889 lines
22 KiB
C
889 lines
22 KiB
C
/* 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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#include <openssl/bn.h>
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#include <assert.h>
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#include <string.h>
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#include "internal.h"
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void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb) {
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BN_ULONG *rr;
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if (na < nb) {
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int itmp;
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BN_ULONG *ltmp;
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itmp = na;
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na = nb;
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nb = itmp;
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ltmp = a;
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a = b;
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b = ltmp;
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}
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rr = &(r[na]);
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if (nb <= 0) {
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(void)bn_mul_words(r, a, na, 0);
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return;
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} else {
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rr[0] = bn_mul_words(r, a, na, b[0]);
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}
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for (;;) {
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if (--nb <= 0) {
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return;
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}
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rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
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if (--nb <= 0) {
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return;
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}
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rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
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if (--nb <= 0) {
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return;
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}
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rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
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if (--nb <= 0) {
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return;
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}
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rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
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rr += 4;
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r += 4;
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b += 4;
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}
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}
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void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n) {
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bn_mul_words(r, a, n, b[0]);
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for (;;) {
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if (--n <= 0) {
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return;
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}
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bn_mul_add_words(&(r[1]), a, n, b[1]);
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if (--n <= 0) {
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return;
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}
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bn_mul_add_words(&(r[2]), a, n, b[2]);
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if (--n <= 0) {
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return;
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}
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bn_mul_add_words(&(r[3]), a, n, b[3]);
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if (--n <= 0) {
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return;
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}
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bn_mul_add_words(&(r[4]), a, n, b[4]);
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r += 4;
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b += 4;
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}
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}
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#if !defined(OPENSSL_X86) || defined(OPENSSL_NO_ASM)
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/* Here follows specialised variants of bn_add_words() and bn_sub_words(). They
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* have the property performing operations on arrays of different sizes. The
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* sizes of those arrays is expressed through cl, which is the common length (
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* basicall, min(len(a),len(b)) ), and dl, which is the delta between the two
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* lengths, calculated as len(a)-len(b). All lengths are the number of
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* BN_ULONGs... For the operations that require a result array as parameter,
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* it must have the length cl+abs(dl). These functions should probably end up
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* in bn_asm.c as soon as there are assembler counterparts for the systems that
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* use assembler files. */
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static BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a,
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const BN_ULONG *b, int cl, int dl) {
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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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}
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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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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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}
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if (++dl >= 0) {
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break;
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}
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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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}
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if (++dl >= 0) {
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break;
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}
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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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}
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if (++dl >= 0) {
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break;
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}
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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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}
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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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} else {
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int save_dl = dl;
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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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}
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if (--dl <= 0) {
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break;
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}
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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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}
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if (--dl <= 0) {
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break;
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}
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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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}
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if (--dl <= 0) {
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break;
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}
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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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}
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if (--dl <= 0) {
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break;
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}
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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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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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}
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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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}
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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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}
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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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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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}
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r[1] = a[1];
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if (--dl <= 0) {
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break;
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}
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r[2] = a[2];
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if (--dl <= 0) {
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break;
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}
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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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}
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return c;
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}
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#else
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/* On other platforms the function is defined in asm. */
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BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
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int cl, int dl);
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#endif
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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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/* dnX may not be positive, but n2/2+dnX has to be */
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static 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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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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/* Only call bn_mul_comba 8 if n2 == 8 and the
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* two arrays are complete [steve]
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*/
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if (n2 == 8 && dna == 0 && dnb == 0) {
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bn_mul_comba8(r, a, b);
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return;
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}
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/* Else do normal multiply */
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if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
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bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
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if ((dna + dnb) < 0) {
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memset(&r[2 * n2 + dna + dnb], 0, sizeof(BN_ULONG) * -(dna + dnb));
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}
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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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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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if (n == 4 && dna == 0 && dnb == 0) {
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/* XXX: bn_mul_comba4 could take extra args to do this well */
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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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}
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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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} else if (n == 8 && dna == 0 && dnb == 0) {
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/* XXX: bn_mul_comba8 could take extra args to do this well */
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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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}
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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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} else {
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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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}
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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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c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
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if (neg) {
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/* if t[32] is negative */
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c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
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} else {
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/* Might have a carry */
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c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
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}
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/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
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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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* c1 holds the carry bits */
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c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
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if (c1) {
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p = &(r[n + n2]);
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lo = *p;
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ln = (lo + c1) & BN_MASK2;
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*p = ln;
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/* The overflow will stop before we over write
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* words we should not overwrite */
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if (ln < (BN_ULONG)c1) {
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do {
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p++;
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lo = *p;
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ln = (lo + 1) & BN_MASK2;
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*p = ln;
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} while (ln == 0);
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}
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}
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}
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/* n+tn is the word length
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* t needs to be n*4 is size, as does r */
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/* tnX may not be negative but less than n */
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static void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
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int tna, int tnb, BN_ULONG *t) {
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int i, j, n2 = n * 2;
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int c1, c2, neg;
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BN_ULONG ln, lo, *p;
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if (n < 8) {
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bn_mul_normal(r, a, n + tna, b, n + tnb);
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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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neg = 0;
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switch (c1 * 3 + c2) {
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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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/* 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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/* 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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/* 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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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);
|
|
}
|
|
}
|
|
}
|
|
|
|
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
|
|
int ret = 0;
|
|
int top, al, bl;
|
|
BIGNUM *rr;
|
|
int i;
|
|
BIGNUM *t = NULL;
|
|
int j = 0, k;
|
|
|
|
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;
|
|
|
|
i = al - bl;
|
|
if (i == 0) {
|
|
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;
|
|
}
|
|
}
|
|
|
|
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;
|
|
t = BN_CTX_get(ctx);
|
|
if (t == 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 (bn_wexpand(rr, top) == NULL) {
|
|
goto err;
|
|
}
|
|
rr->top = top;
|
|
bn_mul_normal(rr->d, a->d, al, b->d, bl);
|
|
|
|
end:
|
|
bn_correct_top(rr);
|
|
if (r != rr && !BN_copy(r, rr)) {
|
|
goto err;
|
|
}
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return ret;
|
|
}
|
|
|
|
/* tmp must have 2*n words */
|
|
static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp) {
|
|
int i, j, max;
|
|
const BN_ULONG *ap;
|
|
BN_ULONG *rp;
|
|
|
|
max = n * 2;
|
|
ap = a;
|
|
rp = r;
|
|
rp[0] = rp[max - 1] = 0;
|
|
rp++;
|
|
j = n;
|
|
|
|
if (--j > 0) {
|
|
ap++;
|
|
rp[j] = bn_mul_words(rp, ap, j, ap[-1]);
|
|
rp += 2;
|
|
}
|
|
|
|
for (i = n - 2; i > 0; i--) {
|
|
j--;
|
|
ap++;
|
|
rp[j] = bn_mul_add_words(rp, ap, j, ap[-1]);
|
|
rp += 2;
|
|
}
|
|
|
|
bn_add_words(r, r, r, max);
|
|
|
|
/* There will not be a carry */
|
|
|
|
bn_sqr_words(tmp, a, n);
|
|
|
|
bn_add_words(r, r, tmp, max);
|
|
}
|
|
|
|
/* r is 2*n words in size,
|
|
* a and b are both n words in size. (There's not actually a 'b' here ...)
|
|
* n must be a power of 2.
|
|
* We multiply and return the result.
|
|
* t must be 2*n 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]
|
|
*/
|
|
static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t) {
|
|
int n = n2 / 2;
|
|
int zero, c1;
|
|
BN_ULONG ln, lo, *p;
|
|
|
|
if (n2 == 4) {
|
|
bn_sqr_comba4(r, a);
|
|
return;
|
|
} else if (n2 == 8) {
|
|
bn_sqr_comba8(r, a);
|
|
return;
|
|
}
|
|
if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
|
|
bn_sqr_normal(r, a, n2, t);
|
|
return;
|
|
}
|
|
/* r=(a[0]-a[1])*(a[1]-a[0]) */
|
|
c1 = bn_cmp_words(a, &(a[n]), n);
|
|
zero = 0;
|
|
if (c1 > 0) {
|
|
bn_sub_words(t, a, &(a[n]), n);
|
|
} else if (c1 < 0) {
|
|
bn_sub_words(t, &(a[n]), a, n);
|
|
} else {
|
|
zero = 1;
|
|
}
|
|
|
|
/* The result will always be negative unless it is zero */
|
|
p = &(t[n2 * 2]);
|
|
|
|
if (!zero) {
|
|
bn_sqr_recursive(&(t[n2]), t, n, p);
|
|
} else {
|
|
memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
|
|
}
|
|
bn_sqr_recursive(r, a, n, p);
|
|
bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);
|
|
|
|
/* t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
|
|
* r[10] holds (a[0]*b[0])
|
|
* r[32] holds (b[1]*b[1]) */
|
|
|
|
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
|
|
|
|
/* t[32] is negative */
|
|
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
|
|
|
|
/* t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
|
|
* r[10] holds (a[0]*a[0])
|
|
* r[32] holds (a[1]*a[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);
|
|
}
|
|
}
|
|
}
|
|
|
|
int BN_mul_word(BIGNUM *bn, BN_ULONG w) {
|
|
BN_ULONG ll;
|
|
|
|
w &= BN_MASK2;
|
|
if (!bn->top) {
|
|
return 1;
|
|
}
|
|
|
|
if (w == 0) {
|
|
BN_zero(bn);
|
|
return 1;
|
|
}
|
|
|
|
ll = bn_mul_words(bn->d, bn->d, bn->top, w);
|
|
if (ll) {
|
|
if (bn_wexpand(bn, bn->top + 1) == NULL) {
|
|
return 0;
|
|
}
|
|
bn->d[bn->top++] = ll;
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
|
|
int max, al;
|
|
int ret = 0;
|
|
BIGNUM *tmp, *rr;
|
|
|
|
al = a->top;
|
|
if (al <= 0) {
|
|
r->top = 0;
|
|
r->neg = 0;
|
|
return 1;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
rr = (a != r) ? r : BN_CTX_get(ctx);
|
|
tmp = BN_CTX_get(ctx);
|
|
if (!rr || !tmp) {
|
|
goto err;
|
|
}
|
|
|
|
max = 2 * al; /* Non-zero (from above) */
|
|
if (bn_wexpand(rr, max) == NULL) {
|
|
goto err;
|
|
}
|
|
|
|
if (al == 4) {
|
|
bn_sqr_comba4(rr->d, a->d);
|
|
} else if (al == 8) {
|
|
bn_sqr_comba8(rr->d, a->d);
|
|
} else {
|
|
if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
|
|
BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
|
|
bn_sqr_normal(rr->d, a->d, al, t);
|
|
} else {
|
|
int j, k;
|
|
|
|
j = BN_num_bits_word((BN_ULONG)al);
|
|
j = 1 << (j - 1);
|
|
k = j + j;
|
|
if (al == j) {
|
|
if (bn_wexpand(tmp, k * 2) == NULL) {
|
|
goto err;
|
|
}
|
|
bn_sqr_recursive(rr->d, a->d, al, tmp->d);
|
|
} else {
|
|
if (bn_wexpand(tmp, max) == NULL) {
|
|
goto err;
|
|
}
|
|
bn_sqr_normal(rr->d, a->d, al, tmp->d);
|
|
}
|
|
}
|
|
}
|
|
|
|
rr->neg = 0;
|
|
/* If the most-significant half of the top word of 'a' is zero, then
|
|
* the square of 'a' will max-1 words. */
|
|
if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l)) {
|
|
rr->top = max - 1;
|
|
} else {
|
|
rr->top = max;
|
|
}
|
|
|
|
if (rr != r && !BN_copy(r, rr)) {
|
|
goto err;
|
|
}
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return ret;
|
|
}
|