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1559 lines
55 KiB
1559 lines
55 KiB
#ifndef ENABLE_MODULE_MUSIG
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/**********************************************************************
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* Copyright (c) 2014 Pieter Wuille *
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* Distributed under the MIT software license, see the accompanying *
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* file COPYING or https://www.gnu.org/licenses/gpl-3.0.en.html*
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**********************************************************************/
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#ifndef SECP256K1_SCALAR_REPR_IMPL_H
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#define SECP256K1_SCALAR_REPR_IMPL_H
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/* Limbs of the secp256k1 order. */
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#define SECP256K1_N_0 ((uint32_t)0xD0364141UL)
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#define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL)
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#define SECP256K1_N_2 ((uint32_t)0xAF48A03BUL)
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#define SECP256K1_N_3 ((uint32_t)0xBAAEDCE6UL)
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#define SECP256K1_N_4 ((uint32_t)0xFFFFFFFEUL)
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#define SECP256K1_N_5 ((uint32_t)0xFFFFFFFFUL)
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#define SECP256K1_N_6 ((uint32_t)0xFFFFFFFFUL)
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#define SECP256K1_N_7 ((uint32_t)0xFFFFFFFFUL)
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/* Limbs of 2^256 minus the secp256k1 order. */
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#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
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#define SECP256K1_N_C_1 (~SECP256K1_N_1)
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#define SECP256K1_N_C_2 (~SECP256K1_N_2)
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#define SECP256K1_N_C_3 (~SECP256K1_N_3)
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#define SECP256K1_N_C_4 (1)
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/* Limbs of half the secp256k1 order. */
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#define SECP256K1_N_H_0 ((uint32_t)0x681B20A0UL)
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#define SECP256K1_N_H_1 ((uint32_t)0xDFE92F46UL)
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#define SECP256K1_N_H_2 ((uint32_t)0x57A4501DUL)
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#define SECP256K1_N_H_3 ((uint32_t)0x5D576E73UL)
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#define SECP256K1_N_H_4 ((uint32_t)0xFFFFFFFFUL)
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#define SECP256K1_N_H_5 ((uint32_t)0xFFFFFFFFUL)
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#define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL)
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#define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL)
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SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
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r->d[0] = 0;
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r->d[1] = 0;
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r->d[2] = 0;
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r->d[3] = 0;
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r->d[4] = 0;
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r->d[5] = 0;
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r->d[6] = 0;
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r->d[7] = 0;
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}
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SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
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r->d[0] = v;
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r->d[1] = 0;
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r->d[2] = 0;
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r->d[3] = 0;
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r->d[4] = 0;
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r->d[5] = 0;
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r->d[6] = 0;
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r->d[7] = 0;
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}
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SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
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VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
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return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1);
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}
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SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
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VERIFY_CHECK(count < 32);
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VERIFY_CHECK(offset + count <= 256);
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if ((offset + count - 1) >> 5 == offset >> 5) {
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return secp256k1_scalar_get_bits(a, offset, count);
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} else {
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VERIFY_CHECK((offset >> 5) + 1 < 8);
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return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & ((((uint32_t)1) << count) - 1);
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}
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}
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SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
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int yes = 0;
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int no = 0;
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no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
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no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */
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no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */
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no |= (a->d[4] < SECP256K1_N_4);
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yes |= (a->d[4] > SECP256K1_N_4) & ~no;
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no |= (a->d[3] < SECP256K1_N_3) & ~yes;
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yes |= (a->d[3] > SECP256K1_N_3) & ~no;
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no |= (a->d[2] < SECP256K1_N_2) & ~yes;
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yes |= (a->d[2] > SECP256K1_N_2) & ~no;
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no |= (a->d[1] < SECP256K1_N_1) & ~yes;
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yes |= (a->d[1] > SECP256K1_N_1) & ~no;
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yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
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return yes;
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}
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SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) {
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uint64_t t;
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VERIFY_CHECK(overflow <= 1);
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t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
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r->d[0] = t & 0xFFFFFFFFUL; t >>= 32;
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t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1;
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r->d[1] = t & 0xFFFFFFFFUL; t >>= 32;
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t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2;
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r->d[2] = t & 0xFFFFFFFFUL; t >>= 32;
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t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3;
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r->d[3] = t & 0xFFFFFFFFUL; t >>= 32;
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t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4;
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r->d[4] = t & 0xFFFFFFFFUL; t >>= 32;
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t += (uint64_t)r->d[5];
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r->d[5] = t & 0xFFFFFFFFUL; t >>= 32;
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t += (uint64_t)r->d[6];
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r->d[6] = t & 0xFFFFFFFFUL; t >>= 32;
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t += (uint64_t)r->d[7];
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r->d[7] = t & 0xFFFFFFFFUL;
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return overflow;
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}
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static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
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int overflow;
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uint64_t t = (uint64_t)a->d[0] + b->d[0];
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r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)a->d[1] + b->d[1];
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r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)a->d[2] + b->d[2];
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r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)a->d[3] + b->d[3];
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r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)a->d[4] + b->d[4];
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r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)a->d[5] + b->d[5];
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r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)a->d[6] + b->d[6];
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r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)a->d[7] + b->d[7];
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r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
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overflow = t + secp256k1_scalar_check_overflow(r);
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VERIFY_CHECK(overflow == 0 || overflow == 1);
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secp256k1_scalar_reduce(r, overflow);
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return overflow;
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}
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static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
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uint64_t t;
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VERIFY_CHECK(bit < 256);
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bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 5) > 7 makes this a noop */
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t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
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r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
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r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F));
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r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F));
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r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F));
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r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F));
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r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F));
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r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
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t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F));
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r->d[7] = t & 0xFFFFFFFFULL;
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#ifdef VERIFY
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VERIFY_CHECK((t >> 32) == 0);
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VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
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#endif
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}
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static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
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int over;
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r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24;
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r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24;
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r->d[2] = (uint32_t)b32[23] | (uint32_t)b32[22] << 8 | (uint32_t)b32[21] << 16 | (uint32_t)b32[20] << 24;
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r->d[3] = (uint32_t)b32[19] | (uint32_t)b32[18] << 8 | (uint32_t)b32[17] << 16 | (uint32_t)b32[16] << 24;
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r->d[4] = (uint32_t)b32[15] | (uint32_t)b32[14] << 8 | (uint32_t)b32[13] << 16 | (uint32_t)b32[12] << 24;
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r->d[5] = (uint32_t)b32[11] | (uint32_t)b32[10] << 8 | (uint32_t)b32[9] << 16 | (uint32_t)b32[8] << 24;
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r->d[6] = (uint32_t)b32[7] | (uint32_t)b32[6] << 8 | (uint32_t)b32[5] << 16 | (uint32_t)b32[4] << 24;
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r->d[7] = (uint32_t)b32[3] | (uint32_t)b32[2] << 8 | (uint32_t)b32[1] << 16 | (uint32_t)b32[0] << 24;
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over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
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if (overflow) {
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*overflow = over;
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}
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}
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static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
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bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7];
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bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6];
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bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5];
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bin[12] = a->d[4] >> 24; bin[13] = a->d[4] >> 16; bin[14] = a->d[4] >> 8; bin[15] = a->d[4];
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bin[16] = a->d[3] >> 24; bin[17] = a->d[3] >> 16; bin[18] = a->d[3] >> 8; bin[19] = a->d[3];
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bin[20] = a->d[2] >> 24; bin[21] = a->d[2] >> 16; bin[22] = a->d[2] >> 8; bin[23] = a->d[2];
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bin[24] = a->d[1] >> 24; bin[25] = a->d[1] >> 16; bin[26] = a->d[1] >> 8; bin[27] = a->d[1];
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bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
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}
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SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
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return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
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}
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static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
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uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
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uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
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r->d[0] = t & nonzero; t >>= 32;
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t += (uint64_t)(~a->d[1]) + SECP256K1_N_1;
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r->d[1] = t & nonzero; t >>= 32;
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t += (uint64_t)(~a->d[2]) + SECP256K1_N_2;
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r->d[2] = t & nonzero; t >>= 32;
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t += (uint64_t)(~a->d[3]) + SECP256K1_N_3;
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r->d[3] = t & nonzero; t >>= 32;
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t += (uint64_t)(~a->d[4]) + SECP256K1_N_4;
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r->d[4] = t & nonzero; t >>= 32;
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t += (uint64_t)(~a->d[5]) + SECP256K1_N_5;
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r->d[5] = t & nonzero; t >>= 32;
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t += (uint64_t)(~a->d[6]) + SECP256K1_N_6;
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r->d[6] = t & nonzero; t >>= 32;
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t += (uint64_t)(~a->d[7]) + SECP256K1_N_7;
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r->d[7] = t & nonzero;
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}
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SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
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return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
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}
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static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
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int yes = 0;
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int no = 0;
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no |= (a->d[7] < SECP256K1_N_H_7);
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yes |= (a->d[7] > SECP256K1_N_H_7) & ~no;
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no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */
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no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */
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no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */
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no |= (a->d[3] < SECP256K1_N_H_3) & ~yes;
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yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
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no |= (a->d[2] < SECP256K1_N_H_2) & ~yes;
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yes |= (a->d[2] > SECP256K1_N_H_2) & ~no;
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no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
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yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
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yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
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return yes;
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}
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static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
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/* If we are flag = 0, mask = 00...00 and this is a no-op;
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* if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
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uint32_t mask = !flag - 1;
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uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
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uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
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r->d[0] = t & nonzero; t >>= 32;
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t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
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r->d[1] = t & nonzero; t >>= 32;
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t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
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r->d[2] = t & nonzero; t >>= 32;
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t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
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r->d[3] = t & nonzero; t >>= 32;
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t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask);
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r->d[4] = t & nonzero; t >>= 32;
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t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask);
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r->d[5] = t & nonzero; t >>= 32;
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t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask);
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r->d[6] = t & nonzero; t >>= 32;
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t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask);
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r->d[7] = t & nonzero;
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return 2 * (mask == 0) - 1;
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}
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/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
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/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
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#define muladd(a,b) { \
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uint32_t tl, th; \
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{ \
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uint64_t t = (uint64_t)a * b; \
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th = t >> 32; /* at most 0xFFFFFFFE */ \
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tl = t; \
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} \
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c0 += tl; /* overflow is handled on the next line */ \
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th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
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c1 += th; /* overflow is handled on the next line */ \
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c2 += (c1 < th) ? 1 : 0; /* never overflows by contract (verified in the next line) */ \
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VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
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}
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/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
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#define muladd_fast(a,b) { \
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uint32_t tl, th; \
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{ \
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uint64_t t = (uint64_t)a * b; \
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th = t >> 32; /* at most 0xFFFFFFFE */ \
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tl = t; \
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} \
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c0 += tl; /* overflow is handled on the next line */ \
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th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
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c1 += th; /* never overflows by contract (verified in the next line) */ \
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VERIFY_CHECK(c1 >= th); \
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}
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/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
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#define muladd2(a,b) { \
|
|
uint32_t tl, th, th2, tl2; \
|
|
{ \
|
|
uint64_t t = (uint64_t)a * b; \
|
|
th = t >> 32; /* at most 0xFFFFFFFE */ \
|
|
tl = t; \
|
|
} \
|
|
th2 = th + th; /* at most 0xFFFFFFFE (in case th was 0x7FFFFFFF) */ \
|
|
c2 += (th2 < th) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
|
|
VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
|
|
tl2 = tl + tl; /* at most 0xFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFF) */ \
|
|
th2 += (tl2 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
|
|
c0 += tl2; /* overflow is handled on the next line */ \
|
|
th2 += (c0 < tl2) ? 1 : 0; /* second overflow is handled on the next line */ \
|
|
c2 += (c0 < tl2) & (th2 == 0); /* never overflows by contract (verified the next line) */ \
|
|
VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
|
|
c1 += th2; /* overflow is handled on the next line */ \
|
|
c2 += (c1 < th2) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
|
|
VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
|
|
}
|
|
|
|
/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
|
|
#define sumadd(a) { \
|
|
unsigned int over; \
|
|
c0 += (a); /* overflow is handled on the next line */ \
|
|
over = (c0 < (a)) ? 1 : 0; \
|
|
c1 += over; /* overflow is handled on the next line */ \
|
|
c2 += (c1 < over) ? 1 : 0; /* never overflows by contract */ \
|
|
}
|
|
|
|
/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
|
|
#define sumadd_fast(a) { \
|
|
c0 += (a); /* overflow is handled on the next line */ \
|
|
c1 += (c0 < (a)) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
|
|
VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
|
|
VERIFY_CHECK(c2 == 0); \
|
|
}
|
|
|
|
/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. */
|
|
#define extract(n) { \
|
|
(n) = c0; \
|
|
c0 = c1; \
|
|
c1 = c2; \
|
|
c2 = 0; \
|
|
}
|
|
|
|
/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. c2 is required to be zero. */
|
|
#define extract_fast(n) { \
|
|
(n) = c0; \
|
|
c0 = c1; \
|
|
c1 = 0; \
|
|
VERIFY_CHECK(c2 == 0); \
|
|
}
|
|
|
|
static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) {
|
|
uint64_t c;
|
|
uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15];
|
|
uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
|
|
uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8;
|
|
|
|
/* 96 bit accumulator. */
|
|
uint32_t c0, c1, c2;
|
|
|
|
/* Reduce 512 bits into 385. */
|
|
/* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */
|
|
c0 = l[0]; c1 = 0; c2 = 0;
|
|
muladd_fast(n0, SECP256K1_N_C_0);
|
|
extract_fast(m0);
|
|
sumadd_fast(l[1]);
|
|
muladd(n1, SECP256K1_N_C_0);
|
|
muladd(n0, SECP256K1_N_C_1);
|
|
extract(m1);
|
|
sumadd(l[2]);
|
|
muladd(n2, SECP256K1_N_C_0);
|
|
muladd(n1, SECP256K1_N_C_1);
|
|
muladd(n0, SECP256K1_N_C_2);
|
|
extract(m2);
|
|
sumadd(l[3]);
|
|
muladd(n3, SECP256K1_N_C_0);
|
|
muladd(n2, SECP256K1_N_C_1);
|
|
muladd(n1, SECP256K1_N_C_2);
|
|
muladd(n0, SECP256K1_N_C_3);
|
|
extract(m3);
|
|
sumadd(l[4]);
|
|
muladd(n4, SECP256K1_N_C_0);
|
|
muladd(n3, SECP256K1_N_C_1);
|
|
muladd(n2, SECP256K1_N_C_2);
|
|
muladd(n1, SECP256K1_N_C_3);
|
|
sumadd(n0);
|
|
extract(m4);
|
|
sumadd(l[5]);
|
|
muladd(n5, SECP256K1_N_C_0);
|
|
muladd(n4, SECP256K1_N_C_1);
|
|
muladd(n3, SECP256K1_N_C_2);
|
|
muladd(n2, SECP256K1_N_C_3);
|
|
sumadd(n1);
|
|
extract(m5);
|
|
sumadd(l[6]);
|
|
muladd(n6, SECP256K1_N_C_0);
|
|
muladd(n5, SECP256K1_N_C_1);
|
|
muladd(n4, SECP256K1_N_C_2);
|
|
muladd(n3, SECP256K1_N_C_3);
|
|
sumadd(n2);
|
|
extract(m6);
|
|
sumadd(l[7]);
|
|
muladd(n7, SECP256K1_N_C_0);
|
|
muladd(n6, SECP256K1_N_C_1);
|
|
muladd(n5, SECP256K1_N_C_2);
|
|
muladd(n4, SECP256K1_N_C_3);
|
|
sumadd(n3);
|
|
extract(m7);
|
|
muladd(n7, SECP256K1_N_C_1);
|
|
muladd(n6, SECP256K1_N_C_2);
|
|
muladd(n5, SECP256K1_N_C_3);
|
|
sumadd(n4);
|
|
extract(m8);
|
|
muladd(n7, SECP256K1_N_C_2);
|
|
muladd(n6, SECP256K1_N_C_3);
|
|
sumadd(n5);
|
|
extract(m9);
|
|
muladd(n7, SECP256K1_N_C_3);
|
|
sumadd(n6);
|
|
extract(m10);
|
|
sumadd_fast(n7);
|
|
extract_fast(m11);
|
|
VERIFY_CHECK(c0 <= 1);
|
|
m12 = c0;
|
|
|
|
/* Reduce 385 bits into 258. */
|
|
/* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */
|
|
c0 = m0; c1 = 0; c2 = 0;
|
|
muladd_fast(m8, SECP256K1_N_C_0);
|
|
extract_fast(p0);
|
|
sumadd_fast(m1);
|
|
muladd(m9, SECP256K1_N_C_0);
|
|
muladd(m8, SECP256K1_N_C_1);
|
|
extract(p1);
|
|
sumadd(m2);
|
|
muladd(m10, SECP256K1_N_C_0);
|
|
muladd(m9, SECP256K1_N_C_1);
|
|
muladd(m8, SECP256K1_N_C_2);
|
|
extract(p2);
|
|
sumadd(m3);
|
|
muladd(m11, SECP256K1_N_C_0);
|
|
muladd(m10, SECP256K1_N_C_1);
|
|
muladd(m9, SECP256K1_N_C_2);
|
|
muladd(m8, SECP256K1_N_C_3);
|
|
extract(p3);
|
|
sumadd(m4);
|
|
muladd(m12, SECP256K1_N_C_0);
|
|
muladd(m11, SECP256K1_N_C_1);
|
|
muladd(m10, SECP256K1_N_C_2);
|
|
muladd(m9, SECP256K1_N_C_3);
|
|
sumadd(m8);
|
|
extract(p4);
|
|
sumadd(m5);
|
|
muladd(m12, SECP256K1_N_C_1);
|
|
muladd(m11, SECP256K1_N_C_2);
|
|
muladd(m10, SECP256K1_N_C_3);
|
|
sumadd(m9);
|
|
extract(p5);
|
|
sumadd(m6);
|
|
muladd(m12, SECP256K1_N_C_2);
|
|
muladd(m11, SECP256K1_N_C_3);
|
|
sumadd(m10);
|
|
extract(p6);
|
|
sumadd_fast(m7);
|
|
muladd_fast(m12, SECP256K1_N_C_3);
|
|
sumadd_fast(m11);
|
|
extract_fast(p7);
|
|
p8 = c0 + m12;
|
|
VERIFY_CHECK(p8 <= 2);
|
|
|
|
/* Reduce 258 bits into 256. */
|
|
/* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */
|
|
c = p0 + (uint64_t)SECP256K1_N_C_0 * p8;
|
|
r->d[0] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p1 + (uint64_t)SECP256K1_N_C_1 * p8;
|
|
r->d[1] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p2 + (uint64_t)SECP256K1_N_C_2 * p8;
|
|
r->d[2] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p3 + (uint64_t)SECP256K1_N_C_3 * p8;
|
|
r->d[3] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p4 + (uint64_t)p8;
|
|
r->d[4] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p5;
|
|
r->d[5] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p6;
|
|
r->d[6] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p7;
|
|
r->d[7] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
|
|
/* Final reduction of r. */
|
|
secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
|
|
}
|
|
|
|
static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) {
|
|
/* 96 bit accumulator. */
|
|
uint32_t c0 = 0, c1 = 0, c2 = 0;
|
|
|
|
/* l[0..15] = a[0..7] * b[0..7]. */
|
|
muladd_fast(a->d[0], b->d[0]);
|
|
extract_fast(l[0]);
|
|
muladd(a->d[0], b->d[1]);
|
|
muladd(a->d[1], b->d[0]);
|
|
extract(l[1]);
|
|
muladd(a->d[0], b->d[2]);
|
|
muladd(a->d[1], b->d[1]);
|
|
muladd(a->d[2], b->d[0]);
|
|
extract(l[2]);
|
|
muladd(a->d[0], b->d[3]);
|
|
muladd(a->d[1], b->d[2]);
|
|
muladd(a->d[2], b->d[1]);
|
|
muladd(a->d[3], b->d[0]);
|
|
extract(l[3]);
|
|
muladd(a->d[0], b->d[4]);
|
|
muladd(a->d[1], b->d[3]);
|
|
muladd(a->d[2], b->d[2]);
|
|
muladd(a->d[3], b->d[1]);
|
|
muladd(a->d[4], b->d[0]);
|
|
extract(l[4]);
|
|
muladd(a->d[0], b->d[5]);
|
|
muladd(a->d[1], b->d[4]);
|
|
muladd(a->d[2], b->d[3]);
|
|
muladd(a->d[3], b->d[2]);
|
|
muladd(a->d[4], b->d[1]);
|
|
muladd(a->d[5], b->d[0]);
|
|
extract(l[5]);
|
|
muladd(a->d[0], b->d[6]);
|
|
muladd(a->d[1], b->d[5]);
|
|
muladd(a->d[2], b->d[4]);
|
|
muladd(a->d[3], b->d[3]);
|
|
muladd(a->d[4], b->d[2]);
|
|
muladd(a->d[5], b->d[1]);
|
|
muladd(a->d[6], b->d[0]);
|
|
extract(l[6]);
|
|
muladd(a->d[0], b->d[7]);
|
|
muladd(a->d[1], b->d[6]);
|
|
muladd(a->d[2], b->d[5]);
|
|
muladd(a->d[3], b->d[4]);
|
|
muladd(a->d[4], b->d[3]);
|
|
muladd(a->d[5], b->d[2]);
|
|
muladd(a->d[6], b->d[1]);
|
|
muladd(a->d[7], b->d[0]);
|
|
extract(l[7]);
|
|
muladd(a->d[1], b->d[7]);
|
|
muladd(a->d[2], b->d[6]);
|
|
muladd(a->d[3], b->d[5]);
|
|
muladd(a->d[4], b->d[4]);
|
|
muladd(a->d[5], b->d[3]);
|
|
muladd(a->d[6], b->d[2]);
|
|
muladd(a->d[7], b->d[1]);
|
|
extract(l[8]);
|
|
muladd(a->d[2], b->d[7]);
|
|
muladd(a->d[3], b->d[6]);
|
|
muladd(a->d[4], b->d[5]);
|
|
muladd(a->d[5], b->d[4]);
|
|
muladd(a->d[6], b->d[3]);
|
|
muladd(a->d[7], b->d[2]);
|
|
extract(l[9]);
|
|
muladd(a->d[3], b->d[7]);
|
|
muladd(a->d[4], b->d[6]);
|
|
muladd(a->d[5], b->d[5]);
|
|
muladd(a->d[6], b->d[4]);
|
|
muladd(a->d[7], b->d[3]);
|
|
extract(l[10]);
|
|
muladd(a->d[4], b->d[7]);
|
|
muladd(a->d[5], b->d[6]);
|
|
muladd(a->d[6], b->d[5]);
|
|
muladd(a->d[7], b->d[4]);
|
|
extract(l[11]);
|
|
muladd(a->d[5], b->d[7]);
|
|
muladd(a->d[6], b->d[6]);
|
|
muladd(a->d[7], b->d[5]);
|
|
extract(l[12]);
|
|
muladd(a->d[6], b->d[7]);
|
|
muladd(a->d[7], b->d[6]);
|
|
extract(l[13]);
|
|
muladd_fast(a->d[7], b->d[7]);
|
|
extract_fast(l[14]);
|
|
VERIFY_CHECK(c1 == 0);
|
|
l[15] = c0;
|
|
}
|
|
|
|
static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar *a) {
|
|
/* 96 bit accumulator. */
|
|
uint32_t c0 = 0, c1 = 0, c2 = 0;
|
|
|
|
/* l[0..15] = a[0..7]^2. */
|
|
muladd_fast(a->d[0], a->d[0]);
|
|
extract_fast(l[0]);
|
|
muladd2(a->d[0], a->d[1]);
|
|
extract(l[1]);
|
|
muladd2(a->d[0], a->d[2]);
|
|
muladd(a->d[1], a->d[1]);
|
|
extract(l[2]);
|
|
muladd2(a->d[0], a->d[3]);
|
|
muladd2(a->d[1], a->d[2]);
|
|
extract(l[3]);
|
|
muladd2(a->d[0], a->d[4]);
|
|
muladd2(a->d[1], a->d[3]);
|
|
muladd(a->d[2], a->d[2]);
|
|
extract(l[4]);
|
|
muladd2(a->d[0], a->d[5]);
|
|
muladd2(a->d[1], a->d[4]);
|
|
muladd2(a->d[2], a->d[3]);
|
|
extract(l[5]);
|
|
muladd2(a->d[0], a->d[6]);
|
|
muladd2(a->d[1], a->d[5]);
|
|
muladd2(a->d[2], a->d[4]);
|
|
muladd(a->d[3], a->d[3]);
|
|
extract(l[6]);
|
|
muladd2(a->d[0], a->d[7]);
|
|
muladd2(a->d[1], a->d[6]);
|
|
muladd2(a->d[2], a->d[5]);
|
|
muladd2(a->d[3], a->d[4]);
|
|
extract(l[7]);
|
|
muladd2(a->d[1], a->d[7]);
|
|
muladd2(a->d[2], a->d[6]);
|
|
muladd2(a->d[3], a->d[5]);
|
|
muladd(a->d[4], a->d[4]);
|
|
extract(l[8]);
|
|
muladd2(a->d[2], a->d[7]);
|
|
muladd2(a->d[3], a->d[6]);
|
|
muladd2(a->d[4], a->d[5]);
|
|
extract(l[9]);
|
|
muladd2(a->d[3], a->d[7]);
|
|
muladd2(a->d[4], a->d[6]);
|
|
muladd(a->d[5], a->d[5]);
|
|
extract(l[10]);
|
|
muladd2(a->d[4], a->d[7]);
|
|
muladd2(a->d[5], a->d[6]);
|
|
extract(l[11]);
|
|
muladd2(a->d[5], a->d[7]);
|
|
muladd(a->d[6], a->d[6]);
|
|
extract(l[12]);
|
|
muladd2(a->d[6], a->d[7]);
|
|
extract(l[13]);
|
|
muladd_fast(a->d[7], a->d[7]);
|
|
extract_fast(l[14]);
|
|
VERIFY_CHECK(c1 == 0);
|
|
l[15] = c0;
|
|
}
|
|
|
|
#undef sumadd
|
|
#undef sumadd_fast
|
|
#undef muladd
|
|
#undef muladd_fast
|
|
#undef muladd2
|
|
#undef extract
|
|
#undef extract_fast
|
|
|
|
static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
|
|
uint32_t l[16];
|
|
secp256k1_scalar_mul_512(l, a, b);
|
|
secp256k1_scalar_reduce_512(r, l);
|
|
}
|
|
|
|
static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
|
|
int ret;
|
|
VERIFY_CHECK(n > 0);
|
|
VERIFY_CHECK(n < 16);
|
|
ret = r->d[0] & ((1 << n) - 1);
|
|
r->d[0] = (r->d[0] >> n) + (r->d[1] << (32 - n));
|
|
r->d[1] = (r->d[1] >> n) + (r->d[2] << (32 - n));
|
|
r->d[2] = (r->d[2] >> n) + (r->d[3] << (32 - n));
|
|
r->d[3] = (r->d[3] >> n) + (r->d[4] << (32 - n));
|
|
r->d[4] = (r->d[4] >> n) + (r->d[5] << (32 - n));
|
|
r->d[5] = (r->d[5] >> n) + (r->d[6] << (32 - n));
|
|
r->d[6] = (r->d[6] >> n) + (r->d[7] << (32 - n));
|
|
r->d[7] = (r->d[7] >> n);
|
|
return ret;
|
|
}
|
|
|
|
static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
|
|
uint32_t l[16];
|
|
secp256k1_scalar_sqr_512(l, a);
|
|
secp256k1_scalar_reduce_512(r, l);
|
|
}
|
|
|
|
#ifdef USE_ENDOMORPHISM
|
|
static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
|
|
r1->d[0] = a->d[0];
|
|
r1->d[1] = a->d[1];
|
|
r1->d[2] = a->d[2];
|
|
r1->d[3] = a->d[3];
|
|
r1->d[4] = 0;
|
|
r1->d[5] = 0;
|
|
r1->d[6] = 0;
|
|
r1->d[7] = 0;
|
|
r2->d[0] = a->d[4];
|
|
r2->d[1] = a->d[5];
|
|
r2->d[2] = a->d[6];
|
|
r2->d[3] = a->d[7];
|
|
r2->d[4] = 0;
|
|
r2->d[5] = 0;
|
|
r2->d[6] = 0;
|
|
r2->d[7] = 0;
|
|
}
|
|
#endif
|
|
|
|
SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
|
|
return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
|
|
}
|
|
|
|
SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
|
|
uint32_t l[16];
|
|
unsigned int shiftlimbs;
|
|
unsigned int shiftlow;
|
|
unsigned int shifthigh;
|
|
VERIFY_CHECK(shift >= 256);
|
|
secp256k1_scalar_mul_512(l, a, b);
|
|
shiftlimbs = shift >> 5;
|
|
shiftlow = shift & 0x1F;
|
|
shifthigh = 32 - shiftlow;
|
|
r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow) : 0;
|
|
secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1);
|
|
}
|
|
|
|
#endif /* SECP256K1_SCALAR_REPR_IMPL_H */
|
|
|
|
#else
|
|
/**********************************************************************
|
|
* Copyright (c) 2014 Pieter Wuille *
|
|
* Distributed under the MIT software license, see the accompanying *
|
|
* file COPYING or https://www.gnu.org/licenses/gpl-3.0.en.html*
|
|
**********************************************************************/
|
|
|
|
#ifndef SECP256K1_SCALAR_REPR_IMPL_H
|
|
#define SECP256K1_SCALAR_REPR_IMPL_H
|
|
|
|
#include <string.h>
|
|
|
|
/* Limbs of the secp256k1 order. */
|
|
#define SECP256K1_N_0 ((uint32_t)0xD0364141UL)
|
|
#define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL)
|
|
#define SECP256K1_N_2 ((uint32_t)0xAF48A03BUL)
|
|
#define SECP256K1_N_3 ((uint32_t)0xBAAEDCE6UL)
|
|
#define SECP256K1_N_4 ((uint32_t)0xFFFFFFFEUL)
|
|
#define SECP256K1_N_5 ((uint32_t)0xFFFFFFFFUL)
|
|
#define SECP256K1_N_6 ((uint32_t)0xFFFFFFFFUL)
|
|
#define SECP256K1_N_7 ((uint32_t)0xFFFFFFFFUL)
|
|
|
|
/* Limbs of 2^256 minus the secp256k1 order. */
|
|
#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
|
|
#define SECP256K1_N_C_1 (~SECP256K1_N_1)
|
|
#define SECP256K1_N_C_2 (~SECP256K1_N_2)
|
|
#define SECP256K1_N_C_3 (~SECP256K1_N_3)
|
|
#define SECP256K1_N_C_4 (1)
|
|
|
|
/* Limbs of half the secp256k1 order. */
|
|
#define SECP256K1_N_H_0 ((uint32_t)0x681B20A0UL)
|
|
#define SECP256K1_N_H_1 ((uint32_t)0xDFE92F46UL)
|
|
#define SECP256K1_N_H_2 ((uint32_t)0x57A4501DUL)
|
|
#define SECP256K1_N_H_3 ((uint32_t)0x5D576E73UL)
|
|
#define SECP256K1_N_H_4 ((uint32_t)0xFFFFFFFFUL)
|
|
#define SECP256K1_N_H_5 ((uint32_t)0xFFFFFFFFUL)
|
|
#define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL)
|
|
#define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL)
|
|
|
|
SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
|
|
r->d[0] = 0;
|
|
r->d[1] = 0;
|
|
r->d[2] = 0;
|
|
r->d[3] = 0;
|
|
r->d[4] = 0;
|
|
r->d[5] = 0;
|
|
r->d[6] = 0;
|
|
r->d[7] = 0;
|
|
}
|
|
|
|
SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
|
|
r->d[0] = v;
|
|
r->d[1] = 0;
|
|
r->d[2] = 0;
|
|
r->d[3] = 0;
|
|
r->d[4] = 0;
|
|
r->d[5] = 0;
|
|
r->d[6] = 0;
|
|
r->d[7] = 0;
|
|
}
|
|
|
|
SECP256K1_INLINE static void secp256k1_scalar_set_u64(secp256k1_scalar *r, uint64_t v) {
|
|
r->d[0] = v;
|
|
r->d[1] = v >> 32;
|
|
r->d[2] = 0;
|
|
r->d[3] = 0;
|
|
r->d[4] = 0;
|
|
r->d[5] = 0;
|
|
r->d[6] = 0;
|
|
r->d[7] = 0;
|
|
}
|
|
|
|
SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
|
|
VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
|
|
return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1);
|
|
}
|
|
|
|
SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
|
|
VERIFY_CHECK(count < 32);
|
|
VERIFY_CHECK(offset + count <= 256);
|
|
if ((offset + count - 1) >> 5 == offset >> 5) {
|
|
return secp256k1_scalar_get_bits(a, offset, count);
|
|
} else {
|
|
VERIFY_CHECK((offset >> 5) + 1 < 8);
|
|
return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & ((((uint32_t)1) << count) - 1);
|
|
}
|
|
}
|
|
|
|
SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
|
|
int yes = 0;
|
|
int no = 0;
|
|
no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
|
|
no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */
|
|
no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */
|
|
no |= (a->d[4] < SECP256K1_N_4);
|
|
yes |= (a->d[4] > SECP256K1_N_4) & ~no;
|
|
no |= (a->d[3] < SECP256K1_N_3) & ~yes;
|
|
yes |= (a->d[3] > SECP256K1_N_3) & ~no;
|
|
no |= (a->d[2] < SECP256K1_N_2) & ~yes;
|
|
yes |= (a->d[2] > SECP256K1_N_2) & ~no;
|
|
no |= (a->d[1] < SECP256K1_N_1) & ~yes;
|
|
yes |= (a->d[1] > SECP256K1_N_1) & ~no;
|
|
yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
|
|
return yes;
|
|
}
|
|
|
|
SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) {
|
|
uint64_t t;
|
|
VERIFY_CHECK(overflow <= 1);
|
|
t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
|
|
r->d[0] = t & 0xFFFFFFFFUL; t >>= 32;
|
|
t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1;
|
|
r->d[1] = t & 0xFFFFFFFFUL; t >>= 32;
|
|
t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2;
|
|
r->d[2] = t & 0xFFFFFFFFUL; t >>= 32;
|
|
t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3;
|
|
r->d[3] = t & 0xFFFFFFFFUL; t >>= 32;
|
|
t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4;
|
|
r->d[4] = t & 0xFFFFFFFFUL; t >>= 32;
|
|
t += (uint64_t)r->d[5];
|
|
r->d[5] = t & 0xFFFFFFFFUL; t >>= 32;
|
|
t += (uint64_t)r->d[6];
|
|
r->d[6] = t & 0xFFFFFFFFUL; t >>= 32;
|
|
t += (uint64_t)r->d[7];
|
|
r->d[7] = t & 0xFFFFFFFFUL;
|
|
return overflow;
|
|
}
|
|
|
|
static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
|
|
int overflow;
|
|
uint64_t t = (uint64_t)a->d[0] + b->d[0];
|
|
r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)a->d[1] + b->d[1];
|
|
r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)a->d[2] + b->d[2];
|
|
r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)a->d[3] + b->d[3];
|
|
r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)a->d[4] + b->d[4];
|
|
r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)a->d[5] + b->d[5];
|
|
r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)a->d[6] + b->d[6];
|
|
r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)a->d[7] + b->d[7];
|
|
r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
overflow = t + secp256k1_scalar_check_overflow(r);
|
|
VERIFY_CHECK(overflow == 0 || overflow == 1);
|
|
secp256k1_scalar_reduce(r, overflow);
|
|
return overflow;
|
|
}
|
|
|
|
static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
|
|
uint64_t t;
|
|
VERIFY_CHECK(bit < 256);
|
|
bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 5) > 7 makes this a noop */
|
|
t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
|
|
r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
|
|
r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F));
|
|
r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F));
|
|
r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F));
|
|
r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F));
|
|
r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F));
|
|
r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
|
|
t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F));
|
|
r->d[7] = t & 0xFFFFFFFFULL;
|
|
#ifdef VERIFY
|
|
VERIFY_CHECK((t >> 32) == 0);
|
|
VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
|
|
#endif
|
|
}
|
|
|
|
static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
|
|
int over;
|
|
r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24;
|
|
r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24;
|
|
r->d[2] = (uint32_t)b32[23] | (uint32_t)b32[22] << 8 | (uint32_t)b32[21] << 16 | (uint32_t)b32[20] << 24;
|
|
r->d[3] = (uint32_t)b32[19] | (uint32_t)b32[18] << 8 | (uint32_t)b32[17] << 16 | (uint32_t)b32[16] << 24;
|
|
r->d[4] = (uint32_t)b32[15] | (uint32_t)b32[14] << 8 | (uint32_t)b32[13] << 16 | (uint32_t)b32[12] << 24;
|
|
r->d[5] = (uint32_t)b32[11] | (uint32_t)b32[10] << 8 | (uint32_t)b32[9] << 16 | (uint32_t)b32[8] << 24;
|
|
r->d[6] = (uint32_t)b32[7] | (uint32_t)b32[6] << 8 | (uint32_t)b32[5] << 16 | (uint32_t)b32[4] << 24;
|
|
r->d[7] = (uint32_t)b32[3] | (uint32_t)b32[2] << 8 | (uint32_t)b32[1] << 16 | (uint32_t)b32[0] << 24;
|
|
over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
|
|
if (overflow) {
|
|
*overflow = over;
|
|
}
|
|
}
|
|
|
|
static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
|
|
bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7];
|
|
bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6];
|
|
bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5];
|
|
bin[12] = a->d[4] >> 24; bin[13] = a->d[4] >> 16; bin[14] = a->d[4] >> 8; bin[15] = a->d[4];
|
|
bin[16] = a->d[3] >> 24; bin[17] = a->d[3] >> 16; bin[18] = a->d[3] >> 8; bin[19] = a->d[3];
|
|
bin[20] = a->d[2] >> 24; bin[21] = a->d[2] >> 16; bin[22] = a->d[2] >> 8; bin[23] = a->d[2];
|
|
bin[24] = a->d[1] >> 24; bin[25] = a->d[1] >> 16; bin[26] = a->d[1] >> 8; bin[27] = a->d[1];
|
|
bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
|
|
}
|
|
|
|
SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
|
|
return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
|
|
}
|
|
|
|
static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
|
|
uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
|
|
uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
|
|
r->d[0] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(~a->d[1]) + SECP256K1_N_1;
|
|
r->d[1] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(~a->d[2]) + SECP256K1_N_2;
|
|
r->d[2] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(~a->d[3]) + SECP256K1_N_3;
|
|
r->d[3] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(~a->d[4]) + SECP256K1_N_4;
|
|
r->d[4] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(~a->d[5]) + SECP256K1_N_5;
|
|
r->d[5] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(~a->d[6]) + SECP256K1_N_6;
|
|
r->d[6] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(~a->d[7]) + SECP256K1_N_7;
|
|
r->d[7] = t & nonzero;
|
|
}
|
|
|
|
SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
|
|
return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
|
|
}
|
|
|
|
static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
|
|
int yes = 0;
|
|
int no = 0;
|
|
no |= (a->d[7] < SECP256K1_N_H_7);
|
|
yes |= (a->d[7] > SECP256K1_N_H_7) & ~no;
|
|
no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */
|
|
no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */
|
|
no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */
|
|
no |= (a->d[3] < SECP256K1_N_H_3) & ~yes;
|
|
yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
|
|
no |= (a->d[2] < SECP256K1_N_H_2) & ~yes;
|
|
yes |= (a->d[2] > SECP256K1_N_H_2) & ~no;
|
|
no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
|
|
yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
|
|
yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
|
|
return yes;
|
|
}
|
|
|
|
static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
|
|
/* If we are flag = 0, mask = 00...00 and this is a no-op;
|
|
* if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
|
|
uint32_t mask = !flag - 1;
|
|
uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
|
|
uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
|
|
r->d[0] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
|
|
r->d[1] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
|
|
r->d[2] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
|
|
r->d[3] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask);
|
|
r->d[4] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask);
|
|
r->d[5] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask);
|
|
r->d[6] = t & nonzero; t >>= 32;
|
|
t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask);
|
|
r->d[7] = t & nonzero;
|
|
return 2 * (mask == 0) - 1;
|
|
}
|
|
|
|
|
|
/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
|
|
|
|
/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
|
|
#define muladd(a,b) { \
|
|
uint32_t tl, th; \
|
|
{ \
|
|
uint64_t t = (uint64_t)a * b; \
|
|
th = t >> 32; /* at most 0xFFFFFFFE */ \
|
|
tl = t; \
|
|
} \
|
|
c0 += tl; /* overflow is handled on the next line */ \
|
|
th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
|
|
c1 += th; /* overflow is handled on the next line */ \
|
|
c2 += (c1 < th) ? 1 : 0; /* never overflows by contract (verified in the next line) */ \
|
|
VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
|
|
}
|
|
|
|
/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
|
|
#define muladd_fast(a,b) { \
|
|
uint32_t tl, th; \
|
|
{ \
|
|
uint64_t t = (uint64_t)a * b; \
|
|
th = t >> 32; /* at most 0xFFFFFFFE */ \
|
|
tl = t; \
|
|
} \
|
|
c0 += tl; /* overflow is handled on the next line */ \
|
|
th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
|
|
c1 += th; /* never overflows by contract (verified in the next line) */ \
|
|
VERIFY_CHECK(c1 >= th); \
|
|
}
|
|
|
|
/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
|
|
#define muladd2(a,b) { \
|
|
uint32_t tl, th, th2, tl2; \
|
|
{ \
|
|
uint64_t t = (uint64_t)a * b; \
|
|
th = t >> 32; /* at most 0xFFFFFFFE */ \
|
|
tl = t; \
|
|
} \
|
|
th2 = th + th; /* at most 0xFFFFFFFE (in case th was 0x7FFFFFFF) */ \
|
|
c2 += (th2 < th) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
|
|
VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
|
|
tl2 = tl + tl; /* at most 0xFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFF) */ \
|
|
th2 += (tl2 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
|
|
c0 += tl2; /* overflow is handled on the next line */ \
|
|
th2 += (c0 < tl2) ? 1 : 0; /* second overflow is handled on the next line */ \
|
|
c2 += (c0 < tl2) & (th2 == 0); /* never overflows by contract (verified the next line) */ \
|
|
VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
|
|
c1 += th2; /* overflow is handled on the next line */ \
|
|
c2 += (c1 < th2) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
|
|
VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
|
|
}
|
|
|
|
/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
|
|
#define sumadd(a) { \
|
|
unsigned int over; \
|
|
c0 += (a); /* overflow is handled on the next line */ \
|
|
over = (c0 < (a)) ? 1 : 0; \
|
|
c1 += over; /* overflow is handled on the next line */ \
|
|
c2 += (c1 < over) ? 1 : 0; /* never overflows by contract */ \
|
|
}
|
|
|
|
/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
|
|
#define sumadd_fast(a) { \
|
|
c0 += (a); /* overflow is handled on the next line */ \
|
|
c1 += (c0 < (a)) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
|
|
VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
|
|
VERIFY_CHECK(c2 == 0); \
|
|
}
|
|
|
|
/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. */
|
|
#define extract(n) { \
|
|
(n) = c0; \
|
|
c0 = c1; \
|
|
c1 = c2; \
|
|
c2 = 0; \
|
|
}
|
|
|
|
/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. c2 is required to be zero. */
|
|
#define extract_fast(n) { \
|
|
(n) = c0; \
|
|
c0 = c1; \
|
|
c1 = 0; \
|
|
VERIFY_CHECK(c2 == 0); \
|
|
}
|
|
|
|
static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) {
|
|
uint64_t c;
|
|
uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15];
|
|
uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
|
|
uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8;
|
|
|
|
/* 96 bit accumulator. */
|
|
uint32_t c0, c1, c2;
|
|
|
|
/* Reduce 512 bits into 385. */
|
|
/* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */
|
|
c0 = l[0]; c1 = 0; c2 = 0;
|
|
muladd_fast(n0, SECP256K1_N_C_0);
|
|
extract_fast(m0);
|
|
sumadd_fast(l[1]);
|
|
muladd(n1, SECP256K1_N_C_0);
|
|
muladd(n0, SECP256K1_N_C_1);
|
|
extract(m1);
|
|
sumadd(l[2]);
|
|
muladd(n2, SECP256K1_N_C_0);
|
|
muladd(n1, SECP256K1_N_C_1);
|
|
muladd(n0, SECP256K1_N_C_2);
|
|
extract(m2);
|
|
sumadd(l[3]);
|
|
muladd(n3, SECP256K1_N_C_0);
|
|
muladd(n2, SECP256K1_N_C_1);
|
|
muladd(n1, SECP256K1_N_C_2);
|
|
muladd(n0, SECP256K1_N_C_3);
|
|
extract(m3);
|
|
sumadd(l[4]);
|
|
muladd(n4, SECP256K1_N_C_0);
|
|
muladd(n3, SECP256K1_N_C_1);
|
|
muladd(n2, SECP256K1_N_C_2);
|
|
muladd(n1, SECP256K1_N_C_3);
|
|
sumadd(n0);
|
|
extract(m4);
|
|
sumadd(l[5]);
|
|
muladd(n5, SECP256K1_N_C_0);
|
|
muladd(n4, SECP256K1_N_C_1);
|
|
muladd(n3, SECP256K1_N_C_2);
|
|
muladd(n2, SECP256K1_N_C_3);
|
|
sumadd(n1);
|
|
extract(m5);
|
|
sumadd(l[6]);
|
|
muladd(n6, SECP256K1_N_C_0);
|
|
muladd(n5, SECP256K1_N_C_1);
|
|
muladd(n4, SECP256K1_N_C_2);
|
|
muladd(n3, SECP256K1_N_C_3);
|
|
sumadd(n2);
|
|
extract(m6);
|
|
sumadd(l[7]);
|
|
muladd(n7, SECP256K1_N_C_0);
|
|
muladd(n6, SECP256K1_N_C_1);
|
|
muladd(n5, SECP256K1_N_C_2);
|
|
muladd(n4, SECP256K1_N_C_3);
|
|
sumadd(n3);
|
|
extract(m7);
|
|
muladd(n7, SECP256K1_N_C_1);
|
|
muladd(n6, SECP256K1_N_C_2);
|
|
muladd(n5, SECP256K1_N_C_3);
|
|
sumadd(n4);
|
|
extract(m8);
|
|
muladd(n7, SECP256K1_N_C_2);
|
|
muladd(n6, SECP256K1_N_C_3);
|
|
sumadd(n5);
|
|
extract(m9);
|
|
muladd(n7, SECP256K1_N_C_3);
|
|
sumadd(n6);
|
|
extract(m10);
|
|
sumadd_fast(n7);
|
|
extract_fast(m11);
|
|
VERIFY_CHECK(c0 <= 1);
|
|
m12 = c0;
|
|
|
|
/* Reduce 385 bits into 258. */
|
|
/* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */
|
|
c0 = m0; c1 = 0; c2 = 0;
|
|
muladd_fast(m8, SECP256K1_N_C_0);
|
|
extract_fast(p0);
|
|
sumadd_fast(m1);
|
|
muladd(m9, SECP256K1_N_C_0);
|
|
muladd(m8, SECP256K1_N_C_1);
|
|
extract(p1);
|
|
sumadd(m2);
|
|
muladd(m10, SECP256K1_N_C_0);
|
|
muladd(m9, SECP256K1_N_C_1);
|
|
muladd(m8, SECP256K1_N_C_2);
|
|
extract(p2);
|
|
sumadd(m3);
|
|
muladd(m11, SECP256K1_N_C_0);
|
|
muladd(m10, SECP256K1_N_C_1);
|
|
muladd(m9, SECP256K1_N_C_2);
|
|
muladd(m8, SECP256K1_N_C_3);
|
|
extract(p3);
|
|
sumadd(m4);
|
|
muladd(m12, SECP256K1_N_C_0);
|
|
muladd(m11, SECP256K1_N_C_1);
|
|
muladd(m10, SECP256K1_N_C_2);
|
|
muladd(m9, SECP256K1_N_C_3);
|
|
sumadd(m8);
|
|
extract(p4);
|
|
sumadd(m5);
|
|
muladd(m12, SECP256K1_N_C_1);
|
|
muladd(m11, SECP256K1_N_C_2);
|
|
muladd(m10, SECP256K1_N_C_3);
|
|
sumadd(m9);
|
|
extract(p5);
|
|
sumadd(m6);
|
|
muladd(m12, SECP256K1_N_C_2);
|
|
muladd(m11, SECP256K1_N_C_3);
|
|
sumadd(m10);
|
|
extract(p6);
|
|
sumadd_fast(m7);
|
|
muladd_fast(m12, SECP256K1_N_C_3);
|
|
sumadd_fast(m11);
|
|
extract_fast(p7);
|
|
p8 = c0 + m12;
|
|
VERIFY_CHECK(p8 <= 2);
|
|
|
|
/* Reduce 258 bits into 256. */
|
|
/* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */
|
|
c = p0 + (uint64_t)SECP256K1_N_C_0 * p8;
|
|
r->d[0] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p1 + (uint64_t)SECP256K1_N_C_1 * p8;
|
|
r->d[1] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p2 + (uint64_t)SECP256K1_N_C_2 * p8;
|
|
r->d[2] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p3 + (uint64_t)SECP256K1_N_C_3 * p8;
|
|
r->d[3] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p4 + (uint64_t)p8;
|
|
r->d[4] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p5;
|
|
r->d[5] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p6;
|
|
r->d[6] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
c += p7;
|
|
r->d[7] = c & 0xFFFFFFFFUL; c >>= 32;
|
|
|
|
/* Final reduction of r. */
|
|
secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
|
|
}
|
|
|
|
static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) {
|
|
/* 96 bit accumulator. */
|
|
uint32_t c0 = 0, c1 = 0, c2 = 0;
|
|
|
|
/* l[0..15] = a[0..7] * b[0..7]. */
|
|
muladd_fast(a->d[0], b->d[0]);
|
|
extract_fast(l[0]);
|
|
muladd(a->d[0], b->d[1]);
|
|
muladd(a->d[1], b->d[0]);
|
|
extract(l[1]);
|
|
muladd(a->d[0], b->d[2]);
|
|
muladd(a->d[1], b->d[1]);
|
|
muladd(a->d[2], b->d[0]);
|
|
extract(l[2]);
|
|
muladd(a->d[0], b->d[3]);
|
|
muladd(a->d[1], b->d[2]);
|
|
muladd(a->d[2], b->d[1]);
|
|
muladd(a->d[3], b->d[0]);
|
|
extract(l[3]);
|
|
muladd(a->d[0], b->d[4]);
|
|
muladd(a->d[1], b->d[3]);
|
|
muladd(a->d[2], b->d[2]);
|
|
muladd(a->d[3], b->d[1]);
|
|
muladd(a->d[4], b->d[0]);
|
|
extract(l[4]);
|
|
muladd(a->d[0], b->d[5]);
|
|
muladd(a->d[1], b->d[4]);
|
|
muladd(a->d[2], b->d[3]);
|
|
muladd(a->d[3], b->d[2]);
|
|
muladd(a->d[4], b->d[1]);
|
|
muladd(a->d[5], b->d[0]);
|
|
extract(l[5]);
|
|
muladd(a->d[0], b->d[6]);
|
|
muladd(a->d[1], b->d[5]);
|
|
muladd(a->d[2], b->d[4]);
|
|
muladd(a->d[3], b->d[3]);
|
|
muladd(a->d[4], b->d[2]);
|
|
muladd(a->d[5], b->d[1]);
|
|
muladd(a->d[6], b->d[0]);
|
|
extract(l[6]);
|
|
muladd(a->d[0], b->d[7]);
|
|
muladd(a->d[1], b->d[6]);
|
|
muladd(a->d[2], b->d[5]);
|
|
muladd(a->d[3], b->d[4]);
|
|
muladd(a->d[4], b->d[3]);
|
|
muladd(a->d[5], b->d[2]);
|
|
muladd(a->d[6], b->d[1]);
|
|
muladd(a->d[7], b->d[0]);
|
|
extract(l[7]);
|
|
muladd(a->d[1], b->d[7]);
|
|
muladd(a->d[2], b->d[6]);
|
|
muladd(a->d[3], b->d[5]);
|
|
muladd(a->d[4], b->d[4]);
|
|
muladd(a->d[5], b->d[3]);
|
|
muladd(a->d[6], b->d[2]);
|
|
muladd(a->d[7], b->d[1]);
|
|
extract(l[8]);
|
|
muladd(a->d[2], b->d[7]);
|
|
muladd(a->d[3], b->d[6]);
|
|
muladd(a->d[4], b->d[5]);
|
|
muladd(a->d[5], b->d[4]);
|
|
muladd(a->d[6], b->d[3]);
|
|
muladd(a->d[7], b->d[2]);
|
|
extract(l[9]);
|
|
muladd(a->d[3], b->d[7]);
|
|
muladd(a->d[4], b->d[6]);
|
|
muladd(a->d[5], b->d[5]);
|
|
muladd(a->d[6], b->d[4]);
|
|
muladd(a->d[7], b->d[3]);
|
|
extract(l[10]);
|
|
muladd(a->d[4], b->d[7]);
|
|
muladd(a->d[5], b->d[6]);
|
|
muladd(a->d[6], b->d[5]);
|
|
muladd(a->d[7], b->d[4]);
|
|
extract(l[11]);
|
|
muladd(a->d[5], b->d[7]);
|
|
muladd(a->d[6], b->d[6]);
|
|
muladd(a->d[7], b->d[5]);
|
|
extract(l[12]);
|
|
muladd(a->d[6], b->d[7]);
|
|
muladd(a->d[7], b->d[6]);
|
|
extract(l[13]);
|
|
muladd_fast(a->d[7], b->d[7]);
|
|
extract_fast(l[14]);
|
|
VERIFY_CHECK(c1 == 0);
|
|
l[15] = c0;
|
|
}
|
|
|
|
static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar *a) {
|
|
/* 96 bit accumulator. */
|
|
uint32_t c0 = 0, c1 = 0, c2 = 0;
|
|
|
|
/* l[0..15] = a[0..7]^2. */
|
|
muladd_fast(a->d[0], a->d[0]);
|
|
extract_fast(l[0]);
|
|
muladd2(a->d[0], a->d[1]);
|
|
extract(l[1]);
|
|
muladd2(a->d[0], a->d[2]);
|
|
muladd(a->d[1], a->d[1]);
|
|
extract(l[2]);
|
|
muladd2(a->d[0], a->d[3]);
|
|
muladd2(a->d[1], a->d[2]);
|
|
extract(l[3]);
|
|
muladd2(a->d[0], a->d[4]);
|
|
muladd2(a->d[1], a->d[3]);
|
|
muladd(a->d[2], a->d[2]);
|
|
extract(l[4]);
|
|
muladd2(a->d[0], a->d[5]);
|
|
muladd2(a->d[1], a->d[4]);
|
|
muladd2(a->d[2], a->d[3]);
|
|
extract(l[5]);
|
|
muladd2(a->d[0], a->d[6]);
|
|
muladd2(a->d[1], a->d[5]);
|
|
muladd2(a->d[2], a->d[4]);
|
|
muladd(a->d[3], a->d[3]);
|
|
extract(l[6]);
|
|
muladd2(a->d[0], a->d[7]);
|
|
muladd2(a->d[1], a->d[6]);
|
|
muladd2(a->d[2], a->d[5]);
|
|
muladd2(a->d[3], a->d[4]);
|
|
extract(l[7]);
|
|
muladd2(a->d[1], a->d[7]);
|
|
muladd2(a->d[2], a->d[6]);
|
|
muladd2(a->d[3], a->d[5]);
|
|
muladd(a->d[4], a->d[4]);
|
|
extract(l[8]);
|
|
muladd2(a->d[2], a->d[7]);
|
|
muladd2(a->d[3], a->d[6]);
|
|
muladd2(a->d[4], a->d[5]);
|
|
extract(l[9]);
|
|
muladd2(a->d[3], a->d[7]);
|
|
muladd2(a->d[4], a->d[6]);
|
|
muladd(a->d[5], a->d[5]);
|
|
extract(l[10]);
|
|
muladd2(a->d[4], a->d[7]);
|
|
muladd2(a->d[5], a->d[6]);
|
|
extract(l[11]);
|
|
muladd2(a->d[5], a->d[7]);
|
|
muladd(a->d[6], a->d[6]);
|
|
extract(l[12]);
|
|
muladd2(a->d[6], a->d[7]);
|
|
extract(l[13]);
|
|
muladd_fast(a->d[7], a->d[7]);
|
|
extract_fast(l[14]);
|
|
VERIFY_CHECK(c1 == 0);
|
|
l[15] = c0;
|
|
}
|
|
|
|
#undef sumadd
|
|
#undef sumadd_fast
|
|
#undef muladd
|
|
#undef muladd_fast
|
|
#undef muladd2
|
|
#undef extract
|
|
#undef extract_fast
|
|
|
|
static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
|
|
uint32_t l[16];
|
|
secp256k1_scalar_mul_512(l, a, b);
|
|
secp256k1_scalar_reduce_512(r, l);
|
|
}
|
|
|
|
static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
|
|
int ret;
|
|
VERIFY_CHECK(n > 0);
|
|
VERIFY_CHECK(n < 16);
|
|
ret = r->d[0] & ((1 << n) - 1);
|
|
r->d[0] = (r->d[0] >> n) + (r->d[1] << (32 - n));
|
|
r->d[1] = (r->d[1] >> n) + (r->d[2] << (32 - n));
|
|
r->d[2] = (r->d[2] >> n) + (r->d[3] << (32 - n));
|
|
r->d[3] = (r->d[3] >> n) + (r->d[4] << (32 - n));
|
|
r->d[4] = (r->d[4] >> n) + (r->d[5] << (32 - n));
|
|
r->d[5] = (r->d[5] >> n) + (r->d[6] << (32 - n));
|
|
r->d[6] = (r->d[6] >> n) + (r->d[7] << (32 - n));
|
|
r->d[7] = (r->d[7] >> n);
|
|
return ret;
|
|
}
|
|
|
|
static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
|
|
uint32_t l[16];
|
|
secp256k1_scalar_sqr_512(l, a);
|
|
secp256k1_scalar_reduce_512(r, l);
|
|
}
|
|
|
|
#ifdef USE_ENDOMORPHISM
|
|
static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
|
|
r1->d[0] = a->d[0];
|
|
r1->d[1] = a->d[1];
|
|
r1->d[2] = a->d[2];
|
|
r1->d[3] = a->d[3];
|
|
r1->d[4] = 0;
|
|
r1->d[5] = 0;
|
|
r1->d[6] = 0;
|
|
r1->d[7] = 0;
|
|
r2->d[0] = a->d[4];
|
|
r2->d[1] = a->d[5];
|
|
r2->d[2] = a->d[6];
|
|
r2->d[3] = a->d[7];
|
|
r2->d[4] = 0;
|
|
r2->d[5] = 0;
|
|
r2->d[6] = 0;
|
|
r2->d[7] = 0;
|
|
}
|
|
#endif
|
|
|
|
SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
|
|
return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
|
|
}
|
|
|
|
SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
|
|
uint32_t l[16];
|
|
unsigned int shiftlimbs;
|
|
unsigned int shiftlow;
|
|
unsigned int shifthigh;
|
|
VERIFY_CHECK(shift >= 256);
|
|
secp256k1_scalar_mul_512(l, a, b);
|
|
shiftlimbs = shift >> 5;
|
|
shiftlow = shift & 0x1F;
|
|
shifthigh = 32 - shiftlow;
|
|
r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
|
|
r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow) : 0;
|
|
secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1);
|
|
}
|
|
|
|
#define ROTL32(x,n) ((x) << (n) | (x) >> (32-(n)))
|
|
#define QUARTERROUND(a,b,c,d) \
|
|
a += b; d = ROTL32(d ^ a, 16); \
|
|
c += d; b = ROTL32(b ^ c, 12); \
|
|
a += b; d = ROTL32(d ^ a, 8); \
|
|
c += d; b = ROTL32(b ^ c, 7);
|
|
|
|
#ifdef WORDS_BIGENDIAN
|
|
#define LE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24))
|
|
#define BE32(p) (p)
|
|
#else
|
|
#define BE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24))
|
|
#define LE32(p) (p)
|
|
#endif
|
|
|
|
void secp256k1_scalar_chacha20(secp256k1_scalar *r1, secp256k1_scalar *r2, const unsigned char *seed, uint64_t idx) {
|
|
size_t n;
|
|
size_t over_count = 0;
|
|
uint32_t seed32[8];
|
|
uint32_t x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
|
|
int over1, over2;
|
|
|
|
memcpy((void *) seed32, (const void *) seed, 32);
|
|
do {
|
|
x0 = 0x61707865;
|
|
x1 = 0x3320646e;
|
|
x2 = 0x79622d32;
|
|
x3 = 0x6b206574;
|
|
x4 = LE32(seed32[0]);
|
|
x5 = LE32(seed32[1]);
|
|
x6 = LE32(seed32[2]);
|
|
x7 = LE32(seed32[3]);
|
|
x8 = LE32(seed32[4]);
|
|
x9 = LE32(seed32[5]);
|
|
x10 = LE32(seed32[6]);
|
|
x11 = LE32(seed32[7]);
|
|
x12 = idx;
|
|
x13 = idx >> 32;
|
|
x14 = 0;
|
|
x15 = over_count;
|
|
|
|
n = 10;
|
|
while (n--) {
|
|
QUARTERROUND(x0, x4, x8,x12)
|
|
QUARTERROUND(x1, x5, x9,x13)
|
|
QUARTERROUND(x2, x6,x10,x14)
|
|
QUARTERROUND(x3, x7,x11,x15)
|
|
QUARTERROUND(x0, x5,x10,x15)
|
|
QUARTERROUND(x1, x6,x11,x12)
|
|
QUARTERROUND(x2, x7, x8,x13)
|
|
QUARTERROUND(x3, x4, x9,x14)
|
|
}
|
|
|
|
x0 += 0x61707865;
|
|
x1 += 0x3320646e;
|
|
x2 += 0x79622d32;
|
|
x3 += 0x6b206574;
|
|
x4 += LE32(seed32[0]);
|
|
x5 += LE32(seed32[1]);
|
|
x6 += LE32(seed32[2]);
|
|
x7 += LE32(seed32[3]);
|
|
x8 += LE32(seed32[4]);
|
|
x9 += LE32(seed32[5]);
|
|
x10 += LE32(seed32[6]);
|
|
x11 += LE32(seed32[7]);
|
|
x12 += idx;
|
|
x13 += idx >> 32;
|
|
x14 += 0;
|
|
x15 += over_count;
|
|
|
|
r1->d[7] = LE32(x0);
|
|
r1->d[6] = LE32(x1);
|
|
r1->d[5] = LE32(x2);
|
|
r1->d[4] = LE32(x3);
|
|
r1->d[3] = LE32(x4);
|
|
r1->d[2] = LE32(x5);
|
|
r1->d[1] = LE32(x6);
|
|
r1->d[0] = LE32(x7);
|
|
r2->d[7] = LE32(x8);
|
|
r2->d[6] = LE32(x9);
|
|
r2->d[5] = LE32(x10);
|
|
r2->d[4] = LE32(x11);
|
|
r2->d[3] = LE32(x12);
|
|
r2->d[2] = LE32(x13);
|
|
r2->d[1] = LE32(x14);
|
|
r2->d[0] = LE32(x15);
|
|
|
|
over1 = secp256k1_scalar_check_overflow(r1);
|
|
over2 = secp256k1_scalar_check_overflow(r2);
|
|
over_count++;
|
|
} while (over1 | over2);
|
|
}
|
|
|
|
#undef ROTL32
|
|
#undef QUARTERROUND
|
|
#undef BE32
|
|
#undef LE32
|
|
|
|
#endif /* SECP256K1_SCALAR_REPR_IMPL_H */
|
|
#endif
|
|
|
|
|