emo/busybox
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
074b33bf16
busybox/networking/tls_sp_c32.c
Denys Vlasenko 074b33bf16 tls: simplify sp_256_ecc_gen_k_10, cosmetic changes 
Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>
2021-04-26 14:33:38 +02:00

967 lines
26 KiB
C
Raw Blame History

/*
* Copyright (C) 2021 Denys Vlasenko
*
* Licensed under GPLv2, see file LICENSE in this source tree.
*/
#include "tls.h"
#define SP_DEBUG 0
#define FIXED_SECRET 0
#define FIXED_PEER_PUBKEY 0
#if SP_DEBUG
# define dbg(...) fprintf(stderr, __VA_ARGS__)
static void dump_hex(const char *fmt, const void *vp, int len)
{
char hexbuf[32 * 1024 + 4];
const uint8_t *p = vp;
bin2hex(hexbuf, (void*)p, len)[0] = '\0';
dbg(fmt, hexbuf);
}
#else
# define dbg(...) ((void)0)
# define dump_hex(...) ((void)0)
#endif
#undef DIGIT_BIT
#define DIGIT_BIT 32
typedef int32_t sp_digit;
/* The code below is taken from parts of
* wolfssl-3.15.3/wolfcrypt/src/sp_c32.c
* and heavily modified.
* Header comment is kept intact:
*/
/* sp.c
*
* Copyright (C) 2006-2018 wolfSSL Inc.
*
* This file is part of wolfSSL.
*
* wolfSSL is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* wolfSSL is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
*/
/* Implementation by Sean Parkinson. */
typedef struct sp_point {
sp_digit x[2 * 10];
sp_digit y[2 * 10];
sp_digit z[2 * 10];
int infinity;
} sp_point;
/* The modulus (prime) of the curve P256. */
static const sp_digit p256_mod[10] = {
0x3ffffff,0x3ffffff,0x3ffffff,0x003ffff,0x0000000,
0x0000000,0x0000000,0x0000400,0x3ff0000,0x03fffff,
};
#define p256_mp_mod ((sp_digit)0x000001)
/* Mask for address to obfuscate which of the two address will be used. */
static const size_t addr_mask[2] = { 0, (size_t)-1 };
/* The base point of curve P256. */
static const sp_point p256_base = {
/* X ordinate */
{ 0x098c296,0x04e5176,0x33a0f4a,0x204b7ac,0x277037d,0x0e9103c,0x3ce6e56,0x1091fe2,0x1f2e12c,0x01ac5f4 },
/* Y ordinate */
{ 0x3bf51f5,0x1901a0d,0x1ececbb,0x15dacc5,0x22bce33,0x303e785,0x27eb4a7,0x1fe6e3b,0x2e2fe1a,0x013f8d0 },
/* Z ordinate */
{ 0x0000001,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000 },
/* infinity */
0
};
/* Write r as big endian to byte aray.
* Fixed length number of bytes written: 32
*
* r A single precision integer.
* a Byte array.
*/
static void sp_256_to_bin(sp_digit* r, uint8_t* a)
{
int i, j, s = 0, b;
for (i = 0; i < 9; i++) {
r[i+1] += r[i] >> 26;
r[i] &= 0x3ffffff;
}
j = 256 / 8 - 1;
a[j] = 0;
for (i=0; i<10 && j>=0; i++) {
b = 0;
a[j--] |= r[i] << s; b += 8 - s;
if (j < 0)
break;
while (b < 26) {
a[j--] = r[i] >> b; b += 8;
if (j < 0)
break;
}
s = 8 - (b - 26);
if (j >= 0)
a[j] = 0;
if (s != 0)
j++;
}
}
/* Read big endian unsigned byte aray into r.
*
* r A single precision integer.
* a Byte array.
* n Number of bytes in array to read.
*/
static void sp_256_from_bin(sp_digit* r, int max, const uint8_t* a, int n)
{
int i, j = 0, s = 0;
r[0] = 0;
for (i = n-1; i >= 0; i--) {
r[j] |= ((sp_digit)a[i]) << s;
if (s >= 18) {
r[j] &= 0x3ffffff;
s = 26 - s;
if (j + 1 >= max)
break;
r[++j] = a[i] >> s;
s = 8 - s;
}
else
s += 8;
}
for (j++; j < max; j++)
r[j] = 0;
}
/* Convert a point of big-endian 32-byte x,y pair to type sp_point. */
static void sp_256_point_from_bin2x32(sp_point* p, const uint8_t *bin2x32)
{
memset(p, 0, sizeof(*p));
/*p->infinity = 0;*/
sp_256_from_bin(p->x, 2 * 10, bin2x32, 32);
sp_256_from_bin(p->y, 2 * 10, bin2x32 + 32, 32);
//static const uint8_t one[1] = { 1 };
//sp_256_from_bin(p->z, 2 * 10, one, 1);
p->z[0] = 1;
}
/* Compare a with b in constant time.
*
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_256_cmp_10(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
int i;
for (i = 9; i >= 0; i--)
r |= (a[i] - b[i]) & (0 - !r);
return r;
}
/* Compare two numbers to determine if they are equal.
*
* return 1 when equal and 0 otherwise.
*/
static int sp_256_cmp_equal_10(const sp_digit* a, const sp_digit* b)
{
#if 1
sp_digit r = 0;
int i;
for (i = 0; i < 10; i++)
r |= (a[i] ^ b[i]);
return r == 0;
#else
return sp_256_cmp_10(a, b) == 0;
#endif
}
/* Normalize the values in each word to 26 bits. */
static void sp_256_norm_10(sp_digit* a)
{
int i;
for (i = 0; i < 9; i++) {
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
}
}
/* Add b to a into r. (r = a + b) */
static void sp_256_add_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
int i;
for (i = 0; i < 10; i++)
r[i] = a[i] + b[i];
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*/
static void sp_256_cond_add_10(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
int i;
for (i = 0; i < 10; i++)
r[i] = a[i] + (b[i] & m);
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*/
static void sp_256_cond_sub_10(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
int i;
for (i = 0; i < 10; i++)
r[i] = a[i] - (b[i] & m);
}
/* Shift number left one bit. Bottom bit is lost. */
static void sp_256_rshift1_10(sp_digit* r, sp_digit* a)
{
int i;
for (i = 0; i < 9; i++)
r[i] = ((a[i] >> 1) | (a[i + 1] << 25)) & 0x3ffffff;
r[9] = a[9] >> 1;
}
/* Multiply a number by Montogmery normalizer mod modulus (prime).
*
* r The resulting Montgomery form number.
* a The number to convert.
*/
static void sp_256_mod_mul_norm_10(sp_digit* r, const sp_digit* a)
{
int64_t t[8];
int64_t a32[8];
int64_t o;
a32[0] = a[0];
a32[0] |= a[1] << 26;
a32[0] &= 0xffffffff;
a32[1] = (sp_digit)(a[1] >> 6);
a32[1] |= a[2] << 20;
a32[1] &= 0xffffffff;
a32[2] = (sp_digit)(a[2] >> 12);
a32[2] |= a[3] << 14;
a32[2] &= 0xffffffff;
a32[3] = (sp_digit)(a[3] >> 18);
a32[3] |= a[4] << 8;
a32[3] &= 0xffffffff;
a32[4] = (sp_digit)(a[4] >> 24);
a32[4] |= a[5] << 2;
a32[4] |= a[6] << 28;
a32[4] &= 0xffffffff;
a32[5] = (sp_digit)(a[6] >> 4);
a32[5] |= a[7] << 22;
a32[5] &= 0xffffffff;
a32[6] = (sp_digit)(a[7] >> 10);
a32[6] |= a[8] << 16;
a32[6] &= 0xffffffff;
a32[7] = (sp_digit)(a[8] >> 16);
a32[7] |= a[9] << 10;
a32[7] &= 0xffffffff;
/* 1 1 0 -1 -1 -1 -1 0 */
t[0] = 0 + a32[0] + a32[1] - a32[3] - a32[4] - a32[5] - a32[6];
/* 0 1 1 0 -1 -1 -1 -1 */
t[1] = 0 + a32[1] + a32[2] - a32[4] - a32[5] - a32[6] - a32[7];
/* 0 0 1 1 0 -1 -1 -1 */
t[2] = 0 + a32[2] + a32[3] - a32[5] - a32[6] - a32[7];
/* -1 -1 0 2 2 1 0 -1 */
t[3] = 0 - a32[0] - a32[1] + 2 * a32[3] + 2 * a32[4] + a32[5] - a32[7];
/* 0 -1 -1 0 2 2 1 0 */
t[4] = 0 - a32[1] - a32[2] + 2 * a32[4] + 2 * a32[5] + a32[6];
/* 0 0 -1 -1 0 2 2 1 */
t[5] = 0 - a32[2] - a32[3] + 2 * a32[5] + 2 * a32[6] + a32[7];
/* -1 -1 0 0 0 1 3 2 */
t[6] = 0 - a32[0] - a32[1] + a32[5] + 3 * a32[6] + 2 * a32[7];
/* 1 0 -1 -1 -1 -1 0 3 */
t[7] = 0 + a32[0] - a32[2] - a32[3] - a32[4] - a32[5] + 3 * a32[7];
t[1] += t[0] >> 32; t[0] &= 0xffffffff;
t[2] += t[1] >> 32; t[1] &= 0xffffffff;
t[3] += t[2] >> 32; t[2] &= 0xffffffff;
t[4] += t[3] >> 32; t[3] &= 0xffffffff;
t[5] += t[4] >> 32; t[4] &= 0xffffffff;
t[6] += t[5] >> 32; t[5] &= 0xffffffff;
t[7] += t[6] >> 32; t[6] &= 0xffffffff;
o = t[7] >> 32; t[7] &= 0xffffffff;
t[0] += o;
t[3] -= o;
t[6] -= o;
t[7] += o;
t[1] += t[0] >> 32; t[0] &= 0xffffffff;
t[2] += t[1] >> 32; t[1] &= 0xffffffff;
t[3] += t[2] >> 32; t[2] &= 0xffffffff;
t[4] += t[3] >> 32; t[3] &= 0xffffffff;
t[5] += t[4] >> 32; t[4] &= 0xffffffff;
t[6] += t[5] >> 32; t[5] &= 0xffffffff;
t[7] += t[6] >> 32; t[6] &= 0xffffffff;
r[0] = (sp_digit)(t[0]) & 0x3ffffff;
r[1] = (sp_digit)(t[0] >> 26);
r[1] |= t[1] << 6;
r[1] &= 0x3ffffff;
r[2] = (sp_digit)(t[1] >> 20);
r[2] |= t[2] << 12;
r[2] &= 0x3ffffff;
r[3] = (sp_digit)(t[2] >> 14);
r[3] |= t[3] << 18;
r[3] &= 0x3ffffff;
r[4] = (sp_digit)(t[3] >> 8);
r[4] |= t[4] << 24;
r[4] &= 0x3ffffff;
r[5] = (sp_digit)(t[4] >> 2) & 0x3ffffff;
r[6] = (sp_digit)(t[4] >> 28);
r[6] |= t[5] << 4;
r[6] &= 0x3ffffff;
r[7] = (sp_digit)(t[5] >> 22);
r[7] |= t[6] << 10;
r[7] &= 0x3ffffff;
r[8] = (sp_digit)(t[6] >> 16);
r[8] |= t[7] << 16;
r[8] &= 0x3ffffff;
r[9] = (sp_digit)(t[7] >> 10);
}
/* Mul a by scalar b and add into r. (r += a * b) */
static void sp_256_mul_add_10(sp_digit* r, const sp_digit* a, sp_digit b)
{
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 10; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x3ffffff;
t >>= 26;
}
r[10] += t;
}
/* Divide the number by 2 mod the modulus (prime). (r = a / 2 % m) */
static void sp_256_div2_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
sp_256_cond_add_10(r, a, m, 0 - (a[0] & 1));
sp_256_norm_10(r);
sp_256_rshift1_10(r, r);
}
/* Shift the result in the high 256 bits down to the bottom. */
static void sp_256_mont_shift_10(sp_digit* r, const sp_digit* a)
{
int i;
sp_digit n, s;
s = a[10];
n = a[9] >> 22;
for (i = 0; i < 9; i++) {
n += (s & 0x3ffffff) << 4;
r[i] = n & 0x3ffffff;
n >>= 26;
s = a[11 + i] + (s >> 26);
}
n += s << 4;
r[9] = n;
memset(&r[10], 0, sizeof(*r) * 10);
}
/* Add two Montgomery form numbers (r = a + b % m) */
static void sp_256_mont_add_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m)
{
sp_256_add_10(r, a, b);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - ((r[9] >> 22) > 0));
sp_256_norm_10(r);
}
/* Double a Montgomery form number (r = a + a % m) */
static void sp_256_mont_dbl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
sp_256_add_10(r, a, a);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - ((r[9] >> 22) > 0));
sp_256_norm_10(r);
}
/* Triple a Montgomery form number (r = a + a + a % m) */
static void sp_256_mont_tpl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
sp_256_add_10(r, a, a);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - ((r[9] >> 22) > 0));
sp_256_norm_10(r);
sp_256_add_10(r, r, a);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - ((r[9] >> 22) > 0));
sp_256_norm_10(r);
}
/* Sub b from a into r. (r = a - b) */
static void sp_256_sub_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
int i;
for (i = 0; i < 10; i++)
r[i] = a[i] - b[i];
}
/* Subtract two Montgomery form numbers (r = a - b % m) */
static void sp_256_mont_sub_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m)
{
sp_256_sub_10(r, a, b);
sp_256_cond_add_10(r, r, m, r[9] >> 22);
sp_256_norm_10(r);
}
/* Reduce the number back to 256 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_256_mont_reduce_10(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
if (mp != 1) {
for (i = 0; i < 9; i++) {
mu = (a[i] * mp) & 0x3ffffff;
sp_256_mul_add_10(a+i, m, mu);
a[i+1] += a[i] >> 26;
}
mu = (a[i] * mp) & 0x3fffffl;
sp_256_mul_add_10(a+i, m, mu);
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
}
else {
for (i = 0; i < 9; i++) {
mu = a[i] & 0x3ffffff;
sp_256_mul_add_10(a+i, p256_mod, mu);
a[i+1] += a[i] >> 26;
}
mu = a[i] & 0x3fffffl;
sp_256_mul_add_10(a+i, p256_mod, mu);
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
}
sp_256_mont_shift_10(a, a);
sp_256_cond_sub_10(a, a, m, 0 - ((a[9] >> 22) > 0));
sp_256_norm_10(a);
}
/* Multiply a and b into r. (r = a * b) */
static void sp_256_mul_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[9]) * b[9];
r[19] = (sp_digit)(c >> 26);
c = (c & 0x3ffffff) << 26;
for (k = 17; k >= 0; k--) {
for (i = 9; i >= 0; i--) {
j = k - i;
if (j >= 10)
break;
if (j < 0)
continue;
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 52;
r[k + 1] = (c >> 26) & 0x3ffffff;
c = (c & 0x3ffffff) << 26;
}
r[0] = (sp_digit)(c >> 26);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_256_mont_mul_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_256_mul_10(r, a, b);
sp_256_mont_reduce_10(r, m, mp);
}
/* Square a and put result in r. (r = a * a) */
static void sp_256_sqr_10(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[9]) * a[9];
r[19] = (sp_digit)(c >> 26);
c = (c & 0x3ffffff) << 26;
for (k = 17; k >= 0; k--) {
for (i = 9; i >= 0; i--) {
j = k - i;
if (j >= 10 || i <= j)
break;
if (j < 0)
continue;
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j)
c += ((int64_t)a[i]) * a[i];
r[k + 2] += c >> 52;
r[k + 1] = (c >> 26) & 0x3ffffff;
c = (c & 0x3ffffff) << 26;
}
r[0] = (sp_digit)(c >> 26);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_256_mont_sqr_10(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_256_sqr_10(r, a);
sp_256_mont_reduce_10(r, m, mp);
}
/* Invert the number, in Montgomery form, modulo the modulus (prime) of the
* P256 curve. (r = 1 / a mod m)
*
* r Inverse result.
* a Number to invert.
* td Temporary data.
*/
/* Mod-2 for the P256 curve. */
static const uint32_t p256_mod_2[8] = {
0xfffffffd,0xffffffff,0xffffffff,0x00000000,
0x00000000,0x00000000,0x00000001,0xffffffff,
};
static void sp_256_mont_inv_10(sp_digit* r, sp_digit* a, sp_digit* td)
{
sp_digit* t = td;
int i;
memcpy(t, a, sizeof(sp_digit) * 10);
for (i = 254; i >= 0; i--) {
sp_256_mont_sqr_10(t, t, p256_mod, p256_mp_mod);
if (p256_mod_2[i / 32] & ((sp_digit)1 << (i % 32)))
sp_256_mont_mul_10(t, t, a, p256_mod, p256_mp_mod);
}
memcpy(r, t, sizeof(sp_digit) * 10);
}
/* Map the Montgomery form projective co-ordinate point to an affine point.
*
* r Resulting affine co-ordinate point.
* p Montgomery form projective co-ordinate point.
* t Temporary ordinate data.
*/
static void sp_256_map_10(sp_point* r, sp_point* p, sp_digit* t)
{
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
int32_t n;
sp_256_mont_inv_10(t1, p->z, t + 2*10);
sp_256_mont_sqr_10(t2, t1, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t1, t2, t1, p256_mod, p256_mp_mod);
/* x /= z^2 */
sp_256_mont_mul_10(r->x, p->x, t2, p256_mod, p256_mp_mod);
memset(r->x + 10, 0, sizeof(r->x) / 2);
sp_256_mont_reduce_10(r->x, p256_mod, p256_mp_mod);
/* Reduce x to less than modulus */
n = sp_256_cmp_10(r->x, p256_mod);
sp_256_cond_sub_10(r->x, r->x, p256_mod, 0 - (n >= 0));
sp_256_norm_10(r->x);
/* y /= z^3 */
sp_256_mont_mul_10(r->y, p->y, t1, p256_mod, p256_mp_mod);
memset(r->y + 10, 0, sizeof(r->y) / 2);
sp_256_mont_reduce_10(r->y, p256_mod, p256_mp_mod);
/* Reduce y to less than modulus */
n = sp_256_cmp_10(r->y, p256_mod);
sp_256_cond_sub_10(r->y, r->y, p256_mod, 0 - (n >= 0));
sp_256_norm_10(r->y);
memset(r->z, 0, sizeof(r->z));
r->z[0] = 1;
}
/* Double the Montgomery form projective point p.
*
* r Result of doubling point.
* p Point to double.
* t Temporary ordinate data.
*/
static void sp_256_proj_point_dbl_10(sp_point* r, sp_point* p, sp_digit* t)
{
sp_point *rp[2];
sp_point tp;
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
sp_digit* x;
sp_digit* y;
sp_digit* z;
int i;
/* When infinity don't double point passed in - constant time. */
rp[0] = r;
rp[1] = &tp;
x = rp[p->infinity]->x;
y = rp[p->infinity]->y;
z = rp[p->infinity]->z;
/* Put point to double into result - good for infinity. */
if (r != p) {
for (i = 0; i < 10; i++)
r->x[i] = p->x[i];
for (i = 0; i < 10; i++)
r->y[i] = p->y[i];
for (i = 0; i < 10; i++)
r->z[i] = p->z[i];
r->infinity = p->infinity;
}
/* T1 = Z * Z */
sp_256_mont_sqr_10(t1, z, p256_mod, p256_mp_mod);
/* Z = Y * Z */
sp_256_mont_mul_10(z, y, z, p256_mod, p256_mp_mod);
/* Z = 2Z */
sp_256_mont_dbl_10(z, z, p256_mod);
/* T2 = X - T1 */
sp_256_mont_sub_10(t2, x, t1, p256_mod);
/* T1 = X + T1 */
sp_256_mont_add_10(t1, x, t1, p256_mod);
/* T2 = T1 * T2 */
sp_256_mont_mul_10(t2, t1, t2, p256_mod, p256_mp_mod);
/* T1 = 3T2 */
sp_256_mont_tpl_10(t1, t2, p256_mod);
/* Y = 2Y */
sp_256_mont_dbl_10(y, y, p256_mod);
/* Y = Y * Y */
sp_256_mont_sqr_10(y, y, p256_mod, p256_mp_mod);
/* T2 = Y * Y */
sp_256_mont_sqr_10(t2, y, p256_mod, p256_mp_mod);
/* T2 = T2/2 */
sp_256_div2_10(t2, t2, p256_mod);
/* Y = Y * X */
sp_256_mont_mul_10(y, y, x, p256_mod, p256_mp_mod);
/* X = T1 * T1 */
sp_256_mont_mul_10(x, t1, t1, p256_mod, p256_mp_mod);
/* X = X - Y */
sp_256_mont_sub_10(x, x, y, p256_mod);
/* X = X - Y */
sp_256_mont_sub_10(x, x, y, p256_mod);
/* Y = Y - X */
sp_256_mont_sub_10(y, y, x, p256_mod);
/* Y = Y * T1 */
sp_256_mont_mul_10(y, y, t1, p256_mod, p256_mp_mod);
/* Y = Y - T2 */
sp_256_mont_sub_10(y, y, t2, p256_mod);
}
/* Add two Montgomery form projective points.
*
* r Result of addition.
* p Frist point to add.
* q Second point to add.
* t Temporary ordinate data.
*/
static void sp_256_proj_point_add_10(sp_point* r, sp_point* p, sp_point* q,
sp_digit* t)
{
sp_point *ap[2];
sp_point *rp[2];
sp_point tp;
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
sp_digit* t3 = t + 4*10;
sp_digit* t4 = t + 6*10;
sp_digit* t5 = t + 8*10;
sp_digit* x;
sp_digit* y;
sp_digit* z;
int i;
/* Ensure only the first point is the same as the result. */
if (q == r) {
sp_point* a = p;
p = q;
q = a;
}
/* Check double */
sp_256_sub_10(t1, p256_mod, q->y);
sp_256_norm_10(t1);
if (sp_256_cmp_equal_10(p->x, q->x)
& sp_256_cmp_equal_10(p->z, q->z)
& (sp_256_cmp_equal_10(p->y, q->y) | sp_256_cmp_equal_10(p->y, t1))
) {
sp_256_proj_point_dbl_10(r, p, t);
}
else {
rp[0] = r;
rp[1] = &tp;
memset(&tp, 0, sizeof(tp));
x = rp[p->infinity | q->infinity]->x;
y = rp[p->infinity | q->infinity]->y;
z = rp[p->infinity | q->infinity]->z;
ap[0] = p;
ap[1] = q;
for (i=0; i<10; i++)
r->x[i] = ap[p->infinity]->x[i];
for (i=0; i<10; i++)
r->y[i] = ap[p->infinity]->y[i];
for (i=0; i<10; i++)
r->z[i] = ap[p->infinity]->z[i];
r->infinity = ap[p->infinity]->infinity;
/* U1 = X1*Z2^2 */
sp_256_mont_sqr_10(t1, q->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t3, t1, q->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t1, t1, x, p256_mod, p256_mp_mod);
/* U2 = X2*Z1^2 */
sp_256_mont_sqr_10(t2, z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t4, t2, z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t2, t2, q->x, p256_mod, p256_mp_mod);
/* S1 = Y1*Z2^3 */
sp_256_mont_mul_10(t3, t3, y, p256_mod, p256_mp_mod);
/* S2 = Y2*Z1^3 */
sp_256_mont_mul_10(t4, t4, q->y, p256_mod, p256_mp_mod);
/* H = U2 - U1 */
sp_256_mont_sub_10(t2, t2, t1, p256_mod);
/* R = S2 - S1 */
sp_256_mont_sub_10(t4, t4, t3, p256_mod);
/* Z3 = H*Z1*Z2 */
sp_256_mont_mul_10(z, z, q->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(z, z, t2, p256_mod, p256_mp_mod);
/* X3 = R^2 - H^3 - 2*U1*H^2 */
sp_256_mont_sqr_10(x, t4, p256_mod, p256_mp_mod);
sp_256_mont_sqr_10(t5, t2, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(y, t1, t5, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t5, t5, t2, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(x, x, t5, p256_mod);
sp_256_mont_dbl_10(t1, y, p256_mod);
sp_256_mont_sub_10(x, x, t1, p256_mod);
/* Y3 = R*(U1*H^2 - X3) - S1*H^3 */
sp_256_mont_sub_10(y, y, x, p256_mod);
sp_256_mont_mul_10(y, y, t4, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t5, t5, t3, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(y, y, t5, p256_mod);
}
}
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
*/
static void sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit* k /*, int map*/)
{
enum { map = 1 }; /* we always convert result to affine coordinates */
sp_point td[3];
sp_point* t[3];
sp_digit tmp[2 * 10 * 5];
sp_digit n;
int i;
int c, y;
memset(td, 0, sizeof(td));
t[0] = &td[0];
t[1] = &td[1];
t[2] = &td[2];
/* t[0] = {0, 0, 1} * norm */
t[0]->infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
sp_256_mod_mul_norm_10(t[1]->x, g->x);
sp_256_mod_mul_norm_10(t[1]->y, g->y);
sp_256_mod_mul_norm_10(t[1]->z, g->z);
i = 9;
c = 22;
n = k[i--] << (26 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1)
break;
n = k[i--];
c = 26;
}
y = (n >> 25) & 1;
n <<= 1;
sp_256_proj_point_add_10(t[y^1], t[0], t[1], tmp);
///FIXME type (or rewrite - get rid of t[] array)
memcpy(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(sp_point));
sp_256_proj_point_dbl_10(t[2], t[2], tmp);
memcpy((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(sp_point));
}
if (map)
sp_256_map_10(r, t[0], tmp);
else
memcpy(r, t[0], sizeof(sp_point));
memset(tmp, 0, sizeof(tmp)); //paranoia
memset(td, 0, sizeof(td)); //paranoia
}
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* k Scalar to multiply by.
*/
static void sp_256_ecc_mulmod_base_10(sp_point* r, sp_digit* k /*, int map*/)
{
sp_256_ecc_mulmod_10(r, &p256_base, k /*, map*/);
}
/* Multiply the point by the scalar and serialize the X ordinate.
* The number is 0 padded to maximum size on output.
*
* priv Scalar to multiply the point by.
* pub2x32 Point to multiply.
* out32 Buffer to hold X ordinate.
*/
static void sp_ecc_secret_gen_256(sp_digit priv[10], const uint8_t *pub2x32, uint8_t* out32)
{
sp_point point[1];
#if FIXED_PEER_PUBKEY
memset((void*)pub2x32, 0x55, 64);
#endif
dump_hex("peerkey %s\n", pub2x32, 32); /* in TLS, this is peer's public key */
dump_hex(" %s\n", pub2x32 + 32, 32);
sp_256_point_from_bin2x32(point, pub2x32);
dump_hex("point->x %s\n", point->x, sizeof(point->x));
dump_hex("point->y %s\n", point->y, sizeof(point->y));
sp_256_ecc_mulmod_10(point, point, priv);
sp_256_to_bin(point->x, out32);
dump_hex("out32: %s\n", out32, 32);
}
/* Generates a scalar that is in the range 1..order-1. */
#define SIMPLIFY 1
/* Add 1 to a. (a = a + 1) */
#if !SIMPLIFY
static void sp_256_add_one_10(sp_digit* a)
{
a[0]++;
sp_256_norm_10(a);
}
#endif
static void sp_256_ecc_gen_k_10(sp_digit k[10])
{
#if !SIMPLIFY
/* The order of the curve P256 minus 2. */
static const sp_digit p256_order2[10] = {
0x063254f,0x272b0bf,0x1e84f3b,0x2b69c5e,0x3bce6fa,
0x3ffffff,0x3ffffff,0x00003ff,0x3ff0000,0x03fffff,
};
#endif
uint8_t buf[32];
for (;;) {
tls_get_random(buf, sizeof(buf));
#if FIXED_SECRET
memset(buf, 0x77, sizeof(buf));
#endif
sp_256_from_bin(k, 10, buf, sizeof(buf));
#if !SIMPLIFY
if (sp_256_cmp_10(k, p256_order2) < 0)
break;
#else
/* non-loopy version (and not needing p256_order2[]):
* if most-significant word seems that k can be larger
* than p256_order2, fix it up:
*/
if (k[9] >= 0x03fffff)
k[9] = 0x03ffffe;
break;
#endif
}
#if !SIMPLIFY
sp_256_add_one_10(k);
#else
if (k[0] == 0)
k[0] = 1;
#endif
#undef SIMPLIFY
}
/* Makes a random EC key pair. */
static void sp_ecc_make_key_256(sp_digit privkey[10], uint8_t *pubkey)
{
sp_point point[1];
sp_256_ecc_gen_k_10(privkey);
sp_256_ecc_mulmod_base_10(point, privkey);
sp_256_to_bin(point->x, pubkey);
sp_256_to_bin(point->y, pubkey + 32);
memset(point, 0, sizeof(point)); //paranoia
}
void FAST_FUNC curve_P256_compute_pubkey_and_premaster(
uint8_t *pubkey2x32, uint8_t *premaster32,
const uint8_t *peerkey2x32)
{
sp_digit privkey[10];
sp_ecc_make_key_256(privkey, pubkey2x32);
dump_hex("pubkey: %s\n", pubkey2x32, 32);
dump_hex(" %s\n", pubkey2x32 + 32, 32);
/* Combine our privkey and peer's public key to generate premaster */
sp_ecc_secret_gen_256(privkey, /*x,y:*/peerkey2x32, premaster32);
dump_hex("premaster: %s\n", premaster32, 32);
}
Reference in New Issue View Git Blame Copy Permalink