458 lines
14 KiB
C
458 lines
14 KiB
C
/* Copyright (c) 2014, Intel Corporation.
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*
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* Permission to use, copy, modify, and/or distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
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* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
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* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
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* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
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// Developers and authors:
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// Shay Gueron (1, 2), and Vlad Krasnov (1)
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// (1) Intel Corporation, Israel Development Center
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// (2) University of Haifa
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// Reference:
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// S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
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// 256 Bit Primes"
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#include <openssl/ec.h>
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#include <assert.h>
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#include <stdint.h>
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#include <string.h>
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#include <openssl/bn.h>
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#include <openssl/crypto.h>
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#include <openssl/err.h>
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#include "../bn/internal.h"
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#include "../delocate.h"
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#include "../../internal.h"
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#include "internal.h"
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#include "p256-x86_64.h"
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#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
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!defined(OPENSSL_SMALL)
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typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
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// One converted into the Montgomery domain
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static const BN_ULONG ONE[P256_LIMBS] = {
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TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
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TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe),
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};
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// Precomputed tables for the default generator
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#include "p256-x86_64-table.h"
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// Recode window to a signed digit, see util-64.c for details
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static unsigned booth_recode_w5(unsigned in) {
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unsigned s, d;
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s = ~((in >> 5) - 1);
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d = (1 << 6) - in - 1;
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d = (d & s) | (in & ~s);
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d = (d >> 1) + (d & 1);
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return (d << 1) + (s & 1);
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}
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static unsigned booth_recode_w7(unsigned in) {
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unsigned s, d;
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s = ~((in >> 7) - 1);
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d = (1 << 8) - in - 1;
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d = (d & s) | (in & ~s);
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d = (d >> 1) + (d & 1);
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return (d << 1) + (s & 1);
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}
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// copy_conditional copies |src| to |dst| if |move| is one and leaves it as-is
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// if |move| is zero.
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//
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// WARNING: this breaks the usual convention of constant-time functions
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// returning masks.
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static void copy_conditional(BN_ULONG dst[P256_LIMBS],
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const BN_ULONG src[P256_LIMBS], BN_ULONG move) {
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BN_ULONG mask1 = ((BN_ULONG)0) - move;
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BN_ULONG mask2 = ~mask1;
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dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
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dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
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dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
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dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
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if (P256_LIMBS == 8) {
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dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
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dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
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dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
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dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
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}
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}
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// is_not_zero returns one iff in != 0 and zero otherwise.
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//
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// WARNING: this breaks the usual convention of constant-time functions
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// returning masks.
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//
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// (define-fun is_not_zero ((in (_ BitVec 64))) (_ BitVec 64)
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// (bvlshr (bvor in (bvsub #x0000000000000000 in)) #x000000000000003f)
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// )
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//
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// (declare-fun x () (_ BitVec 64))
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//
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// (assert (and (= x #x0000000000000000) (= (is_not_zero x) #x0000000000000001)))
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// (check-sat)
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//
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// (assert (and (not (= x #x0000000000000000)) (= (is_not_zero x) #x0000000000000000)))
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// (check-sat)
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//
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static BN_ULONG is_not_zero(BN_ULONG in) {
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in |= (0 - in);
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in >>= BN_BITS2 - 1;
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return in;
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}
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// ecp_nistz256_mod_inverse_mont sets |r| to (|in| * 2^-256)^-1 * 2^256 mod p.
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// That is, |r| is the modular inverse of |in| for input and output in the
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// Montgomery domain.
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static void ecp_nistz256_mod_inverse_mont(BN_ULONG r[P256_LIMBS],
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const BN_ULONG in[P256_LIMBS]) {
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/* The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff
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ffffffff
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We use FLT and used poly-2 as exponent */
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BN_ULONG p2[P256_LIMBS];
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BN_ULONG p4[P256_LIMBS];
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BN_ULONG p8[P256_LIMBS];
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BN_ULONG p16[P256_LIMBS];
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BN_ULONG p32[P256_LIMBS];
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BN_ULONG res[P256_LIMBS];
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int i;
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ecp_nistz256_sqr_mont(res, in);
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ecp_nistz256_mul_mont(p2, res, in); // 3*p
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ecp_nistz256_sqr_mont(res, p2);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_mul_mont(p4, res, p2); // f*p
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ecp_nistz256_sqr_mont(res, p4);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_mul_mont(p8, res, p4); // ff*p
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ecp_nistz256_sqr_mont(res, p8);
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for (i = 0; i < 7; i++) {
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ecp_nistz256_sqr_mont(res, res);
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}
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ecp_nistz256_mul_mont(p16, res, p8); // ffff*p
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ecp_nistz256_sqr_mont(res, p16);
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for (i = 0; i < 15; i++) {
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ecp_nistz256_sqr_mont(res, res);
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}
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ecp_nistz256_mul_mont(p32, res, p16); // ffffffff*p
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ecp_nistz256_sqr_mont(res, p32);
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for (i = 0; i < 31; i++) {
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ecp_nistz256_sqr_mont(res, res);
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}
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ecp_nistz256_mul_mont(res, res, in);
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for (i = 0; i < 32 * 4; i++) {
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ecp_nistz256_sqr_mont(res, res);
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}
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ecp_nistz256_mul_mont(res, res, p32);
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for (i = 0; i < 32; i++) {
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ecp_nistz256_sqr_mont(res, res);
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}
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ecp_nistz256_mul_mont(res, res, p32);
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for (i = 0; i < 16; i++) {
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ecp_nistz256_sqr_mont(res, res);
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}
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ecp_nistz256_mul_mont(res, res, p16);
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for (i = 0; i < 8; i++) {
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ecp_nistz256_sqr_mont(res, res);
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}
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ecp_nistz256_mul_mont(res, res, p8);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_mul_mont(res, res, p4);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_mul_mont(res, res, p2);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_sqr_mont(res, res);
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ecp_nistz256_mul_mont(r, res, in);
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}
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// ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
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// returns one if it fits. Otherwise it returns zero.
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static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
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const BIGNUM *in) {
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if (in->top > P256_LIMBS) {
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return 0;
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}
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OPENSSL_memset(out, 0, sizeof(BN_ULONG) * P256_LIMBS);
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OPENSSL_memcpy(out, in->d, sizeof(BN_ULONG) * in->top);
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return 1;
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}
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// r = p * p_scalar
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static int ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r,
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const EC_POINT *p,
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const EC_SCALAR *p_scalar) {
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assert(p != NULL);
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assert(p_scalar != NULL);
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static const unsigned kWindowSize = 5;
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static const unsigned kMask = (1 << (5 /* kWindowSize */ + 1)) - 1;
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// A |P256_POINT| is (3 * 32) = 96 bytes, and the 64-byte alignment should
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// add no more than 63 bytes of overhead. Thus, |table| should require
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// ~1599 ((96 * 16) + 63) bytes of stack space.
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alignas(64) P256_POINT table[16];
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uint8_t p_str[33];
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OPENSSL_memcpy(p_str, p_scalar->bytes, 32);
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p_str[32] = 0;
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// table[0] is implicitly (0,0,0) (the point at infinity), therefore it is
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// not stored. All other values are actually stored with an offset of -1 in
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// table.
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P256_POINT *row = table;
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if (!ecp_nistz256_bignum_to_field_elem(row[1 - 1].X, &p->X) ||
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!ecp_nistz256_bignum_to_field_elem(row[1 - 1].Y, &p->Y) ||
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!ecp_nistz256_bignum_to_field_elem(row[1 - 1].Z, &p->Z)) {
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OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE);
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return 0;
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}
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ecp_nistz256_point_double(&row[2 - 1], &row[1 - 1]);
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ecp_nistz256_point_add(&row[3 - 1], &row[2 - 1], &row[1 - 1]);
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ecp_nistz256_point_double(&row[4 - 1], &row[2 - 1]);
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ecp_nistz256_point_double(&row[6 - 1], &row[3 - 1]);
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ecp_nistz256_point_double(&row[8 - 1], &row[4 - 1]);
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ecp_nistz256_point_double(&row[12 - 1], &row[6 - 1]);
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ecp_nistz256_point_add(&row[5 - 1], &row[4 - 1], &row[1 - 1]);
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ecp_nistz256_point_add(&row[7 - 1], &row[6 - 1], &row[1 - 1]);
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ecp_nistz256_point_add(&row[9 - 1], &row[8 - 1], &row[1 - 1]);
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ecp_nistz256_point_add(&row[13 - 1], &row[12 - 1], &row[1 - 1]);
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ecp_nistz256_point_double(&row[14 - 1], &row[7 - 1]);
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ecp_nistz256_point_double(&row[10 - 1], &row[5 - 1]);
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ecp_nistz256_point_add(&row[15 - 1], &row[14 - 1], &row[1 - 1]);
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ecp_nistz256_point_add(&row[11 - 1], &row[10 - 1], &row[1 - 1]);
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ecp_nistz256_point_double(&row[16 - 1], &row[8 - 1]);
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BN_ULONG tmp[P256_LIMBS];
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alignas(32) P256_POINT h;
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unsigned index = 255;
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unsigned wvalue = p_str[(index - 1) / 8];
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wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
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ecp_nistz256_select_w5(r, table, booth_recode_w5(wvalue) >> 1);
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while (index >= 5) {
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if (index != 255) {
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unsigned off = (index - 1) / 8;
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wvalue = p_str[off] | p_str[off + 1] << 8;
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wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
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wvalue = booth_recode_w5(wvalue);
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ecp_nistz256_select_w5(&h, table, wvalue >> 1);
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ecp_nistz256_neg(tmp, h.Y);
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copy_conditional(h.Y, tmp, (wvalue & 1));
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ecp_nistz256_point_add(r, r, &h);
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}
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index -= kWindowSize;
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ecp_nistz256_point_double(r, r);
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ecp_nistz256_point_double(r, r);
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ecp_nistz256_point_double(r, r);
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ecp_nistz256_point_double(r, r);
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ecp_nistz256_point_double(r, r);
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}
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// Final window
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wvalue = p_str[0];
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wvalue = (wvalue << 1) & kMask;
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wvalue = booth_recode_w5(wvalue);
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ecp_nistz256_select_w5(&h, table, wvalue >> 1);
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ecp_nistz256_neg(tmp, h.Y);
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copy_conditional(h.Y, tmp, wvalue & 1);
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ecp_nistz256_point_add(r, r, &h);
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return 1;
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}
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static int ecp_nistz256_points_mul(const EC_GROUP *group, EC_POINT *r,
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const EC_SCALAR *g_scalar,
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const EC_POINT *p_,
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const EC_SCALAR *p_scalar, BN_CTX *ctx) {
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assert((p_ != NULL) == (p_scalar != NULL));
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static const unsigned kWindowSize = 7;
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static const unsigned kMask = (1 << (7 /* kWindowSize */ + 1)) - 1;
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alignas(32) union {
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P256_POINT p;
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P256_POINT_AFFINE a;
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} t, p;
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if (g_scalar != NULL) {
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uint8_t p_str[33];
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OPENSSL_memcpy(p_str, g_scalar->bytes, 32);
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p_str[32] = 0;
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// First window
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unsigned wvalue = (p_str[0] << 1) & kMask;
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unsigned index = kWindowSize;
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wvalue = booth_recode_w7(wvalue);
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const PRECOMP256_ROW *const precomputed_table =
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(const PRECOMP256_ROW *)ecp_nistz256_precomputed;
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ecp_nistz256_select_w7(&p.a, precomputed_table[0], wvalue >> 1);
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ecp_nistz256_neg(p.p.Z, p.p.Y);
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copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
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// Convert |p| from affine to Jacobian coordinates. We set Z to zero if |p|
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// is infinity and |ONE| otherwise. |p| was computed from the table, so it
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// is infinity iff |wvalue >> 1| is zero.
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OPENSSL_memset(p.p.Z, 0, sizeof(p.p.Z));
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copy_conditional(p.p.Z, ONE, is_not_zero(wvalue >> 1));
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for (int i = 1; i < 37; i++) {
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unsigned off = (index - 1) / 8;
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wvalue = p_str[off] | p_str[off + 1] << 8;
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wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
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index += kWindowSize;
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wvalue = booth_recode_w7(wvalue);
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ecp_nistz256_select_w7(&t.a, precomputed_table[i], wvalue >> 1);
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ecp_nistz256_neg(t.p.Z, t.a.Y);
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copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
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ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
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}
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}
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const int p_is_infinity = g_scalar == NULL;
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if (p_scalar != NULL) {
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P256_POINT *out = &t.p;
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if (p_is_infinity) {
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out = &p.p;
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}
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if (!ecp_nistz256_windowed_mul(group, out, p_, p_scalar)) {
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return 0;
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}
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if (!p_is_infinity) {
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ecp_nistz256_point_add(&p.p, &p.p, out);
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}
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}
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// Not constant-time, but we're only operating on the public output.
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if (!bn_set_words(&r->X, p.p.X, P256_LIMBS) ||
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!bn_set_words(&r->Y, p.p.Y, P256_LIMBS) ||
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!bn_set_words(&r->Z, p.p.Z, P256_LIMBS)) {
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return 0;
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}
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return 1;
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}
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static int ecp_nistz256_get_affine(const EC_GROUP *group, const EC_POINT *point,
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BIGNUM *x, BIGNUM *y, BN_CTX *ctx) {
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BN_ULONG z_inv2[P256_LIMBS];
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BN_ULONG z_inv3[P256_LIMBS];
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BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
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if (EC_POINT_is_at_infinity(group, point)) {
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OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
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return 0;
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}
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if (!ecp_nistz256_bignum_to_field_elem(point_x, &point->X) ||
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!ecp_nistz256_bignum_to_field_elem(point_y, &point->Y) ||
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!ecp_nistz256_bignum_to_field_elem(point_z, &point->Z)) {
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OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE);
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return 0;
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}
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ecp_nistz256_mod_inverse_mont(z_inv3, point_z);
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ecp_nistz256_sqr_mont(z_inv2, z_inv3);
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// Instead of using |ecp_nistz256_from_mont| to convert the |x| coordinate
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// and then calling |ecp_nistz256_from_mont| again to convert the |y|
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// coordinate below, convert the common factor |z_inv2| once now, saving one
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// reduction.
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ecp_nistz256_from_mont(z_inv2, z_inv2);
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if (x != NULL) {
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BN_ULONG x_aff[P256_LIMBS];
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ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
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if (!bn_set_words(x, x_aff, P256_LIMBS)) {
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OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
if (y != NULL) {
|
|
BN_ULONG y_aff[P256_LIMBS];
|
|
ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
|
|
ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
|
|
if (!bn_set_words(y, y_aff, P256_LIMBS)) {
|
|
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
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->mul = ecp_nistz256_points_mul;
|
|
out->mul_public = ecp_nistz256_points_mul;
|
|
out->field_mul = ec_GFp_mont_field_mul;
|
|
out->field_sqr = ec_GFp_mont_field_sqr;
|
|
out->field_encode = ec_GFp_mont_field_encode;
|
|
out->field_decode = ec_GFp_mont_field_decode;
|
|
};
|
|
|
|
#endif /* !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
|
|
!defined(OPENSSL_SMALL) */
|