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1172 lines
26 KiB
C
1172 lines
26 KiB
C
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/* $OpenBSD: bn_mul.c,v 1.20 2015/02/09 15:49:22 jsing Exp $ */
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/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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* All rights reserved.
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*
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* This package is an SSL implementation written
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* by Eric Young (eay@cryptsoft.com).
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* The implementation was written so as to conform with Netscapes SSL.
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*
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* This library is free for commercial and non-commercial use as long as
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* the following conditions are aheared to. The following conditions
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* apply to all code found in this distribution, be it the RC4, RSA,
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* lhash, DES, etc., code; not just the SSL code. The SSL documentation
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* included with this distribution is covered by the same copyright terms
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* except that the holder is Tim Hudson (tjh@cryptsoft.com).
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*
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* Copyright remains Eric Young's, and as such any Copyright notices in
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* the code are not to be removed.
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* If this package is used in a product, Eric Young should be given attribution
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* as the author of the parts of the library used.
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* This can be in the form of a textual message at program startup or
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* in documentation (online or textual) provided with the package.
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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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* 1. Redistributions of source code must retain the copyright
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* notice, this list of conditions and the following disclaimer.
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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 the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* "This product includes cryptographic software written by
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* Eric Young (eay@cryptsoft.com)"
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* The word 'cryptographic' can be left out if the rouines from the library
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* being used are not cryptographic related :-).
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* 4. If you include any Windows specific code (or a derivative thereof) from
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* the apps directory (application code) you must include an acknowledgement:
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* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
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*
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* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* The licence and distribution terms for any publically available version or
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* derivative of this code cannot be changed. i.e. this code cannot simply be
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* copied and put under another distribution licence
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* [including the GNU Public Licence.]
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*/
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#ifndef BN_DEBUG
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# undef NDEBUG /* avoid conflicting definitions */
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# define NDEBUG
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#endif
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#include <assert.h>
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#include <stdio.h>
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#include <string.h>
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#include <openssl/opensslconf.h>
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#include "bn_lcl.h"
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#if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
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/* Here follows specialised variants of bn_add_words() and
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bn_sub_words(). They have the property performing operations on
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arrays of different sizes. The sizes of those arrays is expressed through
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cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
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which is the delta between the two lengths, calculated as len(a)-len(b).
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All lengths are the number of BN_ULONGs... For the operations that require
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a result array as parameter, it must have the length cl+abs(dl).
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These functions should probably end up in bn_asm.c as soon as there are
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assembler counterparts for the systems that use assembler files. */
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BN_ULONG
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bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl,
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int dl)
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{
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BN_ULONG c, t;
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assert(cl >= 0);
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c = bn_sub_words(r, a, b, cl);
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if (dl == 0)
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return c;
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r += cl;
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a += cl;
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b += cl;
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if (dl < 0) {
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#ifdef BN_COUNT
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fprintf(stderr,
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" bn_sub_part_words %d + %d (dl < 0, c = %d)\n",
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cl, dl, c);
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#endif
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for (;;) {
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t = b[0];
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r[0] = (0 - t - c) & BN_MASK2;
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if (t != 0)
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c = 1;
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if (++dl >= 0)
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break;
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t = b[1];
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r[1] = (0 - t - c) & BN_MASK2;
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if (t != 0)
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c = 1;
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if (++dl >= 0)
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break;
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t = b[2];
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r[2] = (0 - t - c) & BN_MASK2;
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if (t != 0)
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c = 1;
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if (++dl >= 0)
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break;
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t = b[3];
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r[3] = (0 - t - c) & BN_MASK2;
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if (t != 0)
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c = 1;
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if (++dl >= 0)
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break;
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b += 4;
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r += 4;
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}
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} else {
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int save_dl = dl;
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#ifdef BN_COUNT
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fprintf(stderr,
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" bn_sub_part_words %d + %d (dl > 0, c = %d)\n",
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cl, dl, c);
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#endif
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while (c) {
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t = a[0];
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r[0] = (t - c) & BN_MASK2;
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if (t != 0)
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c = 0;
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if (--dl <= 0)
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break;
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t = a[1];
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r[1] = (t - c) & BN_MASK2;
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if (t != 0)
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c = 0;
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if (--dl <= 0)
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break;
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t = a[2];
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r[2] = (t - c) & BN_MASK2;
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if (t != 0)
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c = 0;
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if (--dl <= 0)
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break;
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t = a[3];
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r[3] = (t - c) & BN_MASK2;
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if (t != 0)
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c = 0;
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if (--dl <= 0)
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break;
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save_dl = dl;
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a += 4;
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r += 4;
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}
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if (dl > 0) {
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#ifdef BN_COUNT
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fprintf(stderr,
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" bn_sub_part_words %d + %d (dl > 0, c == 0)\n",
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cl, dl);
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#endif
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if (save_dl > dl) {
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switch (save_dl - dl) {
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case 1:
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r[1] = a[1];
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if (--dl <= 0)
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break;
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case 2:
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r[2] = a[2];
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if (--dl <= 0)
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break;
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case 3:
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r[3] = a[3];
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if (--dl <= 0)
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break;
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}
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a += 4;
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r += 4;
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}
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}
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if (dl > 0) {
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#ifdef BN_COUNT
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fprintf(stderr,
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" bn_sub_part_words %d + %d (dl > 0, copy)\n",
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cl, dl);
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#endif
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for (;;) {
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r[0] = a[0];
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if (--dl <= 0)
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break;
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r[1] = a[1];
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if (--dl <= 0)
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break;
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r[2] = a[2];
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if (--dl <= 0)
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break;
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r[3] = a[3];
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if (--dl <= 0)
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break;
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a += 4;
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r += 4;
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}
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}
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}
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return c;
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}
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#endif
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BN_ULONG
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bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl,
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int dl)
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{
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BN_ULONG c, l, t;
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assert(cl >= 0);
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c = bn_add_words(r, a, b, cl);
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if (dl == 0)
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return c;
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r += cl;
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a += cl;
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b += cl;
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if (dl < 0) {
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int save_dl = dl;
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#ifdef BN_COUNT
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fprintf(stderr,
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" bn_add_part_words %d + %d (dl < 0, c = %d)\n",
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cl, dl, c);
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#endif
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while (c) {
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l = (c + b[0]) & BN_MASK2;
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c = (l < c);
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r[0] = l;
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if (++dl >= 0)
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break;
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l = (c + b[1]) & BN_MASK2;
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c = (l < c);
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r[1] = l;
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if (++dl >= 0)
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break;
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l = (c + b[2]) & BN_MASK2;
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c = (l < c);
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r[2] = l;
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if (++dl >= 0)
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break;
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l = (c + b[3]) & BN_MASK2;
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c = (l < c);
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r[3] = l;
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if (++dl >= 0)
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break;
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save_dl = dl;
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b += 4;
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r += 4;
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}
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if (dl < 0) {
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#ifdef BN_COUNT
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fprintf(stderr,
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" bn_add_part_words %d + %d (dl < 0, c == 0)\n",
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cl, dl);
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#endif
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if (save_dl < dl) {
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switch (dl - save_dl) {
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case 1:
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r[1] = b[1];
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if (++dl >= 0)
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break;
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case 2:
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r[2] = b[2];
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if (++dl >= 0)
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break;
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case 3:
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r[3] = b[3];
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if (++dl >= 0)
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break;
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}
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b += 4;
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r += 4;
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}
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}
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if (dl < 0) {
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#ifdef BN_COUNT
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fprintf(stderr,
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" bn_add_part_words %d + %d (dl < 0, copy)\n",
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cl, dl);
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#endif
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for (;;) {
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r[0] = b[0];
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if (++dl >= 0)
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break;
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r[1] = b[1];
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if (++dl >= 0)
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break;
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r[2] = b[2];
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if (++dl >= 0)
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break;
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r[3] = b[3];
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if (++dl >= 0)
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break;
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b += 4;
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r += 4;
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}
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}
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} else {
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int save_dl = dl;
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#ifdef BN_COUNT
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fprintf(stderr,
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" bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
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#endif
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while (c) {
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t = (a[0] + c) & BN_MASK2;
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c = (t < c);
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r[0] = t;
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if (--dl <= 0)
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break;
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t = (a[1] + c) & BN_MASK2;
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c = (t < c);
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r[1] = t;
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if (--dl <= 0)
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break;
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t = (a[2] + c) & BN_MASK2;
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c = (t < c);
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r[2] = t;
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if (--dl <= 0)
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break;
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t = (a[3] + c) & BN_MASK2;
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c = (t < c);
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r[3] = t;
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if (--dl <= 0)
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break;
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save_dl = dl;
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a += 4;
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r += 4;
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}
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#ifdef BN_COUNT
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fprintf(stderr,
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" bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
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#endif
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if (dl > 0) {
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|
if (save_dl > dl) {
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|
switch (save_dl - dl) {
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|
case 1:
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r[1] = a[1];
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|
if (--dl <= 0)
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|
break;
|
||
|
case 2:
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r[2] = a[2];
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|
if (--dl <= 0)
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|
break;
|
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|
case 3:
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r[3] = a[3];
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if (--dl <= 0)
|
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|
break;
|
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|
}
|
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|
a += 4;
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|
r += 4;
|
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|
}
|
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|
}
|
||
|
if (dl > 0) {
|
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|
#ifdef BN_COUNT
|
||
|
fprintf(stderr,
|
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|
" bn_add_part_words %d + %d (dl > 0, copy)\n",
|
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|
cl, dl);
|
||
|
#endif
|
||
|
for (;;) {
|
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|
r[0] = a[0];
|
||
|
if (--dl <= 0)
|
||
|
break;
|
||
|
r[1] = a[1];
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|
if (--dl <= 0)
|
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|
break;
|
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|
r[2] = a[2];
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|
if (--dl <= 0)
|
||
|
break;
|
||
|
r[3] = a[3];
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|
if (--dl <= 0)
|
||
|
break;
|
||
|
|
||
|
a += 4;
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|
r += 4;
|
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|
}
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|
}
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|
}
|
||
|
return c;
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||
|
}
|
||
|
|
||
|
#ifdef BN_RECURSION
|
||
|
/* Karatsuba recursive multiplication algorithm
|
||
|
* (cf. Knuth, The Art of Computer Programming, Vol. 2) */
|
||
|
|
||
|
/* r is 2*n2 words in size,
|
||
|
* a and b are both n2 words in size.
|
||
|
* n2 must be a power of 2.
|
||
|
* We multiply and return the result.
|
||
|
* t must be 2*n2 words in size
|
||
|
* We calculate
|
||
|
* a[0]*b[0]
|
||
|
* a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
|
||
|
* a[1]*b[1]
|
||
|
*/
|
||
|
/* dnX may not be positive, but n2/2+dnX has to be */
|
||
|
void
|
||
|
bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, int dna,
|
||
|
int dnb, BN_ULONG *t)
|
||
|
{
|
||
|
int n = n2 / 2, c1, c2;
|
||
|
int tna = n + dna, tnb = n + dnb;
|
||
|
unsigned int neg, zero;
|
||
|
BN_ULONG ln, lo, *p;
|
||
|
|
||
|
# ifdef BN_COUNT
|
||
|
fprintf(stderr, " bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
|
||
|
# endif
|
||
|
# ifdef BN_MUL_COMBA
|
||
|
# if 0
|
||
|
if (n2 == 4) {
|
||
|
bn_mul_comba4(r, a, b);
|
||
|
return;
|
||
|
}
|
||
|
# endif
|
||
|
/* Only call bn_mul_comba 8 if n2 == 8 and the
|
||
|
* two arrays are complete [steve]
|
||
|
*/
|
||
|
if (n2 == 8 && dna == 0 && dnb == 0) {
|
||
|
bn_mul_comba8(r, a, b);
|
||
|
return;
|
||
|
}
|
||
|
# endif /* BN_MUL_COMBA */
|
||
|
/* Else do normal multiply */
|
||
|
if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
|
||
|
bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
|
||
|
if ((dna + dnb) < 0)
|
||
|
memset(&r[2*n2 + dna + dnb], 0,
|
||
|
sizeof(BN_ULONG) * -(dna + dnb));
|
||
|
return;
|
||
|
}
|
||
|
/* r=(a[0]-a[1])*(b[1]-b[0]) */
|
||
|
c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
|
||
|
c2 = bn_cmp_part_words(&(b[n]), b,tnb, tnb - n);
|
||
|
zero = neg = 0;
|
||
|
switch (c1 * 3 + c2) {
|
||
|
case -4:
|
||
|
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
|
||
|
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
|
||
|
break;
|
||
|
case -3:
|
||
|
zero = 1;
|
||
|
break;
|
||
|
case -2:
|
||
|
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
|
||
|
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
|
||
|
neg = 1;
|
||
|
break;
|
||
|
case -1:
|
||
|
case 0:
|
||
|
case 1:
|
||
|
zero = 1;
|
||
|
break;
|
||
|
case 2:
|
||
|
bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
|
||
|
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
|
||
|
neg = 1;
|
||
|
break;
|
||
|
case 3:
|
||
|
zero = 1;
|
||
|
break;
|
||
|
case 4:
|
||
|
bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
|
||
|
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
|
||
|
break;
|
||
|
}
|
||
|
|
||
|
# ifdef BN_MUL_COMBA
|
||
|
if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
|
||
|
extra args to do this well */
|
||
|
{
|
||
|
if (!zero)
|
||
|
bn_mul_comba4(&(t[n2]), t, &(t[n]));
|
||
|
else
|
||
|
memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));
|
||
|
|
||
|
bn_mul_comba4(r, a, b);
|
||
|
bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
|
||
|
} else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
|
||
|
take extra args to do this
|
||
|
well */
|
||
|
{
|
||
|
if (!zero)
|
||
|
bn_mul_comba8(&(t[n2]), t, &(t[n]));
|
||
|
else
|
||
|
memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
|
||
|
|
||
|
bn_mul_comba8(r, a, b);
|
||
|
bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
|
||
|
} else
|
||
|
# endif /* BN_MUL_COMBA */
|
||
|
{
|
||
|
p = &(t[n2 * 2]);
|
||
|
if (!zero)
|
||
|
bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
|
||
|
else
|
||
|
memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
|
||
|
bn_mul_recursive(r, a, b, n, 0, 0, p);
|
||
|
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
|
||
|
}
|
||
|
|
||
|
/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
|
||
|
* r[10] holds (a[0]*b[0])
|
||
|
* r[32] holds (b[1]*b[1])
|
||
|
*/
|
||
|
|
||
|
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
|
||
|
|
||
|
if (neg) /* if t[32] is negative */
|
||
|
{
|
||
|
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
|
||
|
} else {
|
||
|
/* Might have a carry */
|
||
|
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
|
||
|
}
|
||
|
|
||
|
/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
|
||
|
* r[10] holds (a[0]*b[0])
|
||
|
* r[32] holds (b[1]*b[1])
|
||
|
* c1 holds the carry bits
|
||
|
*/
|
||
|
c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
|
||
|
if (c1) {
|
||
|
p = &(r[n + n2]);
|
||
|
lo= *p;
|
||
|
ln = (lo + c1) & BN_MASK2;
|
||
|
*p = ln;
|
||
|
|
||
|
/* The overflow will stop before we over write
|
||
|
* words we should not overwrite */
|
||
|
if (ln < (BN_ULONG)c1) {
|
||
|
do {
|
||
|
p++;
|
||
|
lo= *p;
|
||
|
ln = (lo + 1) & BN_MASK2;
|
||
|
*p = ln;
|
||
|
} while (ln == 0);
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
/* n+tn is the word length
|
||
|
* t needs to be n*4 is size, as does r */
|
||
|
/* tnX may not be negative but less than n */
|
||
|
void
|
||
|
bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, int tna,
|
||
|
int tnb, BN_ULONG *t)
|
||
|
{
|
||
|
int i, j, n2 = n * 2;
|
||
|
int c1, c2, neg;
|
||
|
BN_ULONG ln, lo, *p;
|
||
|
|
||
|
# ifdef BN_COUNT
|
||
|
fprintf(stderr, " bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
|
||
|
n, tna, n, tnb);
|
||
|
# endif
|
||
|
if (n < 8) {
|
||
|
bn_mul_normal(r, a, n + tna, b, n + tnb);
|
||
|
return;
|
||
|
}
|
||
|
|
||
|
/* r=(a[0]-a[1])*(b[1]-b[0]) */
|
||
|
c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
|
||
|
c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
|
||
|
neg = 0;
|
||
|
switch (c1 * 3 + c2) {
|
||
|
case -4:
|
||
|
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
|
||
|
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
|
||
|
break;
|
||
|
case -3:
|
||
|
/* break; */
|
||
|
case -2:
|
||
|
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
|
||
|
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
|
||
|
neg = 1;
|
||
|
break;
|
||
|
case -1:
|
||
|
case 0:
|
||
|
case 1:
|
||
|
/* break; */
|
||
|
case 2:
|
||
|
bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
|
||
|
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
|
||
|
neg = 1;
|
||
|
break;
|
||
|
case 3:
|
||
|
/* break; */
|
||
|
case 4:
|
||
|
bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
|
||
|
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
|
||
|
break;
|
||
|
}
|
||
|
/* The zero case isn't yet implemented here. The speedup
|
||
|
would probably be negligible. */
|
||
|
# if 0
|
||
|
if (n == 4) {
|
||
|
bn_mul_comba4(&(t[n2]), t, &(t[n]));
|
||
|
bn_mul_comba4(r, a, b);
|
||
|
bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
|
||
|
memset(&(r[n2 + tn * 2]), 0, sizeof(BN_ULONG) * (n2 - tn * 2));
|
||
|
} else
|
||
|
# endif
|
||
|
if (n == 8) {
|
||
|
bn_mul_comba8(&(t[n2]), t, &(t[n]));
|
||
|
bn_mul_comba8(r, a, b);
|
||
|
bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
|
||
|
memset(&(r[n2 + tna + tnb]), 0,
|
||
|
sizeof(BN_ULONG) * (n2 - tna - tnb));
|
||
|
} else {
|
||
|
p = &(t[n2*2]);
|
||
|
bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
|
||
|
bn_mul_recursive(r, a, b, n, 0, 0, p);
|
||
|
i = n / 2;
|
||
|
/* If there is only a bottom half to the number,
|
||
|
* just do it */
|
||
|
if (tna > tnb)
|
||
|
j = tna - i;
|
||
|
else
|
||
|
j = tnb - i;
|
||
|
if (j == 0) {
|
||
|
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
|
||
|
i, tna - i, tnb - i, p);
|
||
|
memset(&(r[n2 + i * 2]), 0,
|
||
|
sizeof(BN_ULONG) * (n2 - i * 2));
|
||
|
}
|
||
|
else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
|
||
|
{
|
||
|
bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]),
|
||
|
i, tna - i, tnb - i, p);
|
||
|
memset(&(r[n2 + tna + tnb]), 0,
|
||
|
sizeof(BN_ULONG) * (n2 - tna - tnb));
|
||
|
}
|
||
|
else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
|
||
|
{
|
||
|
memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2);
|
||
|
if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&
|
||
|
tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
|
||
|
bn_mul_normal(&(r[n2]), &(a[n]), tna,
|
||
|
&(b[n]), tnb);
|
||
|
} else {
|
||
|
for (;;) {
|
||
|
i /= 2;
|
||
|
/* these simplified conditions work
|
||
|
* exclusively because difference
|
||
|
* between tna and tnb is 1 or 0 */
|
||
|
if (i < tna || i < tnb) {
|
||
|
bn_mul_part_recursive(&(r[n2]),
|
||
|
&(a[n]), &(b[n]), i,
|
||
|
tna - i, tnb - i, p);
|
||
|
break;
|
||
|
} else if (i == tna || i == tnb) {
|
||
|
bn_mul_recursive(&(r[n2]),
|
||
|
&(a[n]), &(b[n]), i,
|
||
|
tna - i, tnb - i, p);
|
||
|
break;
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
|
||
|
* r[10] holds (a[0]*b[0])
|
||
|
* r[32] holds (b[1]*b[1])
|
||
|
*/
|
||
|
|
||
|
c1 = (int)(bn_add_words(t, r,&(r[n2]), n2));
|
||
|
|
||
|
if (neg) /* if t[32] is negative */
|
||
|
{
|
||
|
c1 -= (int)(bn_sub_words(&(t[n2]), t,&(t[n2]), n2));
|
||
|
} else {
|
||
|
/* Might have a carry */
|
||
|
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
|
||
|
}
|
||
|
|
||
|
/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
|
||
|
* r[10] holds (a[0]*b[0])
|
||
|
* r[32] holds (b[1]*b[1])
|
||
|
* c1 holds the carry bits
|
||
|
*/
|
||
|
c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
|
||
|
if (c1) {
|
||
|
p = &(r[n + n2]);
|
||
|
lo= *p;
|
||
|
ln = (lo + c1)&BN_MASK2;
|
||
|
*p = ln;
|
||
|
|
||
|
/* The overflow will stop before we over write
|
||
|
* words we should not overwrite */
|
||
|
if (ln < (BN_ULONG)c1) {
|
||
|
do {
|
||
|
p++;
|
||
|
lo= *p;
|
||
|
ln = (lo + 1) & BN_MASK2;
|
||
|
*p = ln;
|
||
|
} while (ln == 0);
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
/* a and b must be the same size, which is n2.
|
||
|
* r needs to be n2 words and t needs to be n2*2
|
||
|
*/
|
||
|
void
|
||
|
bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, BN_ULONG *t)
|
||
|
{
|
||
|
int n = n2 / 2;
|
||
|
|
||
|
# ifdef BN_COUNT
|
||
|
fprintf(stderr, " bn_mul_low_recursive %d * %d\n",n2,n2);
|
||
|
# endif
|
||
|
|
||
|
bn_mul_recursive(r, a, b, n, 0, 0, &(t[0]));
|
||
|
if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) {
|
||
|
bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2]));
|
||
|
bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
|
||
|
bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2]));
|
||
|
bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
|
||
|
} else {
|
||
|
bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n);
|
||
|
bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n);
|
||
|
bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
|
||
|
bn_add_words(&(r[n]), &(r[n]), &(t[n]), n);
|
||
|
}
|
||
|
}
|
||
|
|
||
|
/* a and b must be the same size, which is n2.
|
||
|
* r needs to be n2 words and t needs to be n2*2
|
||
|
* l is the low words of the output.
|
||
|
* t needs to be n2*3
|
||
|
*/
|
||
|
void
|
||
|
bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
|
||
|
BN_ULONG *t)
|
||
|
{
|
||
|
int i, n;
|
||
|
int c1, c2;
|
||
|
int neg, oneg, zero;
|
||
|
BN_ULONG ll, lc, *lp, *mp;
|
||
|
|
||
|
# ifdef BN_COUNT
|
||
|
fprintf(stderr, " bn_mul_high %d * %d\n",n2,n2);
|
||
|
# endif
|
||
|
n = n2 / 2;
|
||
|
|
||
|
/* Calculate (al-ah)*(bh-bl) */
|
||
|
neg = zero = 0;
|
||
|
c1 = bn_cmp_words(&(a[0]), &(a[n]), n);
|
||
|
c2 = bn_cmp_words(&(b[n]), &(b[0]), n);
|
||
|
switch (c1 * 3 + c2) {
|
||
|
case -4:
|
||
|
bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
|
||
|
bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
|
||
|
break;
|
||
|
case -3:
|
||
|
zero = 1;
|
||
|
break;
|
||
|
case -2:
|
||
|
bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
|
||
|
bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
|
||
|
neg = 1;
|
||
|
break;
|
||
|
case -1:
|
||
|
case 0:
|
||
|
case 1:
|
||
|
zero = 1;
|
||
|
break;
|
||
|
case 2:
|
||
|
bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
|
||
|
bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
|
||
|
neg = 1;
|
||
|
break;
|
||
|
case 3:
|
||
|
zero = 1;
|
||
|
break;
|
||
|
case 4:
|
||
|
bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
|
||
|
bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
|
||
|
break;
|
||
|
}
|
||
|
|
||
|
oneg = neg;
|
||
|
/* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
|
||
|
/* r[10] = (a[1]*b[1]) */
|
||
|
# ifdef BN_MUL_COMBA
|
||
|
if (n == 8) {
|
||
|
bn_mul_comba8(&(t[0]), &(r[0]), &(r[n]));
|
||
|
bn_mul_comba8(r, &(a[n]), &(b[n]));
|
||
|
} else
|
||
|
# endif
|
||
|
{
|
||
|
bn_mul_recursive(&(t[0]), &(r[0]), &(r[n]), n, 0, 0, &(t[n2]));
|
||
|
bn_mul_recursive(r, &(a[n]), &(b[n]), n, 0, 0, &(t[n2]));
|
||
|
}
|
||
|
|
||
|
/* s0 == low(al*bl)
|
||
|
* s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
|
||
|
* We know s0 and s1 so the only unknown is high(al*bl)
|
||
|
* high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
|
||
|
* high(al*bl) == s1 - (r[0]+l[0]+t[0])
|
||
|
*/
|
||
|
if (l != NULL) {
|
||
|
lp = &(t[n2 + n]);
|
||
|
c1 = (int)(bn_add_words(lp, &(r[0]), &(l[0]), n));
|
||
|
} else {
|
||
|
c1 = 0;
|
||
|
lp = &(r[0]);
|
||
|
}
|
||
|
|
||
|
if (neg)
|
||
|
neg = (int)(bn_sub_words(&(t[n2]), lp, &(t[0]), n));
|
||
|
else {
|
||
|
bn_add_words(&(t[n2]), lp, &(t[0]), n);
|
||
|
neg = 0;
|
||
|
}
|
||
|
|
||
|
if (l != NULL) {
|
||
|
bn_sub_words(&(t[n2 + n]), &(l[n]), &(t[n2]), n);
|
||
|
} else {
|
||
|
lp = &(t[n2 + n]);
|
||
|
mp = &(t[n2]);
|
||
|
for (i = 0; i < n; i++)
|
||
|
lp[i] = ((~mp[i]) + 1) & BN_MASK2;
|
||
|
}
|
||
|
|
||
|
/* s[0] = low(al*bl)
|
||
|
* t[3] = high(al*bl)
|
||
|
* t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
|
||
|
* r[10] = (a[1]*b[1])
|
||
|
*/
|
||
|
/* R[10] = al*bl
|
||
|
* R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
|
||
|
* R[32] = ah*bh
|
||
|
*/
|
||
|
/* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
|
||
|
* R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
|
||
|
* R[3]=r[1]+(carry/borrow)
|
||
|
*/
|
||
|
if (l != NULL) {
|
||
|
lp = &(t[n2]);
|
||
|
c1 = (int)(bn_add_words(lp, &(t[n2 + n]), &(l[0]), n));
|
||
|
} else {
|
||
|
lp = &(t[n2 + n]);
|
||
|
c1 = 0;
|
||
|
}
|
||
|
c1 += (int)(bn_add_words(&(t[n2]), lp, &(r[0]), n));
|
||
|
if (oneg)
|
||
|
c1 -= (int)(bn_sub_words(&(t[n2]), &(t[n2]), &(t[0]), n));
|
||
|
else
|
||
|
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), &(t[0]), n));
|
||
|
|
||
|
c2 = (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n2 + n]), n));
|
||
|
c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(r[n]), n));
|
||
|
if (oneg)
|
||
|
c2 -= (int)(bn_sub_words(&(r[0]), &(r[0]), &(t[n]), n));
|
||
|
else
|
||
|
c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n]), n));
|
||
|
|
||
|
if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
|
||
|
{
|
||
|
i = 0;
|
||
|
if (c1 > 0) {
|
||
|
lc = c1;
|
||
|
do {
|
||
|
ll = (r[i] + lc) & BN_MASK2;
|
||
|
r[i++] = ll;
|
||
|
lc = (lc > ll);
|
||
|
} while (lc);
|
||
|
} else {
|
||
|
lc = -c1;
|
||
|
do {
|
||
|
ll = r[i];
|
||
|
r[i++] = (ll - lc) & BN_MASK2;
|
||
|
lc = (lc > ll);
|
||
|
} while (lc);
|
||
|
}
|
||
|
}
|
||
|
if (c2 != 0) /* Add starting at r[1] */
|
||
|
{
|
||
|
i = n;
|
||
|
if (c2 > 0) {
|
||
|
lc = c2;
|
||
|
do {
|
||
|
ll = (r[i] + lc) & BN_MASK2;
|
||
|
r[i++] = ll;
|
||
|
lc = (lc > ll);
|
||
|
} while (lc);
|
||
|
} else {
|
||
|
lc = -c2;
|
||
|
do {
|
||
|
ll = r[i];
|
||
|
r[i++] = (ll - lc) & BN_MASK2;
|
||
|
lc = (lc > ll);
|
||
|
} while (lc);
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
#endif /* BN_RECURSION */
|
||
|
|
||
|
int
|
||
|
BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
|
||
|
{
|
||
|
int ret = 0;
|
||
|
int top, al, bl;
|
||
|
BIGNUM *rr;
|
||
|
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
|
||
|
int i;
|
||
|
#endif
|
||
|
#ifdef BN_RECURSION
|
||
|
BIGNUM *t = NULL;
|
||
|
int j = 0, k;
|
||
|
#endif
|
||
|
|
||
|
#ifdef BN_COUNT
|
||
|
fprintf(stderr, "BN_mul %d * %d\n",a->top,b->top);
|
||
|
#endif
|
||
|
|
||
|
bn_check_top(a);
|
||
|
bn_check_top(b);
|
||
|
bn_check_top(r);
|
||
|
|
||
|
al = a->top;
|
||
|
bl = b->top;
|
||
|
|
||
|
if ((al == 0) || (bl == 0)) {
|
||
|
BN_zero(r);
|
||
|
return (1);
|
||
|
}
|
||
|
top = al + bl;
|
||
|
|
||
|
BN_CTX_start(ctx);
|
||
|
if ((r == a) || (r == b)) {
|
||
|
if ((rr = BN_CTX_get(ctx)) == NULL)
|
||
|
goto err;
|
||
|
} else
|
||
|
rr = r;
|
||
|
rr->neg = a->neg ^ b->neg;
|
||
|
|
||
|
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
|
||
|
i = al - bl;
|
||
|
#endif
|
||
|
#ifdef BN_MUL_COMBA
|
||
|
if (i == 0) {
|
||
|
# if 0
|
||
|
if (al == 4) {
|
||
|
if (bn_wexpand(rr, 8) == NULL)
|
||
|
goto err;
|
||
|
rr->top = 8;
|
||
|
bn_mul_comba4(rr->d, a->d, b->d);
|
||
|
goto end;
|
||
|
}
|
||
|
# endif
|
||
|
if (al == 8) {
|
||
|
if (bn_wexpand(rr, 16) == NULL)
|
||
|
goto err;
|
||
|
rr->top = 16;
|
||
|
bn_mul_comba8(rr->d, a->d, b->d);
|
||
|
goto end;
|
||
|
}
|
||
|
}
|
||
|
#endif /* BN_MUL_COMBA */
|
||
|
#ifdef BN_RECURSION
|
||
|
if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
|
||
|
if (i >= -1 && i <= 1) {
|
||
|
/* Find out the power of two lower or equal
|
||
|
to the longest of the two numbers */
|
||
|
if (i >= 0) {
|
||
|
j = BN_num_bits_word((BN_ULONG)al);
|
||
|
}
|
||
|
if (i == -1) {
|
||
|
j = BN_num_bits_word((BN_ULONG)bl);
|
||
|
}
|
||
|
j = 1 << (j - 1);
|
||
|
assert(j <= al || j <= bl);
|
||
|
k = j + j;
|
||
|
if ((t = BN_CTX_get(ctx)) == NULL)
|
||
|
goto err;
|
||
|
if (al > j || bl > j) {
|
||
|
if (bn_wexpand(t, k * 4) == NULL)
|
||
|
goto err;
|
||
|
if (bn_wexpand(rr, k * 4) == NULL)
|
||
|
goto err;
|
||
|
bn_mul_part_recursive(rr->d, a->d, b->d,
|
||
|
j, al - j, bl - j, t->d);
|
||
|
}
|
||
|
else /* al <= j || bl <= j */
|
||
|
{
|
||
|
if (bn_wexpand(t, k * 2) == NULL)
|
||
|
goto err;
|
||
|
if (bn_wexpand(rr, k * 2) == NULL)
|
||
|
goto err;
|
||
|
bn_mul_recursive(rr->d, a->d, b->d,
|
||
|
j, al - j, bl - j, t->d);
|
||
|
}
|
||
|
rr->top = top;
|
||
|
goto end;
|
||
|
}
|
||
|
#if 0
|
||
|
if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) {
|
||
|
BIGNUM *tmp_bn = (BIGNUM *)b;
|
||
|
if (bn_wexpand(tmp_bn, al) == NULL)
|
||
|
goto err;
|
||
|
tmp_bn->d[bl] = 0;
|
||
|
bl++;
|
||
|
i--;
|
||
|
} else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
|
||
|
BIGNUM *tmp_bn = (BIGNUM *)a;
|
||
|
if (bn_wexpand(tmp_bn, bl) == NULL)
|
||
|
goto err;
|
||
|
tmp_bn->d[al] = 0;
|
||
|
al++;
|
||
|
i++;
|
||
|
}
|
||
|
if (i == 0) {
|
||
|
/* symmetric and > 4 */
|
||
|
/* 16 or larger */
|
||
|
j = BN_num_bits_word((BN_ULONG)al);
|
||
|
j = 1 << (j - 1);
|
||
|
k = j + j;
|
||
|
if ((t = BN_CTX_get(ctx)) == NULL)
|
||
|
goto err;
|
||
|
if (al == j) /* exact multiple */
|
||
|
{
|
||
|
if (bn_wexpand(t, k * 2) == NULL)
|
||
|
goto err;
|
||
|
if (bn_wexpand(rr, k * 2) == NULL)
|
||
|
goto err;
|
||
|
bn_mul_recursive(rr->d, a->d, b->d, al, t->d);
|
||
|
} else {
|
||
|
if (bn_wexpand(t, k * 4) == NULL)
|
||
|
goto err;
|
||
|
if (bn_wexpand(rr, k * 4) == NULL)
|
||
|
goto err;
|
||
|
bn_mul_part_recursive(rr->d, a->d, b->d,
|
||
|
al - j, j, t->d);
|
||
|
}
|
||
|
rr->top = top;
|
||
|
goto end;
|
||
|
}
|
||
|
#endif
|
||
|
}
|
||
|
#endif /* BN_RECURSION */
|
||
|
if (bn_wexpand(rr, top) == NULL)
|
||
|
goto err;
|
||
|
rr->top = top;
|
||
|
bn_mul_normal(rr->d, a->d, al, b->d, bl);
|
||
|
|
||
|
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
|
||
|
end:
|
||
|
#endif
|
||
|
bn_correct_top(rr);
|
||
|
if (r != rr)
|
||
|
BN_copy(r, rr);
|
||
|
ret = 1;
|
||
|
err:
|
||
|
bn_check_top(r);
|
||
|
BN_CTX_end(ctx);
|
||
|
return (ret);
|
||
|
}
|
||
|
|
||
|
void
|
||
|
bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
|
||
|
{
|
||
|
BN_ULONG *rr;
|
||
|
|
||
|
#ifdef BN_COUNT
|
||
|
fprintf(stderr, " bn_mul_normal %d * %d\n", na, nb);
|
||
|
#endif
|
||
|
|
||
|
if (na < nb) {
|
||
|
int itmp;
|
||
|
BN_ULONG *ltmp;
|
||
|
|
||
|
itmp = na;
|
||
|
na = nb;
|
||
|
nb = itmp;
|
||
|
ltmp = a;
|
||
|
a = b;
|
||
|
b = ltmp;
|
||
|
|
||
|
}
|
||
|
rr = &(r[na]);
|
||
|
if (nb <= 0) {
|
||
|
(void)bn_mul_words(r, a, na, 0);
|
||
|
return;
|
||
|
} else
|
||
|
rr[0] = bn_mul_words(r, a, na, b[0]);
|
||
|
|
||
|
for (;;) {
|
||
|
if (--nb <= 0)
|
||
|
return;
|
||
|
rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
|
||
|
if (--nb <= 0)
|
||
|
return;
|
||
|
rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
|
||
|
if (--nb <= 0)
|
||
|
return;
|
||
|
rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
|
||
|
if (--nb <= 0)
|
||
|
return;
|
||
|
rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
|
||
|
rr += 4;
|
||
|
r += 4;
|
||
|
b += 4;
|
||
|
}
|
||
|
}
|
||
|
|
||
|
void
|
||
|
bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
|
||
|
{
|
||
|
#ifdef BN_COUNT
|
||
|
fprintf(stderr, " bn_mul_low_normal %d * %d\n", n, n);
|
||
|
#endif
|
||
|
bn_mul_words(r, a, n, b[0]);
|
||
|
|
||
|
for (;;) {
|
||
|
if (--n <= 0)
|
||
|
return;
|
||
|
bn_mul_add_words(&(r[1]), a, n, b[1]);
|
||
|
if (--n <= 0)
|
||
|
return;
|
||
|
bn_mul_add_words(&(r[2]), a, n, b[2]);
|
||
|
if (--n <= 0)
|
||
|
return;
|
||
|
bn_mul_add_words(&(r[3]), a, n, b[3]);
|
||
|
if (--n <= 0)
|
||
|
return;
|
||
|
bn_mul_add_words(&(r[4]), a, n, b[4]);
|
||
|
r += 4;
|
||
|
b += 4;
|
||
|
}
|
||
|
}
|