xref: /freebsd/contrib/bearssl/src/ec/ec_c25519_m64.c (revision 0957b409a90fd597c1e9124cbaf3edd2b488f4ac)

/*
 * 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.
 * On input, limbs must fit on 60 bits each. On output, result is
 * partially reduced, with max value 2^255+19456; moreover, all
 * limbs will fit on 51 bits, except the low limb, which may have
 * value up to 2^51+19455.
 */
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