mirror of
https://github.com/trezor/trezor-firmware.git
synced 2024-12-26 16:18:22 +00:00
import sources
This commit is contained in:
Pavol Rusnak
commit
ccbc219b29
2
.gitignore
vendored
Normal file
2
.gitignore
vendored
Normal file
@ -0,0 +1,2 @@
|
||||
*.o
|
||||
test
|
||||
2
AUTHORS
Normal file
2
AUTHORS
Normal file
@ -0,0 +1,2 @@
|
||||
Tomas Dzetkulic <dzetkulic@gmail.com>
|
||||
Pavol Rusnak <stick@gk2.sk>
|
||||
20
LICENSE
Normal file
20
LICENSE
Normal file
@ -0,0 +1,20 @@
|
||||
Copyright (c) 2013 Tomas Dzetkulic
|
||||
Copyright (c) 2013 Pavol Rusnak
|
||||
|
||||
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.
|
||||
13
Makefile
Normal file
13
Makefile
Normal file
@ -0,0 +1,13 @@
|
||||
CC = gcc
|
||||
CFLAGS = -Wall
|
||||
OBJS = aux.o ecdsa.o secp256k1.o sha256.o rand.o test.o
|
||||
NAME = test
|
||||
|
||||
%.o: %.c
|
||||
$(CC) $(CFLAGS) -o $@ -c $<
|
||||
|
||||
$(NAME): $(OBJS)
|
||||
gcc $(OBJS) -o $(NAME) -lcrypto
|
||||
|
||||
clean:
|
||||
rm -f $(OBJS) $(NAME)
|
||||
6
README
Normal file
6
README
Normal file
@ -0,0 +1,6 @@
|
||||
MicroECDSA
|
||||
==========
|
||||
|
||||
Heavily optimized ECDSA (secp256k1) signer for embedded devices.
|
||||
|
||||
Distibuted under MIT License.
|
||||
45
aux.c
Normal file
45
aux.c
Normal file
@ -0,0 +1,45 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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 "aux.h"
|
||||
|
||||
inline uint32_t ror(const uint32_t x, const int n)
|
||||
{
|
||||
return (x >> n) | (x << (32 - n));
|
||||
}
|
||||
|
||||
inline uint32_t read_be(const uint8_t *data)
|
||||
{
|
||||
return (((uint32_t)data[0]) << 24) |
|
||||
(((uint32_t)data[1]) << 16) |
|
||||
(((uint32_t)data[2]) << 8) |
|
||||
(((uint32_t)data[3]));
|
||||
}
|
||||
|
||||
inline void write_be(uint8_t *data, uint32_t x)
|
||||
{
|
||||
data[0] = x >> 24;
|
||||
data[1] = x >> 16;
|
||||
data[2] = x >>8;
|
||||
data[3] = x;
|
||||
}
|
||||
38
aux.h
Normal file
38
aux.h
Normal file
@ -0,0 +1,38 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
|
||||
#ifndef __AUX_H__
|
||||
#define __AUX_H__
|
||||
|
||||
#include <stdint.h>
|
||||
|
||||
// rotate uint32 right
|
||||
inline uint32_t ror(const uint32_t x, const int n);
|
||||
|
||||
// read 4 big endian bytes into uint32
|
||||
inline uint32_t read_be(const uint8_t *data);
|
||||
|
||||
// write 4 big endian bytes
|
||||
inline void write_be(uint8_t *data, uint32_t x);
|
||||
|
||||
#endif
|
||||
515
ecdsa.c
Normal file
515
ecdsa.c
Normal file
@ -0,0 +1,515 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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 <stdint.h>
|
||||
#include <stdlib.h>
|
||||
#include <string.h>
|
||||
|
||||
#include "rand.h"
|
||||
#include "sha256.h"
|
||||
#include "ecdsa.h"
|
||||
#include "secp256k1.h"
|
||||
#include "aux.h"
|
||||
|
||||
// assumes x < 2*prime
|
||||
void mod(bignum256 *x, bignum256 const *prime)
|
||||
{
|
||||
int i = 8;
|
||||
uint32_t temp;
|
||||
// compare numbers
|
||||
while (i >= 0 && prime->val[i] == x->val[i]) --i;
|
||||
// if equal
|
||||
if (i==-1) {
|
||||
// set x to zero
|
||||
for (i = 0; i < 9; i++) {
|
||||
x->val[i] = 0;
|
||||
}
|
||||
} else {
|
||||
// if x is greater
|
||||
if (x->val[i] > prime->val[i]) {
|
||||
// substract p from x
|
||||
temp = 0x40000000u;
|
||||
for (i = 0;i < 9; i++) {
|
||||
temp += x->val[i] - prime->val[i];
|
||||
x->val[i] = temp & 0x3FFFFFFF;
|
||||
temp >>= 30;
|
||||
temp += 0x3FFFFFFFu;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// x = k * x
|
||||
// both inputs and result may be bigger than prime but not bigger than 2 * prime
|
||||
void multiply(const bignum256 *k, bignum256 *x, bignum256 const *prime)
|
||||
{
|
||||
int i, j;
|
||||
uint64_t temp = 0;
|
||||
uint32_t res[18], coef;
|
||||
|
||||
// compute lower half of long multiplication
|
||||
for (i = 0;i < 9; i++)
|
||||
{
|
||||
for (j = 0;j <= i; j++) {
|
||||
temp += k->val[j] * (uint64_t)x->val[i-j];
|
||||
}
|
||||
res[i] = temp & 0x3FFFFFFFu;
|
||||
temp >>= 30;
|
||||
}
|
||||
// compute upper half
|
||||
for (;i < 17; i++)
|
||||
{
|
||||
for (j = i - 8; j < 9 ;j++) {
|
||||
temp += k->val[j] * (uint64_t)x->val[i-j];
|
||||
}
|
||||
res[i] = temp & 0x3FFFFFFFu;
|
||||
temp >>= 30;
|
||||
}
|
||||
res[17] = temp;
|
||||
// compute modulo p division is only estimated so this may give result greater than prime but not bigger than 2 * prime
|
||||
for (i = 16;i >= 8; i--) {
|
||||
// estimate (res / prime)
|
||||
coef = (res[i] >> 16) + (res[i+1] << 14);
|
||||
// substract (coef * prime) from res
|
||||
temp = 0x1000000000000000llu + res[i-8] - prime->val[0] * (uint64_t)coef;
|
||||
res[i-8] = temp & 0x3FFFFFFF;
|
||||
for (j = 1; j < 9; j++) {
|
||||
temp >>= 30;
|
||||
temp += 0xFFFFFFFC0000000llu + res[i-8+j] - prime->val[j] * (uint64_t)coef;
|
||||
res[i - 8 + j] = temp & 0x3FFFFFFF;
|
||||
}
|
||||
}
|
||||
// store the result
|
||||
for (i = 0;i < 9; i++) {
|
||||
x->val[i] = res[i];
|
||||
}
|
||||
}
|
||||
|
||||
void fast_mod(bignum256 *x, bignum256 const *prime)
|
||||
{
|
||||
int j;
|
||||
uint32_t coef;
|
||||
uint64_t temp;
|
||||
|
||||
coef = x->val[8] >> 16;
|
||||
if (!coef) return;
|
||||
// substract (coef * prime) from x
|
||||
temp = 0x1000000000000000llu + x->val[0] - prime->val[0] * (uint64_t)coef;
|
||||
x->val[0] = temp & 0x3FFFFFFF;
|
||||
for (j = 1; j < 9; j++) {
|
||||
temp >>= 30;
|
||||
temp += 0xFFFFFFFC0000000llu + x->val[j] - prime->val[j] * (uint64_t)coef;
|
||||
x->val[j] = temp & 0x3FFFFFFF;
|
||||
}
|
||||
}
|
||||
|
||||
// in field G_prime
|
||||
void inverse(bignum256 *x, bignum256 const *prime)
|
||||
{
|
||||
int i, j, k, len1, len2, mask;
|
||||
uint32_t u[9], v[9], s[10], r[10], temp, temp2;
|
||||
fast_mod(x, prime);
|
||||
mod(x, prime);
|
||||
for (i = 0; i < 9; i++) {
|
||||
u[i] = prime->val[i];
|
||||
v[i] = x->val[i];
|
||||
}
|
||||
len1 = 9;
|
||||
s[0] = 1;
|
||||
r[0] = 0;
|
||||
len2 = 1;
|
||||
k = 0;
|
||||
for (;;) {
|
||||
for (i = 0;i < len1; i++) {
|
||||
if (v[i]) break;
|
||||
}
|
||||
if (i == len1) break;
|
||||
for (;;) {
|
||||
for (i = 0;i < 30; i++) {
|
||||
if (u[0] & (1 << i)) break;
|
||||
}
|
||||
if (i == 0) break;
|
||||
mask=(1 << i) - 1;
|
||||
for (j = 0; j + 1 < len1; j++) {
|
||||
u[j] = (u[j] >> i) | ((u[j + 1] & mask) << (30 - i));
|
||||
}
|
||||
u[j] = (u[j] >> i);
|
||||
mask=(1 << (30 - i)) - 1;
|
||||
s[len2] = s[len2 - 1] >> (30 - i);
|
||||
for (j = len2 - 1; j > 0; j--) {
|
||||
s[j] = (s[j - 1] >> (30 - i)) | ((s[j] & mask) << i);
|
||||
}
|
||||
s[0] = (s[0] & mask) << i;
|
||||
if (s[len2]) {
|
||||
r[len2]=0;
|
||||
len2++;
|
||||
}
|
||||
k += i;
|
||||
}
|
||||
for (;;) {
|
||||
for (i = 0;i < 30; i++) {
|
||||
if (v[0] & (1 << i)) break;
|
||||
}
|
||||
if (i == 0) break;
|
||||
mask = (1 << i) - 1;
|
||||
for (j = 0; j + 1 < len1; j++) {
|
||||
v[j] = (v[j] >> i) | ((v[j + 1] & mask) << (30 - i));
|
||||
}
|
||||
v[j] = (v[j] >> i);
|
||||
mask=(1 << (30 - i)) - 1;
|
||||
r[len2] = r[len2 - 1] >> (30 - i);
|
||||
for (j = len2 - 1; j > 0; j--) {
|
||||
r[j] = (r[j - 1] >> (30 - i)) | ((r[j] & mask) << i);
|
||||
}
|
||||
r[0] = (r[0] & mask) << i;
|
||||
if (r[len2]) {
|
||||
s[len2]=0;
|
||||
len2++;
|
||||
}
|
||||
k += i;
|
||||
}
|
||||
|
||||
i = len1 - 1;
|
||||
while (i>0 && u[i] == v[i]) i--;
|
||||
if (u[i] > v[i]) {
|
||||
temp = 0x40000000u + u[0] - v[0];
|
||||
u[0] = (temp >> 1) & 0x1FFFFFFF;
|
||||
temp >>= 30;
|
||||
for (i = 1; i < len1; i++) {
|
||||
temp += 0x3FFFFFFFu + u[i] - v[i];
|
||||
u[i-1] += (temp & 1) << 29;
|
||||
u[i] = (temp >> 1) & 0x1FFFFFFF;
|
||||
temp >>= 30;
|
||||
}
|
||||
temp = temp2 = 0;
|
||||
for (i = 0; i < len2; i++) {
|
||||
temp += s[i] + r[i];
|
||||
temp2 += s[i] << 1;
|
||||
r[i] = temp & 0x3FFFFFFF;
|
||||
s[i] = temp2 & 0x3FFFFFFF;
|
||||
temp >>= 30;
|
||||
temp2 >>= 30;
|
||||
}
|
||||
if (temp != 0 || temp2 != 0) {
|
||||
r[len2] = temp;
|
||||
s[len2] = temp2;
|
||||
len2++;
|
||||
}
|
||||
} else {
|
||||
temp = 0x40000000u + v[0] - u[0];
|
||||
v[0] = (temp >> 1) & 0x1FFFFFFF;
|
||||
temp >>= 30;
|
||||
for (i = 1; i < len1; i++) {
|
||||
temp += 0x3FFFFFFFu + v[i] - u[i];
|
||||
v[i-1] += (temp & 1) << 29;
|
||||
v[i] = (temp >> 1) & 0x1FFFFFFF;
|
||||
temp >>= 30;
|
||||
}
|
||||
temp = temp2 = 0;
|
||||
for (i = 0; i < len2; i++) {
|
||||
temp += s[i] + r[i];
|
||||
temp2 += r[i] << 1;
|
||||
s[i] = temp & 0x3FFFFFFF;
|
||||
r[i] = temp2 & 0x3FFFFFFF;
|
||||
temp >>= 30;
|
||||
temp2 >>= 30;
|
||||
}
|
||||
if (temp != 0 || temp2 != 0) {
|
||||
s[len2] = temp;
|
||||
r[len2] = temp2;
|
||||
len2++;
|
||||
}
|
||||
}
|
||||
if (u[len1 - 1]==0 && v[len1 - 1]==0) len1--;
|
||||
k++;
|
||||
}
|
||||
i = 8;
|
||||
while (i>0 && r[i] == prime->val[i]) i--;
|
||||
if (r[i] >= prime->val[i]) {
|
||||
temp = 1;
|
||||
for (i = 0; i < 9; i++) {
|
||||
temp += 0x3FFFFFFF + r[i] - prime->val[i];
|
||||
r[i] = temp & 0x3FFFFFFF;
|
||||
temp >>= 30;
|
||||
}
|
||||
}
|
||||
temp = 1;
|
||||
for (i = 0;i < 9; i++) {
|
||||
temp += 0x3FFFFFFF + prime->val[i] - r[i];
|
||||
r[i] = temp & 0x3FFFFFFF;
|
||||
temp >>= 30;
|
||||
}
|
||||
int done = 0;
|
||||
#ifdef USE_PRECOMPUTED_IV
|
||||
if (prime == &prime256k1) {
|
||||
for (j = 0; j < 9; j++) {
|
||||
x->val[j] = r[j];
|
||||
}
|
||||
multiply(secp256k1_iv + k - 256, x, prime);
|
||||
fast_mod(x, prime);
|
||||
done = 1;
|
||||
}
|
||||
#endif
|
||||
if (!done) {
|
||||
for (j = 0; j < k; j++) {
|
||||
if (r[0] & 1) {
|
||||
temp = r[0] + prime->val[0];
|
||||
r[0] = (temp >> 1) & 0x1FFFFFFF;
|
||||
temp >>= 30;
|
||||
for (i = 1;i < 9; i++) {
|
||||
temp += r[i] + prime->val[i];
|
||||
r[i-1] += (temp & 1) << 29;
|
||||
r[i] = (temp >> 1) & 0x1FFFFFFF;
|
||||
temp >>= 30;
|
||||
}
|
||||
} else {
|
||||
for (i = 0; i < 8; i++) {
|
||||
r[i] = (r[i] >> 1) | ((r[i+1] & 1) << 29);
|
||||
}
|
||||
r[8] = r[8] >> 1;
|
||||
}
|
||||
}
|
||||
for (j = 0; j < 9; j++) {
|
||||
x->val[j] = r[j];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// res = a - b
|
||||
// b < 2*prime; result not normalized
|
||||
void fast_substract(const bignum256 *a, const bignum256 *b, bignum256 *res)
|
||||
{
|
||||
int i;
|
||||
uint32_t temp = 0;
|
||||
for (i = 0; i < 9; i++) {
|
||||
temp += a->val[i] + 2u *prime256k1.val[i] - b->val[i];
|
||||
res->val[i] = temp & 0x3FFFFFFF;
|
||||
temp >>= 30;
|
||||
}
|
||||
}
|
||||
|
||||
// x2 = x1 + x2;
|
||||
void point_add(const curve_point *x1, curve_point *x2)
|
||||
{
|
||||
int i;
|
||||
uint32_t temp;
|
||||
bignum256 lambda, inv, xr, yr;
|
||||
fast_substract(&(x2->x), &(x1->x), &inv);
|
||||
inverse(&inv, &prime256k1);
|
||||
fast_substract(&(x2->y), &(x1->y), &lambda);
|
||||
multiply(&inv, &lambda, &prime256k1);
|
||||
memcpy(&xr, &lambda, sizeof(bignum256));
|
||||
multiply(&xr, &xr, &prime256k1);
|
||||
temp = 0;
|
||||
for (i = 0;i < 9; i++) {
|
||||
temp += xr.val[i] + 3u * prime256k1.val[i] - x1->x.val[i] - x2->x.val[i];
|
||||
xr.val[i] = temp & 0x3FFFFFFF;
|
||||
temp >>= 30;
|
||||
}
|
||||
fast_mod(&xr, &prime256k1);
|
||||
fast_substract(&(x1->x), &xr, &yr);
|
||||
// no need to fast_mod here
|
||||
// fast_mod(&yr);
|
||||
multiply(&lambda, &yr, &prime256k1);
|
||||
fast_substract(&yr, &(x1->y), &yr);
|
||||
fast_mod(&yr, &prime256k1);
|
||||
memcpy(&(x2->x), &xr, sizeof(bignum256));
|
||||
memcpy(&(x2->y), &yr, sizeof(bignum256));
|
||||
}
|
||||
|
||||
#ifndef USE_PRECOMPUTED_CP
|
||||
// x = x + x;
|
||||
void point_double(curve_point *x)
|
||||
{
|
||||
int i;
|
||||
uint32_t temp;
|
||||
bignum256 lambda, inverse_y, xr, yr;
|
||||
memcpy(&inverse_y, &(x->y), sizeof(bignum256));
|
||||
inverse(&inverse_y, &prime256k1);
|
||||
memcpy(&lambda, &three_over_two256k1, sizeof(bignum256));
|
||||
multiply(&inverse_y, &lambda, &prime256k1);
|
||||
multiply(&(x->x), &lambda, &prime256k1);
|
||||
multiply(&(x->x), &lambda, &prime256k1);
|
||||
memcpy(&xr, &lambda, sizeof(bignum256));
|
||||
multiply(&xr, &xr, &prime256k1);
|
||||
temp = 0;
|
||||
for (i = 0;i < 9; i++) {
|
||||
temp += xr.val[i] + 3u * prime256k1.val[i] - 2u * x->x.val[i];
|
||||
xr.val[i] = temp & 0x3FFFFFFF;
|
||||
temp >>= 30;
|
||||
}
|
||||
fast_mod(&xr, &prime256k1);
|
||||
fast_substract(&(x->x), &xr, &yr);
|
||||
// no need to fast_mod here
|
||||
// fast_mod(&yr);
|
||||
multiply(&lambda, &yr, &prime256k1);
|
||||
fast_substract(&yr, &(x->y), &yr);
|
||||
fast_mod(&yr, &prime256k1);
|
||||
memcpy(&(x->x), &xr, sizeof(bignum256));
|
||||
memcpy(&(x->y), &yr, sizeof(bignum256));
|
||||
}
|
||||
#endif
|
||||
|
||||
// res = k * G
|
||||
void scalar_multiply(bignum256 *k, curve_point *res)
|
||||
{
|
||||
int i, j;
|
||||
// result is zero
|
||||
int is_zero = 1;
|
||||
#ifdef USE_PRECOMPUTED_CP
|
||||
int exp = 0;
|
||||
#else
|
||||
curve_point curr;
|
||||
// initial res
|
||||
memcpy(&curr, &G256k1, sizeof(curve_point));
|
||||
#endif
|
||||
for (i = 0; i < 9; i++) {
|
||||
for (j = 0; j < 30; j++) {
|
||||
if (i == 8 && (k->val[i] >> j) == 0) break;
|
||||
if (k->val[i] & (1u<<j)) {
|
||||
if (is_zero) {
|
||||
#ifdef USE_PRECOMPUTED_CP
|
||||
memcpy(res, secp256k1_cp + exp, sizeof(curve_point));
|
||||
#else
|
||||
memcpy(res, &curr, sizeof(curve_point));
|
||||
#endif
|
||||
is_zero = 0;
|
||||
} else {
|
||||
#ifdef USE_PRECOMPUTED_CP
|
||||
point_add(secp256k1_cp + exp, res);
|
||||
#else
|
||||
point_add(&curr, res);
|
||||
#endif
|
||||
}
|
||||
}
|
||||
#ifdef USE_PRECOMPUTED_CP
|
||||
exp++;
|
||||
#else
|
||||
point_double(&curr);
|
||||
#endif
|
||||
}
|
||||
}
|
||||
mod(&(res->x), &prime256k1);
|
||||
mod(&(res->y), &prime256k1);
|
||||
}
|
||||
|
||||
// write DER encoding of number to buffer
|
||||
void write_der(const bignum256 *x, uint8_t *buf)
|
||||
{
|
||||
int i, j = 8, k = 8, len = 0;
|
||||
uint8_t r = 0, temp;
|
||||
buf[0] = 2;
|
||||
for (i = 0; i < 32; i++) {
|
||||
temp = (x->val[j] >> k) + r;
|
||||
k -= 8;
|
||||
if (k < 0) {
|
||||
r = (x->val[j]) << (-k);
|
||||
k += 30;
|
||||
j--;
|
||||
} else {
|
||||
r = 0;
|
||||
}
|
||||
if (len || temp) {
|
||||
buf[2 + len] = temp;
|
||||
len++;
|
||||
}
|
||||
}
|
||||
buf[1] = len;
|
||||
}
|
||||
|
||||
// uses secp256k1 curve
|
||||
// private key is a 32 byte big endian stored number
|
||||
// message is a data to be signed
|
||||
// len is the message length
|
||||
// sig is at least 70 bytes long array for the signature
|
||||
// sig_len is the pointer to a uint that will contain resulting signature length. note that ((*sig_len) == sig[1]+2)
|
||||
void ecdsa_sign(uint8_t *private_key, uint8_t *message, uint32_t len, uint8_t *sig, uint32_t *sig_len)
|
||||
{
|
||||
uint32_t i;
|
||||
uint64_t temp;
|
||||
uint8_t hash[32];
|
||||
curve_point R;
|
||||
bignum256 k, z;
|
||||
bignum256 *da = &R.y;
|
||||
// compute hash function of message
|
||||
sha256(message, len, hash);
|
||||
// if double hash is required uncomment the following line:
|
||||
// sha256(hash, 32, hash);
|
||||
|
||||
temp = 0;
|
||||
for (i = 0; i < 8; i++) {
|
||||
temp += (((uint64_t)read_be(hash + (7 - i) * 4)) << (2 * i));
|
||||
z.val[i]= temp & 0x3FFFFFFF;
|
||||
temp >>= 30;
|
||||
}
|
||||
z.val[8] = temp;
|
||||
for (;;) {
|
||||
// generate random number k
|
||||
for (i = 0;i < 8; i++) {
|
||||
k.val[i] = random32() & 0x3FFFFFFF;
|
||||
}
|
||||
k.val[8] =random32() & 0xFFFF;
|
||||
// if k is too big or too small, we don't like it
|
||||
if (k.val[5] == 0x3FFFFFFF && k.val[6]==0x3FFFFFFF && k.val[7]==0x3FFFFFFF && k.val[8]==0xFFFF) continue;
|
||||
if (k.val[5] == 0x0 && k.val[6]==0x0 && k.val[7]==0x0 && k.val[8]==0x0) continue;
|
||||
// compute k*G
|
||||
scalar_multiply(&k, &R);
|
||||
// r = (rx mod n)
|
||||
mod(&R.x, &order256k1);
|
||||
// if r is zero, we try different k
|
||||
for (i = 0;i < 9; i++) {
|
||||
if (R.x.val[i] != 0) break;
|
||||
}
|
||||
if (i == 9) continue;
|
||||
inverse(&k, &order256k1);
|
||||
temp = 0;
|
||||
for (i=0; i<8; i++) {
|
||||
temp += (((uint64_t)read_be(private_key + (7 - i) * 4)) << (2 * i));
|
||||
da->val[i] = temp & 0x3FFFFFFF;
|
||||
temp >>= 30;
|
||||
}
|
||||
da->val[8] = temp;
|
||||
multiply(&R.x, da, &order256k1);
|
||||
for (i = 0; i < 8; i++) {
|
||||
da->val[i] += z.val[i];
|
||||
da->val[i+1] += (da->val[i] >> 30);
|
||||
da->val[i] &= 0x3FFFFFFF;
|
||||
}
|
||||
da->val[8] += z.val[8];
|
||||
multiply(da, &k, &order256k1);
|
||||
mod(&k, &order256k1);
|
||||
for (i = 0; i < 9; i++) {
|
||||
if (k.val[i] != 0) break;
|
||||
}
|
||||
if (i == 9) continue;
|
||||
// we are done, R.x and k is the result signature
|
||||
break;
|
||||
}
|
||||
write_der(&R.x, sig + 2);
|
||||
i = sig[3] + 2;
|
||||
write_der(&k, sig + 2 + i);
|
||||
i += sig[3+i] + 2;
|
||||
sig[0] = 0x30;
|
||||
sig[1] = i;
|
||||
*sig_len = i + 2;
|
||||
}
|
||||
32
ecdsa.h
Normal file
32
ecdsa.h
Normal file
@ -0,0 +1,32 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
|
||||
#ifndef __ECDSA_H__
|
||||
#define __ECDSA_H__
|
||||
|
||||
#include <stdint.h>
|
||||
|
||||
// uses secp256k1 curve
|
||||
void ecdsa_sign(uint8_t *private_key, uint8_t *message, uint32_t len, uint8_t *sig, uint32_t *sig_len);
|
||||
|
||||
#endif
|
||||
36
rand.c
Normal file
36
rand.c
Normal file
@ -0,0 +1,36 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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 <stdlib.h>
|
||||
#include <stdint.h>
|
||||
#include <time.h>
|
||||
|
||||
#include "rand.h"
|
||||
|
||||
void init_rand(void) {
|
||||
srand(time(NULL));
|
||||
}
|
||||
|
||||
uint32_t random32(void) {
|
||||
return (rand() & 0xFF) + ((rand() & 0xFF) << 8) + ((rand() & 0xFF) << 16) + ((rand() & 0xFF) << 24);
|
||||
}
|
||||
30
rand.h
Normal file
30
rand.h
Normal file
@ -0,0 +1,30 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
|
||||
#ifndef __RAND_H__
|
||||
#define __RAND_H__
|
||||
|
||||
void init_rand(void);
|
||||
uint32_t random32(void);
|
||||
|
||||
#endif
|
||||
820
secp256k1.c
Normal file
820
secp256k1.c
Normal file
@ -0,0 +1,820 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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 "secp256k1.h"
|
||||
|
||||
const bignum256 prime256k1 = {
|
||||
.val = {0x3ffffc2f, 0x3ffffffb, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0xffff}
|
||||
};
|
||||
|
||||
const curve_point G256k1 = {
|
||||
.x = { .val = {0x16f81798, 0x27ca056c, 0x1ce28d95, 0x26ff36cb, 0x70b0702, 0x18a573a, 0xbbac55a, 0x199fbe77, 0x79be}},
|
||||
.y = { .val = {0x3b10d4b8, 0x311f423f, 0x28554199, 0x5ed1229, 0x1108a8fd, 0x13eff038, 0x3c4655da, 0x369dc9a8, 0x483a}}};
|
||||
|
||||
const bignum256 order256k1 = {
|
||||
.val = {0x10364141, 0x3f497a33, 0x348a03bb, 0x2bb739ab, 0x3ffffeba, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0xffff}};
|
||||
|
||||
const bignum256 three_over_two256k1 = {
|
||||
.val = {0x3ffffe19, 0x3ffffffd, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x7fff}};
|
||||
|
||||
#ifdef USE_PRECOMPUTED_IV
|
||||
|
||||
const bignum256 secp256k1_iv[256] = {
|
||||
{ .val = {0x868192a, 0x20e02474, 0x24a059d, 0x2c88ffb7, 0x32b761bc, 0x1b0b0a57, 0x383999c4, 0x6414554, 0xc9bd}},
|
||||
{ .val = {0x4340c95, 0x3070123a, 0x212502ce, 0x16447fdb, 0x395bb0de, 0xd85852b, 0x1c1ccce2, 0x2320a2aa, 0x64de}},
|
||||
{ .val = {0x21a0462, 0x1838091b, 0x30928167, 0xb223fed, 0x3cadd86f, 0x6c2c295, 0xe0e6671, 0x11905155, 0xb26f}},
|
||||
{ .val = {0x210d0231, 0x2c1c048d, 0x384940b3, 0x25911ff6, 0x3e56ec37, 0x2361614a, 0x27073338, 0x28c828aa, 0x5937}},
|
||||
{ .val = {0x30867f30, 0x360e0244, 0x1c24a059, 0x32c88ffb, 0x1f2b761b, 0x11b0b0a5, 0x1383999c, 0x34641455, 0xac9b}},
|
||||
{ .val = {0x18433f98, 0x3b070122, 0x2e12502c, 0x396447fd, 0x2f95bb0d, 0x8d85852, 0x29c1ccce, 0x3a320a2a, 0x564d}},
|
||||
{ .val = {0xc219fcc, 0x1d838091, 0x37092816, 0x3cb223fe, 0x17cadd86, 0x46c2c29, 0x14e0e667, 0x3d190515, 0x2b26}},
|
||||
{ .val = {0x2610cfe6, 0xec1c048, 0x1b84940b, 0x1e5911ff, 0x2be56ec3, 0x22361614, 0x2a707333, 0x1e8c828a, 0x1593}},
|
||||
{ .val = {0x130867f3, 0x2760e024, 0x2dc24a05, 0x2f2c88ff, 0x15f2b761, 0x311b0b0a, 0x15383999, 0x2f464145, 0xac9}},
|
||||
{ .val = {0x9843211, 0x33b07010, 0x36e12502, 0x3796447f, 0xaf95bb0, 0x388d8585, 0x2a9c1ccc, 0x37a320a2, 0x8564}},
|
||||
{ .val = {0x4c21720, 0x19d83806, 0x3b709281, 0x1bcb223f, 0x257cadd8, 0x1c46c2c2, 0x154e0e66, 0x1bd19051, 0xc2b2}},
|
||||
{ .val = {0x2610b90, 0x2cec1c03, 0x3db84940, 0xde5911f, 0x12be56ec, 0xe236161, 0x2aa70733, 0xde8c828, 0x6159}},
|
||||
{ .val = {0x213085c8, 0x16760e01, 0x3edc24a0, 0x6f2c88f, 0x295f2b76, 0x2711b0b0, 0x15538399, 0x26f46414, 0x30ac}},
|
||||
{ .val = {0x309842e4, 0xb3b0700, 0x3f6e1250, 0x3796447, 0x14af95bb, 0x3388d858, 0xaa9c1cc, 0x137a320a, 0x1856}},
|
||||
{ .val = {0x184c2172, 0x59d8380, 0x3fb70928, 0x21bcb223, 0xa57cadd, 0x19c46c2c, 0x554e0e6, 0x9bd1905, 0xc2b}},
|
||||
{ .val = {0xc2610b9, 0x2cec1c0, 0x3fdb8494, 0x30de5911, 0x52be56e, 0xce23616, 0x22aa7073, 0x24de8c82, 0x615}},
|
||||
{ .val = {0x6130674, 0x16760de, 0x3fedc24a, 0x186f2c88, 0x295f2b7, 0x26711b0b, 0x11553839, 0x326f4641, 0x830a}},
|
||||
{ .val = {0x309833a, 0xb3b06f, 0x1ff6e125, 0x2c379644, 0x214af95b, 0x33388d85, 0x28aa9c1c, 0x1937a320, 0x4185}},
|
||||
{ .val = {0x2184c19d, 0x2059d837, 0xffb7092, 0x361bcb22, 0x30a57cad, 0x199c46c2, 0x14554e0e, 0x2c9bd190, 0x20c2}},
|
||||
{ .val = {0x30c25ee6, 0x102cec19, 0x7fdb849, 0x3b0de591, 0x1852be56, 0xcce2361, 0xa2aa707, 0x164de8c8, 0x9061}},
|
||||
{ .val = {0x38612f73, 0x2816760c, 0x23fedc24, 0x1d86f2c8, 0x2c295f2b, 0x266711b0, 0x5155383, 0x2b26f464, 0x4830}},
|
||||
{ .val = {0x1c3095d1, 0x140b3b04, 0x11ff6e12, 0x2ec37964, 0x1614af95, 0x333388d8, 0x28aa9c1, 0x15937a32, 0xa418}},
|
||||
{ .val = {0xe184900, 0xa059d80, 0x8ffb709, 0x3761bcb2, 0xb0a57ca, 0x3999c46c, 0x14554e0, 0xac9bd19, 0xd20c}},
|
||||
{ .val = {0x70c2480, 0x2502cec0, 0x47fdb84, 0x1bb0de59, 0x5852be5, 0x1ccce236, 0x20a2aa70, 0x564de8c, 0x6906}},
|
||||
{ .val = {0x3861240, 0x12816760, 0x223fedc2, 0x2dd86f2c, 0x2c295f2, 0xe66711b, 0x10515538, 0x2b26f46, 0x3483}},
|
||||
{ .val = {0x1c30920, 0x940b3b0, 0x111ff6e1, 0x16ec3796, 0x21614af9, 0x733388d, 0x828aa9c, 0x215937a3, 0x1a41}},
|
||||
{ .val = {0xe18490, 0x24a059d8, 0x88ffb70, 0x2b761bcb, 0x30b0a57c, 0x3999c46, 0x2414554e, 0x30ac9bd1, 0xd20}},
|
||||
{ .val = {0x70c248, 0x12502cec, 0x2447fdb8, 0x15bb0de5, 0x185852be, 0x1ccce23, 0x320a2aa7, 0x18564de8, 0x690}},
|
||||
{ .val = {0x386124, 0x9281676, 0x3223fedc, 0xadd86f2, 0x2c2c295f, 0x20e66711, 0x19051553, 0xc2b26f4, 0x348}},
|
||||
{ .val = {0x1c3092, 0x4940b3b, 0x1911ff6e, 0x256ec379, 0x361614af, 0x30733388, 0xc828aa9, 0x615937a, 0x1a4}},
|
||||
{ .val = {0x200e1849, 0x24a059d, 0x2c88ffb7, 0x32b761bc, 0x1b0b0a57, 0x383999c4, 0x6414554, 0x30ac9bd, 0xd2}},
|
||||
{ .val = {0x30070a3c, 0x212502cc, 0x16447fdb, 0x395bb0de, 0xd85852b, 0x1c1ccce2, 0x2320a2aa, 0x18564de, 0x8069}},
|
||||
{ .val = {0x1803851e, 0x30928166, 0xb223fed, 0x3cadd86f, 0x6c2c295, 0xe0e6671, 0x11905155, 0x20c2b26f, 0x4034}},
|
||||
{ .val = {0xc01c28f, 0x384940b3, 0x25911ff6, 0x3e56ec37, 0x2361614a, 0x27073338, 0x28c828aa, 0x10615937, 0x201a}},
|
||||
{ .val = {0x2600df5f, 0x1c24a057, 0x32c88ffb, 0x1f2b761b, 0x11b0b0a5, 0x1383999c, 0x34641455, 0x830ac9b, 0x900d}},
|
||||
{ .val = {0x33006dc7, 0x2e125029, 0x396447fd, 0x2f95bb0d, 0x8d85852, 0x29c1ccce, 0x3a320a2a, 0x2418564d, 0xc806}},
|
||||
{ .val = {0x398034fb, 0x37092812, 0x3cb223fe, 0x17cadd86, 0x46c2c29, 0x14e0e667, 0x3d190515, 0x120c2b26, 0xe403}},
|
||||
{ .val = {0x1cc01895, 0x1b849407, 0x1e5911ff, 0x2be56ec3, 0x22361614, 0x2a707333, 0x1e8c828a, 0x29061593, 0xf201}},
|
||||
{ .val = {0x2e600a62, 0x2dc24a01, 0x2f2c88ff, 0x15f2b761, 0x311b0b0a, 0x15383999, 0x2f464145, 0x34830ac9, 0xf900}},
|
||||
{ .val = {0x37300531, 0x36e12500, 0x3796447f, 0xaf95bb0, 0x388d8585, 0x2a9c1ccc, 0x37a320a2, 0x1a418564, 0x7c80}},
|
||||
{ .val = {0x1b9800b0, 0x3b70927e, 0x1bcb223f, 0x257cadd8, 0x1c46c2c2, 0x154e0e66, 0x1bd19051, 0xd20c2b2, 0xbe40}},
|
||||
{ .val = {0xdcc0058, 0x3db8493f, 0xde5911f, 0x12be56ec, 0xe236161, 0x2aa70733, 0xde8c828, 0x6906159, 0x5f20}},
|
||||
{ .val = {0x26e6002c, 0x3edc249f, 0x6f2c88f, 0x295f2b76, 0x2711b0b0, 0x15538399, 0x26f46414, 0x34830ac, 0x2f90}},
|
||||
{ .val = {0x33730016, 0x3f6e124f, 0x3796447, 0x14af95bb, 0x3388d858, 0xaa9c1cc, 0x137a320a, 0x1a41856, 0x17c8}},
|
||||
{ .val = {0x39b9800b, 0x3fb70927, 0x21bcb223, 0xa57cadd, 0x19c46c2c, 0x554e0e6, 0x9bd1905, 0xd20c2b, 0xbe4}},
|
||||
{ .val = {0x3cdcbe1d, 0x3fdb8491, 0x30de5911, 0x52be56e, 0xce23616, 0x22aa7073, 0x24de8c82, 0x690615, 0x85f2}},
|
||||
{ .val = {0x3e6e5d26, 0x3fedc246, 0x186f2c88, 0x295f2b7, 0x26711b0b, 0x11553839, 0x326f4641, 0x34830a, 0xc2f9}},
|
||||
{ .val = {0x1f372e93, 0x1ff6e123, 0x2c379644, 0x214af95b, 0x33388d85, 0x28aa9c1c, 0x1937a320, 0x201a4185, 0x617c}},
|
||||
{ .val = {0x2f9b9561, 0xffb708f, 0x361bcb22, 0x30a57cad, 0x199c46c2, 0x14554e0e, 0x2c9bd190, 0x100d20c2, 0xb0be}},
|
||||
{ .val = {0x37cdc8c8, 0x7fdb845, 0x3b0de591, 0x1852be56, 0xcce2361, 0xa2aa707, 0x164de8c8, 0x8069061, 0xd85f}},
|
||||
{ .val = {0x3be6e464, 0x23fedc22, 0x1d86f2c8, 0x2c295f2b, 0x266711b0, 0x5155383, 0x2b26f464, 0x24034830, 0x6c2f}},
|
||||
{ .val = {0x1df37232, 0x11ff6e11, 0x2ec37964, 0x1614af95, 0x333388d8, 0x28aa9c1, 0x15937a32, 0x3201a418, 0x3617}},
|
||||
{ .val = {0x2ef9b919, 0x8ffb708, 0x3761bcb2, 0xb0a57ca, 0x3999c46c, 0x14554e0, 0xac9bd19, 0x3900d20c, 0x1b0b}},
|
||||
{ .val = {0x177cdaa4, 0x47fdb82, 0x1bb0de59, 0x5852be5, 0x1ccce236, 0x20a2aa70, 0x564de8c, 0x3c806906, 0x8d85}},
|
||||
{ .val = {0xbbe6d52, 0x223fedc1, 0x2dd86f2c, 0x2c295f2, 0xe66711b, 0x10515538, 0x2b26f46, 0x3e403483, 0x46c2}},
|
||||
{ .val = {0x25df36a9, 0x111ff6e0, 0x16ec3796, 0x21614af9, 0x733388d, 0x828aa9c, 0x215937a3, 0x1f201a41, 0x2361}},
|
||||
{ .val = {0x12ef996c, 0x88ffb6e, 0x2b761bcb, 0x30b0a57c, 0x3999c46, 0x2414554e, 0x30ac9bd1, 0x2f900d20, 0x91b0}},
|
||||
{ .val = {0x977ccb6, 0x2447fdb7, 0x15bb0de5, 0x185852be, 0x1ccce23, 0x320a2aa7, 0x18564de8, 0x17c80690, 0x48d8}},
|
||||
{ .val = {0x24bbe65b, 0x3223fedb, 0xadd86f2, 0x2c2c295f, 0x20e66711, 0x19051553, 0xc2b26f4, 0xbe40348, 0x246c}},
|
||||
{ .val = {0x325df145, 0x1911ff6b, 0x256ec379, 0x361614af, 0x30733388, 0xc828aa9, 0x615937a, 0x5f201a4, 0x9236}},
|
||||
{ .val = {0x392ef6ba, 0x2c88ffb3, 0x32b761bc, 0x1b0b0a57, 0x383999c4, 0x6414554, 0x30ac9bd, 0x2f900d2, 0xc91b}},
|
||||
{ .val = {0x3c977b5d, 0x16447fd9, 0x395bb0de, 0xd85852b, 0x1c1ccce2, 0x2320a2aa, 0x18564de, 0x217c8069, 0x648d}},
|
||||
{ .val = {0x3e4bbbc6, 0xb223fea, 0x3cadd86f, 0x6c2c295, 0xe0e6671, 0x11905155, 0x20c2b26f, 0x30be4034, 0xb246}},
|
||||
{ .val = {0x1f25dde3, 0x25911ff5, 0x3e56ec37, 0x2361614a, 0x27073338, 0x28c828aa, 0x10615937, 0x185f201a, 0x5923}},
|
||||
{ .val = {0x2f92ed09, 0x32c88ff8, 0x1f2b761b, 0x11b0b0a5, 0x1383999c, 0x34641455, 0x830ac9b, 0x2c2f900d, 0xac91}},
|
||||
{ .val = {0x17c9749c, 0x396447fa, 0x2f95bb0d, 0x8d85852, 0x29c1ccce, 0x3a320a2a, 0x2418564d, 0x3617c806, 0xd648}},
|
||||
{ .val = {0xbe4ba4e, 0x3cb223fd, 0x17cadd86, 0x46c2c29, 0x14e0e667, 0x3d190515, 0x120c2b26, 0x1b0be403, 0x6b24}},
|
||||
{ .val = {0x25f25d27, 0x1e5911fe, 0x2be56ec3, 0x22361614, 0x2a707333, 0x1e8c828a, 0x29061593, 0xd85f201, 0x3592}},
|
||||
{ .val = {0x12f92cab, 0x2f2c88fd, 0x15f2b761, 0x311b0b0a, 0x15383999, 0x2f464145, 0x34830ac9, 0x6c2f900, 0x9ac9}},
|
||||
{ .val = {0x297c946d, 0x3796447c, 0xaf95bb0, 0x388d8585, 0x2a9c1ccc, 0x37a320a2, 0x1a418564, 0x23617c80, 0xcd64}},
|
||||
{ .val = {0x14be484e, 0x1bcb223c, 0x257cadd8, 0x1c46c2c2, 0x154e0e66, 0x1bd19051, 0xd20c2b2, 0x11b0be40, 0xe6b2}},
|
||||
{ .val = {0xa5f2427, 0xde5911e, 0x12be56ec, 0xe236161, 0x2aa70733, 0xde8c828, 0x6906159, 0x8d85f20, 0x7359}},
|
||||
{ .val = {0x52f902b, 0x6f2c88d, 0x295f2b76, 0x2711b0b0, 0x15538399, 0x26f46414, 0x34830ac, 0x246c2f90, 0xb9ac}},
|
||||
{ .val = {0x2297c62d, 0x3796444, 0x14af95bb, 0x3388d858, 0xaa9c1cc, 0x137a320a, 0x1a41856, 0x123617c8, 0xdcd6}},
|
||||
{ .val = {0x114be12e, 0x21bcb220, 0xa57cadd, 0x19c46c2c, 0x554e0e6, 0x9bd1905, 0xd20c2b, 0x91b0be4, 0xee6b}},
|
||||
{ .val = {0x8a5f097, 0x30de5910, 0x52be56e, 0xce23616, 0x22aa7073, 0x24de8c82, 0x690615, 0x248d85f2, 0x7735}},
|
||||
{ .val = {0x452f663, 0x186f2c86, 0x295f2b7, 0x26711b0b, 0x11553839, 0x326f4641, 0x34830a, 0x3246c2f9, 0xbb9a}},
|
||||
{ .val = {0x2297949, 0x2c379641, 0x214af95b, 0x33388d85, 0x28aa9c1c, 0x1937a320, 0x201a4185, 0x1923617c, 0xddcd}},
|
||||
{ .val = {0x2114babc, 0x361bcb1e, 0x30a57cad, 0x199c46c2, 0x14554e0e, 0x2c9bd190, 0x100d20c2, 0x2c91b0be, 0xeee6}},
|
||||
{ .val = {0x108a5d5e, 0x3b0de58f, 0x1852be56, 0xcce2361, 0xa2aa707, 0x164de8c8, 0x8069061, 0x1648d85f, 0x7773}},
|
||||
{ .val = {0x28452eaf, 0x1d86f2c7, 0x2c295f2b, 0x266711b0, 0x5155383, 0x2b26f464, 0x24034830, 0x2b246c2f, 0x3bb9}},
|
||||
{ .val = {0x3422956f, 0x2ec37961, 0x1614af95, 0x333388d8, 0x28aa9c1, 0x15937a32, 0x3201a418, 0x35923617, 0x9ddc}},
|
||||
{ .val = {0x3a1148cf, 0x3761bcae, 0xb0a57ca, 0x3999c46c, 0x14554e0, 0xac9bd19, 0x3900d20c, 0x1ac91b0b, 0xceee}},
|
||||
{ .val = {0x1d08a27f, 0x1bb0de55, 0x5852be5, 0x1ccce236, 0x20a2aa70, 0x564de8c, 0x3c806906, 0xd648d85, 0xe777}},
|
||||
{ .val = {0x2e844f57, 0x2dd86f28, 0x2c295f2, 0xe66711b, 0x10515538, 0x2b26f46, 0x3e403483, 0x26b246c2, 0xf3bb}},
|
||||
{ .val = {0x174225c3, 0x16ec3792, 0x21614af9, 0x733388d, 0x828aa9c, 0x215937a3, 0x1f201a41, 0x33592361, 0xf9dd}},
|
||||
{ .val = {0xba110f9, 0x2b761bc7, 0x30b0a57c, 0x3999c46, 0x2414554e, 0x30ac9bd1, 0x2f900d20, 0x39ac91b0, 0xfcee}},
|
||||
{ .val = {0x25d08694, 0x15bb0de1, 0x185852be, 0x1ccce23, 0x320a2aa7, 0x18564de8, 0x17c80690, 0x1cd648d8, 0xfe77}},
|
||||
{ .val = {0x32e8434a, 0xadd86f0, 0x2c2c295f, 0x20e66711, 0x19051553, 0xc2b26f4, 0xbe40348, 0x2e6b246c, 0x7f3b}},
|
||||
{ .val = {0x197421a5, 0x256ec378, 0x361614af, 0x30733388, 0xc828aa9, 0x615937a, 0x5f201a4, 0x37359236, 0x3f9d}},
|
||||
{ .val = {0xcba0eea, 0x32b761ba, 0x1b0b0a57, 0x383999c4, 0x6414554, 0x30ac9bd, 0x2f900d2, 0x3b9ac91b, 0x9fce}},
|
||||
{ .val = {0x65d0775, 0x395bb0dd, 0xd85852b, 0x1c1ccce2, 0x2320a2aa, 0x18564de, 0x217c8069, 0x1dcd648d, 0x4fe7}},
|
||||
{ .val = {0x232e81d2, 0x3cadd86c, 0x6c2c295, 0xe0e6671, 0x11905155, 0x20c2b26f, 0x30be4034, 0x2ee6b246, 0xa7f3}},
|
||||
{ .val = {0x119740e9, 0x3e56ec36, 0x2361614a, 0x27073338, 0x28c828aa, 0x10615937, 0x185f201a, 0x37735923, 0x53f9}},
|
||||
{ .val = {0x8cb9e8c, 0x1f2b7619, 0x11b0b0a5, 0x1383999c, 0x34641455, 0x830ac9b, 0x2c2f900d, 0x3bb9ac91, 0xa9fc}},
|
||||
{ .val = {0x2465cf46, 0x2f95bb0c, 0x8d85852, 0x29c1ccce, 0x3a320a2a, 0x2418564d, 0x3617c806, 0x1ddcd648, 0x54fe}},
|
||||
{ .val = {0x1232e7a3, 0x17cadd86, 0x46c2c29, 0x14e0e667, 0x3d190515, 0x120c2b26, 0x1b0be403, 0xeee6b24, 0x2a7f}},
|
||||
{ .val = {0x91971e9, 0x2be56ec1, 0x22361614, 0x2a707333, 0x1e8c828a, 0x29061593, 0xd85f201, 0x27773592, 0x953f}},
|
||||
{ .val = {0x248cb70c, 0x15f2b75e, 0x311b0b0a, 0x15383999, 0x2f464145, 0x34830ac9, 0x6c2f900, 0x33bb9ac9, 0xca9f}},
|
||||
{ .val = {0x12465b86, 0xaf95baf, 0x388d8585, 0x2a9c1ccc, 0x37a320a2, 0x1a418564, 0x23617c80, 0x39ddcd64, 0x654f}},
|
||||
{ .val = {0x29232dc3, 0x257cadd7, 0x1c46c2c2, 0x154e0e66, 0x1bd19051, 0xd20c2b2, 0x11b0be40, 0x3ceee6b2, 0x32a7}},
|
||||
{ .val = {0x349194f9, 0x12be56e9, 0xe236161, 0x2aa70733, 0xde8c828, 0x6906159, 0x8d85f20, 0x3e777359, 0x9953}},
|
||||
{ .val = {0x3a48c894, 0x295f2b72, 0x2711b0b0, 0x15538399, 0x26f46414, 0x34830ac, 0x246c2f90, 0x3f3bb9ac, 0xcca9}},
|
||||
{ .val = {0x1d24644a, 0x14af95b9, 0x3388d858, 0xaa9c1cc, 0x137a320a, 0x1a41856, 0x123617c8, 0x3f9ddcd6, 0x6654}},
|
||||
{ .val = {0x2e923225, 0xa57cadc, 0x19c46c2c, 0x554e0e6, 0x9bd1905, 0xd20c2b, 0x91b0be4, 0x1fceee6b, 0x332a}},
|
||||
{ .val = {0x1749172a, 0x52be56c, 0xce23616, 0x22aa7073, 0x24de8c82, 0x690615, 0x248d85f2, 0xfe77735, 0x9995}},
|
||||
{ .val = {0xba48b95, 0x295f2b6, 0x26711b0b, 0x11553839, 0x326f4641, 0x34830a, 0x3246c2f9, 0x27f3bb9a, 0x4cca}},
|
||||
{ .val = {0x5d243e2, 0x214af959, 0x33388d85, 0x28aa9c1c, 0x1937a320, 0x201a4185, 0x1923617c, 0x13f9ddcd, 0xa665}},
|
||||
{ .val = {0x22e921f1, 0x30a57cac, 0x199c46c2, 0x14554e0e, 0x2c9bd190, 0x100d20c2, 0x2c91b0be, 0x29fceee6, 0x5332}},
|
||||
{ .val = {0x11748f10, 0x1852be54, 0xcce2361, 0xa2aa707, 0x164de8c8, 0x8069061, 0x1648d85f, 0x14fe7773, 0xa999}},
|
||||
{ .val = {0x8ba4788, 0x2c295f2a, 0x266711b0, 0x5155383, 0x2b26f464, 0x24034830, 0x2b246c2f, 0x2a7f3bb9, 0x54cc}},
|
||||
{ .val = {0x45d23c4, 0x1614af95, 0x333388d8, 0x28aa9c1, 0x15937a32, 0x3201a418, 0x35923617, 0x153f9ddc, 0x2a66}},
|
||||
{ .val = {0x222e91e2, 0xb0a57ca, 0x3999c46c, 0x14554e0, 0xac9bd19, 0x3900d20c, 0x1ac91b0b, 0xa9fceee, 0x1533}},
|
||||
{ .val = {0x111748f1, 0x5852be5, 0x1ccce236, 0x20a2aa70, 0x564de8c, 0x3c806906, 0xd648d85, 0x254fe777, 0xa99}},
|
||||
{ .val = {0x288ba290, 0x2c295f0, 0xe66711b, 0x10515538, 0x2b26f46, 0x3e403483, 0x26b246c2, 0x32a7f3bb, 0x854c}},
|
||||
{ .val = {0x1445d148, 0x21614af8, 0x733388d, 0x828aa9c, 0x215937a3, 0x1f201a41, 0x33592361, 0x1953f9dd, 0x42a6}},
|
||||
{ .val = {0xa22e8a4, 0x30b0a57c, 0x3999c46, 0x2414554e, 0x30ac9bd1, 0x2f900d20, 0x39ac91b0, 0xca9fcee, 0x2153}},
|
||||
{ .val = {0x5117452, 0x185852be, 0x1ccce23, 0x320a2aa7, 0x18564de8, 0x17c80690, 0x1cd648d8, 0x2654fe77, 0x10a9}},
|
||||
{ .val = {0x288ba29, 0x2c2c295f, 0x20e66711, 0x19051553, 0xc2b26f4, 0xbe40348, 0x2e6b246c, 0x332a7f3b, 0x854}},
|
||||
{ .val = {0x21445b2c, 0x361614ad, 0x30733388, 0xc828aa9, 0x615937a, 0x5f201a4, 0x37359236, 0x19953f9d, 0x842a}},
|
||||
{ .val = {0x30a22d96, 0x1b0b0a56, 0x383999c4, 0x6414554, 0x30ac9bd, 0x2f900d2, 0x3b9ac91b, 0xcca9fce, 0x4215}},
|
||||
{ .val = {0x185116cb, 0xd85852b, 0x1c1ccce2, 0x2320a2aa, 0x18564de, 0x217c8069, 0x1dcd648d, 0x26654fe7, 0x210a}},
|
||||
{ .val = {0x2c28897d, 0x6c2c293, 0xe0e6671, 0x11905155, 0x20c2b26f, 0x30be4034, 0x2ee6b246, 0x1332a7f3, 0x9085}},
|
||||
{ .val = {0x361442d6, 0x23616147, 0x27073338, 0x28c828aa, 0x10615937, 0x185f201a, 0x37735923, 0x299953f9, 0xc842}},
|
||||
{ .val = {0x3b0a216b, 0x11b0b0a3, 0x1383999c, 0x34641455, 0x830ac9b, 0x2c2f900d, 0x3bb9ac91, 0x14cca9fc, 0x6421}},
|
||||
{ .val = {0x3d850ecd, 0x8d8584f, 0x29c1ccce, 0x3a320a2a, 0x2418564d, 0x3617c806, 0x1ddcd648, 0x2a6654fe, 0xb210}},
|
||||
{ .val = {0x3ec2857e, 0x46c2c25, 0x14e0e667, 0x3d190515, 0x120c2b26, 0x1b0be403, 0xeee6b24, 0x15332a7f, 0xd908}},
|
||||
{ .val = {0x3f6142bf, 0x22361612, 0x2a707333, 0x1e8c828a, 0x29061593, 0xd85f201, 0x27773592, 0xa99953f, 0x6c84}},
|
||||
{ .val = {0x1fb09f77, 0x311b0b07, 0x15383999, 0x2f464145, 0x34830ac9, 0x6c2f900, 0x33bb9ac9, 0x54cca9f, 0xb642}},
|
||||
{ .val = {0x2fd84dd3, 0x388d8581, 0x2a9c1ccc, 0x37a320a2, 0x1a418564, 0x23617c80, 0x39ddcd64, 0x2a6654f, 0xdb21}},
|
||||
{ .val = {0x37ec2501, 0x1c46c2be, 0x154e0e66, 0x1bd19051, 0xd20c2b2, 0x11b0be40, 0x3ceee6b2, 0x215332a7, 0xed90}},
|
||||
{ .val = {0x1bf61098, 0xe23615d, 0x2aa70733, 0xde8c828, 0x6906159, 0x8d85f20, 0x3e777359, 0x10a99953, 0xf6c8}},
|
||||
{ .val = {0x2dfb084c, 0x2711b0ae, 0x15538399, 0x26f46414, 0x34830ac, 0x246c2f90, 0x3f3bb9ac, 0x854cca9, 0x7b64}},
|
||||
{ .val = {0x16fd8426, 0x3388d857, 0xaa9c1cc, 0x137a320a, 0x1a41856, 0x123617c8, 0x3f9ddcd6, 0x42a6654, 0x3db2}},
|
||||
{ .val = {0x2b7ec213, 0x19c46c2b, 0x554e0e6, 0x9bd1905, 0xd20c2b, 0x91b0be4, 0x1fceee6b, 0x215332a, 0x1ed9}},
|
||||
{ .val = {0x35bf5f21, 0xce23613, 0x22aa7073, 0x24de8c82, 0x690615, 0x248d85f2, 0xfe77735, 0x210a9995, 0x8f6c}},
|
||||
{ .val = {0x3adfada8, 0x26711b07, 0x11553839, 0x326f4641, 0x34830a, 0x3246c2f9, 0x27f3bb9a, 0x10854cca, 0xc7b6}},
|
||||
{ .val = {0x3d6fd6d4, 0x33388d83, 0x28aa9c1c, 0x1937a320, 0x201a4185, 0x1923617c, 0x13f9ddcd, 0x842a665, 0x63db}},
|
||||
{ .val = {0x3eb7eb6a, 0x199c46c1, 0x14554e0e, 0x2c9bd190, 0x100d20c2, 0x2c91b0be, 0x29fceee6, 0x24215332, 0x31ed}},
|
||||
{ .val = {0x3f5bf5b5, 0xcce2360, 0xa2aa707, 0x164de8c8, 0x8069061, 0x1648d85f, 0x14fe7773, 0x3210a999, 0x18f6}},
|
||||
{ .val = {0x1fadf8f2, 0x266711ae, 0x5155383, 0x2b26f464, 0x24034830, 0x2b246c2f, 0x2a7f3bb9, 0x190854cc, 0x8c7b}},
|
||||
{ .val = {0xfd6fc79, 0x333388d7, 0x28aa9c1, 0x15937a32, 0x3201a418, 0x35923617, 0x153f9ddc, 0x2c842a66, 0x463d}},
|
||||
{ .val = {0x27eb7c54, 0x3999c469, 0x14554e0, 0xac9bd19, 0x3900d20c, 0x1ac91b0b, 0xa9fceee, 0x36421533, 0xa31e}},
|
||||
{ .val = {0x33f5be2a, 0x1ccce234, 0x20a2aa70, 0x564de8c, 0x3c806906, 0xd648d85, 0x254fe777, 0x1b210a99, 0x518f}},
|
||||
{ .val = {0x19fadf15, 0xe66711a, 0x10515538, 0x2b26f46, 0x3e403483, 0x26b246c2, 0x32a7f3bb, 0x2d90854c, 0x28c7}},
|
||||
{ .val = {0xcfd6da2, 0x733388b, 0x828aa9c, 0x215937a3, 0x1f201a41, 0x33592361, 0x1953f9dd, 0x36c842a6, 0x9463}},
|
||||
{ .val = {0x267eb6d1, 0x3999c45, 0x2414554e, 0x30ac9bd1, 0x2f900d20, 0x39ac91b0, 0xca9fcee, 0x3b642153, 0x4a31}},
|
||||
{ .val = {0x333f5980, 0x1ccce20, 0x320a2aa7, 0x18564de8, 0x17c80690, 0x1cd648d8, 0x2654fe77, 0x3db210a9, 0xa518}},
|
||||
{ .val = {0x199facc0, 0x20e66710, 0x19051553, 0xc2b26f4, 0xbe40348, 0x2e6b246c, 0x332a7f3b, 0x1ed90854, 0x528c}},
|
||||
{ .val = {0xccfd660, 0x30733388, 0xc828aa9, 0x615937a, 0x5f201a4, 0x37359236, 0x19953f9d, 0xf6c842a, 0x2946}},
|
||||
{ .val = {0x667eb30, 0x383999c4, 0x6414554, 0x30ac9bd, 0x2f900d2, 0x3b9ac91b, 0xcca9fce, 0x7b64215, 0x14a3}},
|
||||
{ .val = {0x333f598, 0x1c1ccce2, 0x2320a2aa, 0x18564de, 0x217c8069, 0x1dcd648d, 0x26654fe7, 0x23db210a, 0xa51}},
|
||||
{ .val = {0x199facc, 0xe0e6671, 0x11905155, 0x20c2b26f, 0x30be4034, 0x2ee6b246, 0x1332a7f3, 0x31ed9085, 0x528}},
|
||||
{ .val = {0x20ccfd66, 0x27073338, 0x28c828aa, 0x10615937, 0x185f201a, 0x37735923, 0x299953f9, 0x18f6c842, 0x294}},
|
||||
{ .val = {0x10667eb3, 0x1383999c, 0x34641455, 0x830ac9b, 0x2c2f900d, 0x3bb9ac91, 0x14cca9fc, 0xc7b6421, 0x14a}},
|
||||
{ .val = {0x8333d71, 0x29c1cccc, 0x3a320a2a, 0x2418564d, 0x3617c806, 0x1ddcd648, 0x2a6654fe, 0x63db210, 0x80a5}},
|
||||
{ .val = {0x4199cd0, 0x14e0e664, 0x3d190515, 0x120c2b26, 0x1b0be403, 0xeee6b24, 0x15332a7f, 0x231ed908, 0xc052}},
|
||||
{ .val = {0x20cce68, 0x2a707332, 0x1e8c828a, 0x29061593, 0xd85f201, 0x27773592, 0xa99953f, 0x118f6c84, 0x6029}},
|
||||
{ .val = {0x1066734, 0x15383999, 0x2f464145, 0x34830ac9, 0x6c2f900, 0x33bb9ac9, 0x54cca9f, 0x28c7b642, 0x3014}},
|
||||
{ .val = {0x2083339a, 0x2a9c1ccc, 0x37a320a2, 0x1a418564, 0x23617c80, 0x39ddcd64, 0x2a6654f, 0x1463db21, 0x180a}},
|
||||
{ .val = {0x104199cd, 0x154e0e66, 0x1bd19051, 0xd20c2b2, 0x11b0be40, 0x3ceee6b2, 0x215332a7, 0xa31ed90, 0xc05}},
|
||||
{ .val = {0x820cafe, 0x2aa70731, 0xde8c828, 0x6906159, 0x8d85f20, 0x3e777359, 0x10a99953, 0x2518f6c8, 0x8602}},
|
||||
{ .val = {0x2410657f, 0x15538398, 0x26f46414, 0x34830ac, 0x246c2f90, 0x3f3bb9ac, 0x854cca9, 0x128c7b64, 0x4301}},
|
||||
{ .val = {0x120830d7, 0xaa9c1ca, 0x137a320a, 0x1a41856, 0x123617c8, 0x3f9ddcd6, 0x42a6654, 0x29463db2, 0xa180}},
|
||||
{ .val = {0x9041683, 0x554e0e3, 0x9bd1905, 0xd20c2b, 0x91b0be4, 0x1fceee6b, 0x215332a, 0x14a31ed9, 0xd0c0}},
|
||||
{ .val = {0x24820959, 0x22aa706f, 0x24de8c82, 0x690615, 0x248d85f2, 0xfe77735, 0x210a9995, 0xa518f6c, 0xe860}},
|
||||
{ .val = {0x324102c4, 0x11553835, 0x326f4641, 0x34830a, 0x3246c2f9, 0x27f3bb9a, 0x10854cca, 0x528c7b6, 0xf430}},
|
||||
{ .val = {0x39208162, 0x28aa9c1a, 0x1937a320, 0x201a4185, 0x1923617c, 0x13f9ddcd, 0x842a665, 0x29463db, 0x7a18}},
|
||||
{ .val = {0x1c9040b1, 0x14554e0d, 0x2c9bd190, 0x100d20c2, 0x2c91b0be, 0x29fceee6, 0x24215332, 0x14a31ed, 0x3d0c}},
|
||||
{ .val = {0x2e481e70, 0xa2aa704, 0x164de8c8, 0x8069061, 0x1648d85f, 0x14fe7773, 0x3210a999, 0xa518f6, 0x9e86}},
|
||||
{ .val = {0x17240f38, 0x5155382, 0x2b26f464, 0x24034830, 0x2b246c2f, 0x2a7f3bb9, 0x190854cc, 0x528c7b, 0x4f43}},
|
||||
{ .val = {0xb92079c, 0x28aa9c1, 0x15937a32, 0x3201a418, 0x35923617, 0x153f9ddc, 0x2c842a66, 0x2029463d, 0x27a1}},
|
||||
{ .val = {0x25c903ce, 0x14554e0, 0xac9bd19, 0x3900d20c, 0x1ac91b0b, 0xa9fceee, 0x36421533, 0x3014a31e, 0x13d0}},
|
||||
{ .val = {0x12e481e7, 0x20a2aa70, 0x564de8c, 0x3c806906, 0xd648d85, 0x254fe777, 0x1b210a99, 0x180a518f, 0x9e8}},
|
||||
{ .val = {0x9723f0b, 0x10515536, 0x2b26f46, 0x3e403483, 0x26b246c2, 0x32a7f3bb, 0x2d90854c, 0xc0528c7, 0x84f4}},
|
||||
{ .val = {0x4b91d9d, 0x828aa99, 0x215937a3, 0x1f201a41, 0x33592361, 0x1953f9dd, 0x36c842a6, 0x6029463, 0xc27a}},
|
||||
{ .val = {0x225c8ce6, 0x2414554a, 0x30ac9bd1, 0x2f900d20, 0x39ac91b0, 0xca9fcee, 0x3b642153, 0x3014a31, 0xe13d}},
|
||||
{ .val = {0x112e4673, 0x320a2aa5, 0x18564de8, 0x17c80690, 0x1cd648d8, 0x2654fe77, 0x3db210a9, 0x2180a518, 0x709e}},
|
||||
{ .val = {0x28972151, 0x19051550, 0xc2b26f4, 0xbe40348, 0x2e6b246c, 0x332a7f3b, 0x1ed90854, 0x10c0528c, 0xb84f}},
|
||||
{ .val = {0x144b8ec0, 0xc828aa6, 0x615937a, 0x5f201a4, 0x37359236, 0x19953f9d, 0xf6c842a, 0x28602946, 0xdc27}},
|
||||
{ .val = {0xa25c760, 0x6414553, 0x30ac9bd, 0x2f900d2, 0x3b9ac91b, 0xcca9fce, 0x7b64215, 0x343014a3, 0x6e13}},
|
||||
{ .val = {0x2512e3b0, 0x2320a2a9, 0x18564de, 0x217c8069, 0x1dcd648d, 0x26654fe7, 0x23db210a, 0x3a180a51, 0x3709}},
|
||||
{ .val = {0x328971d8, 0x11905154, 0x20c2b26f, 0x30be4034, 0x2ee6b246, 0x1332a7f3, 0x31ed9085, 0x3d0c0528, 0x1b84}},
|
||||
{ .val = {0x1944b8ec, 0x28c828aa, 0x10615937, 0x185f201a, 0x37735923, 0x299953f9, 0x18f6c842, 0x1e860294, 0xdc2}},
|
||||
{ .val = {0xca25c76, 0x34641455, 0x830ac9b, 0x2c2f900d, 0x3bb9ac91, 0x14cca9fc, 0xc7b6421, 0xf43014a, 0x6e1}},
|
||||
{ .val = {0x26512e3b, 0x3a320a2a, 0x2418564d, 0x3617c806, 0x1ddcd648, 0x2a6654fe, 0x63db210, 0x27a180a5, 0x370}},
|
||||
{ .val = {0x13289535, 0x3d190513, 0x120c2b26, 0x1b0be403, 0xeee6b24, 0x15332a7f, 0x231ed908, 0x13d0c052, 0x81b8}},
|
||||
{ .val = {0x299448b2, 0x1e8c8287, 0x29061593, 0xd85f201, 0x27773592, 0xa99953f, 0x118f6c84, 0x9e86029, 0xc0dc}},
|
||||
{ .val = {0x34ca2459, 0x2f464143, 0x34830ac9, 0x6c2f900, 0x33bb9ac9, 0x54cca9f, 0x28c7b642, 0x4f43014, 0x606e}},
|
||||
{ .val = {0x3a651044, 0x37a3209f, 0x1a418564, 0x23617c80, 0x39ddcd64, 0x2a6654f, 0x1463db21, 0x27a180a, 0xb037}},
|
||||
{ .val = {0x3d328822, 0x1bd1904f, 0xd20c2b2, 0x11b0be40, 0x3ceee6b2, 0x215332a7, 0xa31ed90, 0x213d0c05, 0x581b}},
|
||||
{ .val = {0x3e994411, 0xde8c827, 0x6906159, 0x8d85f20, 0x3e777359, 0x10a99953, 0x2518f6c8, 0x309e8602, 0x2c0d}},
|
||||
{ .val = {0x3f4ca020, 0x26f46411, 0x34830ac, 0x246c2f90, 0x3f3bb9ac, 0x854cca9, 0x128c7b64, 0x384f4301, 0x9606}},
|
||||
{ .val = {0x3fa65010, 0x137a3208, 0x1a41856, 0x123617c8, 0x3f9ddcd6, 0x42a6654, 0x29463db2, 0x1c27a180, 0x4b03}},
|
||||
{ .val = {0x1fd32808, 0x9bd1904, 0xd20c2b, 0x91b0be4, 0x1fceee6b, 0x215332a, 0x14a31ed9, 0x2e13d0c0, 0x2581}},
|
||||
{ .val = {0xfe99404, 0x24de8c82, 0x690615, 0x248d85f2, 0xfe77735, 0x210a9995, 0xa518f6c, 0x3709e860, 0x12c0}},
|
||||
{ .val = {0x7f4ca02, 0x326f4641, 0x34830a, 0x3246c2f9, 0x27f3bb9a, 0x10854cca, 0x528c7b6, 0x1b84f430, 0x960}},
|
||||
{ .val = {0x23fa6501, 0x1937a320, 0x201a4185, 0x1923617c, 0x13f9ddcd, 0x842a665, 0x29463db, 0xdc27a18, 0x4b0}},
|
||||
{ .val = {0x11fd3098, 0x2c9bd18e, 0x100d20c2, 0x2c91b0be, 0x29fceee6, 0x24215332, 0x14a31ed, 0x6e13d0c, 0x8258}},
|
||||
{ .val = {0x8fe984c, 0x164de8c7, 0x8069061, 0x1648d85f, 0x14fe7773, 0x3210a999, 0xa518f6, 0x3709e86, 0x412c}},
|
||||
{ .val = {0x247f4c26, 0x2b26f463, 0x24034830, 0x2b246c2f, 0x2a7f3bb9, 0x190854cc, 0x528c7b, 0x1b84f43, 0x2096}},
|
||||
{ .val = {0x323fa613, 0x15937a31, 0x3201a418, 0x35923617, 0x153f9ddc, 0x2c842a66, 0x2029463d, 0xdc27a1, 0x104b}},
|
||||
{ .val = {0x391fd121, 0xac9bd16, 0x3900d20c, 0x1ac91b0b, 0xa9fceee, 0x36421533, 0x3014a31e, 0x206e13d0, 0x8825}},
|
||||
{ .val = {0x1c8fe6a8, 0x564de89, 0x3c806906, 0xd648d85, 0x254fe777, 0x1b210a99, 0x180a518f, 0x303709e8, 0xc412}},
|
||||
{ .val = {0x2e47f354, 0x2b26f44, 0x3e403483, 0x26b246c2, 0x32a7f3bb, 0x2d90854c, 0xc0528c7, 0x181b84f4, 0x6209}},
|
||||
{ .val = {0x1723f9aa, 0x215937a2, 0x1f201a41, 0x33592361, 0x1953f9dd, 0x36c842a6, 0x6029463, 0x2c0dc27a, 0x3104}},
|
||||
{ .val = {0xb91fcd5, 0x30ac9bd1, 0x2f900d20, 0x39ac91b0, 0xca9fcee, 0x3b642153, 0x3014a31, 0x1606e13d, 0x1882}},
|
||||
{ .val = {0x25c8fc82, 0x18564de6, 0x17c80690, 0x1cd648d8, 0x2654fe77, 0x3db210a9, 0x2180a518, 0xb03709e, 0x8c41}},
|
||||
{ .val = {0x12e47e41, 0xc2b26f3, 0xbe40348, 0x2e6b246c, 0x332a7f3b, 0x1ed90854, 0x10c0528c, 0x2581b84f, 0x4620}},
|
||||
{ .val = {0x29723d38, 0x6159377, 0x5f201a4, 0x37359236, 0x19953f9d, 0xf6c842a, 0x28602946, 0x12c0dc27, 0xa310}},
|
||||
{ .val = {0x34b91e9c, 0x30ac9bb, 0x2f900d2, 0x3b9ac91b, 0xcca9fce, 0x7b64215, 0x343014a3, 0x9606e13, 0x5188}},
|
||||
{ .val = {0x3a5c8f4e, 0x18564dd, 0x217c8069, 0x1dcd648d, 0x26654fe7, 0x23db210a, 0x3a180a51, 0x4b03709, 0x28c4}},
|
||||
{ .val = {0x3d2e47a7, 0x20c2b26e, 0x30be4034, 0x2ee6b246, 0x1332a7f3, 0x31ed9085, 0x3d0c0528, 0x2581b84, 0x1462}},
|
||||
{ .val = {0x1e9721eb, 0x10615935, 0x185f201a, 0x37735923, 0x299953f9, 0x18f6c842, 0x1e860294, 0x12c0dc2, 0x8a31}},
|
||||
{ .val = {0x2f4b8f0d, 0x830ac98, 0x2c2f900d, 0x3bb9ac91, 0x14cca9fc, 0xc7b6421, 0xf43014a, 0x209606e1, 0xc518}},
|
||||
{ .val = {0x17a5c59e, 0x2418564a, 0x3617c806, 0x1ddcd648, 0x2a6654fe, 0x63db210, 0x27a180a5, 0x104b0370, 0xe28c}},
|
||||
{ .val = {0xbd2e2cf, 0x120c2b25, 0x1b0be403, 0xeee6b24, 0x15332a7f, 0x231ed908, 0x13d0c052, 0x82581b8, 0x7146}},
|
||||
{ .val = {0x25e96f7f, 0x29061590, 0xd85f201, 0x27773592, 0xa99953f, 0x118f6c84, 0x9e86029, 0x412c0dc, 0xb8a3}},
|
||||
{ .val = {0x12f4b5d7, 0x34830ac6, 0x6c2f900, 0x33bb9ac9, 0x54cca9f, 0x28c7b642, 0x4f43014, 0x2209606e, 0xdc51}},
|
||||
{ .val = {0x97a5903, 0x1a418561, 0x23617c80, 0x39ddcd64, 0x2a6654f, 0x1463db21, 0x27a180a, 0x3104b037, 0xee28}},
|
||||
{ .val = {0x24bd2a99, 0xd20c2ae, 0x11b0be40, 0x3ceee6b2, 0x215332a7, 0xa31ed90, 0x213d0c05, 0x1882581b, 0xf714}},
|
||||
{ .val = {0x125e9364, 0x6906155, 0x8d85f20, 0x3e777359, 0x10a99953, 0x2518f6c8, 0x309e8602, 0xc412c0d, 0xfb8a}},
|
||||
{ .val = {0x292f49b2, 0x34830aa, 0x246c2f90, 0x3f3bb9ac, 0x854cca9, 0x128c7b64, 0x384f4301, 0x6209606, 0x7dc5}},
|
||||
{ .val = {0x1497a4d9, 0x1a41855, 0x123617c8, 0x3f9ddcd6, 0x42a6654, 0x29463db2, 0x1c27a180, 0x23104b03, 0x3ee2}},
|
||||
{ .val = {0x2a4bd084, 0xd20c28, 0x91b0be4, 0x1fceee6b, 0x215332a, 0x14a31ed9, 0x2e13d0c0, 0x11882581, 0x9f71}},
|
||||
{ .val = {0x1525e842, 0x690614, 0x248d85f2, 0xfe77735, 0x210a9995, 0xa518f6c, 0x3709e860, 0x28c412c0, 0x4fb8}},
|
||||
{ .val = {0xa92f421, 0x34830a, 0x3246c2f9, 0x27f3bb9a, 0x10854cca, 0x528c7b6, 0x1b84f430, 0x14620960, 0x27dc}},
|
||||
{ .val = {0x5497828, 0x201a4183, 0x1923617c, 0x13f9ddcd, 0x842a665, 0x29463db, 0xdc27a18, 0xa3104b0, 0x93ee}},
|
||||
{ .val = {0x22a4bc14, 0x100d20c1, 0x2c91b0be, 0x29fceee6, 0x24215332, 0x14a31ed, 0x6e13d0c, 0x5188258, 0x49f7}},
|
||||
{ .val = {0x31525e0a, 0x8069060, 0x1648d85f, 0x14fe7773, 0x3210a999, 0xa518f6, 0x3709e86, 0x228c412c, 0x24fb}},
|
||||
{ .val = {0x18a92f05, 0x24034830, 0x2b246c2f, 0x2a7f3bb9, 0x190854cc, 0x528c7b, 0x1b84f43, 0x31462096, 0x127d}},
|
||||
{ .val = {0xc54959a, 0x3201a416, 0x35923617, 0x153f9ddc, 0x2c842a66, 0x2029463d, 0xdc27a1, 0x38a3104b, 0x893e}},
|
||||
{ .val = {0x62a4acd, 0x3900d20b, 0x1ac91b0b, 0xa9fceee, 0x36421533, 0x3014a31e, 0x206e13d0, 0x1c518825, 0x449f}},
|
||||
{ .val = {0x2315237e, 0x3c806903, 0xd648d85, 0x254fe777, 0x1b210a99, 0x180a518f, 0x303709e8, 0x2e28c412, 0xa24f}},
|
||||
{ .val = {0x318a91bf, 0x3e403481, 0x26b246c2, 0x32a7f3bb, 0x2d90854c, 0xc0528c7, 0x181b84f4, 0x37146209, 0x5127}},
|
||||
{ .val = {0x38c546f7, 0x1f201a3e, 0x33592361, 0x1953f9dd, 0x36c842a6, 0x6029463, 0x2c0dc27a, 0x3b8a3104, 0xa893}},
|
||||
{ .val = {0x1c62a193, 0x2f900d1d, 0x39ac91b0, 0xca9fcee, 0x3b642153, 0x3014a31, 0x1606e13d, 0x3dc51882, 0xd449}},
|
||||
{ .val = {0x2e314ee1, 0x17c8068c, 0x1cd648d8, 0x2654fe77, 0x3db210a9, 0x2180a518, 0xb03709e, 0x3ee28c41, 0xea24}},
|
||||
{ .val = {0x1718a588, 0xbe40344, 0x2e6b246c, 0x332a7f3b, 0x1ed90854, 0x10c0528c, 0x2581b84f, 0x1f714620, 0xf512}},
|
||||
{ .val = {0xb8c52c4, 0x5f201a2, 0x37359236, 0x19953f9d, 0xf6c842a, 0x28602946, 0x12c0dc27, 0xfb8a310, 0x7a89}},
|
||||
{ .val = {0x5c62962, 0x2f900d1, 0x3b9ac91b, 0xcca9fce, 0x7b64215, 0x343014a3, 0x9606e13, 0x27dc5188, 0x3d44}},
|
||||
{ .val = {0x22e314b1, 0x217c8068, 0x1dcd648d, 0x26654fe7, 0x23db210a, 0x3a180a51, 0x4b03709, 0x13ee28c4, 0x1ea2}},
|
||||
{ .val = {0x11718870, 0x30be4032, 0x2ee6b246, 0x1332a7f3, 0x31ed9085, 0x3d0c0528, 0x2581b84, 0x9f71462, 0x8f51}},
|
||||
{ .val = {0x8b8c438, 0x185f2019, 0x37735923, 0x299953f9, 0x18f6c842, 0x1e860294, 0x12c0dc2, 0x24fb8a31, 0x47a8}},
|
||||
{ .val = {0x245c621c, 0x2c2f900c, 0x3bb9ac91, 0x14cca9fc, 0xc7b6421, 0xf43014a, 0x209606e1, 0x127dc518, 0x23d4}},
|
||||
{ .val = {0x122e310e, 0x3617c806, 0x1ddcd648, 0x2a6654fe, 0x63db210, 0x27a180a5, 0x104b0370, 0x93ee28c, 0x11ea}},
|
||||
{ .val = {0x9171887, 0x1b0be403, 0xeee6b24, 0x15332a7f, 0x231ed908, 0x13d0c052, 0x82581b8, 0x49f7146, 0x8f5}},
|
||||
{ .val = {0x248b8a5b, 0xd85f1ff, 0x27773592, 0xa99953f, 0x118f6c84, 0x9e86029, 0x412c0dc, 0x224fb8a3, 0x847a}},
|
||||
{ .val = {0x3245c345, 0x6c2f8fd, 0x33bb9ac9, 0x54cca9f, 0x28c7b642, 0x4f43014, 0x2209606e, 0x1127dc51, 0xc23d}},
|
||||
{ .val = {0x3922dfba, 0x23617c7c, 0x39ddcd64, 0x2a6654f, 0x1463db21, 0x27a180a, 0x3104b037, 0x2893ee28, 0xe11e}},
|
||||
{ .val = {0x1c916fdd, 0x11b0be3e, 0x3ceee6b2, 0x215332a7, 0xa31ed90, 0x213d0c05, 0x1882581b, 0x1449f714, 0x708f}},
|
||||
{ .val = {0xe48b606, 0x8d85f1d, 0x3e777359, 0x10a99953, 0x2518f6c8, 0x309e8602, 0xc412c0d, 0x2a24fb8a, 0xb847}},
|
||||
{ .val = {0x27245b03, 0x246c2f8e, 0x3f3bb9ac, 0x854cca9, 0x128c7b64, 0x384f4301, 0x6209606, 0x35127dc5, 0x5c23}},
|
||||
{ .val = {0x13922b99, 0x123617c5, 0x3f9ddcd6, 0x42a6654, 0x29463db2, 0x1c27a180, 0x23104b03, 0x3a893ee2, 0xae11}},
|
||||
{ .val = {0x29c913e4, 0x91b0be0, 0x1fceee6b, 0x215332a, 0x14a31ed9, 0x2e13d0c0, 0x11882581, 0x3d449f71, 0xd708}},
|
||||
{ .val = {0x14e489f2, 0x248d85f0, 0xfe77735, 0x210a9995, 0xa518f6c, 0x3709e860, 0x28c412c0, 0x1ea24fb8, 0x6b84}},
|
||||
};
|
||||
|
||||
#endif
|
||||
|
||||
#ifdef USE_PRECOMPUTED_CP
|
||||
|
||||
const curve_point secp256k1_cp[256] = {
|
||||
{.x = { .val = {0x16f81798, 0x27ca056c, 0x1ce28d95, 0x26ff36cb, 0x70b0702, 0x18a573a, 0xbbac55a, 0x199fbe77, 0x79be}},
|
||||
.y = { .val = {0x3b10d4b8, 0x311f423f, 0x28554199, 0x5ed1229, 0x1108a8fd, 0x13eff038, 0x3c4655da, 0x369dc9a8, 0x483a}}},
|
||||
{.x = { .val = {0x1c709ee5, 0x2eb026e5, 0xef3ca7a, 0x1de392e3, 0x7cd85c, 0x1501ba57, 0x17d6d304, 0x1fe5107b, 0xc604}},
|
||||
.y = { .val = {0x10cfe52a, 0xd90c6a5, 0x266d0e12, 0x3d8c994c, 0x2ceaeef7, 0x16106519, 0x1c339a3c, 0x1a3fa98f, 0x1ae1}}},
|
||||
{.x = { .val = {0x28c4cd13, 0x13ea52af, 0x2e075847, 0x1b04e403, 0xb1404cc, 0x3924124c, 0x180f3581, 0x36fc7043, 0xe493}},
|
||||
.y = { .val = {0x7739922, 0x3fa5ef71, 0x3bdfe40c, 0x19eb8cef, 0x251448d9, 0xb88263a, 0x55b7564, 0x264fa835, 0x51ed}}},
|
||||
{.x = { .val = {0x210a2a01, 0x1de13bcf, 0x1af888a6, 0x6f74179, 0xf3c2f0a, 0xe10fedc, 0x2351daff, 0x39785732, 0x2f01}},
|
||||
.y = { .val = {0x2cbde904, 0x1768b2dd, 0x25b7617b, 0x3884f5ae, 0x2d13b4c2, 0x3420a84c, 0x39949293, 0x2a29d054, 0x5c4d}}},
|
||||
{.x = { .val = {0x2a6dec0a, 0x113ba278, 0x7a5ae9c, 0x28c4da6e, 0x23e97b2, 0x6aaf087, 0x29ec5301, 0x33a4ed67, 0xe60f}},
|
||||
.y = { .val = {0x29616821, 0x7ccb339, 0xd23f0be, 0x25a24791, 0x39371012, 0x267cd3d5, 0x195929db, 0x141ce679, 0xf7e3}}},
|
||||
{.x = { .val = {0x7143e65, 0x17436f50, 0x104a61d7, 0x33ff2e26, 0x3378ceda, 0x1b81538b, 0x1a22d47b, 0x2675d3ed, 0xd301}},
|
||||
.y = { .val = {0x24106ab9, 0x16cffc7c, 0xed81960, 0x1d8330d9, 0x380651f, 0x1b7b27a6, 0x3d5c3b3d, 0x236742b8, 0x9503}}},
|
||||
{.x = { .val = {0x3874ef8b, 0xde4639b, 0x1bafd81e, 0x131bc773, 0x32823cfc, 0x147abe0, 0x2eab70b1, 0x30550b45, 0xbf23}},
|
||||
.y = { .val = {0x26831d9f, 0x370dfbf9, 0x11e2f784, 0x8bf1520, 0x1392e4c5, 0x24a282e9, 0x3737ad, 0x219bf0cc, 0x5cb3}}},
|
||||
{.x = { .val = {0x2769a24e, 0x11c1dd15, 0x5356556, 0x3d5735c0, 0x11671cbc, 0x30f427df, 0x37a06696, 0xef900cf, 0x34ff}},
|
||||
.y = { .val = {0x33cc2f1a, 0x124419e9, 0xf8b6818, 0x37c5b0fa, 0x32098c55, 0x18676260, 0x36c553f6, 0x4588e88, 0x5d9d}}},
|
||||
{.x = { .val = {0x15f51508, 0x191b88ff, 0x1ac1ca10, 0x30e72af5, 0x2de238d8, 0x29b8f85c, 0x209d9ea2, 0x98c84b1, 0x8282}},
|
||||
.y = { .val = {0x36e26caf, 0xc6dbabf, 0x37b17bed, 0x3584eb0b, 0x360ace62, 0x95ba0c2, 0x3dfe45e8, 0x2a026155, 0x11f8}}},
|
||||
{.x = { .val = {0x2f34a24d, 0x9b8b003, 0x1e159d09, 0x36f25a36, 0x3918d50a, 0x2a15ea73, 0x39ff3905, 0x1c2ca1e9, 0x4653}},
|
||||
.y = { .val = {0x333887f4, 0xbe3ec82, 0x1d37a10a, 0x23826c85, 0x2ec2c158, 0x3e2f6bf7, 0xc082a4a, 0xc6ce0da, 0x35e5}}},
|
||||
{.x = { .val = {0x2285131f, 0x16e406cb, 0x13b088d, 0x3b1bb372, 0x2d6240aa, 0x12863d9a, 0xbd77d66, 0x3aee388f, 0x241f}},
|
||||
.y = { .val = {0x2750026d, 0x2ecf99bc, 0x10cb5afa, 0x143f43ef, 0x181df8cd, 0x1082f44e, 0xf8d3d6c, 0x1e367fe5, 0x5133}}},
|
||||
{.x = { .val = {0x1b920471, 0x372d8c1a, 0x23de0de, 0xc62e17d, 0x18f8d9fc, 0x1330a60f, 0x2fa79fce, 0x36d3a85c, 0x5d1b}},
|
||||
.y = { .val = {0x37b83103, 0xcc199b, 0x2c56e7b7, 0x3ac7a665, 0x22265679, 0x2ee650e2, 0x39e2e794, 0x2099de4d, 0x2843}}},
|
||||
{.x = { .val = {0x11e5b739, 0xff396d5, 0x12222ed7, 0x2e4e0cff, 0x3c846de0, 0x26731b1b, 0x3865a72f, 0x567dca2, 0x175e}},
|
||||
.y = { .val = {0x29fed695, 0x3be9bffb, 0x124345c6, 0x2d6556b7, 0x371f5eac, 0x3e5e947f, 0x79eba4e, 0x1b83678f, 0xd350}}},
|
||||
{.x = { .val = {0x6bc47d6, 0x39e01279, 0x2da121bc, 0x3f7fad71, 0x39c62130, 0x3ef32384, 0x332d7a5f, 0x4fc0ff, 0x423a}},
|
||||
.y = { .val = {0xb548a34, 0x48db9b6, 0x24f009ed, 0x363b0d4, 0x36b3c772, 0x1e7deeeb, 0x1d970a11, 0x3803f878, 0xb91a}}},
|
||||
{.x = { .val = {0x416824a, 0xb7dbde, 0x33e27413, 0x37d98bce, 0x16877649, 0x1e9eaf3, 0x3b905089, 0x1a916b07, 0x111d}},
|
||||
.y = { .val = {0x2108e9d0, 0x26844750, 0x2daca4ca, 0x1c002265, 0x65952f0, 0x35236ffc, 0x2affbb90, 0x244711e3, 0x696}}},
|
||||
{.x = { .val = {0x1bced775, 0x2d7b7780, 0x2f74e56a, 0x242da297, 0x39dcff72, 0x2576faf2, 0x3c8b8ad7, 0x1b725eb1, 0x4a4a}},
|
||||
.y = { .val = {0x278dd66d, 0xafe3da2, 0x24742acb, 0x3a4336d0, 0xf4571d, 0x3be7dce7, 0x31e72943, 0x46c0598, 0x5299}}},
|
||||
{.x = { .val = {0x3ff4640, 0x9aeb63e, 0x1552ffe5, 0x11071f95, 0x262ee053, 0x3ab016d8, 0xc9c99c, 0x243511ec, 0x363d}},
|
||||
.y = { .val = {0x3bee9de9, 0x800f1fc, 0x199ecb6, 0x2e6a2402, 0x33363145, 0x2d114e5f, 0x32221953, 0x1ceb7f1c, 0x4e2}}},
|
||||
{.x = { .val = {0x2f92c541, 0x9c4a972, 0x2dfb59dd, 0x18bec04b, 0x3b02bf0b, 0x25cf1b24, 0x27e9b553, 0x2619bb66, 0x4c1b}},
|
||||
.y = { .val = {0x68fe020, 0xb13cff7, 0x3eb1ad7, 0x14bab5f9, 0x16e69cc6, 0x32dd4f39, 0x28a0f7fb, 0x24b4c82f, 0xc1f7}}},
|
||||
{.x = { .val = {0x3eaaf3d1, 0x323ca32, 0x228f135e, 0xcfb6f06, 0xb54e32, 0x28bcf01e, 0x3b12b529, 0xe1deea0, 0xa408}},
|
||||
.y = { .val = {0x30b254b9, 0x4ad4d37, 0x2d1ef90b, 0x79d5db, 0x21b3e220, 0x3e0f5a4d, 0x3bc79b8b, 0x3d84bfbb, 0x40e9}}},
|
||||
{.x = { .val = {0x3940d33a, 0x334f6d69, 0x14203b98, 0x3620291, 0x16c86f6e, 0x38f868bd, 0xc0b53a4, 0x319074a3, 0xa804}},
|
||||
.y = { .val = {0x2d46967a, 0xf3a57e9, 0xf736a94, 0x3c632a27, 0x2047e81a, 0x30a10b05, 0x3a6d03de, 0x20c94acb, 0x95be}}},
|
||||
{.x = { .val = {0x1ffdf80c, 0x27de6957, 0x15bcd1b6, 0x3929e068, 0x5638843, 0x912d6dd, 0x3c2be8c6, 0x17c5977c, 0x8b4b}},
|
||||
.y = { .val = {0x1fd4fd36, 0xfbfc319, 0x162ee56b, 0x38cd9518, 0x30da04f9, 0x2f5e04ea, 0x308b4b3f, 0x29bda34, 0x4aad}}},
|
||||
{.x = { .val = {0x755e4be, 0x2cfc99c5, 0x17c997ab, 0x2bd93b90, 0x3c611071, 0x5f1fb20, 0x291718ce, 0x1739384c, 0xed0c}},
|
||||
.y = { .val = {0x207bf42f, 0xfe7e9ba, 0x23ddab16, 0x364e495d, 0x3ea68049, 0x36b5fd69, 0x345bdbf3, 0x27f1ef08, 0x221a}}},
|
||||
{.x = { .val = {0x7cec8ab, 0x12db9b20, 0x20552ced, 0xc95159b, 0x31fae8e5, 0x570fe0f, 0xe694b3b, 0x2c04f113, 0xfaec}},
|
||||
.y = { .val = {0x2b155070, 0x26077f66, 0x5e2e2e8, 0xcaca1ae, 0x2fb13d9c, 0x380b1bb0, 0x2cb57fc2, 0x2d7a43a7, 0xcc09}}},
|
||||
{.x = { .val = {0x1ad1b1f7, 0x1fd93aba, 0x323cd3e0, 0x2cb76093, 0xbcafdb3, 0xc682cdf, 0x2d2f2c87, 0x2284cb72, 0x9bb}},
|
||||
.y = { .val = {0x3811c80, 0x104c189f, 0x752d536, 0x152a103d, 0x63e850f, 0x2774a13e, 0x2e3b9b6f, 0x2cacabfb, 0x945b}}},
|
||||
{.x = { .val = {0x1232fcda, 0x2d845649, 0x2c0e77bc, 0x36ffe9, 0x1548c7b7, 0x1dc7002f, 0x3996d6bf, 0x2ea9b976, 0x723c}},
|
||||
.y = { .val = {0x1eb39f5f, 0x7701a76, 0x37949480, 0x1828194d, 0x24d6e26, 0x44dd222, 0xc498a92, 0x19ed5657, 0x96e8}}},
|
||||
{.x = { .val = {0xca030d5, 0x3f4e0f58, 0x39849071, 0x90290c1, 0x33a3c62d, 0x35f7115d, 0x3744d343, 0x29e190de, 0x57ef}},
|
||||
.y = { .val = {0x34b02f9e, 0x1ead109, 0x1e9974ab, 0x26db4ab9, 0x1e03ec68, 0x189f24a3, 0x8518893, 0x36c2f46d, 0xd712}}},
|
||||
{.x = { .val = {0xc584dd5, 0x3ebf1ddc, 0x27b012a7, 0x2015df8c, 0x226cb910, 0x3dfa7354, 0xbc42a2d, 0x2f50da8a, 0x264b}},
|
||||
.y = { .val = {0x3704ab11, 0x18489e4d, 0x17b8d8de, 0x46090dc, 0x33be226a, 0x1d738930, 0x93b4d4f, 0x1bea53b8, 0xd87c}}},
|
||||
{.x = { .val = {0xb2438e8, 0x2fc9af61, 0x1bdec9d2, 0x22f187f5, 0x36a79da7, 0x21701588, 0xd2bbdac, 0x19492f50, 0xa94c}},
|
||||
.y = { .val = {0x318661f4, 0xb8b236f, 0xe39b2bc, 0x174f1828, 0x19e3a7e, 0x24865414, 0x16280fd7, 0x7f664be, 0xb520}}},
|
||||
{.x = { .val = {0xe7dd7fa, 0x294cfb28, 0x3a919839, 0x11e5848d, 0x2d3b509, 0x3fbb204b, 0x2bf98ba5, 0x293524ef, 0xeebf}},
|
||||
.y = { .val = {0x21de8999, 0x37f53f6b, 0x311f712d, 0x393370e9, 0x38089d9a, 0x39fb6bc5, 0x2f0f269e, 0x2328e5c3, 0x5d9a}}},
|
||||
{.x = { .val = {0x7d297fd, 0x1afba421, 0x36766d67, 0x3a92f023, 0x18495fc4, 0x3180c704, 0x17bfda61, 0x12b5e9ea, 0x381c}},
|
||||
.y = { .val = {0x3d493fc5, 0xeb38c61, 0x3939c009, 0x11440cb6, 0x115eccf0, 0x397e9c26, 0x2eee48f3, 0x3d4ec8e3, 0x936a}}},
|
||||
{.x = { .val = {0x2ede454c, 0x1235c108, 0x3dd08b24, 0x3c7417fb, 0x138c479c, 0x420c765, 0x1c63bcce, 0x2e73416b, 0xe1ef}},
|
||||
.y = { .val = {0x28913797, 0x367f48ce, 0x3a2d4c6a, 0x138c9129, 0x7712346, 0x15307ff9, 0x39be7b01, 0x114c362b, 0xecb}}},
|
||||
{.x = { .val = {0x29eb99a4, 0xcffbacc, 0x3d47b18d, 0x395067cc, 0x3475a8c7, 0x308d7a6b, 0x17010c5a, 0x3e6c689a, 0x5318}},
|
||||
.y = { .val = {0x3e91f92d, 0x31c9bbbb, 0x1e3ec652, 0x7cad034, 0x3405e8a4, 0xb64ebae, 0x1a419577, 0x33fad2fb, 0xf44c}}},
|
||||
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|
||||
{.x = { .val = {0x14b311dd, 0xddf222c, 0x3d71b9cf, 0x38efabbe, 0x2252e03d, 0x202fe82e, 0x2f5acdd5, 0x2eb4a3ea, 0xadd5}},
|
||||
.y = { .val = {0x9d6c38d, 0xbe60bcd, 0x29b9b890, 0x353879d9, 0x19814f52, 0x390d3e0d, 0x1c3a5974, 0xf3d368f, 0xe9c4}}},
|
||||
{.x = { .val = {0xd7c0979, 0x17d90028, 0x5a8c96f, 0xa6cc52f, 0x1ced24a, 0x277cf7fd, 0x317143fa, 0x10caea05, 0x53f2}},
|
||||
.y = { .val = {0x137b36a2, 0x27dfa431, 0x1e8b845f, 0x35693d72, 0x1b07de4b, 0x138f8244, 0x79b7ccd, 0x3bfef07c, 0xbd52}}},
|
||||
{.x = { .val = {0x1d82b151, 0x2d44d032, 0x21fba2db, 0x28290f55, 0x109a8fcc, 0x168454ec, 0x1e56d64, 0xe942b90, 0xd2a6}},
|
||||
.y = { .val = {0x1cf89405, 0x105085d3, 0x84ca52d, 0x3dd42bd, 0x148220a7, 0x2bb962ca, 0x3fcb7565, 0x21bed910, 0xe82d}}},
|
||||
{.x = { .val = {0xa72da5f, 0x31b12eb3, 0x2c413497, 0x2e735acd, 0x3725f922, 0x31c8080c, 0x525e23b, 0x20e9d840, 0xbaf1}},
|
||||
.y = { .val = {0x28f2a0cf, 0x1df398a2, 0x27393613, 0x8cdb172, 0x29b1d18e, 0x22f56375, 0x34d33568, 0x27efa732, 0xdeac}}},
|
||||
{.x = { .val = {0x56c3943, 0x296b2963, 0x2b76a5ff, 0x36f40b55, 0x8f6fd5a, 0xcca41b9, 0x40238f9, 0x3e29f8e1, 0xf7ae}},
|
||||
.y = { .val = {0x2cf442f1, 0xc7d89fe, 0xdcd0034, 0x30c0612a, 0x2b3fcfee, 0x10aef70e, 0x3da797c4, 0x2d1357f, 0x4e3b}}},
|
||||
{.x = { .val = {0x11924459, 0x3eb2515c, 0x3c7a78c1, 0x3cbe8968, 0x1dbb1f7a, 0xb8a7c37, 0x19036c5a, 0x11f2c400, 0xdfb5}},
|
||||
.y = { .val = {0xc65fd9e, 0x28817837, 0x1c031dcf, 0x2bc24c39, 0x864cc22, 0xe273a77, 0x347088b8, 0x34aa6e83, 0x9acc}}},
|
||||
{.x = { .val = {0x1617e073, 0x10dbe6d1, 0x39317b3, 0x2b2f6f4e, 0xfdc866b, 0x39e25b5f, 0x31eb890e, 0x1f88cd51, 0x6458}},
|
||||
.y = { .val = {0x1faf6589, 0x20a6797a, 0x33aeab35, 0x2e428e44, 0x299a185, 0x1b75911f, 0x102e2ae9, 0x33756fda, 0xd99f}}},
|
||||
{.x = { .val = {0x384480d, 0x12f36231, 0x291f2ef4, 0x382da88a, 0x2f0c1294, 0xa2d5324, 0x3940f2cf, 0x35ac50b7, 0xb866}},
|
||||
.y = { .val = {0xc4cafa8, 0x39966d1c, 0x31d86d60, 0x3948a012, 0x1ad7ac24, 0x9e35faa, 0x2eb7089a, 0x2c2cd09a, 0x1914}}},
|
||||
{.x = { .val = {0x1db20d6c, 0x8a736a0, 0x14fe455d, 0x354ab93b, 0x2ba87e2, 0x27459184, 0x2819ec4d, 0x2e242177, 0xec2b}},
|
||||
.y = { .val = {0x229cf4a0, 0x3a67135, 0x7efa98a, 0x288d92fa, 0x940c633, 0x3d9bc194, 0x13a1332, 0x305d9878, 0xccec}}},
|
||||
{.x = { .val = {0x23b09d0f, 0x22983b2c, 0x350becf3, 0x141903, 0x145905e5, 0x35d7bd79, 0x296ced39, 0x29f8e278, 0x71c4}},
|
||||
.y = { .val = {0x320ddb62, 0xdec7c05, 0x262ffc76, 0x1bcac212, 0x3810aa78, 0xf828a4b, 0x2f3ba0af, 0x3eb6dcde, 0x1313}}},
|
||||
{.x = { .val = {0x1d45e458, 0x1635b21b, 0x250e7fd3, 0x2a9b3a8, 0x9de042f, 0x151b4f95, 0xd885b3a, 0x2f783939, 0x8481}},
|
||||
.y = { .val = {0x1779057e, 0x3592c6d6, 0x3262e556, 0x29e710a, 0x2cb2ca90, 0x96fce73, 0x4dd84a, 0x1ee32e95, 0x38ee}}},
|
||||
{.x = { .val = {0x2ce9f114, 0x1510cd49, 0x19561dde, 0xbb5814a, 0x1492bf39, 0x10f1b347, 0x3a8b9fd, 0x29142f4e, 0x9629}},
|
||||
.y = { .val = {0x224aa391, 0x28e5cb12, 0x56af8dc, 0x9564f97, 0xef64db9, 0x2fbf4883, 0x3b6d7576, 0x26ca0317, 0xbf43}}},
|
||||
{.x = { .val = {0x26ca6cc3, 0xf4e3658, 0x187e1838, 0x1df5d1f8, 0x893df14, 0x1cc369f3, 0x24688eb1, 0x711fbc7, 0xb73b}},
|
||||
.y = { .val = {0x254fdba3, 0x2b0d75da, 0x1757f5af, 0x8a89482, 0x8050973, 0x1f592ef3, 0x122a90a5, 0x572ca52, 0x5843}}},
|
||||
{.x = { .val = {0x138f93e0, 0x31b8864b, 0x276899f9, 0x16ca8eed, 0x22fef7d0, 0x2624801e, 0x180311f, 0x5acb6d0, 0xedfe}},
|
||||
.y = { .val = {0x229405ad, 0x3405e4f7, 0x6e227e3, 0xf544031, 0x5d0d25b, 0x1d3ea92c, 0x1db3694d, 0xbc7f29, 0xee69}}},
|
||||
{.x = { .val = {0x2caf666b, 0x3358c0fd, 0xb1ce30b, 0x3f3fb4f1, 0x17f4637f, 0x1a5e6ba0, 0x102aa62b, 0x1295e9e0, 0x1346}},
|
||||
.y = { .val = {0x3f6ecc27, 0x3d256a41, 0x10942e13, 0x3cc02a07, 0xcb0ca48, 0x390cd14f, 0x14580ef7, 0x5640118, 0x69be}}},
|
||||
{.x = { .val = {0x65084ae, 0x1d612718, 0x2abe577c, 0x20af9f73, 0x3e12d191, 0x17223217, 0x5362ec0, 0x3e3d4c89, 0xeb3c}},
|
||||
.y = { .val = {0x396b9480, 0x3d9f07ff, 0x3dbd2a66, 0xad17179, 0x1ca4a1f5, 0x398f73bf, 0x1d70043f, 0x31e088b6, 0xc833}}},
|
||||
{.x = { .val = {0x2e9a5d0, 0x2396f2f3, 0xa201d9f, 0x1dbf3e61, 0x519b2a5, 0x2983c861, 0x199974f7, 0x299f424b, 0xbdf1}},
|
||||
.y = { .val = {0x562ff7b, 0x36d3dc06, 0x1626461c, 0xa02d879, 0x3f7baaa6, 0x2f952a1a, 0x1a1aaa80, 0x240aead9, 0x4095}}},
|
||||
{.x = { .val = {0x3b27e771, 0x3797f05c, 0x37da62ab, 0xed06591, 0x483b48c, 0x2f899ed9, 0xec29cd5, 0x1a9bb771, 0x6885}},
|
||||
.y = { .val = {0x7bbdab6, 0x46358a8, 0x3b0733a6, 0x748bca4, 0x1f7b4a33, 0x1bf52706, 0x1a1fb13b, 0xf7c53de, 0x77a3}}},
|
||||
{.x = { .val = {0x2d83f366, 0x2b68e834, 0x2f28588c, 0x36733b78, 0x1dc97a0c, 0x3d0c2f30, 0x3fe2e9ae, 0x277d6dc4, 0xbc4a}},
|
||||
.y = { .val = {0x181f33c1, 0x1d635999, 0x2547b16d, 0x3a2a7efe, 0x3798caa6, 0x24deb7d2, 0x5c06383, 0x20729b9e, 0xd3a}}},
|
||||
{.x = { .val = {0x33fceb19, 0x20b79517, 0x385c4092, 0x226c887d, 0x27bab42e, 0x171d89b3, 0x2ccc0abc, 0xf578473, 0xda43}},
|
||||
.y = { .val = {0x26f5cc64, 0x2139c482, 0x227b2776, 0x1dff0b64, 0x15e5218e, 0x2ef712be, 0x10301de, 0x36f4c86a, 0xe498}}},
|
||||
{.x = { .val = {0x1acf692a, 0x13789d71, 0x2207e065, 0x3120e29c, 0x16efdbc, 0x3045a607, 0xc7ec1c1, 0x2387ba7a, 0x31e}},
|
||||
.y = { .val = {0x316f667a, 0x330aa13a, 0x1bf73b09, 0x192609f1, 0x16743b70, 0x25c0a43, 0x3353dd9d, 0x1fd6d196, 0xad7e}}},
|
||||
{.x = { .val = {0x1f488b6, 0xaef5ffe, 0x3c7a9159, 0x326fcd8f, 0x257f73e9, 0x38036189, 0x161155d3, 0x2181ea23, 0xa987}},
|
||||
.y = { .val = {0x31dab1d, 0x2569eeec, 0xad5c6d4, 0x343c0659, 0x157c2239, 0x18f9f208, 0x95d61c0, 0x286af562, 0xd181}}},
|
||||
{.x = { .val = {0x25324caa, 0x152acc3f, 0x29472a39, 0x12d978c2, 0x12a32e69, 0x3631d251, 0x18bc0d23, 0x2a5efe0a, 0x8c28}},
|
||||
.y = { .val = {0xbef9482, 0x39c771cf, 0x11cb9459, 0x39e13c11, 0x3cc0eb7a, 0x3fb7cc7d, 0x5193378, 0x118e8cc, 0x40a3}}},
|
||||
{.x = { .val = {0x3611d8e2, 0x37ec807d, 0x249fc4d5, 0x4c3fa37, 0x3f0da2c8, 0x3b569811, 0xa2f196b, 0x3061ca8e, 0xab1a}},
|
||||
.y = { .val = {0x429d15b, 0x69607cf, 0x21e545f0, 0x3be4f4cf, 0x2a42b6f7, 0x297ce76d, 0x117a1e9a, 0x28de8c93, 0x13f4}}},
|
||||
{.x = { .val = {0x2651b3fa, 0x9abb990, 0x32df4342, 0x286cd95d, 0x3f31ef8e, 0xe981c94, 0x2f82d370, 0x3fa6d6fb, 0x2564}},
|
||||
.y = { .val = {0x1e5122d, 0x2e0b9a8c, 0x379816ed, 0x3cdf6ada, 0x3925f14, 0x2852b848, 0x389095f, 0x3de9819e, 0x8ad9}}},
|
||||
{.x = { .val = {0x2e180068, 0x5e38f4e, 0xbd3103b, 0x28f55b08, 0xdc01a7e, 0x1b17030c, 0x5b0cbfc, 0x184dbfeb, 0xff3d}},
|
||||
.y = { .val = {0x188c6077, 0x29aedb8, 0x1f5e67, 0x1d9dbc90, 0x16adc154, 0xdcb376, 0xe40d, 0xe6fa139, 0x1332}}},
|
||||
{.x = { .val = {0x1faccae0, 0x2312e844, 0x24bb3374, 0x22cd4316, 0x71fd23c, 0x3653393c, 0x127a8c1d, 0x259984e5, 0x8ea}},
|
||||
.y = { .val = {0xe62b945, 0x16bcd28c, 0xf0f8e95, 0x2de0efa7, 0x15c5d735, 0x39f033ee, 0x22782e24, 0x3eaef23b, 0x620e}}},
|
||||
{.x = { .val = {0x2190b632, 0xa4c4c76, 0xab5ab9a, 0x33ca88e9, 0x159d8263, 0x19b7cc55, 0x20cd9f3a, 0x18dc5d88, 0xc25f}},
|
||||
.y = { .val = {0x3c9590cf, 0x3bafcf5b, 0x2027a1d6, 0x27c13fe7, 0x9d7980a, 0x12640e0, 0x12873989, 0x13fb7a53, 0x5315}}},
|
||||
{.x = { .val = {0x1466d561, 0xb32cedf, 0x1978b4de, 0x1ed5770c, 0x8544c0c, 0xb60a95a, 0x26bab3e8, 0x237f8f33, 0x2a9e}},
|
||||
.y = { .val = {0x12e76373, 0x25b33d49, 0x3a02182f, 0x7abb05, 0xb96cf5e, 0x1ed6b582, 0x2651fbac, 0x3b69705b, 0x1df}}},
|
||||
{.x = { .val = {0x3f8be384, 0x22f4c810, 0x31db6c3e, 0x3b02ab68, 0x1ef07271, 0x2b5b253f, 0x23e1b251, 0x24290af9, 0xb237}},
|
||||
.y = { .val = {0x2b19880e, 0x4291cf7, 0x9ecb58d, 0x3c013d05, 0x1f94517, 0x143e22aa, 0x15edbe8d, 0x1a524675, 0xfc6b}}},
|
||||
};
|
||||
|
||||
#endif
|
||||
63
secp256k1.h
Normal file
63
secp256k1.h
Normal file
@ -0,0 +1,63 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
|
||||
#ifndef __SECP256K1_H__
|
||||
#define __SECP256K1_H__
|
||||
|
||||
#include <stdint.h>
|
||||
|
||||
#define USE_PRECOMPUTED_IV 1
|
||||
#define USE_PRECOMPUTED_CP 1
|
||||
|
||||
// bignum256 are 256 bits stored as 8*30 bit + 1*16 bit
|
||||
// val[0] are lowest 30 bits, val[8] highest 16 bits
|
||||
typedef struct {
|
||||
uint32_t val[9];
|
||||
} bignum256;
|
||||
|
||||
// curve point x and y
|
||||
typedef struct {
|
||||
bignum256 x, y;
|
||||
} curve_point;
|
||||
|
||||
// secp256k1 prime
|
||||
extern const bignum256 prime256k1;
|
||||
|
||||
// secp256k1 initial curve point
|
||||
extern const curve_point G256k1;
|
||||
|
||||
// secp256k1 order of G
|
||||
extern const bignum256 order256k1;
|
||||
|
||||
// 3/2 in G_p
|
||||
extern const bignum256 three_over_two256k1;
|
||||
|
||||
#ifdef USE_PRECOMPUTED_IV
|
||||
extern const bignum256 secp256k1_iv[256];
|
||||
#endif
|
||||
|
||||
#ifdef USE_PRECOMPUTED_CP
|
||||
extern const curve_point secp256k1_cp[256];
|
||||
#endif
|
||||
|
||||
#endif
|
||||
127
sha256.c
Normal file
127
sha256.c
Normal file
@ -0,0 +1,127 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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 <stdint.h>
|
||||
#include "aux.h"
|
||||
|
||||
// process sha256 chunk (of length 64 bytes)
|
||||
void process_chunk(const uint8_t *chunk, uint32_t *hash)
|
||||
{
|
||||
static const uint32_t k0[64] = {
|
||||
0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,
|
||||
0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,
|
||||
0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
|
||||
0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,
|
||||
0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,
|
||||
0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
|
||||
0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,
|
||||
0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2
|
||||
};
|
||||
uint32_t i, s0, s1, a, b, c, d, e, f, g, h, ch, temp, maj, w[64];
|
||||
|
||||
for (i = 0;i < 16;i++) {
|
||||
w[i] = read_be(chunk + 4 * i);
|
||||
}
|
||||
for (;i < 64;i++) {
|
||||
s0 = ror(w[i-15], 7) ^ ror(w[i-15], 18) ^ (w[i-15]>>3);
|
||||
s1 = ror(w[i-2], 17) ^ ror(w[i-2], 19) ^ (w[i-2]>>10);
|
||||
w[i] = w[i-16] + s0 + w[i-7] + s1;
|
||||
}
|
||||
a = hash[0];
|
||||
b = hash[1];
|
||||
c = hash[2];
|
||||
d = hash[3];
|
||||
e = hash[4];
|
||||
f = hash[5];
|
||||
g = hash[6];
|
||||
h = hash[7];
|
||||
for (i = 0;i < 64;i++) {
|
||||
s1 = ror(e, 6) ^ ror(e, 11) ^ ror(e, 25);
|
||||
ch = (e & f) ^ ((~ e) & g);
|
||||
temp = h + s1 + ch + k0[i] + w[i];
|
||||
d = d + temp;
|
||||
s0 = ror(a, 2) ^ ror(a, 13) ^ ror(a, 22);
|
||||
maj = (a & (b ^ c)) ^ (b & c);
|
||||
temp = temp + s0 + maj;
|
||||
h = g;
|
||||
g = f;
|
||||
f = e;
|
||||
e = d;
|
||||
d = c;
|
||||
c = b;
|
||||
b = a;
|
||||
a = temp;
|
||||
}
|
||||
hash[0] += a;
|
||||
hash[1] += b;
|
||||
hash[2] += c;
|
||||
hash[3] += d;
|
||||
hash[4] += e;
|
||||
hash[5] += f;
|
||||
hash[6] += g;
|
||||
hash[7] += h;
|
||||
}
|
||||
|
||||
// compute sha256 of a message with len length in bytes
|
||||
// hash is a pointer to at least 32byte array
|
||||
void sha256(const uint8_t *msg, const uint32_t len, uint8_t *hash)
|
||||
{
|
||||
// initial hash vales
|
||||
static const uint32_t h0[8] = {
|
||||
0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a, 0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19
|
||||
};
|
||||
uint32_t l = len, i, h[8];
|
||||
uint8_t last_chunks[128]; //for storing last 1 or 2 chunks
|
||||
for (i = 0;i < 8; i++) {
|
||||
h[i] = h0[i];
|
||||
}
|
||||
// process complete message chunks
|
||||
while (l >= 64) {
|
||||
process_chunk(msg, h);
|
||||
l -= 64;
|
||||
msg += 64;
|
||||
}
|
||||
// process rest of the message
|
||||
for (i = 0;i < l; i++) {
|
||||
last_chunks[i] = msg[i];
|
||||
}
|
||||
// add '1' bit
|
||||
last_chunks[i++] = 0x80;
|
||||
// pad message with zeroes
|
||||
for (;(i & 63) != 56; i++) {
|
||||
last_chunks[i]=0;
|
||||
}
|
||||
// add message length in bits
|
||||
l = 8 * len;
|
||||
write_be(last_chunks + i, 0);
|
||||
write_be(last_chunks + i + 4, l);
|
||||
// process remaining 1 or 2 chunks
|
||||
process_chunk(last_chunks, h);
|
||||
if (i > 64) {
|
||||
process_chunk(last_chunks + 64, h);
|
||||
}
|
||||
// write the result
|
||||
for (i = 0;i < 8; i++) {
|
||||
write_be(hash + 4 * i, h[i]);
|
||||
}
|
||||
}
|
||||
31
sha256.h
Normal file
31
sha256.h
Normal file
@ -0,0 +1,31 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
|
||||
#ifndef __SHA256_H_
|
||||
#define __SHA256_H_
|
||||
|
||||
// compute sha256 of a message with len length (in bytes)
|
||||
// hash is a pointer to at least 32 byte array
|
||||
void sha256(const uint8_t *msg, const uint32_t len, uint8_t *hash);
|
||||
|
||||
#endif
|
||||
100
test.c
Normal file
100
test.c
Normal file
@ -0,0 +1,100 @@
|
||||
/**
|
||||
* Copyright (c) 2013 Tomas Dzetkulic
|
||||
* Copyright (c) 2013 Pavol Rusnak
|
||||
*
|
||||
* 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 <openssl/ecdsa.h>
|
||||
#include <openssl/obj_mac.h>
|
||||
#include <openssl/sha.h>
|
||||
#include <stdint.h>
|
||||
|
||||
#include "ecdsa.h"
|
||||
#include "rand.h"
|
||||
|
||||
int main()
|
||||
{
|
||||
uint8_t sig[70], priv_key[32], msg[256], buffer[1000], hash[32], *p;
|
||||
uint32_t sig_len, i, j, msg_len;
|
||||
SHA256_CTX sha256;
|
||||
EC_GROUP *ecgroup;
|
||||
int cnt = 0;
|
||||
|
||||
init_rand();
|
||||
ecgroup = EC_GROUP_new_by_curve_name(NID_secp256k1);
|
||||
|
||||
for (;;) {
|
||||
// random message len between 1 and 256
|
||||
msg_len = (random32() & 0xFF) + 1;
|
||||
// create random message
|
||||
for (i = 0; i <msg_len; i++) {
|
||||
msg[i] = random32() & 0xFF;
|
||||
}
|
||||
// new ECDSA key
|
||||
EC_KEY *eckey = EC_KEY_new();
|
||||
EC_KEY_set_group(eckey, ecgroup);
|
||||
|
||||
// generate the key
|
||||
EC_KEY_generate_key(eckey);
|
||||
p = buffer;
|
||||
// copy key to buffer
|
||||
i2d_ECPrivateKey(eckey, &p);
|
||||
|
||||
// size of the key is in buffer[8] and the key begins right after that
|
||||
i = buffer[8];
|
||||
// extract key data
|
||||
if (i > 32) {
|
||||
for (j = 0;j < 32; j++) {
|
||||
priv_key[j] = buffer[j + i - 23];
|
||||
}
|
||||
} else {
|
||||
for (j = 0; j < 32 - i; j++) {
|
||||
priv_key[j] = 0;
|
||||
}
|
||||
for (j = 0; j < i; j++) {
|
||||
priv_key[j + 32 - i] = buffer[j + 9];
|
||||
}
|
||||
}
|
||||
|
||||
// use our ECDSA signer to sign the message with the key
|
||||
ecdsa_sign(priv_key, msg, msg_len, sig, &sig_len);
|
||||
|
||||
// copy signature to the OpenSSL struct
|
||||
p = sig;
|
||||
ECDSA_SIG *signature = d2i_ECDSA_SIG(NULL, (const uint8_t **)&p, sig_len);
|
||||
|
||||
// compute the digest of the message
|
||||
SHA256_Init(&sha256);
|
||||
SHA256_Update(&sha256, msg, msg_len);
|
||||
SHA256_Final(hash, &sha256);
|
||||
|
||||
// verify all went well, i.e. we can decrypt our signature with OpenSSL
|
||||
if (ECDSA_do_verify(hash, 32, signature, eckey) != 1) {
|
||||
printf("Verification failed\n");
|
||||
break;
|
||||
}
|
||||
ECDSA_SIG_free(signature);
|
||||
EC_KEY_free(eckey);
|
||||
cnt++;
|
||||
if ((cnt % 100) == 0) printf("Passed ... %d\n", cnt);
|
||||
}
|
||||
EC_GROUP_free(ecgroup);
|
||||
return 0;
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user