-/* TODO */
-/* crypto/ec/ecp_smpl.c */
-/* ====================================================================
- * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in
- * the documentation and/or other materials provided with the
- * distribution.
- *
- * 3. All advertising materials mentioning features or use of this
- * software must display the following acknowledgment:
- * "This product includes software developed by the OpenSSL Project
- * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
- *
- * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
- * endorse or promote products derived from this software without
- * prior written permission. For written permission, please contact
- * openssl-core@openssl.org.
+/*
+ * Copyright 2001-2019 The OpenSSL Project Authors. All Rights Reserved.
*
- * 5. Products derived from this software may not be called "OpenSSL"
- * nor may "OpenSSL" appear in their names without prior written
- * permission of the OpenSSL Project.
- *
- * 6. Redistributions of any form whatsoever must retain the following
- * acknowledgment:
- * "This product includes software developed by the OpenSSL Project
- * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
+ * 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
+ */
+
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ * Portions of this software developed by SUN MICROSYSTEMS, INC.,
+ * and contributed to the OpenSSL project.
+ */
+
+#include <openssl/err.h>
+#include <openssl/symhacks.h>
+
+#include "ec_lcl.h"
+
+const EC_METHOD *EC_GFp_simple_method(void)
+{
+ static const EC_METHOD ret = {
+ EC_FLAGS_DEFAULT_OCT,
+ NID_X9_62_prime_field,
+ ec_GFp_simple_group_init,
+ ec_GFp_simple_group_finish,
+ ec_GFp_simple_group_clear_finish,
+ ec_GFp_simple_group_copy,
+ ec_GFp_simple_group_set_curve,
+ ec_GFp_simple_group_get_curve,
+ ec_GFp_simple_group_get_degree,
+ ec_group_simple_order_bits,
+ ec_GFp_simple_group_check_discriminant,
+ ec_GFp_simple_point_init,
+ ec_GFp_simple_point_finish,
+ 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,
+ ec_GFp_simple_point_get_affine_coordinates,
+ 0, 0, 0,
+ ec_GFp_simple_add,
+ ec_GFp_simple_dbl,
+ ec_GFp_simple_invert,
+ ec_GFp_simple_is_at_infinity,
+ ec_GFp_simple_is_on_curve,
+ ec_GFp_simple_cmp,
+ ec_GFp_simple_make_affine,
+ ec_GFp_simple_points_make_affine,
+ 0 /* mul */ ,
+ 0 /* precompute_mult */ ,
+ 0 /* have_precompute_mult */ ,
+ ec_GFp_simple_field_mul,
+ ec_GFp_simple_field_sqr,
+ 0 /* field_div */ ,
+ ec_GFp_simple_field_inv,
+ 0 /* field_encode */ ,
+ 0 /* field_decode */ ,
+ 0, /* field_set_to_one */
+ ec_key_simple_priv2oct,
+ ec_key_simple_oct2priv,
+ 0, /* set private */
+ ec_key_simple_generate_key,
+ ec_key_simple_check_key,
+ ec_key_simple_generate_public_key,
+ 0, /* keycopy */
+ 0, /* keyfinish */
+ ecdh_simple_compute_key,
+ ec_GFp_simple_blind_coordinates
+ };
+
+ return &ret;
+}
+
+/*
+ * Most method functions in this file are designed to work with
+ * non-trivial representations of field elements if necessary
+ * (see ecp_mont.c): while standard modular addition and subtraction
+ * are used, the field_mul and field_sqr methods will be used for
+ * multiplication, and field_encode and field_decode (if defined)
+ * will be used for converting between representations.
*
- * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
- * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
- * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
- * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
- * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
- * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
- * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
- * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
- * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
- * OF THE POSSIBILITY OF SUCH DAMAGE.
- * ====================================================================
+ * Functions ec_GFp_simple_points_make_affine() and
+ * ec_GFp_simple_point_get_affine_coordinates() specifically assume
+ * that if a non-trivial representation is used, it is a Montgomery
+ * representation (i.e. 'encoding' means multiplying by some factor R).
+ */
+
+int ec_GFp_simple_group_init(EC_GROUP *group)
+{
+ group->field = BN_new();
+ group->a = BN_new();
+ group->b = BN_new();
+ if (group->field == NULL || group->a == NULL || group->b == NULL) {
+ BN_free(group->field);
+ BN_free(group->a);
+ BN_free(group->b);
+ return 0;
+ }
+ group->a_is_minus3 = 0;
+ return 1;
+}
+
+void ec_GFp_simple_group_finish(EC_GROUP *group)
+{
+ BN_free(group->field);
+ BN_free(group->a);
+ BN_free(group->b);
+}
+
+void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
+{
+ BN_clear_free(group->field);
+ BN_clear_free(group->a);
+ BN_clear_free(group->b);
+}
+
+int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
+{
+ if (!BN_copy(dest->field, src->field))
+ return 0;
+ if (!BN_copy(dest->a, src->a))
+ return 0;
+ if (!BN_copy(dest->b, src->b))
+ return 0;
+
+ dest->a_is_minus3 = src->a_is_minus3;
+
+ return 1;
+}
+
+int ec_GFp_simple_group_set_curve(EC_GROUP *group,
+ const BIGNUM *p, const BIGNUM *a,
+ const BIGNUM *b, BN_CTX *ctx)
+{
+ int ret = 0;
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *tmp_a;
+
+ /* p must be a prime > 3 */
+ if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
+ ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
+ return 0;
+ }
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ BN_CTX_start(ctx);
+ tmp_a = BN_CTX_get(ctx);
+ if (tmp_a == NULL)
+ goto err;
+
+ /* group->field */
+ if (!BN_copy(group->field, p))
+ goto err;
+ BN_set_negative(group->field, 0);
+
+ /* group->a */
+ if (!BN_nnmod(tmp_a, a, p, ctx))
+ goto err;
+ if (group->meth->field_encode) {
+ if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
+ goto err;
+ } else if (!BN_copy(group->a, tmp_a))
+ goto err;
+
+ /* group->b */
+ if (!BN_nnmod(group->b, b, p, ctx))
+ goto err;
+ if (group->meth->field_encode)
+ if (!group->meth->field_encode(group, group->b, group->b, ctx))
+ goto err;
+
+ /* group->a_is_minus3 */
+ if (!BN_add_word(tmp_a, 3))
+ goto err;
+ group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
+ BIGNUM *b, BN_CTX *ctx)
+{
+ int ret = 0;
+ BN_CTX *new_ctx = NULL;
+
+ if (p != NULL) {
+ if (!BN_copy(p, group->field))
+ return 0;
+ }
+
+ if (a != NULL || b != NULL) {
+ if (group->meth->field_decode) {
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+ if (a != NULL) {
+ if (!group->meth->field_decode(group, a, group->a, ctx))
+ goto err;
+ }
+ if (b != NULL) {
+ if (!group->meth->field_decode(group, b, group->b, ctx))
+ goto err;
+ }
+ } else {
+ if (a != NULL) {
+ if (!BN_copy(a, group->a))
+ goto err;
+ }
+ if (b != NULL) {
+ if (!BN_copy(b, group->b))
+ goto err;
+ }
+ }
+ }
+
+ ret = 1;
+
+ err:
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
+{
+ return BN_num_bits(group->field);
+}
+
+int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
+{
+ int ret = 0;
+ BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
+ const BIGNUM *p = group->field;
+ BN_CTX *new_ctx = NULL;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL) {
+ ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
+ ERR_R_MALLOC_FAILURE);
+ goto err;
+ }
+ }
+ BN_CTX_start(ctx);
+ a = BN_CTX_get(ctx);
+ b = BN_CTX_get(ctx);
+ tmp_1 = BN_CTX_get(ctx);
+ tmp_2 = BN_CTX_get(ctx);
+ order = BN_CTX_get(ctx);
+ if (order == NULL)
+ goto err;
+
+ if (group->meth->field_decode) {
+ if (!group->meth->field_decode(group, a, group->a, ctx))
+ goto err;
+ if (!group->meth->field_decode(group, b, group->b, ctx))
+ goto err;
+ } else {
+ if (!BN_copy(a, group->a))
+ goto err;
+ if (!BN_copy(b, group->b))
+ goto err;
+ }
+
+ /*-
+ * check the discriminant:
+ * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
+ * 0 =< a, b < p
+ */
+ if (BN_is_zero(a)) {
+ if (BN_is_zero(b))
+ goto err;
+ } else if (!BN_is_zero(b)) {
+ if (!BN_mod_sqr(tmp_1, a, p, ctx))
+ goto err;
+ if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
+ goto err;
+ if (!BN_lshift(tmp_1, tmp_2, 2))
+ goto err;
+ /* tmp_1 = 4*a^3 */
+
+ if (!BN_mod_sqr(tmp_2, b, p, ctx))
+ goto err;
+ if (!BN_mul_word(tmp_2, 27))
+ goto err;
+ /* tmp_2 = 27*b^2 */
+
+ if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
+ goto err;
+ if (BN_is_zero(a))
+ goto err;
+ }
+ ret = 1;
+
+ err:
+ if (ctx != NULL)
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_point_init(EC_POINT *point)
+{
+ point->X = BN_new();
+ point->Y = BN_new();
+ point->Z = BN_new();
+ point->Z_is_one = 0;
+
+ if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
+ BN_free(point->X);
+ BN_free(point->Y);
+ BN_free(point->Z);
+ return 0;
+ }
+ return 1;
+}
+
+void ec_GFp_simple_point_finish(EC_POINT *point)
+{
+ BN_free(point->X);
+ BN_free(point->Y);
+ BN_free(point->Z);
+}
+
+void ec_GFp_simple_point_clear_finish(EC_POINT *point)
+{
+ BN_clear_free(point->X);
+ BN_clear_free(point->Y);
+ BN_clear_free(point->Z);
+ point->Z_is_one = 0;
+}
+
+int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
+{
+ if (!BN_copy(dest->X, src->X))
+ return 0;
+ if (!BN_copy(dest->Y, src->Y))
+ return 0;
+ if (!BN_copy(dest->Z, src->Z))
+ return 0;
+ dest->Z_is_one = src->Z_is_one;
+ dest->curve_name = src->curve_name;
+
+ return 1;
+}
+
+int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
+ EC_POINT *point)
+{
+ point->Z_is_one = 0;
+ BN_zero(point->Z);
+ return 1;
+}
+
+int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
+ EC_POINT *point,
+ const BIGNUM *x,
+ const BIGNUM *y,
+ const BIGNUM *z,
+ BN_CTX *ctx)
+{
+ BN_CTX *new_ctx = NULL;
+ int ret = 0;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ if (x != NULL) {
+ if (!BN_nnmod(point->X, x, group->field, ctx))
+ goto err;
+ if (group->meth->field_encode) {
+ if (!group->meth->field_encode(group, point->X, point->X, ctx))
+ goto err;
+ }
+ }
+
+ if (y != NULL) {
+ if (!BN_nnmod(point->Y, y, group->field, ctx))
+ goto err;
+ if (group->meth->field_encode) {
+ if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
+ goto err;
+ }
+ }
+
+ if (z != NULL) {
+ int Z_is_one;
+
+ if (!BN_nnmod(point->Z, z, group->field, ctx))
+ goto err;
+ Z_is_one = BN_is_one(point->Z);
+ if (group->meth->field_encode) {
+ if (Z_is_one && (group->meth->field_set_to_one != 0)) {
+ if (!group->meth->field_set_to_one(group, point->Z, ctx))
+ goto err;
+ } else {
+ if (!group->
+ meth->field_encode(group, point->Z, point->Z, ctx))
+ goto err;
+ }
+ }
+ point->Z_is_one = Z_is_one;
+ }
+
+ ret = 1;
+
+ err:
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
+ const EC_POINT *point,
+ BIGNUM *x, BIGNUM *y,
+ BIGNUM *z, BN_CTX *ctx)
+{
+ BN_CTX *new_ctx = NULL;
+ int ret = 0;
+
+ if (group->meth->field_decode != 0) {
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ if (x != NULL) {
+ if (!group->meth->field_decode(group, x, point->X, ctx))
+ goto err;
+ }
+ if (y != NULL) {
+ if (!group->meth->field_decode(group, y, point->Y, ctx))
+ goto err;
+ }
+ if (z != NULL) {
+ if (!group->meth->field_decode(group, z, point->Z, ctx))
+ goto err;
+ }
+ } else {
+ if (x != NULL) {
+ if (!BN_copy(x, point->X))
+ goto err;
+ }
+ if (y != NULL) {
+ if (!BN_copy(y, point->Y))
+ goto err;
+ }
+ if (z != NULL) {
+ if (!BN_copy(z, point->Z))
+ goto err;
+ }
+ }
+
+ ret = 1;
+
+ err:
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
+ EC_POINT *point,
+ const BIGNUM *x,
+ const BIGNUM *y, BN_CTX *ctx)
+{
+ if (x == NULL || y == NULL) {
+ /*
+ * unlike for projective coordinates, we do not tolerate this
+ */
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
+ ERR_R_PASSED_NULL_PARAMETER);
+ return 0;
+ }
+
+ return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
+ BN_value_one(), ctx);
+}
+
+int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
+ const EC_POINT *point,
+ BIGNUM *x, BIGNUM *y,
+ BN_CTX *ctx)
+{
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *Z, *Z_1, *Z_2, *Z_3;
+ const BIGNUM *Z_;
+ int ret = 0;
+
+ if (EC_POINT_is_at_infinity(group, point)) {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
+ EC_R_POINT_AT_INFINITY);
+ return 0;
+ }
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ BN_CTX_start(ctx);
+ Z = BN_CTX_get(ctx);
+ Z_1 = BN_CTX_get(ctx);
+ Z_2 = BN_CTX_get(ctx);
+ Z_3 = BN_CTX_get(ctx);
+ if (Z_3 == NULL)
+ goto err;
+
+ /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
+
+ if (group->meth->field_decode) {
+ if (!group->meth->field_decode(group, Z, point->Z, ctx))
+ goto err;
+ Z_ = Z;
+ } else {
+ Z_ = point->Z;
+ }
+
+ if (BN_is_one(Z_)) {
+ if (group->meth->field_decode) {
+ if (x != NULL) {
+ if (!group->meth->field_decode(group, x, point->X, ctx))
+ goto err;
+ }
+ if (y != NULL) {
+ if (!group->meth->field_decode(group, y, point->Y, ctx))
+ goto err;
+ }
+ } else {
+ if (x != NULL) {
+ if (!BN_copy(x, point->X))
+ goto err;
+ }
+ if (y != NULL) {
+ if (!BN_copy(y, point->Y))
+ goto err;
+ }
+ }
+ } else {
+ if (!group->meth->field_inv(group, Z_1, Z_, ctx)) {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
+ ERR_R_BN_LIB);
+ goto err;
+ }
+
+ if (group->meth->field_encode == 0) {
+ /* field_sqr works on standard representation */
+ if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
+ goto err;
+ } else {
+ if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
+ goto err;
+ }
+
+ if (x != NULL) {
+ /*
+ * in the Montgomery case, field_mul will cancel out Montgomery
+ * factor in X:
+ */
+ if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
+ goto err;
+ }
+
+ if (y != NULL) {
+ if (group->meth->field_encode == 0) {
+ /*
+ * field_mul works on standard representation
+ */
+ if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
+ goto err;
+ } else {
+ if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
+ goto err;
+ }
+
+ /*
+ * in the Montgomery case, field_mul will cancel out Montgomery
+ * factor in Y:
+ */
+ if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
+ goto err;
+ }
+ }
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
+ const EC_POINT *b, BN_CTX *ctx)
+{
+ int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
+ const BIGNUM *, BN_CTX *);
+ int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+ const BIGNUM *p;
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
+ int ret = 0;
+
+ if (a == b)
+ return EC_POINT_dbl(group, r, a, ctx);
+ if (EC_POINT_is_at_infinity(group, a))
+ return EC_POINT_copy(r, b);
+ if (EC_POINT_is_at_infinity(group, b))
+ return EC_POINT_copy(r, a);
+
+ field_mul = group->meth->field_mul;
+ field_sqr = group->meth->field_sqr;
+ p = group->field;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ BN_CTX_start(ctx);
+ n0 = BN_CTX_get(ctx);
+ n1 = BN_CTX_get(ctx);
+ n2 = BN_CTX_get(ctx);
+ n3 = BN_CTX_get(ctx);
+ n4 = BN_CTX_get(ctx);
+ n5 = BN_CTX_get(ctx);
+ n6 = BN_CTX_get(ctx);
+ if (n6 == NULL)
+ goto end;
+
+ /*
+ * Note that in this function we must not read components of 'a' or 'b'
+ * once we have written the corresponding components of 'r'. ('r' might
+ * be one of 'a' or 'b'.)
+ */
+
+ /* n1, n2 */
+ if (b->Z_is_one) {
+ if (!BN_copy(n1, a->X))
+ goto end;
+ if (!BN_copy(n2, a->Y))
+ goto end;
+ /* n1 = X_a */
+ /* n2 = Y_a */
+ } else {
+ if (!field_sqr(group, n0, b->Z, ctx))
+ goto end;
+ if (!field_mul(group, n1, a->X, n0, ctx))
+ goto end;
+ /* n1 = X_a * Z_b^2 */
+
+ if (!field_mul(group, n0, n0, b->Z, ctx))
+ goto end;
+ if (!field_mul(group, n2, a->Y, n0, ctx))
+ goto end;
+ /* n2 = Y_a * Z_b^3 */
+ }
+
+ /* n3, n4 */
+ if (a->Z_is_one) {
+ if (!BN_copy(n3, b->X))
+ goto end;
+ if (!BN_copy(n4, b->Y))
+ goto end;
+ /* n3 = X_b */
+ /* n4 = Y_b */
+ } else {
+ if (!field_sqr(group, n0, a->Z, ctx))
+ goto end;
+ if (!field_mul(group, n3, b->X, n0, ctx))
+ goto end;
+ /* n3 = X_b * Z_a^2 */
+
+ if (!field_mul(group, n0, n0, a->Z, ctx))
+ goto end;
+ if (!field_mul(group, n4, b->Y, n0, ctx))
+ goto end;
+ /* n4 = Y_b * Z_a^3 */
+ }
+
+ /* n5, n6 */
+ if (!BN_mod_sub_quick(n5, n1, n3, p))
+ goto end;
+ if (!BN_mod_sub_quick(n6, n2, n4, p))
+ goto end;
+ /* n5 = n1 - n3 */
+ /* n6 = n2 - n4 */
+
+ if (BN_is_zero(n5)) {
+ if (BN_is_zero(n6)) {
+ /* a is the same point as b */
+ BN_CTX_end(ctx);
+ ret = EC_POINT_dbl(group, r, a, ctx);
+ ctx = NULL;
+ goto end;
+ } else {
+ /* a is the inverse of b */
+ BN_zero(r->Z);
+ r->Z_is_one = 0;
+ ret = 1;
+ goto end;
+ }
+ }
+
+ /* 'n7', 'n8' */
+ if (!BN_mod_add_quick(n1, n1, n3, p))
+ goto end;
+ if (!BN_mod_add_quick(n2, n2, n4, p))
+ goto end;
+ /* 'n7' = n1 + n3 */
+ /* 'n8' = n2 + n4 */
+
+ /* Z_r */
+ if (a->Z_is_one && b->Z_is_one) {
+ if (!BN_copy(r->Z, n5))
+ goto end;
+ } else {
+ if (a->Z_is_one) {
+ if (!BN_copy(n0, b->Z))
+ goto end;
+ } else if (b->Z_is_one) {
+ if (!BN_copy(n0, a->Z))
+ goto end;
+ } else {
+ if (!field_mul(group, n0, a->Z, b->Z, ctx))
+ goto end;
+ }
+ if (!field_mul(group, r->Z, n0, n5, ctx))
+ goto end;
+ }
+ r->Z_is_one = 0;
+ /* Z_r = Z_a * Z_b * n5 */
+
+ /* X_r */
+ if (!field_sqr(group, n0, n6, ctx))
+ goto end;
+ if (!field_sqr(group, n4, n5, ctx))
+ goto end;
+ if (!field_mul(group, n3, n1, n4, ctx))
+ goto end;
+ if (!BN_mod_sub_quick(r->X, n0, n3, p))
+ goto end;
+ /* X_r = n6^2 - n5^2 * 'n7' */
+
+ /* 'n9' */
+ if (!BN_mod_lshift1_quick(n0, r->X, p))
+ goto end;
+ if (!BN_mod_sub_quick(n0, n3, n0, p))
+ goto end;
+ /* n9 = n5^2 * 'n7' - 2 * X_r */
+
+ /* Y_r */
+ if (!field_mul(group, n0, n0, n6, ctx))
+ goto end;
+ if (!field_mul(group, n5, n4, n5, ctx))
+ goto end; /* now n5 is n5^3 */
+ if (!field_mul(group, n1, n2, n5, ctx))
+ goto end;
+ if (!BN_mod_sub_quick(n0, n0, n1, p))
+ goto end;
+ if (BN_is_odd(n0))
+ if (!BN_add(n0, n0, p))
+ goto end;
+ /* now 0 <= n0 < 2*p, and n0 is even */
+ if (!BN_rshift1(r->Y, n0))
+ goto end;
+ /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
+
+ ret = 1;
+
+ end:
+ if (ctx) /* otherwise we already called BN_CTX_end */
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
+ BN_CTX *ctx)
+{
+ int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
+ const BIGNUM *, BN_CTX *);
+ int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+ const BIGNUM *p;
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *n0, *n1, *n2, *n3;
+ int ret = 0;
+
+ if (EC_POINT_is_at_infinity(group, a)) {
+ BN_zero(r->Z);
+ r->Z_is_one = 0;
+ return 1;
+ }
+
+ field_mul = group->meth->field_mul;
+ field_sqr = group->meth->field_sqr;
+ p = group->field;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ BN_CTX_start(ctx);
+ n0 = BN_CTX_get(ctx);
+ n1 = BN_CTX_get(ctx);
+ n2 = BN_CTX_get(ctx);
+ n3 = BN_CTX_get(ctx);
+ if (n3 == NULL)
+ goto err;
+
+ /*
+ * Note that in this function we must not read components of 'a' once we
+ * have written the corresponding components of 'r'. ('r' might the same
+ * as 'a'.)
+ */
+
+ /* n1 */
+ if (a->Z_is_one) {
+ if (!field_sqr(group, n0, a->X, ctx))
+ goto err;
+ if (!BN_mod_lshift1_quick(n1, n0, p))
+ goto err;
+ if (!BN_mod_add_quick(n0, n0, n1, p))
+ goto err;
+ if (!BN_mod_add_quick(n1, n0, group->a, p))
+ goto err;
+ /* n1 = 3 * X_a^2 + a_curve */
+ } else if (group->a_is_minus3) {
+ if (!field_sqr(group, n1, a->Z, ctx))
+ goto err;
+ if (!BN_mod_add_quick(n0, a->X, n1, p))
+ goto err;
+ if (!BN_mod_sub_quick(n2, a->X, n1, p))
+ goto err;
+ if (!field_mul(group, n1, n0, n2, ctx))
+ goto err;
+ if (!BN_mod_lshift1_quick(n0, n1, p))
+ goto err;
+ if (!BN_mod_add_quick(n1, n0, n1, p))
+ goto err;
+ /*-
+ * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
+ * = 3 * X_a^2 - 3 * Z_a^4
+ */
+ } else {
+ if (!field_sqr(group, n0, a->X, ctx))
+ goto err;
+ if (!BN_mod_lshift1_quick(n1, n0, p))
+ goto err;
+ if (!BN_mod_add_quick(n0, n0, n1, p))
+ goto err;
+ if (!field_sqr(group, n1, a->Z, ctx))
+ goto err;
+ if (!field_sqr(group, n1, n1, ctx))
+ goto err;
+ if (!field_mul(group, n1, n1, group->a, ctx))
+ goto err;
+ if (!BN_mod_add_quick(n1, n1, n0, p))
+ goto err;
+ /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
+ }
+
+ /* Z_r */
+ if (a->Z_is_one) {
+ if (!BN_copy(n0, a->Y))
+ goto err;
+ } else {
+ if (!field_mul(group, n0, a->Y, a->Z, ctx))
+ goto err;
+ }
+ if (!BN_mod_lshift1_quick(r->Z, n0, p))
+ goto err;
+ r->Z_is_one = 0;
+ /* Z_r = 2 * Y_a * Z_a */
+
+ /* n2 */
+ if (!field_sqr(group, n3, a->Y, ctx))
+ goto err;
+ if (!field_mul(group, n2, a->X, n3, ctx))
+ goto err;
+ if (!BN_mod_lshift_quick(n2, n2, 2, p))
+ goto err;
+ /* n2 = 4 * X_a * Y_a^2 */
+
+ /* X_r */
+ if (!BN_mod_lshift1_quick(n0, n2, p))
+ goto err;
+ if (!field_sqr(group, r->X, n1, ctx))
+ goto err;
+ if (!BN_mod_sub_quick(r->X, r->X, n0, p))
+ goto err;
+ /* X_r = n1^2 - 2 * n2 */
+
+ /* n3 */
+ if (!field_sqr(group, n0, n3, ctx))
+ goto err;
+ if (!BN_mod_lshift_quick(n3, n0, 3, p))
+ goto err;
+ /* n3 = 8 * Y_a^4 */
+
+ /* Y_r */
+ if (!BN_mod_sub_quick(n0, n2, r->X, p))
+ goto err;
+ if (!field_mul(group, n0, n1, n0, ctx))
+ goto err;
+ if (!BN_mod_sub_quick(r->Y, n0, n3, p))
+ goto err;
+ /* Y_r = n1 * (n2 - X_r) - n3 */
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
+{
+ if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
+ /* point is its own inverse */
+ return 1;
+
+ return BN_usub(point->Y, group->field, point->Y);
+}
+
+int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
+{
+ return BN_is_zero(point->Z);
+}
+
+int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
+ BN_CTX *ctx)
+{
+ int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
+ const BIGNUM *, BN_CTX *);
+ int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+ const BIGNUM *p;
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *rh, *tmp, *Z4, *Z6;
+ int ret = -1;
+
+ if (EC_POINT_is_at_infinity(group, point))
+ return 1;
+
+ field_mul = group->meth->field_mul;
+ field_sqr = group->meth->field_sqr;
+ p = group->field;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return -1;
+ }
+
+ BN_CTX_start(ctx);
+ rh = BN_CTX_get(ctx);
+ tmp = BN_CTX_get(ctx);
+ Z4 = BN_CTX_get(ctx);
+ Z6 = BN_CTX_get(ctx);
+ if (Z6 == NULL)
+ goto err;
+
+ /*-
+ * We have a curve defined by a Weierstrass equation
+ * y^2 = x^3 + a*x + b.
+ * The point to consider is given in Jacobian projective coordinates
+ * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
+ * Substituting this and multiplying by Z^6 transforms the above equation into
+ * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
+ * To test this, we add up the right-hand side in 'rh'.
+ */
+
+ /* rh := X^2 */
+ if (!field_sqr(group, rh, point->X, ctx))
+ goto err;
+
+ if (!point->Z_is_one) {
+ if (!field_sqr(group, tmp, point->Z, ctx))
+ goto err;
+ if (!field_sqr(group, Z4, tmp, ctx))
+ goto err;
+ if (!field_mul(group, Z6, Z4, tmp, ctx))
+ goto err;
+
+ /* rh := (rh + a*Z^4)*X */
+ if (group->a_is_minus3) {
+ if (!BN_mod_lshift1_quick(tmp, Z4, p))
+ goto err;
+ if (!BN_mod_add_quick(tmp, tmp, Z4, p))
+ goto err;
+ if (!BN_mod_sub_quick(rh, rh, tmp, p))
+ goto err;
+ if (!field_mul(group, rh, rh, point->X, ctx))
+ goto err;
+ } else {
+ if (!field_mul(group, tmp, Z4, group->a, ctx))
+ goto err;
+ if (!BN_mod_add_quick(rh, rh, tmp, p))
+ goto err;
+ if (!field_mul(group, rh, rh, point->X, ctx))
+ goto err;
+ }
+
+ /* rh := rh + b*Z^6 */
+ if (!field_mul(group, tmp, group->b, Z6, ctx))
+ goto err;
+ if (!BN_mod_add_quick(rh, rh, tmp, p))
+ goto err;
+ } else {
+ /* point->Z_is_one */
+
+ /* rh := (rh + a)*X */
+ if (!BN_mod_add_quick(rh, rh, group->a, p))
+ goto err;
+ if (!field_mul(group, rh, rh, point->X, ctx))
+ goto err;
+ /* rh := rh + b */
+ if (!BN_mod_add_quick(rh, rh, group->b, p))
+ goto err;
+ }
+
+ /* 'lh' := Y^2 */
+ if (!field_sqr(group, tmp, point->Y, ctx))
+ goto err;
+
+ ret = (0 == BN_ucmp(tmp, rh));
+
+ err:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
+ const EC_POINT *b, BN_CTX *ctx)
+{
+ /*-
+ * return values:
+ * -1 error
+ * 0 equal (in affine coordinates)
+ * 1 not equal
+ */
+
+ int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
+ const BIGNUM *, BN_CTX *);
+ int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
+ const BIGNUM *tmp1_, *tmp2_;
+ int ret = -1;
+
+ if (EC_POINT_is_at_infinity(group, a)) {
+ return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
+ }
+
+ if (EC_POINT_is_at_infinity(group, b))
+ return 1;
+
+ if (a->Z_is_one && b->Z_is_one) {
+ return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
+ }
+
+ field_mul = group->meth->field_mul;
+ field_sqr = group->meth->field_sqr;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return -1;
+ }
+
+ BN_CTX_start(ctx);
+ tmp1 = BN_CTX_get(ctx);
+ tmp2 = BN_CTX_get(ctx);
+ Za23 = BN_CTX_get(ctx);
+ Zb23 = BN_CTX_get(ctx);
+ if (Zb23 == NULL)
+ goto end;
+
+ /*-
+ * We have to decide whether
+ * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
+ * or equivalently, whether
+ * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
+ */
+
+ if (!b->Z_is_one) {
+ if (!field_sqr(group, Zb23, b->Z, ctx))
+ goto end;
+ if (!field_mul(group, tmp1, a->X, Zb23, ctx))
+ goto end;
+ tmp1_ = tmp1;
+ } else
+ tmp1_ = a->X;
+ if (!a->Z_is_one) {
+ if (!field_sqr(group, Za23, a->Z, ctx))
+ goto end;
+ if (!field_mul(group, tmp2, b->X, Za23, ctx))
+ goto end;
+ tmp2_ = tmp2;
+ } else
+ tmp2_ = b->X;
+
+ /* compare X_a*Z_b^2 with X_b*Z_a^2 */
+ if (BN_cmp(tmp1_, tmp2_) != 0) {
+ ret = 1; /* points differ */
+ goto end;
+ }
+
+ if (!b->Z_is_one) {
+ if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
+ goto end;
+ if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
+ goto end;
+ /* tmp1_ = tmp1 */
+ } else
+ tmp1_ = a->Y;
+ if (!a->Z_is_one) {
+ if (!field_mul(group, Za23, Za23, a->Z, ctx))
+ goto end;
+ if (!field_mul(group, tmp2, b->Y, Za23, ctx))
+ goto end;
+ /* tmp2_ = tmp2 */
+ } else
+ tmp2_ = b->Y;
+
+ /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
+ if (BN_cmp(tmp1_, tmp2_) != 0) {
+ ret = 1; /* points differ */
+ goto end;
+ }
+
+ /* points are equal */
+ ret = 0;
+
+ end:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
+ BN_CTX *ctx)
+{
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *x, *y;
+ int ret = 0;
+
+ if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
+ return 1;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ BN_CTX_start(ctx);
+ x = BN_CTX_get(ctx);
+ y = BN_CTX_get(ctx);
+ if (y == NULL)
+ goto err;
+
+ if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
+ goto err;
+ if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
+ goto err;
+ if (!point->Z_is_one) {
+ ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
+ EC_POINT *points[], BN_CTX *ctx)
+{
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *tmp, *tmp_Z;
+ BIGNUM **prod_Z = NULL;
+ size_t i;
+ int ret = 0;
+
+ if (num == 0)
+ return 1;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ BN_CTX_start(ctx);
+ tmp = BN_CTX_get(ctx);
+ tmp_Z = BN_CTX_get(ctx);
+ if (tmp == NULL || tmp_Z == NULL)
+ goto err;
+
+ prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0]));
+ if (prod_Z == NULL)
+ goto err;
+ for (i = 0; i < num; i++) {
+ prod_Z[i] = BN_new();
+ if (prod_Z[i] == NULL)
+ goto err;
+ }
+
+ /*
+ * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
+ * skipping any zero-valued inputs (pretend that they're 1).
+ */
+
+ if (!BN_is_zero(points[0]->Z)) {
+ if (!BN_copy(prod_Z[0], points[0]->Z))
+ goto err;
+ } else {
+ if (group->meth->field_set_to_one != 0) {
+ if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
+ goto err;
+ } else {
+ if (!BN_one(prod_Z[0]))
+ goto err;
+ }
+ }
+
+ for (i = 1; i < num; i++) {
+ if (!BN_is_zero(points[i]->Z)) {
+ if (!group->
+ meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
+ ctx))
+ goto err;
+ } else {
+ if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
+ goto err;
+ }
+ }
+
+ /*
+ * Now use a single explicit inversion to replace every non-zero
+ * points[i]->Z by its inverse.
+ */
+
+ if (!group->meth->field_inv(group, tmp, prod_Z[num - 1], ctx)) {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
+ goto err;
+ }
+ if (group->meth->field_encode != 0) {
+ /*
+ * In the Montgomery case, we just turned R*H (representing H) into
+ * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
+ * multiply by the Montgomery factor twice.
+ */
+ if (!group->meth->field_encode(group, tmp, tmp, ctx))
+ goto err;
+ if (!group->meth->field_encode(group, tmp, tmp, ctx))
+ goto err;
+ }
+
+ for (i = num - 1; i > 0; --i) {
+ /*
+ * Loop invariant: tmp is the product of the inverses of points[0]->Z
+ * .. points[i]->Z (zero-valued inputs skipped).
+ */
+ if (!BN_is_zero(points[i]->Z)) {
+ /*
+ * Set tmp_Z to the inverse of points[i]->Z (as product of Z
+ * inverses 0 .. i, Z values 0 .. i - 1).
+ */
+ if (!group->
+ meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
+ goto err;
+ /*
+ * Update tmp to satisfy the loop invariant for i - 1.
+ */
+ if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
+ goto err;
+ /* Replace points[i]->Z by its inverse. */
+ if (!BN_copy(points[i]->Z, tmp_Z))
+ goto err;
+ }
+ }
+
+ if (!BN_is_zero(points[0]->Z)) {
+ /* Replace points[0]->Z by its inverse. */
+ if (!BN_copy(points[0]->Z, tmp))
+ goto err;
+ }
+
+ /* Finally, fix up the X and Y coordinates for all points. */
+
+ for (i = 0; i < num; i++) {
+ EC_POINT *p = points[i];
+
+ if (!BN_is_zero(p->Z)) {
+ /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
+
+ if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
+ goto err;
+
+ if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
+ goto err;
+
+ if (group->meth->field_set_to_one != 0) {
+ if (!group->meth->field_set_to_one(group, p->Z, ctx))
+ goto err;
+ } else {
+ if (!BN_one(p->Z))
+ goto err;
+ }
+ p->Z_is_one = 1;
+ }
+ }
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ if (prod_Z != NULL) {
+ for (i = 0; i < num; i++) {
+ if (prod_Z[i] == NULL)
+ break;
+ BN_clear_free(prod_Z[i]);
+ }
+ OPENSSL_free(prod_Z);
+ }
+ return ret;
+}
+
+int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
+ const BIGNUM *b, BN_CTX *ctx)
+{
+ return BN_mod_mul(r, a, b, group->field, ctx);
+}
+
+int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
+ BN_CTX *ctx)
+{
+ return BN_mod_sqr(r, a, group->field, ctx);
+}
+
+/*-
+ * Computes the multiplicative inverse of a in GF(p), storing the result in r.
+ * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
+ * Since we don't have a Mont structure here, SCA hardening is with blinding.
+ */
+int ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
+ BN_CTX *ctx)
+{
+ BIGNUM *e = NULL;
+ BN_CTX *new_ctx = NULL;
+ int ret = 0;
+
+ if (ctx == NULL && (ctx = new_ctx = BN_CTX_secure_new()) == NULL)
+ return 0;
+
+ BN_CTX_start(ctx);
+ if ((e = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ do {
+ if (!BN_rand_range(e, group->field))
+ goto err;
+ } while (BN_is_zero(e));
+
+ /* r := a * e */
+ if (!group->meth->field_mul(group, r, a, e, ctx))
+ goto err;
+ /* r := 1/(a * e) */
+ if (!BN_mod_inverse(r, r, group->field, ctx)) {
+ ECerr(EC_F_EC_GFP_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT);
+ goto err;
+ }
+ /* r := e/(a * e) = 1/a */
+ if (!group->meth->field_mul(group, r, r, e, ctx))
+ goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+/*-
+ * Apply randomization of EC point projective coordinates:
*
- * This product includes cryptographic software written by Eric Young
- * (eay@cryptsoft.com). This product includes software written by Tim
- * Hudson (tjh@cryptsoft.com).
+ * (X, Y ,Z ) = (lambda^2*X, lambda^3*Y, lambda*Z)
+ * lambda = [1,group->field)
*
*/
+int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
+ BN_CTX *ctx)
+{
+ int ret = 0;
+ BIGNUM *lambda = NULL;
+ BIGNUM *temp = NULL;
-#include "ec_lcl.h"
+ BN_CTX_start(ctx);
+ lambda = BN_CTX_get(ctx);
+ temp = BN_CTX_get(ctx);
+ if (temp == NULL) {
+ ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_MALLOC_FAILURE);
+ goto err;
+ }
+ /* make sure lambda is not zero */
+ do {
+ if (!BN_rand_range(lambda, group->field)) {
+ ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_BN_LIB);
+ goto err;
+ }
+ } while (BN_is_zero(lambda));
+
+ /* if field_encode defined convert between representations */
+ if (group->meth->field_encode != NULL
+ && !group->meth->field_encode(group, lambda, lambda, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, p->Z, p->Z, lambda, ctx))
+ goto err;
+ if (!group->meth->field_sqr(group, temp, lambda, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, p->X, p->X, temp, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, temp, temp, lambda, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
+ goto err;
+ p->Z_is_one = 0;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
-const EC_METHOD *EC_GFp_simple_method(void)
- {
- static const EC_METHOD ret = {
- ec_GFp_simple_group_init,
- ec_GFp_simple_group_set_curve_GFp,
- ec_GFp_simple_group_finish,
- ec_GFp_simple_group_clear_finish,
- ec_GFp_simple_group_copy,
- ec_GFp_simple_group_set_generator,
- /* TODO: 'set' and 'get' functions for EC_GROUPs */
- ec_GFp_simple_point_init,
- ec_GFp_simple_point_finish,
- ec_GFp_simple_point_clear_finish,
- ec_GFp_simple_point_copy,
- /* TODO: 'set' and 'get' functions for EC_POINTs */
- ec_GFp_simple_point2oct,
- ec_GFp_simple_oct2point,
- ec_GFp_simple_add,
- ec_GFp_simple_dbl,
- ec_GFp_simple_is_at_infinity,
- ec_GFp_simple_is_on_curve,
- ec_GFp_simple_make_affine,
- ec_GFp_simple_field_mult,
- ec_GFp_simple_field_sqr,
- 0 /* field_encode */,
- 0 /* field_decode */ };
-
- return &ret;
- }
projects / openssl.git / blobdiff