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2702 lines
56 KiB
C
2702 lines
56 KiB
C
/* tfm.c
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*
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* Copyright (C) 2006-2015 wolfSSL Inc.
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*
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* This file is part of wolfSSL. (formerly known as CyaSSL)
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*
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* wolfSSL is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* wolfSSL is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
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*/
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/*
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* Based on public domain TomsFastMath 0.10 by Tom St Denis, tomstdenis@iahu.ca,
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* http://math.libtomcrypt.com
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*/
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/**
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* Edited by Moisés Guimarães (moisesguimaraesm@gmail.com)
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* to fit CyaSSL's needs.
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*/
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#ifdef HAVE_CONFIG_H
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#include <config.h>
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#endif
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/* in case user set USE_FAST_MATH there */
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#include <wolfssl/wolfcrypt/settings.h>
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#ifdef USE_FAST_MATH
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#include <wolfssl/wolfcrypt/tfm.h>
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#include <wolfcrypt/src/asm.c> /* will define asm MACROS or C ones */
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/* math settings check */
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word32 CheckRunTimeSettings(void)
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{
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return CTC_SETTINGS;
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}
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/* math settings size check */
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word32 CheckRunTimeFastMath(void)
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{
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return FP_SIZE;
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}
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/* Functions */
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void fp_add(fp_int *a, fp_int *b, fp_int *c)
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{
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int sa, sb;
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/* get sign of both inputs */
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sa = a->sign;
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sb = b->sign;
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/* handle two cases, not four */
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if (sa == sb) {
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/* both positive or both negative */
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/* add their magnitudes, copy the sign */
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c->sign = sa;
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s_fp_add (a, b, c);
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} else {
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/* one positive, the other negative */
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/* subtract the one with the greater magnitude from */
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/* the one of the lesser magnitude. The result gets */
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/* the sign of the one with the greater magnitude. */
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if (fp_cmp_mag (a, b) == FP_LT) {
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c->sign = sb;
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s_fp_sub (b, a, c);
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} else {
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c->sign = sa;
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s_fp_sub (a, b, c);
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}
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}
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}
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/* unsigned addition */
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void s_fp_add(fp_int *a, fp_int *b, fp_int *c)
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{
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int x, y, oldused;
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register fp_word t;
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y = MAX(a->used, b->used);
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oldused = MIN(c->used, FP_SIZE); /* help static analysis w/ largest size */
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c->used = y;
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t = 0;
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for (x = 0; x < y; x++) {
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t += ((fp_word)a->dp[x]) + ((fp_word)b->dp[x]);
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c->dp[x] = (fp_digit)t;
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t >>= DIGIT_BIT;
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}
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if (t != 0 && x < FP_SIZE) {
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c->dp[c->used++] = (fp_digit)t;
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++x;
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}
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c->used = x;
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for (; x < oldused; x++) {
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c->dp[x] = 0;
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}
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fp_clamp(c);
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}
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/* c = a - b */
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void fp_sub(fp_int *a, fp_int *b, fp_int *c)
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{
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int sa, sb;
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sa = a->sign;
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sb = b->sign;
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if (sa != sb) {
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/* subtract a negative from a positive, OR */
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/* subtract a positive from a negative. */
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/* In either case, ADD their magnitudes, */
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/* and use the sign of the first number. */
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c->sign = sa;
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s_fp_add (a, b, c);
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} else {
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/* subtract a positive from a positive, OR */
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/* subtract a negative from a negative. */
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/* First, take the difference between their */
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/* magnitudes, then... */
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if (fp_cmp_mag (a, b) != FP_LT) {
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/* Copy the sign from the first */
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c->sign = sa;
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/* The first has a larger or equal magnitude */
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s_fp_sub (a, b, c);
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} else {
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/* The result has the *opposite* sign from */
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/* the first number. */
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c->sign = (sa == FP_ZPOS) ? FP_NEG : FP_ZPOS;
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/* The second has a larger magnitude */
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s_fp_sub (b, a, c);
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}
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}
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}
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/* unsigned subtraction ||a|| >= ||b|| ALWAYS! */
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void s_fp_sub(fp_int *a, fp_int *b, fp_int *c)
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{
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int x, oldbused, oldused;
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fp_word t;
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oldused = c->used;
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oldbused = b->used;
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c->used = a->used;
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t = 0;
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for (x = 0; x < oldbused; x++) {
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t = ((fp_word)a->dp[x]) - (((fp_word)b->dp[x]) + t);
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c->dp[x] = (fp_digit)t;
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t = (t >> DIGIT_BIT)&1;
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}
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for (; x < a->used; x++) {
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t = ((fp_word)a->dp[x]) - t;
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c->dp[x] = (fp_digit)t;
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t = (t >> DIGIT_BIT)&1;
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}
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for (; x < oldused; x++) {
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c->dp[x] = 0;
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}
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fp_clamp(c);
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}
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/* c = a * b */
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void fp_mul(fp_int *A, fp_int *B, fp_int *C)
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{
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int y, yy;
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y = MAX(A->used, B->used);
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yy = MIN(A->used, B->used);
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/* call generic if we're out of range */
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if (y + yy > FP_SIZE) {
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fp_mul_comba(A, B, C);
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return ;
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}
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/* pick a comba (unrolled 4/8/16/32 x or rolled) based on the size
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of the largest input. We also want to avoid doing excess mults if the
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inputs are not close to the next power of two. That is, for example,
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if say y=17 then we would do (32-17)^2 = 225 unneeded multiplications
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*/
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#ifdef TFM_MUL3
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if (y <= 3) {
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fp_mul_comba3(A,B,C);
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return;
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}
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#endif
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#ifdef TFM_MUL4
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if (y == 4) {
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fp_mul_comba4(A,B,C);
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return;
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}
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#endif
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#ifdef TFM_MUL6
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if (y <= 6) {
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fp_mul_comba6(A,B,C);
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return;
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}
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#endif
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#ifdef TFM_MUL7
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if (y == 7) {
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fp_mul_comba7(A,B,C);
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return;
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}
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#endif
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#ifdef TFM_MUL8
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if (y == 8) {
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fp_mul_comba8(A,B,C);
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return;
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}
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#endif
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#ifdef TFM_MUL9
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if (y == 9) {
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fp_mul_comba9(A,B,C);
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return;
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}
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#endif
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#ifdef TFM_MUL12
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if (y <= 12) {
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fp_mul_comba12(A,B,C);
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return;
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}
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#endif
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#ifdef TFM_MUL17
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if (y <= 17) {
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fp_mul_comba17(A,B,C);
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return;
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}
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#endif
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#ifdef TFM_SMALL_SET
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if (y <= 16) {
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fp_mul_comba_small(A,B,C);
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return;
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}
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#endif
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#if defined(TFM_MUL20)
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if (y <= 20) {
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fp_mul_comba20(A,B,C);
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return;
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}
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#endif
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#if defined(TFM_MUL24)
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if (yy >= 16 && y <= 24) {
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fp_mul_comba24(A,B,C);
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return;
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}
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#endif
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#if defined(TFM_MUL28)
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if (yy >= 20 && y <= 28) {
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fp_mul_comba28(A,B,C);
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return;
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}
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#endif
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#if defined(TFM_MUL32)
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if (yy >= 24 && y <= 32) {
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fp_mul_comba32(A,B,C);
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return;
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}
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#endif
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#if defined(TFM_MUL48)
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if (yy >= 40 && y <= 48) {
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fp_mul_comba48(A,B,C);
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return;
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}
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#endif
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#if defined(TFM_MUL64)
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if (yy >= 56 && y <= 64) {
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fp_mul_comba64(A,B,C);
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return;
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}
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#endif
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fp_mul_comba(A,B,C);
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}
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void fp_mul_2(fp_int * a, fp_int * b)
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{
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int x, oldused;
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oldused = b->used;
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b->used = a->used;
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{
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register fp_digit r, rr, *tmpa, *tmpb;
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/* alias for source */
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tmpa = a->dp;
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/* alias for dest */
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tmpb = b->dp;
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/* carry */
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r = 0;
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for (x = 0; x < a->used; x++) {
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/* get what will be the *next* carry bit from the
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* MSB of the current digit
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*/
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rr = *tmpa >> ((fp_digit)(DIGIT_BIT - 1));
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/* now shift up this digit, add in the carry [from the previous] */
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*tmpb++ = ((*tmpa++ << ((fp_digit)1)) | r);
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/* copy the carry that would be from the source
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* digit into the next iteration
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*/
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r = rr;
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}
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/* new leading digit? */
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if (r != 0 && b->used != (FP_SIZE-1)) {
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/* add a MSB which is always 1 at this point */
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*tmpb = 1;
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++(b->used);
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}
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/* now zero any excess digits on the destination
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* that we didn't write to
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*/
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tmpb = b->dp + b->used;
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for (x = b->used; x < oldused; x++) {
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*tmpb++ = 0;
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}
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}
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b->sign = a->sign;
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}
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/* c = a * b */
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void fp_mul_d(fp_int *a, fp_digit b, fp_int *c)
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{
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fp_word w;
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int x, oldused;
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oldused = c->used;
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c->used = a->used;
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c->sign = a->sign;
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w = 0;
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for (x = 0; x < a->used; x++) {
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w = ((fp_word)a->dp[x]) * ((fp_word)b) + w;
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c->dp[x] = (fp_digit)w;
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w = w >> DIGIT_BIT;
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}
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if (w != 0 && (a->used != FP_SIZE)) {
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c->dp[c->used++] = (fp_digit) w;
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++x;
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}
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for (; x < oldused; x++) {
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c->dp[x] = 0;
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}
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fp_clamp(c);
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}
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/* c = a * 2**d */
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void fp_mul_2d(fp_int *a, int b, fp_int *c)
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{
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fp_digit carry, carrytmp, shift;
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int x;
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/* copy it */
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fp_copy(a, c);
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/* handle whole digits */
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if (b >= DIGIT_BIT) {
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fp_lshd(c, b/DIGIT_BIT);
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}
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b %= DIGIT_BIT;
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/* shift the digits */
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if (b != 0) {
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carry = 0;
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shift = DIGIT_BIT - b;
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for (x = 0; x < c->used; x++) {
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carrytmp = c->dp[x] >> shift;
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c->dp[x] = (c->dp[x] << b) + carry;
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carry = carrytmp;
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}
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/* store last carry if room */
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if (carry && x < FP_SIZE) {
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c->dp[c->used++] = carry;
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}
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}
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fp_clamp(c);
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}
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/* generic PxQ multiplier */
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#if defined(HAVE_INTEL_MULX)
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INLINE static void fp_mul_comba_mulx(fp_int *A, fp_int *B, fp_int *C)
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{
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int ix, iy, iz, pa;
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fp_int tmp, *dst;
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/* get size of output and trim */
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pa = A->used + B->used;
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if (pa >= FP_SIZE) {
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pa = FP_SIZE-1;
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}
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if (A == C || B == C) {
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fp_init(&tmp);
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dst = &tmp;
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} else {
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fp_zero(C);
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dst = C;
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}
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TFM_INTEL_MUL_COMBA(A, B, dst) ;
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dst->used = pa;
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dst->sign = A->sign ^ B->sign;
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fp_clamp(dst);
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fp_copy(dst, C);
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}
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#endif
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void fp_mul_comba(fp_int *A, fp_int *B, fp_int *C)
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{
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int ix, iy, iz, tx, ty, pa;
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fp_digit c0, c1, c2, *tmpx, *tmpy;
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fp_int tmp, *dst;
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IF_HAVE_INTEL_MULX(fp_mul_comba_mulx(A, B, C), return) ;
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COMBA_START;
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COMBA_CLEAR;
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/* get size of output and trim */
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pa = A->used + B->used;
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if (pa >= FP_SIZE) {
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pa = FP_SIZE-1;
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}
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if (A == C || B == C) {
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fp_init(&tmp);
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dst = &tmp;
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} else {
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fp_zero(C);
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dst = C;
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}
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for (ix = 0; ix < pa; ix++) {
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/* get offsets into the two bignums */
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ty = MIN(ix, B->used-1);
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tx = ix - ty;
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/* setup temp aliases */
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tmpx = A->dp + tx;
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tmpy = B->dp + ty;
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/* this is the number of times the loop will iterrate, essentially its
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while (tx++ < a->used && ty-- >= 0) { ... }
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*/
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iy = MIN(A->used-tx, ty+1);
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/* execute loop */
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COMBA_FORWARD;
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for (iz = 0; iz < iy; ++iz) {
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/* TAO change COMBA_ADD back to MULADD */
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MULADD(*tmpx++, *tmpy--);
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}
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/* store term */
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COMBA_STORE(dst->dp[ix]);
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}
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COMBA_FINI;
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dst->used = pa;
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dst->sign = A->sign ^ B->sign;
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fp_clamp(dst);
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fp_copy(dst, C);
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}
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/* a/b => cb + d == a */
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int fp_div(fp_int *a, fp_int *b, fp_int *c, fp_int *d)
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{
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fp_int q, x, y, t1, t2;
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int n, t, i, norm, neg;
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/* is divisor zero ? */
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if (fp_iszero (b) == 1) {
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return FP_VAL;
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}
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/* if a < b then q=0, r = a */
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if (fp_cmp_mag (a, b) == FP_LT) {
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if (d != NULL) {
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fp_copy (a, d);
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}
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if (c != NULL) {
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fp_zero (c);
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}
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return FP_OKAY;
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}
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|
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fp_init(&q);
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q.used = a->used + 2;
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fp_init(&t1);
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fp_init(&t2);
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fp_init_copy(&x, a);
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fp_init_copy(&y, b);
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/* fix the sign */
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neg = (a->sign == b->sign) ? FP_ZPOS : FP_NEG;
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x.sign = y.sign = FP_ZPOS;
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/* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
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norm = fp_count_bits(&y) % DIGIT_BIT;
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if (norm < (int)(DIGIT_BIT-1)) {
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norm = (DIGIT_BIT-1) - norm;
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fp_mul_2d (&x, norm, &x);
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fp_mul_2d (&y, norm, &y);
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} else {
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norm = 0;
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}
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/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
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n = x.used - 1;
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t = y.used - 1;
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|
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/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
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fp_lshd (&y, n - t); /* y = y*b**{n-t} */
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|
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while (fp_cmp (&x, &y) != FP_LT) {
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++(q.dp[n - t]);
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fp_sub (&x, &y, &x);
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}
|
|
|
|
/* reset y by shifting it back down */
|
|
fp_rshd (&y, n - t);
|
|
|
|
/* step 3. for i from n down to (t + 1) */
|
|
for (i = n; i >= (t + 1); i--) {
|
|
if (i > x.used) {
|
|
continue;
|
|
}
|
|
|
|
/* step 3.1 if xi == yt then set q{i-t-1} to b-1,
|
|
* otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
|
|
if (x.dp[i] == y.dp[t]) {
|
|
q.dp[i - t - 1] = (fp_digit) ((((fp_word)1) << DIGIT_BIT) - 1);
|
|
} else {
|
|
fp_word tmp;
|
|
tmp = ((fp_word) x.dp[i]) << ((fp_word) DIGIT_BIT);
|
|
tmp |= ((fp_word) x.dp[i - 1]);
|
|
tmp /= ((fp_word)y.dp[t]);
|
|
q.dp[i - t - 1] = (fp_digit) (tmp);
|
|
}
|
|
|
|
/* while (q{i-t-1} * (yt * b + y{t-1})) >
|
|
xi * b**2 + xi-1 * b + xi-2
|
|
|
|
do q{i-t-1} -= 1;
|
|
*/
|
|
q.dp[i - t - 1] = (q.dp[i - t - 1] + 1);
|
|
do {
|
|
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1);
|
|
|
|
/* find left hand */
|
|
fp_zero (&t1);
|
|
t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
|
|
t1.dp[1] = y.dp[t];
|
|
t1.used = 2;
|
|
fp_mul_d (&t1, q.dp[i - t - 1], &t1);
|
|
|
|
/* find right hand */
|
|
t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
|
|
t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
|
|
t2.dp[2] = x.dp[i];
|
|
t2.used = 3;
|
|
} while (fp_cmp_mag(&t1, &t2) == FP_GT);
|
|
|
|
/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
|
|
fp_mul_d (&y, q.dp[i - t - 1], &t1);
|
|
fp_lshd (&t1, i - t - 1);
|
|
fp_sub (&x, &t1, &x);
|
|
|
|
/* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
|
|
if (x.sign == FP_NEG) {
|
|
fp_copy (&y, &t1);
|
|
fp_lshd (&t1, i - t - 1);
|
|
fp_add (&x, &t1, &x);
|
|
q.dp[i - t - 1] = q.dp[i - t - 1] - 1;
|
|
}
|
|
}
|
|
|
|
/* now q is the quotient and x is the remainder
|
|
* [which we have to normalize]
|
|
*/
|
|
|
|
/* get sign before writing to c */
|
|
x.sign = x.used == 0 ? FP_ZPOS : a->sign;
|
|
|
|
if (c != NULL) {
|
|
fp_clamp (&q);
|
|
fp_copy (&q, c);
|
|
c->sign = neg;
|
|
}
|
|
|
|
if (d != NULL) {
|
|
fp_div_2d (&x, norm, &x, NULL);
|
|
|
|
/* the following is a kludge, essentially we were seeing the right remainder but
|
|
with excess digits that should have been zero
|
|
*/
|
|
for (i = b->used; i < x.used; i++) {
|
|
x.dp[i] = 0;
|
|
}
|
|
fp_clamp(&x);
|
|
fp_copy (&x, d);
|
|
}
|
|
|
|
return FP_OKAY;
|
|
}
|
|
|
|
/* b = a/2 */
|
|
void fp_div_2(fp_int * a, fp_int * b)
|
|
{
|
|
int x, oldused;
|
|
|
|
oldused = b->used;
|
|
b->used = a->used;
|
|
{
|
|
register fp_digit r, rr, *tmpa, *tmpb;
|
|
|
|
/* source alias */
|
|
tmpa = a->dp + b->used - 1;
|
|
|
|
/* dest alias */
|
|
tmpb = b->dp + b->used - 1;
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = b->used - 1; x >= 0; x--) {
|
|
/* get the carry for the next iteration */
|
|
rr = *tmpa & 1;
|
|
|
|
/* shift the current digit, add in carry and store */
|
|
*tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
|
|
|
|
/* forward carry to next iteration */
|
|
r = rr;
|
|
}
|
|
|
|
/* zero excess digits */
|
|
tmpb = b->dp + b->used;
|
|
for (x = b->used; x < oldused; x++) {
|
|
*tmpb++ = 0;
|
|
}
|
|
}
|
|
b->sign = a->sign;
|
|
fp_clamp (b);
|
|
}
|
|
|
|
/* c = a / 2**b */
|
|
void fp_div_2d(fp_int *a, int b, fp_int *c, fp_int *d)
|
|
{
|
|
int D;
|
|
fp_int t;
|
|
|
|
/* if the shift count is <= 0 then we do no work */
|
|
if (b <= 0) {
|
|
fp_copy (a, c);
|
|
if (d != NULL) {
|
|
fp_zero (d);
|
|
}
|
|
return;
|
|
}
|
|
|
|
fp_init(&t);
|
|
|
|
/* get the remainder */
|
|
if (d != NULL) {
|
|
fp_mod_2d (a, b, &t);
|
|
}
|
|
|
|
/* copy */
|
|
fp_copy(a, c);
|
|
|
|
/* shift by as many digits in the bit count */
|
|
if (b >= (int)DIGIT_BIT) {
|
|
fp_rshd (c, b / DIGIT_BIT);
|
|
}
|
|
|
|
/* shift any bit count < DIGIT_BIT */
|
|
D = (b % DIGIT_BIT);
|
|
if (D != 0) {
|
|
fp_rshb(c, D);
|
|
}
|
|
fp_clamp (c);
|
|
if (d != NULL) {
|
|
fp_copy (&t, d);
|
|
}
|
|
}
|
|
|
|
/* c = a mod b, 0 <= c < b */
|
|
int fp_mod(fp_int *a, fp_int *b, fp_int *c)
|
|
{
|
|
fp_int t;
|
|
int err;
|
|
|
|
fp_init(&t);
|
|
if ((err = fp_div(a, b, NULL, &t)) != FP_OKAY) {
|
|
return err;
|
|
}
|
|
if (t.sign != b->sign) {
|
|
fp_add(&t, b, c);
|
|
} else {
|
|
fp_copy(&t, c);
|
|
}
|
|
return FP_OKAY;
|
|
}
|
|
|
|
/* c = a mod 2**d */
|
|
void fp_mod_2d(fp_int *a, int b, fp_int *c)
|
|
{
|
|
int x;
|
|
|
|
/* zero if count less than or equal to zero */
|
|
if (b <= 0) {
|
|
fp_zero(c);
|
|
return;
|
|
}
|
|
|
|
/* get copy of input */
|
|
fp_copy(a, c);
|
|
|
|
/* if 2**d is larger than we just return */
|
|
if (b >= (DIGIT_BIT * a->used)) {
|
|
return;
|
|
}
|
|
|
|
/* zero digits above the last digit of the modulus */
|
|
for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
|
|
c->dp[x] = 0;
|
|
}
|
|
/* clear the digit that is not completely outside/inside the modulus */
|
|
c->dp[b / DIGIT_BIT] &= ~((fp_digit)0) >> (DIGIT_BIT - b);
|
|
fp_clamp (c);
|
|
}
|
|
|
|
static int fp_invmod_slow (fp_int * a, fp_int * b, fp_int * c)
|
|
{
|
|
fp_int x, y, u, v, A, B, C, D;
|
|
int res;
|
|
|
|
/* b cannot be negative */
|
|
if (b->sign == FP_NEG || fp_iszero(b) == 1) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
/* init temps */
|
|
fp_init(&x); fp_init(&y);
|
|
fp_init(&u); fp_init(&v);
|
|
fp_init(&A); fp_init(&B);
|
|
fp_init(&C); fp_init(&D);
|
|
|
|
/* x = a, y = b */
|
|
if ((res = fp_mod(a, b, &x)) != FP_OKAY) {
|
|
return res;
|
|
}
|
|
fp_copy(b, &y);
|
|
|
|
/* 2. [modified] if x,y are both even then return an error! */
|
|
if (fp_iseven (&x) == 1 && fp_iseven (&y) == 1) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
|
fp_copy (&x, &u);
|
|
fp_copy (&y, &v);
|
|
fp_set (&A, 1);
|
|
fp_set (&D, 1);
|
|
|
|
top:
|
|
/* 4. while u is even do */
|
|
while (fp_iseven (&u) == 1) {
|
|
/* 4.1 u = u/2 */
|
|
fp_div_2 (&u, &u);
|
|
|
|
/* 4.2 if A or B is odd then */
|
|
if (fp_isodd (&A) == 1 || fp_isodd (&B) == 1) {
|
|
/* A = (A+y)/2, B = (B-x)/2 */
|
|
fp_add (&A, &y, &A);
|
|
fp_sub (&B, &x, &B);
|
|
}
|
|
/* A = A/2, B = B/2 */
|
|
fp_div_2 (&A, &A);
|
|
fp_div_2 (&B, &B);
|
|
}
|
|
|
|
/* 5. while v is even do */
|
|
while (fp_iseven (&v) == 1) {
|
|
/* 5.1 v = v/2 */
|
|
fp_div_2 (&v, &v);
|
|
|
|
/* 5.2 if C or D is odd then */
|
|
if (fp_isodd (&C) == 1 || fp_isodd (&D) == 1) {
|
|
/* C = (C+y)/2, D = (D-x)/2 */
|
|
fp_add (&C, &y, &C);
|
|
fp_sub (&D, &x, &D);
|
|
}
|
|
/* C = C/2, D = D/2 */
|
|
fp_div_2 (&C, &C);
|
|
fp_div_2 (&D, &D);
|
|
}
|
|
|
|
/* 6. if u >= v then */
|
|
if (fp_cmp (&u, &v) != FP_LT) {
|
|
/* u = u - v, A = A - C, B = B - D */
|
|
fp_sub (&u, &v, &u);
|
|
fp_sub (&A, &C, &A);
|
|
fp_sub (&B, &D, &B);
|
|
} else {
|
|
/* v - v - u, C = C - A, D = D - B */
|
|
fp_sub (&v, &u, &v);
|
|
fp_sub (&C, &A, &C);
|
|
fp_sub (&D, &B, &D);
|
|
}
|
|
|
|
/* if not zero goto step 4 */
|
|
if (fp_iszero (&u) == 0)
|
|
goto top;
|
|
|
|
/* now a = C, b = D, gcd == g*v */
|
|
|
|
/* if v != 1 then there is no inverse */
|
|
if (fp_cmp_d (&v, 1) != FP_EQ) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
/* if its too low */
|
|
while (fp_cmp_d(&C, 0) == FP_LT) {
|
|
fp_add(&C, b, &C);
|
|
}
|
|
|
|
/* too big */
|
|
while (fp_cmp_mag(&C, b) != FP_LT) {
|
|
fp_sub(&C, b, &C);
|
|
}
|
|
|
|
/* C is now the inverse */
|
|
fp_copy(&C, c);
|
|
return FP_OKAY;
|
|
}
|
|
|
|
|
|
/* c = 1/a (mod b) for odd b only */
|
|
int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
|
|
{
|
|
fp_int x, y, u, v, B, D;
|
|
int neg, loop_check = 0;
|
|
|
|
/* 2. [modified] b must be odd */
|
|
if (fp_iseven (b) == FP_YES) {
|
|
return fp_invmod_slow(a,b,c);
|
|
}
|
|
|
|
/* init all our temps */
|
|
fp_init(&x); fp_init(&y);
|
|
fp_init(&u); fp_init(&v);
|
|
fp_init(&B); fp_init(&D);
|
|
|
|
/* x == modulus, y == value to invert */
|
|
fp_copy(b, &x);
|
|
|
|
/* we need y = |a| */
|
|
fp_abs(a, &y);
|
|
|
|
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
|
fp_copy(&x, &u);
|
|
fp_copy(&y, &v);
|
|
fp_set (&D, 1);
|
|
|
|
top:
|
|
/* 4. while u is even do */
|
|
while (fp_iseven (&u) == FP_YES) {
|
|
/* 4.1 u = u/2 */
|
|
fp_div_2 (&u, &u);
|
|
|
|
/* 4.2 if B is odd then */
|
|
if (fp_isodd (&B) == FP_YES) {
|
|
fp_sub (&B, &x, &B);
|
|
}
|
|
/* B = B/2 */
|
|
fp_div_2 (&B, &B);
|
|
}
|
|
|
|
/* 5. while v is even do */
|
|
while (fp_iseven (&v) == FP_YES) {
|
|
/* 5.1 v = v/2 */
|
|
fp_div_2 (&v, &v);
|
|
|
|
/* 5.2 if D is odd then */
|
|
if (fp_isodd (&D) == FP_YES) {
|
|
/* D = (D-x)/2 */
|
|
fp_sub (&D, &x, &D);
|
|
}
|
|
/* D = D/2 */
|
|
fp_div_2 (&D, &D);
|
|
}
|
|
|
|
/* 6. if u >= v then */
|
|
if (fp_cmp (&u, &v) != FP_LT) {
|
|
/* u = u - v, B = B - D */
|
|
fp_sub (&u, &v, &u);
|
|
fp_sub (&B, &D, &B);
|
|
} else {
|
|
/* v - v - u, D = D - B */
|
|
fp_sub (&v, &u, &v);
|
|
fp_sub (&D, &B, &D);
|
|
}
|
|
|
|
/* if not zero goto step 4 */
|
|
if (fp_iszero (&u) == FP_NO) {
|
|
if (++loop_check > 1024) /* bad input */
|
|
return FP_VAL;
|
|
goto top;
|
|
}
|
|
|
|
/* now a = C, b = D, gcd == g*v */
|
|
|
|
/* if v != 1 then there is no inverse */
|
|
if (fp_cmp_d (&v, 1) != FP_EQ) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
/* b is now the inverse */
|
|
neg = a->sign;
|
|
while (D.sign == FP_NEG) {
|
|
fp_add (&D, b, &D);
|
|
}
|
|
fp_copy (&D, c);
|
|
c->sign = neg;
|
|
return FP_OKAY;
|
|
}
|
|
|
|
/* d = a * b (mod c) */
|
|
int fp_mulmod(fp_int *a, fp_int *b, fp_int *c, fp_int *d)
|
|
{
|
|
fp_int tmp;
|
|
fp_init(&tmp);
|
|
fp_mul(a, b, &tmp);
|
|
return fp_mod(&tmp, c, d);
|
|
}
|
|
|
|
#ifdef TFM_TIMING_RESISTANT
|
|
|
|
/* timing resistant montgomery ladder based exptmod
|
|
|
|
Based on work by Marc Joye, Sung-Ming Yen, "The Montgomery Powering Ladder", Cryptographic Hardware and Embedded Systems, CHES 2002
|
|
*/
|
|
static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
|
|
{
|
|
fp_int R[2];
|
|
fp_digit buf, mp;
|
|
int err, bitcnt, digidx, y;
|
|
|
|
/* now setup montgomery */
|
|
if ((err = fp_montgomery_setup (P, &mp)) != FP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
fp_init(&R[0]);
|
|
fp_init(&R[1]);
|
|
|
|
/* now we need R mod m */
|
|
fp_montgomery_calc_normalization (&R[0], P);
|
|
|
|
/* now set R[0][1] to G * R mod m */
|
|
if (fp_cmp_mag(P, G) != FP_GT) {
|
|
/* G > P so we reduce it first */
|
|
fp_mod(G, P, &R[1]);
|
|
} else {
|
|
fp_copy(G, &R[1]);
|
|
}
|
|
fp_mulmod (&R[1], &R[0], P, &R[1]);
|
|
|
|
/* for j = t-1 downto 0 do
|
|
r_!k = R0*R1; r_k = r_k^2
|
|
*/
|
|
|
|
/* set initial mode and bit cnt */
|
|
bitcnt = 1;
|
|
buf = 0;
|
|
digidx = X->used - 1;
|
|
|
|
for (;;) {
|
|
/* grab next digit as required */
|
|
if (--bitcnt == 0) {
|
|
/* if digidx == -1 we are out of digits so break */
|
|
if (digidx == -1) {
|
|
break;
|
|
}
|
|
/* read next digit and reset bitcnt */
|
|
buf = X->dp[digidx--];
|
|
bitcnt = (int)DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (int)(buf >> (DIGIT_BIT - 1)) & 1;
|
|
buf <<= (fp_digit)1;
|
|
|
|
/* do ops */
|
|
fp_mul(&R[0], &R[1], &R[y^1]); fp_montgomery_reduce(&R[y^1], P, mp);
|
|
fp_sqr(&R[y], &R[y]); fp_montgomery_reduce(&R[y], P, mp);
|
|
}
|
|
|
|
fp_montgomery_reduce(&R[0], P, mp);
|
|
fp_copy(&R[0], Y);
|
|
return FP_OKAY;
|
|
}
|
|
|
|
#else
|
|
|
|
/* y = g**x (mod b)
|
|
* Some restrictions... x must be positive and < b
|
|
*/
|
|
static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
|
|
{
|
|
fp_int M[64], res;
|
|
fp_digit buf, mp;
|
|
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
|
|
|
/* find window size */
|
|
x = fp_count_bits (X);
|
|
if (x <= 21) {
|
|
winsize = 1;
|
|
} else if (x <= 36) {
|
|
winsize = 3;
|
|
} else if (x <= 140) {
|
|
winsize = 4;
|
|
} else if (x <= 450) {
|
|
winsize = 5;
|
|
} else {
|
|
winsize = 6;
|
|
}
|
|
|
|
/* init M array */
|
|
XMEMSET(M, 0, sizeof(M));
|
|
|
|
/* now setup montgomery */
|
|
if ((err = fp_montgomery_setup (P, &mp)) != FP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* setup result */
|
|
fp_init(&res);
|
|
|
|
/* create M table
|
|
*
|
|
* The M table contains powers of the input base, e.g. M[x] = G^x mod P
|
|
*
|
|
* The first half of the table is not computed though accept for M[0] and M[1]
|
|
*/
|
|
|
|
/* now we need R mod m */
|
|
fp_montgomery_calc_normalization (&res, P);
|
|
|
|
/* now set M[1] to G * R mod m */
|
|
if (fp_cmp_mag(P, G) != FP_GT) {
|
|
/* G > P so we reduce it first */
|
|
fp_mod(G, P, &M[1]);
|
|
} else {
|
|
fp_copy(G, &M[1]);
|
|
}
|
|
fp_mulmod (&M[1], &res, P, &M[1]);
|
|
|
|
/* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
|
|
fp_copy (&M[1], &M[1 << (winsize - 1)]);
|
|
for (x = 0; x < (winsize - 1); x++) {
|
|
fp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)]);
|
|
fp_montgomery_reduce (&M[1 << (winsize - 1)], P, mp);
|
|
}
|
|
|
|
/* create upper table */
|
|
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
|
fp_mul(&M[x - 1], &M[1], &M[x]);
|
|
fp_montgomery_reduce(&M[x], P, mp);
|
|
}
|
|
|
|
/* set initial mode and bit cnt */
|
|
mode = 0;
|
|
bitcnt = 1;
|
|
buf = 0;
|
|
digidx = X->used - 1;
|
|
bitcpy = 0;
|
|
bitbuf = 0;
|
|
|
|
for (;;) {
|
|
/* grab next digit as required */
|
|
if (--bitcnt == 0) {
|
|
/* if digidx == -1 we are out of digits so break */
|
|
if (digidx == -1) {
|
|
break;
|
|
}
|
|
/* read next digit and reset bitcnt */
|
|
buf = X->dp[digidx--];
|
|
bitcnt = (int)DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (int)(buf >> (DIGIT_BIT - 1)) & 1;
|
|
buf <<= (fp_digit)1;
|
|
|
|
/* if the bit is zero and mode == 0 then we ignore it
|
|
* These represent the leading zero bits before the first 1 bit
|
|
* in the exponent. Technically this opt is not required but it
|
|
* does lower the # of trivial squaring/reductions used
|
|
*/
|
|
if (mode == 0 && y == 0) {
|
|
continue;
|
|
}
|
|
|
|
/* if the bit is zero and mode == 1 then we square */
|
|
if (mode == 1 && y == 0) {
|
|
fp_sqr(&res, &res);
|
|
fp_montgomery_reduce(&res, P, mp);
|
|
continue;
|
|
}
|
|
|
|
/* else we add it to the window */
|
|
bitbuf |= (y << (winsize - ++bitcpy));
|
|
mode = 2;
|
|
|
|
if (bitcpy == winsize) {
|
|
/* ok window is filled so square as required and multiply */
|
|
/* square first */
|
|
for (x = 0; x < winsize; x++) {
|
|
fp_sqr(&res, &res);
|
|
fp_montgomery_reduce(&res, P, mp);
|
|
}
|
|
|
|
/* then multiply */
|
|
fp_mul(&res, &M[bitbuf], &res);
|
|
fp_montgomery_reduce(&res, P, mp);
|
|
|
|
/* empty window and reset */
|
|
bitcpy = 0;
|
|
bitbuf = 0;
|
|
mode = 1;
|
|
}
|
|
}
|
|
|
|
/* if bits remain then square/multiply */
|
|
if (mode == 2 && bitcpy > 0) {
|
|
/* square then multiply if the bit is set */
|
|
for (x = 0; x < bitcpy; x++) {
|
|
fp_sqr(&res, &res);
|
|
fp_montgomery_reduce(&res, P, mp);
|
|
|
|
/* get next bit of the window */
|
|
bitbuf <<= 1;
|
|
if ((bitbuf & (1 << winsize)) != 0) {
|
|
/* then multiply */
|
|
fp_mul(&res, &M[1], &res);
|
|
fp_montgomery_reduce(&res, P, mp);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* fixup result if Montgomery reduction is used
|
|
* recall that any value in a Montgomery system is
|
|
* actually multiplied by R mod n. So we have
|
|
* to reduce one more time to cancel out the factor
|
|
* of R.
|
|
*/
|
|
fp_montgomery_reduce(&res, P, mp);
|
|
|
|
/* swap res with Y */
|
|
fp_copy (&res, Y);
|
|
return FP_OKAY;
|
|
}
|
|
|
|
#endif
|
|
|
|
int fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
|
|
{
|
|
/* prevent overflows */
|
|
if (P->used > (FP_SIZE/2)) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
if (X->sign == FP_NEG) {
|
|
#ifndef POSITIVE_EXP_ONLY /* reduce stack if assume no negatives */
|
|
int err;
|
|
fp_int tmp;
|
|
|
|
/* yes, copy G and invmod it */
|
|
fp_copy(G, &tmp);
|
|
if ((err = fp_invmod(&tmp, P, &tmp)) != FP_OKAY) {
|
|
return err;
|
|
}
|
|
X->sign = FP_ZPOS;
|
|
err = _fp_exptmod(&tmp, X, P, Y);
|
|
if (X != Y) {
|
|
X->sign = FP_NEG;
|
|
}
|
|
return err;
|
|
#else
|
|
return FP_VAL;
|
|
#endif
|
|
}
|
|
else {
|
|
/* Positive exponent so just exptmod */
|
|
return _fp_exptmod(G, X, P, Y);
|
|
}
|
|
}
|
|
|
|
/* computes a = 2**b */
|
|
void fp_2expt(fp_int *a, int b)
|
|
{
|
|
int z;
|
|
|
|
/* zero a as per default */
|
|
fp_zero (a);
|
|
|
|
if (b < 0) {
|
|
return;
|
|
}
|
|
|
|
z = b / DIGIT_BIT;
|
|
if (z >= FP_SIZE) {
|
|
return;
|
|
}
|
|
|
|
/* set the used count of where the bit will go */
|
|
a->used = z + 1;
|
|
|
|
/* put the single bit in its place */
|
|
a->dp[z] = ((fp_digit)1) << (b % DIGIT_BIT);
|
|
}
|
|
|
|
/* b = a*a */
|
|
void fp_sqr(fp_int *A, fp_int *B)
|
|
{
|
|
int y = A->used;
|
|
|
|
/* call generic if we're out of range */
|
|
if (y + y > FP_SIZE) {
|
|
fp_sqr_comba(A, B);
|
|
return ;
|
|
}
|
|
|
|
#if defined(TFM_SQR3)
|
|
if (y <= 3) {
|
|
fp_sqr_comba3(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR4)
|
|
if (y == 4) {
|
|
fp_sqr_comba4(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR6)
|
|
if (y <= 6) {
|
|
fp_sqr_comba6(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR7)
|
|
if (y == 7) {
|
|
fp_sqr_comba7(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR8)
|
|
if (y == 8) {
|
|
fp_sqr_comba8(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR9)
|
|
if (y == 9) {
|
|
fp_sqr_comba9(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR12)
|
|
if (y <= 12) {
|
|
fp_sqr_comba12(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR17)
|
|
if (y <= 17) {
|
|
fp_sqr_comba17(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SMALL_SET)
|
|
if (y <= 16) {
|
|
fp_sqr_comba_small(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR20)
|
|
if (y <= 20) {
|
|
fp_sqr_comba20(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR24)
|
|
if (y <= 24) {
|
|
fp_sqr_comba24(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR28)
|
|
if (y <= 28) {
|
|
fp_sqr_comba28(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR32)
|
|
if (y <= 32) {
|
|
fp_sqr_comba32(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR48)
|
|
if (y <= 48) {
|
|
fp_sqr_comba48(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
#if defined(TFM_SQR64)
|
|
if (y <= 64) {
|
|
fp_sqr_comba64(A,B);
|
|
return;
|
|
}
|
|
#endif
|
|
fp_sqr_comba(A, B);
|
|
}
|
|
|
|
/* generic comba squarer */
|
|
void fp_sqr_comba(fp_int *A, fp_int *B)
|
|
{
|
|
int pa, ix, iz;
|
|
fp_digit c0, c1, c2;
|
|
fp_int tmp, *dst;
|
|
#ifdef TFM_ISO
|
|
fp_word tt;
|
|
#endif
|
|
|
|
/* get size of output and trim */
|
|
pa = A->used + A->used;
|
|
if (pa >= FP_SIZE) {
|
|
pa = FP_SIZE-1;
|
|
}
|
|
|
|
/* number of output digits to produce */
|
|
COMBA_START;
|
|
COMBA_CLEAR;
|
|
|
|
if (A == B) {
|
|
fp_init(&tmp);
|
|
dst = &tmp;
|
|
} else {
|
|
fp_zero(B);
|
|
dst = B;
|
|
}
|
|
|
|
for (ix = 0; ix < pa; ix++) {
|
|
int tx, ty, iy;
|
|
fp_digit *tmpy, *tmpx;
|
|
|
|
/* get offsets into the two bignums */
|
|
ty = MIN(A->used-1, ix);
|
|
tx = ix - ty;
|
|
|
|
/* setup temp aliases */
|
|
tmpx = A->dp + tx;
|
|
tmpy = A->dp + ty;
|
|
|
|
/* this is the number of times the loop will iterrate,
|
|
while (tx++ < a->used && ty-- >= 0) { ... }
|
|
*/
|
|
iy = MIN(A->used-tx, ty+1);
|
|
|
|
/* now for squaring tx can never equal ty
|
|
* we halve the distance since they approach
|
|
* at a rate of 2x and we have to round because
|
|
* odd cases need to be executed
|
|
*/
|
|
iy = MIN(iy, (ty-tx+1)>>1);
|
|
|
|
/* forward carries */
|
|
COMBA_FORWARD;
|
|
|
|
/* execute loop */
|
|
for (iz = 0; iz < iy; iz++) {
|
|
SQRADD2(*tmpx++, *tmpy--);
|
|
}
|
|
|
|
/* even columns have the square term in them */
|
|
if ((ix&1) == 0) {
|
|
/* TAO change COMBA_ADD back to SQRADD */
|
|
SQRADD(A->dp[ix>>1], A->dp[ix>>1]);
|
|
}
|
|
|
|
/* store it */
|
|
COMBA_STORE(dst->dp[ix]);
|
|
}
|
|
|
|
COMBA_FINI;
|
|
|
|
/* setup dest */
|
|
dst->used = pa;
|
|
fp_clamp (dst);
|
|
if (dst != B) {
|
|
fp_copy(dst, B);
|
|
}
|
|
}
|
|
|
|
int fp_cmp(fp_int *a, fp_int *b)
|
|
{
|
|
if (a->sign == FP_NEG && b->sign == FP_ZPOS) {
|
|
return FP_LT;
|
|
} else if (a->sign == FP_ZPOS && b->sign == FP_NEG) {
|
|
return FP_GT;
|
|
} else {
|
|
/* compare digits */
|
|
if (a->sign == FP_NEG) {
|
|
/* if negative compare opposite direction */
|
|
return fp_cmp_mag(b, a);
|
|
} else {
|
|
return fp_cmp_mag(a, b);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* compare against a single digit */
|
|
int fp_cmp_d(fp_int *a, fp_digit b)
|
|
{
|
|
/* compare based on sign */
|
|
if ((b && a->used == 0) || a->sign == FP_NEG) {
|
|
return FP_LT;
|
|
}
|
|
|
|
/* compare based on magnitude */
|
|
if (a->used > 1) {
|
|
return FP_GT;
|
|
}
|
|
|
|
/* compare the only digit of a to b */
|
|
if (a->dp[0] > b) {
|
|
return FP_GT;
|
|
} else if (a->dp[0] < b) {
|
|
return FP_LT;
|
|
} else {
|
|
return FP_EQ;
|
|
}
|
|
|
|
}
|
|
|
|
int fp_cmp_mag(fp_int *a, fp_int *b)
|
|
{
|
|
int x;
|
|
|
|
if (a->used > b->used) {
|
|
return FP_GT;
|
|
} else if (a->used < b->used) {
|
|
return FP_LT;
|
|
} else {
|
|
for (x = a->used - 1; x >= 0; x--) {
|
|
if (a->dp[x] > b->dp[x]) {
|
|
return FP_GT;
|
|
} else if (a->dp[x] < b->dp[x]) {
|
|
return FP_LT;
|
|
}
|
|
}
|
|
}
|
|
return FP_EQ;
|
|
}
|
|
|
|
/* setups the montgomery reduction */
|
|
int fp_montgomery_setup(fp_int *a, fp_digit *rho)
|
|
{
|
|
fp_digit x, b;
|
|
|
|
/* fast inversion mod 2**k
|
|
*
|
|
* Based on the fact that
|
|
*
|
|
* XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
|
|
* => 2*X*A - X*X*A*A = 1
|
|
* => 2*(1) - (1) = 1
|
|
*/
|
|
b = a->dp[0];
|
|
|
|
if ((b & 1) == 0) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**8 */
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**16 */
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**32 */
|
|
#ifdef FP_64BIT
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**64 */
|
|
#endif
|
|
|
|
/* rho = -1/m mod b */
|
|
*rho = (fp_digit) (((fp_word) 1 << ((fp_word) DIGIT_BIT)) - ((fp_word)x));
|
|
|
|
return FP_OKAY;
|
|
}
|
|
|
|
/* computes a = B**n mod b without division or multiplication useful for
|
|
* normalizing numbers in a Montgomery system.
|
|
*/
|
|
void fp_montgomery_calc_normalization(fp_int *a, fp_int *b)
|
|
{
|
|
int x, bits;
|
|
|
|
/* how many bits of last digit does b use */
|
|
bits = fp_count_bits (b) % DIGIT_BIT;
|
|
if (!bits) bits = DIGIT_BIT;
|
|
|
|
/* compute A = B^(n-1) * 2^(bits-1) */
|
|
if (b->used > 1) {
|
|
fp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1);
|
|
} else {
|
|
fp_set(a, 1);
|
|
bits = 1;
|
|
}
|
|
|
|
/* now compute C = A * B mod b */
|
|
for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
|
|
fp_mul_2 (a, a);
|
|
if (fp_cmp_mag (a, b) != FP_LT) {
|
|
s_fp_sub (a, b, a);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
#ifdef TFM_SMALL_MONT_SET
|
|
#include "fp_mont_small.i"
|
|
#endif
|
|
|
|
#ifdef HAVE_INTEL_MULX
|
|
static inline void innermul8_mulx(fp_digit *c_mulx, fp_digit *cy_mulx, fp_digit *tmpm, fp_digit mu)
|
|
{
|
|
fp_digit _c0, _c1, _c2, _c3, _c4, _c5, _c6, _c7, cy ;
|
|
|
|
cy = *cy_mulx ;
|
|
_c0=c_mulx[0]; _c1=c_mulx[1]; _c2=c_mulx[2]; _c3=c_mulx[3]; _c4=c_mulx[4]; _c5=c_mulx[5]; _c6=c_mulx[6]; _c7=c_mulx[7];
|
|
INNERMUL8_MULX ;
|
|
c_mulx[0]=_c0; c_mulx[1]=_c1; c_mulx[2]=_c2; c_mulx[3]=_c3; c_mulx[4]=_c4; c_mulx[5]=_c5; c_mulx[6]=_c6; c_mulx[7]=_c7;
|
|
*cy_mulx = cy ;
|
|
}
|
|
|
|
/* computes x/R == x (mod N) via Montgomery Reduction */
|
|
static void fp_montgomery_reduce_mulx(fp_int *a, fp_int *m, fp_digit mp)
|
|
{
|
|
fp_digit c[FP_SIZE], *_c, *tmpm, mu = 0;
|
|
int oldused, x, y, pa;
|
|
|
|
/* bail if too large */
|
|
if (m->used > (FP_SIZE/2)) {
|
|
(void)mu; /* shut up compiler */
|
|
return;
|
|
}
|
|
|
|
#ifdef TFM_SMALL_MONT_SET
|
|
if (m->used <= 16) {
|
|
fp_montgomery_reduce_small(a, m, mp);
|
|
return;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* now zero the buff */
|
|
XMEMSET(c, 0, sizeof c);
|
|
pa = m->used;
|
|
|
|
/* copy the input */
|
|
oldused = a->used;
|
|
for (x = 0; x < oldused; x++) {
|
|
c[x] = a->dp[x];
|
|
}
|
|
MONT_START;
|
|
|
|
for (x = 0; x < pa; x++) {
|
|
fp_digit cy = 0;
|
|
/* get Mu for this round */
|
|
LOOP_START;
|
|
_c = c + x;
|
|
tmpm = m->dp;
|
|
y = 0;
|
|
for (; y < (pa & ~7); y += 8) {
|
|
innermul8_mulx(_c, &cy, tmpm, mu) ;
|
|
_c += 8;
|
|
tmpm += 8;
|
|
}
|
|
for (; y < pa; y++) {
|
|
INNERMUL;
|
|
++_c;
|
|
}
|
|
LOOP_END;
|
|
while (cy) {
|
|
PROPCARRY;
|
|
++_c;
|
|
}
|
|
}
|
|
|
|
/* now copy out */
|
|
_c = c + pa;
|
|
tmpm = a->dp;
|
|
for (x = 0; x < pa+1; x++) {
|
|
*tmpm++ = *_c++;
|
|
}
|
|
|
|
for (; x < oldused; x++) {
|
|
*tmpm++ = 0;
|
|
}
|
|
|
|
MONT_FINI;
|
|
|
|
a->used = pa+1;
|
|
fp_clamp(a);
|
|
|
|
/* if A >= m then A = A - m */
|
|
if (fp_cmp_mag (a, m) != FP_LT) {
|
|
s_fp_sub (a, m, a);
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/* computes x/R == x (mod N) via Montgomery Reduction */
|
|
void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
|
|
{
|
|
fp_digit c[FP_SIZE], *_c, *tmpm, mu = 0;
|
|
int oldused, x, y, pa;
|
|
|
|
IF_HAVE_INTEL_MULX(fp_montgomery_reduce_mulx(a, m, mp), return) ;
|
|
|
|
/* bail if too large */
|
|
if (m->used > (FP_SIZE/2)) {
|
|
(void)mu; /* shut up compiler */
|
|
return;
|
|
}
|
|
|
|
#ifdef TFM_SMALL_MONT_SET
|
|
if (m->used <= 16) {
|
|
fp_montgomery_reduce_small(a, m, mp);
|
|
return;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* now zero the buff */
|
|
XMEMSET(c, 0, sizeof c);
|
|
pa = m->used;
|
|
|
|
/* copy the input */
|
|
oldused = a->used;
|
|
for (x = 0; x < oldused; x++) {
|
|
c[x] = a->dp[x];
|
|
}
|
|
MONT_START;
|
|
|
|
for (x = 0; x < pa; x++) {
|
|
fp_digit cy = 0;
|
|
/* get Mu for this round */
|
|
LOOP_START;
|
|
_c = c + x;
|
|
tmpm = m->dp;
|
|
y = 0;
|
|
#if (defined(TFM_SSE2) || defined(TFM_X86_64))
|
|
for (; y < (pa & ~7); y += 8) {
|
|
INNERMUL8 ;
|
|
_c += 8;
|
|
tmpm += 8;
|
|
}
|
|
#endif
|
|
for (; y < pa; y++) {
|
|
INNERMUL;
|
|
++_c;
|
|
}
|
|
LOOP_END;
|
|
while (cy) {
|
|
PROPCARRY;
|
|
++_c;
|
|
}
|
|
}
|
|
|
|
/* now copy out */
|
|
_c = c + pa;
|
|
tmpm = a->dp;
|
|
for (x = 0; x < pa+1; x++) {
|
|
*tmpm++ = *_c++;
|
|
}
|
|
|
|
for (; x < oldused; x++) {
|
|
*tmpm++ = 0;
|
|
}
|
|
|
|
MONT_FINI;
|
|
|
|
a->used = pa+1;
|
|
fp_clamp(a);
|
|
|
|
/* if A >= m then A = A - m */
|
|
if (fp_cmp_mag (a, m) != FP_LT) {
|
|
s_fp_sub (a, m, a);
|
|
}
|
|
}
|
|
|
|
void fp_read_unsigned_bin(fp_int *a, unsigned char *b, int c)
|
|
{
|
|
/* zero the int */
|
|
fp_zero (a);
|
|
|
|
/* If we know the endianness of this architecture, and we're using
|
|
32-bit fp_digits, we can optimize this */
|
|
#if (defined(LITTLE_ENDIAN_ORDER) || defined(BIG_ENDIAN_ORDER)) && defined(FP_32BIT)
|
|
/* But not for both simultaneously */
|
|
#if defined(LITTLE_ENDIAN_ORDER) && defined(BIG_ENDIAN_ORDER)
|
|
#error Both LITTLE_ENDIAN_ORDER and BIG_ENDIAN_ORDER defined.
|
|
#endif
|
|
{
|
|
unsigned char *pd = (unsigned char *)a->dp;
|
|
|
|
if ((unsigned)c > (FP_SIZE * sizeof(fp_digit))) {
|
|
int excess = c - (FP_SIZE * sizeof(fp_digit));
|
|
c -= excess;
|
|
b += excess;
|
|
}
|
|
a->used = (c + sizeof(fp_digit) - 1)/sizeof(fp_digit);
|
|
/* read the bytes in */
|
|
#ifdef BIG_ENDIAN_ORDER
|
|
{
|
|
/* Use Duff's device to unroll the loop. */
|
|
int idx = (c - 1) & ~3;
|
|
switch (c % 4) {
|
|
case 0: do { pd[idx+0] = *b++;
|
|
case 3: pd[idx+1] = *b++;
|
|
case 2: pd[idx+2] = *b++;
|
|
case 1: pd[idx+3] = *b++;
|
|
idx -= 4;
|
|
} while ((c -= 4) > 0);
|
|
}
|
|
}
|
|
#else
|
|
for (c -= 1; c >= 0; c -= 1) {
|
|
pd[c] = *b++;
|
|
}
|
|
#endif
|
|
}
|
|
#else
|
|
/* read the bytes in */
|
|
for (; c > 0; c--) {
|
|
fp_mul_2d (a, 8, a);
|
|
a->dp[0] |= *b++;
|
|
a->used += 1;
|
|
}
|
|
#endif
|
|
fp_clamp (a);
|
|
}
|
|
|
|
void fp_to_unsigned_bin(fp_int *a, unsigned char *b)
|
|
{
|
|
int x;
|
|
fp_int t;
|
|
|
|
fp_init_copy(&t, a);
|
|
|
|
x = 0;
|
|
while (fp_iszero (&t) == FP_NO) {
|
|
b[x++] = (unsigned char) (t.dp[0] & 255);
|
|
fp_div_2d (&t, 8, &t, NULL);
|
|
}
|
|
fp_reverse (b, x);
|
|
}
|
|
|
|
int fp_unsigned_bin_size(fp_int *a)
|
|
{
|
|
int size = fp_count_bits (a);
|
|
return (size / 8 + ((size & 7) != 0 ? 1 : 0));
|
|
}
|
|
|
|
void fp_set(fp_int *a, fp_digit b)
|
|
{
|
|
fp_zero(a);
|
|
a->dp[0] = b;
|
|
a->used = a->dp[0] ? 1 : 0;
|
|
}
|
|
|
|
int fp_count_bits (fp_int * a)
|
|
{
|
|
int r;
|
|
fp_digit q;
|
|
|
|
/* shortcut */
|
|
if (a->used == 0) {
|
|
return 0;
|
|
}
|
|
|
|
/* get number of digits and add that */
|
|
r = (a->used - 1) * DIGIT_BIT;
|
|
|
|
/* take the last digit and count the bits in it */
|
|
q = a->dp[a->used - 1];
|
|
while (q > ((fp_digit) 0)) {
|
|
++r;
|
|
q >>= ((fp_digit) 1);
|
|
}
|
|
return r;
|
|
}
|
|
|
|
int fp_leading_bit(fp_int *a)
|
|
{
|
|
int bit = 0;
|
|
|
|
if (a->used != 0) {
|
|
fp_digit q = a->dp[a->used - 1];
|
|
int qSz = sizeof(fp_digit);
|
|
|
|
while (qSz > 0) {
|
|
if ((unsigned char)q != 0)
|
|
bit = (q & 0x80) != 0;
|
|
q >>= 8;
|
|
qSz--;
|
|
}
|
|
}
|
|
|
|
return bit;
|
|
}
|
|
|
|
void fp_lshd(fp_int *a, int x)
|
|
{
|
|
int y;
|
|
|
|
/* move up and truncate as required */
|
|
y = MIN(a->used + x - 1, (int)(FP_SIZE-1));
|
|
|
|
/* store new size */
|
|
a->used = y + 1;
|
|
|
|
/* move digits */
|
|
for (; y >= x; y--) {
|
|
a->dp[y] = a->dp[y-x];
|
|
}
|
|
|
|
/* zero lower digits */
|
|
for (; y >= 0; y--) {
|
|
a->dp[y] = 0;
|
|
}
|
|
|
|
/* clamp digits */
|
|
fp_clamp(a);
|
|
}
|
|
|
|
|
|
/* right shift by bit count */
|
|
void fp_rshb(fp_int *c, int x)
|
|
{
|
|
register fp_digit *tmpc, mask, shift;
|
|
fp_digit r, rr;
|
|
fp_digit D = x;
|
|
|
|
/* mask */
|
|
mask = (((fp_digit)1) << D) - 1;
|
|
|
|
/* shift for lsb */
|
|
shift = DIGIT_BIT - D;
|
|
|
|
/* alias */
|
|
tmpc = c->dp + (c->used - 1);
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = c->used - 1; x >= 0; x--) {
|
|
/* get the lower bits of this word in a temp */
|
|
rr = *tmpc & mask;
|
|
|
|
/* shift the current word and mix in the carry bits from previous word */
|
|
*tmpc = (*tmpc >> D) | (r << shift);
|
|
--tmpc;
|
|
|
|
/* set the carry to the carry bits of the current word found above */
|
|
r = rr;
|
|
}
|
|
}
|
|
|
|
|
|
void fp_rshd(fp_int *a, int x)
|
|
{
|
|
int y;
|
|
|
|
/* too many digits just zero and return */
|
|
if (x >= a->used) {
|
|
fp_zero(a);
|
|
return;
|
|
}
|
|
|
|
/* shift */
|
|
for (y = 0; y < a->used - x; y++) {
|
|
a->dp[y] = a->dp[y+x];
|
|
}
|
|
|
|
/* zero rest */
|
|
for (; y < a->used; y++) {
|
|
a->dp[y] = 0;
|
|
}
|
|
|
|
/* decrement count */
|
|
a->used -= x;
|
|
fp_clamp(a);
|
|
}
|
|
|
|
/* reverse an array, used for radix code */
|
|
void fp_reverse (unsigned char *s, int len)
|
|
{
|
|
int ix, iy;
|
|
unsigned char t;
|
|
|
|
ix = 0;
|
|
iy = len - 1;
|
|
while (ix < iy) {
|
|
t = s[ix];
|
|
s[ix] = s[iy];
|
|
s[iy] = t;
|
|
++ix;
|
|
--iy;
|
|
}
|
|
}
|
|
|
|
|
|
/* c = a - b */
|
|
void fp_sub_d(fp_int *a, fp_digit b, fp_int *c)
|
|
{
|
|
fp_int tmp;
|
|
fp_init(&tmp);
|
|
fp_set(&tmp, b);
|
|
fp_sub(a, &tmp, c);
|
|
}
|
|
|
|
|
|
/* CyaSSL callers from normal lib */
|
|
|
|
/* init a new mp_int */
|
|
int mp_init (mp_int * a)
|
|
{
|
|
if (a)
|
|
fp_init(a);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
#ifdef ALT_ECC_SIZE
|
|
void fp_init(fp_int *a)
|
|
{
|
|
a->size = FP_SIZE;
|
|
fp_zero(a);
|
|
}
|
|
|
|
void fp_zero(fp_int *a)
|
|
{
|
|
a->used = 0;
|
|
a->sign = FP_ZPOS;
|
|
XMEMSET(a->dp, 0, a->size * sizeof(fp_digit));
|
|
}
|
|
#endif
|
|
|
|
|
|
/* clear one (frees) */
|
|
void mp_clear (mp_int * a)
|
|
{
|
|
fp_zero(a);
|
|
}
|
|
|
|
/* handle up to 6 inits */
|
|
int mp_init_multi(mp_int* a, mp_int* b, mp_int* c, mp_int* d, mp_int* e, mp_int* f)
|
|
{
|
|
if (a)
|
|
fp_init(a);
|
|
if (b)
|
|
fp_init(b);
|
|
if (c)
|
|
fp_init(c);
|
|
if (d)
|
|
fp_init(d);
|
|
if (e)
|
|
fp_init(e);
|
|
if (f)
|
|
fp_init(f);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* high level addition (handles signs) */
|
|
int mp_add (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
fp_add(a, b, c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* high level subtraction (handles signs) */
|
|
int mp_sub (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
fp_sub(a, b, c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* high level multiplication (handles sign) */
|
|
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
fp_mul(a, b, c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* d = a * b (mod c) */
|
|
int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
|
|
{
|
|
return fp_mulmod(a, b, c, d);
|
|
}
|
|
|
|
/* c = a mod b, 0 <= c < b */
|
|
int mp_mod (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
return fp_mod (a, b, c);
|
|
}
|
|
|
|
/* hac 14.61, pp608 */
|
|
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
return fp_invmod(a, b, c);
|
|
}
|
|
|
|
/* this is a shell function that calls either the normal or Montgomery
|
|
* exptmod functions. Originally the call to the montgomery code was
|
|
* embedded in the normal function but that wasted alot of stack space
|
|
* for nothing (since 99% of the time the Montgomery code would be called)
|
|
*/
|
|
int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
|
|
{
|
|
return fp_exptmod(G, X, P, Y);
|
|
}
|
|
|
|
/* compare two ints (signed)*/
|
|
int mp_cmp (mp_int * a, mp_int * b)
|
|
{
|
|
return fp_cmp(a, b);
|
|
}
|
|
|
|
/* compare a digit */
|
|
int mp_cmp_d(mp_int * a, mp_digit b)
|
|
{
|
|
return fp_cmp_d(a, b);
|
|
}
|
|
|
|
/* get the size for an unsigned equivalent */
|
|
int mp_unsigned_bin_size (mp_int * a)
|
|
{
|
|
return fp_unsigned_bin_size(a);
|
|
}
|
|
|
|
/* store in unsigned [big endian] format */
|
|
int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
|
|
{
|
|
fp_to_unsigned_bin(a,b);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
|
|
int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
|
|
{
|
|
fp_read_unsigned_bin(a, (unsigned char *)b, c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
int mp_sub_d(fp_int *a, fp_digit b, fp_int *c)
|
|
{
|
|
fp_sub_d(a, b, c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
#ifdef ALT_ECC_SIZE
|
|
void fp_copy(fp_int *a, fp_int* b)
|
|
{
|
|
if (a != b) {
|
|
b->used = a->used;
|
|
b->sign = a->sign;
|
|
XMEMCPY(b->dp, a->dp, a->used * sizeof(fp_digit));
|
|
}
|
|
}
|
|
|
|
void fp_init_copy(fp_int *a, fp_int* b)
|
|
{
|
|
if (a != b) {
|
|
fp_init(a);
|
|
fp_copy(b, a);
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/* fast math conversion */
|
|
int mp_copy(fp_int* a, fp_int* b)
|
|
{
|
|
fp_copy(a, b);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
/* fast math conversion */
|
|
int mp_isodd(mp_int* a)
|
|
{
|
|
return fp_isodd(a);
|
|
}
|
|
|
|
|
|
/* fast math conversion */
|
|
int mp_iszero(mp_int* a)
|
|
{
|
|
return fp_iszero(a);
|
|
}
|
|
|
|
|
|
/* fast math conversion */
|
|
int mp_count_bits (mp_int* a)
|
|
{
|
|
return fp_count_bits(a);
|
|
}
|
|
|
|
|
|
int mp_leading_bit (mp_int* a)
|
|
{
|
|
return fp_leading_bit(a);
|
|
}
|
|
|
|
|
|
/* fast math conversion */
|
|
void mp_rshb (mp_int* a, int x)
|
|
{
|
|
fp_rshb(a, x);
|
|
}
|
|
|
|
|
|
/* fast math wrappers */
|
|
int mp_set_int(fp_int *a, fp_digit b)
|
|
{
|
|
fp_set(a, b);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
#if defined(WOLFSSL_KEY_GEN) || defined (HAVE_ECC)
|
|
|
|
/* c = a * a (mod b) */
|
|
int fp_sqrmod(fp_int *a, fp_int *b, fp_int *c)
|
|
{
|
|
fp_int tmp;
|
|
fp_init(&tmp);
|
|
fp_sqr(a, &tmp);
|
|
return fp_mod(&tmp, b, c);
|
|
}
|
|
|
|
/* fast math conversion */
|
|
int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c)
|
|
{
|
|
return fp_sqrmod(a, b, c);
|
|
}
|
|
|
|
/* fast math conversion */
|
|
int mp_montgomery_calc_normalization(mp_int *a, mp_int *b)
|
|
{
|
|
fp_montgomery_calc_normalization(a, b);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
#endif /* WOLFSSL_KEYGEN || HAVE_ECC */
|
|
|
|
|
|
#if defined(WOLFSSL_KEY_GEN) || defined(HAVE_COMP_KEY)
|
|
|
|
static const int lnz[16] = {
|
|
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
|
|
};
|
|
|
|
/* Counts the number of lsbs which are zero before the first zero bit */
|
|
int fp_cnt_lsb(fp_int *a)
|
|
{
|
|
int x;
|
|
fp_digit q, qq;
|
|
|
|
/* easy out */
|
|
if (fp_iszero(a) == 1) {
|
|
return 0;
|
|
}
|
|
|
|
/* scan lower digits until non-zero */
|
|
for (x = 0; x < a->used && a->dp[x] == 0; x++);
|
|
q = a->dp[x];
|
|
x *= DIGIT_BIT;
|
|
|
|
/* now scan this digit until a 1 is found */
|
|
if ((q & 1) == 0) {
|
|
do {
|
|
qq = q & 15;
|
|
x += lnz[qq];
|
|
q >>= 4;
|
|
} while (qq == 0);
|
|
}
|
|
return x;
|
|
}
|
|
|
|
|
|
|
|
|
|
static int s_is_power_of_two(fp_digit b, int *p)
|
|
{
|
|
int x;
|
|
|
|
/* fast return if no power of two */
|
|
if ((b==0) || (b & (b-1))) {
|
|
return 0;
|
|
}
|
|
|
|
for (x = 0; x < DIGIT_BIT; x++) {
|
|
if (b == (((fp_digit)1)<<x)) {
|
|
*p = x;
|
|
return 1;
|
|
}
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/* a/b => cb + d == a */
|
|
static int fp_div_d(fp_int *a, fp_digit b, fp_int *c, fp_digit *d)
|
|
{
|
|
fp_int q;
|
|
fp_word w;
|
|
fp_digit t;
|
|
int ix;
|
|
|
|
/* cannot divide by zero */
|
|
if (b == 0) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
/* quick outs */
|
|
if (b == 1 || fp_iszero(a) == 1) {
|
|
if (d != NULL) {
|
|
*d = 0;
|
|
}
|
|
if (c != NULL) {
|
|
fp_copy(a, c);
|
|
}
|
|
return FP_OKAY;
|
|
}
|
|
|
|
/* power of two ? */
|
|
if (s_is_power_of_two(b, &ix) == 1) {
|
|
if (d != NULL) {
|
|
*d = a->dp[0] & ((((fp_digit)1)<<ix) - 1);
|
|
}
|
|
if (c != NULL) {
|
|
fp_div_2d(a, ix, c, NULL);
|
|
}
|
|
return FP_OKAY;
|
|
}
|
|
|
|
/* no easy answer [c'est la vie]. Just division */
|
|
fp_init(&q);
|
|
|
|
q.used = a->used;
|
|
q.sign = a->sign;
|
|
w = 0;
|
|
for (ix = a->used - 1; ix >= 0; ix--) {
|
|
w = (w << ((fp_word)DIGIT_BIT)) | ((fp_word)a->dp[ix]);
|
|
|
|
if (w >= b) {
|
|
t = (fp_digit)(w / b);
|
|
w -= ((fp_word)t) * ((fp_word)b);
|
|
} else {
|
|
t = 0;
|
|
}
|
|
q.dp[ix] = (fp_digit)t;
|
|
}
|
|
|
|
if (d != NULL) {
|
|
*d = (fp_digit)w;
|
|
}
|
|
|
|
if (c != NULL) {
|
|
fp_clamp(&q);
|
|
fp_copy(&q, c);
|
|
}
|
|
|
|
return FP_OKAY;
|
|
}
|
|
|
|
|
|
/* c = a mod b, 0 <= c < b */
|
|
static int fp_mod_d(fp_int *a, fp_digit b, fp_digit *c)
|
|
{
|
|
return fp_div_d(a, b, NULL, c);
|
|
}
|
|
|
|
int mp_mod_d(fp_int *a, fp_digit b, fp_digit *c)
|
|
{
|
|
return fp_mod_d(a, b, c);
|
|
}
|
|
|
|
#endif /* defined(WOLFSSL_KEY_GEN) || defined(HAVE_COMP_KEY) */
|
|
|
|
#ifdef WOLFSSL_KEY_GEN
|
|
|
|
void fp_gcd(fp_int *a, fp_int *b, fp_int *c);
|
|
void fp_lcm(fp_int *a, fp_int *b, fp_int *c);
|
|
int fp_isprime(fp_int *a);
|
|
|
|
int mp_gcd(fp_int *a, fp_int *b, fp_int *c)
|
|
{
|
|
fp_gcd(a, b, c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
int mp_lcm(fp_int *a, fp_int *b, fp_int *c)
|
|
{
|
|
fp_lcm(a, b, c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
int mp_prime_is_prime(mp_int* a, int t, int* result)
|
|
{
|
|
(void)t;
|
|
*result = fp_isprime(a);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Miller-Rabin test of "a" to the base of "b" as described in
|
|
* HAC pp. 139 Algorithm 4.24
|
|
*
|
|
* Sets result to 0 if definitely composite or 1 if probably prime.
|
|
* Randomly the chance of error is no more than 1/4 and often
|
|
* very much lower.
|
|
*/
|
|
static void fp_prime_miller_rabin (fp_int * a, fp_int * b, int *result)
|
|
{
|
|
fp_int n1, y, r;
|
|
int s, j;
|
|
|
|
/* default */
|
|
*result = FP_NO;
|
|
|
|
/* ensure b > 1 */
|
|
if (fp_cmp_d(b, 1) != FP_GT) {
|
|
return;
|
|
}
|
|
|
|
/* get n1 = a - 1 */
|
|
fp_init_copy(&n1, a);
|
|
fp_sub_d(&n1, 1, &n1);
|
|
|
|
/* set 2**s * r = n1 */
|
|
fp_init_copy(&r, &n1);
|
|
|
|
/* count the number of least significant bits
|
|
* which are zero
|
|
*/
|
|
s = fp_cnt_lsb(&r);
|
|
|
|
/* now divide n - 1 by 2**s */
|
|
fp_div_2d (&r, s, &r, NULL);
|
|
|
|
/* compute y = b**r mod a */
|
|
fp_init(&y);
|
|
fp_exptmod(b, &r, a, &y);
|
|
|
|
/* if y != 1 and y != n1 do */
|
|
if (fp_cmp_d (&y, 1) != FP_EQ && fp_cmp (&y, &n1) != FP_EQ) {
|
|
j = 1;
|
|
/* while j <= s-1 and y != n1 */
|
|
while ((j <= (s - 1)) && fp_cmp (&y, &n1) != FP_EQ) {
|
|
fp_sqrmod (&y, a, &y);
|
|
|
|
/* if y == 1 then composite */
|
|
if (fp_cmp_d (&y, 1) == FP_EQ) {
|
|
return;
|
|
}
|
|
++j;
|
|
}
|
|
|
|
/* if y != n1 then composite */
|
|
if (fp_cmp (&y, &n1) != FP_EQ) {
|
|
return;
|
|
}
|
|
}
|
|
|
|
/* probably prime now */
|
|
*result = FP_YES;
|
|
}
|
|
|
|
|
|
/* a few primes */
|
|
static const fp_digit primes[256] = {
|
|
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
|
|
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
|
|
0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
|
|
0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083,
|
|
0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
|
|
0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
|
|
0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
|
|
0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
|
|
|
|
0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
|
|
0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
|
|
0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
|
|
0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
|
|
0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
|
|
0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
|
|
0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
|
|
0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
|
|
|
|
0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
|
|
0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
|
|
0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
|
|
0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
|
|
0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
|
|
0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
|
|
0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
|
|
0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
|
|
|
|
0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
|
|
0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
|
|
0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
|
|
0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
|
|
0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
|
|
0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
|
|
0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
|
|
0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
|
|
};
|
|
|
|
int fp_isprime(fp_int *a)
|
|
{
|
|
fp_int b;
|
|
fp_digit d = 0;
|
|
int r, res;
|
|
|
|
/* do trial division */
|
|
for (r = 0; r < 256; r++) {
|
|
fp_mod_d(a, primes[r], &d);
|
|
if (d == 0) {
|
|
return FP_NO;
|
|
}
|
|
}
|
|
|
|
/* now do 8 miller rabins */
|
|
fp_init(&b);
|
|
for (r = 0; r < 8; r++) {
|
|
fp_set(&b, primes[r]);
|
|
fp_prime_miller_rabin(a, &b, &res);
|
|
if (res == FP_NO) {
|
|
return FP_NO;
|
|
}
|
|
}
|
|
return FP_YES;
|
|
}
|
|
|
|
|
|
/* c = [a, b] */
|
|
void fp_lcm(fp_int *a, fp_int *b, fp_int *c)
|
|
{
|
|
fp_int t1, t2;
|
|
|
|
fp_init(&t1);
|
|
fp_init(&t2);
|
|
fp_gcd(a, b, &t1);
|
|
if (fp_cmp_mag(a, b) == FP_GT) {
|
|
fp_div(a, &t1, &t2, NULL);
|
|
fp_mul(b, &t2, c);
|
|
} else {
|
|
fp_div(b, &t1, &t2, NULL);
|
|
fp_mul(a, &t2, c);
|
|
}
|
|
}
|
|
|
|
|
|
|
|
/* c = (a, b) */
|
|
void fp_gcd(fp_int *a, fp_int *b, fp_int *c)
|
|
{
|
|
fp_int u, v, r;
|
|
|
|
/* either zero than gcd is the largest */
|
|
if (fp_iszero (a) == 1 && fp_iszero (b) == 0) {
|
|
fp_abs (b, c);
|
|
return;
|
|
}
|
|
if (fp_iszero (a) == 0 && fp_iszero (b) == 1) {
|
|
fp_abs (a, c);
|
|
return;
|
|
}
|
|
|
|
/* optimized. At this point if a == 0 then
|
|
* b must equal zero too
|
|
*/
|
|
if (fp_iszero (a) == 1) {
|
|
fp_zero(c);
|
|
return;
|
|
}
|
|
|
|
/* sort inputs */
|
|
if (fp_cmp_mag(a, b) != FP_LT) {
|
|
fp_init_copy(&u, a);
|
|
fp_init_copy(&v, b);
|
|
} else {
|
|
fp_init_copy(&u, b);
|
|
fp_init_copy(&v, a);
|
|
}
|
|
|
|
fp_init(&r);
|
|
while (fp_iszero(&v) == FP_NO) {
|
|
fp_mod(&u, &v, &r);
|
|
fp_copy(&v, &u);
|
|
fp_copy(&r, &v);
|
|
}
|
|
fp_copy(&u, c);
|
|
}
|
|
|
|
#endif /* WOLFSSL_KEY_GEN */
|
|
|
|
|
|
#if defined(HAVE_ECC) || !defined(NO_PWDBASED)
|
|
/* c = a + b */
|
|
void fp_add_d(fp_int *a, fp_digit b, fp_int *c)
|
|
{
|
|
fp_int tmp;
|
|
fp_init(&tmp);
|
|
fp_set(&tmp, b);
|
|
fp_add(a,&tmp,c);
|
|
}
|
|
|
|
/* external compatibility */
|
|
int mp_add_d(fp_int *a, fp_digit b, fp_int *c)
|
|
{
|
|
fp_add_d(a, b, c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
#endif /* HAVE_ECC || !NO_PWDBASED */
|
|
|
|
|
|
#ifdef HAVE_ECC
|
|
|
|
/* chars used in radix conversions */
|
|
static const char *fp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
|
|
|
|
static int fp_read_radix(fp_int *a, const char *str, int radix)
|
|
{
|
|
int y, neg;
|
|
char ch;
|
|
|
|
/* make sure the radix is ok */
|
|
if (radix < 2 || radix > 64) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
/* if the leading digit is a
|
|
* minus set the sign to negative.
|
|
*/
|
|
if (*str == '-') {
|
|
++str;
|
|
neg = FP_NEG;
|
|
} else {
|
|
neg = FP_ZPOS;
|
|
}
|
|
|
|
/* set the integer to the default of zero */
|
|
fp_zero (a);
|
|
|
|
/* process each digit of the string */
|
|
while (*str) {
|
|
/* if the radix < 36 the conversion is case insensitive
|
|
* this allows numbers like 1AB and 1ab to represent the same value
|
|
* [e.g. in hex]
|
|
*/
|
|
ch = (char) ((radix < 36) ? XTOUPPER((unsigned char)*str) : *str);
|
|
for (y = 0; y < 64; y++) {
|
|
if (ch == fp_s_rmap[y]) {
|
|
break;
|
|
}
|
|
}
|
|
|
|
/* if the char was found in the map
|
|
* and is less than the given radix add it
|
|
* to the number, otherwise exit the loop.
|
|
*/
|
|
if (y < radix) {
|
|
fp_mul_d (a, (fp_digit) radix, a);
|
|
fp_add_d (a, (fp_digit) y, a);
|
|
} else {
|
|
break;
|
|
}
|
|
++str;
|
|
}
|
|
|
|
/* set the sign only if a != 0 */
|
|
if (fp_iszero(a) != FP_YES) {
|
|
a->sign = neg;
|
|
}
|
|
return FP_OKAY;
|
|
}
|
|
|
|
/* fast math conversion */
|
|
int mp_read_radix(mp_int *a, const char *str, int radix)
|
|
{
|
|
return fp_read_radix(a, str, radix);
|
|
}
|
|
|
|
/* fast math conversion */
|
|
void mp_set(fp_int *a, fp_digit b)
|
|
{
|
|
fp_set(a,b);
|
|
}
|
|
|
|
/* fast math conversion */
|
|
int mp_sqr(fp_int *A, fp_int *B)
|
|
{
|
|
fp_sqr(A, B);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* fast math conversion */
|
|
int mp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
|
|
{
|
|
fp_montgomery_reduce(a, m, mp);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
/* fast math conversion */
|
|
int mp_montgomery_setup(fp_int *a, fp_digit *rho)
|
|
{
|
|
return fp_montgomery_setup(a, rho);
|
|
}
|
|
|
|
int mp_div_2(fp_int * a, fp_int * b)
|
|
{
|
|
fp_div_2(a, b);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
int mp_init_copy(fp_int * a, fp_int * b)
|
|
{
|
|
fp_init_copy(a, b);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
#ifdef HAVE_COMP_KEY
|
|
|
|
int mp_cnt_lsb(fp_int* a)
|
|
{
|
|
fp_cnt_lsb(a);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
int mp_div_2d(fp_int* a, int b, fp_int* c, fp_int* d)
|
|
{
|
|
fp_div_2d(a, b, c, d);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
#endif /* HAVE_COMP_KEY */
|
|
|
|
|
|
#endif /* HAVE_ECC */
|
|
|
|
#endif /* USE_FAST_MATH */
|
|
|