/* 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);
BN_init(&group->a);
BN_init(&group->b);
BN_init(&group->one);
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);
BN_free(&group->one);
}
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)) {
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);
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 &&
!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));
if (group->meth->field_encode != NULL) {
if (!group->meth->field_encode(group, &group->one, BN_value_one(), ctx)) {
goto err;
}
} else if (!BN_copy(&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, BN_CTX *ctx) {
int ret = 0;
BN_CTX *new_ctx = NULL;
if (p != NULL && !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 && !group->meth->field_decode(group, a, &group->a, ctx)) {
goto err;
}
if (b != NULL && !group->meth->field_decode(group, b, &group->b, ctx)) {
goto err;
}
} else {
if (a != NULL && !BN_copy(a, &group->a)) {
goto err;
}
if (b != NULL && !BN_copy(b, &group->b)) {
goto err;
}
}
}
ret = 1;
err:
BN_CTX_free(new_ctx);
return ret;
}
unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *group) {
return BN_num_bits(&group->field);
}
int ec_GFp_simple_point_init(EC_POINT *point) {
BN_init(&point->X);
BN_init(&point->Y);
BN_init(&point->Z);
return 1;
}
void ec_GFp_simple_point_finish(EC_POINT *point) {
BN_free(&point->X);
BN_free(&point->Y);
BN_free(&point->Z);
}
int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) {
if (!BN_copy(&dest->X, &src->X) ||
!BN_copy(&dest->Y, &src->Y) ||
!BN_copy(&dest->Z, &src->Z)) {
return 0;
}
return 1;
}
int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
EC_POINT *point) {
BN_zero(&point->Z);
return 1;
}
static int set_Jprojective_coordinate_GFp(const EC_GROUP *group, BIGNUM *out,
const BIGNUM *in, BN_CTX *ctx) {
if (in == NULL) {
return 1;
}
if (BN_is_negative(in) ||
BN_cmp(in, &group->field) >= 0) {
OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE);
return 0;
}
if (group->meth->field_encode) {
return group->meth->field_encode(group, out, in, ctx);
}
return BN_copy(out, in) != NULL;
}
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) {
OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER);
return 0;
}
BN_CTX *new_ctx = NULL;
int ret = 0;
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL) {
return 0;
}
}
if (!set_Jprojective_coordinate_GFp(group, &point->X, x, ctx) ||
!set_Jprojective_coordinate_GFp(group, &point->Y, y, ctx) ||
!BN_copy(&point->Z, &group->one)) {
goto err;
}
ret = 1;
err:
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
int b_Z_is_one = BN_cmp(&b->Z, &group->one) == 0;
if (b_Z_is_one) {
if (!BN_copy(n1, &a->X) || !BN_copy(n2, &a->Y)) {
goto end;
}
// n1 = X_a
// n2 = Y_a
} else {
if (!field_sqr(group, n0, &b->Z, ctx) ||
!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) ||
!field_mul(group, n2, &a->Y, n0, ctx)) {
goto end;
}
// n2 = Y_a * Z_b^3
}
// n3, n4
int a_Z_is_one = BN_cmp(&a->Z, &group->one) == 0;
if (a_Z_is_one) {
if (!BN_copy(n3, &b->X) || !BN_copy(n4, &b->Y)) {
goto end;
}
// n3 = X_b
// n4 = Y_b
} else {
if (!field_sqr(group, n0, &a->Z, ctx) ||
!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) ||
!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) ||
!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);
ret = 1;
goto end;
}
}
// 'n7', 'n8'
if (!BN_mod_add_quick(n1, n1, n3, p) ||
!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;
}
}
// Z_r = Z_a * Z_b * n5
// X_r
if (!field_sqr(group, n0, n6, ctx) ||
!field_sqr(group, n4, n5, ctx) ||
!field_mul(group, n3, n1, n4, ctx) ||
!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) ||
!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) ||
!field_mul(group, n5, n4, n5, ctx)) {
goto end; // now n5 is n5^3
}
if (!field_mul(group, n1, n2, n5, ctx) ||
!BN_mod_sub_quick(n0, n0, n1, p)) {
goto end;
}
if (BN_is_odd(n0) && !BN_add(n0, n0, p)) {
goto end;
}
// now 0 <= n0 < 2*p, and n0 is even
if (!BN_rshift1(&r->Y, n0)) {
goto end;
}
// Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2
ret = 1;
end:
if (ctx) {
// otherwise we already called BN_CTX_end
BN_CTX_end(ctx);
}
BN_CTX_free(new_ctx);
return ret;
}
int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
BN_CTX *ctx) {
int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *,
BN_CTX *);
int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
const BIGNUM *p;
BN_CTX *new_ctx = NULL;
BIGNUM *n0, *n1, *n2, *n3;
int ret = 0;
if (EC_POINT_is_at_infinity(group, a)) {
BN_zero(&r->Z);
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 (BN_cmp(&a->Z, &group->one) == 0) {
if (!field_sqr(group, n0, &a->X, ctx) ||
!BN_mod_lshift1_quick(n1, n0, p) ||
!BN_mod_add_quick(n0, n0, n1, p) ||
!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) ||
!BN_mod_add_quick(n0, &a->X, n1, p) ||
!BN_mod_sub_quick(n2, &a->X, n1, p) ||
!field_mul(group, n1, n0, n2, ctx) ||
!BN_mod_lshift1_quick(n0, n1, p) ||
!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) ||
!BN_mod_lshift1_quick(n1, n0, p) ||
!BN_mod_add_quick(n0, n0, n1, p) ||
!field_sqr(group, n1, &a->Z, ctx) ||
!field_sqr(group, n1, n1, ctx) ||
!field_mul(group, n1, n1, &group->a, ctx) ||
!BN_mod_add_quick(n1, n1, n0, p)) {
goto err;
}
// n1 = 3 * X_a^2 + a_curve * Z_a^4
}
// Z_r
if (BN_cmp(&a->Z, &group->one) == 0) {
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;
}
// Z_r = 2 * Y_a * Z_a
// n2
if (!field_sqr(group, n3, &a->Y, ctx) ||
!field_mul(group, n2, &a->X, n3, ctx) ||
!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) ||
!field_sqr(group, &r->X, n1, ctx) ||
!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) ||
!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) ||
!field_mul(group, n0, n1, n0, ctx) ||
!BN_mod_sub_quick(&r->Y, n0, n3, p)) {
goto err;
}
// Y_r = n1 * (n2 - X_r) - n3
ret = 1;
err:
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) {
if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) {
// point is its own inverse
return 1;
}
return BN_usub(&point->Y, &group->field, &point->Y);
}
int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) {
return BN_is_zero(&point->Z);
}
int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
BN_CTX *ctx) {
int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *,
BN_CTX *);
int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
const BIGNUM *p;
BN_CTX *new_ctx = NULL;
BIGNUM *rh, *tmp, *Z4, *Z6;
int ret = 0;
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 0;
}
}
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 (BN_cmp(&point->Z, &group->one) != 0) {
if (!field_sqr(group, tmp, &point->Z, ctx) ||
!field_sqr(group, Z4, tmp, ctx) ||
!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) ||
!BN_mod_add_quick(tmp, tmp, Z4, p) ||
!BN_mod_sub_quick(rh, rh, tmp, p) ||
!field_mul(group, rh, rh, &point->X, ctx)) {
goto err;
}
} else {
if (!field_mul(group, tmp, Z4, &group->a, ctx) ||
!BN_mod_add_quick(rh, rh, tmp, p) ||
!field_mul(group, rh, rh, &point->X, ctx)) {
goto err;
}
}
// rh := rh + b*Z^6
if (!field_mul(group, tmp, &group->b, Z6, ctx) ||
!BN_mod_add_quick(rh, rh, tmp, p)) {
goto err;
}
} else {
// rh := (rh + a)*X
if (!BN_mod_add_quick(rh, rh, &group->a, p) ||
!field_mul(group, rh, rh, &point->X, ctx)) {
goto err;
}
// rh := rh + b
if (!BN_mod_add_quick(rh, rh, &group->b, p)) {
goto err;
}
}
// 'lh' := Y^2
if (!field_sqr(group, tmp, &point->Y, ctx)) {
goto err;
}
ret = (0 == BN_ucmp(tmp, rh));
err:
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
const EC_POINT *b, BN_CTX *ctx) {
// return values:
// -1 error
// 0 equal (in affine coordinates)
// 1 not equal
int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *,
BN_CTX *);
int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
BN_CTX *new_ctx = NULL;
BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
const BIGNUM *tmp1_, *tmp2_;
int ret = -1;
if (ec_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 = BN_cmp(&a->Z, &group->one) == 0;
int b_Z_is_one = BN_cmp(&b->Z, &group->one) == 0;
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) ||
!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) ||
!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) ||
!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) ||
!field_mul(group, tmp2, &b->Y, Za23, ctx)) {
goto end;
}
// tmp2_ = tmp2
} else {
tmp2_ = &b->Y;
}
// compare Y_a*Z_b^3 with Y_b*Z_a^3
if (BN_cmp(tmp1_, tmp2_) != 0) {
ret = 1; // points differ
goto end;
}
// points are equal
ret = 0;
end:
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
BN_CTX *ctx) {
BN_CTX *new_ctx = NULL;
BIGNUM *x, *y;
int ret = 0;
if (BN_cmp(&point->Z, &group->one) == 0 ||
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) ||
!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
goto err;
}
if (BN_cmp(&point->Z, &group->one) != 0) {
OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
goto err;
}
ret = 1;
err:
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
EC_POINT *points[], BN_CTX *ctx) {
BN_CTX *new_ctx = NULL;
BIGNUM *tmp, *tmp_Z;
BIGNUM **prod_Z = NULL;
int ret = 0;
if (num == 0) {
return 1;
}
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL) {
return 0;
}
}
BN_CTX_start(ctx);
tmp = BN_CTX_get(ctx);
tmp_Z = BN_CTX_get(ctx);
if (tmp == NULL || tmp_Z == NULL) {
goto err;
}
prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0]));
if (prod_Z == NULL) {
goto err;
}
OPENSSL_memset(prod_Z, 0, num * sizeof(prod_Z[0]));
for (size_t i = 0; i < num; i++) {
prod_Z[i] = BN_new();
if (prod_Z[i] == NULL) {
goto err;
}
}
// Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
// skipping any zero-valued inputs (pretend that they're 1).
if (!BN_is_zero(&points[0]->Z)) {
if (!BN_copy(prod_Z[0], &points[0]->Z)) {
goto err;
}
} else {
if (BN_copy(prod_Z[0], &group->one) == NULL) {
goto err;
}
}
for (size_t i = 1; i < num; i++) {
if (!BN_is_zero(&points[i]->Z)) {
if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1],
&points[i]->Z, ctx)) {
goto err;
}
} else {
if (!BN_copy(prod_Z[i], prod_Z[i - 1])) {
goto err;
}
}
}
// Now use a single explicit inversion to replace every non-zero points[i]->Z
// by its inverse. We use |BN_mod_inverse_odd| instead of doing a constant-
// time inversion using Fermat's Little Theorem because this function is
// usually only used for converting multiples of a public key point to
// affine, and a public key point isn't secret. If we were to use Fermat's
// Little Theorem then the cost of the inversion would usually be so high
// that converting the multiples to affine would be counterproductive.
int no_inverse;
if (!BN_mod_inverse_odd(tmp, &no_inverse, prod_Z[num - 1], &group->field,
ctx)) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
goto err;
}
if (group->meth->field_encode != NULL) {
// In the Montgomery case, we just turned R*H (representing H)
// into 1/(R*H), but we need R*(1/H) (representing 1/H);
// i.e. we need to multiply by the Montgomery factor twice.
if (!group->meth->field_encode(group, tmp, tmp, ctx) ||
!group->meth->field_encode(group, tmp, tmp, ctx)) {
goto err;
}
}
for (size_t i = num - 1; i > 0; --i) {
// Loop invariant: tmp is the product of the inverses of
// points[0]->Z .. points[i]->Z (zero-valued inputs skipped).
if (BN_is_zero(&points[i]->Z)) {
continue;
}
// Set tmp_Z to the inverse of points[i]->Z (as product
// of Z inverses 0 .. i, Z values 0 .. i - 1).
if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx) ||
// Update tmp to satisfy the loop invariant for i - 1.
!group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx) ||
// Replace points[i]->Z by its inverse.
!BN_copy(&points[i]->Z, tmp_Z)) {
goto err;
}
}
// Replace points[0]->Z by its inverse.
if (!BN_is_zero(&points[0]->Z) && !BN_copy(&points[0]->Z, tmp)) {
goto err;
}
// Finally, fix up the X and Y coordinates for all points.
for (size_t i = 0; i < num; i++) {
EC_POINT *p = points[i];
if (!BN_is_zero(&p->Z)) {
// turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1).
if (!group->meth->field_sqr(group, tmp, &p->Z, ctx) ||
!group->meth->field_mul(group, &p->X, &p->X, tmp, ctx) ||
!group->meth->field_mul(group, tmp, tmp, &p->Z, ctx) ||
!group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) {
goto err;
}
if (BN_copy(&p->Z, &group->one) == NULL) {
goto err;
}
}
}
ret = 1;
err:
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
if (prod_Z != NULL) {
for (size_t i = 0; i < num; i++) {
if (prod_Z[i] == NULL) {
break;
}
BN_clear_free(prod_Z[i]);
}
OPENSSL_free(prod_Z);
}
return ret;
}
int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
const BIGNUM *b, BN_CTX *ctx) {
return BN_mod_mul(r, a, b, &group->field, ctx);
}
int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
BN_CTX *ctx) {
return BN_mod_sqr(r, a, &group->field, ctx);
}