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Pavol Rusnak 11 years ago
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2
.gitignore vendored
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*.o
test

2
AUTHORS
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Tomas Dzetkulic <dzetkulic@gmail.com>
Pavol Rusnak <stick@gk2.sk>

20
LICENSE
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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.

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Makefile
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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
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MicroECDSA
==========
Heavily optimized ECDSA (secp256k1) signer for embedded devices.
Distibuted under MIT License.

45
aux.c
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/**
* 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
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/**
* 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
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/**
* 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;
}

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ecdsa.h
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/**
* 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

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rand.c
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/**
* 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);
}

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/**
* 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

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/**
* 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}},
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{ .val = {0x8333d71, 0x29c1cccc, 0x3a320a2a, 0x2418564d, 0x3617c806, 0x1ddcd648, 0x2a6654fe, 0x63db210, 0x80a5}},
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{ .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}},
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{ .val = {0xb92079c, 0x28aa9c1, 0x15937a32, 0x3201a418, 0x35923617, 0x153f9ddc, 0x2c842a66, 0x2029463d, 0x27a1}},
{ .val = {0x25c903ce, 0x14554e0, 0xac9bd19, 0x3900d20c, 0x1ac91b0b, 0xa9fceee, 0x36421533, 0x3014a31e, 0x13d0}},
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{ .val = {0x144b8ec0, 0xc828aa6, 0x615937a, 0x5f201a4, 0x37359236, 0x19953f9d, 0xf6c842a, 0x28602946, 0xdc27}},
{ .val = {0xa25c760, 0x6414553, 0x30ac9bd, 0x2f900d2, 0x3b9ac91b, 0xcca9fce, 0x7b64215, 0x343014a3, 0x6e13}},
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{ .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}},
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.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
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/**
* 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
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/**
* 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
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/**
* 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
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/**
* 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;
}
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