Fixed comment.

[BearSSL] / src / ec / ec_c25519_m64.c

/*
 * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
 *
 * Permission is hereby granted, free of charge, to any person obtaining 
 * a copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 *
 * The above copyright notice and this permission notice shall be 
 * included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 */

#include "inner.h"

#if BR_INT128 || BR_UMUL128

#if BR_UMUL128
#include <intrin.h>
#endif

static const unsigned char GEN[] = {
        0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
};

static const unsigned char ORDER[] = {
        0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
        0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
        0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
        0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
};

static const unsigned char *
api_generator(int curve, size_t *len)
{
        (void)curve;
        *len = 32;
        return GEN;
}

static const unsigned char *
api_order(int curve, size_t *len)
{
        (void)curve;
        *len = 32;
        return ORDER;
}

static size_t
api_xoff(int curve, size_t *len)
{
        (void)curve;
        *len = 32;
        return 0;
}

/*
 * A field element is encoded as four 64-bit integers, in basis 2^63.
 * Operations return partially reduced values, which may range up to
 * 2^255+37.
 */

#define MASK63   (((uint64_t)1 << 63) - (uint64_t)1)

/*
 * Swap two field elements, conditionally on a flag.
 */
static inline void
f255_cswap(uint64_t *a, uint64_t *b, uint32_t ctl)
{
        uint64_t m, w;

        m = -(uint64_t)ctl;
        w = m & (a[0] ^ b[0]); a[0] ^= w; b[0] ^= w;
        w = m & (a[1] ^ b[1]); a[1] ^= w; b[1] ^= w;
        w = m & (a[2] ^ b[2]); a[2] ^= w; b[2] ^= w;
        w = m & (a[3] ^ b[3]); a[3] ^= w; b[3] ^= w;
}

/*
 * Addition in the field.
 */
static inline void
f255_add(uint64_t *d, const uint64_t *a, const uint64_t *b)
{
#if BR_INT128

        uint64_t t0, t1, t2, t3, cc;
        unsigned __int128 z;

        z = (unsigned __int128)a[0] + (unsigned __int128)b[0];
        t0 = (uint64_t)z;
        z = (unsigned __int128)a[1] + (unsigned __int128)b[1] + (z >> 64);
        t1 = (uint64_t)z;
        z = (unsigned __int128)a[2] + (unsigned __int128)b[2] + (z >> 64);
        t2 = (uint64_t)z;
        z = (unsigned __int128)a[3] + (unsigned __int128)b[3] + (z >> 64);
        t3 = (uint64_t)z & MASK63;
        cc = (uint64_t)(z >> 63);

        /*
         * Since operands are at most 2^255+37, the sum is at most
         * 2^256+74; thus, the carry cc is equal to 0, 1 or 2.
         *
         * We use: 2^255 = 19 mod p.
         * Since we add 0, 19 or 38 to a value that fits on 255 bits,
         * the result is at most 2^255+37.
         */
        z = (unsigned __int128)t0 + (unsigned __int128)(19 * cc);
        d[0] = (uint64_t)z;
        z = (unsigned __int128)t1 + (z >> 64);
        d[1] = (uint64_t)z;
        z = (unsigned __int128)t2 + (z >> 64);
        d[2] = (uint64_t)z;
        d[3] = t3 + (uint64_t)(z >> 64);

#elif BR_UMUL128

        uint64_t t0, t1, t2, t3, cc;
        unsigned char k;

        k = _addcarry_u64(0, a[0], b[0], &t0);
        k = _addcarry_u64(k, a[1], b[1], &t1);
        k = _addcarry_u64(k, a[2], b[2], &t2);
        k = _addcarry_u64(k, a[3], b[3], &t3);
        cc = (k << 1) + (t3 >> 63);
        t3 &= MASK63;

        /*
         * Since operands are at most 2^255+37, the sum is at most
         * 2^256+74; thus, the carry cc is equal to 0, 1 or 2.
         *
         * We use: 2^255 = 19 mod p.
         * Since we add 0, 19 or 38 to a value that fits on 255 bits,
         * the result is at most 2^255+37.
         */
        k = _addcarry_u64(0, t0, 19 * cc, &d[0]);
        k = _addcarry_u64(k, t1, 0, &d[1]);
        k = _addcarry_u64(k, t2, 0, &d[2]);
        (void)_addcarry_u64(k, t3, 0, &d[3]);

#endif
}

/*
 * Subtraction.
 */
static inline void
f255_sub(uint64_t *d, const uint64_t *a, const uint64_t *b)
{
#if BR_INT128

        /*
         * We compute t = 2^256 - 38 + a - b, which is necessarily
         * positive but lower than 2^256 + 2^255, since a <= 2^255 + 37
         * and b <= 2^255 + 37. We then subtract 0, p or 2*p, depending
         * on the two upper bits of t (bits 255 and 256).
         */

        uint64_t t0, t1, t2, t3, t4, cc;
        unsigned __int128 z;

        z = (unsigned __int128)a[0] - (unsigned __int128)b[0] - 38;
        t0 = (uint64_t)z;
        cc = -(uint64_t)(z >> 64);
        z = (unsigned __int128)a[1] - (unsigned __int128)b[1]
                - (unsigned __int128)cc;
        t1 = (uint64_t)z;
        cc = -(uint64_t)(z >> 64);
        z = (unsigned __int128)a[2] - (unsigned __int128)b[2]
                - (unsigned __int128)cc;
        t2 = (uint64_t)z;
        cc = -(uint64_t)(z >> 64);
        z = (unsigned __int128)a[3] - (unsigned __int128)b[3]
                - (unsigned __int128)cc;
        t3 = (uint64_t)z;
        t4 = 1 + (uint64_t)(z >> 64);

        /*
         * We have a 257-bit result. The two top bits can be 00, 01 or 10,
         * but not 11 (value t <= 2^256 - 38 + 2^255 + 37 = 2^256 + 2^255 - 1).
         * Therefore, we can truncate to 255 bits, and add 0, 19 or 38.
         * This guarantees that the result is at most 2^255+37.
         */
        cc = (38 & -t4) + (19 & -(t3 >> 63));
        t3 &= MASK63;
        z = (unsigned __int128)t0 + (unsigned __int128)cc;
        d[0] = (uint64_t)z;
        z = (unsigned __int128)t1 + (z >> 64);
        d[1] = (uint64_t)z;
        z = (unsigned __int128)t2 + (z >> 64);
        d[2] = (uint64_t)z;
        d[3] = t3 + (uint64_t)(z >> 64);

#elif BR_UMUL128

        /*
         * We compute t = 2^256 - 38 + a - b, which is necessarily
         * positive but lower than 2^256 + 2^255, since a <= 2^255 + 37
         * and b <= 2^255 + 37. We then subtract 0, p or 2*p, depending
         * on the two upper bits of t (bits 255 and 256).
         */

        uint64_t t0, t1, t2, t3, t4;
        unsigned char k;

        k = _subborrow_u64(0, a[0], b[0], &t0);
        k = _subborrow_u64(k, a[1], b[1], &t1);
        k = _subborrow_u64(k, a[2], b[2], &t2);
        k = _subborrow_u64(k, a[3], b[3], &t3);
        (void)_subborrow_u64(k, 1, 0, &t4);

        k = _subborrow_u64(0, t0, 38, &t0);
        k = _subborrow_u64(k, t1, 0, &t1);
        k = _subborrow_u64(k, t2, 0, &t2);
        k = _subborrow_u64(k, t3, 0, &t3);
        (void)_subborrow_u64(k, t4, 0, &t4);

        /*
         * We have a 257-bit result. The two top bits can be 00, 01 or 10,
         * but not 11 (value t <= 2^256 - 38 + 2^255 + 37 = 2^256 + 2^255 - 1).
         * Therefore, we can truncate to 255 bits, and add 0, 19 or 38.
         * This guarantees that the result is at most 2^255+37.
         */
        t4 = (38 & -t4) + (19 & -(t3 >> 63));
        t3 &= MASK63;
        k = _addcarry_u64(0, t0, t4, &d[0]);
        k = _addcarry_u64(k, t1, 0, &d[1]);
        k = _addcarry_u64(k, t2, 0, &d[2]);
        (void)_addcarry_u64(k, t3, 0, &d[3]);

#endif
}

/*
 * Multiplication.
 */
static inline void
f255_mul(uint64_t *d, uint64_t *a, uint64_t *b)
{
#if BR_INT128

        unsigned __int128 z;
        uint64_t t0, t1, t2, t3, t4, t5, t6, t7, th;

        /*
         * Compute the product a*b over plain integers.
         */
        z = (unsigned __int128)a[0] * (unsigned __int128)b[0];
        t0 = (uint64_t)z;
        z = (unsigned __int128)a[0] * (unsigned __int128)b[1] + (z >> 64);
        t1 = (uint64_t)z;
        z = (unsigned __int128)a[0] * (unsigned __int128)b[2] + (z >> 64);
        t2 = (uint64_t)z;
        z = (unsigned __int128)a[0] * (unsigned __int128)b[3] + (z >> 64);
        t3 = (uint64_t)z;
        t4 = (uint64_t)(z >> 64);

        z = (unsigned __int128)a[1] * (unsigned __int128)b[0]
                + (unsigned __int128)t1;
        t1 = (uint64_t)z;
        z = (unsigned __int128)a[1] * (unsigned __int128)b[1]
                + (unsigned __int128)t2 + (z >> 64);
        t2 = (uint64_t)z;
        z = (unsigned __int128)a[1] * (unsigned __int128)b[2]
                + (unsigned __int128)t3 + (z >> 64);
        t3 = (uint64_t)z;
        z = (unsigned __int128)a[1] * (unsigned __int128)b[3]
                + (unsigned __int128)t4 + (z >> 64);
        t4 = (uint64_t)z;
        t5 = (uint64_t)(z >> 64);

        z = (unsigned __int128)a[2] * (unsigned __int128)b[0]
                + (unsigned __int128)t2;
        t2 = (uint64_t)z;
        z = (unsigned __int128)a[2] * (unsigned __int128)b[1]
                + (unsigned __int128)t3 + (z >> 64);
        t3 = (uint64_t)z;
        z = (unsigned __int128)a[2] * (unsigned __int128)b[2]
                + (unsigned __int128)t4 + (z >> 64);
        t4 = (uint64_t)z;
        z = (unsigned __int128)a[2] * (unsigned __int128)b[3]
                + (unsigned __int128)t5 + (z >> 64);
        t5 = (uint64_t)z;
        t6 = (uint64_t)(z >> 64);

        z = (unsigned __int128)a[3] * (unsigned __int128)b[0]
                + (unsigned __int128)t3;
        t3 = (uint64_t)z;
        z = (unsigned __int128)a[3] * (unsigned __int128)b[1]
                + (unsigned __int128)t4 + (z >> 64);
        t4 = (uint64_t)z;
        z = (unsigned __int128)a[3] * (unsigned __int128)b[2]
                + (unsigned __int128)t5 + (z >> 64);
        t5 = (uint64_t)z;
        z = (unsigned __int128)a[3] * (unsigned __int128)b[3]
                + (unsigned __int128)t6 + (z >> 64);
        t6 = (uint64_t)z;
        t7 = (uint64_t)(z >> 64);

        /*
         * Modulo p, we have:
         *
         *   2^255 = 19
         *   2^510 = 19*19 = 361
         *
         * We split the intermediate t into three parts, in basis
         * 2^255. The low one will be in t0..t3; the middle one in t4..t7.
         * The upper one can only be a single bit (th), since the
         * multiplication operands are at most 2^255+37 each.
         */
        th = t7 >> 62;
        t7 = ((t7 << 1) | (t6 >> 63)) & MASK63;
        t6 = (t6 << 1) | (t5 >> 63);
        t5 = (t5 << 1) | (t4 >> 63);
        t4 = (t4 << 1) | (t3 >> 63);
        t3 &= MASK63;

        /*
         * Multiply the middle part (t4..t7) by 19. We truncate it to
         * 255 bits; the extra bits will go along with th.
         */
        z = (unsigned __int128)t4 * 19;
        t4 = (uint64_t)z;
        z = (unsigned __int128)t5 * 19 + (z >> 64);
        t5 = (uint64_t)z;
        z = (unsigned __int128)t6 * 19 + (z >> 64);
        t6 = (uint64_t)z;
        z = (unsigned __int128)t7 * 19 + (z >> 64);
        t7 = (uint64_t)z & MASK63;

        th = (361 & -th) + (19 * (uint64_t)(z >> 63));

        /*
         * Add elements together.
         * At this point:
         *   t0..t3 fits on 255 bits.
         *   t4..t7 fits on 255 bits.
         *   th <= 361 + 342 = 703.
         */
        z = (unsigned __int128)t0 + (unsigned __int128)t4
                + (unsigned __int128)th;
        t0 = (uint64_t)z;
        z = (unsigned __int128)t1 + (unsigned __int128)t5 + (z >> 64);
        t1 = (uint64_t)z;
        z = (unsigned __int128)t2 + (unsigned __int128)t6 + (z >> 64);
        t2 = (uint64_t)z;
        z = (unsigned __int128)t3 + (unsigned __int128)t7 + (z >> 64);
        t3 = (uint64_t)z & MASK63;
        th = (uint64_t)(z >> 63);

        /*
         * Since the sum is at most 2^256 + 703, the two upper bits, in th,
         * can only have value 0, 1 or 2. We just add th*19, which
         * guarantees a result of at most 2^255+37.
         */
        z = (unsigned __int128)t0 + (19 * th);
        d[0] = (uint64_t)z;
        z = (unsigned __int128)t1 + (z >> 64);
        d[1] = (uint64_t)z;
        z = (unsigned __int128)t2 + (z >> 64);
        d[2] = (uint64_t)z;
        d[3] = t3 + (uint64_t)(z >> 64);

#elif BR_UMUL128

        uint64_t t0, t1, t2, t3, t4, t5, t6, t7, th;
        uint64_t h0, h1, h2, h3;
        unsigned char k;

        /*
         * Compute the product a*b over plain integers.
         */
        t0 = _umul128(a[0], b[0], &h0);
        t1 = _umul128(a[0], b[1], &h1);
        k = _addcarry_u64(0, t1, h0, &t1);
        t2 = _umul128(a[0], b[2], &h2);
        k = _addcarry_u64(k, t2, h1, &t2);
        t3 = _umul128(a[0], b[3], &h3);
        k = _addcarry_u64(k, t3, h2, &t3);
        (void)_addcarry_u64(k, h3, 0, &t4);

        k = _addcarry_u64(0, _umul128(a[1], b[0], &h0), t1, &t1);
        k = _addcarry_u64(k, _umul128(a[1], b[1], &h1), t2, &t2);
        k = _addcarry_u64(k, _umul128(a[1], b[2], &h2), t3, &t3);
        k = _addcarry_u64(k, _umul128(a[1], b[3], &h3), t4, &t4);
        t5 = k;
        k = _addcarry_u64(0, t2, h0, &t2);
        k = _addcarry_u64(k, t3, h1, &t3);
        k = _addcarry_u64(k, t4, h2, &t4);
        (void)_addcarry_u64(k, t5, h3, &t5);

        k = _addcarry_u64(0, _umul128(a[2], b[0], &h0), t2, &t2);
        k = _addcarry_u64(k, _umul128(a[2], b[1], &h1), t3, &t3);
        k = _addcarry_u64(k, _umul128(a[2], b[2], &h2), t4, &t4);
        k = _addcarry_u64(k, _umul128(a[2], b[3], &h3), t5, &t5);
        t6 = k;
        k = _addcarry_u64(0, t3, h0, &t3);
        k = _addcarry_u64(k, t4, h1, &t4);
        k = _addcarry_u64(k, t5, h2, &t5);
        (void)_addcarry_u64(k, t6, h3, &t6);

        k = _addcarry_u64(0, _umul128(a[3], b[0], &h0), t3, &t3);
        k = _addcarry_u64(k, _umul128(a[3], b[1], &h1), t4, &t4);
        k = _addcarry_u64(k, _umul128(a[3], b[2], &h2), t5, &t5);
        k = _addcarry_u64(k, _umul128(a[3], b[3], &h3), t6, &t6);
        t7 = k;
        k = _addcarry_u64(0, t4, h0, &t4);
        k = _addcarry_u64(k, t5, h1, &t5);
        k = _addcarry_u64(k, t6, h2, &t6);
        (void)_addcarry_u64(k, t7, h3, &t7);

        /*
         * Modulo p, we have:
         *
         *   2^255 = 19
         *   2^510 = 19*19 = 361
         *
         * We split the intermediate t into three parts, in basis
         * 2^255. The low one will be in t0..t3; the middle one in t4..t7.
         * The upper one can only be a single bit (th), since the
         * multiplication operands are at most 2^255+37 each.
         */
        th = t7 >> 62;
        t7 = ((t7 << 1) | (t6 >> 63)) & MASK63;
        t6 = (t6 << 1) | (t5 >> 63);
        t5 = (t5 << 1) | (t4 >> 63);
        t4 = (t4 << 1) | (t3 >> 63);
        t3 &= MASK63;

        /*
         * Multiply the middle part (t4..t7) by 19. We truncate it to
         * 255 bits; the extra bits will go along with th.
         */
        t4 = _umul128(t4, 19, &h0);
        t5 = _umul128(t5, 19, &h1);
        t6 = _umul128(t6, 19, &h2);
        t7 = _umul128(t7, 19, &h3);
        k = _addcarry_u64(0, t5, h0, &t5);
        k = _addcarry_u64(k, t6, h1, &t6);
        k = _addcarry_u64(k, t7, h2, &t7);
        (void)_addcarry_u64(k, h3, 0, &h3);
        th = (361 & -th) + (19 * ((h3 << 1) + (t7 >> 63)));
        t7 &= MASK63;

        /*
         * Add elements together.
         * At this point:
         *   t0..t3 fits on 255 bits.
         *   t4..t7 fits on 255 bits.
         *   th <= 361 + 342 = 703.
         */
        k = _addcarry_u64(0, t0, t4, &t0);
        k = _addcarry_u64(k, t1, t5, &t1);
        k = _addcarry_u64(k, t2, t6, &t2);
        k = _addcarry_u64(k, t3, t7, &t3);
        t4 = k;
        k = _addcarry_u64(0, t0, th, &t0);
        k = _addcarry_u64(k, t1, 0, &t1);
        k = _addcarry_u64(k, t2, 0, &t2);
        k = _addcarry_u64(k, t3, 0, &t3);
        (void)_addcarry_u64(k, t4, 0, &t4);

        th = (t4 << 1) + (t3 >> 63);
        t3 &= MASK63;

        /*
         * Since the sum is at most 2^256 + 703, the two upper bits, in th,
         * can only have value 0, 1 or 2. We just add th*19, which
         * guarantees a result of at most 2^255+37.
         */
        k = _addcarry_u64(0, t0, 19 * th, &d[0]);
        k = _addcarry_u64(k, t1, 0, &d[1]);
        k = _addcarry_u64(k, t2, 0, &d[2]);
        (void)_addcarry_u64(k, t3, 0, &d[3]);

#endif
}

/*
 * Multiplication by A24 = 121665.
 */
static inline void
f255_mul_a24(uint64_t *d, const uint64_t *a)
{
#if BR_INT128

        uint64_t t0, t1, t2, t3;
        unsigned __int128 z;

        z = (unsigned __int128)a[0] * 121665;
        t0 = (uint64_t)z;
        z = (unsigned __int128)a[1] * 121665 + (z >> 64);
        t1 = (uint64_t)z;
        z = (unsigned __int128)a[2] * 121665 + (z >> 64);
        t2 = (uint64_t)z;
        z = (unsigned __int128)a[3] * 121665 + (z >> 64);
        t3 = (uint64_t)z & MASK63;

        z = (unsigned __int128)t0 + (19 * (uint64_t)(z >> 63));
        t0 = (uint64_t)z;
        z = (unsigned __int128)t1 + (z >> 64);
        t1 = (uint64_t)z;
        z = (unsigned __int128)t2 + (z >> 64);
        t2 = (uint64_t)z;
        t3 = t3 + (uint64_t)(z >> 64);

        z = (unsigned __int128)t0 + (19 & -(t3 >> 63));
        d[0] = (uint64_t)z;
        z = (unsigned __int128)t1 + (z >> 64);
        d[1] = (uint64_t)z;
        z = (unsigned __int128)t2 + (z >> 64);
        d[2] = (uint64_t)z;
        d[3] = (t3 & MASK63) + (uint64_t)(z >> 64);

#elif BR_UMUL128

        uint64_t t0, t1, t2, t3, t4, h0, h1, h2, h3;
        unsigned char k;

        t0 = _umul128(a[0], 121665, &h0);
        t1 = _umul128(a[1], 121665, &h1);
        k = _addcarry_u64(0, t1, h0, &t1);
        t2 = _umul128(a[2], 121665, &h2);
        k = _addcarry_u64(k, t2, h1, &t2);
        t3 = _umul128(a[3], 121665, &h3);
        k = _addcarry_u64(k, t3, h2, &t3);
        (void)_addcarry_u64(k, h3, 0, &t4);

        t4 = (t4 << 1) + (t3 >> 63);
        t3 &= MASK63;
        k = _addcarry_u64(0, t0, 19 * t4, &t0);
        k = _addcarry_u64(k, t1, 0, &t1);
        k = _addcarry_u64(k, t2, 0, &t2);
        (void)_addcarry_u64(k, t3, 0, &t3);

        t4 = 19 & -(t3 >> 63);
        t3 &= MASK63;
        k = _addcarry_u64(0, t0, t4, &d[0]);
        k = _addcarry_u64(k, t1, 0, &d[1]);
        k = _addcarry_u64(k, t2, 0, &d[2]);
        (void)_addcarry_u64(k, t3, 0, &d[3]);

#endif
}

/*
 * Finalize reduction.
 */
static inline void
f255_final_reduce(uint64_t *a)
{
#if BR_INT128

        uint64_t t0, t1, t2, t3, m;
        unsigned __int128 z;

        /*
         * We add 19. If the result (in t) is below 2^255, then a[]
         * is already less than 2^255-19, thus already reduced.
         * Otherwise, we subtract 2^255 from t[], in which case we
         * have t = a - (2^255-19), and that's our result.
         */
        z = (unsigned __int128)a[0] + 19;
        t0 = (uint64_t)z;
        z = (unsigned __int128)a[1] + (z >> 64);
        t1 = (uint64_t)z;
        z = (unsigned __int128)a[2] + (z >> 64);
        t2 = (uint64_t)z;
        t3 = a[3] + (uint64_t)(z >> 64);

        m = -(t3 >> 63);
        t3 &= MASK63;
        a[0] ^= m & (a[0] ^ t0);
        a[1] ^= m & (a[1] ^ t1);
        a[2] ^= m & (a[2] ^ t2);
        a[3] ^= m & (a[3] ^ t3);

#elif BR_UMUL128

        uint64_t t0, t1, t2, t3, m;
        unsigned char k;

        /*
         * We add 19. If the result (in t) is below 2^255, then a[]
         * is already less than 2^255-19, thus already reduced.
         * Otherwise, we subtract 2^255 from t[], in which case we
         * have t = a - (2^255-19), and that's our result.
         */
        k = _addcarry_u64(0, a[0], 19, &t0);
        k = _addcarry_u64(k, a[1], 0, &t1);
        k = _addcarry_u64(k, a[2], 0, &t2);
        (void)_addcarry_u64(k, a[3], 0, &t3);

        m = -(t3 >> 63);
        t3 &= MASK63;
        a[0] ^= m & (a[0] ^ t0);
        a[1] ^= m & (a[1] ^ t1);
        a[2] ^= m & (a[2] ^ t2);
        a[3] ^= m & (a[3] ^ t3);

#endif
}

static uint32_t
api_mul(unsigned char *G, size_t Glen,
        const unsigned char *kb, size_t kblen, int curve)
{
        unsigned char k[32];
        uint64_t x1[4], x2[4], z2[4], x3[4], z3[4];
        uint32_t swap;
        int i;

        (void)curve;

        /*
         * Points are encoded over exactly 32 bytes. Multipliers must fit
         * in 32 bytes as well.
         */
        if (Glen != 32 || kblen > 32) {
                return 0;
        }

        /*
         * RFC 7748 mandates that the high bit of the last point byte must
         * be ignored/cleared.
         */
        x1[0] = br_dec64le(&G[ 0]);
        x1[1] = br_dec64le(&G[ 8]);
        x1[2] = br_dec64le(&G[16]);
        x1[3] = br_dec64le(&G[24]) & MASK63;

        /*
         * We can use memset() to clear values, because exact-width types
         * like uint64_t are guaranteed to have no padding bits or
         * trap representations.
         */
        memset(x2, 0, sizeof x2);
        x2[0] = 1;
        memset(z2, 0, sizeof z2);
        memcpy(x3, x1, sizeof x1);
        memcpy(z3, x2, sizeof x2);

        /*
         * The multiplier is provided in big-endian notation, and
         * possibly shorter than 32 bytes.
         */
        memset(k, 0, (sizeof k) - kblen);
        memcpy(k + (sizeof k) - kblen, kb, kblen);
        k[31] &= 0xF8;
        k[0] &= 0x7F;
        k[0] |= 0x40;

        swap = 0;

        for (i = 254; i >= 0; i --) {
                uint64_t a[4], aa[4], b[4], bb[4], e[4];
                uint64_t c[4], d[4], da[4], cb[4];
                uint32_t kt;

                kt = (k[31 - (i >> 3)] >> (i & 7)) & 1;
                swap ^= kt;
                f255_cswap(x2, x3, swap);
                f255_cswap(z2, z3, swap);
                swap = kt;

                /* A = x_2 + z_2 */
                f255_add(a, x2, z2);

                /* AA = A^2 */
                f255_mul(aa, a, a);

                /* B = x_2 - z_2 */
                f255_sub(b, x2, z2);

                /* BB = B^2 */
                f255_mul(bb, b, b);

                /* E = AA - BB */
                f255_sub(e, aa, bb);

                /* C = x_3 + z_3 */
                f255_add(c, x3, z3);

                /* D = x_3 - z_3 */
                f255_sub(d, x3, z3);

                /* DA = D * A */
                f255_mul(da, d, a);

                /* CB = C * B */
                f255_mul(cb, c, b);

                /* x_3 = (DA + CB)^2 */
                f255_add(x3, da, cb);
                f255_mul(x3, x3, x3);

                /* z_3 = x_1 * (DA - CB)^2 */
                f255_sub(z3, da, cb);
                f255_mul(z3, z3, z3);
                f255_mul(z3, x1, z3);

                /* x_2 = AA * BB */
                f255_mul(x2, aa, bb);

                /* z_2 = E * (AA + a24 * E) */
                f255_mul_a24(z2, e);
                f255_add(z2, aa, z2);
                f255_mul(z2, e, z2);
        }

        f255_cswap(x2, x3, swap);
        f255_cswap(z2, z3, swap);

        /*
         * Compute 1/z2 = z2^(p-2). Since p = 2^255-19, we can mutualize
         * most non-squarings. We use x1 and x3, now useless, as temporaries.
         */
        memcpy(x1, z2, sizeof z2);
        for (i = 0; i < 15; i ++) {
                f255_mul(x1, x1, x1);
                f255_mul(x1, x1, z2);
        }
        memcpy(x3, x1, sizeof x1);
        for (i = 0; i < 14; i ++) {
                int j;

                for (j = 0; j < 16; j ++) {
                        f255_mul(x3, x3, x3);
                }
                f255_mul(x3, x3, x1);
        }
        for (i = 14; i >= 0; i --) {
                f255_mul(x3, x3, x3);
                if ((0xFFEB >> i) & 1) {
                        f255_mul(x3, z2, x3);
                }
        }

        /*
         * Compute x2/z2. We have 1/z2 in x3.
         */
        f255_mul(x2, x2, x3);
        f255_final_reduce(x2);

        /*
         * Encode the final x2 value in little-endian.
         */
        br_enc64le(G,      x2[0]);
        br_enc64le(G +  8, x2[1]);
        br_enc64le(G + 16, x2[2]);
        br_enc64le(G + 24, x2[3]);
        return 1;
}

static size_t
api_mulgen(unsigned char *R,
        const unsigned char *x, size_t xlen, int curve)
{
        const unsigned char *G;
        size_t Glen;

        G = api_generator(curve, &Glen);
        memcpy(R, G, Glen);
        api_mul(R, Glen, x, xlen, curve);
        return Glen;
}

static uint32_t
api_muladd(unsigned char *A, const unsigned char *B, size_t len,
        const unsigned char *x, size_t xlen,
        const unsigned char *y, size_t ylen, int curve)
{
        /*
         * We don't implement this method, since it is used for ECDSA
         * only, and there is no ECDSA over Curve25519 (which instead
         * uses EdDSA).
         */
        (void)A;
        (void)B;
        (void)len;
        (void)x;
        (void)xlen;
        (void)y;
        (void)ylen;
        (void)curve;
        return 0;
}

/* see bearssl_ec.h */
const br_ec_impl br_ec_c25519_m64 = {
        (uint32_t)0x20000000,
        &api_generator,
        &api_order,
        &api_xoff,
        &api_mul,
        &api_mulgen,
        &api_muladd
};

/* see bearssl_ec.h */
const br_ec_impl *
br_ec_c25519_m64_get(void)
{
        return &br_ec_c25519_m64;
}

#else

/* see bearssl_ec.h */
const br_ec_impl *
br_ec_c25519_m64_get(void)
{
        return 0;
}

#endif