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463 lines
14 KiB
463 lines
14 KiB
/* crypto/ec/ec2_mult.c */ |
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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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/* ==================================================================== |
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* Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. |
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* |
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* Redistribution and use in source and binary forms, with or without |
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* modification, are permitted provided that the following conditions |
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* are met: |
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* |
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* 1. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
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* |
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* 2. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in |
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* the documentation and/or other materials provided with the |
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* distribution. |
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* |
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* 3. All advertising materials mentioning features or use of this |
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* software must display the following acknowledgment: |
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* "This product includes software developed by the OpenSSL Project |
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* for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
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* |
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* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
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* endorse or promote products derived from this software without |
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* prior written permission. For written permission, please contact |
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* openssl-core@openssl.org. |
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* |
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* 5. Products derived from this software may not be called "OpenSSL" |
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* nor may "OpenSSL" appear in their names without prior written |
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* permission of the OpenSSL Project. |
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* |
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* 6. Redistributions of any form whatsoever must retain the following |
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* acknowledgment: |
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* "This product includes software developed by the OpenSSL Project |
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* for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
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* |
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* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
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* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
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* OF THE POSSIBILITY OF SUCH DAMAGE. |
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* ==================================================================== |
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* |
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* This product includes cryptographic software written by Eric Young |
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* (eay@cryptsoft.com). This product includes software written by Tim |
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* Hudson (tjh@cryptsoft.com). |
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* |
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*/ |
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#include <openssl/err.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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/*- |
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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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|
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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, group->field.top); |
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bn_wexpand(z1, group->field.top); |
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bn_wexpand(x2, group->field.top); |
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bn_wexpand(z2, group->field.top); |
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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 = scalar->top - 1; |
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mask = BN_TBIT; |
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word = scalar->d[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 = scalar->d[i]; |
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while (mask) { |
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BN_consttime_swap(word & mask, x1, x2, group->field.top); |
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BN_consttime_swap(word & mask, z1, z2, group->field.top); |
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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, group->field.top); |
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BN_consttime_swap(word & mask, z1, z2, group->field.top); |
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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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if (p) |
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EC_POINT_free(p); |
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if (acc) |
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EC_POINT_free(acc); |
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if (new_ctx != NULL) |
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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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|
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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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