godotengine
/
godot
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
godot/drivers/builtin_openssl2/crypto/ec/ec2_mult.c

464 lines
14 KiB
C
Raw Blame History

/* crypto/ec/ec2_mult.c */
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* The Elliptic Curve Public-Key Crypto Library (ECC Code) included
* herein is developed by SUN MICROSYSTEMS, INC., and is contributed
* to the OpenSSL project.
*
* The ECC Code is licensed pursuant to the OpenSSL open source
* license provided below.
*
* The software is originally written by Sheueling Chang Shantz and
* Douglas Stebila of Sun Microsystems Laboratories.
*
*/
/* ====================================================================
* Copyright (c) 1998-2003 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).
*
*/
#include <openssl/err.h>
#include "ec_lcl.h"
#ifndef OPENSSL_NO_EC2M
/*-
* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
* coordinates.
* Uses algorithm Mdouble in appendix of
* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
* modified to not require precomputation of c=b^{2^{m-1}}.
*/
static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z,
BN_CTX *ctx)
{
BIGNUM *t1;
int ret = 0;
/* Since Mdouble is static we can guarantee that ctx != NULL. */
BN_CTX_start(ctx);
t1 = BN_CTX_get(ctx);
if (t1 == NULL)
goto err;
if (!group->meth->field_sqr(group, x, x, ctx))
goto err;
if (!group->meth->field_sqr(group, t1, z, ctx))
goto err;
if (!group->meth->field_mul(group, z, x, t1, ctx))
goto err;
if (!group->meth->field_sqr(group, x, x, ctx))
goto err;
if (!group->meth->field_sqr(group, t1, t1, ctx))
goto err;
if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
goto err;
if (!BN_GF2m_add(x, x, t1))
goto err;
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/*-
* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
* projective coordinates.
* Uses algorithm Madd in appendix of
* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
*/
static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1,
BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2,
BN_CTX *ctx)
{
BIGNUM *t1, *t2;
int ret = 0;
/* Since Madd is static we can guarantee that ctx != NULL. */
BN_CTX_start(ctx);
t1 = BN_CTX_get(ctx);
t2 = BN_CTX_get(ctx);
if (t2 == NULL)
goto err;
if (!BN_copy(t1, x))
goto err;
if (!group->meth->field_mul(group, x1, x1, z2, ctx))
goto err;
if (!group->meth->field_mul(group, z1, z1, x2, ctx))
goto err;
if (!group->meth->field_mul(group, t2, x1, z1, ctx))
goto err;
if (!BN_GF2m_add(z1, z1, x1))
goto err;
if (!group->meth->field_sqr(group, z1, z1, ctx))
goto err;
if (!group->meth->field_mul(group, x1, z1, t1, ctx))
goto err;
if (!BN_GF2m_add(x1, x1, t2))
goto err;
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/*-
* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
* using Montgomery point multiplication algorithm Mxy() in appendix of
* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
* Returns:
* 0 on error
* 1 if return value should be the point at infinity
* 2 otherwise
*/
static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y,
BIGNUM *x1, BIGNUM *z1, BIGNUM *x2, BIGNUM *z2,
BN_CTX *ctx)
{
BIGNUM *t3, *t4, *t5;
int ret = 0;
if (BN_is_zero(z1)) {
BN_zero(x2);
BN_zero(z2);
return 1;
}
if (BN_is_zero(z2)) {
if (!BN_copy(x2, x))
return 0;
if (!BN_GF2m_add(z2, x, y))
return 0;
return 2;
}
/* Since Mxy is static we can guarantee that ctx != NULL. */
BN_CTX_start(ctx);
t3 = BN_CTX_get(ctx);
t4 = BN_CTX_get(ctx);
t5 = BN_CTX_get(ctx);
if (t5 == NULL)
goto err;
if (!BN_one(t5))
goto err;
if (!group->meth->field_mul(group, t3, z1, z2, ctx))
goto err;
if (!group->meth->field_mul(group, z1, z1, x, ctx))
goto err;
if (!BN_GF2m_add(z1, z1, x1))
goto err;
if (!group->meth->field_mul(group, z2, z2, x, ctx))
goto err;
if (!group->meth->field_mul(group, x1, z2, x1, ctx))
goto err;
if (!BN_GF2m_add(z2, z2, x2))
goto err;
if (!group->meth->field_mul(group, z2, z2, z1, ctx))
goto err;
if (!group->meth->field_sqr(group, t4, x, ctx))
goto err;
if (!BN_GF2m_add(t4, t4, y))
goto err;
if (!group->meth->field_mul(group, t4, t4, t3, ctx))
goto err;
if (!BN_GF2m_add(t4, t4, z2))
goto err;
if (!group->meth->field_mul(group, t3, t3, x, ctx))
goto err;
if (!group->meth->field_div(group, t3, t5, t3, ctx))
goto err;
if (!group->meth->field_mul(group, t4, t3, t4, ctx))
goto err;
if (!group->meth->field_mul(group, x2, x1, t3, ctx))
goto err;
if (!BN_GF2m_add(z2, x2, x))
goto err;
if (!group->meth->field_mul(group, z2, z2, t4, ctx))
goto err;
if (!BN_GF2m_add(z2, z2, y))
goto err;
ret = 2;
err:
BN_CTX_end(ctx);
return ret;
}
/*-
* Computes scalar*point and stores the result in r.
* point can not equal r.
* Uses a modified algorithm 2P of
* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
*
* To protect against side-channel attack the function uses constant time swap,
* avoiding conditional branches.
*/
static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group,
EC_POINT *r,
const BIGNUM *scalar,
const EC_POINT *point,
BN_CTX *ctx)
{
BIGNUM *x1, *x2, *z1, *z2;
int ret = 0, i;
BN_ULONG mask, word;
if (r == point) {
ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
return 0;
}
/* if result should be point at infinity */
if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
EC_POINT_is_at_infinity(group, point)) {
return EC_POINT_set_to_infinity(group, r);
}
/* only support affine coordinates */
if (!point->Z_is_one)
return 0;
/*
* Since point_multiply is static we can guarantee that ctx != NULL.
*/
BN_CTX_start(ctx);
x1 = BN_CTX_get(ctx);
z1 = BN_CTX_get(ctx);
if (z1 == NULL)
goto err;
x2 = &r->X;
z2 = &r->Y;
bn_wexpand(x1, group->field.top);
bn_wexpand(z1, group->field.top);
bn_wexpand(x2, group->field.top);
bn_wexpand(z2, group->field.top);
if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
goto err; /* x1 = x */
if (!BN_one(z1))
goto err; /* z1 = 1 */
if (!group->meth->field_sqr(group, z2, x1, ctx))
goto err; /* z2 = x1^2 = x^2 */
if (!group->meth->field_sqr(group, x2, z2, ctx))
goto err;
if (!BN_GF2m_add(x2, x2, &group->b))
goto err; /* x2 = x^4 + b */
/* find top most bit and go one past it */
i = scalar->top - 1;
mask = BN_TBIT;
word = scalar->d[i];
while (!(word & mask))
mask >>= 1;
mask >>= 1;
/* if top most bit was at word break, go to next word */
if (!mask) {
i--;
mask = BN_TBIT;
}
for (; i >= 0; i--) {
word = scalar->d[i];
while (mask) {
BN_consttime_swap(word & mask, x1, x2, group->field.top);
BN_consttime_swap(word & mask, z1, z2, group->field.top);
if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
goto err;
if (!gf2m_Mdouble(group, x1, z1, ctx))
goto err;
BN_consttime_swap(word & mask, x1, x2, group->field.top);
BN_consttime_swap(word & mask, z1, z2, group->field.top);
mask >>= 1;
}
mask = BN_TBIT;
}
/* convert out of "projective" coordinates */
i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
if (i == 0)
goto err;
else if (i == 1) {
if (!EC_POINT_set_to_infinity(group, r))
goto err;
} else {
if (!BN_one(&r->Z))
goto err;
r->Z_is_one = 1;
}
/* GF(2^m) field elements should always have BIGNUM::neg = 0 */
BN_set_negative(&r->X, 0);
BN_set_negative(&r->Y, 0);
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/*-
* Computes the sum
* scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
* gracefully ignoring NULL scalar values.
*/
int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
const BIGNUM *scalar, size_t num,
const EC_POINT *points[], const BIGNUM *scalars[],
BN_CTX *ctx)
{
BN_CTX *new_ctx = NULL;
int ret = 0;
size_t i;
EC_POINT *p = NULL;
EC_POINT *acc = NULL;
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
return 0;
}
/*
* This implementation is more efficient than the wNAF implementation for
* 2 or fewer points. Use the ec_wNAF_mul implementation for 3 or more
* points, or if we can perform a fast multiplication based on
* precomputation.
*/
if ((scalar && (num > 1)) || (num > 2)
|| (num == 0 && EC_GROUP_have_precompute_mult(group))) {
ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
goto err;
}
if ((p = EC_POINT_new(group)) == NULL)
goto err;
if ((acc = EC_POINT_new(group)) == NULL)
goto err;
if (!EC_POINT_set_to_infinity(group, acc))
goto err;
if (scalar) {
if (!ec_GF2m_montgomery_point_multiply
(group, p, scalar, group->generator, ctx))
goto err;
if (BN_is_negative(scalar))
if (!group->meth->invert(group, p, ctx))
goto err;
if (!group->meth->add(group, acc, acc, p, ctx))
goto err;
}
for (i = 0; i < num; i++) {
if (!ec_GF2m_montgomery_point_multiply
(group, p, scalars[i], points[i], ctx))
goto err;
if (BN_is_negative(scalars[i]))
if (!group->meth->invert(group, p, ctx))
goto err;
if (!group->meth->add(group, acc, acc, p, ctx))
goto err;
}
if (!EC_POINT_copy(r, acc))
goto err;
ret = 1;
err:
if (p)
EC_POINT_free(p);
if (acc)
EC_POINT_free(acc);
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
return ret;
}
/*
* Precomputation for point multiplication: fall back to wNAF methods because
* ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate
*/
int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
{
return ec_wNAF_precompute_mult(group, ctx);
}
int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
{
return ec_wNAF_have_precompute_mult(group);
}
#endif
Reference in New Issue View Git Blame Copy Permalink