/*
* 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"
/*
* Parameters for the field:
* - field modulus p = 2^255-19
* - R^2 mod p (R = 2^(31k) for the smallest k such that R >= p)
*/
static const uint32_t C255_P[] = {
0x00000107,
0x7FFFFFED, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x0000007F
};
#define P0I 0x286BCA1B
static const uint32_t C255_R2[] = {
0x00000107,
0x00000000, 0x02D20000, 0x00000000, 0x00000000, 0x00000000,
0x00000000, 0x00000000, 0x00000000, 0x00000000
};
static const uint32_t C255_A24[] = {
0x00000107,
0x53000000, 0x0000468B, 0x00000000, 0x00000000, 0x00000000,
0x00000000, 0x00000000, 0x00000000, 0x00000000
};
/* obsolete
#include <stdio.h>
#include <stdlib.h>
static void
print_int_mont(const char *name, const uint32_t *x)
{
uint32_t y[10];
unsigned char tmp[32];
size_t u;
printf("%s = ", name);
memcpy(y, x, sizeof y);
br_i31_from_monty(y, C255_P, P0I);
br_i31_encode(tmp, sizeof tmp, y);
for (u = 0; u < sizeof tmp; u ++) {
printf("%02X", tmp[u]);
}
printf("\n");
}
*/
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 < 10; 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 void
c255_add(uint32_t *d, const uint32_t *a, const uint32_t *b)
{
uint32_t ctl;
uint32_t t[10];
memcpy(t, a, sizeof t);
ctl = br_i31_add(t, b, 1);
ctl |= NOT(br_i31_sub(t, C255_P, 0));
br_i31_sub(t, C255_P, ctl);
memcpy(d, t, sizeof t);
}
static void
c255_sub(uint32_t *d, const uint32_t *a, const uint32_t *b)
{
uint32_t t[10];
memcpy(t, a, sizeof t);
br_i31_add(t, C255_P, br_i31_sub(t, b, 1));
memcpy(d, t, sizeof t);
}
static void
c255_mul(uint32_t *d, const uint32_t *a, const uint32_t *b)
{
uint32_t t[10];
br_i31_montymul(t, a, b, C255_P, P0I);
memcpy(d, t, sizeof t);
}
static void
byteswap(unsigned char *G)
{
int i;
for (i = 0; i < 16; i ++) {
unsigned char t;
t = G[i];
G[i] = G[31 - i];
G[31 - i] = t;
}
}
static uint32_t
api_mul(unsigned char *G, size_t Glen,
const unsigned char *kb, size_t kblen, int curve)
{
uint32_t x1[10], x2[10], x3[10], z2[10], z3[10];
uint32_t a[10], aa[10], b[10], bb[10];
uint32_t c[10], d[10], e[10], da[10], cb[10];
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;
/*
* Byteswap the point encoding, because it uses little-endian, and
* the generic decoding routine uses big-endian.
*/
byteswap(G);
/*
* Decode the point ('u' coordinate). This should be reduced
* modulo p, but we prefer to avoid the dependency on
* br_i31_decode_reduce(). Instead, we use br_i31_decode_mod()
* with a synthetic modulus of value 2^255 (this must work
* since G was truncated to 255 bits), then use a conditional
* subtraction. We use br_i31_decode_mod() and not
* br_i31_decode(), because the ec_prime_i31 implementation uses
* the former but not the latter.
* br_i31_decode_reduce(a, G, 32, C255_P);
*/
br_i31_zero(b, 0x108);
b[9] = 0x0080;
br_i31_decode_mod(a, G, 32, b);
a[0] = 0x107;
br_i31_sub(a, C255_P, NOT(br_i31_sub(a, C255_P, 0)));
/*
* Initialise variables x1, x2, z2, x3 and z3. We set all of them
* into Montgomery representation.
*/
br_i31_montymul(x1, a, C255_R2, C255_P, P0I);
memcpy(x3, x1, sizeof x1);
br_i31_zero(z2, C255_P[0]);
memcpy(x2, z2, sizeof z2);
x2[1] = 0x13000000;
memcpy(z3, x2, sizeof x2);
/*
* kb[] is in big-endian notation, but possibly shorter than k[].
*/
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_mont("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_mont("x2", x2);
print_int_mont("z2", z2);
print_int_mont("x3", x3);
print_int_mont("z3", z3);
*/
c255_add(a, x2, z2);
c255_mul(aa, a, a);
c255_sub(b, x2, z2);
c255_mul(bb, b, b);
c255_sub(e, aa, bb);
c255_add(c, x3, z3);
c255_sub(d, x3, z3);
c255_mul(da, d, a);
c255_mul(cb, c, b);
/* obsolete
print_int_mont("a ", a);
print_int_mont("aa", aa);
print_int_mont("b ", b);
print_int_mont("bb", bb);
print_int_mont("e ", e);
print_int_mont("c ", c);
print_int_mont("d ", d);
print_int_mont("da", da);
print_int_mont("cb", cb);
*/
c255_add(x3, da, cb);
c255_mul(x3, x3, x3);
c255_sub(z3, da, cb);
c255_mul(z3, z3, z3);
c255_mul(z3, z3, x1);
c255_mul(x2, aa, bb);
c255_mul(z2, C255_A24, e);
c255_add(z2, z2, aa);
c255_mul(z2, e, z2);
/* obsolete
print_int_mont("x2", x2);
print_int_mont("z2", z2);
print_int_mont("x3", x3);
print_int_mont("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 ++) {
c255_mul(a, a, a);
c255_mul(a, a, z2);
}
memcpy(b, a, sizeof a);
for (i = 0; i < 14; i ++) {
int j;
for (j = 0; j < 16; j ++) {
c255_mul(b, b, b);
}
c255_mul(b, b, a);
}
for (i = 14; i >= 0; i --) {
c255_mul(b, b, b);
if ((0xFFEB >> i) & 1) {
c255_mul(b, z2, b);
}
}
c255_mul(b, x2, b);
/*
* To avoid a dependency on br_i31_from_monty(), we use
* a Montgomery multiplication with 1.
* memcpy(x2, b, sizeof b);
* br_i31_from_monty(x2, C255_P, P0I);
*/
br_i31_zero(a, C255_P[0]);
a[1] = 1;
br_i31_montymul(x2, a, b, C255_P, P0I);
br_i31_encode(G, 32, x2);
byteswap(G);
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_i31 = {
(uint32_t)0x20000000,
&api_generator,
&api_order,
&api_xoff,
&api_mul,
&api_mulgen,
&api_muladd
};