blob: 52dd634afab8990bc9057f18c1d7797f8f3b7d82 [file] [log] [blame]
/* Copyright (c) 2014, Intel Corporation.
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
/* Developers and authors:
* Shay Gueron (1, 2), and Vlad Krasnov (1)
* (1) Intel Corporation, Israel Development Center
* (2) University of Haifa
* Reference:
* S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
* 256 Bit Primes" */
#include <openssl/ec.h>
#include <stdint.h>
#include <string.h>
#include <openssl/bn.h>
#include <openssl/crypto.h>
#include <openssl/err.h>
#include "../bn/internal.h"
#include "../ec/internal.h"
#include "../internal.h"
#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
!defined(OPENSSL_SMALL)
#if BN_BITS2 != 64
#define TOBN(hi, lo) lo, hi
#else
#define TOBN(hi, lo) ((BN_ULONG)hi << 32 | lo)
#endif
#if defined(__GNUC__)
#define ALIGN32 __attribute((aligned(32)))
#elif defined(_MSC_VER)
#define ALIGN32 __declspec(align(32))
#else
#define ALIGN32
#endif
#define ALIGNPTR(p, N) ((uint8_t *)p + N - (size_t)p % N)
#define P256_LIMBS (256 / BN_BITS2)
typedef struct {
BN_ULONG X[P256_LIMBS];
BN_ULONG Y[P256_LIMBS];
BN_ULONG Z[P256_LIMBS];
} P256_POINT;
typedef struct {
BN_ULONG X[P256_LIMBS];
BN_ULONG Y[P256_LIMBS];
} P256_POINT_AFFINE;
typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
/* Functions implemented in assembly */
/* Modular mul by 2: res = 2*a mod P */
void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS]);
/* Modular div by 2: res = a/2 mod P */
void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS]);
/* Modular mul by 3: res = 3*a mod P */
void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS]);
/* Modular add: res = a+b mod P */
void ecp_nistz256_add(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS],
const BN_ULONG b[P256_LIMBS]);
/* Modular sub: res = a-b mod P */
void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS],
const BN_ULONG b[P256_LIMBS]);
/* Modular neg: res = -a mod P */
void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
/* Montgomery mul: res = a*b*2^-256 mod P */
void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS],
const BN_ULONG b[P256_LIMBS]);
/* Montgomery sqr: res = a*a*2^-256 mod P */
void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS]);
/* Convert a number from Montgomery domain, by multiplying with 1 */
void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG in[P256_LIMBS]);
/* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG in[P256_LIMBS]);
/* Functions that perform constant time access to the precomputed tables */
void ecp_nistz256_select_w5(P256_POINT *val, const P256_POINT *in_t, int index);
void ecp_nistz256_select_w7(P256_POINT_AFFINE *val,
const P256_POINT_AFFINE *in_t, int index);
/* 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 ecp_nistputil.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);
}
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);
}
}
void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
void ecp_nistz256_point_add(P256_POINT *r, const P256_POINT *a,
const P256_POINT *b);
void ecp_nistz256_point_add_affine(P256_POINT *r, const P256_POINT *a,
const P256_POINT_AFFINE *b);
/* r = in^-1 mod p */
static void ecp_nistz256_mod_inverse(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(res, res, in);
memcpy(r, res, sizeof(res));
}
/* ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
* returns one if it fits. Otherwise it returns zero. */
static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
const BIGNUM *in) {
if (in->top > P256_LIMBS) {
return 0;
}
memset(out, 0, sizeof(BN_ULONG) * P256_LIMBS);
memcpy(out, in->d, sizeof(BN_ULONG) * in->top);
return 1;
}
/* r = sum(scalar[i]*point[i]) */
static int ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r,
const BIGNUM **scalar,
const EC_POINT **point, int num,
BN_CTX *ctx) {
static const unsigned kWindowSize = 5;
static const unsigned kMask = (1 << (5 /* kWindowSize */ + 1)) - 1;
void *table_storage = OPENSSL_malloc(num * 16 * sizeof(P256_POINT) + 64);
uint8_t(*p_str)[33] = OPENSSL_malloc(num * 33 * sizeof(uint8_t));
const BIGNUM **scalars = OPENSSL_malloc(num * sizeof(BIGNUM *));
int ret = 0;
BN_CTX *new_ctx = NULL;
int ctx_started = 0;
if (table_storage == NULL ||
p_str == NULL ||
scalars == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
P256_POINT(*table)[16] = (void *)ALIGNPTR(table_storage, 64);
int i;
for (i = 0; i < num; i++) {
P256_POINT *row = table[i];
if (BN_num_bits(scalar[i]) > 256 || BN_is_negative(scalar[i])) {
if (!ctx_started) {
if (ctx == NULL) {
new_ctx = BN_CTX_new();
if (new_ctx == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
ctx = new_ctx;
}
BN_CTX_start(ctx);
ctx_started = 1;
}
BIGNUM *mod = BN_CTX_get(ctx);
if (mod == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
if (!BN_nnmod(mod, scalar[i], &group->order, ctx)) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
goto err;
}
scalars[i] = mod;
} else {
scalars[i] = scalar[i];
}
int j;
for (j = 0; j < scalars[i]->top * BN_BYTES; j += BN_BYTES) {
BN_ULONG d = scalars[i]->d[j / BN_BYTES];
p_str[i][j + 0] = d & 0xff;
p_str[i][j + 1] = (d >> 8) & 0xff;
p_str[i][j + 2] = (d >> 16) & 0xff;
p_str[i][j + 3] = (d >>= 24) & 0xff;
if (BN_BYTES == 8) {
d >>= 8;
p_str[i][j + 4] = d & 0xff;
p_str[i][j + 5] = (d >> 8) & 0xff;
p_str[i][j + 6] = (d >> 16) & 0xff;
p_str[i][j + 7] = (d >> 24) & 0xff;
}
}
for (; j < 33; j++) {
p_str[i][j] = 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. */
if (!ecp_nistz256_bignum_to_field_elem(row[1 - 1].X, &point[i]->X) ||
!ecp_nistz256_bignum_to_field_elem(row[1 - 1].Y, &point[i]->Y) ||
!ecp_nistz256_bignum_to_field_elem(row[1 - 1].Z, &point[i]->Z)) {
OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE);
goto err;
}
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_add(&row[16 - 1], &row[15 - 1], &row[1 - 1]);
}
BN_ULONG tmp[P256_LIMBS];
ALIGN32 P256_POINT h;
unsigned index = 255;
unsigned wvalue = p_str[0][(index - 1) / 8];
wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
ecp_nistz256_select_w5(r, table[0], booth_recode_w5(wvalue) >> 1);
while (index >= 5) {
for (i = (index == 255 ? 1 : 0); i < num; i++) {
unsigned off = (index - 1) / 8;
wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
wvalue = booth_recode_w5(wvalue);
ecp_nistz256_select_w5(&h, table[i], 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 */
for (i = 0; i < num; i++) {
wvalue = p_str[i][0];
wvalue = (wvalue << 1) & kMask;
wvalue = booth_recode_w5(wvalue);
ecp_nistz256_select_w5(&h, table[i], wvalue >> 1);
ecp_nistz256_neg(tmp, h.Y);
copy_conditional(h.Y, tmp, wvalue & 1);
ecp_nistz256_point_add(r, r, &h);
}
ret = 1;
err:
OPENSSL_free(table_storage);
OPENSSL_free(p_str);
OPENSSL_free((BIGNUM**) scalars);
if (ctx_started) {
BN_CTX_end(ctx);
}
BN_CTX_free(new_ctx);
return ret;
}
/* r = scalar*G + sum(scalars[i]*points[i]) */
static int ecp_nistz256_points_mul(
const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num,
const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) {
static const unsigned kWindowSize = 7;
static const unsigned kMask = (1 << (7 /* kWindowSize */ + 1)) - 1;
ALIGN32 union {
P256_POINT p;
P256_POINT_AFFINE a;
} t, p;
int ret = 0;
BN_CTX *new_ctx = NULL;
int ctx_started = 0;
if (scalar == NULL && num == 0) {
return EC_POINT_set_to_infinity(group, r);
}
/* Need 256 bits for space for all coordinates. */
if (bn_wexpand(&r->X, P256_LIMBS) == NULL ||
bn_wexpand(&r->Y, P256_LIMBS) == NULL ||
bn_wexpand(&r->Z, P256_LIMBS) == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
r->X.top = P256_LIMBS;
r->Y.top = P256_LIMBS;
r->Z.top = P256_LIMBS;
if (scalar) {
if (BN_num_bits(scalar) > 256 || BN_is_negative(scalar)) {
if (ctx == NULL) {
new_ctx = BN_CTX_new();
if (new_ctx == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
ctx = new_ctx;
}
BN_CTX_start(ctx);
ctx_started = 1;
BIGNUM *tmp_scalar = BN_CTX_get(ctx);
if (tmp_scalar == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
goto err;
}
scalar = tmp_scalar;
}
uint8_t p_str[33] = {0};
int i;
for (i = 0; i < scalar->top * BN_BYTES; i += BN_BYTES) {
BN_ULONG d = scalar->d[i / BN_BYTES];
p_str[i + 0] = d & 0xff;
p_str[i + 1] = (d >> 8) & 0xff;
p_str[i + 2] = (d >> 16) & 0xff;
p_str[i + 3] = (d >>= 24) & 0xff;
if (BN_BYTES == 8) {
d >>= 8;
p_str[i + 4] = d & 0xff;
p_str[i + 5] = (d >> 8) & 0xff;
p_str[i + 6] = (d >> 16) & 0xff;
p_str[i + 7] = (d >> 24) & 0xff;
}
}
for (; i < (int) sizeof(p_str); i++) {
p_str[i] = 0;
}
/* First window */
unsigned wvalue = (p_str[0] << 1) & kMask;
unsigned index = kWindowSize;
wvalue = booth_recode_w7(wvalue);
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);
memcpy(p.p.Z, ONE, sizeof(ONE));
for (i = 1; i < 37; i++) {
unsigned off = (index - 1) / 8;
wvalue = p_str[off] | p_str[off + 1] << 8;
wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
index += kWindowSize;
wvalue = booth_recode_w7(wvalue);
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);
}
}
const int p_is_infinity = !scalar;
if (num) {
P256_POINT *out = &t.p;
if (p_is_infinity) {
out = &p.p;
}
if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx)) {
goto err;
}
if (!p_is_infinity) {
ecp_nistz256_point_add(&p.p, &p.p, out);
}
}
memcpy(r->X.d, p.p.X, sizeof(p.p.X));
memcpy(r->Y.d, p.p.Y, sizeof(p.p.Y));
memcpy(r->Z.d, p.p.Z, sizeof(p.p.Z));
/* Not constant-time, but we're only operating on the public output. */
bn_correct_top(&r->X);
bn_correct_top(&r->Y);
bn_correct_top(&r->Z);
r->Z_is_one = BN_is_one(&r->Z);
ret = 1;
err:
if (ctx_started) {
BN_CTX_end(ctx);
}
BN_CTX_free(new_ctx);
return ret;
}
static int ecp_nistz256_get_affine(const EC_GROUP *group, const EC_POINT *point,
BIGNUM *x, BIGNUM *y, BN_CTX *ctx) {
BN_ULONG z_inv2[P256_LIMBS];
BN_ULONG z_inv3[P256_LIMBS];
BN_ULONG x_aff[P256_LIMBS];
BN_ULONG y_aff[P256_LIMBS];
BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
if (EC_POINT_is_at_infinity(group, point)) {
OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
return 0;
}
if (!ecp_nistz256_bignum_to_field_elem(point_x, &point->X) ||
!ecp_nistz256_bignum_to_field_elem(point_y, &point->Y) ||
!ecp_nistz256_bignum_to_field_elem(point_z, &point->Z)) {
OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE);
return 0;
}
ecp_nistz256_mod_inverse(z_inv3, point_z);
ecp_nistz256_sqr_mont(z_inv2, z_inv3);
ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
if (x != NULL) {
if (bn_wexpand(x, P256_LIMBS) == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
return 0;
}
x->top = P256_LIMBS;
ecp_nistz256_from_mont(x->d, x_aff);
bn_correct_top(x);
}
if (y != NULL) {
ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
if (bn_wexpand(y, P256_LIMBS) == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
return 0;
}
y->top = P256_LIMBS;
ecp_nistz256_from_mont(y->d, y_aff);
bn_correct_top(y);
}
return 1;
}
const EC_METHOD *EC_GFp_nistz256_method(void) {
static const EC_METHOD ret = {
ec_GFp_mont_group_init,
ec_GFp_mont_group_finish,
ec_GFp_mont_group_clear_finish,
ec_GFp_mont_group_copy,
ec_GFp_mont_group_set_curve,
ecp_nistz256_get_affine,
ecp_nistz256_points_mul,
ec_GFp_mont_field_mul,
ec_GFp_mont_field_sqr,
ec_GFp_mont_field_encode,
ec_GFp_mont_field_decode,
ec_GFp_mont_field_set_to_one,
};
return &ret;
}
#endif /* !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
!defined(OPENSSL_SMALL) */