curve25519.c

/****************************************************************************
 * crypto/curve25519.c
 * $OpenBSD: curve25519.c,v 1.2 2020/07/22 13:54:30 tobhe Exp $
 *
 * Copyright (C) 2018-2020 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights
 * Reserved.
 * Copyright (C) 2015-2016 The fiat-crypto Authors.
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 *
 * This contains two implementation: a machine-generated formally verified
 * implementation of Curve25519 ECDH from:
 * <https://github.com/mit-plv/fiat-crypto>. Though originally machine
 * generated, it has been tweaked to be suitable for use in the kernel.
 * It is optimized for 32-bit machines and machines that cannot work
 * efficiently with 128-bit integer types.
 ****************************************************************************/

/****************************************************************************
 * Included Files
 ****************************************************************************/

#include <endian.h>
#include <sys/types.h>
#include <string.h>
#include <crypto/curve25519.h>

/****************************************************************************
 * Private Type Definitions
 ****************************************************************************/

/* fe means field element. Here the field is \Z/(2^255-19). An element t,
 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
 * t[3]+2^102 t[4]+...+2^230 t[9].
 * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc.
 * Multiplication and carrying produce fe from fe_loose.
 */

typedef struct fe
{
  uint32_t v[10];
} fe;

/* fe_loose limbs are bounded by
 * 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc
 * Addition and subtraction produce fe_loose from (fe, fe).
 */

typedef struct fe_loose
{
  uint32_t v[10];
} fe_loose;

/****************************************************************************
 * Private Data
 ****************************************************************************/

static const uint8_t g_null_point[CURVE25519_KEY_SIZE];
static const uint8_t g_base_point[CURVE25519_KEY_SIZE] =
{
  9
};

/****************************************************************************
 * Private Functions
 ****************************************************************************/

static uint32_t get_unaligned_le32(FAR const uint8_t *a)
{
  uint32_t l;

  memcpy(&l, a, sizeof(l));
  return letoh32(l);
}

static void fe_frombytes_impl(uint32_t h[10], FAR const uint8_t *s)
{
  /* Ignores top bit of s. */

  uint32_t a0 = get_unaligned_le32(s);
  uint32_t a1 = get_unaligned_le32(s + 4);
  uint32_t a2 = get_unaligned_le32(s + 8);
  uint32_t a3 = get_unaligned_le32(s + 12);
  uint32_t a4 = get_unaligned_le32(s + 16);
  uint32_t a5 = get_unaligned_le32(s + 20);
  uint32_t a6 = get_unaligned_le32(s + 24);
  uint32_t a7 = get_unaligned_le32(s + 28);

  /* 26 used, 32 - 26 left.   26 */

  h[0] = a0 & ((1 << 26) - 1);

  /* (32 - 26) + 19 = 6 + 19 = 25 */

  h[1] = (a0 >> 26) | ((a1 & ((1 << 19) - 1)) << 6);

  /* (32 - 19) + 13 = 13 + 13 = 26 */

  h[2] = (a1 >> 19) | ((a2 & ((1 << 13) - 1)) << 13);

  /* (32 - 13) + 6 = 19 + 6 = 25 */

  h[3] = (a2 >> 13) | ((a3 & ((1 <<  6) - 1)) << 19);

  /* (32 - 6) = 26 */

  h[4] = (a3 >>  6);

  /* 25 */

  h[5] = a4 & ((1 << 25) - 1);

  /* (32 - 25) + 19 = 7 + 19 = 26 */

  h[6] = (a4 >> 25) | ((a5 & ((1 << 19) - 1)) <<  7);

  /* (32 - 19) + 12 = 13 + 12 = 25 */

  h[7] = (a5 >> 19) | ((a6 & ((1 << 12) - 1)) << 13);

  /* (32 - 12) + 6 = 20 + 6 = 26 */

  h[8] = (a6 >> 12) | ((a7 & ((1 <<  6) - 1)) << 20);

  /* 25 */

  h[9] = (a7 >> 6) & ((1 << 25) - 1);
}

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

/* uint8_t c - bool */

static uint8_t /* bool */
addcarryx_u25(uint8_t c, uint32_t a, uint32_t b, FAR uint32_t *low)
{
  /* This function extracts 25 bits of result and 1 bit of carry
   * (26 total), so a 32-bit intermediate is sufficient.
   */

  uint32_t x = a + b + c;

  *low = x & ((1 << 25) - 1);
  return (x >> 25) & 1;
}

/* uint8_t c - bool */

static uint8_t /* bool */
addcarryx_u26(uint8_t c, uint32_t a, uint32_t b, FAR uint32_t *low)
{
  /* This function extracts 26 bits of result and 1 bit of carry
   * (27 total), so a 32-bit intermediate is sufficient.
   */

  uint32_t x = a + b + c;

  *low = x & ((1 << 26) - 1);
  return (x >> 26) & 1;
}

/* uint8_t c - bool */

static uint8_t /* bool */
subborrow_u25(uint8_t c, uint32_t a, uint32_t b, FAR uint32_t *low)
{
  /* This function extracts 25 bits of result and 1 bit of borrow
   * (26 total), so a 32-bit intermediate is sufficient.
   */

  uint32_t x = a - b - c;

  *low = x & ((1 << 25) - 1);
  return x >> 31;
}

/* uint8_t c - bool */

static uint8_t /* bool */
subborrow_u26(uint8_t c, uint32_t a, uint32_t b, FAR uint32_t *low)
{
  /* This function extracts 26 bits of result and 1 bit of borrow
   * (27 total), so a 32-bit intermediate is sufficient.
   */

  uint32_t x = a - b - c;

  *low = x & ((1 << 26) - 1);
  return x >> 31;
}

static uint32_t
cmovznz32(uint32_t t, uint32_t z, uint32_t nz)
{
  t = - !!t;  /* all set if nonzero, 0 if 0 */
  return (t & nz) | ((~t) & z);
}

static void fe_freeze(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 x20;

  /* bool */

  uint8_t  x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20);
  uint32_t x23;

  /* bool */

  uint8_t  x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23);
  uint32_t x26;

  /* bool */

  uint8_t  x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26);
  uint32_t x29;

  /* bool */

  uint8_t  x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29);
  uint32_t x32;

  /* bool */

  uint8_t  x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32);
  uint32_t x35;

  /* bool */

  uint8_t  x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35);
  uint32_t x38;

  /* bool */

  uint8_t  x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38);
  uint32_t x41;

  /* bool */

  uint8_t  x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41);
  uint32_t x44;

  /* bool */

  uint8_t  x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44);
  uint32_t x47;

  /* bool */

  uint8_t  x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47);
  uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff);
  uint32_t x50 = (x49 & 0x3ffffed);
  uint32_t x52;

  /* bool */

  uint8_t  x53 = addcarryx_u26(0x0, x20, x50, &x52);
  uint32_t x54 = (x49 & 0x1ffffff);
  uint32_t x56;

  /* bool */

  uint8_t  x57 = addcarryx_u25(x53, x23, x54, &x56);
  uint32_t x58 = (x49 & 0x3ffffff);
  uint32_t x60;

  /* bool */

  uint8_t  x61 = addcarryx_u26(x57, x26, x58, &x60);
  uint32_t x62 = (x49 & 0x1ffffff);
  uint32_t x64;

  /* bool */

  uint8_t  x65 = addcarryx_u25(x61, x29, x62, &x64);
  uint32_t x66 = (x49 & 0x3ffffff);
  uint32_t x68;

  /* bool */

  uint8_t  x69 = addcarryx_u26(x65, x32, x66, &x68);
  uint32_t x70 = (x49 & 0x1ffffff);
  uint32_t x72;

  /* bool */

  uint8_t  x73 = addcarryx_u25(x69, x35, x70, &x72);
  uint32_t x74 = (x49 & 0x3ffffff);
  uint32_t x76;

  /* bool */

  uint8_t  x77 = addcarryx_u26(x73, x38, x74, &x76);
  uint32_t x78 = (x49 & 0x1ffffff);
  uint32_t x80;

  /* bool */

  uint8_t  x81 = addcarryx_u25(x77, x41, x78, &x80);
  uint32_t x82 = (x49 & 0x3ffffff);
  uint32_t x84;

  /* bool */

  uint8_t  x85 = addcarryx_u26(x81, x44, x82, &x84);
  uint32_t x86 = (x49 & 0x1ffffff);
  uint32_t x88;

  addcarryx_u25(x85, x47, x86, &x88);

  out[0] = x52;
  out[1] = x56;
  out[2] = x60;
  out[3] = x64;
  out[4] = x68;
  out[5] = x72;
  out[6] = x76;
  out[7] = x80;
  out[8] = x84;
  out[9] = x88;
}

static void fe_tobytes(uint8_t s[32], FAR const fe *f)
{
  uint32_t h[10];

  fe_freeze(h, f->v);
  s[0]  = h[0] >> 0;
  s[1]  = h[0] >> 8;
  s[2]  = h[0] >> 16;
  s[3]  = (h[0] >> 24) | (h[1] << 2);
  s[4]  = h[1] >> 6;
  s[5]  = h[1] >> 14;
  s[6]  = (h[1] >> 22) | (h[2] << 3);
  s[7]  = h[2] >> 5;
  s[8]  = h[2] >> 13;
  s[9]  = (h[2] >> 21) | (h[3] << 5);
  s[10] = h[3] >> 3;
  s[11] = h[3] >> 11;
  s[12] = (h[3] >> 19) | (h[4] << 6);
  s[13] = h[4] >> 2;
  s[14] = h[4] >> 10;
  s[15] = h[4] >> 18;
  s[16] = h[5] >> 0;
  s[17] = h[5] >> 8;
  s[18] = h[5] >> 16;
  s[19] = (h[5] >> 24) | (h[6] << 1);
  s[20] = h[6] >> 7;
  s[21] = h[6] >> 15;
  s[22] = (h[6] >> 23) | (h[7] << 3);
  s[23] = h[7] >> 5;
  s[24] = h[7] >> 13;
  s[25] = (h[7] >> 21) | (h[8] << 4);
  s[26] = h[8] >> 4;
  s[27] = h[8] >> 12;
  s[28] = (h[8] >> 20) | (h[9] << 6);
  s[29] = h[9] >> 2;
  s[30] = h[9] >> 10;
  s[31] = h[9] >> 18;
}

/* h = f */

static void fe_copy(FAR fe *h, FAR const fe *f)
{
  memmove(h, f, sizeof(uint32_t) * 10);
}

static void fe_copy_lt(FAR fe_loose *h, FAR const fe *f)
{
  memmove(h, f, sizeof(uint32_t) * 10);
}

/* h = 0 */

static void fe_0(FAR fe *h)
{
  memset(h, 0, sizeof(uint32_t) * 10);
}

/* h = 1 */

static void fe_1(FAR fe *h)
{
  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.
 */

static void fe_add(FAR fe_loose *h, FAR const fe *f, FAR const fe *g)
{
  fe_add_impl(h->v, f->v, g->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.
 */

static void fe_sub(FAR fe_loose *h, FAR const fe *f, FAR const fe *g)
{
  fe_sub_impl(h->v, f->v, g->v);
}

static void fe_mul_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];
  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;
}

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

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

static void fe_mul_tll(FAR fe *h, FAR const fe_loose *f,
                       FAR 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])
{
  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;
}

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

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

static void fe_loose_invert(FAR fe *out, FAR 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(FAR fe *out, FAR const fe *z)
{
  fe_loose l;

  fe_copy_lt(&l, z);
  fe_loose_invert(out, &l);
}

/* 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(FAR fe *f, FAR fe *g, unsigned int b)
{
  unsigned i;

  b = 0 - b;
  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])
{
  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;
}

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

/****************************************************************************
 * Public Functions
 ****************************************************************************/

int curve25519(uint8_t out[CURVE25519_KEY_SIZE],
               const uint8_t scalar[CURVE25519_KEY_SIZE],
               const uint8_t point[CURVE25519_KEY_SIZE])
{
  fe        x1, x2, z2, x3, z3;
  fe_loose  x2l, z2l, x3l;
  unsigned  swap = 0;
  int       pos;
  uint8_t   e[32];

  memcpy(e, scalar, 32);
  curve25519_clamp_secret(e);

  /* The following implementation was transcribed to Coq and proven to
   * correspond to unary scalar multiplication in affine coordinates given
   * that x1 != 0 is the x coordinate of some point on the curve. It was
   * also checked in Coq that doing a ladderstep with x1 = x3 = 0 gives
   * z2' = z3' = 0, and z2 = z3 = 0 gives z2' = z3' = 0. The statement was
   * quantified over the underlying field, so it applies to Curve25519
   * itself and the quadratic twist of Curve25519. It was not proven in
   * Coq that prime-field arithmetic correctly simulates extension-field
   * arithmetic on prime-field values. The decoding of the byte array
   * representation of e was not considered.
   *
   * Specification of Montgomery curves in affine coordinates:
   * <https://github.com/mit-plv/fiat-crypto/blob/ \
   *  2456d821825521f7e03e65882cc3521795b0320f/ \
   *  src/Spec/MontgomeryCurve.v#L27>
   *
   * Proof that these form a group that is isomorphic to a Weierstrass
   * curve:
   * <https://github.com/mit-plv/fiat-crypto/blob/ \
   *  2456d821825521f7e03e65882cc3521795b0320f/ \
   *  src/Curves/Montgomery/AffineProofs.v#L35>
   *
   * Coq transcription and correctness proof of the loop
   * (where scalarbits=255):
   * <https://github.com/mit-plv/fiat-crypto/blob/ \
   *  2456d821825521f7e03e65882cc3521795b0320f/ \
   *  src/Curves/Montgomery/XZ.v#L118>
   * <https://github.com/mit-plv/fiat-crypto/blob/ \
   *  2456d821825521f7e03e65882cc3521795b0320f/ \
   *  src/Curves/Montgomery/XZProofs.v#L278>
   * preconditions: 0 <= e < 2^255 (not necessarily e < order),
   * fe_invert(0) = 0
   */

  fe_frombytes(&x1, point);
  fe_1(&x2);
  fe_0(&z2);
  fe_copy(&x3, &x1);
  fe_1(&z3);

  for (pos = 254; pos >= 0; --pos)
    {
      fe       tmp0, tmp1;
      fe_loose tmp0l, tmp1l;

      /* loop invariant as of right before the test, for the case
       * where x1 != 0:
       *   pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3
       *   is nonzero
       *   let r := e >> (pos+1) in the following equalities of
       *   projective points:
       *   to_xz (r*P)   === if swap then (x3, z3) else (x2, z2)
       *   to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3)
       *   x1 is the nonzero x coordinate of the nonzero
       *   point (r*P-(r+1)*P)
       */

      unsigned b = 1 & (e[pos / 8] >> (pos & 7));
      swap ^= b;
      fe_cswap(&x2, &x3, swap);
      fe_cswap(&z2, &z3, swap);
      swap = b;

      /* Coq transcription of ladderstep formula (called from
       * transcribed loop):
       * <https://github.com/mit-plv/fiat-crypto/blob/ \
       *  2456d821825521f7e03e65882cc3521795b0320f/ \
       *  src/Curves/Montgomery/XZ.v#L89> \
       * <https://github.com/mit-plv/fiat-crypto/blob/ \
       *  2456d821825521f7e03e65882cc3521795b0320f/ \
       *  src/Curves/Montgomery/XZProofs.v#L131>
       * x1 != 0
       * <https://github.com/mit-plv/fiat-crypto/blob/ \
       *  2456d821825521f7e03e65882cc3521795b0320f/ \
       *  src/Curves/Montgomery/XZProofs.v#L217> \
       * x1  = 0
       * <https://github.com/mit-plv/fiat-crypto/blob/ \
       *  2456d821825521f7e03e65882cc3521795b0320f/ \
       *  src/Curves/Montgomery/XZProofs.v#L147>
       */

      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);
    }

  /* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3)
   * else (x2, z2)
   */

  fe_cswap(&x2, &x3, swap);
  fe_cswap(&z2, &z3, swap);

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

  explicit_bzero(&x1, sizeof(x1));
  explicit_bzero(&x2, sizeof(x2));
  explicit_bzero(&z2, sizeof(z2));
  explicit_bzero(&x3, sizeof(x3));
  explicit_bzero(&z3, sizeof(z3));
  explicit_bzero(&x2l, sizeof(x2l));
  explicit_bzero(&z2l, sizeof(z2l));
  explicit_bzero(&x3l, sizeof(x3l));
  explicit_bzero(&e, sizeof(e));
  return timingsafe_bcmp(out, g_null_point, CURVE25519_KEY_SIZE);
}

int curve25519_generate_public(uint8_t pub[CURVE25519_KEY_SIZE],
                               const uint8_t secret[CURVE25519_KEY_SIZE])
{
  if (timingsafe_bcmp(secret, g_null_point, CURVE25519_KEY_SIZE) == 0)
    {
      return 0;
    }

  return curve25519(pub, secret, g_base_point);
}