From ccbc219b29f1f91054807479a4400987694fd651 Mon Sep 17 00:00:00 2001 From: Pavol Rusnak Date: Sat, 17 Aug 2013 14:20:15 +0200 Subject: [PATCH] import sources --- .gitignore | 2 + AUTHORS | 2 + LICENSE | 20 ++ Makefile | 13 + README | 6 + aux.c | 45 +++ aux.h | 38 +++ ecdsa.c | 515 +++++++++++++++++++++++++++++++++ ecdsa.h | 32 ++ rand.c | 36 +++ rand.h | 30 ++ secp256k1.c | 820 ++++++++++++++++++++++++++++++++++++++++++++++++++++ secp256k1.h | 63 ++++ sha256.c | 127 ++++++++ sha256.h | 31 ++ test.c | 100 +++++++ 16 files changed, 1880 insertions(+) create mode 100644 .gitignore create mode 100644 AUTHORS create mode 100644 LICENSE create mode 100644 Makefile create mode 100644 README create mode 100644 aux.c create mode 100644 aux.h create mode 100644 ecdsa.c create mode 100644 ecdsa.h create mode 100644 rand.c create mode 100644 rand.h create mode 100644 secp256k1.c create mode 100644 secp256k1.h create mode 100644 sha256.c create mode 100644 sha256.h create mode 100644 test.c diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000000..76758b086d --- /dev/null +++ b/.gitignore @@ -0,0 +1,2 @@ +*.o +test diff --git a/AUTHORS b/AUTHORS new file mode 100644 index 0000000000..51c9bdab08 --- /dev/null +++ b/AUTHORS @@ -0,0 +1,2 @@ +Tomas Dzetkulic +Pavol Rusnak diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000000..f43bfa74cc --- /dev/null +++ b/LICENSE @@ -0,0 +1,20 @@ +Copyright (c) 2013 Tomas Dzetkulic +Copyright (c) 2013 Pavol Rusnak + +Permission is hereby granted, free of charge, to any person obtaining +a copy of this software and associated documentation files (the "Software"), +to deal in the Software without restriction, including without limitation +the rights to use, copy, modify, merge, publish, distribute, sublicense, +and/or sell copies of the Software, and to permit persons to whom the +Software is furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included +in all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS +OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES +OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +OTHER DEALINGS IN THE SOFTWARE. diff --git a/Makefile b/Makefile new file mode 100644 index 0000000000..dae2048f08 --- /dev/null +++ b/Makefile @@ -0,0 +1,13 @@ +CC = gcc +CFLAGS = -Wall +OBJS = aux.o ecdsa.o secp256k1.o sha256.o rand.o test.o +NAME = test + +%.o: %.c + $(CC) $(CFLAGS) -o $@ -c $< + +$(NAME): $(OBJS) + gcc $(OBJS) -o $(NAME) -lcrypto + +clean: + rm -f $(OBJS) $(NAME) diff --git a/README b/README new file mode 100644 index 0000000000..8709b7f080 --- /dev/null +++ b/README @@ -0,0 +1,6 @@ +MicroECDSA +========== + +Heavily optimized ECDSA (secp256k1) signer for embedded devices. + +Distibuted under MIT License. diff --git a/aux.c b/aux.c new file mode 100644 index 0000000000..61f6285c7f --- /dev/null +++ b/aux.c @@ -0,0 +1,45 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#include "aux.h" + +inline uint32_t ror(const uint32_t x, const int n) +{ + return (x >> n) | (x << (32 - n)); +} + +inline uint32_t read_be(const uint8_t *data) +{ + return (((uint32_t)data[0]) << 24) | + (((uint32_t)data[1]) << 16) | + (((uint32_t)data[2]) << 8) | + (((uint32_t)data[3])); +} + +inline void write_be(uint8_t *data, uint32_t x) +{ + data[0] = x >> 24; + data[1] = x >> 16; + data[2] = x >>8; + data[3] = x; +} diff --git a/aux.h b/aux.h new file mode 100644 index 0000000000..059579eb46 --- /dev/null +++ b/aux.h @@ -0,0 +1,38 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#ifndef __AUX_H__ +#define __AUX_H__ + +#include + +// 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 diff --git a/ecdsa.c b/ecdsa.c new file mode 100644 index 0000000000..7f86ccb17c --- /dev/null +++ b/ecdsa.c @@ -0,0 +1,515 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#include +#include +#include + +#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<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; +} diff --git a/ecdsa.h b/ecdsa.h new file mode 100644 index 0000000000..6968bfa079 --- /dev/null +++ b/ecdsa.h @@ -0,0 +1,32 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#ifndef __ECDSA_H__ +#define __ECDSA_H__ + +#include + +// uses secp256k1 curve +void ecdsa_sign(uint8_t *private_key, uint8_t *message, uint32_t len, uint8_t *sig, uint32_t *sig_len); + +#endif diff --git a/rand.c b/rand.c new file mode 100644 index 0000000000..24b990a27f --- /dev/null +++ b/rand.c @@ -0,0 +1,36 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#include +#include +#include + +#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); +} diff --git a/rand.h b/rand.h new file mode 100644 index 0000000000..2ee45ed639 --- /dev/null +++ b/rand.h @@ -0,0 +1,30 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#ifndef __RAND_H__ +#define __RAND_H__ + +void init_rand(void); +uint32_t random32(void); + +#endif diff --git a/secp256k1.c b/secp256k1.c new file mode 100644 index 0000000000..6149afec8a --- /dev/null +++ b/secp256k1.c @@ -0,0 +1,820 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#include "secp256k1.h" + +const bignum256 prime256k1 = { +.val = {0x3ffffc2f, 0x3ffffffb, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0xffff} +}; + +const curve_point G256k1 = { +.x = { .val = {0x16f81798, 0x27ca056c, 0x1ce28d95, 0x26ff36cb, 0x70b0702, 0x18a573a, 0xbbac55a, 0x199fbe77, 0x79be}}, +.y = { .val = {0x3b10d4b8, 0x311f423f, 0x28554199, 0x5ed1229, 0x1108a8fd, 0x13eff038, 0x3c4655da, 0x369dc9a8, 0x483a}}}; + +const bignum256 order256k1 = { +.val = {0x10364141, 0x3f497a33, 0x348a03bb, 0x2bb739ab, 0x3ffffeba, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0xffff}}; + +const bignum256 three_over_two256k1 = { +.val = {0x3ffffe19, 0x3ffffffd, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x7fff}}; + +#ifdef USE_PRECOMPUTED_IV + +const bignum256 secp256k1_iv[256] = { +{ .val = {0x868192a, 0x20e02474, 0x24a059d, 0x2c88ffb7, 0x32b761bc, 0x1b0b0a57, 0x383999c4, 0x6414554, 0xc9bd}}, +{ .val = {0x4340c95, 0x3070123a, 0x212502ce, 0x16447fdb, 0x395bb0de, 0xd85852b, 0x1c1ccce2, 0x2320a2aa, 0x64de}}, +{ .val = {0x21a0462, 0x1838091b, 0x30928167, 0xb223fed, 0x3cadd86f, 0x6c2c295, 0xe0e6671, 0x11905155, 0xb26f}}, +{ .val = {0x210d0231, 0x2c1c048d, 0x384940b3, 0x25911ff6, 0x3e56ec37, 0x2361614a, 0x27073338, 0x28c828aa, 0x5937}}, +{ .val = {0x30867f30, 0x360e0244, 0x1c24a059, 0x32c88ffb, 0x1f2b761b, 0x11b0b0a5, 0x1383999c, 0x34641455, 0xac9b}}, +{ .val = {0x18433f98, 0x3b070122, 0x2e12502c, 0x396447fd, 0x2f95bb0d, 0x8d85852, 0x29c1ccce, 0x3a320a2a, 0x564d}}, +{ .val = {0xc219fcc, 0x1d838091, 0x37092816, 0x3cb223fe, 0x17cadd86, 0x46c2c29, 0x14e0e667, 0x3d190515, 0x2b26}}, +{ .val = {0x2610cfe6, 0xec1c048, 0x1b84940b, 0x1e5911ff, 0x2be56ec3, 0x22361614, 0x2a707333, 0x1e8c828a, 0x1593}}, +{ .val = {0x130867f3, 0x2760e024, 0x2dc24a05, 0x2f2c88ff, 0x15f2b761, 0x311b0b0a, 0x15383999, 0x2f464145, 0xac9}}, +{ .val = {0x9843211, 0x33b07010, 0x36e12502, 0x3796447f, 0xaf95bb0, 0x388d8585, 0x2a9c1ccc, 0x37a320a2, 0x8564}}, +{ .val = {0x4c21720, 0x19d83806, 0x3b709281, 0x1bcb223f, 0x257cadd8, 0x1c46c2c2, 0x154e0e66, 0x1bd19051, 0xc2b2}}, +{ .val = {0x2610b90, 0x2cec1c03, 0x3db84940, 0xde5911f, 0x12be56ec, 0xe236161, 0x2aa70733, 0xde8c828, 0x6159}}, +{ .val = {0x213085c8, 0x16760e01, 0x3edc24a0, 0x6f2c88f, 0x295f2b76, 0x2711b0b0, 0x15538399, 0x26f46414, 0x30ac}}, +{ .val = {0x309842e4, 0xb3b0700, 0x3f6e1250, 0x3796447, 0x14af95bb, 0x3388d858, 0xaa9c1cc, 0x137a320a, 0x1856}}, +{ .val = {0x184c2172, 0x59d8380, 0x3fb70928, 0x21bcb223, 0xa57cadd, 0x19c46c2c, 0x554e0e6, 0x9bd1905, 0xc2b}}, +{ .val = {0xc2610b9, 0x2cec1c0, 0x3fdb8494, 0x30de5911, 0x52be56e, 0xce23616, 0x22aa7073, 0x24de8c82, 0x615}}, +{ .val = {0x6130674, 0x16760de, 0x3fedc24a, 0x186f2c88, 0x295f2b7, 0x26711b0b, 0x11553839, 0x326f4641, 0x830a}}, +{ .val = {0x309833a, 0xb3b06f, 0x1ff6e125, 0x2c379644, 0x214af95b, 0x33388d85, 0x28aa9c1c, 0x1937a320, 0x4185}}, +{ .val = {0x2184c19d, 0x2059d837, 0xffb7092, 0x361bcb22, 0x30a57cad, 0x199c46c2, 0x14554e0e, 0x2c9bd190, 0x20c2}}, +{ .val = {0x30c25ee6, 0x102cec19, 0x7fdb849, 0x3b0de591, 0x1852be56, 0xcce2361, 0xa2aa707, 0x164de8c8, 0x9061}}, +{ .val = {0x38612f73, 0x2816760c, 0x23fedc24, 0x1d86f2c8, 0x2c295f2b, 0x266711b0, 0x5155383, 0x2b26f464, 0x4830}}, +{ .val = {0x1c3095d1, 0x140b3b04, 0x11ff6e12, 0x2ec37964, 0x1614af95, 0x333388d8, 0x28aa9c1, 0x15937a32, 0xa418}}, +{ .val = {0xe184900, 0xa059d80, 0x8ffb709, 0x3761bcb2, 0xb0a57ca, 0x3999c46c, 0x14554e0, 0xac9bd19, 0xd20c}}, +{ .val = {0x70c2480, 0x2502cec0, 0x47fdb84, 0x1bb0de59, 0x5852be5, 0x1ccce236, 0x20a2aa70, 0x564de8c, 0x6906}}, +{ .val = {0x3861240, 0x12816760, 0x223fedc2, 0x2dd86f2c, 0x2c295f2, 0xe66711b, 0x10515538, 0x2b26f46, 0x3483}}, +{ .val = {0x1c30920, 0x940b3b0, 0x111ff6e1, 0x16ec3796, 0x21614af9, 0x733388d, 0x828aa9c, 0x215937a3, 0x1a41}}, +{ .val = {0xe18490, 0x24a059d8, 0x88ffb70, 0x2b761bcb, 0x30b0a57c, 0x3999c46, 0x2414554e, 0x30ac9bd1, 0xd20}}, +{ .val = {0x70c248, 0x12502cec, 0x2447fdb8, 0x15bb0de5, 0x185852be, 0x1ccce23, 0x320a2aa7, 0x18564de8, 0x690}}, +{ .val = {0x386124, 0x9281676, 0x3223fedc, 0xadd86f2, 0x2c2c295f, 0x20e66711, 0x19051553, 0xc2b26f4, 0x348}}, +{ .val = {0x1c3092, 0x4940b3b, 0x1911ff6e, 0x256ec379, 0x361614af, 0x30733388, 0xc828aa9, 0x615937a, 0x1a4}}, +{ .val = {0x200e1849, 0x24a059d, 0x2c88ffb7, 0x32b761bc, 0x1b0b0a57, 0x383999c4, 0x6414554, 0x30ac9bd, 0xd2}}, +{ .val = {0x30070a3c, 0x212502cc, 0x16447fdb, 0x395bb0de, 0xd85852b, 0x1c1ccce2, 0x2320a2aa, 0x18564de, 0x8069}}, +{ .val = {0x1803851e, 0x30928166, 0xb223fed, 0x3cadd86f, 0x6c2c295, 0xe0e6671, 0x11905155, 0x20c2b26f, 0x4034}}, +{ .val = {0xc01c28f, 0x384940b3, 0x25911ff6, 0x3e56ec37, 0x2361614a, 0x27073338, 0x28c828aa, 0x10615937, 0x201a}}, +{ .val = {0x2600df5f, 0x1c24a057, 0x32c88ffb, 0x1f2b761b, 0x11b0b0a5, 0x1383999c, 0x34641455, 0x830ac9b, 0x900d}}, +{ .val = {0x33006dc7, 0x2e125029, 0x396447fd, 0x2f95bb0d, 0x8d85852, 0x29c1ccce, 0x3a320a2a, 0x2418564d, 0xc806}}, +{ .val = {0x398034fb, 0x37092812, 0x3cb223fe, 0x17cadd86, 0x46c2c29, 0x14e0e667, 0x3d190515, 0x120c2b26, 0xe403}}, +{ .val = {0x1cc01895, 0x1b849407, 0x1e5911ff, 0x2be56ec3, 0x22361614, 0x2a707333, 0x1e8c828a, 0x29061593, 0xf201}}, +{ .val = {0x2e600a62, 0x2dc24a01, 0x2f2c88ff, 0x15f2b761, 0x311b0b0a, 0x15383999, 0x2f464145, 0x34830ac9, 0xf900}}, +{ .val = {0x37300531, 0x36e12500, 0x3796447f, 0xaf95bb0, 0x388d8585, 0x2a9c1ccc, 0x37a320a2, 0x1a418564, 0x7c80}}, +{ .val = {0x1b9800b0, 0x3b70927e, 0x1bcb223f, 0x257cadd8, 0x1c46c2c2, 0x154e0e66, 0x1bd19051, 0xd20c2b2, 0xbe40}}, +{ .val = {0xdcc0058, 0x3db8493f, 0xde5911f, 0x12be56ec, 0xe236161, 0x2aa70733, 0xde8c828, 0x6906159, 0x5f20}}, +{ .val = {0x26e6002c, 0x3edc249f, 0x6f2c88f, 0x295f2b76, 0x2711b0b0, 0x15538399, 0x26f46414, 0x34830ac, 0x2f90}}, +{ .val = {0x33730016, 0x3f6e124f, 0x3796447, 0x14af95bb, 0x3388d858, 0xaa9c1cc, 0x137a320a, 0x1a41856, 0x17c8}}, +{ .val = {0x39b9800b, 0x3fb70927, 0x21bcb223, 0xa57cadd, 0x19c46c2c, 0x554e0e6, 0x9bd1905, 0xd20c2b, 0xbe4}}, +{ .val = {0x3cdcbe1d, 0x3fdb8491, 0x30de5911, 0x52be56e, 0xce23616, 0x22aa7073, 0x24de8c82, 0x690615, 0x85f2}}, +{ .val = {0x3e6e5d26, 0x3fedc246, 0x186f2c88, 0x295f2b7, 0x26711b0b, 0x11553839, 0x326f4641, 0x34830a, 0xc2f9}}, +{ .val = {0x1f372e93, 0x1ff6e123, 0x2c379644, 0x214af95b, 0x33388d85, 0x28aa9c1c, 0x1937a320, 0x201a4185, 0x617c}}, +{ .val = {0x2f9b9561, 0xffb708f, 0x361bcb22, 0x30a57cad, 0x199c46c2, 0x14554e0e, 0x2c9bd190, 0x100d20c2, 0xb0be}}, +{ .val = {0x37cdc8c8, 0x7fdb845, 0x3b0de591, 0x1852be56, 0xcce2361, 0xa2aa707, 0x164de8c8, 0x8069061, 0xd85f}}, +{ .val = {0x3be6e464, 0x23fedc22, 0x1d86f2c8, 0x2c295f2b, 0x266711b0, 0x5155383, 0x2b26f464, 0x24034830, 0x6c2f}}, +{ .val = {0x1df37232, 0x11ff6e11, 0x2ec37964, 0x1614af95, 0x333388d8, 0x28aa9c1, 0x15937a32, 0x3201a418, 0x3617}}, +{ .val = {0x2ef9b919, 0x8ffb708, 0x3761bcb2, 0xb0a57ca, 0x3999c46c, 0x14554e0, 0xac9bd19, 0x3900d20c, 0x1b0b}}, +{ .val = {0x177cdaa4, 0x47fdb82, 0x1bb0de59, 0x5852be5, 0x1ccce236, 0x20a2aa70, 0x564de8c, 0x3c806906, 0x8d85}}, +{ .val = {0xbbe6d52, 0x223fedc1, 0x2dd86f2c, 0x2c295f2, 0xe66711b, 0x10515538, 0x2b26f46, 0x3e403483, 0x46c2}}, +{ .val = {0x25df36a9, 0x111ff6e0, 0x16ec3796, 0x21614af9, 0x733388d, 0x828aa9c, 0x215937a3, 0x1f201a41, 0x2361}}, +{ .val = {0x12ef996c, 0x88ffb6e, 0x2b761bcb, 0x30b0a57c, 0x3999c46, 0x2414554e, 0x30ac9bd1, 0x2f900d20, 0x91b0}}, +{ .val = {0x977ccb6, 0x2447fdb7, 0x15bb0de5, 0x185852be, 0x1ccce23, 0x320a2aa7, 0x18564de8, 0x17c80690, 0x48d8}}, +{ .val = {0x24bbe65b, 0x3223fedb, 0xadd86f2, 0x2c2c295f, 0x20e66711, 0x19051553, 0xc2b26f4, 0xbe40348, 0x246c}}, +{ .val = {0x325df145, 0x1911ff6b, 0x256ec379, 0x361614af, 0x30733388, 0xc828aa9, 0x615937a, 0x5f201a4, 0x9236}}, +{ .val = {0x392ef6ba, 0x2c88ffb3, 0x32b761bc, 0x1b0b0a57, 0x383999c4, 0x6414554, 0x30ac9bd, 0x2f900d2, 0xc91b}}, +{ .val = {0x3c977b5d, 0x16447fd9, 0x395bb0de, 0xd85852b, 0x1c1ccce2, 0x2320a2aa, 0x18564de, 0x217c8069, 0x648d}}, +{ .val = {0x3e4bbbc6, 0xb223fea, 0x3cadd86f, 0x6c2c295, 0xe0e6671, 0x11905155, 0x20c2b26f, 0x30be4034, 0xb246}}, +{ .val = {0x1f25dde3, 0x25911ff5, 0x3e56ec37, 0x2361614a, 0x27073338, 0x28c828aa, 0x10615937, 0x185f201a, 0x5923}}, +{ .val = {0x2f92ed09, 0x32c88ff8, 0x1f2b761b, 0x11b0b0a5, 0x1383999c, 0x34641455, 0x830ac9b, 0x2c2f900d, 0xac91}}, +{ .val = {0x17c9749c, 0x396447fa, 0x2f95bb0d, 0x8d85852, 0x29c1ccce, 0x3a320a2a, 0x2418564d, 0x3617c806, 0xd648}}, +{ .val = {0xbe4ba4e, 0x3cb223fd, 0x17cadd86, 0x46c2c29, 0x14e0e667, 0x3d190515, 0x120c2b26, 0x1b0be403, 0x6b24}}, +{ .val = {0x25f25d27, 0x1e5911fe, 0x2be56ec3, 0x22361614, 0x2a707333, 0x1e8c828a, 0x29061593, 0xd85f201, 0x3592}}, +{ .val = {0x12f92cab, 0x2f2c88fd, 0x15f2b761, 0x311b0b0a, 0x15383999, 0x2f464145, 0x34830ac9, 0x6c2f900, 0x9ac9}}, +{ .val = {0x297c946d, 0x3796447c, 0xaf95bb0, 0x388d8585, 0x2a9c1ccc, 0x37a320a2, 0x1a418564, 0x23617c80, 0xcd64}}, +{ .val = {0x14be484e, 0x1bcb223c, 0x257cadd8, 0x1c46c2c2, 0x154e0e66, 0x1bd19051, 0xd20c2b2, 0x11b0be40, 0xe6b2}}, +{ .val = {0xa5f2427, 0xde5911e, 0x12be56ec, 0xe236161, 0x2aa70733, 0xde8c828, 0x6906159, 0x8d85f20, 0x7359}}, +{ .val = {0x52f902b, 0x6f2c88d, 0x295f2b76, 0x2711b0b0, 0x15538399, 0x26f46414, 0x34830ac, 0x246c2f90, 0xb9ac}}, +{ .val = {0x2297c62d, 0x3796444, 0x14af95bb, 0x3388d858, 0xaa9c1cc, 0x137a320a, 0x1a41856, 0x123617c8, 0xdcd6}}, +{ .val = {0x114be12e, 0x21bcb220, 0xa57cadd, 0x19c46c2c, 0x554e0e6, 0x9bd1905, 0xd20c2b, 0x91b0be4, 0xee6b}}, +{ .val = {0x8a5f097, 0x30de5910, 0x52be56e, 0xce23616, 0x22aa7073, 0x24de8c82, 0x690615, 0x248d85f2, 0x7735}}, +{ .val = {0x452f663, 0x186f2c86, 0x295f2b7, 0x26711b0b, 0x11553839, 0x326f4641, 0x34830a, 0x3246c2f9, 0xbb9a}}, +{ .val = {0x2297949, 0x2c379641, 0x214af95b, 0x33388d85, 0x28aa9c1c, 0x1937a320, 0x201a4185, 0x1923617c, 0xddcd}}, +{ .val = {0x2114babc, 0x361bcb1e, 0x30a57cad, 0x199c46c2, 0x14554e0e, 0x2c9bd190, 0x100d20c2, 0x2c91b0be, 0xeee6}}, +{ .val = {0x108a5d5e, 0x3b0de58f, 0x1852be56, 0xcce2361, 0xa2aa707, 0x164de8c8, 0x8069061, 0x1648d85f, 0x7773}}, +{ .val = {0x28452eaf, 0x1d86f2c7, 0x2c295f2b, 0x266711b0, 0x5155383, 0x2b26f464, 0x24034830, 0x2b246c2f, 0x3bb9}}, +{ .val = {0x3422956f, 0x2ec37961, 0x1614af95, 0x333388d8, 0x28aa9c1, 0x15937a32, 0x3201a418, 0x35923617, 0x9ddc}}, +{ .val = {0x3a1148cf, 0x3761bcae, 0xb0a57ca, 0x3999c46c, 0x14554e0, 0xac9bd19, 0x3900d20c, 0x1ac91b0b, 0xceee}}, +{ .val = {0x1d08a27f, 0x1bb0de55, 0x5852be5, 0x1ccce236, 0x20a2aa70, 0x564de8c, 0x3c806906, 0xd648d85, 0xe777}}, +{ .val = {0x2e844f57, 0x2dd86f28, 0x2c295f2, 0xe66711b, 0x10515538, 0x2b26f46, 0x3e403483, 0x26b246c2, 0xf3bb}}, +{ .val = {0x174225c3, 0x16ec3792, 0x21614af9, 0x733388d, 0x828aa9c, 0x215937a3, 0x1f201a41, 0x33592361, 0xf9dd}}, +{ .val = {0xba110f9, 0x2b761bc7, 0x30b0a57c, 0x3999c46, 0x2414554e, 0x30ac9bd1, 0x2f900d20, 0x39ac91b0, 0xfcee}}, +{ .val = {0x25d08694, 0x15bb0de1, 0x185852be, 0x1ccce23, 0x320a2aa7, 0x18564de8, 0x17c80690, 0x1cd648d8, 0xfe77}}, +{ .val = {0x32e8434a, 0xadd86f0, 0x2c2c295f, 0x20e66711, 0x19051553, 0xc2b26f4, 0xbe40348, 0x2e6b246c, 0x7f3b}}, +{ .val = {0x197421a5, 0x256ec378, 0x361614af, 0x30733388, 0xc828aa9, 0x615937a, 0x5f201a4, 0x37359236, 0x3f9d}}, +{ .val = {0xcba0eea, 0x32b761ba, 0x1b0b0a57, 0x383999c4, 0x6414554, 0x30ac9bd, 0x2f900d2, 0x3b9ac91b, 0x9fce}}, +{ .val = {0x65d0775, 0x395bb0dd, 0xd85852b, 0x1c1ccce2, 0x2320a2aa, 0x18564de, 0x217c8069, 0x1dcd648d, 0x4fe7}}, +{ .val = {0x232e81d2, 0x3cadd86c, 0x6c2c295, 0xe0e6671, 0x11905155, 0x20c2b26f, 0x30be4034, 0x2ee6b246, 0xa7f3}}, +{ .val = {0x119740e9, 0x3e56ec36, 0x2361614a, 0x27073338, 0x28c828aa, 0x10615937, 0x185f201a, 0x37735923, 0x53f9}}, +{ .val = {0x8cb9e8c, 0x1f2b7619, 0x11b0b0a5, 0x1383999c, 0x34641455, 0x830ac9b, 0x2c2f900d, 0x3bb9ac91, 0xa9fc}}, +{ .val = {0x2465cf46, 0x2f95bb0c, 0x8d85852, 0x29c1ccce, 0x3a320a2a, 0x2418564d, 0x3617c806, 0x1ddcd648, 0x54fe}}, +{ .val = {0x1232e7a3, 0x17cadd86, 0x46c2c29, 0x14e0e667, 0x3d190515, 0x120c2b26, 0x1b0be403, 0xeee6b24, 0x2a7f}}, +{ .val = {0x91971e9, 0x2be56ec1, 0x22361614, 0x2a707333, 0x1e8c828a, 0x29061593, 0xd85f201, 0x27773592, 0x953f}}, +{ .val = {0x248cb70c, 0x15f2b75e, 0x311b0b0a, 0x15383999, 0x2f464145, 0x34830ac9, 0x6c2f900, 0x33bb9ac9, 0xca9f}}, +{ .val = {0x12465b86, 0xaf95baf, 0x388d8585, 0x2a9c1ccc, 0x37a320a2, 0x1a418564, 0x23617c80, 0x39ddcd64, 0x654f}}, +{ .val = {0x29232dc3, 0x257cadd7, 0x1c46c2c2, 0x154e0e66, 0x1bd19051, 0xd20c2b2, 0x11b0be40, 0x3ceee6b2, 0x32a7}}, +{ .val = {0x349194f9, 0x12be56e9, 0xe236161, 0x2aa70733, 0xde8c828, 0x6906159, 0x8d85f20, 0x3e777359, 0x9953}}, +{ .val = {0x3a48c894, 0x295f2b72, 0x2711b0b0, 0x15538399, 0x26f46414, 0x34830ac, 0x246c2f90, 0x3f3bb9ac, 0xcca9}}, +{ .val = 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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 = 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0x842a665, 0x63db}}, +{ .val = {0x3eb7eb6a, 0x199c46c1, 0x14554e0e, 0x2c9bd190, 0x100d20c2, 0x2c91b0be, 0x29fceee6, 0x24215332, 0x31ed}}, +{ .val = {0x3f5bf5b5, 0xcce2360, 0xa2aa707, 0x164de8c8, 0x8069061, 0x1648d85f, 0x14fe7773, 0x3210a999, 0x18f6}}, +{ .val = {0x1fadf8f2, 0x266711ae, 0x5155383, 0x2b26f464, 0x24034830, 0x2b246c2f, 0x2a7f3bb9, 0x190854cc, 0x8c7b}}, +{ .val = {0xfd6fc79, 0x333388d7, 0x28aa9c1, 0x15937a32, 0x3201a418, 0x35923617, 0x153f9ddc, 0x2c842a66, 0x463d}}, +{ .val = {0x27eb7c54, 0x3999c469, 0x14554e0, 0xac9bd19, 0x3900d20c, 0x1ac91b0b, 0xa9fceee, 0x36421533, 0xa31e}}, +{ .val = {0x33f5be2a, 0x1ccce234, 0x20a2aa70, 0x564de8c, 0x3c806906, 0xd648d85, 0x254fe777, 0x1b210a99, 0x518f}}, +{ .val = {0x19fadf15, 0xe66711a, 0x10515538, 0x2b26f46, 0x3e403483, 0x26b246c2, 0x32a7f3bb, 0x2d90854c, 0x28c7}}, +{ .val = {0xcfd6da2, 0x733388b, 0x828aa9c, 0x215937a3, 0x1f201a41, 0x33592361, 0x1953f9dd, 0x36c842a6, 0x9463}}, +{ .val = {0x267eb6d1, 0x3999c45, 0x2414554e, 0x30ac9bd1, 0x2f900d20, 0x39ac91b0, 0xca9fcee, 0x3b642153, 0x4a31}}, +{ .val = {0x333f5980, 0x1ccce20, 0x320a2aa7, 0x18564de8, 0x17c80690, 0x1cd648d8, 0x2654fe77, 0x3db210a9, 0xa518}}, +{ .val = {0x199facc0, 0x20e66710, 0x19051553, 0xc2b26f4, 0xbe40348, 0x2e6b246c, 0x332a7f3b, 0x1ed90854, 0x528c}}, +{ .val = {0xccfd660, 0x30733388, 0xc828aa9, 0x615937a, 0x5f201a4, 0x37359236, 0x19953f9d, 0xf6c842a, 0x2946}}, +{ .val = {0x667eb30, 0x383999c4, 0x6414554, 0x30ac9bd, 0x2f900d2, 0x3b9ac91b, 0xcca9fce, 0x7b64215, 0x14a3}}, +{ .val = {0x333f598, 0x1c1ccce2, 0x2320a2aa, 0x18564de, 0x217c8069, 0x1dcd648d, 0x26654fe7, 0x23db210a, 0xa51}}, +{ .val = {0x199facc, 0xe0e6671, 0x11905155, 0x20c2b26f, 0x30be4034, 0x2ee6b246, 0x1332a7f3, 0x31ed9085, 0x528}}, +{ .val = {0x20ccfd66, 0x27073338, 0x28c828aa, 0x10615937, 0x185f201a, 0x37735923, 0x299953f9, 0x18f6c842, 0x294}}, +{ .val = {0x10667eb3, 0x1383999c, 0x34641455, 0x830ac9b, 0x2c2f900d, 0x3bb9ac91, 0x14cca9fc, 0xc7b6421, 0x14a}}, +{ .val = {0x8333d71, 0x29c1cccc, 0x3a320a2a, 0x2418564d, 0x3617c806, 0x1ddcd648, 0x2a6654fe, 0x63db210, 0x80a5}}, +{ .val = {0x4199cd0, 0x14e0e664, 0x3d190515, 0x120c2b26, 0x1b0be403, 0xeee6b24, 0x15332a7f, 0x231ed908, 0xc052}}, +{ .val = {0x20cce68, 0x2a707332, 0x1e8c828a, 0x29061593, 0xd85f201, 0x27773592, 0xa99953f, 0x118f6c84, 0x6029}}, +{ .val = {0x1066734, 0x15383999, 0x2f464145, 0x34830ac9, 0x6c2f900, 0x33bb9ac9, 0x54cca9f, 0x28c7b642, 0x3014}}, +{ .val = {0x2083339a, 0x2a9c1ccc, 0x37a320a2, 0x1a418564, 0x23617c80, 0x39ddcd64, 0x2a6654f, 0x1463db21, 0x180a}}, +{ .val = {0x104199cd, 0x154e0e66, 0x1bd19051, 0xd20c2b2, 0x11b0be40, 0x3ceee6b2, 0x215332a7, 0xa31ed90, 0xc05}}, +{ .val = {0x820cafe, 0x2aa70731, 0xde8c828, 0x6906159, 0x8d85f20, 0x3e777359, 0x10a99953, 0x2518f6c8, 0x8602}}, +{ .val = {0x2410657f, 0x15538398, 0x26f46414, 0x34830ac, 0x246c2f90, 0x3f3bb9ac, 0x854cca9, 0x128c7b64, 0x4301}}, +{ .val = {0x120830d7, 0xaa9c1ca, 0x137a320a, 0x1a41856, 0x123617c8, 0x3f9ddcd6, 0x42a6654, 0x29463db2, 0xa180}}, +{ .val = {0x9041683, 0x554e0e3, 0x9bd1905, 0xd20c2b, 0x91b0be4, 0x1fceee6b, 0x215332a, 0x14a31ed9, 0xd0c0}}, +{ .val = {0x24820959, 0x22aa706f, 0x24de8c82, 0x690615, 0x248d85f2, 0xfe77735, 0x210a9995, 0xa518f6c, 0xe860}}, +{ .val = {0x324102c4, 0x11553835, 0x326f4641, 0x34830a, 0x3246c2f9, 0x27f3bb9a, 0x10854cca, 0x528c7b6, 0xf430}}, +{ .val = {0x39208162, 0x28aa9c1a, 0x1937a320, 0x201a4185, 0x1923617c, 0x13f9ddcd, 0x842a665, 0x29463db, 0x7a18}}, +{ .val = {0x1c9040b1, 0x14554e0d, 0x2c9bd190, 0x100d20c2, 0x2c91b0be, 0x29fceee6, 0x24215332, 0x14a31ed, 0x3d0c}}, +{ .val = {0x2e481e70, 0xa2aa704, 0x164de8c8, 0x8069061, 0x1648d85f, 0x14fe7773, 0x3210a999, 0xa518f6, 0x9e86}}, +{ .val = {0x17240f38, 0x5155382, 0x2b26f464, 0x24034830, 0x2b246c2f, 0x2a7f3bb9, 0x190854cc, 0x528c7b, 0x4f43}}, +{ .val = {0xb92079c, 0x28aa9c1, 0x15937a32, 0x3201a418, 0x35923617, 0x153f9ddc, 0x2c842a66, 0x2029463d, 0x27a1}}, +{ .val = {0x25c903ce, 0x14554e0, 0xac9bd19, 0x3900d20c, 0x1ac91b0b, 0xa9fceee, 0x36421533, 0x3014a31e, 0x13d0}}, +{ .val = {0x12e481e7, 0x20a2aa70, 0x564de8c, 0x3c806906, 0xd648d85, 0x254fe777, 0x1b210a99, 0x180a518f, 0x9e8}}, +{ .val = {0x9723f0b, 0x10515536, 0x2b26f46, 0x3e403483, 0x26b246c2, 0x32a7f3bb, 0x2d90854c, 0xc0528c7, 0x84f4}}, +{ .val = {0x4b91d9d, 0x828aa99, 0x215937a3, 0x1f201a41, 0x33592361, 0x1953f9dd, 0x36c842a6, 0x6029463, 0xc27a}}, +{ .val = {0x225c8ce6, 0x2414554a, 0x30ac9bd1, 0x2f900d20, 0x39ac91b0, 0xca9fcee, 0x3b642153, 0x3014a31, 0xe13d}}, +{ .val = {0x112e4673, 0x320a2aa5, 0x18564de8, 0x17c80690, 0x1cd648d8, 0x2654fe77, 0x3db210a9, 0x2180a518, 0x709e}}, +{ .val = {0x28972151, 0x19051550, 0xc2b26f4, 0xbe40348, 0x2e6b246c, 0x332a7f3b, 0x1ed90854, 0x10c0528c, 0xb84f}}, +{ .val = {0x144b8ec0, 0xc828aa6, 0x615937a, 0x5f201a4, 0x37359236, 0x19953f9d, 0xf6c842a, 0x28602946, 0xdc27}}, +{ .val = {0xa25c760, 0x6414553, 0x30ac9bd, 0x2f900d2, 0x3b9ac91b, 0xcca9fce, 0x7b64215, 0x343014a3, 0x6e13}}, +{ .val = {0x2512e3b0, 0x2320a2a9, 0x18564de, 0x217c8069, 0x1dcd648d, 0x26654fe7, 0x23db210a, 0x3a180a51, 0x3709}}, +{ .val = {0x328971d8, 0x11905154, 0x20c2b26f, 0x30be4034, 0x2ee6b246, 0x1332a7f3, 0x31ed9085, 0x3d0c0528, 0x1b84}}, +{ .val = {0x1944b8ec, 0x28c828aa, 0x10615937, 0x185f201a, 0x37735923, 0x299953f9, 0x18f6c842, 0x1e860294, 0xdc2}}, +{ .val = {0xca25c76, 0x34641455, 0x830ac9b, 0x2c2f900d, 0x3bb9ac91, 0x14cca9fc, 0xc7b6421, 0xf43014a, 0x6e1}}, +{ .val = {0x26512e3b, 0x3a320a2a, 0x2418564d, 0x3617c806, 0x1ddcd648, 0x2a6654fe, 0x63db210, 0x27a180a5, 0x370}}, +{ .val = {0x13289535, 0x3d190513, 0x120c2b26, 0x1b0be403, 0xeee6b24, 0x15332a7f, 0x231ed908, 0x13d0c052, 0x81b8}}, +{ .val = {0x299448b2, 0x1e8c8287, 0x29061593, 0xd85f201, 0x27773592, 0xa99953f, 0x118f6c84, 0x9e86029, 0xc0dc}}, +{ .val = {0x34ca2459, 0x2f464143, 0x34830ac9, 0x6c2f900, 0x33bb9ac9, 0x54cca9f, 0x28c7b642, 0x4f43014, 0x606e}}, +{ .val = {0x3a651044, 0x37a3209f, 0x1a418564, 0x23617c80, 0x39ddcd64, 0x2a6654f, 0x1463db21, 0x27a180a, 0xb037}}, +{ .val = {0x3d328822, 0x1bd1904f, 0xd20c2b2, 0x11b0be40, 0x3ceee6b2, 0x215332a7, 0xa31ed90, 0x213d0c05, 0x581b}}, +{ .val = {0x3e994411, 0xde8c827, 0x6906159, 0x8d85f20, 0x3e777359, 0x10a99953, 0x2518f6c8, 0x309e8602, 0x2c0d}}, +{ .val = {0x3f4ca020, 0x26f46411, 0x34830ac, 0x246c2f90, 0x3f3bb9ac, 0x854cca9, 0x128c7b64, 0x384f4301, 0x9606}}, +{ .val = {0x3fa65010, 0x137a3208, 0x1a41856, 0x123617c8, 0x3f9ddcd6, 0x42a6654, 0x29463db2, 0x1c27a180, 0x4b03}}, +{ .val = {0x1fd32808, 0x9bd1904, 0xd20c2b, 0x91b0be4, 0x1fceee6b, 0x215332a, 0x14a31ed9, 0x2e13d0c0, 0x2581}}, +{ .val = {0xfe99404, 0x24de8c82, 0x690615, 0x248d85f2, 0xfe77735, 0x210a9995, 0xa518f6c, 0x3709e860, 0x12c0}}, +{ .val = {0x7f4ca02, 0x326f4641, 0x34830a, 0x3246c2f9, 0x27f3bb9a, 0x10854cca, 0x528c7b6, 0x1b84f430, 0x960}}, +{ .val = {0x23fa6501, 0x1937a320, 0x201a4185, 0x1923617c, 0x13f9ddcd, 0x842a665, 0x29463db, 0xdc27a18, 0x4b0}}, +{ .val = {0x11fd3098, 0x2c9bd18e, 0x100d20c2, 0x2c91b0be, 0x29fceee6, 0x24215332, 0x14a31ed, 0x6e13d0c, 0x8258}}, +{ .val = {0x8fe984c, 0x164de8c7, 0x8069061, 0x1648d85f, 0x14fe7773, 0x3210a999, 0xa518f6, 0x3709e86, 0x412c}}, +{ .val = {0x247f4c26, 0x2b26f463, 0x24034830, 0x2b246c2f, 0x2a7f3bb9, 0x190854cc, 0x528c7b, 0x1b84f43, 0x2096}}, +{ .val = {0x323fa613, 0x15937a31, 0x3201a418, 0x35923617, 0x153f9ddc, 0x2c842a66, 0x2029463d, 0xdc27a1, 0x104b}}, +{ .val = {0x391fd121, 0xac9bd16, 0x3900d20c, 0x1ac91b0b, 0xa9fceee, 0x36421533, 0x3014a31e, 0x206e13d0, 0x8825}}, +{ .val = {0x1c8fe6a8, 0x564de89, 0x3c806906, 0xd648d85, 0x254fe777, 0x1b210a99, 0x180a518f, 0x303709e8, 0xc412}}, +{ .val = {0x2e47f354, 0x2b26f44, 0x3e403483, 0x26b246c2, 0x32a7f3bb, 0x2d90854c, 0xc0528c7, 0x181b84f4, 0x6209}}, +{ .val = {0x1723f9aa, 0x215937a2, 0x1f201a41, 0x33592361, 0x1953f9dd, 0x36c842a6, 0x6029463, 0x2c0dc27a, 0x3104}}, +{ .val = {0xb91fcd5, 0x30ac9bd1, 0x2f900d20, 0x39ac91b0, 0xca9fcee, 0x3b642153, 0x3014a31, 0x1606e13d, 0x1882}}, +{ .val = {0x25c8fc82, 0x18564de6, 0x17c80690, 0x1cd648d8, 0x2654fe77, 0x3db210a9, 0x2180a518, 0xb03709e, 0x8c41}}, +{ .val = {0x12e47e41, 0xc2b26f3, 0xbe40348, 0x2e6b246c, 0x332a7f3b, 0x1ed90854, 0x10c0528c, 0x2581b84f, 0x4620}}, +{ .val = {0x29723d38, 0x6159377, 0x5f201a4, 0x37359236, 0x19953f9d, 0xf6c842a, 0x28602946, 0x12c0dc27, 0xa310}}, +{ .val = {0x34b91e9c, 0x30ac9bb, 0x2f900d2, 0x3b9ac91b, 0xcca9fce, 0x7b64215, 0x343014a3, 0x9606e13, 0x5188}}, +{ .val = {0x3a5c8f4e, 0x18564dd, 0x217c8069, 0x1dcd648d, 0x26654fe7, 0x23db210a, 0x3a180a51, 0x4b03709, 0x28c4}}, +{ .val = {0x3d2e47a7, 0x20c2b26e, 0x30be4034, 0x2ee6b246, 0x1332a7f3, 0x31ed9085, 0x3d0c0528, 0x2581b84, 0x1462}}, +{ .val = {0x1e9721eb, 0x10615935, 0x185f201a, 0x37735923, 0x299953f9, 0x18f6c842, 0x1e860294, 0x12c0dc2, 0x8a31}}, +{ .val = {0x2f4b8f0d, 0x830ac98, 0x2c2f900d, 0x3bb9ac91, 0x14cca9fc, 0xc7b6421, 0xf43014a, 0x209606e1, 0xc518}}, +{ .val = {0x17a5c59e, 0x2418564a, 0x3617c806, 0x1ddcd648, 0x2a6654fe, 0x63db210, 0x27a180a5, 0x104b0370, 0xe28c}}, +{ .val = {0xbd2e2cf, 0x120c2b25, 0x1b0be403, 0xeee6b24, 0x15332a7f, 0x231ed908, 0x13d0c052, 0x82581b8, 0x7146}}, +{ .val = {0x25e96f7f, 0x29061590, 0xd85f201, 0x27773592, 0xa99953f, 0x118f6c84, 0x9e86029, 0x412c0dc, 0xb8a3}}, +{ .val = {0x12f4b5d7, 0x34830ac6, 0x6c2f900, 0x33bb9ac9, 0x54cca9f, 0x28c7b642, 0x4f43014, 0x2209606e, 0xdc51}}, +{ .val = {0x97a5903, 0x1a418561, 0x23617c80, 0x39ddcd64, 0x2a6654f, 0x1463db21, 0x27a180a, 0x3104b037, 0xee28}}, +{ .val = {0x24bd2a99, 0xd20c2ae, 0x11b0be40, 0x3ceee6b2, 0x215332a7, 0xa31ed90, 0x213d0c05, 0x1882581b, 0xf714}}, +{ .val = {0x125e9364, 0x6906155, 0x8d85f20, 0x3e777359, 0x10a99953, 0x2518f6c8, 0x309e8602, 0xc412c0d, 0xfb8a}}, +{ .val = {0x292f49b2, 0x34830aa, 0x246c2f90, 0x3f3bb9ac, 0x854cca9, 0x128c7b64, 0x384f4301, 0x6209606, 0x7dc5}}, +{ .val = {0x1497a4d9, 0x1a41855, 0x123617c8, 0x3f9ddcd6, 0x42a6654, 0x29463db2, 0x1c27a180, 0x23104b03, 0x3ee2}}, +{ .val = {0x2a4bd084, 0xd20c28, 0x91b0be4, 0x1fceee6b, 0x215332a, 0x14a31ed9, 0x2e13d0c0, 0x11882581, 0x9f71}}, +{ .val = {0x1525e842, 0x690614, 0x248d85f2, 0xfe77735, 0x210a9995, 0xa518f6c, 0x3709e860, 0x28c412c0, 0x4fb8}}, +{ .val = {0xa92f421, 0x34830a, 0x3246c2f9, 0x27f3bb9a, 0x10854cca, 0x528c7b6, 0x1b84f430, 0x14620960, 0x27dc}}, +{ .val = {0x5497828, 0x201a4183, 0x1923617c, 0x13f9ddcd, 0x842a665, 0x29463db, 0xdc27a18, 0xa3104b0, 0x93ee}}, +{ .val = {0x22a4bc14, 0x100d20c1, 0x2c91b0be, 0x29fceee6, 0x24215332, 0x14a31ed, 0x6e13d0c, 0x5188258, 0x49f7}}, +{ .val = {0x31525e0a, 0x8069060, 0x1648d85f, 0x14fe7773, 0x3210a999, 0xa518f6, 0x3709e86, 0x228c412c, 0x24fb}}, +{ .val = {0x18a92f05, 0x24034830, 0x2b246c2f, 0x2a7f3bb9, 0x190854cc, 0x528c7b, 0x1b84f43, 0x31462096, 0x127d}}, +{ .val = {0xc54959a, 0x3201a416, 0x35923617, 0x153f9ddc, 0x2c842a66, 0x2029463d, 0xdc27a1, 0x38a3104b, 0x893e}}, +{ .val = {0x62a4acd, 0x3900d20b, 0x1ac91b0b, 0xa9fceee, 0x36421533, 0x3014a31e, 0x206e13d0, 0x1c518825, 0x449f}}, +{ .val = {0x2315237e, 0x3c806903, 0xd648d85, 0x254fe777, 0x1b210a99, 0x180a518f, 0x303709e8, 0x2e28c412, 0xa24f}}, +{ .val = {0x318a91bf, 0x3e403481, 0x26b246c2, 0x32a7f3bb, 0x2d90854c, 0xc0528c7, 0x181b84f4, 0x37146209, 0x5127}}, +{ .val = {0x38c546f7, 0x1f201a3e, 0x33592361, 0x1953f9dd, 0x36c842a6, 0x6029463, 0x2c0dc27a, 0x3b8a3104, 0xa893}}, +{ .val = {0x1c62a193, 0x2f900d1d, 0x39ac91b0, 0xca9fcee, 0x3b642153, 0x3014a31, 0x1606e13d, 0x3dc51882, 0xd449}}, +{ .val = {0x2e314ee1, 0x17c8068c, 0x1cd648d8, 0x2654fe77, 0x3db210a9, 0x2180a518, 0xb03709e, 0x3ee28c41, 0xea24}}, +{ .val = {0x1718a588, 0xbe40344, 0x2e6b246c, 0x332a7f3b, 0x1ed90854, 0x10c0528c, 0x2581b84f, 0x1f714620, 0xf512}}, +{ .val = {0xb8c52c4, 0x5f201a2, 0x37359236, 0x19953f9d, 0xf6c842a, 0x28602946, 0x12c0dc27, 0xfb8a310, 0x7a89}}, +{ .val = {0x5c62962, 0x2f900d1, 0x3b9ac91b, 0xcca9fce, 0x7b64215, 0x343014a3, 0x9606e13, 0x27dc5188, 0x3d44}}, +{ .val = {0x22e314b1, 0x217c8068, 0x1dcd648d, 0x26654fe7, 0x23db210a, 0x3a180a51, 0x4b03709, 0x13ee28c4, 0x1ea2}}, +{ .val = {0x11718870, 0x30be4032, 0x2ee6b246, 0x1332a7f3, 0x31ed9085, 0x3d0c0528, 0x2581b84, 0x9f71462, 0x8f51}}, +{ .val = {0x8b8c438, 0x185f2019, 0x37735923, 0x299953f9, 0x18f6c842, 0x1e860294, 0x12c0dc2, 0x24fb8a31, 0x47a8}}, +{ .val = {0x245c621c, 0x2c2f900c, 0x3bb9ac91, 0x14cca9fc, 0xc7b6421, 0xf43014a, 0x209606e1, 0x127dc518, 0x23d4}}, +{ .val = {0x122e310e, 0x3617c806, 0x1ddcd648, 0x2a6654fe, 0x63db210, 0x27a180a5, 0x104b0370, 0x93ee28c, 0x11ea}}, +{ .val = {0x9171887, 0x1b0be403, 0xeee6b24, 0x15332a7f, 0x231ed908, 0x13d0c052, 0x82581b8, 0x49f7146, 0x8f5}}, +{ .val = {0x248b8a5b, 0xd85f1ff, 0x27773592, 0xa99953f, 0x118f6c84, 0x9e86029, 0x412c0dc, 0x224fb8a3, 0x847a}}, +{ .val = {0x3245c345, 0x6c2f8fd, 0x33bb9ac9, 0x54cca9f, 0x28c7b642, 0x4f43014, 0x2209606e, 0x1127dc51, 0xc23d}}, +{ .val = {0x3922dfba, 0x23617c7c, 0x39ddcd64, 0x2a6654f, 0x1463db21, 0x27a180a, 0x3104b037, 0x2893ee28, 0xe11e}}, +{ .val = {0x1c916fdd, 0x11b0be3e, 0x3ceee6b2, 0x215332a7, 0xa31ed90, 0x213d0c05, 0x1882581b, 0x1449f714, 0x708f}}, +{ .val = {0xe48b606, 0x8d85f1d, 0x3e777359, 0x10a99953, 0x2518f6c8, 0x309e8602, 0xc412c0d, 0x2a24fb8a, 0xb847}}, +{ .val = {0x27245b03, 0x246c2f8e, 0x3f3bb9ac, 0x854cca9, 0x128c7b64, 0x384f4301, 0x6209606, 0x35127dc5, 0x5c23}}, +{ .val = {0x13922b99, 0x123617c5, 0x3f9ddcd6, 0x42a6654, 0x29463db2, 0x1c27a180, 0x23104b03, 0x3a893ee2, 0xae11}}, +{ .val = {0x29c913e4, 0x91b0be0, 0x1fceee6b, 0x215332a, 0x14a31ed9, 0x2e13d0c0, 0x11882581, 0x3d449f71, 0xd708}}, +{ .val = {0x14e489f2, 0x248d85f0, 0xfe77735, 0x210a9995, 0xa518f6c, 0x3709e860, 0x28c412c0, 0x1ea24fb8, 0x6b84}}, +}; + +#endif + +#ifdef USE_PRECOMPUTED_CP + +const curve_point secp256k1_cp[256] = { +{.x = { .val = {0x16f81798, 0x27ca056c, 0x1ce28d95, 0x26ff36cb, 0x70b0702, 0x18a573a, 0xbbac55a, 0x199fbe77, 0x79be}}, + .y = { .val = {0x3b10d4b8, 0x311f423f, 0x28554199, 0x5ed1229, 0x1108a8fd, 0x13eff038, 0x3c4655da, 0x369dc9a8, 0x483a}}}, +{.x = { .val = {0x1c709ee5, 0x2eb026e5, 0xef3ca7a, 0x1de392e3, 0x7cd85c, 0x1501ba57, 0x17d6d304, 0x1fe5107b, 0xc604}}, + .y = { .val = {0x10cfe52a, 0xd90c6a5, 0x266d0e12, 0x3d8c994c, 0x2ceaeef7, 0x16106519, 0x1c339a3c, 0x1a3fa98f, 0x1ae1}}}, +{.x = { .val = {0x28c4cd13, 0x13ea52af, 0x2e075847, 0x1b04e403, 0xb1404cc, 0x3924124c, 0x180f3581, 0x36fc7043, 0xe493}}, + .y = { .val = {0x7739922, 0x3fa5ef71, 0x3bdfe40c, 0x19eb8cef, 0x251448d9, 0xb88263a, 0x55b7564, 0x264fa835, 0x51ed}}}, +{.x = { .val = {0x210a2a01, 0x1de13bcf, 0x1af888a6, 0x6f74179, 0xf3c2f0a, 0xe10fedc, 0x2351daff, 0x39785732, 0x2f01}}, + .y = { .val = {0x2cbde904, 0x1768b2dd, 0x25b7617b, 0x3884f5ae, 0x2d13b4c2, 0x3420a84c, 0x39949293, 0x2a29d054, 0x5c4d}}}, +{.x = { .val = {0x2a6dec0a, 0x113ba278, 0x7a5ae9c, 0x28c4da6e, 0x23e97b2, 0x6aaf087, 0x29ec5301, 0x33a4ed67, 0xe60f}}, + .y = { .val = {0x29616821, 0x7ccb339, 0xd23f0be, 0x25a24791, 0x39371012, 0x267cd3d5, 0x195929db, 0x141ce679, 0xf7e3}}}, +{.x = { .val = {0x7143e65, 0x17436f50, 0x104a61d7, 0x33ff2e26, 0x3378ceda, 0x1b81538b, 0x1a22d47b, 0x2675d3ed, 0xd301}}, + .y = { .val = {0x24106ab9, 0x16cffc7c, 0xed81960, 0x1d8330d9, 0x380651f, 0x1b7b27a6, 0x3d5c3b3d, 0x236742b8, 0x9503}}}, +{.x = { .val = {0x3874ef8b, 0xde4639b, 0x1bafd81e, 0x131bc773, 0x32823cfc, 0x147abe0, 0x2eab70b1, 0x30550b45, 0xbf23}}, + .y = { .val = {0x26831d9f, 0x370dfbf9, 0x11e2f784, 0x8bf1520, 0x1392e4c5, 0x24a282e9, 0x3737ad, 0x219bf0cc, 0x5cb3}}}, +{.x = { .val = {0x2769a24e, 0x11c1dd15, 0x5356556, 0x3d5735c0, 0x11671cbc, 0x30f427df, 0x37a06696, 0xef900cf, 0x34ff}}, + .y = { .val = {0x33cc2f1a, 0x124419e9, 0xf8b6818, 0x37c5b0fa, 0x32098c55, 0x18676260, 0x36c553f6, 0x4588e88, 0x5d9d}}}, +{.x = { .val = {0x15f51508, 0x191b88ff, 0x1ac1ca10, 0x30e72af5, 0x2de238d8, 0x29b8f85c, 0x209d9ea2, 0x98c84b1, 0x8282}}, + .y = { .val = {0x36e26caf, 0xc6dbabf, 0x37b17bed, 0x3584eb0b, 0x360ace62, 0x95ba0c2, 0x3dfe45e8, 0x2a026155, 0x11f8}}}, +{.x = { .val = {0x2f34a24d, 0x9b8b003, 0x1e159d09, 0x36f25a36, 0x3918d50a, 0x2a15ea73, 0x39ff3905, 0x1c2ca1e9, 0x4653}}, + .y = { .val = {0x333887f4, 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0x277cf7fd, 0x317143fa, 0x10caea05, 0x53f2}}, + .y = { .val = {0x137b36a2, 0x27dfa431, 0x1e8b845f, 0x35693d72, 0x1b07de4b, 0x138f8244, 0x79b7ccd, 0x3bfef07c, 0xbd52}}}, +{.x = { .val = {0x1d82b151, 0x2d44d032, 0x21fba2db, 0x28290f55, 0x109a8fcc, 0x168454ec, 0x1e56d64, 0xe942b90, 0xd2a6}}, + .y = { .val = {0x1cf89405, 0x105085d3, 0x84ca52d, 0x3dd42bd, 0x148220a7, 0x2bb962ca, 0x3fcb7565, 0x21bed910, 0xe82d}}}, +{.x = { .val = {0xa72da5f, 0x31b12eb3, 0x2c413497, 0x2e735acd, 0x3725f922, 0x31c8080c, 0x525e23b, 0x20e9d840, 0xbaf1}}, + .y = { .val = {0x28f2a0cf, 0x1df398a2, 0x27393613, 0x8cdb172, 0x29b1d18e, 0x22f56375, 0x34d33568, 0x27efa732, 0xdeac}}}, +{.x = { .val = {0x56c3943, 0x296b2963, 0x2b76a5ff, 0x36f40b55, 0x8f6fd5a, 0xcca41b9, 0x40238f9, 0x3e29f8e1, 0xf7ae}}, + .y = { .val = {0x2cf442f1, 0xc7d89fe, 0xdcd0034, 0x30c0612a, 0x2b3fcfee, 0x10aef70e, 0x3da797c4, 0x2d1357f, 0x4e3b}}}, +{.x = { .val = {0x11924459, 0x3eb2515c, 0x3c7a78c1, 0x3cbe8968, 0x1dbb1f7a, 0xb8a7c37, 0x19036c5a, 0x11f2c400, 0xdfb5}}, + .y = { .val = {0xc65fd9e, 0x28817837, 0x1c031dcf, 0x2bc24c39, 0x864cc22, 0xe273a77, 0x347088b8, 0x34aa6e83, 0x9acc}}}, +{.x = { .val = {0x1617e073, 0x10dbe6d1, 0x39317b3, 0x2b2f6f4e, 0xfdc866b, 0x39e25b5f, 0x31eb890e, 0x1f88cd51, 0x6458}}, + .y = { .val = {0x1faf6589, 0x20a6797a, 0x33aeab35, 0x2e428e44, 0x299a185, 0x1b75911f, 0x102e2ae9, 0x33756fda, 0xd99f}}}, +{.x = { .val = {0x384480d, 0x12f36231, 0x291f2ef4, 0x382da88a, 0x2f0c1294, 0xa2d5324, 0x3940f2cf, 0x35ac50b7, 0xb866}}, + .y = { .val = {0xc4cafa8, 0x39966d1c, 0x31d86d60, 0x3948a012, 0x1ad7ac24, 0x9e35faa, 0x2eb7089a, 0x2c2cd09a, 0x1914}}}, +{.x = { .val = {0x1db20d6c, 0x8a736a0, 0x14fe455d, 0x354ab93b, 0x2ba87e2, 0x27459184, 0x2819ec4d, 0x2e242177, 0xec2b}}, + .y = { .val = {0x229cf4a0, 0x3a67135, 0x7efa98a, 0x288d92fa, 0x940c633, 0x3d9bc194, 0x13a1332, 0x305d9878, 0xccec}}}, +{.x = { .val = {0x23b09d0f, 0x22983b2c, 0x350becf3, 0x141903, 0x145905e5, 0x35d7bd79, 0x296ced39, 0x29f8e278, 0x71c4}}, + .y = { .val = {0x320ddb62, 0xdec7c05, 0x262ffc76, 0x1bcac212, 0x3810aa78, 0xf828a4b, 0x2f3ba0af, 0x3eb6dcde, 0x1313}}}, +{.x = { .val = {0x1d45e458, 0x1635b21b, 0x250e7fd3, 0x2a9b3a8, 0x9de042f, 0x151b4f95, 0xd885b3a, 0x2f783939, 0x8481}}, + .y = { .val = {0x1779057e, 0x3592c6d6, 0x3262e556, 0x29e710a, 0x2cb2ca90, 0x96fce73, 0x4dd84a, 0x1ee32e95, 0x38ee}}}, +{.x = { .val = {0x2ce9f114, 0x1510cd49, 0x19561dde, 0xbb5814a, 0x1492bf39, 0x10f1b347, 0x3a8b9fd, 0x29142f4e, 0x9629}}, + .y = { .val = {0x224aa391, 0x28e5cb12, 0x56af8dc, 0x9564f97, 0xef64db9, 0x2fbf4883, 0x3b6d7576, 0x26ca0317, 0xbf43}}}, +{.x = { .val = {0x26ca6cc3, 0xf4e3658, 0x187e1838, 0x1df5d1f8, 0x893df14, 0x1cc369f3, 0x24688eb1, 0x711fbc7, 0xb73b}}, + .y = { .val = {0x254fdba3, 0x2b0d75da, 0x1757f5af, 0x8a89482, 0x8050973, 0x1f592ef3, 0x122a90a5, 0x572ca52, 0x5843}}}, +{.x = { .val = {0x138f93e0, 0x31b8864b, 0x276899f9, 0x16ca8eed, 0x22fef7d0, 0x2624801e, 0x180311f, 0x5acb6d0, 0xedfe}}, + .y = { .val = {0x229405ad, 0x3405e4f7, 0x6e227e3, 0xf544031, 0x5d0d25b, 0x1d3ea92c, 0x1db3694d, 0xbc7f29, 0xee69}}}, +{.x = { .val = {0x2caf666b, 0x3358c0fd, 0xb1ce30b, 0x3f3fb4f1, 0x17f4637f, 0x1a5e6ba0, 0x102aa62b, 0x1295e9e0, 0x1346}}, + .y = { .val = {0x3f6ecc27, 0x3d256a41, 0x10942e13, 0x3cc02a07, 0xcb0ca48, 0x390cd14f, 0x14580ef7, 0x5640118, 0x69be}}}, +{.x = { .val = {0x65084ae, 0x1d612718, 0x2abe577c, 0x20af9f73, 0x3e12d191, 0x17223217, 0x5362ec0, 0x3e3d4c89, 0xeb3c}}, + .y = { .val = {0x396b9480, 0x3d9f07ff, 0x3dbd2a66, 0xad17179, 0x1ca4a1f5, 0x398f73bf, 0x1d70043f, 0x31e088b6, 0xc833}}}, +{.x = { .val = {0x2e9a5d0, 0x2396f2f3, 0xa201d9f, 0x1dbf3e61, 0x519b2a5, 0x2983c861, 0x199974f7, 0x299f424b, 0xbdf1}}, + .y = { .val = {0x562ff7b, 0x36d3dc06, 0x1626461c, 0xa02d879, 0x3f7baaa6, 0x2f952a1a, 0x1a1aaa80, 0x240aead9, 0x4095}}}, +{.x = { .val = {0x3b27e771, 0x3797f05c, 0x37da62ab, 0xed06591, 0x483b48c, 0x2f899ed9, 0xec29cd5, 0x1a9bb771, 0x6885}}, + .y = { .val = {0x7bbdab6, 0x46358a8, 0x3b0733a6, 0x748bca4, 0x1f7b4a33, 0x1bf52706, 0x1a1fb13b, 0xf7c53de, 0x77a3}}}, +{.x = { .val = {0x2d83f366, 0x2b68e834, 0x2f28588c, 0x36733b78, 0x1dc97a0c, 0x3d0c2f30, 0x3fe2e9ae, 0x277d6dc4, 0xbc4a}}, + .y = { .val = {0x181f33c1, 0x1d635999, 0x2547b16d, 0x3a2a7efe, 0x3798caa6, 0x24deb7d2, 0x5c06383, 0x20729b9e, 0xd3a}}}, +{.x = { .val = {0x33fceb19, 0x20b79517, 0x385c4092, 0x226c887d, 0x27bab42e, 0x171d89b3, 0x2ccc0abc, 0xf578473, 0xda43}}, + .y = { .val = {0x26f5cc64, 0x2139c482, 0x227b2776, 0x1dff0b64, 0x15e5218e, 0x2ef712be, 0x10301de, 0x36f4c86a, 0xe498}}}, +{.x = { .val = {0x1acf692a, 0x13789d71, 0x2207e065, 0x3120e29c, 0x16efdbc, 0x3045a607, 0xc7ec1c1, 0x2387ba7a, 0x31e}}, + .y = { .val = {0x316f667a, 0x330aa13a, 0x1bf73b09, 0x192609f1, 0x16743b70, 0x25c0a43, 0x3353dd9d, 0x1fd6d196, 0xad7e}}}, +{.x = { .val = {0x1f488b6, 0xaef5ffe, 0x3c7a9159, 0x326fcd8f, 0x257f73e9, 0x38036189, 0x161155d3, 0x2181ea23, 0xa987}}, + .y = { .val = {0x31dab1d, 0x2569eeec, 0xad5c6d4, 0x343c0659, 0x157c2239, 0x18f9f208, 0x95d61c0, 0x286af562, 0xd181}}}, +{.x = { .val = {0x25324caa, 0x152acc3f, 0x29472a39, 0x12d978c2, 0x12a32e69, 0x3631d251, 0x18bc0d23, 0x2a5efe0a, 0x8c28}}, + .y = { .val = {0xbef9482, 0x39c771cf, 0x11cb9459, 0x39e13c11, 0x3cc0eb7a, 0x3fb7cc7d, 0x5193378, 0x118e8cc, 0x40a3}}}, +{.x = { .val = {0x3611d8e2, 0x37ec807d, 0x249fc4d5, 0x4c3fa37, 0x3f0da2c8, 0x3b569811, 0xa2f196b, 0x3061ca8e, 0xab1a}}, + .y = { .val = {0x429d15b, 0x69607cf, 0x21e545f0, 0x3be4f4cf, 0x2a42b6f7, 0x297ce76d, 0x117a1e9a, 0x28de8c93, 0x13f4}}}, +{.x = { .val = {0x2651b3fa, 0x9abb990, 0x32df4342, 0x286cd95d, 0x3f31ef8e, 0xe981c94, 0x2f82d370, 0x3fa6d6fb, 0x2564}}, + .y = { .val = {0x1e5122d, 0x2e0b9a8c, 0x379816ed, 0x3cdf6ada, 0x3925f14, 0x2852b848, 0x389095f, 0x3de9819e, 0x8ad9}}}, +{.x = { .val = {0x2e180068, 0x5e38f4e, 0xbd3103b, 0x28f55b08, 0xdc01a7e, 0x1b17030c, 0x5b0cbfc, 0x184dbfeb, 0xff3d}}, + .y = { .val = {0x188c6077, 0x29aedb8, 0x1f5e67, 0x1d9dbc90, 0x16adc154, 0xdcb376, 0xe40d, 0xe6fa139, 0x1332}}}, +{.x = { .val = {0x1faccae0, 0x2312e844, 0x24bb3374, 0x22cd4316, 0x71fd23c, 0x3653393c, 0x127a8c1d, 0x259984e5, 0x8ea}}, + .y = { .val = {0xe62b945, 0x16bcd28c, 0xf0f8e95, 0x2de0efa7, 0x15c5d735, 0x39f033ee, 0x22782e24, 0x3eaef23b, 0x620e}}}, +{.x = { .val = {0x2190b632, 0xa4c4c76, 0xab5ab9a, 0x33ca88e9, 0x159d8263, 0x19b7cc55, 0x20cd9f3a, 0x18dc5d88, 0xc25f}}, + .y = { .val = {0x3c9590cf, 0x3bafcf5b, 0x2027a1d6, 0x27c13fe7, 0x9d7980a, 0x12640e0, 0x12873989, 0x13fb7a53, 0x5315}}}, +{.x = { .val = {0x1466d561, 0xb32cedf, 0x1978b4de, 0x1ed5770c, 0x8544c0c, 0xb60a95a, 0x26bab3e8, 0x237f8f33, 0x2a9e}}, + .y = { .val = {0x12e76373, 0x25b33d49, 0x3a02182f, 0x7abb05, 0xb96cf5e, 0x1ed6b582, 0x2651fbac, 0x3b69705b, 0x1df}}}, +{.x = { .val = {0x3f8be384, 0x22f4c810, 0x31db6c3e, 0x3b02ab68, 0x1ef07271, 0x2b5b253f, 0x23e1b251, 0x24290af9, 0xb237}}, + .y = { .val = {0x2b19880e, 0x4291cf7, 0x9ecb58d, 0x3c013d05, 0x1f94517, 0x143e22aa, 0x15edbe8d, 0x1a524675, 0xfc6b}}}, +}; + +#endif diff --git a/secp256k1.h b/secp256k1.h new file mode 100644 index 0000000000..0e22f6c70c --- /dev/null +++ b/secp256k1.h @@ -0,0 +1,63 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#ifndef __SECP256K1_H__ +#define __SECP256K1_H__ + +#include + +#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 diff --git a/sha256.c b/sha256.c new file mode 100644 index 0000000000..d4d6e43f9b --- /dev/null +++ b/sha256.c @@ -0,0 +1,127 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#include +#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]); + } +} diff --git a/sha256.h b/sha256.h new file mode 100644 index 0000000000..5405a60089 --- /dev/null +++ b/sha256.h @@ -0,0 +1,31 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#ifndef __SHA256_H_ +#define __SHA256_H_ + +// compute sha256 of a message with len length (in bytes) +// hash is a pointer to at least 32 byte array +void sha256(const uint8_t *msg, const uint32_t len, uint8_t *hash); + +#endif diff --git a/test.c b/test.c new file mode 100644 index 0000000000..10d2a5e1bb --- /dev/null +++ b/test.c @@ -0,0 +1,100 @@ +/** + * Copyright (c) 2013 Tomas Dzetkulic + * Copyright (c) 2013 Pavol Rusnak + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES + * OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, + * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +#include +#include +#include +#include + +#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 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; +}