416 lines
12 KiB
C
416 lines
12 KiB
C
/*
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* Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved.
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*
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* Licensed under the OpenSSL license (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*/
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/* ====================================================================
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* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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*
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* The Elliptic Curve Public-Key Crypto Library (ECC Code) included
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* herein is developed by SUN MICROSYSTEMS, INC., and is contributed
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* to the OpenSSL project.
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*
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* The ECC Code is licensed pursuant to the OpenSSL open source
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* license provided below.
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*
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* The software is originally written by Sheueling Chang Shantz and
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* Douglas Stebila of Sun Microsystems Laboratories.
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*
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*/
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#include <openssl/err.h>
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#include "internal/bn_int.h"
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#include "ec_lcl.h"
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#ifndef OPENSSL_NO_EC2M
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/*-
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* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
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* coordinates.
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* Uses algorithm Mdouble in appendix of
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* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
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* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
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* modified to not require precomputation of c=b^{2^{m-1}}.
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*/
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static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z,
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BN_CTX *ctx)
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{
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BIGNUM *t1;
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int ret = 0;
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/* Since Mdouble is static we can guarantee that ctx != NULL. */
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BN_CTX_start(ctx);
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t1 = BN_CTX_get(ctx);
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if (t1 == NULL)
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goto err;
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if (!group->meth->field_sqr(group, x, x, ctx))
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goto err;
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if (!group->meth->field_sqr(group, t1, z, ctx))
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goto err;
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if (!group->meth->field_mul(group, z, x, t1, ctx))
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goto err;
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if (!group->meth->field_sqr(group, x, x, ctx))
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goto err;
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if (!group->meth->field_sqr(group, t1, t1, ctx))
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goto err;
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if (!group->meth->field_mul(group, t1, group->b, t1, ctx))
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goto err;
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if (!BN_GF2m_add(x, x, t1))
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goto err;
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ret = 1;
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err:
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BN_CTX_end(ctx);
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return ret;
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}
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/*-
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* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
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* projective coordinates.
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* Uses algorithm Madd in appendix of
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* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
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* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
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*/
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static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1,
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BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2,
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BN_CTX *ctx)
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{
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BIGNUM *t1, *t2;
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int ret = 0;
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/* Since Madd is static we can guarantee that ctx != NULL. */
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BN_CTX_start(ctx);
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t1 = BN_CTX_get(ctx);
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t2 = BN_CTX_get(ctx);
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if (t2 == NULL)
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goto err;
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if (!BN_copy(t1, x))
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goto err;
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if (!group->meth->field_mul(group, x1, x1, z2, ctx))
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goto err;
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if (!group->meth->field_mul(group, z1, z1, x2, ctx))
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goto err;
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if (!group->meth->field_mul(group, t2, x1, z1, ctx))
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goto err;
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if (!BN_GF2m_add(z1, z1, x1))
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goto err;
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if (!group->meth->field_sqr(group, z1, z1, ctx))
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goto err;
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if (!group->meth->field_mul(group, x1, z1, t1, ctx))
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goto err;
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if (!BN_GF2m_add(x1, x1, t2))
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goto err;
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ret = 1;
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err:
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BN_CTX_end(ctx);
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return ret;
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}
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/*-
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* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
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* using Montgomery point multiplication algorithm Mxy() in appendix of
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* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
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* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
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* Returns:
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* 0 on error
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* 1 if return value should be the point at infinity
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* 2 otherwise
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*/
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static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y,
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BIGNUM *x1, BIGNUM *z1, BIGNUM *x2, BIGNUM *z2,
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BN_CTX *ctx)
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{
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BIGNUM *t3, *t4, *t5;
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int ret = 0;
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if (BN_is_zero(z1)) {
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BN_zero(x2);
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BN_zero(z2);
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return 1;
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}
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if (BN_is_zero(z2)) {
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if (!BN_copy(x2, x))
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return 0;
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if (!BN_GF2m_add(z2, x, y))
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return 0;
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return 2;
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}
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/* Since Mxy is static we can guarantee that ctx != NULL. */
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BN_CTX_start(ctx);
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t3 = BN_CTX_get(ctx);
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t4 = BN_CTX_get(ctx);
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t5 = BN_CTX_get(ctx);
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if (t5 == NULL)
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goto err;
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if (!BN_one(t5))
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goto err;
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if (!group->meth->field_mul(group, t3, z1, z2, ctx))
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goto err;
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if (!group->meth->field_mul(group, z1, z1, x, ctx))
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goto err;
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if (!BN_GF2m_add(z1, z1, x1))
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goto err;
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if (!group->meth->field_mul(group, z2, z2, x, ctx))
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goto err;
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if (!group->meth->field_mul(group, x1, z2, x1, ctx))
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goto err;
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if (!BN_GF2m_add(z2, z2, x2))
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goto err;
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if (!group->meth->field_mul(group, z2, z2, z1, ctx))
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goto err;
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if (!group->meth->field_sqr(group, t4, x, ctx))
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goto err;
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if (!BN_GF2m_add(t4, t4, y))
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goto err;
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if (!group->meth->field_mul(group, t4, t4, t3, ctx))
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goto err;
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if (!BN_GF2m_add(t4, t4, z2))
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goto err;
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if (!group->meth->field_mul(group, t3, t3, x, ctx))
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goto err;
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if (!group->meth->field_div(group, t3, t5, t3, ctx))
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goto err;
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if (!group->meth->field_mul(group, t4, t3, t4, ctx))
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goto err;
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if (!group->meth->field_mul(group, x2, x1, t3, ctx))
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goto err;
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if (!BN_GF2m_add(z2, x2, x))
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goto err;
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if (!group->meth->field_mul(group, z2, z2, t4, ctx))
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goto err;
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if (!BN_GF2m_add(z2, z2, y))
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goto err;
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ret = 2;
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err:
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BN_CTX_end(ctx);
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return ret;
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}
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/*-
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* Computes scalar*point and stores the result in r.
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* point can not equal r.
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* Uses a modified algorithm 2P of
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* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
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* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
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*
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* To protect against side-channel attack the function uses constant time swap,
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* avoiding conditional branches.
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*/
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static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group,
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EC_POINT *r,
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const BIGNUM *scalar,
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const EC_POINT *point,
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BN_CTX *ctx)
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{
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BIGNUM *x1, *x2, *z1, *z2;
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int ret = 0, i;
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BN_ULONG mask, word;
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if (r == point) {
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ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
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return 0;
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}
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/* if result should be point at infinity */
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if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
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EC_POINT_is_at_infinity(group, point)) {
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return EC_POINT_set_to_infinity(group, r);
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}
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/* only support affine coordinates */
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if (!point->Z_is_one)
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return 0;
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/*
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* Since point_multiply is static we can guarantee that ctx != NULL.
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*/
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BN_CTX_start(ctx);
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x1 = BN_CTX_get(ctx);
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z1 = BN_CTX_get(ctx);
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if (z1 == NULL)
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goto err;
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x2 = r->X;
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z2 = r->Y;
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bn_wexpand(x1, bn_get_top(group->field));
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bn_wexpand(z1, bn_get_top(group->field));
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bn_wexpand(x2, bn_get_top(group->field));
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bn_wexpand(z2, bn_get_top(group->field));
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if (!BN_GF2m_mod_arr(x1, point->X, group->poly))
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goto err; /* x1 = x */
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if (!BN_one(z1))
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goto err; /* z1 = 1 */
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if (!group->meth->field_sqr(group, z2, x1, ctx))
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goto err; /* z2 = x1^2 = x^2 */
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if (!group->meth->field_sqr(group, x2, z2, ctx))
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goto err;
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if (!BN_GF2m_add(x2, x2, group->b))
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goto err; /* x2 = x^4 + b */
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/* find top most bit and go one past it */
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i = bn_get_top(scalar) - 1;
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mask = BN_TBIT;
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word = bn_get_words(scalar)[i];
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while (!(word & mask))
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mask >>= 1;
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mask >>= 1;
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/* if top most bit was at word break, go to next word */
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if (!mask) {
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i--;
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mask = BN_TBIT;
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}
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for (; i >= 0; i--) {
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word = bn_get_words(scalar)[i];
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while (mask) {
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BN_consttime_swap(word & mask, x1, x2, bn_get_top(group->field));
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BN_consttime_swap(word & mask, z1, z2, bn_get_top(group->field));
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if (!gf2m_Madd(group, point->X, x2, z2, x1, z1, ctx))
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goto err;
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if (!gf2m_Mdouble(group, x1, z1, ctx))
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goto err;
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BN_consttime_swap(word & mask, x1, x2, bn_get_top(group->field));
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BN_consttime_swap(word & mask, z1, z2, bn_get_top(group->field));
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mask >>= 1;
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}
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mask = BN_TBIT;
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}
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/* convert out of "projective" coordinates */
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i = gf2m_Mxy(group, point->X, point->Y, x1, z1, x2, z2, ctx);
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if (i == 0)
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goto err;
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else if (i == 1) {
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if (!EC_POINT_set_to_infinity(group, r))
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goto err;
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} else {
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if (!BN_one(r->Z))
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goto err;
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r->Z_is_one = 1;
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}
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/* GF(2^m) field elements should always have BIGNUM::neg = 0 */
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BN_set_negative(r->X, 0);
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BN_set_negative(r->Y, 0);
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ret = 1;
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err:
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BN_CTX_end(ctx);
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return ret;
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}
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/*-
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* Computes the sum
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* scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
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* gracefully ignoring NULL scalar values.
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*/
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int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
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const BIGNUM *scalar, size_t num,
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const EC_POINT *points[], const BIGNUM *scalars[],
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BN_CTX *ctx)
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{
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BN_CTX *new_ctx = NULL;
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int ret = 0;
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size_t i;
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EC_POINT *p = NULL;
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EC_POINT *acc = NULL;
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if (ctx == NULL) {
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ctx = new_ctx = BN_CTX_new();
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if (ctx == NULL)
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return 0;
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}
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/*
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* This implementation is more efficient than the wNAF implementation for
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* 2 or fewer points. Use the ec_wNAF_mul implementation for 3 or more
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* points, or if we can perform a fast multiplication based on
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* precomputation.
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*/
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if ((scalar && (num > 1)) || (num > 2)
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|| (num == 0 && EC_GROUP_have_precompute_mult(group))) {
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ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
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goto err;
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}
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if ((p = EC_POINT_new(group)) == NULL)
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goto err;
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if ((acc = EC_POINT_new(group)) == NULL)
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goto err;
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if (!EC_POINT_set_to_infinity(group, acc))
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goto err;
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if (scalar) {
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if (!ec_GF2m_montgomery_point_multiply
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(group, p, scalar, group->generator, ctx))
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goto err;
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if (BN_is_negative(scalar))
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if (!group->meth->invert(group, p, ctx))
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goto err;
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if (!group->meth->add(group, acc, acc, p, ctx))
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goto err;
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}
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for (i = 0; i < num; i++) {
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if (!ec_GF2m_montgomery_point_multiply
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(group, p, scalars[i], points[i], ctx))
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goto err;
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if (BN_is_negative(scalars[i]))
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if (!group->meth->invert(group, p, ctx))
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goto err;
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if (!group->meth->add(group, acc, acc, p, ctx))
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goto err;
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}
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if (!EC_POINT_copy(r, acc))
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goto err;
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ret = 1;
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err:
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EC_POINT_free(p);
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EC_POINT_free(acc);
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BN_CTX_free(new_ctx);
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return ret;
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}
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/*
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* Precomputation for point multiplication: fall back to wNAF methods because
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* ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate
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*/
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int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
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{
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return ec_wNAF_precompute_mult(group, ctx);
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}
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int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
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{
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return ec_wNAF_have_precompute_mult(group);
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}
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#endif
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