1157 lines
24 KiB
C
1157 lines
24 KiB
C
/* crypto/bn/bn_mul.c */
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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 <stdio.h>
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#include <assert.h>
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#include "cryptlib.h"
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#include "bn_lcl.h"
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#if defined(NO_ASM) || !defined(__i386) /* Assembler implementation exists only for x86 */
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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 bn_sub_part_words(BN_ULONG *r,
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const BN_ULONG *a, const BN_ULONG *b,
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int cl, 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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{
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#ifdef BN_COUNT
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fprintf(stderr, " bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
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#endif
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for (;;)
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{
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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) c=1;
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if (++dl >= 0) 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) c=1;
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if (++dl >= 0) 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) c=1;
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if (++dl >= 0) 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) c=1;
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if (++dl >= 0) 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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{
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int save_dl = dl;
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#ifdef BN_COUNT
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fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);
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#endif
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while(c)
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{
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t = a[0];
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r[0] = (t-c)&BN_MASK2;
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if (t != 0) c=0;
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if (--dl <= 0) 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) c=0;
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if (--dl <= 0) 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) c=0;
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if (--dl <= 0) 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) c=0;
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if (--dl <= 0) 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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{
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#ifdef BN_COUNT
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fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
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#endif
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if (save_dl > dl)
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{
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switch (save_dl - dl)
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{
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case 1:
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r[1] = a[1];
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if (--dl <= 0) break;
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case 2:
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r[2] = a[2];
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if (--dl <= 0) break;
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case 3:
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r[3] = a[3];
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if (--dl <= 0) 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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{
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#ifdef BN_COUNT
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fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);
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#endif
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for(;;)
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{
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r[0] = a[0];
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if (--dl <= 0) break;
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r[1] = a[1];
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if (--dl <= 0) break;
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r[2] = a[2];
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if (--dl <= 0) break;
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r[3] = a[3];
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if (--dl <= 0) 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 bn_add_part_words(BN_ULONG *r,
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const BN_ULONG *a, const BN_ULONG *b,
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int cl, 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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{
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int save_dl = dl;
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#ifdef BN_COUNT
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fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
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#endif
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while (c)
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{
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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) 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) 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) 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) 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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{
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#ifdef BN_COUNT
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fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);
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#endif
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if (save_dl < dl)
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{
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switch (dl - save_dl)
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{
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case 1:
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r[1] = b[1];
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if (++dl >= 0) break;
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case 2:
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r[2] = b[2];
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if (++dl >= 0) break;
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case 3:
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r[3] = b[3];
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if (++dl >= 0) 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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{
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#ifdef BN_COUNT
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fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);
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#endif
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for(;;)
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{
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r[0] = b[0];
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if (++dl >= 0) break;
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r[1] = b[1];
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if (++dl >= 0) break;
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r[2] = b[2];
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if (++dl >= 0) break;
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r[3] = b[3];
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if (++dl >= 0) 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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}
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else
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{
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int save_dl = dl;
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#ifdef BN_COUNT
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fprintf(stderr, " 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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{
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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) 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) 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) 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) 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, " 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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{
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if (save_dl > dl)
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{
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switch (save_dl - dl)
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{
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case 1:
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r[1] = a[1];
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if (--dl <= 0) break;
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case 2:
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r[2] = a[2];
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if (--dl <= 0) break;
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case 3:
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r[3] = a[3];
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if (--dl <= 0) 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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{
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#ifdef BN_COUNT
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fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);
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#endif
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for(;;)
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{
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r[0] = a[0];
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if (--dl <= 0) break;
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r[1] = a[1];
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if (--dl <= 0) break;
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r[2] = a[2];
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if (--dl <= 0) break;
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r[3] = a[3];
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if (--dl <= 0) 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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#ifdef BN_RECURSION
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/* Karatsuba recursive multiplication algorithm
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* (cf. Knuth, The Art of Computer Programming, Vol. 2) */
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/* r is 2*n2 words in size,
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* a and b are both n2 words in size.
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* n2 must be a power of 2.
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* We multiply and return the result.
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* t must be 2*n2 words in size
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* We calculate
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* a[0]*b[0]
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* a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
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* a[1]*b[1]
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*/
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void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
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int dna, int dnb, BN_ULONG *t)
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{
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int n=n2/2,c1,c2;
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int tna=n+dna, tnb=n+dnb;
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unsigned int neg,zero;
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BN_ULONG ln,lo,*p;
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# ifdef BN_COUNT
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fprintf(stderr," bn_mul_recursive %d * %d\n",n2,n2);
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# endif
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# ifdef BN_MUL_COMBA
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# if 0
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if (n2 == 4)
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{
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bn_mul_comba4(r,a,b);
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return;
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}
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# endif
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if (n2 == 8)
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{
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bn_mul_comba8(r,a,b);
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return;
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}
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# endif /* BN_MUL_COMBA */
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if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
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{
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/* This should not happen */
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bn_mul_normal(r,a,n2,b,n2);
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return;
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}
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/* r=(a[0]-a[1])*(b[1]-b[0]) */
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c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
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c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
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zero=neg=0;
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switch (c1*3+c2)
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{
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case -4:
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bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
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bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
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break;
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case -3:
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zero=1;
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break;
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case -2:
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bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
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bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */
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neg=1;
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break;
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case -1:
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case 0:
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case 1:
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zero=1;
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break;
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case 2:
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bn_sub_part_words(t, a, &(a[n]),tna,n-tna); /* + */
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bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
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neg=1;
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break;
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case 3:
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zero=1;
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break;
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case 4:
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bn_sub_part_words(t, a, &(a[n]),tna,n-tna);
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bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n);
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break;
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}
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# ifdef BN_MUL_COMBA
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if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
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extra args to do this well */
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{
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if (!zero)
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bn_mul_comba4(&(t[n2]),t,&(t[n]));
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else
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memset(&(t[n2]),0,8*sizeof(BN_ULONG));
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bn_mul_comba4(r,a,b);
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bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
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}
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else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
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take extra args to do this
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well */
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{
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if (!zero)
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bn_mul_comba8(&(t[n2]),t,&(t[n]));
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else
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memset(&(t[n2]),0,16*sizeof(BN_ULONG));
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bn_mul_comba8(r,a,b);
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bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
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}
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else
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# endif /* BN_MUL_COMBA */
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{
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p= &(t[n2*2]);
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if (!zero)
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bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
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else
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memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
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bn_mul_recursive(r,a,b,n,0,0,p);
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bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
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}
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/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
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* r[10] holds (a[0]*b[0])
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* r[32] holds (b[1]*b[1])
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*/
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c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
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if (neg) /* if t[32] is negative */
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{
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c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
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}
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else
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{
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/* Might have a carry */
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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 */
|
|
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;
|
|
unsigned int c1,c2,neg,zero;
|
|
BN_ULONG ln,lo,*p;
|
|
|
|
# ifdef BN_COUNT
|
|
fprintf(stderr," bn_mul_part_recursive (%d+%d) * (%d+%d)\n",
|
|
tna, n, tnb, n);
|
|
# 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);
|
|
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;
|
|
}
|
|
/* 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;
|
|
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 < 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)
|
|
{
|
|
int sav_j =0;
|
|
/* 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);
|
|
}
|
|
sav_j = j;
|
|
j = 1<<(j-1);
|
|
assert(j <= al || j <= bl);
|
|
k = j+j;
|
|
t = BN_CTX_get(ctx);
|
|
if (al > j || bl > j)
|
|
{
|
|
bn_wexpand(t,k*4);
|
|
bn_wexpand(rr,k*4);
|
|
bn_mul_part_recursive(rr->d,a->d,b->d,
|
|
j,al-j,bl-j,t->d);
|
|
}
|
|
else /* al <= j || bl <= j */
|
|
{
|
|
bn_wexpand(t,k*2);
|
|
bn_wexpand(rr,k*2);
|
|
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;
|
|
bn_wexpand(tmp_bn,al);
|
|
tmp_bn->d[bl]=0;
|
|
bl++;
|
|
i--;
|
|
}
|
|
else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
|
|
{
|
|
BIGNUM *tmp_bn = (BIGNUM *)a;
|
|
bn_wexpand(tmp_bn,bl);
|
|
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;
|
|
t = BN_CTX_get(ctx);
|
|
if (al == j) /* exact multiple */
|
|
{
|
|
bn_wexpand(t,k*2);
|
|
bn_wexpand(rr,k*2);
|
|
bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
|
|
}
|
|
else
|
|
{
|
|
bn_wexpand(t,k*4);
|
|
bn_wexpand(rr,k*4);
|
|
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_fix_top(rr);
|
|
if (r != rr) BN_copy(r,rr);
|
|
ret=1;
|
|
err:
|
|
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;
|
|
}
|
|
}
|