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refactor code -> bignum.c/h

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pull/25/head
Pavol Rusnak 11 years ago
parent 603acbd1be
commit 07d1c22730
20 changed files with 548 additions and 522 deletions
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4
Makefile
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@ -1,6 +1,6 @@
CC = gcc
CFLAGS = -Wall -Os
OBJS = aux.o ecdsa.o secp256k1.o sha2.o rand.o hmac.o
OBJS = bignum.o ecdsa.o secp256k1.o sha2.o rand.o hmac.o
all: test-rfc6979 test-speed test-verify
@ -17,4 +17,4 @@ test-verify: test-verify.o $(OBJS)
gcc test-verify.o $(OBJS) -o test-verify -lcrypto
clean:
rm -f $(OBJS) test-speed test-verify
rm -f $(OBJS) test-rfc6979 test-speed test-verify

45
aux.c
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@ -1,45 +0,0 @@
/**
* 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;
}

396
bignum.c
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@ -0,0 +1,396 @@
/**
* 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 "bignum.h"
#include "secp256k1.h"
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;
}
void bn_read_be(const uint8_t *in_number, bignum256 *out_number)
{
int i;
uint64_t temp = 0;
for (i = 0; i < 8; i++) {
temp += (((uint64_t)read_be(in_number + (7 - i) * 4)) << (2 * i));
out_number->val[i]= temp & 0x3FFFFFFF;
temp >>= 30;
}
out_number->val[8] = temp;
}
void bn_write_be(const bignum256 *in_number, uint8_t *out_number)
{
int i, shift = 30 + 16 - 32;
uint64_t temp = in_number->val[8];
for (i = 0; i < 8; i++) {
temp <<= 30;
temp |= in_number->val[7 - i];
write_be(out_number + i * 4, temp >> shift);
shift -= 2;
}
}
int bn_is_zero(const bignum256 *a)
{
int i;
for (i = 0; i < 9; i++) {
if (a->val[i] != 0) return 0;
}
return 1;
}
int bn_is_less(const bignum256 *a, const bignum256 *b)
{
int i;
for (i = 8; i >= 0; i--) {
if (a->val[i] < b->val[i]) return 1;
if (a->val[i] > b->val[i]) return 0;
}
return 0;
}
// assumes x < 2*prime
void bn_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 bn_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 bn_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;
}
}
#ifndef INVERSE_FAST
#ifdef USE_PRECOMPUTED_IV
#warning USE_PRECOMPUTED_IV will not be used, please undef
#endif
// in field G_prime, small but slow
void bn_inverse(bignum256 *x, bignum256 const *prime)
{
uint32_t i, j, limb;
bignum256 res;
res.val[0] = 1;
for (i = 1; i < 9; i++) {
res.val[i] = 0;
}
for (i = 0; i < 9; i++) {
limb = prime->val[i];
// this is not enough in general but fine for secp256k1 because prime->val[0] > 1
if (i == 0) limb -= 2;
for (j = 0; j < 30; j++) {
if (i == 8 && limb == 0) break;
if (limb & 1) {
multiply(x, &res, prime);
}
limb >>= 1;
multiply(x, x, prime);
}
}
bn_mod(&res, prime);
memcpy(x, &res, sizeof(bignum256));
}
#else
// in field G_prime, big but fast
void bn_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;
bn_fast_mod(x, prime);
bn_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];
}
bn_multiply(secp256k1_iv + k - 256, x, prime);
bn_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];
}
}
}
#endif
// res = a - b
// b < 2*prime; result not normalized
void bn_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;
}
}

37
aux.h → bignum.h
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@ -21,13 +21,24 @@
* OTHER DEALINGS IN THE SOFTWARE.
*/
#ifndef __AUX_H__
#define __AUX_H__
#ifndef __BIGNUM_H__
#define __BIGNUM_H__
#include <stdint.h>
// rotate uint32 right
uint32_t ror(const uint32_t x, const int n);
// use precomputed Inverse Values of powers of two
#define USE_PRECOMPUTED_IV 1
// use precomputed Curve Points (some scalar multiples of curve base point G)
#define USE_PRECOMPUTED_CP 1
#define INVERSE_FAST 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;
// read 4 big endian bytes into uint32
uint32_t read_be(const uint8_t *data);
@ -35,4 +46,22 @@ uint32_t read_be(const uint8_t *data);
// write 4 big endian bytes
void write_be(uint8_t *data, uint32_t x);
void bn_read_be(const uint8_t *in_number, bignum256 *out_number);
void bn_write_be(const bignum256 *in_number, uint8_t *out_number);
int bn_is_zero(const bignum256 *a);
int bn_is_less(const bignum256 *a, const bignum256 *b);
void bn_mod(bignum256 *x, bignum256 const *prime);
void bn_multiply(const bignum256 *k, bignum256 *x, bignum256 const *prime);
void bn_fast_mod(bignum256 *x, bignum256 const *prime);
void bn_inverse(bignum256 *x, bignum256 const *prime);
void bn_substract(const bignum256 *a, const bignum256 *b, bignum256 *res);
#endif

530
ecdsa.c
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@ -25,324 +25,11 @@
#include <stdlib.h>
#include <string.h>
#include "bignum.h"
#include "rand.h"
#include "sha2.h"
#include "hmac.h"
#include "ecdsa.h"
#include "aux.h"
#define INVERSE_FAST 1
// 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;
}
}
#ifndef INVERSE_FAST
#ifdef USE_PRECOMPUTED_IV
#warning USE_PRECOMPUTED_IV will not be used, please undef
#endif
// in field G_prime, small but slow
void inverse(bignum256 *x, bignum256 const *prime)
{
uint32_t i, j, limb;
bignum256 res;
res.val[0] = 1;
for (i = 1; i < 9; i++) {
res.val[i] = 0;
}
for (i = 0; i < 9; i++) {
limb = prime->val[i];
// this is not enough in general but fine for secp256k1 because prime->val[0] > 1
if (i == 0) limb -= 2;
for (j = 0; j < 30; j++) {
if (i == 8 && limb == 0) break;
if (limb & 1) {
multiply(x, &res, prime);
}
limb >>= 1;
multiply(x, x, prime);
}
}
mod(&res, prime);
memcpy(x, &res, sizeof(bignum256));
}
#else
// in field G_prime, big but fast
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];
}
}
}
#endif
// 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;
}
}
// cp2 = cp1 + cp2
void point_add(const curve_point *cp1, curve_point *cp2)
@ -350,25 +37,25 @@ void point_add(const curve_point *cp1, curve_point *cp2)
int i;
uint32_t temp;
bignum256 lambda, inv, xr, yr;
fast_substract(&(cp2->x), &(cp1->x), &inv);
inverse(&inv, &prime256k1);
fast_substract(&(cp2->y), &(cp1->y), &lambda);
multiply(&inv, &lambda, &prime256k1);
bn_substract(&(cp2->x), &(cp1->x), &inv);
bn_inverse(&inv, &prime256k1);
bn_substract(&(cp2->y), &(cp1->y), &lambda);
bn_multiply(&inv, &lambda, &prime256k1);
memcpy(&xr, &lambda, sizeof(bignum256));
multiply(&xr, &xr, &prime256k1);
bn_multiply(&xr, &xr, &prime256k1);
temp = 0;
for (i = 0; i < 9; i++) {
temp += xr.val[i] + 3u * prime256k1.val[i] - cp1->x.val[i] - cp2->x.val[i];
xr.val[i] = temp & 0x3FFFFFFF;
temp >>= 30;
}
fast_mod(&xr, &prime256k1);
fast_substract(&(cp1->x), &xr, &yr);
bn_fast_mod(&xr, &prime256k1);
bn_substract(&(cp1->x), &xr, &yr);
// no need to fast_mod here
// fast_mod(&yr);
multiply(&lambda, &yr, &prime256k1);
fast_substract(&yr, &(cp1->y), &yr);
fast_mod(&yr, &prime256k1);
// bn_fast_mod(&yr);
bn_multiply(&lambda, &yr, &prime256k1);
bn_substract(&yr, &(cp1->y), &yr);
bn_fast_mod(&yr, &prime256k1);
memcpy(&(cp2->x), &xr, sizeof(bignum256));
memcpy(&(cp2->y), &yr, sizeof(bignum256));
}
@ -380,26 +67,26 @@ void point_double(curve_point *cp)
uint32_t temp;
bignum256 lambda, inverse_y, xr, yr;
memcpy(&inverse_y, &(cp->y), sizeof(bignum256));
inverse(&inverse_y, &prime256k1);
bn_inverse(&inverse_y, &prime256k1);
memcpy(&lambda, &three_over_two256k1, sizeof(bignum256));
multiply(&inverse_y, &lambda, &prime256k1);
multiply(&(cp->x), &lambda, &prime256k1);
multiply(&(cp->x), &lambda, &prime256k1);
bn_multiply(&inverse_y, &lambda, &prime256k1);
bn_multiply(&(cp->x), &lambda, &prime256k1);
bn_multiply(&(cp->x), &lambda, &prime256k1);
memcpy(&xr, &lambda, sizeof(bignum256));
multiply(&xr, &xr, &prime256k1);
bn_multiply(&xr, &xr, &prime256k1);
temp = 0;
for (i = 0; i < 9; i++) {
temp += xr.val[i] + 3u * prime256k1.val[i] - 2u * cp->x.val[i];
xr.val[i] = temp & 0x3FFFFFFF;
temp >>= 30;
}
fast_mod(&xr, &prime256k1);
fast_substract(&(cp->x), &xr, &yr);
bn_fast_mod(&xr, &prime256k1);
bn_substract(&(cp->x), &xr, &yr);
// no need to fast_mod here
// fast_mod(&yr);
multiply(&lambda, &yr, &prime256k1);
fast_substract(&yr, &(cp->y), &yr);
fast_mod(&yr, &prime256k1);
// bn_fast_mod(&yr);
bn_multiply(&lambda, &yr, &prime256k1);
bn_substract(&yr, &(cp->y), &yr);
bn_fast_mod(&yr, &prime256k1);
memcpy(&(cp->x), &xr, sizeof(bignum256));
memcpy(&(cp->y), &yr, sizeof(bignum256));
}
@ -443,12 +130,39 @@ void scalar_multiply(bignum256 *k, curve_point *res)
#endif
}
}
mod(&(res->x), &prime256k1);
mod(&(res->y), &prime256k1);
bn_mod(&(res->x), &prime256k1);
bn_mod(&(res->y), &prime256k1);
}
// does not validate that this is valid der encoding
// assumes it is der encoding containing 1 number
void der_read_single(const uint8_t *der, bignum256 *elem)
{
int i, j;
uint8_t val[32];
i = 1 + der[1];
j = 31;
// we ignore all bytes after 32nd. if there are any, those are either zero or invalid for secp256k1
while (i > 1 && j >= 0) {
val[j] = der[i];
i--; j--;
}
for (i = 0; i <= j; i++) {
val[i] = 0;
}
bn_read_be(val, elem);
}
// does not validate that this is valid der encoding
// assumes it is der encoding containing 2 numbers (either public key or ecdsa signature)
void der_read_pair(const uint8_t *der, bignum256 *elem1, bignum256 *elem2)
{
der_read_single(der + 2, elem1);
der_read_single(der + 4 + der[3], elem2);
}
// write DER encoding of number to buffer
void write_der(const bignum256 *x, uint8_t *buf)
void der_write(const bignum256 *x, uint8_t *buf)
{
int i, j = 8, k = 8, len = 0;
uint8_t r = 0, temp;
@ -471,49 +185,6 @@ void write_der(const bignum256 *x, uint8_t *buf)
buf[1] = len;
}
void read_32byte_big_endian(const uint8_t *in_number, bignum256 *out_number)
{
int i;
uint64_t temp = 0;
for (i = 0; i < 8; i++) {
temp += (((uint64_t)read_be(in_number + (7 - i) * 4)) << (2 * i));
out_number->val[i]= temp & 0x3FFFFFFF;
temp >>= 30;
}
out_number->val[8] = temp;
}
void write_32byte_big_endian(const bignum256 *in_number, uint8_t *out_number)
{
int i, shift = 30 + 16 - 32;
uint64_t temp = in_number->val[8];
for (i = 0; i < 8; i++) {
temp <<= 30;
temp |= in_number->val[7 - i];
write_be(out_number + i * 4, temp >> shift);
shift -= 2;
}
}
int is_zero(const bignum256 *a)
{
int i;
for (i = 0; i < 9; i++) {
if (a->val[i] != 0) return 0;
}
return 1;
}
int is_less(const bignum256 *a, const bignum256 *b)
{
int i;
for (i = 8; i >= 0; i--) {
if (a->val[i] < b->val[i]) return 1;
if (a->val[i] > b->val[i]) return 0;
}
return 0;
}
// generate random K for signing
void generate_k_random(bignum256 *k) {
int i;
@ -537,9 +208,9 @@ void generate_k_rfc6979(bignum256 *secret, const uint8_t *priv_key, const uint8_
bignum256 z1;
memcpy(bx, priv_key, 32);
read_32byte_big_endian(hash, &z1);
mod(&z1, &order256k1);
write_32byte_big_endian(&z1, bx + 32);
bn_read_be(hash, &z1);
bn_mod(&z1, &order256k1);
bn_write_be(&z1, bx + 32);
memset(v, 1, sizeof(v));
memset(k, 0, sizeof(k));
@ -558,8 +229,8 @@ void generate_k_rfc6979(bignum256 *secret, const uint8_t *priv_key, const uint8_
for (;;) {
hmac_sha256(k, sizeof(k), v, sizeof(v), t);
read_32byte_big_endian(t, secret);
if ( !is_zero(secret) && is_less(secret, &order256k1) ) {
bn_read_be(t, secret);
if ( !bn_is_zero(secret) && bn_is_less(secret, &order256k1) ) {
return;
}
memcpy(buf, v, sizeof(v));
@ -587,7 +258,7 @@ void ecdsa_sign(const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, u
// if double hash is required uncomment the following line:
// SHA256_Raw(hash, 32, hash);
read_32byte_big_endian(hash, &z);
bn_read_be(hash, &z);
for (;;) {
// generate random number k
@ -599,23 +270,23 @@ void ecdsa_sign(const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, u
// compute k*G
scalar_multiply(&k, &R);
// r = (rx mod n)
mod(&R.x, &order256k1);
bn_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);
read_32byte_big_endian(priv_key, da);
multiply(&R.x, da, &order256k1);
bn_inverse(&k, &order256k1);
bn_read_be(priv_key, da);
bn_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);
bn_multiply(da, &k, &order256k1);
bn_mod(&k, &order256k1);
for (i = 0; i < 9; i++) {
if (k.val[i] != 0) break;
}
@ -623,9 +294,9 @@ void ecdsa_sign(const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, u
// we are done, R.x and k is the result signature
break;
}
write_der(&R.x, sig + 2);
der_write(&R.x, sig + 2);
i = sig[3] + 2;
write_der(&k, sig + 2 + i);
der_write(&k, sig + 2 + i);
i += sig[3 + i] + 2;
sig[0] = 0x30;
sig[1] = i;
@ -641,45 +312,18 @@ void ecdsa_get_public_key(const uint8_t *priv_key, uint8_t *pub_key, uint32_t *p
curve_point R;
bignum256 k;
read_32byte_big_endian(priv_key, &k);
bn_read_be(priv_key, &k);
// compute k*G
scalar_multiply(&k, &R);
write_der(&R.x, pub_key + 2);
der_write(&R.x, pub_key + 2);
i = pub_key[3] + 2;
write_der(&R.y, pub_key + 2 + i);
der_write(&R.y, pub_key + 2 + i);
i += pub_key[3 + i] + 2;
pub_key[0] = 0x30;
pub_key[1] = i;
*pub_key_len = i + 2;
}
// does not validate that this is valid der encoding
// assumes it is der encoding containing 1 number
void read_der_single(const uint8_t *der, bignum256 *elem)
{
int i, j;
uint8_t val[32];
i = 1 + der[1];
j = 31;
// we ignore all bytes after 32nd. if there are any, those are either zero or invalid for secp256k1
while (i > 1 && j >= 0) {
val[j] = der[i];
i--; j--;
}
for (i = 0; i <= j; i++) {
val[i] = 0;
}
read_32byte_big_endian(val, elem);
}
// does not validate that this is valid der encoding
// assumes it is der encoding containing 2 numbers (either public key or ecdsa signature)
void read_der_pair(const uint8_t *der, bignum256 *elem1, bignum256 *elem2)
{
read_der_single(der + 2, elem1);
read_der_single(der + 4 + der[3], elem2);
}
// uses secp256k1 curve
// pub_key and signature are DER encoded
// msg is a data that was signed
@ -698,21 +342,21 @@ int ecdsa_verify(const uint8_t *pub_key, const uint8_t *signature, const uint8_t
// if double hash is required uncomment the following line:
// SHA256_Raw(hash, 32, hash);
read_32byte_big_endian(hash, &z);
read_der_pair(pub_key, &pub.x, &pub.y);
read_der_pair(signature, &r, &s);
if (is_zero(&r) ||
is_zero(&s) ||
(!is_less(&r, &order256k1)) ||
(!is_less(&s, &order256k1))) return 1;
inverse(&s, &order256k1); // s^-1
multiply(&s, &z, &order256k1); // z*s^-1
mod(&z, &order256k1);
multiply(&r, &s, &order256k1); // r*s^-1
mod(&s, &order256k1);
if (is_zero(&z)) {
bn_read_be(hash, &z);
der_read_pair(pub_key, &pub.x, &pub.y);
der_read_pair(signature, &r, &s);
if (bn_is_zero(&r) ||
bn_is_zero(&s) ||
(!bn_is_less(&r, &order256k1)) ||
(!bn_is_less(&s, &order256k1))) return 1;
bn_inverse(&s, &order256k1); // s^-1
bn_multiply(&s, &z, &order256k1); // z*s^-1
bn_mod(&z, &order256k1);
bn_multiply(&r, &s, &order256k1); // r*s^-1
bn_mod(&s, &order256k1);
if (bn_is_zero(&z)) {
// our message hashes to zero
// I don't expect this to happen any time soon
res_is_zero = 1;
@ -731,8 +375,8 @@ int ecdsa_verify(const uint8_t *pub_key, const uint8_t *signature, const uint8_t
}
}
mod(&(res.x), &prime256k1);
mod(&(res.x), &order256k1);
bn_mod(&(res.x), &prime256k1);
bn_mod(&(res.x), &order256k1);
for (i = 0; i < 9; i++) {
if (res.x.val[i] != r.val[i]) {
return 1;

2
ecdsa.h
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@ -28,7 +28,7 @@
#include "secp256k1.h"
// uses secp256k1 curve
// all functions use secp256k1 curve
void ecdsa_sign(const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, uint8_t *sig, uint32_t *sig_len);
void ecdsa_get_public_key(const uint8_t *priv_key, uint8_t *pub_key, uint32_t *pub_key_len);
int ecdsa_verify(const uint8_t *pub_key, const uint8_t *signature, const uint8_t *msg, uint32_t msg_len);

12
secp256k1.h
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@ -26,17 +26,7 @@
#include <stdint.h>
// use precomputed Inverse Values of powers of two
#define USE_PRECOMPUTED_IV 1
// use precomputed Curve Points (some scalar multiples of curve base point G)
#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;
#include "bignum.h"
// curve point x and y
typedef struct {

25
sha2.c
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@ -82,6 +82,11 @@
* made).
*/
#ifndef LITTLE_ENDIAN
#define LITTLE_ENDIAN 1234
#define BIG_ENDIAN 4321
#endif
#ifndef BYTE_ORDER
#define BYTE_ORDER LITTLE_ENDIAN
#endif
@ -176,7 +181,7 @@ void SHA512_Transform(SHA512_CTX*, const sha2_word64*);
/*** SHA-XYZ INITIAL HASH VALUES AND CONSTANTS ************************/
/* Hash constant words K for SHA-256: */
const static sha2_word32 K256[64] = {
static const sha2_word32 K256[64] = {
0x428a2f98UL, 0x71374491UL, 0xb5c0fbcfUL, 0xe9b5dba5UL,
0x3956c25bUL, 0x59f111f1UL, 0x923f82a4UL, 0xab1c5ed5UL,
0xd807aa98UL, 0x12835b01UL, 0x243185beUL, 0x550c7dc3UL,
@ -196,7 +201,7 @@ const static sha2_word32 K256[64] = {
};
/* Initial hash value H for SHA-256: */
const static sha2_word32 sha256_initial_hash_value[8] = {
static const sha2_word32 sha256_initial_hash_value[8] = {
0x6a09e667UL,
0xbb67ae85UL,
0x3c6ef372UL,
@ -208,7 +213,7 @@ const static sha2_word32 sha256_initial_hash_value[8] = {
};
/* Hash constant words K for SHA-384 and SHA-512: */
const static sha2_word64 K512[80] = {
static const sha2_word64 K512[80] = {
0x428a2f98d728ae22ULL, 0x7137449123ef65cdULL,
0xb5c0fbcfec4d3b2fULL, 0xe9b5dba58189dbbcULL,
0x3956c25bf348b538ULL, 0x59f111f1b605d019ULL,
@ -252,7 +257,7 @@ const static sha2_word64 K512[80] = {
};
/* Initial hash value H for SHA-384 */
const static sha2_word64 sha384_initial_hash_value[8] = {
static const sha2_word64 sha384_initial_hash_value[8] = {
0xcbbb9d5dc1059ed8ULL,
0x629a292a367cd507ULL,
0x9159015a3070dd17ULL,
@ -264,7 +269,7 @@ const static sha2_word64 sha384_initial_hash_value[8] = {
};
/* Initial hash value H for SHA-512 */
const static sha2_word64 sha512_initial_hash_value[8] = {
static const sha2_word64 sha512_initial_hash_value[8] = {
0x6a09e667f3bcc908ULL,
0xbb67ae8584caa73bULL,
0x3c6ef372fe94f82bULL,
@ -548,7 +553,8 @@ void SHA256_Final(sha2_byte digest[], SHA256_CTX* context) {
*context->buffer = 0x80;
}
/* Set the bit count: */
*(sha2_word64*)&context->buffer[SHA256_SHORT_BLOCK_LENGTH] = context->bitcount;
sha2_word64 *t = (sha2_word64 *)&context->buffer[SHA256_SHORT_BLOCK_LENGTH];
*t = context->bitcount;
/* Final transform: */
SHA256_Transform(context, (sha2_word32*)context->buffer);
@ -866,8 +872,11 @@ void SHA512_Last(SHA512_CTX* context) {
*context->buffer = 0x80;
}
/* Store the length of input data (in bits): */
*(sha2_word64*)&context->buffer[SHA512_SHORT_BLOCK_LENGTH] = context->bitcount[1];
*(sha2_word64*)&context->buffer[SHA512_SHORT_BLOCK_LENGTH+8] = context->bitcount[0];
sha2_word64 *t;
t = (sha2_word64 *)&context->buffer[SHA512_SHORT_BLOCK_LENGTH];
*t = context->bitcount[1];
t = (sha2_word64 *)&context->buffer[SHA512_SHORT_BLOCK_LENGTH+8];
*t = context->bitcount[0];
/* Final transform: */
SHA512_Transform(context, (sha2_word64*)context->buffer);

5
speed-stm32/Makefile
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@ -1,8 +1,9 @@
NAME = speed
OBJS += aux.o
OBJS += bignum.o
OBJS += ecdsa.o
OBJS += rand.o
OBJS += secp256k1.o
OBJS += sha256.o
OBJS += hmac.o
OBJS += sha2.o
include Makefile.include

1
speed-stm32/aux.c
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@ -1 +0,0 @@
../aux.c

1
speed-stm32/aux.h
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@ -1 +0,0 @@
../aux.h

1
speed-stm32/bignum.c
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@ -0,0 +1 @@
../bignum.c

1
speed-stm32/bignum.h
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@ -0,0 +1 @@
../bignum.h

1
speed-stm32/hmac.c
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@ -0,0 +1 @@
../hmac.c

1
speed-stm32/hmac.h
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@ -0,0 +1 @@
../hmac.h

1
speed-stm32/sha2.c
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@ -0,0 +1 @@
../sha2.c

1
speed-stm32/sha2.h
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@ -0,0 +1 @@
../sha2.h

1
speed-stm32/sha256.c
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@ -1 +0,0 @@
../sha256.c

1
speed-stm32/sha256.h
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@ -1 +0,0 @@
../sha256.h

4
test-rfc6979.c
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@ -21,6 +21,7 @@
*/
#include <stdio.h>
#include "bignum.h"
#include "ecdsa.h"
#include "sha2.h"
@ -29,7 +30,6 @@ uint8_t kb[32];
uint8_t priv[32] = {0xcc, 0xa9, 0xfb, 0xcc, 0x1b, 0x41, 0xe5, 0xa9, 0x5d, 0x36, 0x9e, 0xaa, 0x6d, 0xdc, 0xff, 0x73, 0xb6, 0x1a, 0x4e, 0xfa, 0xa2, 0x79, 0xcf, 0xc6, 0x56, 0x7e, 0x8d, 0xaa, 0x39, 0xcb, 0xaf, 0x50};
uint8_t hash[32];
void write_32byte_big_endian(const bignum256 *in_number, uint8_t *out_number);
void generate_k_rfc6979(bignum256 *k, const uint8_t *priv_key, const uint8_t *hash);
int main()
@ -40,7 +40,7 @@ int main()
printf("hash : ");
for (i = 0; i < 32; i++) printf("%02x", hash[i]); printf("\n");
generate_k_rfc6979(&k, priv, hash);
write_32byte_big_endian(&k, kb);
bn_write_be(&k, kb);
printf("expected : 2df40ca70e639d89528a6b670d9d48d9165fdc0febc0974056bdce192b8e16a3\n");
printf("got : ");

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