Page MenuHomePhabricator
Differential D9405 Diff 28172 src/secp256k1/src/field_5x52_impl.h

Changeset View

Standalone View

View Options

src/secp256k1/src/field_5x52_impl.h

/*********************************************************************** /***********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille * * Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying * * Distributed under the MIT software license, see the accompanying *
* file COPYING or https://www.opensource.org/licenses/mit-license.php.* * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
***********************************************************************/ ***********************************************************************/
#ifndef SECP256K1_FIELD_REPR_IMPL_H #ifndef SECP256K1_FIELD_REPR_IMPL_H
#define SECP256K1_FIELD_REPR_IMPL_H #define SECP256K1_FIELD_REPR_IMPL_H
#if defined HAVE_CONFIG_H #if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h" #include "libsecp256k1-config.h"
#endif #endif
#include "util.h" #include "util.h"
#include "field.h" #include "field.h"
#include "modinv64_impl.h"
#if defined(USE_ASM_X86_64) #if defined(USE_ASM_X86_64)
#include "field_5x52_asm_impl.h" #include "field_5x52_asm_impl.h"
#else #else
#include "field_5x52_int128_impl.h" #include "field_5x52_int128_impl.h"
#endif #endif
/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F, /** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
▲ Show 20 Lines • Show All 469 Lines • ▼ Show 20 Linesstatic SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL); r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL);
r->n[4] = a->n[3] >> 16; r->n[4] = a->n[3] >> 16;
#ifdef VERIFY #ifdef VERIFY
r->magnitude = 1; r->magnitude = 1;
r->normalized = 1; r->normalized = 1;
#endif #endif
} }
static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) { static void secp256k1_fe_from_signed62(secp256k1_fe *r, const secp256k1_modinv64_signed62 *a) {
secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1; const uint64_t M52 = UINT64_MAX >> 12;
int j; const uint64_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4];
/** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in
* { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
* [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
*/
secp256k1_fe_sqr(&x2, a);
secp256k1_fe_mul(&x2, &x2, a);
secp256k1_fe_sqr(&x3, &x2); /* The output from secp256k1_modinv64{_var} should be normalized to range [0,modulus), and
secp256k1_fe_mul(&x3, &x3, a); * have limbs in [0,2^62). The modulus is < 2^256, so the top limb must be below 2^(256-62*4).
*/
x6 = x3; VERIFY_CHECK(a0 >> 62 == 0);
for (j=0; j<3; j++) { VERIFY_CHECK(a1 >> 62 == 0);
secp256k1_fe_sqr(&x6, &x6); VERIFY_CHECK(a2 >> 62 == 0);
} VERIFY_CHECK(a3 >> 62 == 0);
secp256k1_fe_mul(&x6, &x6, &x3); VERIFY_CHECK(a4 >> 8 == 0);
r->n[0] = a0 & M52;
r->n[1] = (a0 >> 52 | a1 << 10) & M52;
r->n[2] = (a1 >> 42 | a2 << 20) & M52;
r->n[3] = (a2 >> 32 | a3 << 30) & M52;
r->n[4] = (a3 >> 22 | a4 << 40);
x9 = x6; #ifdef VERIFY
for (j=0; j<3; j++) { r->magnitude = 1;
secp256k1_fe_sqr(&x9, &x9); r->normalized = 1;
secp256k1_fe_verify(r);
#endif
} }
secp256k1_fe_mul(&x9, &x9, &x3);
x11 = x9; static void secp256k1_fe_to_signed62(secp256k1_modinv64_signed62 *r, const secp256k1_fe *a) {
for (j=0; j<2; j++) { const uint64_t M62 = UINT64_MAX >> 2;
secp256k1_fe_sqr(&x11, &x11); const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4];
}
secp256k1_fe_mul(&x11, &x11, &x2);
x22 = x11; #ifdef VERIFY
for (j=0; j<11; j++) { VERIFY_CHECK(a->normalized);
secp256k1_fe_sqr(&x22, &x22); #endif
}
secp256k1_fe_mul(&x22, &x22, &x11);
x44 = x22; r->v[0] = (a0 | a1 << 52) & M62;
for (j=0; j<22; j++) { r->v[1] = (a1 >> 10 | a2 << 42) & M62;
secp256k1_fe_sqr(&x44, &x44); r->v[2] = (a2 >> 20 | a3 << 32) & M62;
r->v[3] = (a3 >> 30 | a4 << 22) & M62;
r->v[4] = a4 >> 40;
} }
secp256k1_fe_mul(&x44, &x44, &x22);
x88 = x44; static const secp256k1_modinv64_modinfo secp256k1_const_modinfo_fe = {
for (j=0; j<44; j++) { {{-0x1000003D1LL, 0, 0, 0, 256}},
secp256k1_fe_sqr(&x88, &x88); 0x27C7F6E22DDACACFLL
} };
secp256k1_fe_mul(&x88, &x88, &x44);
x176 = x88; static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) {
for (j=0; j<88; j++) { secp256k1_fe tmp;
secp256k1_fe_sqr(&x176, &x176); secp256k1_modinv64_signed62 s;
}
secp256k1_fe_mul(&x176, &x176, &x88);
x220 = x176; tmp = *x;
for (j=0; j<44; j++) { secp256k1_fe_normalize(&tmp);
secp256k1_fe_sqr(&x220, &x220); secp256k1_fe_to_signed62(&s, &tmp);
} secp256k1_modinv64(&s, &secp256k1_const_modinfo_fe);
secp256k1_fe_mul(&x220, &x220, &x44); secp256k1_fe_from_signed62(r, &s);
x223 = x220; #ifdef VERIFY
for (j=0; j<3; j++) { VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp));
secp256k1_fe_sqr(&x223, &x223); #endif
} }
secp256k1_fe_mul(&x223, &x223, &x3);
/* The final result is then assembled using a sliding window over the blocks. */ static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
secp256k1_fe tmp;
secp256k1_modinv64_signed62 s;
t1 = x223; tmp = *x;
for (j=0; j<23; j++) { secp256k1_fe_normalize_var(&tmp);
secp256k1_fe_sqr(&t1, &t1); secp256k1_fe_to_signed62(&s, &tmp);
} secp256k1_modinv64_var(&s, &secp256k1_const_modinfo_fe);
secp256k1_fe_mul(&t1, &t1, &x22); secp256k1_fe_from_signed62(r, &s);
for (j=0; j<5; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(&t1, &t1, a);
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(&t1, &t1, &x2);
for (j=0; j<2; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(r, a, &t1);
}
static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) { #ifdef VERIFY
#if defined(USE_FIELD_INV_BUILTIN) VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp));
secp256k1_fe_inv(r, a);
#elif defined(USE_FIELD_INV_NUM)
secp256k1_num n, m;
static const secp256k1_fe negone = SECP256K1_FE_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL
);
/* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
static const unsigned char prime[32] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
};
unsigned char b[32];
int res;
secp256k1_fe c = *a;
secp256k1_fe_normalize_var(&c);
secp256k1_fe_get_b32(b, &c);
secp256k1_num_set_bin(&n, b, 32);
secp256k1_num_set_bin(&m, prime, 32);
secp256k1_num_mod_inverse(&n, &n, &m);
secp256k1_num_get_bin(b, 32, &n);
res = secp256k1_fe_set_b32(r, b);
(void)res;
VERIFY_CHECK(res);
/* Verify the result is the (unique) valid inverse using non-GMP code. */
secp256k1_fe_mul(&c, &c, r);
secp256k1_fe_add(&c, &negone);
CHECK(secp256k1_fe_normalizes_to_zero_var(&c));
#else
#error "Please select field inverse implementation"
#endif #endif
} }
#endif /* SECP256K1_FIELD_REPR_IMPL_H */ #endif /* SECP256K1_FIELD_REPR_IMPL_H */