t x65 = (x64 >> 0x1a);
  { uint32_t x66 = ((uint32_t)x64 & 0x3ffffff);
  { uint64_t x67 = (x65 + x61);
  { uint64_t x68 = (x67 >> 0x19);
  { uint32_t x69 = ((uint32_t)x67 & 0x1ffffff);
  { uint64_t x70 = (x68 + x58);
  { uint64_t x71 = (x70 >> 0x1a);
  { uint32_t x72 = ((uint32_t)x70 & 0x3ffffff);
  { uint64_t x73 = (x71 + x55);
  { uint64_t x74 = (x73 >> 0x19);
  { uint32_t x75 = ((uint32_t)x73 & 0x1ffffff);
  { uint64_t x76 = (x74 + x52);
  { uint64_t x77 = (x76 >> 0x1a);
  { uint32_t x78 = ((uint32_t)x76 & 0x3ffffff);
  { uint64_t x79 = (x77 + x49);
  { uint64_t x80 = (x79 >> 0x19);
  { uint32_t x81 = ((uint32_t)x79 & 0x1ffffff);
  { uint64_t x82 = (x80 + x46);
  { uint64_t x83 = (x82 >> 0x1a);
  { uint32_t x84 = ((uint32_t)x82 & 0x3ffffff);
  { uint64_t x85 = (x83 + x43);
  { uint64_t x86 = (x85 >> 0x19);
  { uint32_t x87 = ((uint32_t)x85 & 0x1ffffff);
  { uint64_t x88 = (x86 + x40);
  { uint64_t x89 = (x88 >> 0x1a);
  { uint32_t x90 = ((uint32_t)x88 & 0x3ffffff);
  { uint64_t x91 = (x89 + x28);
  { uint64_t x92 = (x91 >> 0x19);
  { uint32_t x93 = ((uint32_t)x91 & 0x1ffffff);
  { uint64_t x94 = (x66 + (0x13 * x92));
  { uint32_t x95 = (uint32_t) (x94 >> 0x1a);
  { uint32_t x96 = ((uint32_t)x94 & 0x3ffffff);
  { uint32_t x97 = (x95 + x69);
  { uint32_t x98 = (x97 >> 0x19);
  { uint32_t x99 = (x97 & 0x1ffffff);
  out[0] = x96;
  out[1] = x99;
  out[2] = (x98 + x72);
  out[3] = x75;
  out[4] = x78;
  out[5] = x81;
  out[6] = x84;
  out[7] = x87;
  out[8] = x90;
  out[9] = x93;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
  assert_fe(out);
}

static void fe_sq_tl(fe *h, const fe_loose *f) {
  fe_sqr_impl(h->v, f->v);
}

static void fe_sq_tt(fe *h, const fe *f) {
  fe_sqr_impl(h->v, f->v);
}

static void fe_loose_invert(fe *out, const fe_loose *z) {
  fe t0;
  fe t1;
  fe t2;
  fe t3;
  int i;

  fe_sq_tl(&t0, z);
  fe_sq_tt(&t1, &t0);
  for (i = 1; i < 2; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_tlt(&t1, z, &t1);
  fe_mul_ttt(&t0, &t0, &t1);
  fe_sq_tt(&t2, &t0);
  fe_mul_ttt(&t1, &t1, &t2);
  fe_sq_tt(&t2, &t1);
  for (i = 1; i < 5; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t1, &t2, &t1);
  fe_sq_tt(&t2, &t1);
  for (i = 1; i < 10; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t2, &t2, &t1);
  fe_sq_tt(&t3, &t2);
  for (i = 1; i < 20; ++i) {
    fe_sq_tt(&t3, &t3);
  }
  fe_mul_ttt(&t2, &t3, &t2);
  fe_sq_tt(&t2, &t2);
  for (i = 1; i < 10; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t1, &t2, &t1);
  fe_sq_tt(&t2, &t1);
  for (i = 1; i < 50; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t2, &t2, &t1);
  fe_sq_tt(&t3, &t2);
  for (i = 1; i < 100; ++i) {
    fe_sq_tt(&t3, &t3);
  }
  fe_mul_ttt(&t2, &t3, &t2);
  fe_sq_tt(&t2, &t2);
  for (i = 1; i < 50; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t1, &t2, &t1);
  fe_sq_tt(&t1, &t1);
  for (i = 1; i < 5; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(out, &t1, &t0);
}

static void fe_invert(fe *out, const fe *z) {
  fe_loose l;
  fe_copy_lt(&l, z);
  fe_loose_invert(out, &l);
}

static void fe_neg_impl(uint32_t out[10], const uint32_t in2[10]) {
  { const uint32_t x20 = 0;
  { const uint32_t x21 = 0;
  { const uint32_t x19 = 0;
  { const uint32_t x17 = 0;
  { const uint32_t x15 = 0;
  { const uint32_t x13 = 0;
  { const uint32_t x11 = 0;
  { const uint32_t x9 = 0;
  { const uint32_t x7 = 0;
  { const uint32_t x5 = 0;
  { const uint32_t x38 = in2[9];
  { const uint32_t x39 = in2[8];
  { const uint32_t x37 = in2[7];
  { const uint32_t x35 = in2[6];
  { const uint32_t x33 = in2[5];
  { const uint32_t x31 = in2[4];
  { const uint32_t x29 = in2[3];
  { const uint32_t x27 = in2[2];
  { const uint32_t x25 = in2[1];
  { const uint32_t x23 = in2[0];
  out[0] = ((0x7ffffda + x5) - x23);
  out[1] = ((0x3fffffe + x7) - x25);
  out[2] = ((0x7fffffe + x9) - x27);
  out[3] = ((0x3fffffe + x11) - x29);
  out[4] = ((0x7fffffe + x13) - x31);
  out[5] = ((0x3fffffe + x15) - x33);
  out[6] = ((0x7fffffe + x17) - x35);
  out[7] = ((0x3fffffe + x19) - x37);
  out[8] = ((0x7fffffe + x21) - x39);
  out[9] = ((0x3fffffe + x20) - x38);
  }}}}}}}}}}}}}}}}}}}}
}

// h = -f
//
// Preconditions:
//    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
//
// Postconditions:
//    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
static void fe_neg(fe_loose *h, const fe *f) {
  assert_fe(f->v);
  fe_neg_impl(h->v, f->v);
  assert_fe_loose(h->v);
}

// Replace (f,g) with (g,g) if b == 1;
// replace (f,g) with (f,g) if b == 0.
//
// Preconditions: b in {0,1}.
static void fe_cmov(fe_loose *f, const fe_loose *g, unsigned b) {
  b = 0-b;
  unsigned i;
  for (i = 0; i < 10; i++) {
    uint32_t x = f->v[i] ^ g->v[i];
    x &= b;
    f->v[i] ^= x;
  }
}

// return 0 if f == 0
// return 1 if f != 0
//
// Preconditions:
//    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
static int fe_isnonzero(const fe_loose *f) {
  uint8_t s[32];
  fe_loose_tobytes(s, f);

  static const uint8_t zero[32] = {0};
  return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
}

// return 1 if f is in {1,3,5,...,q-2}
// return 0 if f is in {0,2,4,...,q-1}
//
// Preconditions:
//    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
static int fe_isnegative(const fe *f) {
  uint8_t s[32];
  fe_tobytes(s, f);
  return s[0] & 1;
}

// NOTE: based on fiat-crypto fe_mul, edited for in2=2*in1
static void fe_sq2_impl(uint32_t out[10], const uint32_t in1[10]) {
  assert_fe_loose(in1);
  { const uint32_t x20 = in1[9];
  { const uint32_t x21 = in1[8];
  { const uint32_t x19 = in1[7];
  { const uint32_t x17 = in1[6];
  { const uint32_t x15 = in1[5];
  { const uint32_t x13 = in1[4];
  { const uint32_t x11 = in1[3];
  { const uint32_t x9 = in1[2];
  { const uint32_t x7 = in1[1];
  { const uint32_t x5 = in1[0];
  { const uint32_t x38 = 2*in1[9];
  { const uint32_t x39 = 2*in1[8];
  { const uint32_t x37 = 2*in1[7];
  { const uint32_t x35 = 2*in1[6];
  { const uint32_t x33 = 2*in1[5];
  { const uint32_t x31 = 2*in1[4];
  { const uint32_t x29 = 2*in1[3];
  { const uint32_t x27 = 2*in1[2];
  { const uint32_t x25 = 2*in1[1];
  { const uint32_t x23 = 2*in1[0];
  { uint64_t x40 = ((uint64_t)x23 * x5);
  { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
  { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
  { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
  { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
  { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
  { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
  { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
  { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
  { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
  { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
  { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
  { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
  { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
  { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
  { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
  { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
  { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
  { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
  { uint64_t x59 = (x48 + (x58 << 0x4));
  { uint64_t x60 = (x59 + (x58 << 0x1));
  { uint64_t x61 = (x60 + x58);
  { uint64_t x62 = (x47 + (x57 << 0x4));
  { uint64_t x63 = (x62 + (x57 << 0x1));
  { uint64_t x64 = (x63 + x57);
  { uint64_t x65 = (x46 + (x56 << 0x4));
  { uint64_t x66 = (x65 + (x56 << 0x1));
  { uint64_t x67 = (x66 + x56);
  { uint64_t x68 = (x45 + (x55 << 0x4));
  { uint64_t x69 = (x68 + (x55 << 0x1));
  { uint64_t x70 = (x69 + x55);
  { uint64_t x71 = (x44 + (x54 << 0x4));
  { uint64_t x72 = (x71 + (x54 << 0x1));
  { uint64_t x73 = (x72 + x54);
  { uint64_t x74 = (x43 + (x53 << 0x4));
  { uint64_t x75 = (x74 + (x53 << 0x1));
  { uint64_t x76 = (x75 + x53);
  { uint64_t x77 = (x42 + (x52 << 0x4));
  { uint64_t x78 = (x77 + (x52 << 0x1));
  { uint64_t x79 = (x78 + x52);
  { uint64_t x80 = (x41 + (x51 << 0x4));
  { uint64_t x81 = (x80 + (x51 << 0x1));
  { uint64_t x82 = (x81 + x51);
  { uint64_t x83 = (x40 + (x50 << 0x4));
  { uint64_t x84 = (x83 + (x50 << 0x1));
  { uint64_t x85 = (x84 + x50);
  { uint64_t x86 = (x85 >> 0x1a);
  { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
  { uint64_t x88 = (x86 + x82);
  { uint64_t x89 = (x88 >> 0x19);
  { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
  { uint64_t x91 = (x89 + x79);
  { uint64_t x92 = (x91 >> 0x1a);
  { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
  { uint64_t x94 = (x92 + x76);
  { uint64_t x95 = (x94 >> 0x19);
  { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
  { uint64_t x97 = (x95 + x73);
  { uint64_t x98 = (x97 >> 0x1a);
  { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
  { uint64_t x100 = (x98 + x70);
  { uint64_t x101 = (x100 >> 0x19);
  { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
  { uint64_t x103 = (x101 + x67);
  { uint64_t x104 = (x103 >> 0x1a);
  { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
  { uint64_t x106 = (x104 + x64);
  { uint64_t x107 = (x106 >> 0x19);
  { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
  { uint64_t x109 = (x107 + x61);
  { uint64_t x110 = (x109 >> 0x1a);
  { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
  { uint64_t x112 = (x110 + x49);
  { uint64_t x113 = (x112 >> 0x19);
  { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
  { uint64_t x115 = (x87 + (0x13 * x113));
  { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
  { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
  { uint32_t x118 = (x116 + x90);
  { uint32_t x119 = (x118 >> 0x19);
  { uint32_t x120 = (x118 & 0x1ffffff);
  out[0] = x117;
  out[1] = x120;
  out[2] = (x119 + x93);
  out[3] = x96;
  out[4] = x99;
  out[5] = x102;
  out[6] = x105;
  out[7] = x108;
  out[8] = x111;
  out[9] = x114;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
  assert_fe(out);
}

static void fe_sq2_tt(fe *h, const fe *f) {
  fe_sq2_impl(h->v, f->v);
}

static void fe_pow22523(fe *out, const fe *z) {
  fe t0;
  fe t1;
  fe t2;
  int i;

  fe_sq_tt(&t0, z);
  fe_sq_tt(&t1, &t0);
  for (i = 1; i < 2; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t1, z, &t1);
  fe_mul_ttt(&t0, &t0, &t1);
  fe_sq_tt(&t0, &t0);
  fe_mul_ttt(&t0, &t1, &t0);
  fe_sq_tt(&t1, &t0);
  for (i = 1; i < 5; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t0, &t1, &t0);
  fe_sq_tt(&t1, &t0);
  for (i = 1; i < 10; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t1, &t1, &t0);
  fe_sq_tt(&t2, &t1);
  for (i = 1; i < 20; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t1, &t2, &t1);
  fe_sq_tt(&t1, &t1);
  for (i = 1; i < 10; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t0, &t1, &t0);
  fe_sq_tt(&t1, &t0);
  for (i = 1; i < 50; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t1, &t1, &t0);
  fe_sq_tt(&t2, &t1);
  for (i = 1; i < 100; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t1, &t2, &t1);
  fe_sq_tt(&t1, &t1);
  for (i = 1; i < 50; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t0, &t1, &t0);
  fe_sq_tt(&t0, &t0);
  for (i = 1; i < 2; ++i) {
    fe_sq_tt(&t0, &t0);
  }
  fe_mul_ttt(out, &t0, z);
}

void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h) {
  fe recip;
  fe x;
  fe y;

  fe_invert(&recip, &h->Z);
  fe_mul_ttt(&x, &h->X, &recip);
  fe_mul_ttt(&y, &h->Y, &recip);
  fe_tobytes(s, &y);
  s[31] ^= fe_isnegative(&x) << 7;
}

static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
  fe recip;
  fe x;
  fe y;

  fe_invert(&recip, &h->Z);
  fe_mul_ttt(&x, &h->X, &recip);
  fe_mul_ttt(&y, &h->Y, &recip);
  fe_tobytes(s, &y);
  s[31] ^= fe_isnegative(&x) << 7;
}

static const fe d = {{56195235, 13857412, 51736253, 6949390,   114729,
                     24766616,  60832955, 30306712,  48412415, 21499315}};

static const fe sqrtm1 = {{34513072, 25610706,  9377949,  3500415, 12389472,
                          33281959,   41962654, 31548777, 326685,  11406482}};

int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
  fe u;
  fe_loose v;
  fe v3;
  fe vxx;
  fe_loose check;

  fe_frombytes(&h->Y, s);
  fe_1(&h->Z);
  fe_sq_tt(&v3, &h->Y);
  fe_mul_ttt(&vxx, &v3, &d);
  fe_sub(&v, &v3, &h->Z);  // u = y^2-1
  fe_carry(&u, &v);
  fe_add(&v, &vxx, &h->Z);  // v = dy^2+1

  fe_sq_tl(&v3, &v);
  fe_mul_ttl(&v3, &v3, &v);  // v3 = v^3
  fe_sq_tt(&h->X, &v3);
  fe_mul_ttl(&h->X, &h->X, &v);
  fe_mul_ttt(&h->X, &h->X, &u);  // x = uv^7

  fe_pow22523(&h->X, &h->X);  // x = (uv^7)^((q-5)/8)
  fe_mul_ttt(&h->X, &h->X, &v3);
  fe_mul_ttt(&h->X, &h->X, &u);  // x = uv^3(uv^7)^((q-5)/8)

  fe_sq_tt(&vxx, &h->X);
  fe_mul_ttl(&vxx, &vxx, &v);
  fe_sub(&check, &vxx, &u);
  if (fe_isnonzero(&check)) {
    fe_add(&check, &vxx, &u);
    if (fe_isnonzero(&check)) {
      return -1;
    }
    fe_mul_ttt(&h->X, &h->X, &sqrtm1);
  }

  if (fe_isnegative(&h->X) != (s[31] >> 7)) {
    fe_loose t;
    fe_neg(&t, &h->X);
    fe_carry(&h->X, &t);
  }

  fe_mul_ttt(&h->T, &h->X, &h->Y);
  return 0;
}

static void ge_p2_0(ge_p2 *h) {
  fe_0(&h->X);
  fe_1(&h->Y);
  fe_1(&h->Z);
}

static void ge_p3_0(ge_p3 *h) {
  fe_0(&h->X);
  fe_1(&h->Y);
  fe_1(&h->Z);
  fe_0(&h->T);
}

static void ge_cached_0(ge_cached *h) {
  fe_loose_1(&h->YplusX);
  fe_loose_1(&h->YminusX);
  fe_loose_1(&h->Z);
  fe_loose_0(&h->T2d);
}

static void ge_precomp_0(ge_precomp *h) {
  fe_loose_1(&h->yplusx);
  fe_loose_1(&h->yminusx);
  fe_loose_0(&h->xy2d);
}

// r = p
static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
  fe_copy(&r->X, &p->X);
  fe_copy(&r->Y, &p->Y);
  fe_copy(&r->Z, &p->Z);
}

static const fe d2 = {{45281625, 27714825,  36363642, 13898781, 229458,
                      15978800,  54557047, 27058993,  29715967, 9444199}};

// r = p
void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
  fe_add(&r->YplusX, &p->Y, &p->X);
  fe_sub(&r->YminusX, &p->Y, &p->X);
  fe_copy_lt(&r->Z, &p->Z);
  fe_mul_ltt(&r->T2d, &p->T, &d2);
}

// r = p
void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
  fe_mul_tll(&r->X, &p->X, &p->T);
  fe_mul_tll(&r->Y, &p->Y, &p->Z);
  fe_mul_tll(&r->Z, &p->Z, &p->T);
}

// r = p
void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
  fe_mul_tll(&r->X, &p->X, &p->T);
  fe_mul_tll(&r->Y, &p->Y, &p->Z);
  fe_mul_tll(&r->Z, &p->Z, &p->T);
  fe_mul_tll(&r->T, &p->X, &p->Y);
}

// r = p
static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) {
  ge_p3 t;
  x25519_ge_p1p1_to_p3(&t, p);
  x25519_ge_p3_to_cached(r, &t);
}

// r = 2 * p
static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
  fe trX, trZ, trT;
  fe t0;

  fe_sq_tt(&trX, &p->X);
  fe_sq_tt(&trZ, &p->Y);
  fe_sq2_tt(&trT, &p->Z);
  fe_add(&r->Y, &p->X, &p->Y);
  fe_sq_tl(&t0, &r->Y);

  fe_add(&r->Y, &trZ, &trX);
  fe_sub(&r->Z, &trZ, &trX);
  fe_carry(&trZ, &r->Y);
  fe_sub(&r->X, &t0, &trZ);
  fe_carry(&trZ, &r->Z);
  fe_sub(&r->T, &trT, &trZ);
}

// r = 2 * p
static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
  ge_p2 q;
  ge_p3_to_p2(&q, p);
  ge_p2_dbl(r, &q);
}

// r = p + q
static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
  fe trY, trZ, trT;

  fe_add(&r->X, &p->Y, &p->X);
  fe_sub(&r->Y, &p->Y, &p->X);
  fe_mul_tll(&trZ, &r->X, &q->yplusx);
  fe_mul_tll(&trY, &r->Y, &q->yminusx);
  fe_mul_tlt(&trT, &q->xy2d, &p->T);
  fe_add(&r->T, &p->Z, &p->Z);
  fe_sub(&r->X, &trZ, &trY);
  fe_add(&r->Y, &trZ, &trY);
  fe_carry(&trZ, &r->T);
  fe_add(&r->Z, &trZ, &trT);
  fe_sub(&r->T, &trZ, &trT);
}

// r = p - q
static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
  fe trY, trZ, trT;

  fe_add(&r->X, &p->Y, &p->X);
  fe_sub(&r->Y, &p->Y, &p->X);
  fe_mul_tll(&trZ, &r->X, &q->yminusx);
  fe_mul_tll(&trY, &r->Y, &q->yplusx);
  fe_mul_tlt(&trT, &q->xy2d, &p->T);
  fe_add(&r->T, &p->Z, &p->Z);
  fe_sub(&r->X, &trZ, &trY);
  fe_add(&r->Y, &trZ, &trY);
  fe_carry(&trZ, &r->T);
  fe_sub(&r->Z, &trZ, &trT);
  fe_add(&r->T, &trZ, &trT);
}

// r = p + q
void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
  fe trX, trY, trZ, trT;

  fe_add(&r->X, &p->Y, &p->X);
  fe_sub(&r->Y, &p->Y, &p->X);
  fe_mul_tll(&trZ, &r->X, &q->YplusX);
  fe_mul_tll(&trY, &r->Y, &q->YminusX);
  fe_mul_tlt(&trT, &q->T2d, &p->T);
  fe_mul_ttl(&trX, &p->Z, &q->Z);
  fe_add(&r->T, &trX, &trX);
  fe_sub(&r->X, &trZ, &trY);
  fe_add(&r->Y, &trZ, &trY);
  fe_carry(&trZ, &r->T);
  fe_add(&r->Z, &trZ, &trT);
  fe_sub(&r->T, &trZ, &trT);
}

// r = p - q
void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
  fe trX, trY, trZ, trT;

  fe_add(&r->X, &p->Y, &p->X);
  fe_sub(&r->Y, &p->Y, &p->X);
  fe_mul_tll(&trZ, &r->X, &q->YminusX);
  fe_mul_tll(&trY, &r->Y, &q->YplusX);
  fe_mul_tlt(&trT, &q->T2d, &p->T);
  fe_mul_ttl(&trX, &p->Z, &q->Z);
  fe_add(&r->T, &trX, &trX);
  fe_sub(&r->X, &trZ, &trY);
  fe_add(&r->Y, &trZ, &trY);
  fe_carry(&trZ, &r->T);
  fe_sub(&r->Z, &trZ, &trT);
  fe_add(&r->T, &trZ, &trT);
}

static uint8_t equal(signed char b, signed char c) {
  uint8_t ub = b;
  uint8_t uc = c;
  uint8_t x = ub ^ uc;  // 0: yes; 1..255: no
  uint32_t y = x;       // 0: yes; 1..255: no
  y -= 1;               // 4294967295: yes; 0..254: no
  y >>= 31;             // 1: yes; 0: no
  return y;
}

static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
  fe_cmov(&t->yplusx, &u->yplusx, b);
  fe_cmov(&t->yminusx, &u->yminusx, b);
  fe_cmov(&t->xy2d, &u->xy2d, b);
}

void x25519_ge_scalarmult_small_precomp(
    ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) {
  // precomp_table is first expanded into matching |ge_precomp|
  // elements.
  ge_precomp multiples[15];

  unsigned i;
  for (i = 0; i < 15; i++) {
    const uint8_t *bytes = &precomp_table[i*(2 * 32)];
    fe x, y;
    fe_frombytes(&x, bytes);
    fe_frombytes(&y, bytes + 32);

    ge_precomp *out = &multiples[i];
    fe_add(&out->yplusx, &y, &x);
    fe_sub(&out->yminusx, &y, &x);
    fe_mul_ltt(&out->xy2d, &x, &y);
    fe_mul_llt(&out->xy2d, &out->xy2d, &d2);
  }

  // See the comment above |k25519SmallPrecomp| about the structure of the
  // precomputed elements. This loop does 64 additions and 64 doublings to
  // calculate the result.
  ge_p3_0(h);

  for (i = 63; i < 64; i--) {
    unsigned j;
    signed char index = 0;

    for (j = 0; j < 4; j++) {
      const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7));
      index |= (bit << j);
    }

    ge_precomp e;
    ge_precomp_0(&e);

    for (j = 1; j < 16; j++) {
      cmov(&e, &multiples[j-1], equal(index, j));
    }

    ge_cached cached;
    ge_p1p1 r;
    x25519_ge_p3_to_cached(&cached, h);
    x25519_ge_add(&r, h, &cached);
    x25519_ge_p1p1_to_p3(h, &r);

    ge_madd(&r, h, &e);
    x25519_ge_p1p1_to_p3(h, &r);
  }
}

#if defined(OPENSSL_SMALL)

// This block of code replaces the standard base-point table with a much smaller
// one. The standard table is 30,720 bytes while this one is just 960.
//
// This table contains 15 pairs of group elements, (x, y), where each field
// element is serialised with |fe_tobytes|. If |i| is the index of the group
// element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
// is the most significant bit). The value of the group element is then:
// (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator.
static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {
    0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95,
    0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
    0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66,
    0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
    0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
    0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e,
    0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4,
    0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62,
    0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba,
    0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd,
    0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61,
    0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c,
    0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c,
    0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5,
    0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3,
    0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18,
    0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2,
    0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95,
    0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b,
    0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90,
    0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52,
    0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb,
    0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c,
    0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e,
    0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e,
    0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a,
    0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43,
    0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53,
    0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8,
    0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89,
    0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef,
    0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60,
    0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a,
    0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8,
    0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54,
    0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b,
    0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd,
    0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb,
    0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c,
    0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b,
    0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63,
    0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a,
    0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07,
    0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa,
    0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a,
    0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84,
    0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc,
    0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42,
    0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0,
    0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0,
    0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a,
    0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5,
    0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c,
    0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27,
    0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31,
    0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c,
    0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87,
    0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0,
    0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23,
    0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2,
    0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87,
    0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d,
    0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b,
    0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d,
    0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6,
    0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84,
    0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04,
    0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19,
    0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b,
    0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a,
    0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea,
    0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30,
    0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7,
    0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa,
    0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5,
    0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71,
    0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab,
    0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb,
    0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c,
    0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25,
};

void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) {
  x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp);
}

#else

// k25519Precomp[i][j] = (j+1)*256^i*B
static const ge_precomp k25519Precomp[32][8] = {
    {
        {
            {{25967493, 19198397, 29566455, 3660896, 54414519, 4014786,
             27544626, 21800161, 61029707, 2047604}},
            {{54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692,
             5043384, 19500929, 18085054}},
            {{58370664, 4489569, 9688441, 18769238, 10184608, 21191052,
             29287918, 11864899, 42594502, 29115885}},
        },
        {
            {{54292951, 20578084, 45527620, 11784319, 41753206, 30803714,
             55390960, 29739860, 66750418, 23343128}},
            {{45405608, 6903824, 27185491, 6451973, 37531140, 24000426,
             51492312, 11189267, 40279186, 28235350}},
            {{26966623, 11152617, 32442495, 15396054, 14353839, 20802097,
             63980037, 24013313, 51636816, 29387734}},
        },
        {
            {{15636272, 23865875, 24204772, 25642034, 616976, 16869170,
             27787599, 18782243, 28944399, 32004408}},
            {{16568933, 4717097, 55552716, 32452109, 15682895, 21747389,
             16354576, 21778470, 7689661, 11199574}},
            {{30464137, 27578307, 55329429, 17883566, 23220364, 15915852,
             7512774, 10017326, 49359771, 23634074}},
        },
        {
            {{50071967, 13921891, 10945806, 27521001, 27105051, 17470053,
             38182653, 15006022, 3284568, 27277892}},
            {{23599295, 25248385, 55915199, 25867015, 13236773, 10506355,
             7464579, 9656445, 13059162, 10374397}},
            {{7798537, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
             29715387, 66467155, 33453106}},
        },
        {
            {{10861363, 11473154, 27284546, 1981175, 37044515, 12577860,
             32867885, 14515107, 51670560, 10819379}},
            {{4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196,
             12483687, 54440373, 5581305}},
            {{19563141, 16186464, 37722007, 4097518, 10237984, 29206317,
             28542349, 13850243, 43430843, 17738489}},
        },
        {
            {{51736881, 20691677, 32573249, 4720197, 40672342, 5875510,
             47920237, 18329612, 57289923, 21468654}},
            {{58559652, 109982, 15149363, 2178705, 22900618, 4543417, 3044240,
             17864545, 1762327, 14866737}},
            {{48909169, 17603008, 56635573, 1707277, 49922944, 3916100,
             38872452, 3959420, 27914454, 4383652}},
        },
        {
            {{5153727, 9909285, 1723747, 30776558, 30523604, 5516873, 19480852,
             5230134, 43156425, 18378665}},
            {{36839857, 30090922, 7665485, 10083793, 28475525, 1649722,
             20654025, 16520125, 30598449, 7715701}},
            {{28881826, 14381568, 9657904, 3680757, 46927229, 7843315,
             35708204, 1370707, 29794553, 32145132}},
        },
        {
            {{14499471, 30824833, 33917750, 29299779, 28494861, 14271267,
             30290735, 10876454, 33954766, 2381725}},
            {{59913433, 30899068, 52378708, 462250, 39384538, 3941371,
             60872247, 3696004, 34808032, 15351954}},
            {{27431194, 8222322, 16448760, 29646437, 48401861, 11938354,
             34147463, 30583916, 29551812, 10109425}},
        },
    },
    {
        {
            {{53451805, 20399000, 35825113, 11777097, 21447386, 6519384,
             64730580, 31926875, 10092782, 28790261}},
            {{27939166, 14210322, 4677035, 16277044, 44144402, 21156292,
             34600109, 12005537, 49298737, 12803509}},
            {{17228999, 17892808, 65875336, 300139, 65883994, 21839654,
             30364212, 24516238, 18016356, 4397660}},
        },
        {
            {{56150021, 25864224, 4776340, 18600194, 27850027, 17952220,
             40489757, 14544524, 49631360, 982638}},
            {{29253598, 15796703, 64244882, 23645547, 10057022, 3163536, 7332899,
             29434304, 46061167, 9934962}},
            {{5793284, 16271923, 42977250, 23438027, 29188559, 1206517,
             52360934, 4559894, 36984942, 22656481}},
        },
        {
            {{39464912, 22061425, 16282656, 22517939, 28414020, 18542168,
             24191033, 4541697, 53770555, 5500567}},
            {{12650548, 32057319, 9052870, 11355358, 49428827, 25154267,
             49678271, 12264342, 10874051, 13524335}},
            {{25556948, 30508442, 714650, 2510400, 23394682, 23139102, 33119037,
             5080568, 44580805, 5376627}},
        },
        {
            {{41020600, 29543379, 50095164, 30016803, 60382070, 1920896,
             44787559, 24106988, 4535767, 1569007}},
            {{64853442, 14606629, 45416424, 25514613, 28430648, 8775819,
             36614302, 3044289, 31848280, 12543772}},
            {{45080285, 2943892, 35251351, 6777305, 13784462, 29262229,
             39731668, 31491700, 7718481, 14474653}},
        },
        {
            {{2385296, 2454213, 44477544, 46602, 62670929, 17874016, 656964,
             26317767, 24316167, 28300865}},
            {{13741529, 10911568, 33875447, 24950694, 46931033, 32521134,
             33040650, 20129900, 46379407, 8321685}},
            {{21060490, 31341688, 15712756, 29218333, 1639039, 10656336,
             23845965, 21679594, 57124405, 608371}},
        },
        {
            {{53436132, 18466845, 56219170, 25997372, 61071954, 11305546,
             1123968, 26773855, 27229398, 23887}},
            {{43864724, 33260226, 55364135, 14712570, 37643165, 31524814,
             12797023, 27114124, 65475458, 16678953}},
            {{37608244, 4770661, 51054477, 14001337, 7830047, 9564805,
             65600720, 28759386, 49939598, 4904952}},
        },
        {
            {{24059538, 14617003, 19037157, 18514524, 19766092, 18648003,
             5169210, 16191880, 2128236, 29227599}},
            {{50127693, 4124965, 58568254, 22900634, 30336521, 19449185,
             37302527, 916032, 60226322, 30567899}},
            {{44477957, 12419371, 59974635, 26081060, 50629959, 16739174,
             285431, 2763829, 15736322, 4143876}},
        },
        {
            {{2379333, 11839345, 62998462, 27565766, 11274297, 794957, 212801,
             18959769, 23527083, 17096164}},
            {{33431108, 22423954, 49269897, 17927531, 8909498, 8376530,
             34483524, 4087880, 51919953, 19138217}},
            {{1767664, 7197987, 53903638, 31531796, 54017513, 448825, 5799055,
             4357868, 62334673, 17231393}},
        },
    },
    {
        {
            {{6721966, 13833823, 43585476, 32003117, 26354292, 21691111,
             23365146, 29604700, 7390889, 2759800}},
            {{4409022, 2052381, 23373853, 10530217, 7676779, 20668478, 21302352,
             29290375, 1244379, 20634787}},
            {{62687625, 7169618, 4982368, 30596842, 30256824, 30776892, 14086412,
             9208236, 15886429, 16489664}},
        },
        {
            {{1996056, 10375649, 14346367, 13311202, 60234729, 17116020,
             53415665, 398368, 36502409, 32841498}},
            {{41801399, 9795879, 64331450, 14878808, 33577029, 14780362,
             13348553, 12076947, 36272402, 5113181}},
            {{49338080, 11797795, 31950843, 13929123, 41220562, 12288343,
             36767763, 26218045, 13847710, 5387222}},
        },
        {
            {{48526701, 30138214, 17824842, 31213466, 22744342, 23111821,
             8763060, 3617786, 47508202, 10370990}},
            {{20246567, 19185054, 22358228, 33010720, 18507282, 23140436,
             14554436, 24808340, 32232923, 16763880}},
            {{9648486, 10094563, 26416693, 14745928, 36734546, 27081810,
             11094160, 15689506, 3140038, 17044340}},
        },
        {
            {{50948792, 5472694, 31895588, 4744994, 8823515, 10365685,
             39884064, 9448612, 38334410, 366294}},
            {{19153450, 11523972, 56012374, 27051289, 42461232, 5420646,
             28344573, 8041113, 719605, 11671788}},
            {{8678006, 2694440, 60300850, 2517371, 4964326, 11152271, 51675948,
             18287915, 27000812, 23358879}},
        },
        {
            {{51950941, 7134311, 8639287, 30739555, 59873175, 10421741, 564065,
             5336097, 6750977, 19033406}},
            {{11836410, 29574944, 26297893, 16080799, 23455045, 15735944,
             1695823, 24735310, 8169719, 16220347}},
            {{48993007, 8653646, 17578566, 27461813, 59083086, 17541668,
             55964556, 30926767, 61118155, 19388398}},
        },
        {
            {{43800366, 22586119, 15213227, 23473218, 36255258, 22504427,
             27884328, 2847284, 2655861, 1738395}},
            {{39571412, 19301410, 41772562, 25551651, 57738101, 8129820,
             21651608, 30315096, 48021414, 22549153}},
            {{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
             5821408, 10478196, 8544890}},
        },
        {
            {{32173102, 17425121, 24896206, 3921497, 22579056, 30143578,
             19270448, 12217473, 17789017, 30158437}},
            {{36555903, 31326030, 51530034, 23407230, 13243888, 517024,
             15479401, 29701199, 30460519, 1052596}},
            {{55493970, 13323617, 32618793, 8175907, 51878691, 12596686,
             27491595, 28942073, 3179267, 24075541}},
        },
        {
            {{31947050, 19187781, 62468280, 18214510, 51982886, 27514722,
             52352086, 17142691, 19072639, 24043372}},
            {{11685058, 11822410, 3158003, 19601838, 33402193, 29389366,
             5977895, 28339415, 473098, 5040608}},
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            {{59231455, 32054473, 8324672, 4690079, 6261860, 890446, 24538107,
             24984246, 57419264, 30522764}},
            {{25008885, 22782833, 62803832, 23916421, 16265035, 15721635,
             683793, 21730648, 15723478, 18390951}},
            {{57448220, 12374378, 40101865, 26528283, 59384749, 21239917,
             11879681, 5400171, 519526, 32318556}},
        },
        {
            {{22258397, 17222199, 59239046, 14613015, 44588609, 30603508,
             46754982, 7315966, 16648397, 7605640}},
            {{59027556, 25089834, 58885552, 9719709, 19259459, 18206220,
             23994941, 28272877, 57640015, 4763277}},
            {{45409620, 9220968, 51378240, 1084136, 41632757, 30702041,
             31088446, 25789909, 55752334, 728111}},
        },
        {
            {{26047201, 21802961, 60208540, 17032633, 24092067, 9158119,
             62835319, 20998873, 37743427, 28056159}},
            {{17510331, 33231575, 5854288, 8403524, 17133918, 30441820, 38997856,
             12327944, 10750447, 10014012}},
            {{56796096, 3936951, 9156313, 24656749, 16498691, 32559785,
             39627812, 32887699, 3424690, 7540221}},
        },
        {
            {{30322361, 26590322, 11361004, 29411115, 7433303, 4989748, 60037442,
             17237212, 57864598, 15258045}},
            {{13054543, 30774935, 19155473, 469045, 54626067, 4566041, 5631406,
             2711395, 1062915, 28418087}},
            {{47868616, 22299832, 37599834, 26054466, 61273100, 13005410,
             61042375, 12194496, 32960380, 1459310}},
        },
    },
    {
        {
            {{19852015, 7027924, 23669353, 10020366, 8586503, 26896525, 394196,
             27452547, 18638002, 22379495}},
            {{31395515, 15098109, 26581030, 8030562, 50580950, 28547297,
             9012485, 25970078, 60465776, 28111795}},
            {{57916680, 31207054, 65111764, 4529533, 25766844, 607986, 67095642,
             9677542, 34813975, 27098423}},
        },
        {
            {{64664349, 33404494, 29348901, 8186665, 1873760, 12489863, 36174285,
             25714739, 59256019, 25416002}},
            {{51872508, 18120922, 7766469, 746860, 26346930, 23332670,
             39775412, 10754587, 57677388, 5203575}},
            {{31834314, 14135496, 66338857, 5159117, 20917671, 16786336,
             59640890, 26216907, 31809242, 7347066}},
        },
        {
            {{57502122, 21680191, 20414458, 13033986, 13716524, 21862551,
             19797969, 21343177, 15192875, 31466942}},
            {{54445282, 31372712, 1168161, 29749623, 26747876, 19416341,
             10609329, 12694420, 33473243, 20172328}},
            {{33184999, 11180355, 15832085, 22169002, 65475192, 225883,
             15089336, 22530529, 60973201, 14480052}},
        },
        {
            {{31308717, 27934434, 31030839, 31657333, 15674546, 26971549,
             5496207, 13685227, 27595050, 8737275}},
            {{46790012, 18404192, 10933842, 17376410, 8335351, 26008410,
             36100512, 20943827, 26498113, 66511}},
            {{22644435, 24792703, 50437087, 4884561, 64003250, 19995065,
             30540765, 29267685, 53781076, 26039336}},
        },
        {
            {{39091017, 9834844, 18617207, 30873120, 63706907, 20246925,
             8205539, 13585437, 49981399, 15115438}},
            {{23711543, 32881517, 31206560, 25191721, 6164646, 23844445,
             33572981, 32128335, 8236920, 16492939}},
            {{43198286, 20038905, 40809380, 29050590, 25005589, 25867162,
             19574901, 10071562, 6708380, 27332008}},
        },
        {
            {{2101372, 28624378, 19702730, 2367575, 51681697, 1047674, 5301017,
             9328700, 29955601, 21876122}},
            {{3096359, 9271816, 45488000, 18032587, 52260867, 25961494,
             41216721, 20918836, 57191288, 6216607}},
            {{34493015, 338662, 41913253, 2510421, 37895298, 19734218,
             24822829, 27407865, 40341383, 7525078}},
        },
        {
            {{44042215, 19568808, 16133486, 25658254, 63719298, 778787,
             66198528, 30771936, 47722230, 11994100}},
            {{21691500, 19929806, 66467532, 19187410, 3285880, 30070836,
             42044197, 9718257, 59631427, 13381417}},
            {{18445390, 29352196, 14979845, 11622458, 65381754, 29971451,
             23111647, 27179185, 28535281, 15779576}},
        },
        {
            {{30098034, 3089662, 57874477, 16662134, 45801924, 11308410,
             53040410, 12021729, 9955285, 17251076}},
            {{9734894, 18977602, 59635230, 24415696, 2060391, 11313496,
             48682835, 9924398, 20194861, 13380996}},
            {{40730762, 25589224, 44941042, 15789296, 49053522, 27385639,
             65123949, 15707770, 26342023, 10146099}},
        },
    },
    {
        {
            {{41091971, 33334488, 21339190, 33513044, 19745255, 30675732,
             37471583, 2227039, 21612326, 33008704}},
            {{54031477, 1184227, 23562814, 27583990, 46757619, 27205717,
             25764460, 12243797, 46252298, 11649657}},
            {{57077370, 11262625, 27384172, 2271902, 26947504, 17556661, 39943,
             6114064, 33514190, 2333242}},
        },
        {
            {{45675257, 21132610, 8119781, 7219913, 45278342, 24538297,
             60429113, 20883793, 24350577, 20104431}},
            {{62992557, 22282898, 43222677, 4843614, 37020525, 690622,
             35572776, 23147595, 8317859, 12352766}},
            {{18200138, 19078521, 34021104, 30857812, 43406342, 24451920,
             43556767, 31266881, 20712162, 6719373}},
        },
        {
            {{26656189, 6075253, 59250308, 1886071, 38764821, 4262325, 11117530,
             29791222, 26224234, 30256974}},
            {{49939907, 18700334, 63713187, 17184554, 47154818, 14050419,
             21728352, 9493610, 18620611, 17125804}},
            {{53785524, 13325348, 11432106, 5964811, 18609221, 6062965,
             61839393, 23828875, 36407290, 17074774}},
        },
        {
            {{43248326, 22321272, 26961356, 1640861, 34695752, 16816491,
             12248508, 28313793, 13735341, 1934062}},
            {{25089769, 6742589, 17081145, 20148166, 21909292, 17486451,
             51972569, 29789085, 45830866, 5473615}},
            {{31883658, 25593331, 1083431, 21982029, 22828470, 13290673,
             59983779, 12469655, 29111212, 28103418}},
        },
        {
            {{24244947, 18504025, 40845887, 2791539, 52111265, 16666677,
             24367466, 6388839, 56813277, 452382}},
            {{41468082, 30136590, 5217915, 16224624, 19987036, 29472163,
             42872612, 27639183, 15766061, 8407814}},
            {{46701865, 13990230, 15495425, 16395525, 5377168, 15166495,
             58191841, 29165478, 59040954, 2276717}},
        },
        {
            {{30157899, 12924066, 49396814, 9245752, 19895028, 3368142,
             43281277, 5096218, 22740376, 26251015}},
            {{2041139, 19298082, 7783686, 13876377, 41161879, 20201972,
             24051123, 13742383, 51471265, 13295221}},
            {{33338218, 25048699, 12532112, 7977527, 9106186, 31839181,
             49388668, 28941459, 62657506, 18884987}},
        },
        {
            {{47063583, 5454096, 52762316, 6447145, 28862071, 1883651,
             64639598, 29412551, 7770568, 9620597}},
            {{23208049, 7979712, 33071466, 8149229, 1758231, 22719437, 30945527,
             31860109, 33606523, 18786461}},
            {{1439939, 17283952, 66028874, 32760649, 4625401, 10647766, 62065063,
             1220117, 30494170, 22113633}},
        },
        {
            {{62071265, 20526136, 64138304, 30492664, 15640973, 26852766,
             40369837, 926049, 65424525, 20220784}},
            {{13908495, 30005160, 30919927, 27280607, 45587000, 7989038,
             9021034, 9078865, 3353509, 4033511}},
            {{37445433, 18440821, 32259990, 33209950, 24295848, 20642309,
             23161162, 8839127, 27485041, 7356032}},
        },
    },
    {
        {
            {{9661008, 705443, 11980065, 28184278, 65480320, 14661172, 60762722,
             2625014, 28431036, 16782598}},
            {{43269631, 25243016, 41163352, 7480957, 49427195, 25200248,
             44562891, 14150564, 15970762, 4099461}},
            {{29262576, 16756590, 26350592, 24760869, 8529670, 22346382,
             13617292, 23617289, 11465738, 8317062}},
        },
        {
            {{41615764, 26591503, 32500199, 24135381, 44070139, 31252209,
             14898636, 3848455, 20969334, 28396916}},
            {{46724414, 19206718, 48772458, 13884721, 34069410, 2842113,
             45498038, 29904543, 11177094, 14989547}},
            {{42612143, 21838415, 16959895, 2278463, 12066309, 10137771,
             13515641, 2581286, 38621356, 9930239}},
        },
        {
            {{49357223, 31456605, 16544299, 20545132, 51194056, 18605350,
             18345766, 20150679, 16291480, 28240394}},
            {{33879670, 2553287, 32678213, 9875984, 8534129, 6889387, 57432090,
             6957616, 4368891, 9788741}},
            {{16660737, 7281060, 56278106, 12911819, 20108584, 25452756,
             45386327, 24941283, 16250551, 22443329}},
        },
        {
            {{47343357, 2390525, 50557833, 14161979, 1905286, 6414907, 4689584,
             10604807, 36918461, 4782746}},
            {{65754325, 14736940, 59741422, 20261545, 7710541, 19398842,
             57127292, 4383044, 22546403, 437323}},
            {{31665558, 21373968, 50922033, 1491338, 48740239, 3294681,
             27343084, 2786261, 36475274, 19457415}},
        },
        {
            {{52641566, 32870716, 33734756, 7448551, 19294360, 14334329,
             47418233, 2355318, 47824193, 27440058}},
            {{15121312, 17758270, 6377019, 27523071, 56310752, 20596586,
             18952176, 15496498, 37728731, 11754227}},
            {{64471568, 20071356, 8488726, 19250536, 12728760, 31931939,
             7141595, 11724556, 22761615, 23420291}},
        },
        {
            {{16918416, 11729663, 49025285, 3022986, 36093132, 20214772,
             38367678, 21327038, 32851221, 11717399}},
            {{11166615, 7338049, 60386341, 4531519, 37640192, 26252376,
             31474878, 3483633, 65915689, 29523600}},
            {{66923210, 9921304, 31456609, 20017994, 55095045, 13348922,
             33142652, 6546660, 47123585, 29606055}},
        },
        {
            {{34648249, 11266711, 55911757, 25655328, 31703693, 3855903,
             58571733, 20721383, 36336829, 18068118}},
            {{49102387, 12709067, 3991746, 27075244, 45617340, 23004006,
             35973516, 17504552, 10928916, 3011958}},
            {{60151107, 17960094, 31696058, 334240, 29576716, 14796075,
             36277808, 20749251, 18008030, 10258577}},
        },
        {
            {{44660220, 15655568, 7018479, 29144429, 36794597, 32352840,
             65255398, 1367119, 25127874, 6671743}},
            {{29701166, 19180498, 56230743, 9279287, 67091296, 13127209,
             21382910, 11042292, 25838796, 4642684}},
            {{46678630, 14955536, 42982517, 8124618, 61739576, 27563961,
             30468146, 19653792, 18423288, 4177476}},
        },
    },
};

static uint8_t negative(signed char b) {
  uint32_t x = b;
  x >>= 31;  // 1: yes; 0: no
  return x;
}

static void table_select(ge_precomp *t, int pos, signed char b) {
  ge_precomp minust;
  uint8_t bnegative = negative(b);
  uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);

  ge_precomp_0(t);
  cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
  cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
  cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
  cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
  cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
  cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
  cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
  cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
  fe_copy_ll(&minust.yplusx, &t->yminusx);
  fe_copy_ll(&minust.yminusx, &t->yplusx);

  // NOTE: the input table is canonical, but types don't encode it
  fe tmp;
  fe_carry(&tmp, &t->xy2d);
  fe_neg(&minust.xy2d, &tmp);

  cmov(t, &minust, bnegative);
}

// h = a * B
// where a = a[0]+256*a[1]+...+256^31 a[31]
// B is the Ed25519 base point (x,4/5) with x positive.
//
// Preconditions:
//   a[31] <= 127
void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
  signed char e[64];
  signed char carry;
  ge_p1p1 r;
  ge_p2 s;
  ge_precomp t;
  int i;

  for (i = 0; i < 32; ++i) {
    e[2 * i + 0] = (a[i] >> 0) & 15;
    e[2 * i + 1] = (a[i] >> 4) & 15;
  }
  // each e[i] is between 0 and 15
  // e[63] is between 0 and 7

  carry = 0;
  for (i = 0; i < 63; ++i) {
    e[i] += carry;
    carry = e[i] + 8;
    carry >>= 4;
    e[i] -= carry << 4;
  }
  e[63] += carry;
  // each e[i] is between -8 and 8

  ge_p3_0(h);
  for (i = 1; i < 64; i += 2) {
    table_select(&t, i / 2, e[i]);
    ge_madd(&r, h, &t);
    x25519_ge_p1p1_to_p3(h, &r);
  }

  ge_p3_dbl(&r, h);
  x25519_ge_p1p1_to_p2(&s, &r);
  ge_p2_dbl(&r, &s);
  x25519_ge_p1p1_to_p2(&s, &r);
  ge_p2_dbl(&r, &s);
  x25519_ge_p1p1_to_p2(&s, &r);
  ge_p2_dbl(&r, &s);
  x25519_ge_p1p1_to_p3(h, &r);

  for (i = 0; i < 64; i += 2) {
    table_select(&t, i / 2, e[i]);
    ge_madd(&r, h, &t);
    x25519_ge_p1p1_to_p3(h, &r);
  }
}

#endif

static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) {
  fe_cmov(&t->YplusX, &u->YplusX, b);
  fe_cmov(&t->YminusX, &u->YminusX, b);
  fe_cmov(&t->Z, &u->Z, b);
  fe_cmov(&t->T2d, &u->T2d, b);
}

// r = scalar * A.
// where a = a[0]+256*a[1]+...+256^31 a[31].
void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) {
  ge_p2 Ai_p2[8];
  ge_cached Ai[16];
  ge_p1p1 t;

  ge_cached_0(&Ai[0]);
  x25519_ge_p3_to_cached(&Ai[1], A);
  ge_p3_to_p2(&Ai_p2[1], A);

  unsigned i;
  for (i = 2; i < 16; i += 2) {
    ge_p2_dbl(&t, &Ai_p2[i / 2]);
    ge_p1p1_to_cached(&Ai[i], &t);
    if (i < 8) {
      x25519_ge_p1p1_to_p2(&Ai_p2[i], &t);
    }
    x25519_ge_add(&t, A, &Ai[i]);
    ge_p1p1_to_cached(&Ai[i + 1], &t);
    if (i < 7) {
      x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t);
    }
  }

  ge_p2_0(r);
  ge_p3 u;

  for (i = 0; i < 256; i += 4) {
    ge_p2_dbl(&t, r);
    x25519_ge_p1p1_to_p2(r, &t);
    ge_p2_dbl(&t, r);
    x25519_ge_p1p1_to_p2(r, &t);
    ge_p2_dbl(&t, r);
    x25519_ge_p1p1_to_p2(r, &t);
    ge_p2_dbl(&t, r);
    x25519_ge_p1p1_to_p3(&u, &t);

    uint8_t index = scalar[31 - i/8];
    index >>= 4 - (i & 4);
    index &= 0xf;

    unsigned j;
    ge_cached selected;
    ge_cached_0(&selected);
    for (j = 0; j < 16; j++) {
      cmov_cached(&selected, &Ai[j], equal(j, index));
    }

    x25519_ge_add(&t, &u, &selected);
    x25519_ge_p1p1_to_p2(r, &t);
  }
}

static void slide(signed char *r, const uint8_t *a) {
  int i;
  int b;
  int k;

  for (i = 0; i < 256; ++i) {
    r[i] = 1 & (a[i >> 3] >> (i & 7));
  }

  for (i = 0; i < 256; ++i) {
    if (r[i]) {
      for (b = 1; b <= 6 && i + b < 256; ++b) {
        if (r[i + b]) {
          if (r[i] + (r[i + b] << b) <= 15) {
            r[i] += r[i + b] << b;
            r[i + b] = 0;
          } else if (r[i] - (r[i + b] << b) >= -15) {
            r[i] -= r[i + b] << b;
            for (k = i + b; k < 256; ++k) {
              if (!r[k]) {
                r[k] = 1;
                break;
              }
              r[k] = 0;
            }
          } else {
            break;
          }
        }
      }
    }
  }
}

static const ge_precomp Bi[8] = {
    {
        {{25967493, 19198397, 29566455, 3660896, 54414519, 4014786, 27544626,
         21800161, 61029707, 2047604}},
        {{54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692,
         5043384, 19500929, 18085054}},
        {{58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918,
         11864899, 42594502, 29115885}},
    },
    {
        {{15636272, 23865875, 24204772, 25642034, 616976, 16869170, 27787599,
         18782243, 28944399, 32004408}},
        {{16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576,
         21778470, 7689661, 11199574}},
        {{30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774,
         10017326, 49359771, 23634074}},
    },
    {
        {{10861363, 11473154, 27284546, 1981175, 37044515, 12577860, 32867885,
         14515107, 51670560, 10819379}},
        {{4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196,
         12483687, 54440373, 5581305}},
        {{19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349,
         13850243, 43430843, 17738489}},
    },
    {
        {{5153727, 9909285, 1723747, 30776558, 30523604, 5516873, 19480852,
         5230134, 43156425, 18378665}},
        {{36839857, 30090922, 7665485, 10083793, 28475525, 1649722, 20654025,
         16520125, 30598449, 7715701}},
        {{28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204,
         1370707, 29794553, 32145132}},
    },
    {
        {{44589871, 26862249, 14201701, 24808930, 43598457, 8844725, 18474211,
         32192982, 54046167, 13821876}},
        {{60653668, 25714560, 3374701, 28813570, 40010246, 22982724, 31655027,
         26342105, 18853321, 19333481}},
        {{4566811, 20590564, 38133974, 21313742, 59506191, 30723862, 58594505,
         23123294, 2207752, 30344648}},
    },
    {
        {{41954014, 29368610, 29681143, 7868801, 60254203, 24130566, 54671499,
         32891431, 35997400, 17421995}},
        {{25576264, 30851218, 7349803, 21739588, 16472781, 9300885, 3844789,
         15725684, 171356, 6466918}},
        {{23103977, 13316479, 9739013, 17404951, 817874, 18515490, 8965338,
         19466374, 36393951, 16193876}},
    },
    {
        {{33587053, 3180712, 64714734, 14003686, 50205390, 17283591, 17238397,
         4729455, 49034351, 9256799}},
        {{41926547, 29380300, 32336397, 5036987, 45872047, 11360616, 22616405,
         9761698, 47281666, 630304}},
        {{53388152, 2639452, 42871404, 26147950, 9494426, 27780403, 60554312,
         17593437, 64659607, 19263131}},
    },
    {
        {{63957664, 28508356, 9282713, 6866145, 35201802, 32691408, 48168288,
         15033783, 25105118, 25659556}},
        {{42782475, 15950225, 35307649, 18961608, 55446126, 28463506,
         1573891, 30928545, 2198789, 17749813}},
        {{64009494, 10324966, 64867251, 7453182, 61661885, 30818928, 53296841,
         17317989, 34647629, 21263748}},
    },
};

// r = a * A + b * B
// where a = a[0]+256*a[1]+...+256^31 a[31].
// and b = b[0]+256*b[1]+...+256^31 b[31].
// B is the Ed25519 base point (x,4/5) with x positive.
static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
                                         const ge_p3 *A, const uint8_t *b) {
  signed char aslide[256];
  signed char bslide[256];
  ge_cached Ai[8];  // A,3A,5A,7A,9A,11A,13A,15A
  ge_p1p1 t;
  ge_p3 u;
  ge_p3 A2;
  int i;

  slide(aslide, a);
  slide(bslide, b);

  x25519_ge_p3_to_cached(&Ai[0], A);
  ge_p3_dbl(&t, A);
  x25519_ge_p1p1_to_p3(&A2, &t);
  x25519_ge_add(&t, &A2, &Ai[0]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[1], &u);
  x25519_ge_add(&t, &A2, &Ai[1]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[2], &u);
  x25519_ge_add(&t, &A2, &Ai[2]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[3], &u);
  x25519_ge_add(&t, &A2, &Ai[3]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[4], &u);
  x25519_ge_add(&t, &A2, &Ai[4]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[5], &u);
  x25519_ge_add(&t, &A2, &Ai[5]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[6], &u);
  x25519_ge_add(&t, &A2, &Ai[6]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[7], &u);

  ge_p2_0(r);

  for (i = 255; i >= 0; --i) {
    if (aslide[i] || bslide[i]) {
      break;
    }
  }

  for (; i >= 0; --i) {
    ge_p2_dbl(&t, r);

    if (aslide[i] > 0) {
      x25519_ge_p1p1_to_p3(&u, &t);
      x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]);
    } else if (aslide[i] < 0) {
      x25519_ge_p1p1_to_p3(&u, &t);
      x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
    }

    if (bslide[i] > 0) {
      x25519_ge_p1p1_to_p3(&u, &t);
      ge_madd(&t, &u, &Bi[bslide[i] / 2]);
    } else if (bslide[i] < 0) {
      x25519_ge_p1p1_to_p3(&u, &t);
      ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
    }

    x25519_ge_p1p1_to_p2(r, &t);
  }
}

// The set of scalars is \Z/l
// where l = 2^252 + 27742317777372353535851937790883648493.

// Input:
//   s[0]+256*s[1]+...+256^63*s[63] = s
//
// Output:
//   s[0]+256*s[1]+...+256^31*s[31] = s mod l
//   where l = 2^252 + 27742317777372353535851937790883648493.
//   Overwrites s in place.
void x25519_sc_reduce(uint8_t *s) {
  int64_t s0 = 2097151 & load_3(s);
  int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
  int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
  int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
  int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
  int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
  int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
  int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
  int64_t s8 = 2097151 & load_3(s + 21);
  int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
  int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
  int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
  int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
  int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
  int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
  int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
  int64_t s16 = 2097151 & load_3(s + 42);
  int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
  int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
  int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
  int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
  int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
  int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
  int64_t s23 = (load_4(s + 60) >> 3);
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;
  int64_t carry10;
  int64_t carry11;
  int64_t carry12;
  int64_t carry13;
  int64_t carry14;
  int64_t carry15;
  int64_t carry16;

  s11 += s23 * 666643;
  s12 += s23 * 470296;
  s13 += s23 * 654183;
  s14 -= s23 * 997805;
  s15 += s23 * 136657;
  s16 -= s23 * 683901;
  s23 = 0;

  s10 += s22 * 666643;
  s11 += s22 * 470296;
  s12 += s22 * 654183;
  s13 -= s22 * 997805;
  s14 += s22 * 136657;
  s15 -= s22 * 683901;
  s22 = 0;

  s9 += s21 * 666643;
  s10 += s21 * 470296;
  s11 += s21 * 654183;
  s12 -= s21 * 997805;
  s13 += s21 * 136657;
  s14 -= s21 * 683901;
  s21 = 0;

  s8 += s20 * 666643;
  s9 += s20 * 470296;
  s10 += s20 * 654183;
  s11 -= s20 * 997805;
  s12 += s20 * 136657;
  s13 -= s20 * 683901;
  s20 = 0;

  s7 += s19 * 666643;
  s8 += s19 * 470296;
  s9 += s19 * 654183;
  s10 -= s19 * 997805;
  s11 += s19 * 136657;
  s12 -= s19 * 683901;
  s19 = 0;

  s6 += s18 * 666643;
  s7 += s18 * 470296;
  s8 += s18 * 654183;
  s9 -= s18 * 997805;
  s10 += s18 * 136657;
  s11 -= s18 * 683901;
  s18 = 0;

  carry6 = (s6 + (1 << 20)) >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry8 = (s8 + (1 << 20)) >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry10 = (s10 + (1 << 20)) >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;
  carry12 = (s12 + (1 << 20)) >> 21;
  s13 += carry12;
  s12 -= carry12 << 21;
  carry14 = (s14 + (1 << 20)) >> 21;
  s15 += carry14;
  s14 -= carry14 << 21;
  carry16 = (s16 + (1 << 20)) >> 21;
  s17 += carry16;
  s16 -= carry16 << 21;

  carry7 = (s7 + (1 << 20)) >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry9 = (s9 + (1 << 20)) >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry11 = (s11 + (1 << 20)) >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;
  carry13 = (s13 + (1 << 20)) >> 21;
  s14 += carry13;
  s13 -= carry13 << 21;
  carry15 = (s15 + (1 << 20)) >> 21;
  s16 += carry15;
  s15 -= carry15 << 21;

  s5 += s17 * 666643;
  s6 += s17 * 470296;
  s7 += s17 * 654183;
  s8 -= s17 * 997805;
  s9 += s17 * 136657;
  s10 -= s17 * 683901;
  s17 = 0;

  s4 += s16 * 666643;
  s5 += s16 * 470296;
  s6 += s16 * 654183;
  s7 -= s16 * 997805;
  s8 += s16 * 136657;
  s9 -= s16 * 683901;
  s16 = 0;

  s3 += s15 * 666643;
  s4 += s15 * 470296;
  s5 += s15 * 654183;
  s6 -= s15 * 997805;
  s7 += s15 * 136657;
  s8 -= s15 * 683901;
  s15 = 0;

  s2 += s14 * 666643;
  s3 += s14 * 470296;
  s4 += s14 * 654183;
  s5 -= s14 * 997805;
  s6 += s14 * 136657;
  s7 -= s14 * 683901;
  s14 = 0;

  s1 += s13 * 666643;
  s2 += s13 * 470296;
  s3 += s13 * 654183;
  s4 -= s13 * 997805;
  s5 += s13 * 136657;
  s6 -= s13 * 683901;
  s13 = 0;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = (s0 + (1 << 20)) >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry2 = (s2 + (1 << 20)) >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry4 = (s4 + (1 << 20)) >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry6 = (s6 + (1 << 20)) >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry8 = (s8 + (1 << 20)) >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry10 = (s10 + (1 << 20)) >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;

  carry1 = (s1 + (1 << 20)) >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry3 = (s3 + (1 << 20)) >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry5 = (s5 + (1 << 20)) >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry7 = (s7 + (1 << 20)) >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry9 = (s9 + (1 << 20)) >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry11 = (s11 + (1 << 20)) >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = s0 >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry1 = s1 >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry2 = s2 >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry3 = s3 >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry4 = s4 >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry5 = s5 >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry6 = s6 >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry7 = s7 >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry8 = s8 >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry9 = s9 >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry10 = s10 >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;
  carry11 = s11 >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = s0 >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry1 = s1 >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry2 = s2 >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry3 = s3 >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry4 = s4 >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry5 = s5 >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry6 = s6 >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry7 = s7 >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry8 = s8 >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry9 = s9 >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry10 = s10 >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;

  s[0] = s0 >> 0;
  s[1] = s0 >> 8;
  s[2] = (s0 >> 16) | (s1 << 5);
  s[3] = s1 >> 3;
  s[4] = s1 >> 11;
  s[5] = (s1 >> 19) | (s2 << 2);
  s[6] = s2 >> 6;
  s[7] = (s2 >> 14) | (s3 << 7);
  s[8] = s3 >> 1;
  s[9] = s3 >> 9;
  s[10] = (s3 >> 17) | (s4 << 4);
  s[11] = s4 >> 4;
  s[12] = s4 >> 12;
  s[13] = (s4 >> 20) | (s5 << 1);
  s[14] = s5 >> 7;
  s[15] = (s5 >> 15) | (s6 << 6);
  s[16] = s6 >> 2;
  s[17] = s6 >> 10;
  s[18] = (s6 >> 18) | (s7 << 3);
  s[19] = s7 >> 5;
  s[20] = s7 >> 13;
  s[21] = s8 >> 0;
  s[22] = s8 >> 8;
  s[23] = (s8 >> 16) | (s9 << 5);
  s[24] = s9 >> 3;
  s[25] = s9 >> 11;
  s[26] = (s9 >> 19) | (s10 << 2);
  s[27] = s10 >> 6;
  s[28] = (s10 >> 14) | (s11 << 7);
  s[29] = s11 >> 1;
  s[30] = s11 >> 9;
  s[31] = s11 >> 17;
}

// Input:
//   a[0]+256*a[1]+...+256^31*a[31] = a
//   b[0]+256*b[1]+...+256^31*b[31] = b
//   c[0]+256*c[1]+...+256^31*c[31] = c
//
// Output:
//   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
//   where l = 2^252 + 27742317777372353535851937790883648493.
static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
                      const uint8_t *c) {
  int64_t a0 = 2097151 & load_3(a);
  int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
  int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
  int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
  int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
  int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
  int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
  int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
  int64_t a8 = 2097151 & load_3(a + 21);
  int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
  int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
  int64_t a11 = (load_4(a + 28) >> 7);
  int64_t b0 = 2097151 & load_3(b);
  int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
  int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
  int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
  int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
  int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
  int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
  int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
  int64_t b8 = 2097151 & load_3(b + 21);
  int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
  int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
  int64_t b11 = (load_4(b + 28) >> 7);
  int64_t c0 = 2097151 & load_3(c);
  int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
  int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
  int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
  int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
  int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
  int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
  int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
  int64_t c8 = 2097151 & load_3(c + 21);
  int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
  int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
  int64_t c11 = (load_4(c + 28) >> 7);
  int64_t s0;
  int64_t s1;
  int64_t s2;
  int64_t s3;
  int64_t s4;
  int64_t s5;
  int64_t s6;
  int64_t s7;
  int64_t s8;
  int64_t s9;
  int64_t s10;
  int64_t s11;
  int64_t s12;
  int64_t s13;
  int64_t s14;
  int64_t s15;
  int64_t s16;
  int64_t s17;
  int64_t s18;
  int64_t s19;
  int64_t s20;
  int64_t s21;
  int64_t s22;
  int64_t s23;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;
  int64_t carry10;
  int64_t carry11;
  int64_t carry12;
  int64_t carry13;
  int64_t carry14;
  int64_t carry15;
  int64_t carry16;
  int64_t carry17;
  int64_t carry18;
  int64_t carry19;
  int64_t carry20;
  int64_t carry21;
  int64_t carry22;

  s0 = c0 + a0 * b0;
  s1 = c1 + a0 * b1 + a1 * b0;
  s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
  s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
  s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
  s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
  s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
  s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
       a6 * b1 + a7 * b0;
  s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
       a6 * b2 + a7 * b1 + a8 * b0;
  s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
       a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
  s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
        a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
  s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
        a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
  s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
        a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
  s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
        a9 * b4 + a10 * b3 + a11 * b2;
  s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
        a10 * b4 + a11 * b3;
  s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
        a11 * b4;
  s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
  s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
  s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
  s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
  s20 = a9 * b11 + a10 * b10 + a11 * b9;
  s21 = a10 * b11 + a11 * b10;
  s22 = a11 * b11;
  s23 = 0;

  carry0 = (s0 + (1 << 20)) >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry2 = (s2 + (1 << 20)) >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry4 = (s4 + (1 << 20)) >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry6 = (s6 + (1 << 20)) >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry8 = (s8 + (1 << 20)) >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry10 = (s10 + (1 << 20)) >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;
  carry12 = (s12 + (1 << 20)) >> 21;
  s13 += carry12;
  s12 -= carry12 << 21;
  carry14 = (s14 + (1 << 20)) >> 21;
  s15 += carry14;
  s14 -= carry14 << 21;
  carry16 = (s16 + (1 << 20)) >> 21;
  s17 += carry16;
  s16 -= carry16 << 21;
  carry18 = (s18 + (1 << 20)) >> 21;
  s19 += carry18;
  s18 -= carry18 << 21;
  carry20 = (s20 + (1 << 20)) >> 21;
  s21 += carry20;
  s20 -= carry20 << 21;
  carry22 = (s22 + (1 << 20)) >> 21;
  s23 += carry22;
  s22 -= carry22 << 21;

  carry1 = (s1 + (1 << 20)) >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry3 = (s3 + (1 << 20)) >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry5 = (s5 + (1 << 20)) >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry7 = (s7 + (1 << 20)) >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry9 = (s9 + (1 << 20)) >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry11 = (s11 + (1 << 20)) >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;
  carry13 = (s13 + (1 << 20)) >> 21;
  s14 += carry13;
  s13 -= carry13 << 21;
  carry15 = (s15 + (1 << 20)) >> 21;
  s16 += carry15;
  s15 -= carry15 << 21;
  carry17 = (s17 + (1 << 20)) >> 21;
  s18 += carry17;
  s17 -= carry17 << 21;
  carry19 = (s19 + (1 << 20)) >> 21;
  s20 += carry19;
  s19 -= carry19 << 21;
  carry21 = (s21 + (1 << 20)) >> 21;
  s22 += carry21;
  s21 -= carry21 << 21;

  s11 += s23 * 666643;
  s12 += s23 * 470296;
  s13 += s23 * 654183;
  s14 -= s23 * 997805;
  s15 += s23 * 136657;
  s16 -= s23 * 683901;
  s23 = 0;

  s10 += s22 * 666643;
  s11 += s22 * 470296;
  s12 += s22 * 654183;
  s13 -= s22 * 997805;
  s14 += s22 * 136657;
  s15 -= s22 * 683901;
  s22 = 0;

  s9 += s21 * 666643;
  s10 += s21 * 470296;
  s11 += s21 * 654183;
  s12 -= s21 * 997805;
  s13 += s21 * 136657;
  s14 -= s21 * 683901;
  s21 = 0;

  s8 += s20 * 666643;
  s9 += s20 * 470296;
  s10 += s20 * 654183;
  s11 -= s20 * 997805;
  s12 += s20 * 136657;
  s13 -= s20 * 683901;
  s20 = 0;

  s7 += s19 * 666643;
  s8 += s19 * 470296;
  s9 += s19 * 654183;
  s10 -= s19 * 997805;
  s11 += s19 * 136657;
  s12 -= s19 * 683901;
  s19 = 0;

  s6 += s18 * 666643;
  s7 += s18 * 470296;
  s8 += s18 * 654183;
  s9 -= s18 * 997805;
  s10 += s18 * 136657;
  s11 -= s18 * 683901;
  s18 = 0;

  carry6 = (s6 + (1 << 20)) >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry8 = (s8 + (1 << 20)) >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry10 = (s10 + (1 << 20)) >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;
  carry12 = (s12 + (1 << 20)) >> 21;
  s13 += carry12;
  s12 -= carry12 << 21;
  carry14 = (s14 + (1 << 20)) >> 21;
  s15 += carry14;
  s14 -= carry14 << 21;
  carry16 = (s16 + (1 << 20)) >> 21;
  s17 += carry16;
  s16 -= carry16 << 21;

  carry7 = (s7 + (1 << 20)) >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry9 = (s9 + (1 << 20)) >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry11 = (s11 + (1 << 20)) >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;
  carry13 = (s13 + (1 << 20)) >> 21;
  s14 += carry13;
  s13 -= carry13 << 21;
  carry15 = (s15 + (1 << 20)) >> 21;
  s16 += carry15;
  s15 -= carry15 << 21;

  s5 += s17 * 666643;
  s6 += s17 * 470296;
  s7 += s17 * 654183;
  s8 -= s17 * 997805;
  s9 += s17 * 136657;
  s10 -= s17 * 683901;
  s17 = 0;

  s4 += s16 * 666643;
  s5 += s16 * 470296;
  s6 += s16 * 654183;
  s7 -= s16 * 997805;
  s8 += s16 * 136657;
  s9 -= s16 * 683901;
  s16 = 0;

  s3 += s15 * 666643;
  s4 += s15 * 470296;
  s5 += s15 * 654183;
  s6 -= s15 * 997805;
  s7 += s15 * 136657;
  s8 -= s15 * 683901;
  s15 = 0;

  s2 += s14 * 666643;
  s3 += s14 * 470296;
  s4 += s14 * 654183;
  s5 -= s14 * 997805;
  s6 += s14 * 136657;
  s7 -= s14 * 683901;
  s14 = 0;

  s1 += s13 * 666643;
  s2 += s13 * 470296;
  s3 += s13 * 654183;
  s4 -= s13 * 997805;
  s5 += s13 * 136657;
  s6 -= s13 * 683901;
  s13 = 0;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = (s0 + (1 << 20)) >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry2 = (s2 + (1 << 20)) >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry4 = (s4 + (1 << 20)) >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry6 = (s6 + (1 << 20)) >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry8 = (s8 + (1 << 20)) >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry10 = (s10 + (1 << 20)) >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;

  carry1 = (s1 + (1 << 20)) >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry3 = (s3 + (1 << 20)) >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry5 = (s5 + (1 << 20)) >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry7 = (s7 + (1 << 20)) >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry9 = (s9 + (1 << 20)) >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry11 = (s11 + (1 << 20)) >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = s0 >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry1 = s1 >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry2 = s2 >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry3 = s3 >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry4 = s4 >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry5 = s5 >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry6 = s6 >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry7 = s7 >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry8 = s8 >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry9 = s9 >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry10 = s10 >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;
  carry11 = s11 >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = s0 >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry1 = s1 >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry2 = s2 >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry3 = s3 >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry4 = s4 >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry5 = s5 >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry6 = s6 >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry7 = s7 >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry8 = s8 >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry9 = s9 >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry10 = s10 >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;

  s[0] = s0 >> 0;
  s[1] = s0 >> 8;
  s[2] = (s0 >> 16) | (s1 << 5);
  s[3] = s1 >> 3;
  s[4] = s1 >> 11;
  s[5] = (s1 >> 19) | (s2 << 2);
  s[6] = s2 >> 6;
  s[7] = (s2 >> 14) | (s3 << 7);
  s[8] = s3 >> 1;
  s[9] = s3 >> 9;
  s[10] = (s3 >> 17) | (s4 << 4);
  s[11] = s4 >> 4;
  s[12] = s4 >> 12;
  s[13] = (s4 >> 20) | (s5 << 1);
  s[14] = s5 >> 7;
  s[15] = (s5 >> 15) | (s6 << 6);
  s[16] = s6 >> 2;
  s[17] = s6 >> 10;
  s[18] = (s6 >> 18) | (s7 << 3);
  s[19] = s7 >> 5;
  s[20] = s7 >> 13;
  s[21] = s8 >> 0;
  s[22] = s8 >> 8;
  s[23] = (s8 >> 16) | (s9 << 5);
  s[24] = s9 >> 3;
  s[25] = s9 >> 11;
  s[26] = (s9 >> 19) | (s10 << 2);
  s[27] = s10 >> 6;
  s[28] = (s10 >> 14) | (s11 << 7);
  s[29] = s11 >> 1;
  s[30] = s11 >> 9;
  s[31] = s11 >> 17;
}

void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) {
  uint8_t seed[32];
  RAND_bytes(seed, 32);
  ED25519_keypair_from_seed(out_public_key, out_private_key, seed);
}

int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
                 const uint8_t private_key[64]) {
  uint8_t az[SHA512_DIGEST_LENGTH];
  SHA512(private_key, 32, az);

  az[0] &= 248;
  az[31] &= 63;
  az[31] |= 64;

  SHA512_CTX hash_ctx;
  SHA512_Init(&hash_ctx);
  SHA512_Update(&hash_ctx, az + 32, 32);
  SHA512_Update(&hash_ctx, message, message_len);
  uint8_t nonce[SHA512_DIGEST_LENGTH];
  SHA512_Final(nonce, &hash_ctx);

  x25519_sc_reduce(nonce);
  ge_p3 R;
  x25519_ge_scalarmult_base(&R, nonce);
  ge_p3_tobytes(out_sig, &R);

  SHA512_Init(&hash_ctx);
  SHA512_Update(&hash_ctx, out_sig, 32);
  SHA512_Update(&hash_ctx, private_key + 32, 32);
  SHA512_Update(&hash_ctx, message, message_len);
  uint8_t hram[SHA512_DIGEST_LENGTH];
  SHA512_Final(hram, &hash_ctx);

  x25519_sc_reduce(hram);
  sc_muladd(out_sig + 32, hram, az, nonce);

  return 1;
}

int ED25519_verify(const uint8_t *message, size_t message_len,
                   const uint8_t signature[64], const uint8_t public_key[32]) {
  ge_p3 A;
  if ((signature[63] & 224) != 0 ||
      x25519_ge_frombytes_vartime(&A, public_key) != 0) {
    return 0;
  }

  fe_loose t;
  fe_neg(&t, &A.X);
  fe_carry(&A.X, &t);
  fe_neg(&t, &A.T);
  fe_carry(&A.T, &t);

  uint8_t pkcopy[32];
  OPENSSL_memcpy(pkcopy, public_key, 32);
  uint8_t rcopy[32];
  OPENSSL_memcpy(rcopy, signature, 32);
  uint8_t scopy[32];
  OPENSSL_memcpy(scopy, signature + 32, 32);

  SHA512_CTX hash_ctx;
  SHA512_Init(&hash_ctx);
  SHA512_Update(&hash_ctx, signature, 32);
  SHA512_Update(&hash_ctx, public_key, 32);
  SHA512_Update(&hash_ctx, message, message_len);
  uint8_t h[SHA512_DIGEST_LENGTH];
  SHA512_Final(h, &hash_ctx);

  x25519_sc_reduce(h);

  ge_p2 R;
  ge_double_scalarmult_vartime(&R, h, &A, scopy);

  uint8_t rcheck[32];
  x25519_ge_tobytes(rcheck, &R);

  return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
}

void ED25519_keypair_from_seed(uint8_t out_public_key[32],
                               uint8_t out_private_key[64],
                               const uint8_t seed[32]) {
  uint8_t az[SHA512_DIGEST_LENGTH];
  SHA512(seed, 32, az);

  az[0] &= 248;
  az[31] &= 63;
  az[31] |= 64;

  ge_p3 A;
  x25519_ge_scalarmult_base(&A, az);
  ge_p3_tobytes(out_public_key, &A);

  OPENSSL_memcpy(out_private_key, seed, 32);
  OPENSSL_memcpy(out_private_key + 32, out_public_key, 32);
}


#if defined(BORINGSSL_X25519_X86_64)

static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
                               const uint8_t point[32]) {
  x25519_x86_64(out, scalar, point);
}

#else

// Replace (f,g) with (g,f) if b == 1;
// replace (f,g) with (f,g) if b == 0.
//
// Preconditions: b in {0,1}.
static void fe_cswap(fe *f, fe *g, unsigned int b) {
  b = 0-b;
  unsigned i;
  for (i = 0; i < 10; i++) {
    uint32_t x = f->v[i] ^ g->v[i];
    x &= b;
    f->v[i] ^= x;
    g->v[i] ^= x;
  }
}

// NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0..
static void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10]) {
  assert_fe_loose(in1);
  { const uint32_t x20 = in1[9];
  { const uint32_t x21 = in1[8];
  { const uint32_t x19 = in1[7];
  { const uint32_t x17 = in1[6];
  { const uint32_t x15 = in1[5];
  { const uint32_t x13 = in1[4];
  { const uint32_t x11 = in1[3];
  { const uint32_t x9 = in1[2];
  { const uint32_t x7 = in1[1];
  { const uint32_t x5 = in1[0];
  { const uint32_t x38 = 0;
  { const uint32_t x39 = 0;
  { const uint32_t x37 = 0;
  { const uint32_t x35 = 0;
  { const uint32_t x33 = 0;
  { const uint32_t x31 = 0;
  { const uint32_t x29 = 0;
  { const uint32_t x27 = 0;
  { const uint32_t x25 = 0;
  { const uint32_t x23 = 121666;
  { uint64_t x40 = ((uint64_t)x23 * x5);
  { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
  { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
  { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
  { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
  { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
  { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
  { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
  { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
  { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
  { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
  { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
  { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
  { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
  { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
  { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
  { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
  { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
  { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
  { uint64_t x59 = (x48 + (x58 << 0x4));
  { uint64_t x60 = (x59 + (x58 << 0x1));
  { uint64_t x61 = (x60 + x58);
  { uint64_t x62 = (x47 + (x57 << 0x4));
  { uint64_t x63 = (x62 + (x57 << 0x1));
  { uint64_t x64 = (x63 + x57);
  { uint64_t x65 = (x46 + (x56 << 0x4));
  { uint64_t x66 = (x65 + (x56 << 0x1));
  { uint64_t x67 = (x66 + x56);
  { uint64_t x68 = (x45 + (x55 << 0x4));
  { uint64_t x69 = (x68 + (x55 << 0x1));
  { uint64_t x70 = (x69 + x55);
  { uint64_t x71 = (x44 + (x54 << 0x4));
  { uint64_t x72 = (x71 + (x54 << 0x1));
  { uint64_t x73 = (x72 + x54);
  { uint64_t x74 = (x43 + (x53 << 0x4));
  { uint64_t x75 = (x74 + (x53 << 0x1));
  { uint64_t x76 = (x75 + x53);
  { uint64_t x77 = (x42 + (x52 << 0x4));
  { uint64_t x78 = (x77 + (x52 << 0x1));
  { uint64_t x79 = (x78 + x52);
  { uint64_t x80 = (x41 + (x51 << 0x4));
  { uint64_t x81 = (x80 + (x51 << 0x1));
  { uint64_t x82 = (x81 + x51);
  { uint64_t x83 = (x40 + (x50 << 0x4));
  { uint64_t x84 = (x83 + (x50 << 0x1));
  { uint64_t x85 = (x84 + x50);
  { uint64_t x86 = (x85 >> 0x1a);
  { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
  { uint64_t x88 = (x86 + x82);
  { uint64_t x89 = (x88 >> 0x19);
  { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
  { uint64_t x91 = (x89 + x79);
  { uint64_t x92 = (x91 >> 0x1a);
  { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
  { uint64_t x94 = (x92 + x76);
  { uint64_t x95 = (x94 >> 0x19);
  { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
  { uint64_t x97 = (x95 + x73);
  { uint64_t x98 = (x97 >> 0x1a);
  { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
  { uint64_t x100 = (x98 + x70);
  { uint64_t x101 = (x100 >> 0x19);
  { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
  { uint64_t x103 = (x101 + x67);
  { uint64_t x104 = (x103 >> 0x1a);
  { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
  { uint64_t x106 = (x104 + x64);
  { uint64_t x107 = (x106 >> 0x19);
  { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
  { uint64_t x109 = (x107 + x61);
  { uint64_t x110 = (x109 >> 0x1a);
  { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
  { uint64_t x112 = (x110 + x49);
  { uint64_t x113 = (x112 >> 0x19);
  { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
  { uint64_t x115 = (x87 + (0x13 * x113));
  { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
  { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
  { uint32_t x118 = (x116 + x90);
  { uint32_t x119 = (x118 >> 0x19);
  { uint32_t x120 = (x118 & 0x1ffffff);
  out[0] = x117;
  out[1] = x120;
  out[2] = (x119 + x93);
  out[3] = x96;
  out[4] = x99;
  out[5] = x102;
  out[6] = x105;
  out[7] = x108;
  out[8] = x111;
  out[9] = x114;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
  assert_fe(out);
}

static void fe_mul121666(fe *h, const fe_loose *f) {
  assert_fe_loose(f->v);
  fe_mul_121666_impl(h->v, f->v);
  assert_fe(h->v);
}

static void x25519_scalar_mult_generic(uint8_t out[32],
                                       const uint8_t scalar[32],
                                       const uint8_t point[32]) {
  fe x1, x2, z2, x3, z3, tmp0, tmp1;
  fe_loose x2l, z2l, x3l, tmp0l, tmp1l;

  uint8_t e[32];
  OPENSSL_memcpy(e, scalar, 32);
  e[0] &= 248;
  e[31] &= 127;
  e[31] |= 64;
  fe_frombytes(&x1, point);
  fe_1(&x2);
  fe_0(&z2);
  fe_copy(&x3, &x1);
  fe_1(&z3);

  unsigned swap = 0;
  int pos;
  for (pos = 254; pos >= 0; --pos) {
    unsigned b = 1 & (e[pos / 8] >> (pos & 7));
    swap ^= b;
    fe_cswap(&x2, &x3, swap);
    fe_cswap(&z2, &z3, swap);
    swap = b;
    fe_sub(&tmp0l, &x3, &z3);
    fe_sub(&tmp1l, &x2, &z2);
    fe_add(&x2l, &x2, &z2);
    fe_add(&z2l, &x3, &z3);
    fe_mul_tll(&z3, &tmp0l, &x2l);
    fe_mul_tll(&z2, &z2l, &tmp1l);
    fe_sq_tl(&tmp0, &tmp1l);
    fe_sq_tl(&tmp1, &x2l);
    fe_add(&x3l, &z3, &z2);
    fe_sub(&z2l, &z3, &z2);
    fe_mul_ttt(&x2, &tmp1, &tmp0);
    fe_sub(&tmp1l, &tmp1, &tmp0);
    fe_sq_tl(&z2, &z2l);
    fe_mul121666(&z3, &tmp1l);
    fe_sq_tl(&x3, &x3l);
    fe_add(&tmp0l, &tmp0, &z3);
    fe_mul_ttt(&z3, &x1, &z2);
    fe_mul_tll(&z2, &tmp1l, &tmp0l);
  }
  fe_cswap(&x2, &x3, swap);
  fe_cswap(&z2, &z3, swap);

  fe_invert(&z2, &z2);
  fe_mul_ttt(&x2, &x2, &z2);
  fe_tobytes(out, &x2);
}

static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
                               const uint8_t point[32]) {
#if defined(BORINGSSL_X25519_NEON)
  if (CRYPTO_is_NEON_capable()) {
    x25519_NEON(out, scalar, point);
    return;
  }
#endif

  x25519_scalar_mult_generic(out, scalar, point);
}

#endif  // BORINGSSL_X25519_X86_64


void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) {
  RAND_bytes(out_private_key, 32);

  // All X25519 implementations should decode scalars correctly (see
  // https://tools.ietf.org/html/rfc7748#section-5). However, if an
  // implementation doesn't then it might interoperate with random keys a
  // fraction of the time because they'll, randomly, happen to be correctly
  // formed.
  //
  // Thus we do the opposite of the masking here to make sure that our private
  // keys are never correctly masked and so, hopefully, any incorrect
  // implementations are deterministically broken.
  //
  // This does not affect security because, although we're throwing away
  // entropy, a valid implementation of scalarmult should throw away the exact
  // same bits anyway.
  out_private_key[0] |= 7;
  out_private_key[31] &= 63;
  out_private_key[31] |= 128;

  X25519_public_from_private(out_public_value, out_private_key);
}

int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
           const uint8_t peer_public_value[32]) {
  static const uint8_t kZeros[32] = {0};
  x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
  // The all-zero output results when the input is a point of small order.
  return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
}

#if defined(BORINGSSL_X25519_X86_64)

// When |BORINGSSL_X25519_X86_64| is set, base point multiplication is done with
// the Montgomery ladder because it's faster. Otherwise it's done using the
// Ed25519 tables.

void X25519_public_from_private(uint8_t out_public_value[32],
                                const uint8_t private_key[32]) {
  static const uint8_t kMongomeryBasePoint[32] = {9};
  x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint);
}

#else

void X25519_public_from_private(uint8_t out_public_value[32],
                                const uint8_t private_key[32]) {
#if defined(BORINGSSL_X25519_NEON)
  if (CRYPTO_is_NEON_capable()) {
    static const uint8_t kMongomeryBasePoint[32] = {9};
    x25519_NEON(out_public_value, private_key, kMongomeryBasePoint);
    return;
  }
#endif

  uint8_t e[32];
  OPENSSL_memcpy(e, private_key, 32);
  e[0] &= 248;
  e[31] &= 127;
  e[31] |= 64;

  ge_p3 A;
  x25519_ge_scalarmult_base(&A, e);

  // We only need the u-coordinate of the curve25519 point. The map is
  // u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y).
  fe_loose zplusy, zminusy;
  fe zminusy_inv;
  fe_add(&zplusy, &A.Z, &A.Y);
  fe_sub(&zminusy, &A.Z, &A.Y);
  fe_loose_invert(&zminusy_inv, &zminusy);
  fe_mul_tlt(&zminusy_inv, &zplusy, &zminusy_inv);
  fe_tobytes(out_public_value, &zminusy_inv);
}

#endif  // BORINGSSL_X25519_X86_64