From 1d20b0247c35f440d3fdc3d21de19b2d5256c3cf Mon Sep 17 00:00:00 2001 From: Gustav Simonsson Date: Mon, 28 Sep 2015 17:46:17 +0200 Subject: Update libsecp256k1 --- .../secp256k1/libsecp256k1/src/scalar_8x32_impl.h | 721 +++++++++++++++++++++ 1 file changed, 721 insertions(+) create mode 100644 crypto/secp256k1/libsecp256k1/src/scalar_8x32_impl.h (limited to 'crypto/secp256k1/libsecp256k1/src/scalar_8x32_impl.h') diff --git a/crypto/secp256k1/libsecp256k1/src/scalar_8x32_impl.h b/crypto/secp256k1/libsecp256k1/src/scalar_8x32_impl.h new file mode 100644 index 000000000..aae4f35c0 --- /dev/null +++ b/crypto/secp256k1/libsecp256k1/src/scalar_8x32_impl.h @@ -0,0 +1,721 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef _SECP256K1_SCALAR_REPR_IMPL_H_ +#define _SECP256K1_SCALAR_REPR_IMPL_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 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); +} + +#endif -- cgit v1.2.3