/*
- * Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright 2014-2020 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright (c) 2014, Intel Corporation. All Rights Reserved.
+ * Copyright (c) 2015, CloudFlare, Inc.
*
- * Licensed under the OpenSSL license (the "License"). You may not use
+ * Licensed under the Apache License 2.0 (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, 3)
+ * (1) Intel Corporation, Israel Development Center, Haifa, Israel
+ * (2) University of Haifa, Israel
+ * (3) CloudFlare, Inc.
+ *
+ * Reference:
+ * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
+ * 256 Bit Primes"
*/
-/******************************************************************************
- * *
- * Copyright 2014 Intel Corporation *
- * *
- * Licensed under the Apache License, Version 2.0 (the "License"); *
- * you may not use this file except in compliance with the License. *
- * You may obtain a copy of the License at *
- * *
- * http://www.apache.org/licenses/LICENSE-2.0 *
- * *
- * Unless required by applicable law or agreed to in writing, software *
- * distributed under the License is distributed on an "AS IS" BASIS, *
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
- * See the License for the specific language governing permissions and *
- * limitations under the License. *
- * *
- ******************************************************************************
- * *
- * 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" *
- * *
- ******************************************************************************/
+/*
+ * ECDSA low level APIs are deprecated for public use, but still ok for
+ * internal use.
+ */
+#include "internal/deprecated.h"
#include <string.h>
#include "internal/cryptlib.h"
-#include "internal/bn_int.h"
-#include "ec_lcl.h"
+#include "crypto/bn.h"
+#include "ec_local.h"
+#include "internal/refcount.h"
#if BN_BITS2 != 64
# define TOBN(hi,lo) lo,hi
*/
PRECOMP256_ROW *precomp;
void *precomp_storage;
- int references;
+ CRYPTO_REF_COUNT references;
CRYPTO_RWLOCK *lock;
};
return res;
}
+/*
+ * For reference, this macro is used only when new ecp_nistz256 assembly
+ * module is being developed. For example, configure with
+ * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions
+ * performing simplest arithmetic operations on 256-bit vectors. Then
+ * work on implementation of higher-level functions performing point
+ * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION
+ * and never define it again. (The correct macro denoting presence of
+ * ecp_nistz256 module is ECP_NISTZ256_ASM.)
+ */
#ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
void ecp_nistz256_point_add(P256_POINT *r,
ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
/*
- * This should not happen during sign/ecdh, so no constant time violation
+ * The formulae are incorrect if the points are equal so we check for
+ * this and do doubling if this happens.
+ *
+ * Points here are in Jacobian projective coordinates (Xi, Yi, Zi)
+ * that are bound to the affine coordinates (xi, yi) by the following
+ * equations:
+ * - xi = Xi / (Zi)^2
+ * - y1 = Yi / (Zi)^3
+ *
+ * For the sake of optimization, the algorithm operates over
+ * intermediate variables U1, U2 and S1, S2 that are derived from
+ * the projective coordinates:
+ * - U1 = X1 * (Z2)^2 ; U2 = X2 * (Z1)^2
+ * - S1 = Y1 * (Z2)^3 ; S2 = Y2 * (Z1)^3
+ *
+ * It is easy to prove that is_equal(U1, U2) implies that the affine
+ * x-coordinates are equal, or either point is at infinity.
+ * Likewise is_equal(S1, S2) implies that the affine y-coordinates are
+ * equal, or either point is at infinity.
+ *
+ * The special case of either point being the point at infinity (Z1 or Z2
+ * is zero), is handled separately later on in this function, so we avoid
+ * jumping to point_double here in those special cases.
+ *
+ * When both points are inverse of each other, we know that the affine
+ * x-coordinates are equal, and the y-coordinates have different sign.
+ * Therefore since U1 = U2, we know H = 0, and therefore Z3 = H*Z1*Z2
+ * will equal 0, thus the result is infinity, if we simply let this
+ * function continue normally.
+ *
+ * We use bitwise operations to avoid potential side-channels introduced by
+ * the short-circuiting behaviour of boolean operators.
*/
- if (is_equal(U1, U2) && !in1infty && !in2infty) {
- if (is_equal(S1, S2)) {
- ecp_nistz256_point_double(r, a);
- return;
- } else {
- memset(r, 0, sizeof(*r));
- return;
- }
+ if (is_equal(U1, U2) & ~in1infty & ~in2infty & is_equal(S1, S2)) {
+ /*
+ * This is obviously not constant-time but it should never happen during
+ * single point multiplication, so there is no timing leak for ECDH or
+ * ECDSA signing.
+ */
+ ecp_nistz256_point_double(r, a);
+ return;
}
ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
}
/* Coordinates of G, for which we have precomputed tables */
-const static BN_ULONG def_xG[P256_LIMBS] = {
+static const BN_ULONG def_xG[P256_LIMBS] = {
TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
};
-const static BN_ULONG def_yG[P256_LIMBS] = {
+static const BN_ULONG def_yG[P256_LIMBS] = {
TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
};
return 0;
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
goto err;
}
* It would be faster to use EC_POINTs_make_affine and
* make multiple points affine at the same time.
*/
- if (!EC_POINT_make_affine(group, P, ctx))
+ if (group->meth->make_affine == NULL
+ || !group->meth->make_affine(group, P, ctx))
goto err;
if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
!ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
ret = 1;
err:
- if (ctx != NULL)
- BN_CTX_end(ctx);
+ BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
EC_nistz256_pre_comp_free(pre_comp);
*/
#if defined(ECP_NISTZ256_AVX2)
# if !(defined(__x86_64) || defined(__x86_64__) || \
- defined(_M_AMD64) || defined(_MX64)) || \
+ defined(_M_AMD64) || defined(_M_X64)) || \
!(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
# undef ECP_NISTZ256_AVX2
# else
const P256_POINT_AFFINE *in,
BN_CTX *ctx)
{
- BIGNUM *x, *y;
- BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
int ret = 0;
- x = BN_new();
- if (x == NULL)
- return 0;
- y = BN_new();
- if (y == NULL) {
- BN_free(x);
- return 0;
- }
- memcpy(d_x, in->X, sizeof(d_x));
- bn_set_static_words(x, d_x, P256_LIMBS);
-
- memcpy(d_y, in->Y, sizeof(d_y));
- bn_set_static_words(y, d_y, P256_LIMBS);
-
- ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
-
- BN_free(x);
- BN_free(y);
+ if ((ret = bn_set_words(out->X, in->X, P256_LIMBS))
+ && (ret = bn_set_words(out->Y, in->Y, P256_LIMBS))
+ && (ret = bn_set_words(out->Z, ONE, P256_LIMBS)))
+ out->Z_is_one = 1;
return ret;
}
const BIGNUM *scalars[], BN_CTX *ctx)
{
int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
- size_t j;
unsigned char p_str[33] = { 0 };
const PRECOMP256_ROW *preComputedTable = NULL;
const NISTZ256_PRE_COMP *pre_comp = NULL;
const EC_POINT *generator = NULL;
- BN_CTX *new_ctx = NULL;
const BIGNUM **new_scalars = NULL;
const EC_POINT **new_points = NULL;
unsigned int idx = 0;
return 0;
}
- if (group->meth != r->meth) {
- ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
- return 0;
- }
-
- if ((scalar == NULL) && (num == 0))
- return EC_POINT_set_to_infinity(group, r);
-
- for (j = 0; j < num; j++) {
- if (group->meth != points[j]->meth) {
- ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
- return 0;
- }
- }
-
- if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
- if (ctx == NULL)
- goto err;
- }
-
BN_CTX_start(ctx);
if (scalar) {
if (pre_comp_generator == NULL)
goto err;
+ ecp_nistz256_gather_w7(&p.a, pre_comp->precomp[0], 1);
if (!ecp_nistz256_set_from_affine(pre_comp_generator,
- group, pre_comp->precomp[0],
- ctx)) {
+ group, &p.a, ctx)) {
EC_POINT_free(pre_comp_generator);
goto err;
}
ret = 1;
err:
- if (ctx)
- BN_CTX_end(ctx);
- BN_CTX_free(new_ctx);
+ BN_CTX_end(ctx);
OPENSSL_free(new_points);
OPENSSL_free(new_scalars);
return ret;
{
int i;
if (p != NULL)
- CRYPTO_atomic_add(&p->references, 1, &i, p->lock);
+ CRYPTO_UP_REF(&p->references, &i, p->lock);
return p;
}
if (pre == NULL)
return;
- CRYPTO_atomic_add(&pre->references, -1, &i, pre->lock);
- REF_PRINT_COUNT("EC_nistz256", x);
+ CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
+ REF_PRINT_COUNT("EC_nistz256", pre);
if (i > 0)
return;
REF_ASSERT_ISNT(i < 0);
return HAVEPRECOMP(group, nistz256);
}
+#if defined(__x86_64) || defined(__x86_64__) || \
+ defined(_M_AMD64) || defined(_M_X64) || \
+ defined(__powerpc64__) || defined(_ARCH_PP64) || \
+ defined(__aarch64__)
+/*
+ * Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P)
+ */
+void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG a[P256_LIMBS],
+ const BN_ULONG b[P256_LIMBS]);
+void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS],
+ const BN_ULONG a[P256_LIMBS],
+ BN_ULONG rep);
+
+static int ecp_nistz256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r,
+ const BIGNUM *x, BN_CTX *ctx)
+{
+ /* RR = 2^512 mod ord(p256) */
+ static const BN_ULONG RR[P256_LIMBS] = {
+ TOBN(0x83244c95,0xbe79eea2), TOBN(0x4699799c,0x49bd6fa6),
+ TOBN(0x2845b239,0x2b6bec59), TOBN(0x66e12d94,0xf3d95620)
+ };
+ /* The constant 1 (unlike ONE that is one in Montgomery representation) */
+ static const BN_ULONG one[P256_LIMBS] = {
+ TOBN(0,1), TOBN(0,0), TOBN(0,0), TOBN(0,0)
+ };
+ /*
+ * We don't use entry 0 in the table, so we omit it and address
+ * with -1 offset.
+ */
+ BN_ULONG table[15][P256_LIMBS];
+ BN_ULONG out[P256_LIMBS], t[P256_LIMBS];
+ int i, ret = 0;
+ enum {
+ i_1 = 0, i_10, i_11, i_101, i_111, i_1010, i_1111,
+ i_10101, i_101010, i_101111, i_x6, i_x8, i_x16, i_x32
+ };
+
+ /*
+ * Catch allocation failure early.
+ */
+ if (bn_wexpand(r, P256_LIMBS) == NULL) {
+ ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB);
+ goto err;
+ }
+
+ if ((BN_num_bits(x) > 256) || BN_is_negative(x)) {
+ BIGNUM *tmp;
+
+ if ((tmp = BN_CTX_get(ctx)) == NULL
+ || !BN_nnmod(tmp, x, group->order, ctx)) {
+ ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB);
+ goto err;
+ }
+ x = tmp;
+ }
+
+ if (!ecp_nistz256_bignum_to_field_elem(t, x)) {
+ ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, EC_R_COORDINATES_OUT_OF_RANGE);
+ goto err;
+ }
+
+ ecp_nistz256_ord_mul_mont(table[0], t, RR);
+#if 0
+ /*
+ * Original sparse-then-fixed-window algorithm, retained for reference.
+ */
+ for (i = 2; i < 16; i += 2) {
+ ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1);
+ ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]);
+ }
+
+ /*
+ * The top 128bit of the exponent are highly redudndant, so we
+ * perform an optimized flow
+ */
+ ecp_nistz256_ord_sqr_mont(t, table[15-1], 4); /* f0 */
+ ecp_nistz256_ord_mul_mont(t, t, table[15-1]); /* ff */
+
+ ecp_nistz256_ord_sqr_mont(out, t, 8); /* ff00 */
+ ecp_nistz256_ord_mul_mont(out, out, t); /* ffff */
+
+ ecp_nistz256_ord_sqr_mont(t, out, 16); /* ffff0000 */
+ ecp_nistz256_ord_mul_mont(t, t, out); /* ffffffff */
+
+ ecp_nistz256_ord_sqr_mont(out, t, 64); /* ffffffff0000000000000000 */
+ ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffff */
+
+ ecp_nistz256_ord_sqr_mont(out, out, 32); /* ffffffff00000000ffffffff00000000 */
+ ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffffffffffff */
+
+ /*
+ * The bottom 128 bit of the exponent are processed with fixed 4-bit window
+ */
+ for(i = 0; i < 32; i++) {
+ /* expLo - the low 128 bits of the exponent we use (ord(p256) - 2),
+ * split into nibbles */
+ static const unsigned char expLo[32] = {
+ 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4,
+ 0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf
+ };
+
+ ecp_nistz256_ord_sqr_mont(out, out, 4);
+ /* The exponent is public, no need in constant-time access */
+ ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]);
+ }
+#else
+ /*
+ * 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%, on grand scale sign operation is not that
+ * much faster, not more that 2%...
+ */
+
+ /* pre-calculate powers */
+ 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]);
+
+ /* calculations */
+ ecp_nistz256_ord_sqr_mont(out, table[i_x32], 64);
+ ecp_nistz256_ord_mul_mont(out, out, table[i_x32]);
+
+ for (i = 0; i < 27; i++) {
+ static const struct { unsigned char p, i; } chain[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 }
+ };
+
+ ecp_nistz256_ord_sqr_mont(out, out, chain[i].p);
+ ecp_nistz256_ord_mul_mont(out, out, table[chain[i].i]);
+ }
+#endif
+ ecp_nistz256_ord_mul_mont(out, out, one);
+
+ /*
+ * Can't fail, but check return code to be consistent anyway.
+ */
+ if (!bn_set_words(r, out, P256_LIMBS))
+ goto err;
+
+ ret = 1;
+err:
+ return ret;
+}
+#else
+# define ecp_nistz256_inv_mod_ord NULL
+#endif
+
const EC_METHOD *EC_GFp_nistz256_method(void)
{
static const EC_METHOD ret = {
ec_GFp_simple_point_clear_finish,
ec_GFp_simple_point_copy,
ec_GFp_simple_point_set_to_infinity,
- ec_GFp_simple_set_Jprojective_coordinates_GFp,
- ec_GFp_simple_get_Jprojective_coordinates_GFp,
ec_GFp_simple_point_set_affine_coordinates,
ecp_nistz256_get_affine,
0, 0, 0,
ec_GFp_mont_field_mul,
ec_GFp_mont_field_sqr,
0, /* field_div */
+ ec_GFp_mont_field_inv,
ec_GFp_mont_field_encode,
ec_GFp_mont_field_decode,
ec_GFp_mont_field_set_to_one,
ec_key_simple_generate_public_key,
0, /* keycopy */
0, /* keyfinish */
- ecdh_simple_compute_key
+ ecdh_simple_compute_key,
+ ecdsa_simple_sign_setup,
+ ecdsa_simple_sign_sig,
+ ecdsa_simple_verify_sig,
+ ecp_nistz256_inv_mod_ord, /* can be #define-d NULL */
+ 0, /* blind_coordinates */
+ 0, /* ladder_pre */
+ 0, /* ladder_step */
+ 0 /* ladder_post */
};
return &ret;
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