/* Copyright (C) 1995-1998 Eric Young ([email protected]) * All rights reserved. * * This package is an SSL implementation written * by Eric Young ([email protected]). * The implementation was written so as to conform with Netscapes SSL. * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson ([email protected]). * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. * * 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 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 acknowledgement: * "This product includes cryptographic software written by * Eric Young ([email protected])" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson ([email protected])" * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND * ANY EXPRESS 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 AUTHOR OR 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. * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence * [including the GNU Public Licence.] */ #include <openssl/bn.h> #include <assert.h> #include <stdlib.h> #include <string.h> #include <openssl/err.h> #include <openssl/mem.h> #include "internal.h" #include "../../internal.h" #define BN_MUL_RECURSIVE_SIZE_NORMAL … #define BN_SQR_RECURSIVE_SIZE_NORMAL … static void bn_abs_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, size_t num, BN_ULONG *tmp) { … } static void bn_mul_normal(BN_ULONG *r, const BN_ULONG *a, size_t na, const BN_ULONG *b, size_t nb) { … } // bn_sub_part_words sets |r| to |a| - |b|. It returns the borrow bit, which is // one if the operation underflowed and zero otherwise. |cl| is the common // length, that is, the shorter of len(a) or len(b). |dl| is the delta length, // that is, len(a) - len(b). |r|'s length matches the larger of |a| and |b|, or // cl + abs(dl). // // TODO(davidben): Make this take |size_t|. The |cl| + |dl| calling convention // is confusing. static BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl, int dl) { … } // bn_abs_sub_part_words computes |r| = |a| - |b|, storing the absolute value // and returning a mask of all ones if the result was negative and all zeros if // the result was positive. |cl| and |dl| follow the |bn_sub_part_words| calling // convention. // // TODO(davidben): Make this take |size_t|. The |cl| + |dl| calling convention // is confusing. static BN_ULONG bn_abs_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl, int dl, BN_ULONG *tmp) { … } int bn_abs_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { … } // Karatsuba recursive multiplication algorithm // (cf. Knuth, The Art of Computer Programming, Vol. 2) // bn_mul_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r| has // length 2*|n2|, |a| has length |n2| + |dna|, |b| has length |n2| + |dnb|, and // |t| has length 4*|n2|. |n2| must be a power of two. Finally, we must have // -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dna| <= 0 and // -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dnb| <= 0. // // TODO(davidben): Simplify and |size_t| the calling convention around lengths // here. static void bn_mul_recursive(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int n2, int dna, int dnb, BN_ULONG *t) { … } // bn_mul_part_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r| // has length 4*|n|, |a| has length |n| + |tna|, |b| has length |n| + |tnb|, and // |t| has length 8*|n|. |n| must be a power of two. Additionally, we must have // 0 <= tna < n and 0 <= tnb < n, and |tna| and |tnb| must differ by at most // one. // // TODO(davidben): Make this take |size_t| and perhaps the actual lengths of |a| // and |b|. static void bn_mul_part_recursive(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int n, int tna, int tnb, BN_ULONG *t) { … } // bn_mul_impl implements |BN_mul| and |bn_mul_consttime|. Note this function // breaks |BIGNUM| invariants and may return a negative zero. This is handled by // the callers. static int bn_mul_impl(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { … } int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { … } int bn_mul_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { … } void bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a, const BN_ULONG *b, size_t num_b) { … } // tmp must have 2*n words static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, size_t n, BN_ULONG *tmp) { … } // bn_sqr_recursive sets |r| to |a|^2, using |t| as scratch space. |r| has // length 2*|n2|, |a| has length |n2|, and |t| has length 4*|n2|. |n2| must be // a power of two. static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, size_t n2, BN_ULONG *t) { … } int BN_mul_word(BIGNUM *bn, BN_ULONG w) { … } int bn_sqr_consttime(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) { … } int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) { … } void bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a) { … }
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