You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
 
 
 
 
 
 

665 lines
24 KiB

/**********************************************************************
* 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_t *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_t *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_t *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_t *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_t *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_t *r, uint32_t overflow) {
VERIFY_CHECK(overflow <= 1);
uint64_t 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 void secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
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;
secp256k1_scalar_reduce(r, t + secp256k1_scalar_check_overflow(r));
}
static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
VERIFY_CHECK(bit < 256);
uint64_t t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << bit);
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_t *r, const unsigned char *b32, int *overflow) {
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;
int 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_t* 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_t *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_t *r, const secp256k1_scalar_t *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_t *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_t *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;
}
/* 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; \
{ \
uint64_t t = (uint64_t)a * b; \
th = t >> 32; /* at most 0xFFFFFFFE */ \
tl = t; \
} \
uint32_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)); \
uint32_t 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) { \
c0 += (a); /* overflow is handled on the next line */ \
unsigned int 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_t *r, const uint32_t *l) {
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];
/* 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);
uint32_t m0; extract_fast(m0);
sumadd_fast(l[1]);
muladd(n1, SECP256K1_N_C_0);
muladd(n0, SECP256K1_N_C_1);
uint32_t m1; extract(m1);
sumadd(l[2]);
muladd(n2, SECP256K1_N_C_0);
muladd(n1, SECP256K1_N_C_1);
muladd(n0, SECP256K1_N_C_2);
uint32_t m2; 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);
uint32_t m3; 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);
uint32_t m4; 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);
uint32_t m5; 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);
uint32_t m6; 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);
uint32_t m7; extract(m7);
muladd(n7, SECP256K1_N_C_1);
muladd(n6, SECP256K1_N_C_2);
muladd(n5, SECP256K1_N_C_3);
sumadd(n4);
uint32_t m8; extract(m8);
muladd(n7, SECP256K1_N_C_2);
muladd(n6, SECP256K1_N_C_3);
sumadd(n5);
uint32_t m9; extract(m9);
muladd(n7, SECP256K1_N_C_3);
sumadd(n6);
uint32_t m10; extract(m10);
sumadd_fast(n7);
uint32_t m11; extract_fast(m11);
VERIFY_CHECK(c0 <= 1);
uint32_t 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);
uint32_t p0; extract_fast(p0);
sumadd_fast(m1);
muladd(m9, SECP256K1_N_C_0);
muladd(m8, SECP256K1_N_C_1);
uint32_t p1; extract(p1);
sumadd(m2);
muladd(m10, SECP256K1_N_C_0);
muladd(m9, SECP256K1_N_C_1);
muladd(m8, SECP256K1_N_C_2);
uint32_t p2; 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);
uint32_t p3; 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);
uint32_t p4; extract(p4);
sumadd(m5);
muladd(m12, SECP256K1_N_C_1);
muladd(m11, SECP256K1_N_C_2);
muladd(m10, SECP256K1_N_C_3);
sumadd(m9);
uint32_t p5; extract(p5);
sumadd(m6);
muladd(m12, SECP256K1_N_C_2);
muladd(m11, SECP256K1_N_C_3);
sumadd(m10);
uint32_t p6; extract(p6);
sumadd_fast(m7);
muladd_fast(m12, SECP256K1_N_C_3);
sumadd_fast(m11);
uint32_t p7; extract_fast(p7);
uint32_t p8 = c0 + m12;
VERIFY_CHECK(p8 <= 2);
/* Reduce 258 bits into 256. */
/* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */
uint64_t 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[16], const secp256k1_scalar_t *a, const secp256k1_scalar_t *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[16], const secp256k1_scalar_t *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_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
uint32_t l[16];
secp256k1_scalar_mul_512(l, a, b);
secp256k1_scalar_reduce_512(r, l);
}
static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
uint32_t l[16];
secp256k1_scalar_sqr_512(l, a);
secp256k1_scalar_reduce_512(r, l);
}
static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *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;
}
SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *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_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift) {
VERIFY_CHECK(shift >= 256);
uint32_t l[16];
secp256k1_scalar_mul_512(l, a, b);
unsigned int shiftlimbs = shift >> 5;
unsigned int shiftlow = shift & 0x1F;
unsigned int 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;
if ((l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1) {
secp256k1_scalar_add_bit(r, 0);
}
}
#endif