/* Originally written by Bodo Moeller for the OpenSSL project.
* ====================================================================
* Copyright (c) 1998-2005 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 the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the OpenSSL open source
* license provided above.
*
* The elliptic curve binary polynomial software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
* Laboratories. */
#include <openssl/ec.h>
#include <string.h>
#include <openssl/bn.h>
#include <openssl/err.h>
#include <openssl/mem.h>
#include "internal.h"
#include "../../internal.h"
// 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 here 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);
group->a_is_minus3 = 0;
return 1;
}
void ec_GFp_simple_group_finish(EC_GROUP *group) {
BN_free(&group->field);
}
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;
// p must be a prime > 3
if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FIELD);
return 0;
}
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL) {
return 0;
}
}
BN_CTX_start(ctx);
BIGNUM *tmp = BN_CTX_get(ctx);
if (tmp == NULL) {
goto err;
}
// group->field
if (!BN_copy(&group->field, p)) {
goto err;
}
BN_set_negative(&group->field, 0);
// Store the field in minimal form, so it can be used with |BN_ULONG| arrays.
bn_set_minimal_width(&group->field);
// group->a
if (!BN_nnmod(tmp, a, &group->field, ctx) ||
!ec_bignum_to_felem(group, &group->a, tmp)) {
goto err;
}
// group->a_is_minus3
if (!BN_add_word(tmp, 3)) {
goto err;
}
group->a_is_minus3 = (0 == BN_cmp(tmp, &group->field));
// group->b
if (!BN_nnmod(tmp, b, &group->field, ctx) ||
!ec_bignum_to_felem(group, &group->b, tmp)) {
goto err;
}
if (!ec_bignum_to_felem(group, &group->one, BN_value_one())) {
goto err;
}
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) {
if ((p != NULL && !BN_copy(p, &group->field)) ||
(a != NULL && !ec_felem_to_bignum(group, a, &group->a)) ||
(b != NULL && !ec_felem_to_bignum(group, b, &group->b))) {
return 0;
}
return 1;
}
void ec_GFp_simple_point_init(EC_RAW_POINT *point) {
OPENSSL_memset(&point->X, 0, sizeof(EC_FELEM));
OPENSSL_memset(&point->Y, 0, sizeof(EC_FELEM));
OPENSSL_memset(&point->Z, 0, sizeof(EC_FELEM));
}
void ec_GFp_simple_point_copy(EC_RAW_POINT *dest, const EC_RAW_POINT *src) {
OPENSSL_memcpy(&dest->X, &src->X, sizeof(EC_FELEM));
OPENSSL_memcpy(&dest->Y, &src->Y, sizeof(EC_FELEM));
OPENSSL_memcpy(&dest->Z, &src->Z, sizeof(EC_FELEM));
}
void ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
EC_RAW_POINT *point) {
// Although it is strictly only necessary to zero Z, we zero the entire point
// in case |point| was stack-allocated and yet to be initialized.
ec_GFp_simple_point_init(point);
}
int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
EC_RAW_POINT *point,
const BIGNUM *x,
const BIGNUM *y) {
if (x == NULL || y == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER);
return 0;
}
if (!ec_bignum_to_felem(group, &point->X, x) ||
!ec_bignum_to_felem(group, &point->Y, y)) {
return 0;
}
OPENSSL_memcpy(&point->Z, &group->one, sizeof(EC_FELEM));
return 1;
}
void ec_GFp_simple_invert(const EC_GROUP *group, EC_RAW_POINT *point) {
ec_felem_neg(group, &point->Y, &point->Y);
}
int ec_GFp_simple_is_at_infinity(const EC_GROUP *group,
const EC_RAW_POINT *point) {
return ec_felem_non_zero_mask(group, &point->Z) == 0;
}
int ec_GFp_simple_is_on_curve(const EC_GROUP *group,
const EC_RAW_POINT *point) {
if (ec_GFp_simple_is_at_infinity(group, point)) {
return 1;
}
// 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'.
void (*const felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a,
const EC_FELEM *b) = group->meth->felem_mul;
void (*const felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a) =
group->meth->felem_sqr;
// rh := X^2
EC_FELEM rh;
felem_sqr(group, &rh, &point->X);
EC_FELEM tmp, Z4, Z6;
if (!ec_felem_equal(group, &point->Z, &group->one)) {
felem_sqr(group, &tmp, &point->Z);
felem_sqr(group, &Z4, &tmp);
felem_mul(group, &Z6, &Z4, &tmp);
// rh := (rh + a*Z^4)*X
if (group->a_is_minus3) {
ec_felem_add(group, &tmp, &Z4, &Z4);
ec_felem_add(group, &tmp, &tmp, &Z4);
ec_felem_sub(group, &rh, &rh, &tmp);
felem_mul(group, &rh, &rh, &point->X);
} else {
felem_mul(group, &tmp, &Z4, &group->a);
ec_felem_add(group, &rh, &rh, &tmp);
felem_mul(group, &rh, &rh, &point->X);
}
// rh := rh + b*Z^6
felem_mul(group, &tmp, &group->b, &Z6);
ec_felem_add(group, &rh, &rh, &tmp);
} else {
// rh := (rh + a)*X
ec_felem_add(group, &rh, &rh, &group->a);
felem_mul(group, &rh, &rh, &point->X);
// rh := rh + b
ec_felem_add(group, &rh, &rh, &group->b);
}
// 'lh' := Y^2
felem_sqr(group, &tmp, &point->Y);
return ec_felem_equal(group, &tmp, &rh);
}
int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_RAW_POINT *a,
const EC_RAW_POINT *b) {
// Note this function returns zero if |a| and |b| are equal and 1 if they are
// not equal.
if (ec_GFp_simple_is_at_infinity(group, a)) {
return ec_GFp_simple_is_at_infinity(group, b) ? 0 : 1;
}
if (ec_GFp_simple_is_at_infinity(group, b)) {
return 1;
}
int a_Z_is_one = ec_felem_equal(group, &a->Z, &group->one);
int b_Z_is_one = ec_felem_equal(group, &b->Z, &group->one);
if (a_Z_is_one && b_Z_is_one) {
return !ec_felem_equal(group, &a->X, &b->X) ||
!ec_felem_equal(group, &a->Y, &b->Y);
}
void (*const felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a,
const EC_FELEM *b) = group->meth->felem_mul;
void (*const felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a) =
group->meth->felem_sqr;
// 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).
EC_FELEM tmp1, tmp2, Za23, Zb23;
const EC_FELEM *tmp1_, *tmp2_;
if (!b_Z_is_one) {
felem_sqr(group, &Zb23, &b->Z);
felem_mul(group, &tmp1, &a->X, &Zb23);
tmp1_ = &tmp1;
} else {
tmp1_ = &a->X;
}
if (!a_Z_is_one) {
felem_sqr(group, &Za23, &a->Z);
felem_mul(group, &tmp2, &b->X, &Za23);
tmp2_ = &tmp2;
} else {
tmp2_ = &b->X;
}
// Compare X_a*Z_b^2 with X_b*Z_a^2.
if (!ec_felem_equal(group, tmp1_, tmp2_)) {
return 1; // The points differ.
}
if (!b_Z_is_one) {
felem_mul(group, &Zb23, &Zb23, &b->Z);
felem_mul(group, &tmp1, &a->Y, &Zb23);
// tmp1_ = &tmp1
} else {
tmp1_ = &a->Y;
}
if (!a_Z_is_one) {
felem_mul(group, &Za23, &Za23, &a->Z);
felem_mul(group, &tmp2, &b->Y, &Za23);
// tmp2_ = &tmp2
} else {
tmp2_ = &b->Y;
}
// Compare Y_a*Z_b^3 with Y_b*Z_a^3.
if (!ec_felem_equal(group, tmp1_, tmp2_)) {
return 1; // The points differ.
}
// The points are equal.
return 0;
}
int ec_GFp_simple_mont_inv_mod_ord_vartime(const EC_GROUP *group,
EC_SCALAR *out,
const EC_SCALAR *in) {
// This implementation (in fact) runs in constant time,
// even though for this interface it is not mandatory.
// out = in^-1 in the Montgomery domain. This is
// |ec_scalar_to_montgomery| followed by |ec_scalar_inv_montgomery|, but
// |ec_scalar_inv_montgomery| followed by |ec_scalar_from_montgomery| is
// equivalent and slightly more efficient.
ec_scalar_inv_montgomery(group, out, in);
ec_scalar_from_montgomery(group, out, out);
return 1;
}
int ec_GFp_simple_cmp_x_coordinate(const EC_GROUP *group, const EC_RAW_POINT *p,
const EC_SCALAR *r) {
if (ec_GFp_simple_is_at_infinity(group, p)) {
// |ec_get_x_coordinate_as_scalar| will check this internally, but this way
// we do not push to the error queue.
return 0;
}
EC_SCALAR x;
return ec_get_x_coordinate_as_scalar(group, &x, p) &&
ec_scalar_equal_vartime(group, &x, r);
}