/*
* Copyright (c) 2017 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"
/* obsolete
#include <stdio.h>
#include <stdlib.h>
static void
print_int(const char *name, const uint32_t *x)
{
size_t u;
unsigned char tmp[36];
printf("%s = ", name);
for (u = 0; u < 20; u ++) {
if (x[u] > 0x1FFF) {
printf("INVALID:");
for (u = 0; u < 20; u ++) {
printf(" %04X", x[u]);
}
printf("\n");
return;
}
}
memset(tmp, 0, sizeof tmp);
for (u = 0; u < 20; u ++) {
uint32_t w;
int j, k;
w = x[u];
j = 13 * (int)u;
k = j & 7;
if (k != 0) {
w <<= k;
j -= k;
}
k = j >> 3;
tmp[35 - k] |= (unsigned char)w;
tmp[34 - k] |= (unsigned char)(w >> 8);
tmp[33 - k] |= (unsigned char)(w >> 16);
tmp[32 - k] |= (unsigned char)(w >> 24);
}
for (u = 4; u < 36; u ++) {
printf("%02X", tmp[u]);
}
printf("\n");
}
*/
/*
* If BR_NO_ARITH_SHIFT is undefined, or defined to 0, then we _assume_
* that right-shifting a signed negative integer copies the sign bit
* (arithmetic right-shift). This is "implementation-defined behaviour",
* i.e. it is not undefined, but it may differ between compilers. Each
* compiler is supposed to document its behaviour in that respect. GCC
* explicitly defines that an arithmetic right shift is used. We expect
* all other compilers to do the same, because underlying CPU offer an
* arithmetic right shift opcode that could not be used otherwise.
*/
#if BR_NO_ARITH_SHIFT
#define ARSH(x, n) (((uint32_t)(x) >> (n)) \
| ((-((uint32_t)(x) >> 31)) << (32 - (n))))
#else
#define ARSH(x, n) ((*(int32_t *)&(x)) >> (n))
#endif
/*
* Convert an integer from unsigned little-endian encoding to a sequence of
* 13-bit words in little-endian order. The final "partial" word is
* returned.
*/
static uint32_t
le8_to_le13(uint32_t *dst, const unsigned char *src, size_t len)
{
uint32_t acc;
int acc_len;
acc = 0;
acc_len = 0;
while (len -- > 0) {
acc |= (uint32_t)(*src ++) << acc_len;
acc_len += 8;
if (acc_len >= 13) {
*dst ++ = acc & 0x1FFF;
acc >>= 13;
acc_len -= 13;
}
}
return acc;
}
/*
* Convert an integer (13-bit words, little-endian) to unsigned
* little-endian encoding. The total encoding length is provided; all
* the destination bytes will be filled.
*/
static void
le13_to_le8(unsigned char *dst, size_t len, const uint32_t *src)
{
uint32_t acc;
int acc_len;
acc = 0;
acc_len = 0;
while (len -- > 0) {
if (acc_len < 8) {
acc |= (*src ++) << acc_len;
acc_len += 13;
}
*dst ++ = (unsigned char)acc;
acc >>= 8;
acc_len -= 8;
}
}
/*
* Normalise an array of words to a strict 13 bits per word. Returned
* value is the resulting carry. The source (w) and destination (d)
* arrays may be identical, but shall not overlap partially.
*/
static inline uint32_t
norm13(uint32_t *d, const uint32_t *w, size_t len)
{
size_t u;
uint32_t cc;
cc = 0;
for (u = 0; u < len; u ++) {
int32_t z;
z = w[u] + cc;
d[u] = z & 0x1FFF;
cc = ARSH(z, 13);
}
return cc;
}
/*
* mul20() multiplies two 260-bit integers together. Each word must fit
* on 13 bits; source operands use 20 words, destination operand
* receives 40 words. All overlaps allowed.
*
* square20() computes the square of a 260-bit integer. Each word must
* fit on 13 bits; source operand uses 20 words, destination operand
* receives 40 words. All overlaps allowed.
*/
#if BR_SLOW_MUL15
static void
mul20(uint32_t *d, const uint32_t *a, const uint32_t *b)
{
/*
* Two-level Karatsuba: turns a 20x20 multiplication into
* nine 5x5 multiplications. We use 13-bit words but do not
* propagate carries immediately, so words may expand:
*
* - First Karatsuba decomposition turns the 20x20 mul on
* 13-bit words into three 10x10 muls, two on 13-bit words
* and one on 14-bit words.
*
* - Second Karatsuba decomposition further splits these into:
*
* * four 5x5 muls on 13-bit words
* * four 5x5 muls on 14-bit words
* * one 5x5 mul on 15-bit words
*
* Highest word value is 8191, 16382 or 32764, for 13-bit, 14-bit
* or 15-bit words, respectively.
*/
uint32_t u[45], v[45], w[90];
uint32_t cc;
int i;
#define ZADD(dw, d_off, s1w, s1_off, s2w, s2_off) do { \
(dw)[5 * (d_off) + 0] = (s1w)[5 * (s1_off) + 0] \
+ (s2w)[5 * (s2_off) + 0]; \
(dw)[5 * (d_off) + 1] = (s1w)[5 * (s1_off) + 1] \
+ (s2w)[5 * (s2_off) + 1]; \
(dw)[5 * (d_off) + 2] = (s1w)[5 * (s1_off) + 2] \
+ (s2w)[5 * (s2_off) + 2]; \
(dw)[5 * (d_off) + 3] = (s1w)[5 * (s1_off) + 3] \
+ (s2w)[5 * (s2_off) + 3]; \
(dw)[5 * (d_off) + 4] = (s1w)[5 * (s1_off) + 4] \
+ (s2w)[5 * (s2_off) + 4]; \
} while (0)
#define ZADDT(dw, d_off, sw, s_off) do { \
(dw)[5 * (d_off) + 0] += (sw)[5 * (s_off) + 0]; \
(dw)[5 * (d_off) + 1] += (sw)[5 * (s_off) + 1]; \
(dw)[5 * (d_off) + 2] += (sw)[5 * (s_off) + 2]; \
(dw)[5 * (d_off) + 3] += (sw)[5 * (s_off) + 3]; \
(dw)[5 * (d_off) + 4] += (sw)[5 * (s_off) + 4]; \
} while (0)
#define ZSUB2F(dw, d_off, s1w, s1_off, s2w, s2_off) do { \
(dw)[5 * (d_off) + 0] -= (s1w)[5 * (s1_off) + 0] \
+ (s2w)[5 * (s2_off) + 0]; \
(dw)[5 * (d_off) + 1] -= (s1w)[5 * (s1_off) + 1] \
+ (s2w)[5 * (s2_off) + 1]; \
(dw)[5 * (d_off) + 2] -= (s1w)[5 * (s1_off) + 2] \
+ (s2w)[5 * (s2_off) + 2]; \
(dw)[5 * (d_off) + 3] -= (s1w)[5 * (s1_off) + 3] \
+ (s2w)[5 * (s2_off) + 3]; \
(dw)[5 * (d_off) + 4] -= (s1w)[5 * (s1_off) + 4] \
+ (s2w)[5 * (s2_off) + 4]; \
} while (0)
#define CPR1(w, cprcc) do { \
uint32_t cprz = (w) + cprcc; \
(w) = cprz & 0x1FFF; \
cprcc = cprz >> 13; \
} while (0)
#define CPR(dw, d_off) do { \
uint32_t cprcc; \
cprcc = 0; \
CPR1((dw)[(d_off) + 0], cprcc); \
CPR1((dw)[(d_off) + 1], cprcc); \
CPR1((dw)[(d_off) + 2], cprcc); \
CPR1((dw)[(d_off) + 3], cprcc); \
CPR1((dw)[(d_off) + 4], cprcc); \
CPR1((dw)[(d_off) + 5], cprcc); \
CPR1((dw)[(d_off) + 6], cprcc); \
CPR1((dw)[(d_off) + 7], cprcc); \
CPR1((dw)[(d_off) + 8], cprcc); \
(dw)[(d_off) + 9] = cprcc; \
} while (0)
memcpy(u, a, 20 * sizeof *a);
ZADD(u, 4, a, 0, a, 1);
ZADD(u, 5, a, 2, a, 3);
ZADD(u, 6, a, 0, a, 2);
ZADD(u, 7, a, 1, a, 3);
ZADD(u, 8, u, 6, u, 7);
memcpy(v, b, 20 * sizeof *b);
ZADD(v, 4, b, 0, b, 1);
ZADD(v, 5, b, 2, b, 3);
ZADD(v, 6, b, 0, b, 2);
ZADD(v, 7, b, 1, b, 3);
ZADD(v, 8, v, 6, v, 7);
/*
* Do the eight first 8x8 muls. Source words are at most 16382
* each, so we can add product results together "as is" in 32-bit
* words.
*/
for (i = 0; i < 40; i += 5) {
w[(i << 1) + 0] = MUL15(u[i + 0], v[i + 0]);
w[(i << 1) + 1] = MUL15(u[i + 0], v[i + 1])
+ MUL15(u[i + 1], v[i + 0]);
w[(i << 1) + 2] = MUL15(u[i + 0], v[i + 2])
+ MUL15(u[i + 1], v[i + 1])
+ MUL15(u[i + 2], v[i + 0]);
w[(i << 1) + 3] = MUL15(u[i + 0], v[i + 3])
+ MUL15(u[i + 1], v[i + 2])
+ MUL15(u[i + 2], v[i + 1])
+ MUL15(u[i + 3], v[i + 0]);
w[(i << 1) + 4] = MUL15(u[i + 0], v[i + 4])
+ MUL15(u[i + 1], v[i + 3])
+ MUL15(u[i + 2], v[i + 2])
+ MUL15(u[i + 3], v[i + 1])
+ MUL15(u[i + 4], v[i + 0]);
w[(i << 1) + 5] = MUL15(u[i + 1], v[i + 4])
+ MUL15(u[i + 2], v[i + 3])
+ MUL15(u[i + 3], v[i + 2])
+ MUL15(u[i + 4], v[i + 1]);
w[(i << 1) + 6] = MUL15(u[i + 2], v[i + 4])
+ MUL15(u[i + 3], v[i + 3])
+ MUL15(u[i + 4], v[i + 2]);
w[(i << 1) + 7] = MUL15(u[i + 3], v[i + 4])
+ MUL15(u[i + 4], v[i + 3]);
w[(i << 1) + 8] = MUL15(u[i + 4], v[i + 4]);
w[(i << 1) + 9] = 0;
}
/*
* For the 9th multiplication, source words are up to 32764,
* so we must do some carry propagation. If we add up to
* 4 products and the carry is no more than 524224, then the
* result fits in 32 bits, and the next carry will be no more
* than 524224 (because 4*(32764^2)+524224 < 8192*524225).
*
* We thus just skip one of the products in the middle word,
* then do a carry propagation (this reduces words to 13 bits
* each, except possibly the last, which may use up to 17 bits
* or so), then add the missing product.
*/
w[80 + 0] = MUL15(u[40 + 0], v[40 + 0]);
w[80 + 1] = MUL15(u[40 + 0], v[40 + 1])
+ MUL15(u[40 + 1], v[40 + 0]);
w[80 + 2] = MUL15(u[40 + 0], v[40 + 2])
+ MUL15(u[40 + 1], v[40 + 1])
+ MUL15(u[40 + 2], v[40 + 0]);
w[80 + 3] = MUL15(u[40 + 0], v[40 + 3])
+ MUL15(u[40 + 1], v[40 + 2])
+ MUL15(u[40 + 2], v[40 + 1])
+ MUL15(u[40 + 3], v[40 + 0]);
w[80 + 4] = MUL15(u[40 + 0], v[40 + 4])
+ MUL15(u[40 + 1], v[40 + 3])
+ MUL15(u[40 + 2], v[40 + 2])
+ MUL15(u[40 + 3], v[40 + 1]);
/* + MUL15(u[40 + 4], v[40 + 0]) */
w[80 + 5] = MUL15(u[40 + 1], v[40 + 4])
+ MUL15(u[40 + 2], v[40 + 3])
+ MUL15(u[40 + 3], v[40 + 2])
+ MUL15(u[40 + 4], v[40 + 1]);
w[80 + 6] = MUL15(u[40 + 2], v[40 + 4])
+ MUL15(u[40 + 3], v[40 + 3])
+ MUL15(u[40 + 4], v[40 + 2]);
w[80 + 7] = MUL15(u[40 + 3], v[40 + 4])
+ MUL15(u[40 + 4], v[40 + 3]);
w[80 + 8] = MUL15(u[40 + 4], v[40 + 4]);
CPR(w, 80);
w[80 + 4] += MUL15(u[40 + 4], v[40 + 0]);
/*
* The products on 14-bit words in slots 6 and 7 yield values
* up to 5*(16382^2) each, and we need to subtract two such
* values from the higher word. We need the subtraction to fit
* in a _signed_ 32-bit integer, i.e. 31 bits + a sign bit.
* However, 10*(16382^2) does not fit. So we must perform a
* bit of reduction here.
*/
CPR(w, 60);
CPR(w, 70);
/*
* Recompose results.
*/
/* 0..1*0..1 into 0..3 */
ZSUB2F(w, 8, w, 0, w, 2);
ZSUB2F(w, 9, w, 1, w, 3);
ZADDT(w, 1, w, 8);
ZADDT(w, 2, w, 9);
/* 2..3*2..3 into 4..7 */
ZSUB2F(w, 10, w, 4, w, 6);
ZSUB2F(w, 11, w, 5, w, 7);
ZADDT(w, 5, w, 10);
ZADDT(w, 6, w, 11);
/* (0..1+2..3)*(0..1+2..3) into 12..15 */
ZSUB2F(w, 16, w, 12, w, 14);
ZSUB2F(w, 17, w, 13, w, 15);
ZADDT(w, 13, w, 16);
ZADDT(w, 14, w, 17);
/* first-level recomposition */
ZSUB2F(w, 12, w, 0, w, 4);
ZSUB2F(w, 13, w, 1, w, 5);
ZSUB2F(w, 14, w, 2, w, 6);
ZSUB2F(w, 15, w, 3, w, 7);
ZADDT(w, 2, w, 12);
ZADDT(w, 3, w, 13);
ZADDT(w, 4, w, 14);
ZADDT(w, 5, w, 15);
/*
* Perform carry propagation to bring all words down to 13 bits.
*/
cc = norm13(d, w, 40);
d[39] += (cc << 13);
#undef ZADD
#undef ZADDT
#undef ZSUB2F
#undef CPR1
#undef CPR
}
static inline void
square20(uint32_t *d, const uint32_t *a)
{
mul20(d, a, a);
}
#else
static void
mul20(uint32_t *d, const uint32_t *a, const uint32_t *b)
{
uint32_t t[39];
t[ 0] = MUL15(a[ 0], b[ 0]);
t[ 1] = MUL15(a[ 0], b[ 1])
+ MUL15(a[ 1], b[ 0]);
t[ 2] = MUL15(a[ 0], b[ 2])
+ MUL15(a[ 1], b[ 1])
+ MUL15(a[ 2], b[ 0]);
t[ 3] = MUL15(a[ 0], b[ 3])
+ MUL15(a[ 1], b[ 2])
+ MUL15(a[ 2], b[ 1])
+ MUL15(a[ 3], b[ 0]);
t[ 4] = MUL15(a[ 0], b[ 4])
+ MUL15(a[ 1], b[ 3])
+ MUL15(a[ 2], b[ 2])
+ MUL15(a[ 3], b[ 1])
+ MUL15(a[ 4], b[ 0]);
t[ 5] = MUL15(a[ 0], b[ 5])
+ MUL15(a[ 1], b[ 4])
+ MUL15(a[ 2], b[ 3])
+ MUL15(a[ 3], b[ 2])
+ MUL15(a[ 4], b[ 1])
+ MUL15(a[ 5], b[ 0]);
t[ 6] = MUL15(a[ 0], b[ 6])
+ MUL15(a[ 1], b[ 5])
+ MUL15(a[ 2], b[ 4])
+ MUL15(a[ 3], b[ 3])
+ MUL15(a[ 4], b[ 2])
+ MUL15(a[ 5], b[ 1])
+ MUL15(a[ 6], b[ 0]);
t[ 7] = MUL15(a[ 0], b[ 7])
+ MUL15(a[ 1], b[ 6])
+ MUL15(a[ 2], b[ 5])
+ MUL15(a[ 3], b[ 4])
+ MUL15(a[ 4], b[ 3])
+ MUL15(a[ 5], b[ 2])
+ MUL15(a[ 6], b[ 1])
+ MUL15(a[ 7], b[ 0]);
t[ 8] = MUL15(a[ 0], b[ 8])
+ MUL15(a[ 1], b[ 7])
+ MUL15(a[ 2], b[ 6])
+ MUL15(a[ 3], b[ 5])
+ MUL15(a[ 4], b[ 4])
+ MUL15(a[ 5], b[ 3])
+ MUL15(a[ 6], b[ 2])
+ MUL15(a[ 7], b[ 1])
+ MUL15(a[ 8], b[ 0]);
t[ 9] = MUL15(a[ 0], b[ 9])
+ MUL15(a[ 1], b[ 8])
+ MUL15(a[ 2], b[ 7])
+ MUL15(a[ 3], b[ 6])
+ MUL15(a[ 4], b[ 5])
+ MUL15(a[ 5], b[ 4])
+ MUL15(a[ 6], b[ 3])
+ MUL15(a[ 7], b[ 2])
+ MUL15(a[ 8], b[ 1])
+ MUL15(a[ 9], b[ 0]);
t[10] = MUL15(a[ 0], b[10])
+ MUL15(a[ 1], b[ 9])
+ MUL15(a[ 2], b[ 8])
+ MUL15(a[ 3], b[ 7])
+ MUL15(a[ 4], b[ 6])
+ MUL15(a[ 5], b[ 5])
+ MUL15(a[ 6], b[ 4])
+ MUL15(a[ 7], b[ 3])
+ MUL15(a[ 8], b[ 2])
+ MUL15(a[ 9], b[ 1])
+ MUL15(a[10], b[ 0]);
t[11] = MUL15(a[ 0], b[11])
+ MUL15(a[ 1], b[10])
+ MUL15(a[ 2], b[ 9])
+ MUL15(a[ 3], b[ 8])
+ MUL15(a[ 4], b[ 7])
+ MUL15(a[ 5], b[ 6])
+ MUL15(a[ 6], b[ 5])
+ MUL15(a[ 7], b[ 4])
+ MUL15(a[ 8], b[ 3])
+ MUL15(a[ 9], b[ 2])
+ MUL15(a[10], b[ 1])
+ MUL15(a[11], b[ 0]);
t[12] = MUL15(a[ 0], b[12])
+ MUL15(a[ 1], b[11])
+ MUL15(a[ 2], b[10])
+ MUL15(a[ 3], b[ 9])
+ MUL15(a[ 4], b[ 8])
+ MUL15(a[ 5], b[ 7])
+ MUL15(a[ 6], b[ 6])
+ MUL15(a[ 7], b[ 5])
+ MUL15(a[ 8], b[ 4])
+ MUL15(a[ 9], b[ 3])
+ MUL15(a[10], b[ 2])
+ MUL15(a[11], b[ 1])
+ MUL15(a[12], b[ 0]);
t[13] = MUL15(a[ 0], b[13])
+ MUL15(a[ 1], b[12])
+ MUL15(a[ 2], b[11])
+ MUL15(a[ 3], b[10])
+ MUL15(a[ 4], b[ 9])
+ MUL15(a[ 5], b[ 8])
+ MUL15(a[ 6], b[ 7])
+ MUL15(a[ 7], b[ 6])
+ MUL15(a[ 8], b[ 5])
+ MUL15(a[ 9], b[ 4])
+ MUL15(a[10], b[ 3])
+ MUL15(a[11], b[ 2])
+ MUL15(a[12], b[ 1])
+ MUL15(a[13], b[ 0]);
t[14] = MUL15(a[ 0], b[14])
+ MUL15(a[ 1], b[13])
+ MUL15(a[ 2], b[12])
+ MUL15(a[ 3], b[11])
+ MUL15(a[ 4], b[10])
+ MUL15(a[ 5], b[ 9])
+ MUL15(a[ 6], b[ 8])
+ MUL15(a[ 7], b[ 7])
+ MUL15(a[ 8], b[ 6])
+ MUL15(a[ 9], b[ 5])
+ MUL15(a[10], b[ 4])
+ MUL15(a[11], b[ 3])
+ MUL15(a[12], b[ 2])
+ MUL15(a[13], b[ 1])
+ MUL15(a[14], b[ 0]);
t[15] = MUL15(a[ 0], b[15])
+ MUL15(a[ 1], b[14])
+ MUL15(a[ 2], b[13])
+ MUL15(a[ 3], b[12])
+ MUL15(a[ 4], b[11])
+ MUL15(a[ 5], b[10])
+ MUL15(a[ 6], b[ 9])
+ MUL15(a[ 7], b[ 8])
+ MUL15(a[ 8], b[ 7])
+ MUL15(a[ 9], b[ 6])
+ MUL15(a[10], b[ 5])
+ MUL15(a[11], b[ 4])
+ MUL15(a[12], b[ 3])
+ MUL15(a[13], b[ 2])
+ MUL15(a[14], b[ 1])
+ MUL15(a[15], b[ 0]);
t[16] = MUL15(a[ 0], b[16])
+ MUL15(a[ 1], b[15])
+ MUL15(a[ 2], b[14])
+ MUL15(a[ 3], b[13])
+ MUL15(a[ 4], b[12])
+ MUL15(a[ 5], b[11])
+ MUL15(a[ 6], b[10])
+ MUL15(a[ 7], b[ 9])
+ MUL15(a[ 8], b[ 8])
+ MUL15(a[ 9], b[ 7])
+ MUL15(a[10], b[ 6])
+ MUL15(a[11], b[ 5])
+ MUL15(a[12], b[ 4])
+ MUL15(a[13], b[ 3])
+ MUL15(a[14], b[ 2])
+ MUL15(a[15], b[ 1])
+ MUL15(a[16], b[ 0]);
t[17] = MUL15(a[ 0], b[17])
+ MUL15(a[ 1], b[16])
+ MUL15(a[ 2], b[15])
+ MUL15(a[ 3], b[14])
+ MUL15(a[ 4], b[13])
+ MUL15(a[ 5], b[12])
+ MUL15(a[ 6], b[11])
+ MUL15(a[ 7], b[10])
+ MUL15(a[ 8], b[ 9])
+ MUL15(a[ 9], b[ 8])
+ MUL15(a[10], b[ 7])
+ MUL15(a[11], b[ 6])
+ MUL15(a[12], b[ 5])
+ MUL15(a[13], b[ 4])
+ MUL15(a[14], b[ 3])
+ MUL15(a[15], b[ 2])
+ MUL15(a[16], b[ 1])
+ MUL15(a[17], b[ 0]);
t[18] = MUL15(a[ 0], b[18])
+ MUL15(a[ 1], b[17])
+ MUL15(a[ 2], b[16])
+ MUL15(a[ 3], b[15])
+ MUL15(a[ 4], b[14])
+ MUL15(a[ 5], b[13])
+ MUL15(a[ 6], b[12])
+ MUL15(a[ 7], b[11])
+ MUL15(a[ 8], b[10])
+ MUL15(a[ 9], b[ 9])
+ MUL15(a[10], b[ 8])
+ MUL15(a[11], b[ 7])
+ MUL15(a[12], b[ 6])
+ MUL15(a[13], b[ 5])
+ MUL15(a[14], b[ 4])
+ MUL15(a[15], b[ 3])
+ MUL15(a[16], b[ 2])
+ MUL15(a[17], b[ 1])
+ MUL15(a[18], b[ 0]);
t[19] = MUL15(a[ 0], b[19])
+ MUL15(a[ 1], b[18])
+ MUL15(a[ 2], b[17])
+ MUL15(a[ 3], b[16])
+ MUL15(a[ 4], b[15])
+ MUL15(a[ 5], b[14])
+ MUL15(a[ 6], b[13])
+ MUL15(a[ 7], b[12])
+ MUL15(a[ 8], b[11])
+ MUL15(a[ 9], b[10])
+ MUL15(a[10], b[ 9])
+ MUL15(a[11], b[ 8])
+ MUL15(a[12], b[ 7])
+ MUL15(a[13], b[ 6])
+ MUL15(a[14], b[ 5])
+ MUL15(a[15], b[ 4])
+ MUL15(a[16], b[ 3])
+ MUL15(a[17], b[ 2])
+ MUL15(a[18], b[ 1])
+ MUL15(a[19], b[ 0]);
t[20] = MUL15(a[ 1], b[19])
+ MUL15(a[ 2], b[18])
+ MUL15(a[ 3], b[17])
+ MUL15(a[ 4], b[16])
+ MUL15(a[ 5], b[15])
+ MUL15(a[ 6], b[14])
+ MUL15(a[ 7], b[13])
+ MUL15(a[ 8], b[12])
+ MUL15(a[ 9], b[11])
+ MUL15(a[10], b[10])
+ MUL15(a[11], b[ 9])
+ MUL15(a[12], b[ 8])
+ MUL15(a[13], b[ 7])
+ MUL15(a[14], b[ 6])
+ MUL15(a[15], b[ 5])
+ MUL15(a[16], b[ 4])
+ MUL15(a[17], b[ 3])
+ MUL15(a[18], b[ 2])
+ MUL15(a[19], b[ 1]);
t[21] = MUL15(a[ 2], b[19])
+ MUL15(a[ 3], b[18])
+ MUL15(a[ 4], b[17])
+ MUL15(a[ 5], b[16])
+ MUL15(a[ 6], b[15])
+ MUL15(a[ 7], b[14])
+ MUL15(a[ 8], b[13])
+ MUL15(a[ 9], b[12])
+ MUL15(a[10], b[11])
+ MUL15(a[11], b[10])
+ MUL15(a[12], b[ 9])
+ MUL15(a[13], b[ 8])
+ MUL15(a[14], b[ 7])
+ MUL15(a[15], b[ 6])
+ MUL15(a[16], b[ 5])
+ MUL15(a[17], b[ 4])
+ MUL15(a[18], b[ 3])
+ MUL15(a[19], b[ 2]);
t[22] = MUL15(a[ 3], b[19])
+ MUL15(a[ 4], b[18])
+ MUL15(a[ 5], b[17])
+ MUL15(a[ 6], b[16])
+ MUL15(a[ 7], b[15])
+ MUL15(a[ 8], b[14])
+ MUL15(a[ 9], b[13])
+ MUL15(a[10], b[12])
+ MUL15(a[11], b[11])
+ MUL15(a[12], b[10])
+ MUL15(a[13], b[ 9])
+ MUL15(a[14], b[ 8])
+ MUL15(a[15], b[ 7])
+ MUL15(a[16], b[ 6])
+ MUL15(a[17], b[ 5])
+ MUL15(a[18], b[ 4])
+ MUL15(a[19], b[ 3]);
t[23] = MUL15(a[ 4], b[19])
+ MUL15(a[ 5], b[18])
+ MUL15(a[ 6], b[17])
+ MUL15(a[ 7], b[16])
+ MUL15(a[ 8], b[15])
+ MUL15(a[ 9], b[14])
+ MUL15(a[10], b[13])
+ MUL15(a[11], b[12])
+ MUL15(a[12], b[11])
+ MUL15(a[13], b[10])
+ MUL15(a[14], b[ 9])
+ MUL15(a[15], b[ 8])
+ MUL15(a[16], b[ 7])
+ MUL15(a[17], b[ 6])
+ MUL15(a[18], b[ 5])
+ MUL15(a[19], b[ 4]);
t[24] = MUL15(a[ 5], b[19])
+ MUL15(a[ 6], b[18])
+ MUL15(a[ 7], b[17])
+ MUL15(a[ 8], b[16])
+ MUL15(a[ 9], b[15])
+ MUL15(a[10], b[14])
+ MUL15(a[11], b[13])
+ MUL15(a[12], b[12])
+ MUL15(a[13], b[11])
+ MUL15(a[14], b[10])
+ MUL15(a[15], b[ 9])
+ MUL15(a[16], b[ 8])
+ MUL15(a[17], b[ 7])
+ MUL15(a[18], b[ 6])
+ MUL15(a[19], b[ 5]);
t[25] = MUL15(a[ 6], b[19])
+ MUL15(a[ 7], b[18])
+ MUL15(a[ 8], b[17])
+ MUL15(a[ 9], b[16])
+ MUL15(a[10], b[15])
+ MUL15(a[11], b[14])
+ MUL15(a[12], b[13])
+ MUL15(a[13], b[12])
+ MUL15(a[14], b[11])
+ MUL15(a[15], b[10])
+ MUL15(a[16], b[ 9])
+ MUL15(a[17], b[ 8])
+ MUL15(a[18], b[ 7])
+ MUL15(a[19], b[ 6]);
t[26] = MUL15(a[ 7], b[19])
+ MUL15(a[ 8], b[18])
+ MUL15(a[ 9], b[17])
+ MUL15(a[10], b[16])
+ MUL15(a[11], b[15])
+ MUL15(a[12], b[14])
+ MUL15(a[13], b[13])
+ MUL15(a[14], b[12])
+ MUL15(a[15], b[11])
+ MUL15(a[16], b[10])
+ MUL15(a[17], b[ 9])
+ MUL15(a[18], b[ 8])
+ MUL15(a[19], b[ 7]);
t[27] = MUL15(a[ 8], b[19])
+ MUL15(a[ 9], b[18])
+ MUL15(a[10], b[17])
+ MUL15(a[11], b[16])
+ MUL15(a[12], b[15])
+ MUL15(a[13], b[14])
+ MUL15(a[14], b[13])
+ MUL15(a[15], b[12])
+ MUL15(a[16], b[11])
+ MUL15(a[17], b[10])
+ MUL15(a[18], b[ 9])
+ MUL15(a[19], b[ 8]);
t[28] = MUL15(a[ 9], b[19])
+ MUL15(a[10], b[18])
+ MUL15(a[11], b[17])
+ MUL15(a[12], b[16])
+ MUL15(a[13], b[15])
+ MUL15(a[14], b[14])
+ MUL15(a[15], b[13])
+ MUL15(a[16], b[12])
+ MUL15(a[17], b[11])
+ MUL15(a[18], b[10])
+ MUL15(a[19], b[ 9]);
t[29] = MUL15(a[10], b[19])
+ MUL15(a[11], b[18])
+ MUL15(a[12], b[17])
+ MUL15(a[13], b[16])
+ MUL15(a[14], b[15])
+ MUL15(a[15], b[14])
+ MUL15(a[16], b[13])
+ MUL15(a[17], b[12])
+ MUL15(a[18], b[11])
+ MUL15(a[19], b[10]);
t[30] = MUL15(a[11], b[19])
+ MUL15(a[12], b[18])
+ MUL15(a[13], b[17])
+ MUL15(a[14], b[16])
+ MUL15(a[15], b[15])
+ MUL15(a[16], b[14])
+ MUL15(a[17], b[13])
+ MUL15(a[18], b[12])
+ MUL15(a[19], b[11]);
t[31] = MUL15(a[12], b[19])
+ MUL15(a[13], b[18])
+ MUL15(a[14], b[17])
+ MUL15(a[15], b[16])
+ MUL15(a[16], b[15])
+ MUL15(a[17], b[14])
+ MUL15(a[18], b[13])
+ MUL15(a[19], b[12]);
t[32] = MUL15(a[13], b[19])
+ MUL15(a[14], b[18])
+ MUL15(a[15], b[17])
+ MUL15(a[16], b[16])
+ MUL15(a[17], b[15])
+ MUL15(a[18], b[14])
+ MUL15(a[19], b[13]);
t[33] = MUL15(a[14], b[19])
+ MUL15(a[15], b[18])
+ MUL15(a[16], b[17])
+ MUL15(a[17], b[16])
+ MUL15(a[18], b[15])
+ MUL15(a[19], b[14]);
t[34] = MUL15(a[15], b[19])
+ MUL15(a[16], b[18])
+ MUL15(a[17], b[17])
+ MUL15(a[18], b[16])
+ MUL15(a[19], b[15]);
t[35] = MUL15(a[16], b[19])
+ MUL15(a[17], b[18])
+ MUL15(a[18], b[17])
+ MUL15(a[19], b[16]);
t[36] = MUL15(a[17], b[19])
+ MUL15(a[18], b[18])
+ MUL15(a[19], b[17]);
t[37] = MUL15(a[18], b[19])
+ MUL15(a[19], b[18]);
t[38] = MUL15(a[19], b[19]);
d[39] = norm13(d, t, 39);
}
static void
square20(uint32_t *d, const uint32_t *a)
{
uint32_t t[39];
t[ 0] = MUL15(a[ 0], a[ 0]);
t[ 1] = ((MUL15(a[ 0], a[ 1])) << 1);
t[ 2] = MUL15(a[ 1], a[ 1])
+ ((MUL15(a[ 0], a[ 2])) << 1);
t[ 3] = ((MUL15(a[ 0], a[ 3])
+ MUL15(a[ 1], a[ 2])) << 1);
t[ 4] = MUL15(a[ 2], a[ 2])
+ ((MUL15(a[ 0], a[ 4])
+ MUL15(a[ 1], a[ 3])) << 1);
t[ 5] = ((MUL15(a[ 0], a[ 5])
+ MUL15(a[ 1], a[ 4])
+ MUL15(a[ 2], a[ 3])) << 1);
t[ 6] = MUL15(a[ 3], a[ 3])
+ ((MUL15(a[ 0], a[ 6])
+ MUL15(a[ 1], a[ 5])
+ MUL15(a[ 2], a[ 4])) << 1);
t[ 7] = ((MUL15(a[ 0], a[ 7])
+ MUL15(a[ 1], a[ 6])
+ MUL15(a[ 2], a[ 5])
+ MUL15(a[ 3], a[ 4])) << 1);
t[ 8] = MUL15(a[ 4], a[ 4])
+ ((MUL15(a[ 0], a[ 8])
+ MUL15(a[ 1], a[ 7])
+ MUL15(a[ 2], a[ 6])
+ MUL15(a[ 3], a[ 5])) << 1);
t[ 9] = ((MUL15(a[ 0], a[ 9])
+ MUL15(a[ 1], a[ 8])
+ MUL15(a[ 2], a[ 7])
+ MUL15(a[ 3], a[ 6])
+ MUL15(a[ 4], a[ 5])) << 1);
t[10] = MUL15(a[ 5], a[ 5])
+ ((MUL15(a[ 0], a[10])
+ MUL15(a[ 1], a[ 9])
+ MUL15(a[ 2], a[ 8])
+ MUL15(a[ 3], a[ 7])
+ MUL15(a[ 4], a[ 6])) << 1);
t[11] = ((MUL15(a[ 0], a[11])
+ MUL15(a[ 1], a[10])
+ MUL15(a[ 2], a[ 9])
+ MUL15(a[ 3], a[ 8])
+ MUL15(a[ 4], a[ 7])
+ MUL15(a[ 5], a[ 6])) << 1);
t[12] = MUL15(a[ 6], a[ 6])
+ ((MUL15(a[ 0], a[12])
+ MUL15(a[ 1], a[11])
+ MUL15(a[ 2], a[10])
+ MUL15(a[ 3], a[ 9])
+ MUL15(a[ 4], a[ 8])
+ MUL15(a[ 5], a[ 7])) << 1);
t[13] = ((MUL15(a[ 0], a[13])
+ MUL15(a[ 1], a[12])
+ MUL15(a[ 2], a[11])
+ MUL15(a[ 3], a[10])
+ MUL15(a[ 4], a[ 9])
+ MUL15(a[ 5], a[ 8])
+ MUL15(a[ 6], a[ 7])) << 1);
t[14] = MUL15(a[ 7], a[ 7])
+ ((MUL15(a[ 0], a[14])
+ MUL15(a[ 1], a[13])
+ MUL15(a[ 2], a[12])
+ MUL15(a[ 3], a[11])
+ MUL15(a[ 4], a[10])
+ MUL15(a[ 5], a[ 9])
+ MUL15(a[ 6], a[ 8])) << 1);
t[15] = ((MUL15(a[ 0], a[15])
+ MUL15(a[ 1], a[14])
+ MUL15(a[ 2], a[13])
+ MUL15(a[ 3], a[12])
+ MUL15(a[ 4], a[11])
+ MUL15(a[ 5], a[10])
+ MUL15(a[ 6], a[ 9])
+ MUL15(a[ 7], a[ 8])) << 1);
t[16] = MUL15(a[ 8], a[ 8])
+ ((MUL15(a[ 0], a[16])
+ MUL15(a[ 1], a[15])
+ MUL15(a[ 2], a[14])
+ MUL15(a[ 3], a[13])
+ MUL15(a[ 4], a[12])
+ MUL15(a[ 5], a[11])
+ MUL15(a[ 6], a[10])
+ MUL15(a[ 7], a[ 9])) << 1);
t[17] = ((MUL15(a[ 0], a[17])
+ MUL15(a[ 1], a[16])
+ MUL15(a[ 2], a[15])
+ MUL15(a[ 3], a[14])
+ MUL15(a[ 4], a[13])
+ MUL15(a[ 5], a[12])
+ MUL15(a[ 6], a[11])
+ MUL15(a[ 7], a[10])
+ MUL15(a[ 8], a[ 9])) << 1);
t[18] = MUL15(a[ 9], a[ 9])
+ ((MUL15(a[ 0], a[18])
+ MUL15(a[ 1], a[17])
+ MUL15(a[ 2], a[16])
+ MUL15(a[ 3], a[15])
+ MUL15(a[ 4], a[14])
+ MUL15(a[ 5], a[13])
+ MUL15(a[ 6], a[12])
+ MUL15(a[ 7], a[11])
+ MUL15(a[ 8], a[10])) << 1);
t[19] = ((MUL15(a[ 0], a[19])
+ MUL15(a[ 1], a[18])
+ MUL15(a[ 2], a[17])
+ MUL15(a[ 3], a[16])
+ MUL15(a[ 4], a[15])
+ MUL15(a[ 5], a[14])
+ MUL15(a[ 6], a[13])
+ MUL15(a[ 7], a[12])
+ MUL15(a[ 8], a[11])
+ MUL15(a[ 9], a[10])) << 1);
t[20] = MUL15(a[10], a[10])
+ ((MUL15(a[ 1], a[19])
+ MUL15(a[ 2], a[18])
+ MUL15(a[ 3], a[17])
+ MUL15(a[ 4], a[16])
+ MUL15(a[ 5], a[15])
+ MUL15(a[ 6], a[14])
+ MUL15(a[ 7], a[13])
+ MUL15(a[ 8], a[12])
+ MUL15(a[ 9], a[11])) << 1);
t[21] = ((MUL15(a[ 2], a[19])
+ MUL15(a[ 3], a[18])
+ MUL15(a[ 4], a[17])
+ MUL15(a[ 5], a[16])
+ MUL15(a[ 6], a[15])
+ MUL15(a[ 7], a[14])
+ MUL15(a[ 8], a[13])
+ MUL15(a[ 9], a[12])
+ MUL15(a[10], a[11])) << 1);
t[22] = MUL15(a[11], a[11])
+ ((MUL15(a[ 3], a[19])
+ MUL15(a[ 4], a[18])
+ MUL15(a[ 5], a[17])
+ MUL15(a[ 6], a[16])
+ MUL15(a[ 7], a[15])
+ MUL15(a[ 8], a[14])
+ MUL15(a[ 9], a[13])
+ MUL15(a[10], a[12])) << 1);
t[23] = ((MUL15(a[ 4], a[19])
+ MUL15(a[ 5], a[18])
+ MUL15(a[ 6], a[17])
+ MUL15(a[ 7], a[16])
+ MUL15(a[ 8], a[15])
+ MUL15(a[ 9], a[14])
+ MUL15(a[10], a[13])
+ MUL15(a[11], a[12])) << 1);
t[24] = MUL15(a[12], a[12])
+ ((MUL15(a[ 5], a[19])
+ MUL15(a[ 6], a[18])
+ MUL15(a[ 7], a[17])
+ MUL15(a[ 8], a[16])
+ MUL15(a[ 9], a[15])
+ MUL15(a[10], a[14])
+ MUL15(a[11], a[13])) << 1);
t[25] = ((MUL15(a[ 6], a[19])
+ MUL15(a[ 7], a[18])
+ MUL15(a[ 8], a[17])
+ MUL15(a[ 9], a[16])
+ MUL15(a[10], a[15])
+ MUL15(a[11], a[14])
+ MUL15(a[12], a[13])) << 1);
t[26] = MUL15(a[13], a[13])
+ ((MUL15(a[ 7], a[19])
+ MUL15(a[ 8], a[18])
+ MUL15(a[ 9], a[17])
+ MUL15(a[10], a[16])
+ MUL15(a[11], a[15])
+ MUL15(a[12], a[14])) << 1);
t[27] = ((MUL15(a[ 8], a[19])
+ MUL15(a[ 9], a[18])
+ MUL15(a[10], a[17])
+ MUL15(a[11], a[16])
+ MUL15(a[12], a[15])
+ MUL15(a[13], a[14])) << 1);
t[28] = MUL15(a[14], a[14])
+ ((MUL15(a[ 9], a[19])
+ MUL15(a[10], a[18])
+ MUL15(a[11], a[17])
+ MUL15(a[12], a[16])
+ MUL15(a[13], a[15])) << 1);
t[29] = ((MUL15(a[10], a[19])
+ MUL15(a[11], a[18])
+ MUL15(a[12], a[17])
+ MUL15(a[13], a[16])
+ MUL15(a[14], a[15])) << 1);
t[30] = MUL15(a[15], a[15])
+ ((MUL15(a[11], a[19])
+ MUL15(a[12], a[18])
+ MUL15(a[13], a[17])
+ MUL15(a[14], a[16])) << 1);
t[31] = ((MUL15(a[12], a[19])
+ MUL15(a[13], a[18])
+ MUL15(a[14], a[17])
+ MUL15(a[15], a[16])) << 1);
t[32] = MUL15(a[16], a[16])
+ ((MUL15(a[13], a[19])
+ MUL15(a[14], a[18])
+ MUL15(a[15], a[17])) << 1);
t[33] = ((MUL15(a[14], a[19])
+ MUL15(a[15], a[18])
+ MUL15(a[16], a[17])) << 1);
t[34] = MUL15(a[17], a[17])
+ ((MUL15(a[15], a[19])
+ MUL15(a[16], a[18])) << 1);
t[35] = ((MUL15(a[16], a[19])
+ MUL15(a[17], a[18])) << 1);
t[36] = MUL15(a[18], a[18])
+ ((MUL15(a[17], a[19])) << 1);
t[37] = ((MUL15(a[18], a[19])) << 1);
t[38] = MUL15(a[19], a[19]);
d[39] = norm13(d, t, 39);
}
#endif
/*
* Perform a "final reduction" in field F255 (field for Curve25519)
* The source value must be less than twice the modulus. If the value
* is not lower than the modulus, then the modulus is subtracted and
* this function returns 1; otherwise, it leaves it untouched and it
* returns 0.
*/
static uint32_t
reduce_final_f255(uint32_t *d)
{
uint32_t t[20];
uint32_t cc;
int i;
memcpy(t, d, sizeof t);
cc = 19;
for (i = 0; i < 20; i ++) {
uint32_t w;
w = t[i] + cc;
cc = w >> 13;
t[i] = w & 0x1FFF;
}
cc = t[19] >> 8;
t[19] &= 0xFF;
CCOPY(cc, d, t, sizeof t);
return cc;
}
static void
f255_mulgen(uint32_t *d, const uint32_t *a, const uint32_t *b, int square)
{
uint32_t t[40], cc, w;
/*
* Compute raw multiplication. All result words fit in 13 bits
* each; upper word (t[39]) must fit on 5 bits, since the product
* of two 256-bit integers must fit on 512 bits.
*/
if (square) {
square20(t, a);
} else {
mul20(t, a, b);
}
/*
* Modular reduction: each high word is added where necessary.
* Since the modulus is 2^255-19 and word 20 corresponds to
* offset 20*13 = 260, word 20+k must be added to word k with
* a factor of 19*2^5 = 608. The extra bits in word 19 are also
* added that way.
*/
cc = MUL15(t[19] >> 8, 19);
t[19] &= 0xFF;
#define MM1(x) do { \
w = t[x] + cc + MUL15(t[(x) + 20], 608); \
t[x] = w & 0x1FFF; \
cc = w >> 13; \
} while (0)
MM1( 0);
MM1( 1);
MM1( 2);
MM1( 3);
MM1( 4);
MM1( 5);
MM1( 6);
MM1( 7);
MM1( 8);
MM1( 9);
MM1(10);
MM1(11);
MM1(12);
MM1(13);
MM1(14);
MM1(15);
MM1(16);
MM1(17);
MM1(18);
MM1(19);
#undef MM1
cc = MUL15(w >> 8, 19);
t[19] &= 0xFF;
#define MM2(x) do { \
w = t[x] + cc; \
d[x] = w & 0x1FFF; \
cc = w >> 13; \
} while (0)
MM2( 0);
MM2( 1);
MM2( 2);
MM2( 3);
MM2( 4);
MM2( 5);
MM2( 6);
MM2( 7);
MM2( 8);
MM2( 9);
MM2(10);
MM2(11);
MM2(12);
MM2(13);
MM2(14);
MM2(15);
MM2(16);
MM2(17);
MM2(18);
MM2(19);
#undef MM2
}
/*
* Perform a multiplication of two integers modulo 2^255-19.
* Operands are arrays of 20 words, each containing 13 bits of data, in
* little-endian order. Input value may be up to 2^256-1; on output, value
* fits on 256 bits and is lower than twice the modulus.
*
* f255_mul() is the general multiplication, f255_square() is specialised
* for squarings.
*/
#define f255_mul(d, a, b) f255_mulgen(d, a, b, 0)
#define f255_square(d, a) f255_mulgen(d, a, a, 1)
/*
* Add two values in F255. Partial reduction is performed (down to less
* than twice the modulus).
*/
static void
f255_add(uint32_t *d, const uint32_t *a, const uint32_t *b)
{
int i;
uint32_t cc, w;
cc = 0;
for (i = 0; i < 20; i ++) {
w = a[i] + b[i] + cc;
d[i] = w & 0x1FFF;
cc = w >> 13;
}
cc = MUL15(w >> 8, 19);
d[19] &= 0xFF;
for (i = 0; i < 20; i ++) {
w = d[i] + cc;
d[i] = w & 0x1FFF;
cc = w >> 13;
}
}
/*
* Subtract one value from another in F255. Partial reduction is
* performed (down to less than twice the modulus).
*/
static void
f255_sub(uint32_t *d, const uint32_t *a, const uint32_t *b)
{
/*
* We actually compute a - b + 2*p, so that the final value is
* necessarily positive.
*/
int i;
uint32_t cc, w;
cc = (uint32_t)-38;
for (i = 0; i < 20; i ++) {
w = a[i] - b[i] + cc;
d[i] = w & 0x1FFF;
cc = ARSH(w, 13);
}
cc = MUL15((w + 0x200) >> 8, 19);
d[19] &= 0xFF;
for (i = 0; i < 20; i ++) {
w = d[i] + cc;
d[i] = w & 0x1FFF;
cc = w >> 13;
}
}
/*
* Multiply an integer by the 'A24' constant (121665). Partial reduction
* is performed (down to less than twice the modulus).
*/
static void
f255_mul_a24(uint32_t *d, const uint32_t *a)
{
int i;
uint32_t cc, w;
cc = 0;
for (i = 0; i < 20; i ++) {
w = MUL15(a[i], 121665) + cc;
d[i] = w & 0x1FFF;
cc = w >> 13;
}
cc = MUL15(w >> 8, 19);
d[19] &= 0xFF;
for (i = 0; i < 20; i ++) {
w = d[i] + cc;
d[i] = w & 0x1FFF;
cc = w >> 13;
}
}
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;
}
static void
cswap(uint32_t *a, uint32_t *b, uint32_t ctl)
{
int i;
ctl = -ctl;
for (i = 0; i < 20; i ++) {
uint32_t aw, bw, tw;
aw = a[i];
bw = b[i];
tw = ctl & (aw ^ bw);
a[i] = aw ^ tw;
b[i] = bw ^ tw;
}
}
static uint32_t
api_mul(unsigned char *G, size_t Glen,
const unsigned char *kb, size_t kblen, int curve)
{
uint32_t x1[20], x2[20], x3[20], z2[20], z3[20];
uint32_t a[20], aa[20], b[20], bb[20];
uint32_t c[20], d[20], e[20], da[20], cb[20];
unsigned char k[32];
uint32_t swap;
int i;
(void)curve;
/*
* Points are encoded over exactly 32 bytes. Multipliers must fit
* in 32 bytes as well.
* RFC 7748 mandates that the high bit of the last point byte must
* be ignored/cleared.
*/
if (Glen != 32 || kblen > 32) {
return 0;
}
G[31] &= 0x7F;
/*
* Initialise variables x1, x2, z2, x3 and z3. We set all of them
* into Montgomery representation.
*/
x1[19] = le8_to_le13(x1, G, 32);
memcpy(x3, x1, sizeof x1);
memset(z2, 0, sizeof z2);
memset(x2, 0, sizeof x2);
x2[0] = 1;
memset(z3, 0, sizeof z3);
z3[0] = 1;
memset(k, 0, (sizeof k) - kblen);
memcpy(k + (sizeof k) - kblen, kb, kblen);
k[31] &= 0xF8;
k[0] &= 0x7F;
k[0] |= 0x40;
/* obsolete
print_int("x1", x1);
*/
swap = 0;
for (i = 254; i >= 0; i --) {
uint32_t kt;
kt = (k[31 - (i >> 3)] >> (i & 7)) & 1;
swap ^= kt;
cswap(x2, x3, swap);
cswap(z2, z3, swap);
swap = kt;
/* obsolete
print_int("x2", x2);
print_int("z2", z2);
print_int("x3", x3);
print_int("z3", z3);
*/
f255_add(a, x2, z2);
f255_square(aa, a);
f255_sub(b, x2, z2);
f255_square(bb, b);
f255_sub(e, aa, bb);
f255_add(c, x3, z3);
f255_sub(d, x3, z3);
f255_mul(da, d, a);
f255_mul(cb, c, b);
/* obsolete
print_int("a ", a);
print_int("aa", aa);
print_int("b ", b);
print_int("bb", bb);
print_int("e ", e);
print_int("c ", c);
print_int("d ", d);
print_int("da", da);
print_int("cb", cb);
*/
f255_add(x3, da, cb);
f255_square(x3, x3);
f255_sub(z3, da, cb);
f255_square(z3, z3);
f255_mul(z3, z3, x1);
f255_mul(x2, aa, bb);
f255_mul_a24(z2, e);
f255_add(z2, z2, aa);
f255_mul(z2, e, z2);
/* obsolete
print_int("x2", x2);
print_int("z2", z2);
print_int("x3", x3);
print_int("z3", z3);
*/
}
cswap(x2, x3, swap);
cswap(z2, z3, swap);
/*
* Inverse z2 with a modular exponentiation. This is a simple
* square-and-multiply algorithm; we mutualise most non-squarings
* since the exponent contains almost only ones.
*/
memcpy(a, z2, sizeof z2);
for (i = 0; i < 15; i ++) {
f255_square(a, a);
f255_mul(a, a, z2);
}
memcpy(b, a, sizeof a);
for (i = 0; i < 14; i ++) {
int j;
for (j = 0; j < 16; j ++) {
f255_square(b, b);
}
f255_mul(b, b, a);
}
for (i = 14; i >= 0; i --) {
f255_square(b, b);
if ((0xFFEB >> i) & 1) {
f255_mul(b, z2, b);
}
}
f255_mul(x2, x2, b);
reduce_final_f255(x2);
le13_to_le8(G, 32, x2);
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_m15 = {
(uint32_t)0x20000000,
&api_generator,
&api_order,
&api_xoff,
&api_mul,
&api_mulgen,
&api_muladd
};