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-rw-r--r--openssl/crypto/ec/ecp_smpl.c3435
1 files changed, 1719 insertions, 1716 deletions
diff --git a/openssl/crypto/ec/ecp_smpl.c b/openssl/crypto/ec/ecp_smpl.c
index 4d26f8bdf..766f5fc51 100644
--- a/openssl/crypto/ec/ecp_smpl.c
+++ b/openssl/crypto/ec/ecp_smpl.c
@@ -1,1716 +1,1719 @@
-/* crypto/ec/ecp_smpl.c */
-/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
- * for the OpenSSL project.
- * Includes code written by Bodo Moeller for the OpenSSL project.
-*/
-/* ====================================================================
- * Copyright (c) 1998-2002 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.
- *
- * 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/)"
- *
- * 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.
- * ====================================================================
- *
- * This product includes cryptographic software written by Eric Young
- * (eay@cryptsoft.com). This product includes software written by Tim
- * Hudson (tjh@cryptsoft.com).
- *
- */
-/* ====================================================================
- * 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 = {
- 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_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,
- ec_GFp_simple_set_compressed_coordinates,
- ec_GFp_simple_point2oct,
- ec_GFp_simple_oct2point,
- 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 */,
- 0 /* field_encode */,
- 0 /* field_decode */,
- 0 /* field_set_to_one */ };
-
- 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.
-
- * 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)
- {
- BN_init(&group->field);
- BN_init(&group->a);
- BN_init(&group->b);
- 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);
- if (new_ctx != NULL)
- 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:
- if (new_ctx)
- 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);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return ret;
- }
-
-
-int ec_GFp_simple_point_init(EC_POINT *point)
- {
- BN_init(&point->X);
- BN_init(&point->Y);
- BN_init(&point->Z);
- point->Z_is_one = 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;
-
- 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:
- if (new_ctx != NULL)
- 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:
- if (new_ctx != NULL)
- 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 (!BN_mod_inverse(Z_1, Z_, &group->field, 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);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return ret;
- }
-
-
-int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
- const BIGNUM *x_, int y_bit, BN_CTX *ctx)
- {
- BN_CTX *new_ctx = NULL;
- BIGNUM *tmp1, *tmp2, *x, *y;
- int ret = 0;
-
- /* clear error queue*/
- ERR_clear_error();
-
- if (ctx == NULL)
- {
- ctx = new_ctx = BN_CTX_new();
- if (ctx == NULL)
- return 0;
- }
-
- y_bit = (y_bit != 0);
-
- BN_CTX_start(ctx);
- tmp1 = BN_CTX_get(ctx);
- tmp2 = BN_CTX_get(ctx);
- x = BN_CTX_get(ctx);
- y = BN_CTX_get(ctx);
- if (y == NULL) goto err;
-
- /* Recover y. We have a Weierstrass equation
- * y^2 = x^3 + a*x + b,
- * so y is one of the square roots of x^3 + a*x + b.
- */
-
- /* tmp1 := x^3 */
- if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
- if (group->meth->field_decode == 0)
- {
- /* field_{sqr,mul} work on standard representation */
- if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
- if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
- }
- else
- {
- if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
- if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
- }
-
- /* tmp1 := tmp1 + a*x */
- if (group->a_is_minus3)
- {
- if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
- if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
- if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
- }
- else
- {
- if (group->meth->field_decode)
- {
- if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
- if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
- }
- else
- {
- /* field_mul works on standard representation */
- if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
- }
-
- if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
- }
-
- /* tmp1 := tmp1 + b */
- if (group->meth->field_decode)
- {
- if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
- if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
- }
- else
- {
- if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
- }
-
- if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
- {
- unsigned long err = ERR_peek_last_error();
-
- if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
- {
- ERR_clear_error();
- ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
- }
- else
- ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
- goto err;
- }
-
- if (y_bit != BN_is_odd(y))
- {
- if (BN_is_zero(y))
- {
- int kron;
-
- kron = BN_kronecker(x, &group->field, ctx);
- if (kron == -2) goto err;
-
- if (kron == 1)
- ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);
- else
- /* BN_mod_sqrt() should have cought this error (not a square) */
- ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
- goto err;
- }
- if (!BN_usub(y, &group->field, y)) goto err;
- }
- if (y_bit != BN_is_odd(y))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);
- goto err;
- }
-
- if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return ret;
- }
-
-
-size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
- unsigned char *buf, size_t len, BN_CTX *ctx)
- {
- size_t ret;
- BN_CTX *new_ctx = NULL;
- int used_ctx = 0;
- BIGNUM *x, *y;
- size_t field_len, i, skip;
-
- if ((form != POINT_CONVERSION_COMPRESSED)
- && (form != POINT_CONVERSION_UNCOMPRESSED)
- && (form != POINT_CONVERSION_HYBRID))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
- goto err;
- }
-
- if (EC_POINT_is_at_infinity(group, point))
- {
- /* encodes to a single 0 octet */
- if (buf != NULL)
- {
- if (len < 1)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
- return 0;
- }
- buf[0] = 0;
- }
- return 1;
- }
-
-
- /* ret := required output buffer length */
- field_len = BN_num_bytes(&group->field);
- ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
-
- /* if 'buf' is NULL, just return required length */
- if (buf != NULL)
- {
- if (len < ret)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
- goto err;
- }
-
- if (ctx == NULL)
- {
- ctx = new_ctx = BN_CTX_new();
- if (ctx == NULL)
- return 0;
- }
-
- BN_CTX_start(ctx);
- used_ctx = 1;
- 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 ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
- buf[0] = form + 1;
- else
- buf[0] = form;
-
- i = 1;
-
- skip = field_len - BN_num_bytes(x);
- if (skip > field_len)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
- goto err;
- }
- while (skip > 0)
- {
- buf[i++] = 0;
- skip--;
- }
- skip = BN_bn2bin(x, buf + i);
- i += skip;
- if (i != 1 + field_len)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
- goto err;
- }
-
- if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
- {
- skip = field_len - BN_num_bytes(y);
- if (skip > field_len)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
- goto err;
- }
- while (skip > 0)
- {
- buf[i++] = 0;
- skip--;
- }
- skip = BN_bn2bin(y, buf + i);
- i += skip;
- }
-
- if (i != ret)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
- goto err;
- }
- }
-
- if (used_ctx)
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return ret;
-
- err:
- if (used_ctx)
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return 0;
- }
-
-
-int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
- const unsigned char *buf, size_t len, BN_CTX *ctx)
- {
- point_conversion_form_t form;
- int y_bit;
- BN_CTX *new_ctx = NULL;
- BIGNUM *x, *y;
- size_t field_len, enc_len;
- int ret = 0;
-
- if (len == 0)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
- return 0;
- }
- form = buf[0];
- y_bit = form & 1;
- form = form & ~1U;
- if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
- && (form != POINT_CONVERSION_UNCOMPRESSED)
- && (form != POINT_CONVERSION_HYBRID))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- return 0;
- }
- if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- return 0;
- }
-
- if (form == 0)
- {
- if (len != 1)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- return 0;
- }
-
- return EC_POINT_set_to_infinity(group, point);
- }
-
- field_len = BN_num_bytes(&group->field);
- enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
-
- if (len != enc_len)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- return 0;
- }
-
- 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 (!BN_bin2bn(buf + 1, field_len, x)) goto err;
- if (BN_ucmp(x, &group->field) >= 0)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- goto err;
- }
-
- if (form == POINT_CONVERSION_COMPRESSED)
- {
- if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
- }
- else
- {
- if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
- if (BN_ucmp(y, &group->field) >= 0)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- goto err;
- }
- if (form == POINT_CONVERSION_HYBRID)
- {
- if (y_bit != BN_is_odd(y))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- goto err;
- }
- }
-
- if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
- }
-
- if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
- goto err;
- }
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- 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);
- if (new_ctx != NULL)
- 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);
- if (new_ctx != NULL)
- 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);
- if (new_ctx != NULL)
- 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 (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);
- if (new_ctx != NULL)
- 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);
- if (new_ctx != NULL)
- 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 *tmp0, *tmp1;
- size_t pow2 = 0;
- BIGNUM **heap = 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);
- tmp0 = BN_CTX_get(ctx);
- tmp1 = BN_CTX_get(ctx);
- if (tmp0 == NULL || tmp1 == NULL) goto err;
-
- /* Before converting the individual points, compute inverses of all Z values.
- * Modular inversion is rather slow, but luckily we can do with a single
- * explicit inversion, plus about 3 multiplications per input value.
- */
-
- pow2 = 1;
- while (num > pow2)
- pow2 <<= 1;
- /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
- * We need twice that. */
- pow2 <<= 1;
-
- heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
- if (heap == NULL) goto err;
-
- /* The array is used as a binary tree, exactly as in heapsort:
- *
- * heap[1]
- * heap[2] heap[3]
- * heap[4] heap[5] heap[6] heap[7]
- * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
- *
- * We put the Z's in the last line;
- * then we set each other node to the product of its two child-nodes (where
- * empty or 0 entries are treated as ones);
- * then we invert heap[1];
- * then we invert each other node by replacing it by the product of its
- * parent (after inversion) and its sibling (before inversion).
- */
- heap[0] = NULL;
- for (i = pow2/2 - 1; i > 0; i--)
- heap[i] = NULL;
- for (i = 0; i < num; i++)
- heap[pow2/2 + i] = &points[i]->Z;
- for (i = pow2/2 + num; i < pow2; i++)
- heap[i] = NULL;
-
- /* set each node to the product of its children */
- for (i = pow2/2 - 1; i > 0; i--)
- {
- heap[i] = BN_new();
- if (heap[i] == NULL) goto err;
-
- if (heap[2*i] != NULL)
- {
- if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
- {
- if (!BN_copy(heap[i], heap[2*i])) goto err;
- }
- else
- {
- if (BN_is_zero(heap[2*i]))
- {
- if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
- }
- else
- {
- if (!group->meth->field_mul(group, heap[i],
- heap[2*i], heap[2*i + 1], ctx)) goto err;
- }
- }
- }
- }
-
- /* invert heap[1] */
- if (!BN_is_zero(heap[1]))
- {
- if (!BN_mod_inverse(heap[1], heap[1], &group->field, 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 have need to multiply by the Montgomery factor twice */
- if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
- if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
- }
-
- /* set other heap[i]'s to their inverses */
- for (i = 2; i < pow2/2 + num; i += 2)
- {
- /* i is even */
- if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
- {
- if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
- if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
- if (!BN_copy(heap[i], tmp0)) goto err;
- if (!BN_copy(heap[i + 1], tmp1)) goto err;
- }
- else
- {
- if (!BN_copy(heap[i], heap[i/2])) goto err;
- }
- }
-
- /* we have replaced all non-zero Z's by their inverses, now fix up all the 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, tmp1, &p->Z, ctx)) goto err;
- if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
-
- if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
- if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, 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);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- if (heap != NULL)
- {
- /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
- for (i = pow2/2 - 1; i > 0; i--)
- {
- if (heap[i] != NULL)
- BN_clear_free(heap[i]);
- }
- OPENSSL_free(heap);
- }
- 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);
- }
+/* crypto/ec/ecp_smpl.c */
+/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
+ * for the OpenSSL project.
+ * Includes code written by Bodo Moeller for the OpenSSL project.
+*/
+/* ====================================================================
+ * Copyright (c) 1998-2002 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.
+ *
+ * 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/)"
+ *
+ * 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.
+ * ====================================================================
+ *
+ * This product includes cryptographic software written by Eric Young
+ * (eay@cryptsoft.com). This product includes software written by Tim
+ * Hudson (tjh@cryptsoft.com).
+ *
+ */
+/* ====================================================================
+ * 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 = {
+ 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_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,
+ ec_GFp_simple_set_compressed_coordinates,
+ ec_GFp_simple_point2oct,
+ ec_GFp_simple_oct2point,
+ 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 */,
+ 0 /* field_encode */,
+ 0 /* field_decode */,
+ 0 /* field_set_to_one */ };
+
+ 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.
+
+ * 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)
+ {
+ BN_init(&group->field);
+ BN_init(&group->a);
+ BN_init(&group->b);
+ 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);
+ if (new_ctx != NULL)
+ 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:
+ if (new_ctx)
+ 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);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
+
+
+int ec_GFp_simple_point_init(EC_POINT *point)
+ {
+ BN_init(&point->X);
+ BN_init(&point->Y);
+ BN_init(&point->Z);
+ point->Z_is_one = 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;
+
+ 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:
+ if (new_ctx != NULL)
+ 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:
+ if (new_ctx != NULL)
+ 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 (!BN_mod_inverse(Z_1, Z_, &group->field, 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);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
+
+
+int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
+ const BIGNUM *x_, int y_bit, BN_CTX *ctx)
+ {
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *tmp1, *tmp2, *x, *y;
+ int ret = 0;
+
+ /* clear error queue*/
+ ERR_clear_error();
+
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ y_bit = (y_bit != 0);
+
+ BN_CTX_start(ctx);
+ tmp1 = BN_CTX_get(ctx);
+ tmp2 = BN_CTX_get(ctx);
+ x = BN_CTX_get(ctx);
+ y = BN_CTX_get(ctx);
+ if (y == NULL) goto err;
+
+ /* Recover y. We have a Weierstrass equation
+ * y^2 = x^3 + a*x + b,
+ * so y is one of the square roots of x^3 + a*x + b.
+ */
+
+ /* tmp1 := x^3 */
+ if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
+ if (group->meth->field_decode == 0)
+ {
+ /* field_{sqr,mul} work on standard representation */
+ if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
+ if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
+ }
+ else
+ {
+ if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
+ if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
+ }
+
+ /* tmp1 := tmp1 + a*x */
+ if (group->a_is_minus3)
+ {
+ if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
+ if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
+ if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+ }
+ else
+ {
+ if (group->meth->field_decode)
+ {
+ if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
+ if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
+ }
+ else
+ {
+ /* field_mul works on standard representation */
+ if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
+ }
+
+ if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+ }
+
+ /* tmp1 := tmp1 + b */
+ if (group->meth->field_decode)
+ {
+ if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
+ if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+ }
+ else
+ {
+ if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
+ }
+
+ if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
+ {
+ unsigned long err = ERR_peek_last_error();
+
+ if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
+ {
+ ERR_clear_error();
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
+ }
+ else
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
+ goto err;
+ }
+
+ if (y_bit != BN_is_odd(y))
+ {
+ if (BN_is_zero(y))
+ {
+ int kron;
+
+ kron = BN_kronecker(x, &group->field, ctx);
+ if (kron == -2) goto err;
+
+ if (kron == 1)
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);
+ else
+ /* BN_mod_sqrt() should have cought this error (not a square) */
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
+ goto err;
+ }
+ if (!BN_usub(y, &group->field, y)) goto err;
+ }
+ if (y_bit != BN_is_odd(y))
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+
+ if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
+
+
+size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
+ unsigned char *buf, size_t len, BN_CTX *ctx)
+ {
+ size_t ret;
+ BN_CTX *new_ctx = NULL;
+ int used_ctx = 0;
+ BIGNUM *x, *y;
+ size_t field_len, i, skip;
+
+ if ((form != POINT_CONVERSION_COMPRESSED)
+ && (form != POINT_CONVERSION_UNCOMPRESSED)
+ && (form != POINT_CONVERSION_HYBRID))
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
+ goto err;
+ }
+
+ if (EC_POINT_is_at_infinity(group, point))
+ {
+ /* encodes to a single 0 octet */
+ if (buf != NULL)
+ {
+ if (len < 1)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
+ return 0;
+ }
+ buf[0] = 0;
+ }
+ return 1;
+ }
+
+
+ /* ret := required output buffer length */
+ field_len = BN_num_bytes(&group->field);
+ ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
+
+ /* if 'buf' is NULL, just return required length */
+ if (buf != NULL)
+ {
+ if (len < ret)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
+ goto err;
+ }
+
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ BN_CTX_start(ctx);
+ used_ctx = 1;
+ 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 ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
+ buf[0] = form + 1;
+ else
+ buf[0] = form;
+
+ i = 1;
+
+ skip = field_len - BN_num_bytes(x);
+ if (skip > field_len)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+ while (skip > 0)
+ {
+ buf[i++] = 0;
+ skip--;
+ }
+ skip = BN_bn2bin(x, buf + i);
+ i += skip;
+ if (i != 1 + field_len)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+
+ if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
+ {
+ skip = field_len - BN_num_bytes(y);
+ if (skip > field_len)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+ while (skip > 0)
+ {
+ buf[i++] = 0;
+ skip--;
+ }
+ skip = BN_bn2bin(y, buf + i);
+ i += skip;
+ }
+
+ if (i != ret)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+ }
+
+ if (used_ctx)
+ BN_CTX_end(ctx);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+
+ err:
+ if (used_ctx)
+ BN_CTX_end(ctx);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return 0;
+ }
+
+
+int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
+ const unsigned char *buf, size_t len, BN_CTX *ctx)
+ {
+ point_conversion_form_t form;
+ int y_bit;
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *x, *y;
+ size_t field_len, enc_len;
+ int ret = 0;
+
+ if (len == 0)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
+ return 0;
+ }
+ form = buf[0];
+ y_bit = form & 1;
+ form = form & ~1U;
+ if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
+ && (form != POINT_CONVERSION_UNCOMPRESSED)
+ && (form != POINT_CONVERSION_HYBRID))
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+ return 0;
+ }
+ if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+ return 0;
+ }
+
+ if (form == 0)
+ {
+ if (len != 1)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+ return 0;
+ }
+
+ return EC_POINT_set_to_infinity(group, point);
+ }
+
+ field_len = BN_num_bytes(&group->field);
+ enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
+
+ if (len != enc_len)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+ return 0;
+ }
+
+ 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 (!BN_bin2bn(buf + 1, field_len, x)) goto err;
+ if (BN_ucmp(x, &group->field) >= 0)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+ goto err;
+ }
+
+ if (form == POINT_CONVERSION_COMPRESSED)
+ {
+ if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
+ }
+ else
+ {
+ if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
+ if (BN_ucmp(y, &group->field) >= 0)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+ goto err;
+ }
+ if (form == POINT_CONVERSION_HYBRID)
+ {
+ if (y_bit != BN_is_odd(y))
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+ goto err;
+ }
+ }
+
+ if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+ }
+
+ if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
+ goto err;
+ }
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ if (new_ctx != NULL)
+ 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);
+ if (new_ctx != NULL)
+ 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);
+ if (new_ctx != NULL)
+ 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);
+ if (new_ctx != NULL)
+ 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);
+ if (new_ctx != NULL)
+ 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);
+ if (new_ctx != NULL)
+ 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 *tmp0, *tmp1;
+ size_t pow2 = 0;
+ BIGNUM **heap = 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);
+ tmp0 = BN_CTX_get(ctx);
+ tmp1 = BN_CTX_get(ctx);
+ if (tmp0 == NULL || tmp1 == NULL) goto err;
+
+ /* Before converting the individual points, compute inverses of all Z values.
+ * Modular inversion is rather slow, but luckily we can do with a single
+ * explicit inversion, plus about 3 multiplications per input value.
+ */
+
+ pow2 = 1;
+ while (num > pow2)
+ pow2 <<= 1;
+ /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
+ * We need twice that. */
+ pow2 <<= 1;
+
+ heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
+ if (heap == NULL) goto err;
+
+ /* The array is used as a binary tree, exactly as in heapsort:
+ *
+ * heap[1]
+ * heap[2] heap[3]
+ * heap[4] heap[5] heap[6] heap[7]
+ * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
+ *
+ * We put the Z's in the last line;
+ * then we set each other node to the product of its two child-nodes (where
+ * empty or 0 entries are treated as ones);
+ * then we invert heap[1];
+ * then we invert each other node by replacing it by the product of its
+ * parent (after inversion) and its sibling (before inversion).
+ */
+ heap[0] = NULL;
+ for (i = pow2/2 - 1; i > 0; i--)
+ heap[i] = NULL;
+ for (i = 0; i < num; i++)
+ heap[pow2/2 + i] = &points[i]->Z;
+ for (i = pow2/2 + num; i < pow2; i++)
+ heap[i] = NULL;
+
+ /* set each node to the product of its children */
+ for (i = pow2/2 - 1; i > 0; i--)
+ {
+ heap[i] = BN_new();
+ if (heap[i] == NULL) goto err;
+
+ if (heap[2*i] != NULL)
+ {
+ if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
+ {
+ if (!BN_copy(heap[i], heap[2*i])) goto err;
+ }
+ else
+ {
+ if (BN_is_zero(heap[2*i]))
+ {
+ if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
+ }
+ else
+ {
+ if (!group->meth->field_mul(group, heap[i],
+ heap[2*i], heap[2*i + 1], ctx)) goto err;
+ }
+ }
+ }
+ }
+
+ /* invert heap[1] */
+ if (!BN_is_zero(heap[1]))
+ {
+ if (!BN_mod_inverse(heap[1], heap[1], &group->field, 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 have need to multiply by the Montgomery factor twice */
+ if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
+ if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
+ }
+
+ /* set other heap[i]'s to their inverses */
+ for (i = 2; i < pow2/2 + num; i += 2)
+ {
+ /* i is even */
+ if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
+ {
+ if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
+ if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
+ if (!BN_copy(heap[i], tmp0)) goto err;
+ if (!BN_copy(heap[i + 1], tmp1)) goto err;
+ }
+ else
+ {
+ if (!BN_copy(heap[i], heap[i/2])) goto err;
+ }
+ }
+
+ /* we have replaced all non-zero Z's by their inverses, now fix up all the 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, tmp1, &p->Z, ctx)) goto err;
+ if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
+
+ if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
+ if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, 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);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ if (heap != NULL)
+ {
+ /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
+ for (i = pow2/2 - 1; i > 0; i--)
+ {
+ if (heap[i] != NULL)
+ BN_clear_free(heap[i]);
+ }
+ OPENSSL_free(heap);
+ }
+ 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);
+ }
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-02 15:10:48 +0000