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8618f2bfe0
boringssl/crypto/fipsmodule/ec/p256-x86_64.c
David Benjamin 8618f2bfe0 Optimize EC_GFp_mont_method's cmp_x_coordinate. 
For simplicity, punt order > field or width mismatches. Analogous
optimizations are possible, but the generic path works fine and no
commonly-used curve looks hits those cases.

Before:
Did 5888 ECDSA P-384 verify operations in 3094535us (1902.7 ops/sec)
After [+6.7%]:
Did 6107 ECDSA P-384 verify operations in 3007515us (2030.6 ops/sec)

Also we can fill in p - order generically and avoid extra copies of some
constants.

Change-Id: I38e1b6d51b28ed4f8cb74697b00a4f0fbc5efc3c
Reviewed-on: https://boringssl-review.googlesource.com/c/33068
Commit-Queue: David Benjamin <davidben@google.com>
CQ-Verified: CQ bot account: commit-bot@chromium.org <commit-bot@chromium.org>
Reviewed-by: Adam Langley <agl@google.com>
2018-11-13 01:48:21 +00:00

657 lines
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/*
* Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved.
* Copyright (c) 2014, Intel Corporation. All Rights Reserved.
*
* Licensed under the OpenSSL license (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*
* Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1)
* (1) Intel Corporation, Israel Development Center, Haifa, Israel
* (2) University of Haifa, Israel
*
* Reference:
* S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
* 256 Bit Primes"
*/
#include <openssl/ec.h>
#include <assert.h>
#include <stdint.h>
#include <string.h>
#include <openssl/bn.h>
#include <openssl/crypto.h>
#include <openssl/err.h>
#include "../bn/internal.h"
#include "../delocate.h"
#include "../../internal.h"
#include "internal.h"
#include "p256-x86_64.h"
#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
!defined(OPENSSL_SMALL)
typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
// One converted into the Montgomery domain
static const BN_ULONG ONE[P256_LIMBS] = {
TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe),
};
// Precomputed tables for the default generator
#include "p256-x86_64-table.h"
// Recode window to a signed digit, see util-64.c for details
static unsigned booth_recode_w5(unsigned in) {
unsigned s, d;
s = ~((in >> 5) - 1);
d = (1 << 6) - in - 1;
d = (d & s) | (in & ~s);
d = (d >> 1) + (d & 1);
return (d << 1) + (s & 1);
}
static unsigned booth_recode_w7(unsigned in) {
unsigned s, d;
s = ~((in >> 7) - 1);
d = (1 << 8) - in - 1;
d = (d & s) | (in & ~s);
d = (d >> 1) + (d & 1);
return (d << 1) + (s & 1);
}
// copy_conditional copies |src| to |dst| if |move| is one and leaves it as-is
// if |move| is zero.
//
// WARNING: this breaks the usual convention of constant-time functions
// returning masks.
static void copy_conditional(BN_ULONG dst[P256_LIMBS],
const BN_ULONG src[P256_LIMBS], BN_ULONG move) {
BN_ULONG mask1 = ((BN_ULONG)0) - move;
BN_ULONG mask2 = ~mask1;
dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
if (P256_LIMBS == 8) {
dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
}
}
// is_not_zero returns one iff in != 0 and zero otherwise.
//
// WARNING: this breaks the usual convention of constant-time functions
// returning masks.
//
// (define-fun is_not_zero ((in (_ BitVec 64))) (_ BitVec 64)
// (bvlshr (bvor in (bvsub #x0000000000000000 in)) #x000000000000003f)
// )
//
// (declare-fun x () (_ BitVec 64))
//
// (assert (and (= x #x0000000000000000) (= (is_not_zero x) #x0000000000000001)))
// (check-sat)
//
// (assert (and (not (= x #x0000000000000000)) (= (is_not_zero x) #x0000000000000000)))
// (check-sat)
//
static BN_ULONG is_not_zero(BN_ULONG in) {
in |= (0 - in);
in >>= BN_BITS2 - 1;
return in;
}
// ecp_nistz256_mod_inverse_mont sets |r| to (|in| * 2^-256)^-1 * 2^256 mod p.
// That is, |r| is the modular inverse of |in| for input and output in the
// Montgomery domain.
static void ecp_nistz256_mod_inverse_mont(BN_ULONG r[P256_LIMBS],
const BN_ULONG in[P256_LIMBS]) {
/* The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff
ffffffff
We use FLT and used poly-2 as exponent */
BN_ULONG p2[P256_LIMBS];
BN_ULONG p4[P256_LIMBS];
BN_ULONG p8[P256_LIMBS];
BN_ULONG p16[P256_LIMBS];
BN_ULONG p32[P256_LIMBS];
BN_ULONG res[P256_LIMBS];
int i;
ecp_nistz256_sqr_mont(res, in);
ecp_nistz256_mul_mont(p2, res, in); // 3*p
ecp_nistz256_sqr_mont(res, p2);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(p4, res, p2); // f*p
ecp_nistz256_sqr_mont(res, p4);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(p8, res, p4); // ff*p
ecp_nistz256_sqr_mont(res, p8);
for (i = 0; i < 7; i++) {
ecp_nistz256_sqr_mont(res, res);
}
ecp_nistz256_mul_mont(p16, res, p8); // ffff*p
ecp_nistz256_sqr_mont(res, p16);
for (i = 0; i < 15; i++) {
ecp_nistz256_sqr_mont(res, res);
}
ecp_nistz256_mul_mont(p32, res, p16); // ffffffff*p
ecp_nistz256_sqr_mont(res, p32);
for (i = 0; i < 31; i++) {
ecp_nistz256_sqr_mont(res, res);
}
ecp_nistz256_mul_mont(res, res, in);
for (i = 0; i < 32 * 4; i++) {
ecp_nistz256_sqr_mont(res, res);
}
ecp_nistz256_mul_mont(res, res, p32);
for (i = 0; i < 32; i++) {
ecp_nistz256_sqr_mont(res, res);
}
ecp_nistz256_mul_mont(res, res, p32);
for (i = 0; i < 16; i++) {
ecp_nistz256_sqr_mont(res, res);
}
ecp_nistz256_mul_mont(res, res, p16);
for (i = 0; i < 8; i++) {
ecp_nistz256_sqr_mont(res, res);
}
ecp_nistz256_mul_mont(res, res, p8);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(res, res, p4);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(res, res, p2);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(r, res, in);
}
// r = p * p_scalar
static void ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r,
const EC_RAW_POINT *p,
const EC_SCALAR *p_scalar) {
assert(p != NULL);
assert(p_scalar != NULL);
assert(group->field.width == P256_LIMBS);
static const unsigned kWindowSize = 5;
static const unsigned kMask = (1 << (5 /* kWindowSize */ + 1)) - 1;
// A |P256_POINT| is (3 * 32) = 96 bytes, and the 64-byte alignment should
// add no more than 63 bytes of overhead. Thus, |table| should require
// ~1599 ((96 * 16) + 63) bytes of stack space.
alignas(64) P256_POINT table[16];
uint8_t p_str[33];
OPENSSL_memcpy(p_str, p_scalar->bytes, 32);
p_str[32] = 0;
// table[0] is implicitly (0,0,0) (the point at infinity), therefore it is
// not stored. All other values are actually stored with an offset of -1 in
// table.
P256_POINT *row = table;
assert(group->field.width == P256_LIMBS);
OPENSSL_memcpy(row[1 - 1].X, p->X.words, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(row[1 - 1].Y, p->Y.words, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(row[1 - 1].Z, p->Z.words, P256_LIMBS * sizeof(BN_ULONG));
ecp_nistz256_point_double(&row[2 - 1], &row[1 - 1]);
ecp_nistz256_point_add(&row[3 - 1], &row[2 - 1], &row[1 - 1]);
ecp_nistz256_point_double(&row[4 - 1], &row[2 - 1]);
ecp_nistz256_point_double(&row[6 - 1], &row[3 - 1]);
ecp_nistz256_point_double(&row[8 - 1], &row[4 - 1]);
ecp_nistz256_point_double(&row[12 - 1], &row[6 - 1]);
ecp_nistz256_point_add(&row[5 - 1], &row[4 - 1], &row[1 - 1]);
ecp_nistz256_point_add(&row[7 - 1], &row[6 - 1], &row[1 - 1]);
ecp_nistz256_point_add(&row[9 - 1], &row[8 - 1], &row[1 - 1]);
ecp_nistz256_point_add(&row[13 - 1], &row[12 - 1], &row[1 - 1]);
ecp_nistz256_point_double(&row[14 - 1], &row[7 - 1]);
ecp_nistz256_point_double(&row[10 - 1], &row[5 - 1]);
ecp_nistz256_point_add(&row[15 - 1], &row[14 - 1], &row[1 - 1]);
ecp_nistz256_point_add(&row[11 - 1], &row[10 - 1], &row[1 - 1]);
ecp_nistz256_point_double(&row[16 - 1], &row[8 - 1]);
BN_ULONG tmp[P256_LIMBS];
alignas(32) P256_POINT h;
unsigned index = 255;
unsigned wvalue = p_str[(index - 1) / 8];
wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
ecp_nistz256_select_w5(r, table, booth_recode_w5(wvalue) >> 1);
while (index >= 5) {
if (index != 255) {
unsigned off = (index - 1) / 8;
wvalue = p_str[off] | p_str[off + 1] << 8;
wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
wvalue = booth_recode_w5(wvalue);
ecp_nistz256_select_w5(&h, table, wvalue >> 1);
ecp_nistz256_neg(tmp, h.Y);
copy_conditional(h.Y, tmp, (wvalue & 1));
ecp_nistz256_point_add(r, r, &h);
}
index -= kWindowSize;
ecp_nistz256_point_double(r, r);
ecp_nistz256_point_double(r, r);
ecp_nistz256_point_double(r, r);
ecp_nistz256_point_double(r, r);
ecp_nistz256_point_double(r, r);
}
// Final window
wvalue = p_str[0];
wvalue = (wvalue << 1) & kMask;
wvalue = booth_recode_w5(wvalue);
ecp_nistz256_select_w5(&h, table, wvalue >> 1);
ecp_nistz256_neg(tmp, h.Y);
copy_conditional(h.Y, tmp, wvalue & 1);
ecp_nistz256_point_add(r, r, &h);
}
typedef union {
P256_POINT p;
P256_POINT_AFFINE a;
} p256_point_union_t;
static unsigned calc_first_wvalue(unsigned *index, const uint8_t p_str[33]) {
static const unsigned kWindowSize = 7;
static const unsigned kMask = (1 << (7 /* kWindowSize */ + 1)) - 1;
*index = kWindowSize;
unsigned wvalue = (p_str[0] << 1) & kMask;
return booth_recode_w7(wvalue);
}
static unsigned calc_wvalue(unsigned *index, const uint8_t p_str[33]) {
static const unsigned kWindowSize = 7;
static const unsigned kMask = (1 << (7 /* kWindowSize */ + 1)) - 1;
const unsigned off = (*index - 1) / 8;
unsigned wvalue = p_str[off] | p_str[off + 1] << 8;
wvalue = (wvalue >> ((*index - 1) % 8)) & kMask;
*index += kWindowSize;
return booth_recode_w7(wvalue);
}
static void mul_p_add_and_store(const EC_GROUP *group, EC_RAW_POINT *r,
const EC_SCALAR *g_scalar,
const EC_RAW_POINT *p_,
const EC_SCALAR *p_scalar,
p256_point_union_t *t, p256_point_union_t *p) {
const int p_is_infinity = g_scalar == NULL;
if (p_scalar != NULL) {
P256_POINT *out = &t->p;
if (p_is_infinity) {
out = &p->p;
}
ecp_nistz256_windowed_mul(group, out, p_, p_scalar);
if (!p_is_infinity) {
ecp_nistz256_point_add(&p->p, &p->p, out);
}
}
assert(group->field.width == P256_LIMBS);
OPENSSL_memcpy(r->X.words, p->p.X, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(r->Y.words, p->p.Y, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(r->Z.words, p->p.Z, P256_LIMBS * sizeof(BN_ULONG));
}
static void ecp_nistz256_points_mul(const EC_GROUP *group, EC_RAW_POINT *r,
const EC_SCALAR *g_scalar,
const EC_RAW_POINT *p_,
const EC_SCALAR *p_scalar) {
assert((p_ != NULL) == (p_scalar != NULL));
alignas(32) p256_point_union_t t, p;
if (g_scalar != NULL) {
uint8_t p_str[33];
OPENSSL_memcpy(p_str, g_scalar->bytes, 32);
p_str[32] = 0;
// First window
unsigned index = 0;
unsigned wvalue = calc_first_wvalue(&index, p_str);
const PRECOMP256_ROW *const precomputed_table =
(const PRECOMP256_ROW *)ecp_nistz256_precomputed;
ecp_nistz256_select_w7(&p.a, precomputed_table[0], wvalue >> 1);
ecp_nistz256_neg(p.p.Z, p.p.Y);
copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
// Convert |p| from affine to Jacobian coordinates. We set Z to zero if |p|
// is infinity and |ONE| otherwise. |p| was computed from the table, so it
// is infinity iff |wvalue >> 1| is zero.
OPENSSL_memset(p.p.Z, 0, sizeof(p.p.Z));
copy_conditional(p.p.Z, ONE, is_not_zero(wvalue >> 1));
for (int i = 1; i < 37; i++) {
wvalue = calc_wvalue(&index, p_str);
ecp_nistz256_select_w7(&t.a, precomputed_table[i], wvalue >> 1);
ecp_nistz256_neg(t.p.Z, t.a.Y);
copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
}
}
mul_p_add_and_store(group, r, g_scalar, p_, p_scalar, &t, &p);
}
static void ecp_nistz256_points_mul_public(const EC_GROUP *group,
EC_RAW_POINT *r,
const EC_SCALAR *g_scalar,
const EC_RAW_POINT *p_,
const EC_SCALAR *p_scalar) {
assert(p_ != NULL && p_scalar != NULL && g_scalar != NULL);
alignas(32) p256_point_union_t t, p;
uint8_t p_str[33];
OPENSSL_memcpy(p_str, g_scalar->bytes, 32);
p_str[32] = 0;
// First window
unsigned index = 0;
unsigned wvalue = calc_first_wvalue(&index, p_str);
const PRECOMP256_ROW *const precomputed_table =
(const PRECOMP256_ROW *)ecp_nistz256_precomputed;
// Convert |p| from affine to Jacobian coordinates. We set Z to zero if |p|
// is infinity and |ONE| otherwise. |p| was computed from the table, so it
// is infinity iff |wvalue >> 1| is zero.
if ((wvalue >> 1) != 0) {
OPENSSL_memcpy(&p.a, &precomputed_table[0][(wvalue >> 1) - 1], sizeof(p.a));
OPENSSL_memcpy(&p.p.Z, ONE, sizeof(p.p.Z));
} else {
OPENSSL_memset(&p.a, 0, sizeof(p.a));
OPENSSL_memset(p.p.Z, 0, sizeof(p.p.Z));
}
if ((wvalue & 1) == 1) {
ecp_nistz256_neg(p.p.Y, p.p.Y);
}
for (int i = 1; i < 37; i++) {
wvalue = calc_wvalue(&index, p_str);
if ((wvalue >> 1) == 0) {
continue;
}
OPENSSL_memcpy(&t.a, &precomputed_table[i][(wvalue >> 1) - 1], sizeof(p.a));
if ((wvalue & 1) == 1) {
ecp_nistz256_neg(t.a.Y, t.a.Y);
}
ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
}
mul_p_add_and_store(group, r, g_scalar, p_, p_scalar, &t, &p);
}
static int ecp_nistz256_get_affine(const EC_GROUP *group,
const EC_RAW_POINT *point, EC_FELEM *x,
EC_FELEM *y) {
if (ec_GFp_simple_is_at_infinity(group, point)) {
OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
return 0;
}
BN_ULONG z_inv2[P256_LIMBS];
BN_ULONG z_inv3[P256_LIMBS];
assert(group->field.width == P256_LIMBS);
ecp_nistz256_mod_inverse_mont(z_inv3, point->Z.words);
ecp_nistz256_sqr_mont(z_inv2, z_inv3);
// Instead of using |ecp_nistz256_from_mont| to convert the |x| coordinate
// and then calling |ecp_nistz256_from_mont| again to convert the |y|
// coordinate below, convert the common factor |z_inv2| once now, saving one
// reduction.
ecp_nistz256_from_mont(z_inv2, z_inv2);
if (x != NULL) {
ecp_nistz256_mul_mont(x->words, z_inv2, point->X.words);
}
if (y != NULL) {
ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
ecp_nistz256_mul_mont(y->words, z_inv3, point->Y.words);
}
return 1;
}
static void ecp_nistz256_add(const EC_GROUP *group, EC_RAW_POINT *r,
const EC_RAW_POINT *a_, const EC_RAW_POINT *b_) {
P256_POINT a, b;
OPENSSL_memcpy(a.X, a_->X.words, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(a.Y, a_->Y.words, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(a.Z, a_->Z.words, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(b.X, b_->X.words, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(b.Y, b_->Y.words, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(b.Z, b_->Z.words, P256_LIMBS * sizeof(BN_ULONG));
ecp_nistz256_point_add(&a, &a, &b);
OPENSSL_memcpy(r->X.words, a.X, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(r->Y.words, a.Y, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(r->Z.words, a.Z, P256_LIMBS * sizeof(BN_ULONG));
}
static void ecp_nistz256_dbl(const EC_GROUP *group, EC_RAW_POINT *r,
const EC_RAW_POINT *a_) {
P256_POINT a;
OPENSSL_memcpy(a.X, a_->X.words, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(a.Y, a_->Y.words, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(a.Z, a_->Z.words, P256_LIMBS * sizeof(BN_ULONG));
ecp_nistz256_point_double(&a, &a);
OPENSSL_memcpy(r->X.words, a.X, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(r->Y.words, a.Y, P256_LIMBS * sizeof(BN_ULONG));
OPENSSL_memcpy(r->Z.words, a.Z, P256_LIMBS * sizeof(BN_ULONG));
}
static void ecp_nistz256_inv_mod_ord(const EC_GROUP *group, EC_SCALAR *out,
const EC_SCALAR *in) {
// table[i] stores a power of |in| corresponding to the matching enum value.
enum {
// The following indices specify the power in binary.
i_1 = 0,
i_10,
i_11,
i_101,
i_111,
i_1010,
i_1111,
i_10101,
i_101010,
i_101111,
// The following indices specify 2^N-1, or N ones in a row.
i_x6,
i_x8,
i_x16,
i_x32
};
BN_ULONG table[15][P256_LIMBS];
// https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion
//
// Even though this code path spares 12 squarings, 4.5%, and 13
// multiplications, 25%, the overall sign operation is not that much faster,
// not more that 2%. Most of the performance of this function comes from the
// scalar operations.
// Pre-calculate powers.
OPENSSL_memcpy(table[i_1], in->words, P256_LIMBS * sizeof(BN_ULONG));
ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1);
ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]);
ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]);
ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]);
ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1);
ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]);
ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1);
ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]);
ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1);
ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]);
ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]);
ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2);
ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]);
ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8);
ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]);
ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16);
ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]);
// Compute |in| raised to the order-2.
ecp_nistz256_ord_sqr_mont(out->words, table[i_x32], 64);
ecp_nistz256_ord_mul_mont(out->words, out->words, table[i_x32]);
static const struct {
uint8_t p, i;
} kChain[27] = {{32, i_x32}, {6, i_101111}, {5, i_111}, {4, i_11},
{5, i_1111}, {5, i_10101}, {4, i_101}, {3, i_101},
{3, i_101}, {5, i_111}, {9, i_101111}, {6, i_1111},
{2, i_1}, {5, i_1}, {6, i_1111}, {5, i_111},
{4, i_111}, {5, i_111}, {5, i_101}, {3, i_11},
{10, i_101111}, {2, i_11}, {5, i_11}, {5, i_11},
{3, i_1}, {7, i_10101}, {6, i_1111}};
for (size_t i = 0; i < OPENSSL_ARRAY_SIZE(kChain); i++) {
ecp_nistz256_ord_sqr_mont(out->words, out->words, kChain[i].p);
ecp_nistz256_ord_mul_mont(out->words, out->words, table[kChain[i].i]);
}
}
static int ecp_nistz256_mont_inv_mod_ord_vartime(const EC_GROUP *group,
EC_SCALAR *out,
const EC_SCALAR *in) {
if ((OPENSSL_ia32cap_P[1] & (1 << 28)) == 0) {
// No AVX support; fallback to generic code.
return ec_GFp_simple_mont_inv_mod_ord_vartime(group, out, in);
}
assert(group->order.width == P256_LIMBS);
if (!beeu_mod_inverse_vartime(out->words, in->words, group->order.d)) {
return 0;
}
// The result should be returned in the Montgomery domain.
ec_scalar_to_montgomery(group, out, out);
return 1;
}
static int ecp_nistz256_cmp_x_coordinate(const EC_GROUP *group,
const EC_RAW_POINT *p,
const EC_SCALAR *r) {
if (ec_GFp_simple_is_at_infinity(group, p)) {
return 0;
}
assert(group->order.width == P256_LIMBS);
assert(group->field.width == P256_LIMBS);
// We wish to compare X/Z^2 with r. This is equivalent to comparing X with
// r*Z^2. Note that X and Z are represented in Montgomery form, while r is
// not.
BN_ULONG r_Z2[P256_LIMBS], Z2_mont[P256_LIMBS], X[P256_LIMBS];
ecp_nistz256_mul_mont(Z2_mont, p->Z.words, p->Z.words);
ecp_nistz256_mul_mont(r_Z2, r->words, Z2_mont);
ecp_nistz256_from_mont(X, p->X.words);
if (OPENSSL_memcmp(r_Z2, X, sizeof(r_Z2)) == 0) {
return 1;
}
// During signing the x coefficient is reduced modulo the group order.
// Therefore there is a small possibility, less than 1/2^128, that group_order
// < p.x < P. in that case we need not only to compare against |r| but also to
// compare against r+group_order.
if (bn_less_than_words(r->words, group->field_minus_order.words,
P256_LIMBS)) {
// We can ignore the carry because: r + group_order < p < 2^256.
bn_add_words(r_Z2, r->words, group->order.d, P256_LIMBS);
ecp_nistz256_mul_mont(r_Z2, r_Z2, Z2_mont);
if (OPENSSL_memcmp(r_Z2, X, sizeof(r_Z2)) == 0) {
return 1;
}
}
return 0;
}
DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_nistz256_method) {
out->group_init = ec_GFp_mont_group_init;
out->group_finish = ec_GFp_mont_group_finish;
out->group_set_curve = ec_GFp_mont_group_set_curve;
out->point_get_affine_coordinates = ecp_nistz256_get_affine;
out->add = ecp_nistz256_add;
out->dbl = ecp_nistz256_dbl;
out->mul = ecp_nistz256_points_mul;
out->mul_public = ecp_nistz256_points_mul_public;
out->felem_mul = ec_GFp_mont_felem_mul;
out->felem_sqr = ec_GFp_mont_felem_sqr;
out->bignum_to_felem = ec_GFp_mont_bignum_to_felem;
out->felem_to_bignum = ec_GFp_mont_felem_to_bignum;
out->scalar_inv_montgomery = ecp_nistz256_inv_mod_ord;
out->scalar_inv_montgomery_vartime = ecp_nistz256_mont_inv_mod_ord_vartime;
out->cmp_x_coordinate = ecp_nistz256_cmp_x_coordinate;
};
#endif /* !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
!defined(OPENSSL_SMALL) */
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