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- /* 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 <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 "../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);
- }
-
- /* 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 = p * p_scalar */
- static int ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r,
- const EC_POINT *p, const BIGNUM *p_scalar,
- BN_CTX *ctx) {
- assert(p != NULL);
- assert(p_scalar != NULL);
-
- 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];
-
-
- int ret = 0;
- BN_CTX *new_ctx = NULL;
- int ctx_started = 0;
-
- if (BN_num_bits(p_scalar) > 256 || BN_is_negative(p_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 *mod = BN_CTX_get(ctx);
- if (mod == NULL) {
- OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
- goto err;
- }
- if (!BN_nnmod(mod, p_scalar, &group->order, ctx)) {
- OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
- goto err;
- }
- p_scalar = mod;
- }
-
- int j;
- for (j = 0; j < p_scalar->top * BN_BYTES; j += BN_BYTES) {
- BN_ULONG d = p_scalar->d[j / BN_BYTES];
-
- p_str[j + 0] = d & 0xff;
- p_str[j + 1] = (d >> 8) & 0xff;
- p_str[j + 2] = (d >> 16) & 0xff;
- p_str[j + 3] = (d >>= 24) & 0xff;
- if (BN_BYTES == 8) {
- d >>= 8;
- p_str[j + 4] = d & 0xff;
- p_str[j + 5] = (d >> 8) & 0xff;
- p_str[j + 6] = (d >> 16) & 0xff;
- p_str[j + 7] = (d >> 24) & 0xff;
- }
- }
-
- for (; j < 33; j++) {
- p_str[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. */
- P256_POINT *row = table;
-
- if (!ecp_nistz256_bignum_to_field_elem(row[1 - 1].X, &p->X) ||
- !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Y, &p->Y) ||
- !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Z, &p->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_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);
-
- ret = 1;
-
- err:
- if (ctx_started) {
- BN_CTX_end(ctx);
- }
- BN_CTX_free(new_ctx);
- return ret;
- }
-
- static int ecp_nistz256_points_mul(
- const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
- const EC_POINT *p_, const BIGNUM *p_scalar, BN_CTX *ctx) {
- assert((p_ != NULL) == (p_scalar != NULL));
-
- static const unsigned kWindowSize = 7;
- static const unsigned kMask = (1 << (7 /* kWindowSize */ + 1)) - 1;
-
- alignas(32) union {
- P256_POINT p;
- P256_POINT_AFFINE a;
- } t, p;
-
- int ret = 0;
- BN_CTX *new_ctx = NULL;
- int ctx_started = 0;
-
- if (g_scalar != NULL) {
- if (BN_num_bits(g_scalar) > 256 || BN_is_negative(g_scalar)) {
- if (ctx == NULL) {
- new_ctx = BN_CTX_new();
- if (new_ctx == NULL) {
- goto err;
- }
- ctx = new_ctx;
- }
- BN_CTX_start(ctx);
- ctx_started = 1;
- BIGNUM *tmp_scalar = BN_CTX_get(ctx);
- if (tmp_scalar == NULL) {
- goto err;
- }
-
- if (!BN_nnmod(tmp_scalar, g_scalar, &group->order, ctx)) {
- OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
- goto err;
- }
- g_scalar = tmp_scalar;
- }
-
- uint8_t p_str[33] = {0};
- int i;
- for (i = 0; i < g_scalar->top * BN_BYTES; i += BN_BYTES) {
- BN_ULONG d = g_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);
-
- /* 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. */
- memset(p.p.Z, 0, sizeof(p.p.Z));
- copy_conditional(p.p.Z, ONE, is_not_zero(wvalue >> 1));
-
- 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 = g_scalar == NULL;
- if (p_scalar != NULL) {
- P256_POINT *out = &t.p;
- if (p_is_infinity) {
- out = &p.p;
- }
-
- if (!ecp_nistz256_windowed_mul(group, out, p_, p_scalar, ctx)) {
- goto err;
- }
-
- if (!p_is_infinity) {
- ecp_nistz256_point_add(&p.p, &p.p, out);
- }
- }
-
- /* Not constant-time, but we're only operating on the public output. */
- if (!bn_set_words(&r->X, p.p.X, P256_LIMBS) ||
- !bn_set_words(&r->Y, p.p.Y, P256_LIMBS) ||
- !bn_set_words(&r->Z, p.p.Z, P256_LIMBS)) {
- return 0;
- }
-
- 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 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_mont(z_inv3, point_z);
- ecp_nistz256_sqr_mont(z_inv2, z_inv3);
-
- /* TODO(davidben): The two calls to |ecp_nistz256_from_mont| may be factored
- * into one call now that other operations also reduce mod P. */
-
- if (x != NULL) {
- BN_ULONG x_aff[P256_LIMBS];
- ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
- ecp_nistz256_from_mont(x_aff, x_aff);
- if (!bn_set_words(x, x_aff, P256_LIMBS)) {
- 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);
- ecp_nistz256_from_mont(y_aff, y_aff);
- if (!bn_set_words(y, y_aff, P256_LIMBS)) {
- OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
- return 0;
- }
- }
-
- return 1;
- }
-
-
- const EC_METHOD EC_GFp_nistz256_method = {
- ec_GFp_mont_group_init,
- ec_GFp_mont_group_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,
- };
-
- #endif /* !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
- !defined(OPENSSL_SMALL) */
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