/*
 * Copyright (c) 2015, Google Inc.
 *
 * Permission to use, copy, modify, and/or distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
 * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
 * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
 * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 *
 * Modifications Copyright 2017 Velo Payments, Inc.  All rights reserved.
 */

/*
 * This code is mostly 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 this file has the ISC license just to keep licencing
 * simple.
 *
 * The field functions are shared by Ed25519 and X25519 where possible.
 */

#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <vccrypt/compare.h>
#include <vccrypt/hash.h>
#include <vccrypt/prng.h>

#include "curve25519.h"
#include "curve25519_internal.h"

static const int64_t kBottom25Bits = 0x1ffffffLL;
static const int64_t kBottom26Bits = 0x3ffffffLL;
static const int64_t kTop39Bits = 0xfffffffffe000000LL;
static const int64_t kTop38Bits = 0xfffffffffc000000LL;

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;
}

static void fe_frombytes(fe h, const uint8_t* s)
{
    /* Ignores top bit of h. */
    int64_t h0 = load_4(s);
    int64_t h1 = load_3(s + 4) << 6;
    int64_t h2 = load_3(s + 7) << 5;
    int64_t h3 = load_3(s + 10) << 3;
    int64_t h4 = load_3(s + 13) << 2;
    int64_t h5 = load_4(s + 16);
    int64_t h6 = load_3(s + 20) << 7;
    int64_t h7 = load_3(s + 23) << 5;
    int64_t h8 = load_3(s + 26) << 4;
    int64_t h9 = (load_3(s + 29) & 8388607) << 2;
    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;

    carry9 = h9 + (1 << 24);
    h0 += (carry9 >> 25) * 19;
    h9 -= carry9 & kTop39Bits;
    carry1 = h1 + (1 << 24);
    h2 += carry1 >> 25;
    h1 -= carry1 & kTop39Bits;
    carry3 = h3 + (1 << 24);
    h4 += carry3 >> 25;
    h3 -= carry3 & kTop39Bits;
    carry5 = h5 + (1 << 24);
    h6 += carry5 >> 25;
    h5 -= carry5 & kTop39Bits;
    carry7 = h7 + (1 << 24);
    h8 += carry7 >> 25;
    h7 -= carry7 & kTop39Bits;

    carry0 = h0 + (1 << 25);
    h1 += carry0 >> 26;
    h0 -= carry0 & kTop38Bits;
    carry2 = h2 + (1 << 25);
    h3 += carry2 >> 26;
    h2 -= carry2 & kTop38Bits;
    carry4 = h4 + (1 << 25);
    h5 += carry4 >> 26;
    h4 -= carry4 & kTop38Bits;
    carry6 = h6 + (1 << 25);
    h7 += carry6 >> 26;
    h6 -= carry6 & kTop38Bits;
    carry8 = h8 + (1 << 25);
    h9 += carry8 >> 26;
    h8 -= carry8 & kTop38Bits;

    h[0] = h0;
    h[1] = h1;
    h[2] = h2;
    h[3] = h3;
    h[4] = h4;
    h[5] = h5;
    h[6] = h6;
    h[7] = h7;
    h[8] = h8;
    h[9] = h9;
}

/* 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(uint8_t* s, const fe 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;
}

/* h = f */
static void fe_copy(fe h, const fe f)
{
    memmove(h, f, sizeof(int32_t) * 10);
}

/* h = 0 */
static void fe_0(fe h)
{
    memset(h, 0, sizeof(int32_t) * 10);
}

/* h = 1 */
static void fe_1(fe h)
{
    memset(h, 0, sizeof(int32_t) * 10);
    h[0] = 1;
}

/* 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 h, const fe f, const fe g)
{
    unsigned i;

    for (i = 0; i < 10; i++)
    {
        h[i] = f[i] + g[i];
    }
}

/* 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 h, const fe f, const fe g)
{
    unsigned i;

    for (i = 0; i < 10; i++)
    {
        h[i] = f[i] - g[i];
    }
}

/* h = f * g
 * Can overlap h with f or g.
 *
 * Preconditions:
 *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 *    |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 *
 * Postconditions:
 *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
 *
 * Notes on implementation strategy:
 *
 * Using schoolbook multiplication.
 * Karatsuba would save a little in some cost models.
 *
 * Most multiplications by 2 and 19 are 32-bit precomputations;
 * cheaper than 64-bit postcomputations.
 *
 * There is one remaining multiplication by 19 in the carry chain;
 * one *19 precomputation can be merged into this,
 * but the resulting data flow is considerably less clean.
 *
 * There are 12 carries below.
 * 10 of them are 2-way parallelizable and vectorizable.
 * Can get away with 11 carries, but then data flow is much deeper.
 *
 * With tighter constraints on inputs can squeeze carries into int32. */
static void fe_mul(fe h, const fe f, const fe g)
{
    int32_t f0 = f[0];
    int32_t f1 = f[1];
    int32_t f2 = f[2];
    int32_t f3 = f[3];
    int32_t f4 = f[4];
    int32_t f5 = f[5];
    int32_t f6 = f[6];
    int32_t f7 = f[7];
    int32_t f8 = f[8];
    int32_t f9 = f[9];
    int32_t g0 = g[0];
    int32_t g1 = g[1];
    int32_t g2 = g[2];
    int32_t g3 = g[3];
    int32_t g4 = g[4];
    int32_t g5 = g[5];
    int32_t g6 = g[6];
    int32_t g7 = g[7];
    int32_t g8 = g[8];
    int32_t g9 = g[9];
    int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
    int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
    int32_t g3_19 = 19 * g3;
    int32_t g4_19 = 19 * g4;
    int32_t g5_19 = 19 * g5;
    int32_t g6_19 = 19 * g6;
    int32_t g7_19 = 19 * g7;
    int32_t g8_19 = 19 * g8;
    int32_t g9_19 = 19 * g9;
    int32_t f1_2 = 2 * f1;
    int32_t f3_2 = 2 * f3;
    int32_t f5_2 = 2 * f5;
    int32_t f7_2 = 2 * f7;
    int32_t f9_2 = 2 * f9;
    int64_t f0g0 = f0 * (int64_t)g0;
    int64_t f0g1 = f0 * (int64_t)g1;
    int64_t f0g2 = f0 * (int64_t)g2;
    int64_t f0g3 = f0 * (int64_t)g3;
    int64_t f0g4 = f0 * (int64_t)g4;
    int64_t f0g5 = f0 * (int64_t)g5;
    int64_t f0g6 = f0 * (int64_t)g6;
    int64_t f0g7 = f0 * (int64_t)g7;
    int64_t f0g8 = f0 * (int64_t)g8;
    int64_t f0g9 = f0 * (int64_t)g9;
    int64_t f1g0 = f1 * (int64_t)g0;
    int64_t f1g1_2 = f1_2 * (int64_t)g1;
    int64_t f1g2 = f1 * (int64_t)g2;
    int64_t f1g3_2 = f1_2 * (int64_t)g3;
    int64_t f1g4 = f1 * (int64_t)g4;
    int64_t f1g5_2 = f1_2 * (int64_t)g5;
    int64_t f1g6 = f1 * (int64_t)g6;
    int64_t f1g7_2 = f1_2 * (int64_t)g7;
    int64_t f1g8 = f1 * (int64_t)g8;
    int64_t f1g9_38 = f1_2 * (int64_t)g9_19;
    int64_t f2g0 = f2 * (int64_t)g0;
    int64_t f2g1 = f2 * (int64_t)g1;
    int64_t f2g2 = f2 * (int64_t)g2;
    int64_t f2g3 = f2 * (int64_t)g3;
    int64_t f2g4 = f2 * (int64_t)g4;
    int64_t f2g5 = f2 * (int64_t)g5;
    int64_t f2g6 = f2 * (int64_t)g6;
    int64_t f2g7 = f2 * (int64_t)g7;
    int64_t f2g8_19 = f2 * (int64_t)g8_19;
    int64_t f2g9_19 = f2 * (int64_t)g9_19;
    int64_t f3g0 = f3 * (int64_t)g0;
    int64_t f3g1_2 = f3_2 * (int64_t)g1;
    int64_t f3g2 = f3 * (int64_t)g2;
    int64_t f3g3_2 = f3_2 * (int64_t)g3;
    int64_t f3g4 = f3 * (int64_t)g4;
    int64_t f3g5_2 = f3_2 * (int64_t)g5;
    int64_t f3g6 = f3 * (int64_t)g6;
    int64_t f3g7_38 = f3_2 * (int64_t)g7_19;
    int64_t f3g8_19 = f3 * (int64_t)g8_19;
    int64_t f3g9_38 = f3_2 * (int64_t)g9_19;
    int64_t f4g0 = f4 * (int64_t)g0;
    int64_t f4g1 = f4 * (int64_t)g1;
    int64_t f4g2 = f4 * (int64_t)g2;
    int64_t f4g3 = f4 * (int64_t)g3;
    int64_t f4g4 = f4 * (int64_t)g4;
    int64_t f4g5 = f4 * (int64_t)g5;
    int64_t f4g6_19 = f4 * (int64_t)g6_19;
    int64_t f4g7_19 = f4 * (int64_t)g7_19;
    int64_t f4g8_19 = f4 * (int64_t)g8_19;
    int64_t f4g9_19 = f4 * (int64_t)g9_19;
    int64_t f5g0 = f5 * (int64_t)g0;
    int64_t f5g1_2 = f5_2 * (int64_t)g1;
    int64_t f5g2 = f5 * (int64_t)g2;
    int64_t f5g3_2 = f5_2 * (int64_t)g3;
    int64_t f5g4 = f5 * (int64_t)g4;
    int64_t f5g5_38 = f5_2 * (int64_t)g5_19;
    int64_t f5g6_19 = f5 * (int64_t)g6_19;
    int64_t f5g7_38 = f5_2 * (int64_t)g7_19;
    int64_t f5g8_19 = f5 * (int64_t)g8_19;
    int64_t f5g9_38 = f5_2 * (int64_t)g9_19;
    int64_t f6g0 = f6 * (int64_t)g0;
    int64_t f6g1 = f6 * (int64_t)g1;
    int64_t f6g2 = f6 * (int64_t)g2;
    int64_t f6g3 = f6 * (int64_t)g3;
    int64_t f6g4_19 = f6 * (int64_t)g4_19;
    int64_t f6g5_19 = f6 * (int64_t)g5_19;
    int64_t f6g6_19 = f6 * (int64_t)g6_19;
    int64_t f6g7_19 = f6 * (int64_t)g7_19;
    int64_t f6g8_19 = f6 * (int64_t)g8_19;
    int64_t f6g9_19 = f6 * (int64_t)g9_19;
    int64_t f7g0 = f7 * (int64_t)g0;
    int64_t f7g1_2 = f7_2 * (int64_t)g1;
    int64_t f7g2 = f7 * (int64_t)g2;
    int64_t f7g3_38 = f7_2 * (int64_t)g3_19;
    int64_t f7g4_19 = f7 * (int64_t)g4_19;
    int64_t f7g5_38 = f7_2 * (int64_t)g5_19;
    int64_t f7g6_19 = f7 * (int64_t)g6_19;
    int64_t f7g7_38 = f7_2 * (int64_t)g7_19;
    int64_t f7g8_19 = f7 * (int64_t)g8_19;
    int64_t f7g9_38 = f7_2 * (int64_t)g9_19;
    int64_t f8g0 = f8 * (int64_t)g0;
    int64_t f8g1 = f8 * (int64_t)g1;
    int64_t f8g2_19 = f8 * (int64_t)g2_19;
    int64_t f8g3_19 = f8 * (int64_t)g3_19;
    int64_t f8g4_19 = f8 * (int64_t)g4_19;
    int64_t f8g5_19 = f8 * (int64_t)g5_19;
    int64_t f8g6_19 = f8 * (int64_t)g6_19;
    int64_t f8g7_19 = f8 * (int64_t)g7_19;
    int64_t f8g8_19 = f8 * (int64_t)g8_19;
    int64_t f8g9_19 = f8 * (int64_t)g9_19;
    int64_t f9g0 = f9 * (int64_t)g0;
    int64_t f9g1_38 = f9_2 * (int64_t)g1_19;
    int64_t f9g2_19 = f9 * (int64_t)g2_19;
    int64_t f9g3_38 = f9_2 * (int64_t)g3_19;
    int64_t f9g4_19 = f9 * (int64_t)g4_19;
    int64_t f9g5_38 = f9_2 * (int64_t)g5_19;
    int64_t f9g6_19 = f9 * (int64_t)g6_19;
    int64_t f9g7_38 = f9_2 * (int64_t)g7_19;
    int64_t f9g8_19 = f9 * (int64_t)g8_19;
    int64_t f9g9_38 = f9_2 * (int64_t)g9_19;
    int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 +
        f8g2_19 + f9g1_38;
    int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 +
        f8g3_19 + f9g2_19;
    int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 +
        f8g4_19 + f9g3_38;
    int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 +
        f8g5_19 + f9g4_19;
    int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 +
        f8g6_19 + f9g5_38;
    int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 +
        f8g7_19 + f9g6_19;
    int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 +
        f8g8_19 + f9g7_38;
    int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 +
        f8g9_19 + f9g8_19;
    int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 +
        f8g0 + f9g9_38;
    int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 +
        f8g1 + f9g0;
    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;

    /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
     *   i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
     * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
     *   i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */

    carry0 = h0 + (1 << 25);
    h1 += carry0 >> 26;
    h0 -= carry0 & kTop38Bits;
    carry4 = h4 + (1 << 25);
    h5 += carry4 >> 26;
    h4 -= carry4 & kTop38Bits;
    /* |h0| <= 2^25 */
    /* |h4| <= 2^25 */
    /* |h1| <= 1.71*2^59 */
    /* |h5| <= 1.71*2^59 */

    carry1 = h1 + (1 << 24);
    h2 += carry1 >> 25;
    h1 -= carry1 & kTop39Bits;
    carry5 = h5 + (1 << 24);
    h6 += carry5 >> 25;
    h5 -= carry5 & kTop39Bits;
    /* |h1| <= 2^24; from now on fits into int32 */
    /* |h5| <= 2^24; from now on fits into int32 */
    /* |h2| <= 1.41*2^60 */
    /* |h6| <= 1.41*2^60 */

    carry2 = h2 + (1 << 25);
    h3 += carry2 >> 26;
    h2 -= carry2 & kTop38Bits;
    carry6 = h6 + (1 << 25);
    h7 += carry6 >> 26;
    h6 -= carry6 & kTop38Bits;
    /* |h2| <= 2^25; from now on fits into int32 unchanged */
    /* |h6| <= 2^25; from now on fits into int32 unchanged */
    /* |h3| <= 1.71*2^59 */
    /* |h7| <= 1.71*2^59 */

    carry3 = h3 + (1 << 24);
    h4 += carry3 >> 25;
    h3 -= carry3 & kTop39Bits;
    carry7 = h7 + (1 << 24);
    h8 += carry7 >> 25;
    h7 -= carry7 & kTop39Bits;
    /* |h3| <= 2^24; from now on fits into int32 unchanged */
    /* |h7| <= 2^24; from now on fits into int32 unchanged */
    /* |h4| <= 1.72*2^34 */
    /* |h8| <= 1.41*2^60 */

    carry4 = h4 + (1 << 25);
    h5 += carry4 >> 26;
    h4 -= carry4 & kTop38Bits;
    carry8 = h8 + (1 << 25);
    h9 += carry8 >> 26;
    h8 -= carry8 & kTop38Bits;
    /* |h4| <= 2^25; from now on fits into int32 unchanged */
    /* |h8| <= 2^25; from now on fits into int32 unchanged */
    /* |h5| <= 1.01*2^24 */
    /* |h9| <= 1.71*2^59 */

    carry9 = h9 + (1 << 24);
    h0 += (carry9 >> 25) * 19;
    h9 -= carry9 & kTop39Bits;
    /* |h9| <= 2^24; from now on fits into int32 unchanged */
    /* |h0| <= 1.1*2^39 */

    carry0 = h0 + (1 << 25);
    h1 += carry0 >> 26;
    h0 -= carry0 & kTop38Bits;
    /* |h0| <= 2^25; from now on fits into int32 unchanged */
    /* |h1| <= 1.01*2^24 */

    h[0] = h0;
    h[1] = h1;
    h[2] = h2;
    h[3] = h3;
    h[4] = h4;
    h[5] = h5;
    h[6] = h6;
    h[7] = h7;
    h[8] = h8;
    h[9] = h9;
}

/* h = f * f
 * Can overlap h with f.
 *
 * Preconditions:
 *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 *
 * Postconditions:
 *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
 *
 * See fe_mul.c for discussion of implementation strategy. */
static void fe_sq(fe h, const fe f)
{
    int32_t f0 = f[0];
    int32_t f1 = f[1];
    int32_t f2 = f[2];
    int32_t f3 = f[3];
    int32_t f4 = f[4];
    int32_t f5 = f[5];
    int32_t f6 = f[6];
    int32_t f7 = f[7];
    int32_t f8 = f[8];
    int32_t f9 = f[9];
    int32_t f0_2 = 2 * f0;
    int32_t f1_2 = 2 * f1;
    int32_t f2_2 = 2 * f2;
    int32_t f3_2 = 2 * f3;
    int32_t f4_2 = 2 * f4;
    int32_t f5_2 = 2 * f5;
    int32_t f6_2 = 2 * f6;
    int32_t f7_2 = 2 * f7;
    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
    int64_t f0f0 = f0 * (int64_t)f0;
    int64_t f0f1_2 = f0_2 * (int64_t)f1;
    int64_t f0f2_2 = f0_2 * (int64_t)f2;
    int64_t f0f3_2 = f0_2 * (int64_t)f3;
    int64_t f0f4_2 = f0_2 * (int64_t)f4;
    int64_t f0f5_2 = f0_2 * (int64_t)f5;
    int64_t f0f6_2 = f0_2 * (int64_t)f6;
    int64_t f0f7_2 = f0_2 * (int64_t)f7;
    int64_t f0f8_2 = f0_2 * (int64_t)f8;
    int64_t f0f9_2 = f0_2 * (int64_t)f9;
    int64_t f1f1_2 = f1_2 * (int64_t)f1;
    int64_t f1f2_2 = f1_2 * (int64_t)f2;
    int64_t f1f3_4 = f1_2 * (int64_t)f3_2;
    int64_t f1f4_2 = f1_2 * (int64_t)f4;
    int64_t f1f5_4 = f1_2 * (int64_t)f5_2;
    int64_t f1f6_2 = f1_2 * (int64_t)f6;
    int64_t f1f7_4 = f1_2 * (int64_t)f7_2;
    int64_t f1f8_2 = f1_2 * (int64_t)f8;
    int64_t f1f9_76 = f1_2 * (int64_t)f9_38;
    int64_t f2f2 = f2 * (int64_t)f2;
    int64_t f2f3_2 = f2_2 * (int64_t)f3;
    int64_t f2f4_2 = f2_2 * (int64_t)f4;
    int64_t f2f5_2 = f2_2 * (int64_t)f5;
    int64_t f2f6_2 = f2_2 * (int64_t)f6;
    int64_t f2f7_2 = f2_2 * (int64_t)f7;
    int64_t f2f8_38 = f2_2 * (int64_t)f8_19;
    int64_t f2f9_38 = f2 * (int64_t)f9_38;
    int64_t f3f3_2 = f3_2 * (int64_t)f3;
    int64_t f3f4_2 = f3_2 * (int64_t)f4;
    int64_t f3f5_4 = f3_2 * (int64_t)f5_2;
    int64_t f3f6_2 = f3_2 * (int64_t)f6;
    int64_t f3f7_76 = f3_2 * (int64_t)f7_38;
    int64_t f3f8_38 = f3_2 * (int64_t)f8_19;
    int64_t f3f9_76 = f3_2 * (int64_t)f9_38;
    int64_t f4f4 = f4 * (int64_t)f4;
    int64_t f4f5_2 = f4_2 * (int64_t)f5;
    int64_t f4f6_38 = f4_2 * (int64_t)f6_19;
    int64_t f4f7_38 = f4 * (int64_t)f7_38;
    int64_t f4f8_38 = f4_2 * (int64_t)f8_19;
    int64_t f4f9_38 = f4 * (int64_t)f9_38;
    int64_t f5f5_38 = f5 * (int64_t)f5_38;
    int64_t f5f6_38 = f5_2 * (int64_t)f6_19;
    int64_t f5f7_76 = f5_2 * (int64_t)f7_38;
    int64_t f5f8_38 = f5_2 * (int64_t)f8_19;
    int64_t f5f9_76 = f5_2 * (int64_t)f9_38;
    int64_t f6f6_19 = f6 * (int64_t)f6_19;
    int64_t f6f7_38 = f6 * (int64_t)f7_38;
    int64_t f6f8_38 = f6_2 * (int64_t)f8_19;
    int64_t f6f9_38 = f6 * (int64_t)f9_38;
    int64_t f7f7_38 = f7 * (int64_t)f7_38;
    int64_t f7f8_38 = f7_2 * (int64_t)f8_19;
    int64_t f7f9_76 = f7_2 * (int64_t)f9_38;
    int64_t f8f8_19 = f8 * (int64_t)f8_19;
    int64_t f8f9_38 = f8 * (int64_t)f9_38;
    int64_t f9f9_38 = f9 * (int64_t)f9_38;
    int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
    int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
    int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
    int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
    int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
    int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
    int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
    int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
    int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
    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;

    carry0 = h0 + (1 << 25);
    h1 += carry0 >> 26;
    h0 -= carry0 & kTop38Bits;
    carry4 = h4 + (1 << 25);
    h5 += carry4 >> 26;
    h4 -= carry4 & kTop38Bits;

    carry1 = h1 + (1 << 24);
    h2 += carry1 >> 25;
    h1 -= carry1 & kTop39Bits;
    carry5 = h5 + (1 << 24);
    h6 += carry5 >> 25;
    h5 -= carry5 & kTop39Bits;

    carry2 = h2 + (1 << 25);
    h3 += carry2 >> 26;
    h2 -= carry2 & kTop38Bits;
    carry6 = h6 + (1 << 25);
    h7 += carry6 >> 26;
    h6 -= carry6 & kTop38Bits;

    carry3 = h3 + (1 << 24);
    h4 += carry3 >> 25;
    h3 -= carry3 & kTop39Bits;
    carry7 = h7 + (1 << 24);
    h8 += carry7 >> 25;
    h7 -= carry7 & kTop39Bits;

    carry4 = h4 + (1 << 25);
    h5 += carry4 >> 26;
    h4 -= carry4 & kTop38Bits;
    carry8 = h8 + (1 << 25);
    h9 += carry8 >> 26;
    h8 -= carry8 & kTop38Bits;

    carry9 = h9 + (1 << 24);
    h0 += (carry9 >> 25) * 19;
    h9 -= carry9 & kTop39Bits;

    carry0 = h0 + (1 << 25);
    h1 += carry0 >> 26;
    h0 -= carry0 & kTop38Bits;

    h[0] = h0;
    h[1] = h1;
    h[2] = h2;
    h[3] = h3;
    h[4] = h4;
    h[5] = h5;
    h[6] = h6;
    h[7] = h7;
    h[8] = h8;
    h[9] = h9;
}

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

    fe_sq(t0, z);
    for (i = 1; i < 1; ++i)
    {
        fe_sq(t0, t0);
    }
    fe_sq(t1, t0);
    for (i = 1; i < 2; ++i)
    {
        fe_sq(t1, t1);
    }
    fe_mul(t1, z, t1);
    fe_mul(t0, t0, t1);
    fe_sq(t2, t0);
    for (i = 1; i < 1; ++i)
    {
        fe_sq(t2, t2);
    }
    fe_mul(t1, t1, t2);
    fe_sq(t2, t1);
    for (i = 1; i < 5; ++i)
    {
        fe_sq(t2, t2);
    }
    fe_mul(t1, t2, t1);
    fe_sq(t2, t1);
    for (i = 1; i < 10; ++i)
    {
        fe_sq(t2, t2);
    }
    fe_mul(t2, t2, t1);
    fe_sq(t3, t2);
    for (i = 1; i < 20; ++i)
    {
        fe_sq(t3, t3);
    }
    fe_mul(t2, t3, t2);
    fe_sq(t2, t2);
    for (i = 1; i < 10; ++i)
    {
        fe_sq(t2, t2);
    }
    fe_mul(t1, t2, t1);
    fe_sq(t2, t1);
    for (i = 1; i < 50; ++i)
    {
        fe_sq(t2, t2);
    }
    fe_mul(t2, t2, t1);
    fe_sq(t3, t2);
    for (i = 1; i < 100; ++i)
    {
        fe_sq(t3, t3);
    }
    fe_mul(t2, t3, t2);
    fe_sq(t2, t2);
    for (i = 1; i < 50; ++i)
    {
        fe_sq(t2, t2);
    }
    fe_mul(t1, t2, t1);
    fe_sq(t1, t1);
    for (i = 1; i < 5; ++i)
    {
        fe_sq(t1, t1);
    }
    fe_mul(out, t1, t0);
}

/* 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 h, const fe f)
{
    unsigned i;

    for (i = 0; i < 10; i++)
    {
        h[i] = -f[i];
    }
}

/* 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 f, const fe g, unsigned b)
{
    b = 0 - b;
    unsigned i;

    for (i = 0; i < 10; i++)
    {
        int32_t x = f[i] ^ g[i];
        x &= b;
        f[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 f)
{
    uint8_t s[32];
    fe_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;
}

/* h = 2 * f * f
 * Can overlap h with f.
 *
 * Preconditions:
 *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 *
 * Postconditions:
 *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
 *
 * See fe_mul.c for discussion of implementation strategy. */
static void fe_sq2(fe h, const fe f)
{
    int32_t f0 = f[0];
    int32_t f1 = f[1];
    int32_t f2 = f[2];
    int32_t f3 = f[3];
    int32_t f4 = f[4];
    int32_t f5 = f[5];
    int32_t f6 = f[6];
    int32_t f7 = f[7];
    int32_t f8 = f[8];
    int32_t f9 = f[9];
    int32_t f0_2 = 2 * f0;
    int32_t f1_2 = 2 * f1;
    int32_t f2_2 = 2 * f2;
    int32_t f3_2 = 2 * f3;
    int32_t f4_2 = 2 * f4;
    int32_t f5_2 = 2 * f5;
    int32_t f6_2 = 2 * f6;
    int32_t f7_2 = 2 * f7;
    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
    int64_t f0f0 = f0 * (int64_t)f0;
    int64_t f0f1_2 = f0_2 * (int64_t)f1;
    int64_t f0f2_2 = f0_2 * (int64_t)f2;
    int64_t f0f3_2 = f0_2 * (int64_t)f3;
    int64_t f0f4_2 = f0_2 * (int64_t)f4;
    int64_t f0f5_2 = f0_2 * (int64_t)f5;
    int64_t f0f6_2 = f0_2 * (int64_t)f6;
    int64_t f0f7_2 = f0_2 * (int64_t)f7;
    int64_t f0f8_2 = f0_2 * (int64_t)f8;
    int64_t f0f9_2 = f0_2 * (int64_t)f9;
    int64_t f1f1_2 = f1_2 * (int64_t)f1;
    int64_t f1f2_2 = f1_2 * (int64_t)f2;
    int64_t f1f3_4 = f1_2 * (int64_t)f3_2;
    int64_t f1f4_2 = f1_2 * (int64_t)f4;
    int64_t f1f5_4 = f1_2 * (int64_t)f5_2;
    int64_t f1f6_2 = f1_2 * (int64_t)f6;
    int64_t f1f7_4 = f1_2 * (int64_t)f7_2;
    int64_t f1f8_2 = f1_2 * (int64_t)f8;
    int64_t f1f9_76 = f1_2 * (int64_t)f9_38;
    int64_t f2f2 = f2 * (int64_t)f2;
    int64_t f2f3_2 = f2_2 * (int64_t)f3;
    int64_t f2f4_2 = f2_2 * (int64_t)f4;
    int64_t f2f5_2 = f2_2 * (int64_t)f5;
    int64_t f2f6_2 = f2_2 * (int64_t)f6;
    int64_t f2f7_2 = f2_2 * (int64_t)f7;
    int64_t f2f8_38 = f2_2 * (int64_t)f8_19;
    int64_t f2f9_38 = f2 * (int64_t)f9_38;
    int64_t f3f3_2 = f3_2 * (int64_t)f3;
    int64_t f3f4_2 = f3_2 * (int64_t)f4;
    int64_t f3f5_4 = f3_2 * (int64_t)f5_2;
    int64_t f3f6_2 = f3_2 * (int64_t)f6;
    int64_t f3f7_76 = f3_2 * (int64_t)f7_38;
    int64_t f3f8_38 = f3_2 * (int64_t)f8_19;
    int64_t f3f9_76 = f3_2 * (int64_t)f9_38;
    int64_t f4f4 = f4 * (int64_t)f4;
    int64_t f4f5_2 = f4_2 * (int64_t)f5;
    int64_t f4f6_38 = f4_2 * (int64_t)f6_19;
    int64_t f4f7_38 = f4 * (int64_t)f7_38;
    int64_t f4f8_38 = f4_2 * (int64_t)f8_19;
    int64_t f4f9_38 = f4 * (int64_t)f9_38;
    int64_t f5f5_38 = f5 * (int64_t)f5_38;
    int64_t f5f6_38 = f5_2 * (int64_t)f6_19;
    int64_t f5f7_76 = f5_2 * (int64_t)f7_38;
    int64_t f5f8_38 = f5_2 * (int64_t)f8_19;
    int64_t f5f9_76 = f5_2 * (int64_t)f9_38;
    int64_t f6f6_19 = f6 * (int64_t)f6_19;
    int64_t f6f7_38 = f6 * (int64_t)f7_38;
    int64_t f6f8_38 = f6_2 * (int64_t)f8_19;
    int64_t f6f9_38 = f6 * (int64_t)f9_38;
    int64_t f7f7_38 = f7 * (int64_t)f7_38;
    int64_t f7f8_38 = f7_2 * (int64_t)f8_19;
    int64_t f7f9_76 = f7_2 * (int64_t)f9_38;
    int64_t f8f8_19 = f8 * (int64_t)f8_19;
    int64_t f8f9_38 = f8 * (int64_t)f9_38;
    int64_t f9f9_38 = f9 * (int64_t)f9_38;
    int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
    int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
    int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
    int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
    int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
    int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
    int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
    int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
    int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
    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;

    h0 += h0;
    h1 += h1;
    h2 += h2;
    h3 += h3;
    h4 += h4;
    h5 += h5;
    h6 += h6;
    h7 += h7;
    h8 += h8;
    h9 += h9;

    carry0 = h0 + (1 << 25);
    h1 += carry0 >> 26;
    h0 -= carry0 & kTop38Bits;
    carry4 = h4 + (1 << 25);
    h5 += carry4 >> 26;
    h4 -= carry4 & kTop38Bits;

    carry1 = h1 + (1 << 24);
    h2 += carry1 >> 25;
    h1 -= carry1 & kTop39Bits;
    carry5 = h5 + (1 << 24);
    h6 += carry5 >> 25;
    h5 -= carry5 & kTop39Bits;

    carry2 = h2 + (1 << 25);
    h3 += carry2 >> 26;
    h2 -= carry2 & kTop38Bits;
    carry6 = h6 + (1 << 25);
    h7 += carry6 >> 26;
    h6 -= carry6 & kTop38Bits;

    carry3 = h3 + (1 << 24);
    h4 += carry3 >> 25;
    h3 -= carry3 & kTop39Bits;
    carry7 = h7 + (1 << 24);
    h8 += carry7 >> 25;
    h7 -= carry7 & kTop39Bits;

    carry4 = h4 + (1 << 25);
    h5 += carry4 >> 26;
    h4 -= carry4 & kTop38Bits;
    carry8 = h8 + (1 << 25);
    h9 += carry8 >> 26;
    h8 -= carry8 & kTop38Bits;

    carry9 = h9 + (1 << 24);
    h0 += (carry9 >> 25) * 19;
    h9 -= carry9 & kTop39Bits;

    carry0 = h0 + (1 << 25);
    h1 += carry0 >> 26;
    h0 -= carry0 & kTop38Bits;

    h[0] = h0;
    h[1] = h1;
    h[2] = h2;
    h[3] = h3;
    h[4] = h4;
    h[5] = h5;
    h[6] = h6;
    h[7] = h7;
    h[8] = h8;
    h[9] = h9;
}

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

    fe_sq(t0, z);
    for (i = 1; i < 1; ++i)
    {
        fe_sq(t0, t0);
    }
    fe_sq(t1, t0);
    for (i = 1; i < 2; ++i)
    {
        fe_sq(t1, t1);
    }
    fe_mul(t1, z, t1);
    fe_mul(t0, t0, t1);
    fe_sq(t0, t0);
    for (i = 1; i < 1; ++i)
    {
        fe_sq(t0, t0);
    }
    fe_mul(t0, t1, t0);
    fe_sq(t1, t0);
    for (i = 1; i < 5; ++i)
    {
        fe_sq(t1, t1);
    }
    fe_mul(t0, t1, t0);
    fe_sq(t1, t0);
    for (i = 1; i < 10; ++i)
    {
        fe_sq(t1, t1);
    }
    fe_mul(t1, t1, t0);
    fe_sq(t2, t1);
    for (i = 1; i < 20; ++i)
    {
        fe_sq(t2, t2);
    }
    fe_mul(t1, t2, t1);
    fe_sq(t1, t1);
    for (i = 1; i < 10; ++i)
    {
        fe_sq(t1, t1);
    }
    fe_mul(t0, t1, t0);
    fe_sq(t1, t0);
    for (i = 1; i < 50; ++i)
    {
        fe_sq(t1, t1);
    }
    fe_mul(t1, t1, t0);
    fe_sq(t2, t1);
    for (i = 1; i < 100; ++i)
    {
        fe_sq(t2, t2);
    }
    fe_mul(t1, t2, t1);
    fe_sq(t1, t1);
    for (i = 1; i < 50; ++i)
    {
        fe_sq(t1, t1);
    }
    fe_mul(t0, t1, t0);
    fe_sq(t0, t0);
    for (i = 1; i < 2; ++i)
    {
        fe_sq(t0, t0);
    }
    fe_mul(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(x, h->X, recip);
    fe_mul(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(x, h->X, recip);
    fe_mul(y, h->Y, recip);
    fe_tobytes(s, y);
    s[31] ^= fe_isnegative(x) << 7;
}

static const fe d = { -10913610, 13857413, -15372611, 6949391, 114729,
    -8787816, -6275908, -3247719, -18696448, -12055116 };

static const fe sqrtm1 = { -32595792, -7943725, 9377950, 3500415, 12389472,
    -272473, -25146209, -2005654, 326686, 11406482 };

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

    fe_frombytes(h->Y, s);
    fe_1(h->Z);
    fe_sq(u, h->Y);
    fe_mul(v, u, d);
    fe_sub(u, u, h->Z); /* u = y^2-1 */
    fe_add(v, v, h->Z); /* v = dy^2+1 */

    fe_sq(v3, v);
    fe_mul(v3, v3, v); /* v3 = v^3 */
    fe_sq(h->X, v3);
    fe_mul(h->X, h->X, v);
    fe_mul(h->X, h->X, u); /* x = uv^7 */

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

    fe_sq(vxx, h->X);
    fe_mul(vxx, vxx, v);
    fe_sub(check, vxx, u); /* vx^2-u */
    if (fe_isnonzero(check))
    {
        fe_add(check, vxx, u); /* vx^2+u */
        if (fe_isnonzero(check))
        {
            return -1;
        }
        fe_mul(h->X, h->X, sqrtm1);
    }

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

    fe_mul(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_1(h->YplusX);
    fe_1(h->YminusX);
    fe_1(h->Z);
    fe_0(h->T2d);
}

static void ge_precomp_0(ge_precomp* h)
{
    fe_1(h->yplusx);
    fe_1(h->yminusx);
    fe_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 = { -21827239, -5839606, -30745221, 13898782, 229458,
    15978800, -12551817, -6495438, 29715968, 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(r->Z, p->Z);
    fe_mul(r->T2d, p->T, d2);
}

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

/* r = p */
void x25519_ge_p1p1_to_p3(ge_p3* r, const ge_p1p1* p)
{
    fe_mul(r->X, p->X, p->T);
    fe_mul(r->Y, p->Y, p->Z);
    fe_mul(r->Z, p->Z, p->T);
    fe_mul(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 t0;

    fe_sq(r->X, p->X);
    fe_sq(r->Z, p->Y);
    fe_sq2(r->T, p->Z);
    fe_add(r->Y, p->X, p->Y);
    fe_sq(t0, r->Y);
    fe_add(r->Y, r->Z, r->X);
    fe_sub(r->Z, r->Z, r->X);
    fe_sub(r->X, t0, r->Y);
    fe_sub(r->T, r->T, r->Z);
}

/* 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 t0;

    fe_add(r->X, p->Y, p->X);
    fe_sub(r->Y, p->Y, p->X);
    fe_mul(r->Z, r->X, q->yplusx);
    fe_mul(r->Y, r->Y, q->yminusx);
    fe_mul(r->T, q->xy2d, p->T);
    fe_add(t0, p->Z, p->Z);
    fe_sub(r->X, r->Z, r->Y);
    fe_add(r->Y, r->Z, r->Y);
    fe_add(r->Z, t0, r->T);
    fe_sub(r->T, t0, r->T);
}

/* r = p - q */
static void ge_msub(ge_p1p1* r, const ge_p3* p, const ge_precomp* q)
{
    fe t0;

    fe_add(r->X, p->Y, p->X);
    fe_sub(r->Y, p->Y, p->X);
    fe_mul(r->Z, r->X, q->yminusx);
    fe_mul(r->Y, r->Y, q->yplusx);
    fe_mul(r->T, q->xy2d, p->T);
    fe_add(t0, p->Z, p->Z);
    fe_sub(r->X, r->Z, r->Y);
    fe_add(r->Y, r->Z, r->Y);
    fe_sub(r->Z, t0, r->T);
    fe_add(r->T, t0, r->T);
}

/* r = p + q */
void x25519_ge_add(ge_p1p1* r, const ge_p3* p, const ge_cached* q)
{
    fe t0;

    fe_add(r->X, p->Y, p->X);
    fe_sub(r->Y, p->Y, p->X);
    fe_mul(r->Z, r->X, q->YplusX);
    fe_mul(r->Y, r->Y, q->YminusX);
    fe_mul(r->T, q->T2d, p->T);
    fe_mul(r->X, p->Z, q->Z);
    fe_add(t0, r->X, r->X);
    fe_sub(r->X, r->Z, r->Y);
    fe_add(r->Y, r->Z, r->Y);
    fe_add(r->Z, t0, r->T);
    fe_sub(r->T, t0, r->T);
}

/* r = p - q */
void x25519_ge_sub(ge_p1p1* r, const ge_p3* p, const ge_cached* q)
{
    fe t0;

    fe_add(r->X, p->Y, p->X);
    fe_sub(r->Y, p->Y, p->X);
    fe_mul(r->Z, r->X, q->YminusX);
    fe_mul(r->Y, r->Y, q->YplusX);
    fe_mul(r->T, q->T2d, p->T);
    fe_mul(r->X, p->Z, q->Z);
    fe_add(t0, r->X, r->X);
    fe_sub(r->X, r->Z, r->Y);
    fe_add(r->Y, r->Z, r->Y);
    fe_sub(r->Z, t0, r->T);
    fe_add(r->T, t0, r->T);
}

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(out->xy2d, x, y);
        fe_mul(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,
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    0xec,
    0x31,
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    0xb0,
    0x53,
    0x60,
    0xc3,
    0x8c,
    0xbe,
    0xc1,
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    0x88,
    0x2b,
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};

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, -14356035, 29566456, 3660896, -12694345, 4014787,
                27544626, -11754271, -6079156, 2047605 },
            { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
                5043384, 19500929, -15469378 },
            { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
                29287919, 11864899, -24514362, -4438546 },
        },
        {
            { -12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
                -11717903, -3814571, -358445, -10211303 },
            { -21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
                -15616551, 11189268, -26829678, -5319081 },
            { 26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
                -3128826, -9541118, -15472047, -4166697 },
        },
        {
            { 15636291, -9688557, 24204773, -7912398, 616977, -16685262,
                27787600, -14772189, 28944400, -1550024 },
            { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
                16354577, -11775962, 7689662, 11199574 },
            { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
                7512774, 10017326, -17749093, -9920357 },
        },
        {
            { -17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
                -28926210, 15006023, 3284568, -6276540 },
            { 23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
                7464579, 9656445, 13059162, 10374397 },
            { 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
                -3839045, -641708, -101325 },
        },
        {
            { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
                32867885, 14515107, -15438304, 10819380 },
            { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
                12483688, -12668491, 5581306 },
            { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
                28542350, 13850243, -23678021, -15815942 },
        },
        {
            { -15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
                -19188627, -15224819, -9818940, -12085777 },
            { -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
                -15689887, 1762328, 14866737 },
            { -18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
                -28236412, 3959421, 27914454, 4383652 },
        },
        {
            { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
                5230134, -23952439, -15175766 },
            { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
                20654025, 16520125, 30598449, 7715701 },
            { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
                -31400660, 1370708, 29794553, -1409300 },
        },
        {
            { 14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
                30290735, 10876454, -33154098, 2381726 },
            { -7195431, -2655363, -14730155, 462251, -27724326, 3941372,
                -6236617, 3696005, -32300832, 15351955 },
            { 27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
                -32961401, -2970515, 29551813, 10109425 },
        },
    },
    {
        {
            { -13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
                -2378284, -1627556, 10092783, -4764171 },
            { 27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
                -32508754, 12005538, -17810127, 12803510 },
            { 17228999, -15661624, -1233527, 300140, -1224870, -11714777,
                30364213, -9038194, 18016357, 4397660 },
        },
        {
            { -10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
                -26619106, 14544525, -17477504, 982639 },
            { 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
                -4120128, -21047696, 9934963 },
            { 5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
                -14747930, 4559895, -30123922, -10897950 },
        },
        {
            { -27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
                24191034, 4541697, -13338309, 5500568 },
            { 12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
                -17430592, 12264343, 10874051, 13524335 },
            { 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
                5080568, -22528059, 5376628 },
        },
        {
            { -26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
                -22321305, -9447443, 4535768, 1569007 },
            { -2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
                -30494562, 3044290, 31848280, 12543772 },
            { -22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
                -27377195, -2062731, 7718482, 14474653 },
        },
        {
            { 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
                -7236665, 24316168, -5253567 },
            { 13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
                33040651, -13424532, -20729456, 8321686 },
            { 21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
                23845965, -11874838, -9984458, 608372 },
        },
        {
            { -13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
                1123968, -6780577, 27229399, 23887 },
            { -23244140, -294205, -11744728, 14712571, -29465699, -2029617,
                12797024, -6440308, -1633405, 16678954 },
            { -29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
                -1508144, -4795045, -17169265, 4904953 },
        },
        {
            { 24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
                5169211, 16191880, 2128236, -4326833 },
            { -16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
                -29806336, 916033, -6882542, -2986532 },
            { -22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
                285431, 2763829, 15736322, 4143876 },
        },
        {
            { 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
                -14594663, 23527084, -16458268 },
            { 33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
                -32625340, 4087881, -15188911, -14416214 },
            { 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
                4357868, -4774191, -16323038 },
        },
    },
    {
        {
            { 6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
                23365147, -3949732, 7390890, 2759800 },
            { 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
                -4264057, 1244380, -12919645 },
            { -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
                9208236, 15886429, 16489664 },
        },
        {
            { 1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
                -13693198, 398369, -30606455, -712933 },
            { -25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
                13348553, 12076947, -30836462, 5113182 },
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                -31135347, -16049879, 10928917, 3011958 },
            { -6957757, -15594337, 31696059, 334240, 29576716, 14796075,
                -30831056, -12805180, 18008031, 10258577 },
        },
        {
            { -22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
                -1853465, 1367120, 25127874, 6671743 },
            { 29701166, -14373934, -10878120, 9279288, -17568, 13127210,
                21382910, 11042292, 25838796, 4642684 },
            { -20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
                30468147, -13900640, 18423289, 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(minust.yplusx, t->yminusx);
    fe_copy(minust.yminusx, t->yplusx);
    fe_neg(minust.xy2d, t->xy2d);
    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, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
            -11754271, -6079156, 2047605 },
        { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
            5043384, 19500929, -15469378 },
        { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
            11864899, -24514362, -4438546 },
    },
    {
        { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
            -14772189, 28944400, -1550024 },
        { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
            -11775962, 7689662, 11199574 },
        { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
            10017326, -17749093, -9920357 },
    },
    {
        { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
            14515107, -15438304, 10819380 },
        { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
            12483688, -12668491, 5581306 },
        { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
            13850243, -23678021, -15815942 },
    },
    {
        { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
            5230134, -23952439, -15175766 },
        { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
            16520125, 30598449, 7715701 },
        { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
            1370708, 29794553, -1409300 },
    },
    {
        { -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
            -1361450, -13062696, 13821877 },
        { -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
            -7212327, 18853322, -14220951 },
        { 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
            -10431137, 2207753, -3209784 },
    },
    {
        { -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
            -663000, -31111463, -16132436 },
        { 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
            15725684, 171356, 6466918 },
        { 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
            -14088058, -30714912, 16193877 },
    },
    {
        { -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
            4729455, -18074513, 9256800 },
        { -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
            9761698, -19827198, 630305 },
        { -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
            -15960994, -2449256, -14291300 },
    },
    {
        { -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
            15033784, 25105118, -7894876 },
        { -24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
            1573892, -2625887, 2198790, -15804619 },
        { -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
            -16236442, -32461234, -12290683 },
    },
};

/* 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;
}

int ED25519_keypair(
    uint8_t out_public_key[32], uint8_t out_private_key[64],
    vccrypt_prng_context_t* prng_ctx, vccrypt_hash_options_t* sha512_opts)
{
    int retval = 0;

    /* generate a seed for this keypair */
    uint8_t seed[32];
    if (0 != vccrypt_prng_read_c(prng_ctx, seed, 32))
    {
        retval = 1;
        goto cleanup;
    }

    /* create output buffer for sha-512 */
    vccrypt_buffer_t az_buf;
    if (0 != vccrypt_buffer_init(&az_buf, sha512_opts->alloc_opts, 64))
    {
        retval = 2;
        goto cleanup;
    }

    /* create SHA-512 context for AZ */
    vccrypt_hash_context_t sha512_ctx;
    if (0 != vccrypt_hash_init(sha512_opts, &sha512_ctx))
    {
        retval = 3;
        goto az_buf_cleanup;
    }
    /* add data to the digest */
    if (0 != vccrypt_hash_digest(&sha512_ctx, seed, 32))
    {
        retval = 4;
        goto sha512_ctx_cleanup;
    }
    /* finalize the digest */
    if (0 != vccrypt_hash_finalize(&sha512_ctx, &az_buf))
    {
        retval = 5;
        goto sha512_ctx_cleanup;
    }

    uint8_t* az = (uint8_t*)az_buf.data;

    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);

    memcpy(out_private_key, seed, 32);
    memmove(out_private_key + 32, out_public_key, 32);

sha512_ctx_cleanup:
    dispose((disposable_t*)&sha512_ctx);

az_buf_cleanup:
    dispose((disposable_t*)&az_buf);

cleanup:
    return retval;
}

int ED25519_sign(
    uint8_t* out_sig, const uint8_t* message, size_t message_len,
    const uint8_t private_key[64], vccrypt_hash_options_t* sha512_opts)
{
    int retval = 0;

    /* create the output buffer for the SHA-512 az operation */
    vccrypt_buffer_t az_buf;
    if (0 != vccrypt_buffer_init(&az_buf, sha512_opts->alloc_opts, 64))
    {
        retval = 2;
        goto cleanup;
    }
    /* create SHA-512 context for AZ */
    vccrypt_hash_context_t sha512_ctx;
    if (0 != vccrypt_hash_init(sha512_opts, &sha512_ctx))
    {
        retval = 3;
        goto az_buf_cleanup;
    }
    /* add data to digest */
    if (0 != vccrypt_hash_digest(&sha512_ctx, private_key, 32))
    {
        retval = 4;
        goto sha512_ctx_cleanup;
    }
    /* finalize the digest */
    if (0 != vccrypt_hash_finalize(&sha512_ctx, &az_buf))
    {
        retval = 5;
        goto sha512_ctx_cleanup;
    }

    uint8_t* az = (uint8_t*)az_buf.data;

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

    /* re-use the sha-context by disposing and re-initializing. */
    dispose((disposable_t*)&sha512_ctx);
    /* create SHA-512 context for nonce */
    if (0 != vccrypt_hash_init(sha512_opts, &sha512_ctx))
    {
        retval = 6;
        goto az_buf_cleanup;
    }
    /* create the output buffer for the nonce */
    vccrypt_buffer_t nonce_buf;
    if (0 != vccrypt_buffer_init(&nonce_buf, sha512_opts->alloc_opts, 64))
    {
        retval = 7;
        goto sha512_ctx_cleanup;
    }
    /* add az subset to digest */
    if (0 != vccrypt_hash_digest(&sha512_ctx, az + 32, 32))
    {
        retval = 8;
        goto nonce_cleanup;
    }
    /* add message to the digest */
    if (0 != vccrypt_hash_digest(&sha512_ctx, message, message_len))
    {
        retval = 9;
        goto nonce_cleanup;
    }
    /* finalize the digest */
    if (0 != vccrypt_hash_finalize(&sha512_ctx, &nonce_buf))
    {
        retval = 10;
        goto nonce_cleanup;
    }

    uint8_t* nonce = (uint8_t*)nonce_buf.data;

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

    /* re-use the sha-context by disposing and re-initializing. */
    dispose((disposable_t*)&sha512_ctx);
    /* create SHA-512 context for nonce */
    if (0 != vccrypt_hash_init(sha512_opts, &sha512_ctx))
    {
        retval = 11;
        dispose((disposable_t*)&nonce_buf);
        goto az_buf_cleanup;
    }
    /* create the output buffer for the hram */
    vccrypt_buffer_t hram_buf;
    if (0 != vccrypt_buffer_init(&hram_buf, sha512_opts->alloc_opts, 64))
    {
        retval = 12;
        goto nonce_cleanup;
    }
    /* add out_sig to the digest */
    if (0 != vccrypt_hash_digest(&sha512_ctx, out_sig, 32))
    {
        retval = 13;
        goto hram_cleanup;
    }
    /* add public key to the digest (last 32 bytes of private key) */
    if (0 != vccrypt_hash_digest(&sha512_ctx, private_key + 32, 32))
    {
        retval = 14;
        goto hram_cleanup;
    }
    /* add message to the digest */
    if (0 != vccrypt_hash_digest(&sha512_ctx, message, message_len))
    {
        retval = 15;
        goto hram_cleanup;
    }
    /* finalize the hram digest */
    if (0 != vccrypt_hash_finalize(&sha512_ctx, &hram_buf))
    {
        retval = 16;
        goto hram_cleanup;
    }

    uint8_t* hram = (uint8_t*)hram_buf.data;

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

hram_cleanup:
    dispose((disposable_t*)&hram_buf);

nonce_cleanup:
    dispose((disposable_t*)&nonce_buf);

sha512_ctx_cleanup:
    dispose((disposable_t*)&sha512_ctx);

az_buf_cleanup:
    dispose((disposable_t*)&az_buf);

cleanup:
    return retval;
}

int ED25519_verify(
    const uint8_t* message, size_t message_len, const uint8_t signature[64],
    const uint8_t public_key[32], vccrypt_hash_options_t* sha512_opts)
{
    int retval = 99;
    ge_p3 A;

    if ((signature[63] & 224) != 0 || x25519_ge_frombytes_vartime(&A, public_key) != 0)
    {
        return 1;
    }

    fe_neg(A.X, A.X);
    fe_neg(A.T, A.T);

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

    /* create the output buffer for SHA-512 hash verify */
    vccrypt_buffer_t h_buf;
    if (0 != vccrypt_buffer_init(&h_buf, sha512_opts->alloc_opts, 64))
    {
        retval = 2;
        goto cleanup;
    }
    /* create SHA-512 context for hash verify */
    vccrypt_hash_context_t sha512_ctx;
    if (0 != vccrypt_hash_init(sha512_opts, &sha512_ctx))
    {
        retval = 3;
        goto h_buf_cleanup;
    }
    /* add signature subset to digest */
    if (0 != vccrypt_hash_digest(&sha512_ctx, signature, 32))
    {
        retval = 4;
        goto sha512_ctx_cleanup;
    }
    /* add public key to digest */
    if (0 != vccrypt_hash_digest(&sha512_ctx, public_key, 32))
    {
        retval = 5;
        goto sha512_ctx_cleanup;
    }
    /* add message to digest */
    if (0 != vccrypt_hash_digest(&sha512_ctx, message, message_len))
    {
        retval = 6;
        goto sha512_ctx_cleanup;
    }
    /* finalize the digest */
    if (0 != vccrypt_hash_finalize(&sha512_ctx, &h_buf))
    {
        retval = 7;
        goto sha512_ctx_cleanup;
    }

    uint8_t* h = (uint8_t*)h_buf.data;

    x25519_sc_reduce(h);

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

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

    retval = crypto_memcmp(rcheck, rcopy, sizeof(rcheck));

sha512_ctx_cleanup:
    dispose((disposable_t*)&sha512_ctx);

h_buf_cleanup:
    dispose((disposable_t*)&h_buf);

cleanup:
    return retval;
}

/* 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++)
    {
        int32_t x = f[i] ^ g[i];
        x &= b;
        f[i] ^= x;
        g[i] ^= x;
    }
}

/* h = f * 121666
 * Can overlap h with f.
 *
 * Preconditions:
 *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,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_mul121666(fe h, fe f)
{
    int32_t f0 = f[0];
    int32_t f1 = f[1];
    int32_t f2 = f[2];
    int32_t f3 = f[3];
    int32_t f4 = f[4];
    int32_t f5 = f[5];
    int32_t f6 = f[6];
    int32_t f7 = f[7];
    int32_t f8 = f[8];
    int32_t f9 = f[9];
    int64_t h0 = f0 * (int64_t)121666;
    int64_t h1 = f1 * (int64_t)121666;
    int64_t h2 = f2 * (int64_t)121666;
    int64_t h3 = f3 * (int64_t)121666;
    int64_t h4 = f4 * (int64_t)121666;
    int64_t h5 = f5 * (int64_t)121666;
    int64_t h6 = f6 * (int64_t)121666;
    int64_t h7 = f7 * (int64_t)121666;
    int64_t h8 = f8 * (int64_t)121666;
    int64_t h9 = f9 * (int64_t)121666;
    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;

    carry9 = h9 + (1 << 24);
    h0 += (carry9 >> 25) * 19;
    h9 -= carry9 & kTop39Bits;
    carry1 = h1 + (1 << 24);
    h2 += carry1 >> 25;
    h1 -= carry1 & kTop39Bits;
    carry3 = h3 + (1 << 24);
    h4 += carry3 >> 25;
    h3 -= carry3 & kTop39Bits;
    carry5 = h5 + (1 << 24);
    h6 += carry5 >> 25;
    h5 -= carry5 & kTop39Bits;
    carry7 = h7 + (1 << 24);
    h8 += carry7 >> 25;
    h7 -= carry7 & kTop39Bits;

    carry0 = h0 + (1 << 25);
    h1 += carry0 >> 26;
    h0 -= carry0 & kTop38Bits;
    carry2 = h2 + (1 << 25);
    h3 += carry2 >> 26;
    h2 -= carry2 & kTop38Bits;
    carry4 = h4 + (1 << 25);
    h5 += carry4 >> 26;
    h4 -= carry4 & kTop38Bits;
    carry6 = h6 + (1 << 25);
    h7 += carry6 >> 26;
    h6 -= carry6 & kTop38Bits;
    carry8 = h8 + (1 << 25);
    h9 += carry8 >> 26;
    h8 -= carry8 & kTop38Bits;

    h[0] = h0;
    h[1] = h1;
    h[2] = h2;
    h[3] = h3;
    h[4] = h4;
    h[5] = h5;
    h[6] = h6;
    h[7] = h7;
    h[8] = h8;
    h[9] = h9;
}

void x25519_scalar_mult(
    uint8_t out[32], const uint8_t scalar[32], const uint8_t point[32])
{
    fe x1, x2, z2, x3, z3, tmp0, tmp1;

    uint8_t e[32];
    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(tmp0, x3, z3);
        fe_sub(tmp1, x2, z2);
        fe_add(x2, x2, z2);
        fe_add(z2, x3, z3);
        fe_mul(z3, tmp0, x2);
        fe_mul(z2, z2, tmp1);
        fe_sq(tmp0, tmp1);
        fe_sq(tmp1, x2);
        fe_add(x3, z3, z2);
        fe_sub(z2, z3, z2);
        fe_mul(x2, tmp1, tmp0);
        fe_sub(tmp1, tmp1, tmp0);
        fe_sq(z2, z2);
        fe_mul121666(z3, tmp1);
        fe_sq(x3, x3);
        fe_add(tmp0, tmp0, z3);
        fe_mul(z3, x1, z2);
        fe_mul(z2, tmp1, tmp0);
    }
    fe_cswap(x2, x3, swap);
    fe_cswap(z2, z3, swap);

    fe_invert(z2, z2);
    fe_mul(x2, x2, z2);
    fe_tobytes(out, x2);
}

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);
}

int X25519_keypair(
    uint8_t out_public_value[X25519_KEY_LENGTH],
    uint8_t out_private_key[X25519_KEY_LENGTH],
    vccrypt_prng_context_t* prng_ctx)
{
    /* 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. */
    if (0 != vccrypt_prng_read_c(prng_ctx, out_private_key, 32))
    {
        return 1;
    }

    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);

    return 0;
}

int X25519(
    uint8_t out_shared_key[X25519_KEY_LENGTH],
    const uint8_t private_key[X25519_KEY_LENGTH],
    const uint8_t peer_public_value[X25519_KEY_LENGTH])
{
    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;
}
