[164] | 1 | /* integer.c
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| 2 | *
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| 3 | * Copyright (C) 2006-2015 wolfSSL Inc.
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| 4 | *
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| 5 | * This file is part of wolfSSL. (formerly known as CyaSSL)
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| 6 | *
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| 7 | * wolfSSL is free software; you can redistribute it and/or modify
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| 8 | * it under the terms of the GNU General Public License as published by
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| 9 | * the Free Software Foundation; either version 2 of the License, or
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| 10 | * (at your option) any later version.
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| 11 | *
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| 12 | * wolfSSL is distributed in the hope that it will be useful,
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | * GNU General Public License for more details.
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| 16 | *
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| 17 | * You should have received a copy of the GNU General Public License
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| 18 | * along with this program; if not, write to the Free Software
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| 19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
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| 20 | */
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| 21 |
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| 22 |
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| 23 | /*
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| 24 | * Based on public domain LibTomMath 0.38 by Tom St Denis, tomstdenis@iahu.ca,
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| 25 | * http://math.libtomcrypt.com
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| 26 | */
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| 27 |
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| 28 |
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| 29 | #ifdef HAVE_CONFIG_H
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| 30 | #include <config.h>
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| 31 | #endif
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| 32 |
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| 33 | /* in case user set USE_FAST_MATH there */
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| 34 | #include <wolfssl/wolfcrypt/settings.h>
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| 35 |
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| 36 | #ifndef NO_BIG_INT
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| 37 |
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| 38 | #ifndef USE_FAST_MATH
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| 39 |
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| 40 | #include <wolfssl/wolfcrypt/integer.h>
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| 41 |
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| 42 | #ifndef NO_WOLFSSL_SMALL_STACK
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| 43 | #ifndef WOLFSSL_SMALL_STACK
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| 44 | #define WOLFSSL_SMALL_STACK
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| 45 | #endif
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| 46 | #endif
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| 47 |
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| 48 | #ifdef SHOW_GEN
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| 49 | #ifdef FREESCALE_MQX
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| 50 | #if MQX_USE_IO_OLD
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| 51 | #include <fio.h>
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| 52 | #else
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| 53 | #include <nio.h>
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| 54 | #endif
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| 55 | #else
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| 56 | #include <stdio.h>
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| 57 | #endif
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| 58 | #endif
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| 59 |
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| 60 | /* reverse an array, used for radix code */
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| 61 | static void
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| 62 | bn_reverse (unsigned char *s, int len)
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| 63 | {
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| 64 | int ix, iy;
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| 65 | unsigned char t;
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| 66 |
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| 67 | ix = 0;
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| 68 | iy = len - 1;
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| 69 | while (ix < iy) {
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| 70 | t = s[ix];
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| 71 | s[ix] = s[iy];
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| 72 | s[iy] = t;
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| 73 | ++ix;
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| 74 | --iy;
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| 75 | }
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| 76 | }
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| 77 |
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| 78 | /* math settings check */
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| 79 | word32 CheckRunTimeSettings(void)
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| 80 | {
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| 81 | return CTC_SETTINGS;
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| 82 | }
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| 83 |
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| 84 |
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| 85 | /* handle up to 6 inits */
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| 86 | int mp_init_multi(mp_int* a, mp_int* b, mp_int* c, mp_int* d, mp_int* e,
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| 87 | mp_int* f)
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| 88 | {
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| 89 | int res = MP_OKAY;
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| 90 |
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| 91 | if (a && ((res = mp_init(a)) != MP_OKAY))
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| 92 | return res;
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| 93 |
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| 94 | if (b && ((res = mp_init(b)) != MP_OKAY)) {
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| 95 | mp_clear(a);
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| 96 | return res;
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| 97 | }
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| 98 |
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| 99 | if (c && ((res = mp_init(c)) != MP_OKAY)) {
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| 100 | mp_clear(a); mp_clear(b);
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| 101 | return res;
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| 102 | }
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| 103 |
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| 104 | if (d && ((res = mp_init(d)) != MP_OKAY)) {
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| 105 | mp_clear(a); mp_clear(b); mp_clear(c);
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| 106 | return res;
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| 107 | }
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| 108 |
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| 109 | if (e && ((res = mp_init(e)) != MP_OKAY)) {
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| 110 | mp_clear(a); mp_clear(b); mp_clear(c); mp_clear(d);
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| 111 | return res;
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| 112 | }
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| 113 |
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| 114 | if (f && ((res = mp_init(f)) != MP_OKAY)) {
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| 115 | mp_clear(a); mp_clear(b); mp_clear(c); mp_clear(d); mp_clear(e);
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| 116 | return res;
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| 117 | }
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| 118 |
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| 119 | return res;
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| 120 | }
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| 121 |
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| 122 |
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| 123 | /* init a new mp_int */
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| 124 | int mp_init (mp_int * a)
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| 125 | {
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| 126 | int i;
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| 127 |
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| 128 | /* allocate memory required and clear it */
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| 129 | a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC, 0,
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| 130 | DYNAMIC_TYPE_BIGINT);
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| 131 | if (a->dp == NULL) {
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| 132 | return MP_MEM;
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| 133 | }
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| 134 |
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| 135 | /* set the digits to zero */
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| 136 | for (i = 0; i < MP_PREC; i++) {
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| 137 | a->dp[i] = 0;
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| 138 | }
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| 139 |
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| 140 | /* set the used to zero, allocated digits to the default precision
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| 141 | * and sign to positive */
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| 142 | a->used = 0;
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| 143 | a->alloc = MP_PREC;
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| 144 | a->sign = MP_ZPOS;
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| 145 |
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| 146 | return MP_OKAY;
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| 147 | }
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| 148 |
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| 149 |
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| 150 | /* clear one (frees) */
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| 151 | void
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| 152 | mp_clear (mp_int * a)
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| 153 | {
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| 154 | int i;
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| 155 |
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| 156 | if (a == NULL)
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| 157 | return;
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| 158 |
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| 159 | /* only do anything if a hasn't been freed previously */
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| 160 | if (a->dp != NULL) {
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| 161 | /* first zero the digits */
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| 162 | for (i = 0; i < a->used; i++) {
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| 163 | a->dp[i] = 0;
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| 164 | }
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| 165 |
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| 166 | /* free ram */
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| 167 | XFREE(a->dp, 0, DYNAMIC_TYPE_BIGINT);
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| 168 |
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| 169 | /* reset members to make debugging easier */
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| 170 | a->dp = NULL;
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| 171 | a->alloc = a->used = 0;
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| 172 | a->sign = MP_ZPOS;
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| 173 | }
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| 174 | }
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| 175 |
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| 176 |
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| 177 | /* get the size for an unsigned equivalent */
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| 178 | int mp_unsigned_bin_size (mp_int * a)
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| 179 | {
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| 180 | int size = mp_count_bits (a);
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| 181 | return (size / 8 + ((size & 7) != 0 ? 1 : 0));
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| 182 | }
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| 183 |
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| 184 |
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| 185 | /* returns the number of bits in an int */
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| 186 | int
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| 187 | mp_count_bits (mp_int * a)
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| 188 | {
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| 189 | int r;
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| 190 | mp_digit q;
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| 191 |
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| 192 | /* shortcut */
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| 193 | if (a->used == 0) {
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| 194 | return 0;
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| 195 | }
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| 196 |
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| 197 | /* get number of digits and add that */
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| 198 | r = (a->used - 1) * DIGIT_BIT;
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| 199 |
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| 200 | /* take the last digit and count the bits in it */
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| 201 | q = a->dp[a->used - 1];
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| 202 | while (q > ((mp_digit) 0)) {
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| 203 | ++r;
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| 204 | q >>= ((mp_digit) 1);
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| 205 | }
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| 206 | return r;
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| 207 | }
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| 208 |
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| 209 |
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| 210 | int mp_leading_bit (mp_int * a)
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| 211 | {
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| 212 | int bit = 0;
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| 213 | mp_int t;
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| 214 |
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| 215 | if (mp_init_copy(&t, a) != MP_OKAY)
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| 216 | return 0;
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| 217 |
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| 218 | while (mp_iszero(&t) == 0) {
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| 219 | #ifndef MP_8BIT
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| 220 | bit = (t.dp[0] & 0x80) != 0;
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| 221 | #else
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| 222 | bit = (t.dp[0] | ((t.dp[1] & 0x01) << 7)) & 0x80 != 0;
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| 223 | #endif
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| 224 | if (mp_div_2d (&t, 8, &t, NULL) != MP_OKAY)
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| 225 | break;
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| 226 | }
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| 227 | mp_clear(&t);
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| 228 | return bit;
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| 229 | }
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| 230 |
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| 231 |
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| 232 | /* store in unsigned [big endian] format */
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| 233 | int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
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| 234 | {
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| 235 | int x, res;
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| 236 | mp_int t;
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| 237 |
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| 238 | if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
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| 239 | return res;
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| 240 | }
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| 241 |
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| 242 | x = 0;
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| 243 | while (mp_iszero (&t) == 0) {
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| 244 | #ifndef MP_8BIT
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| 245 | b[x++] = (unsigned char) (t.dp[0] & 255);
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| 246 | #else
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| 247 | b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
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| 248 | #endif
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| 249 | if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
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| 250 | mp_clear (&t);
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| 251 | return res;
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| 252 | }
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| 253 | }
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| 254 | bn_reverse (b, x);
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| 255 | mp_clear (&t);
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| 256 | return MP_OKAY;
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| 257 | }
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| 258 |
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| 259 |
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| 260 | /* creates "a" then copies b into it */
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| 261 | int mp_init_copy (mp_int * a, mp_int * b)
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| 262 | {
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| 263 | int res;
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| 264 |
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| 265 | if ((res = mp_init (a)) != MP_OKAY) {
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| 266 | return res;
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| 267 | }
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| 268 | return mp_copy (b, a);
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| 269 | }
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| 270 |
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| 271 |
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| 272 | /* copy, b = a */
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| 273 | int
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| 274 | mp_copy (mp_int * a, mp_int * b)
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| 275 | {
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| 276 | int res, n;
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| 277 |
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| 278 | /* if dst == src do nothing */
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| 279 | if (a == b) {
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| 280 | return MP_OKAY;
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| 281 | }
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| 282 |
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| 283 | /* grow dest */
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| 284 | if (b->alloc < a->used) {
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| 285 | if ((res = mp_grow (b, a->used)) != MP_OKAY) {
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| 286 | return res;
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| 287 | }
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| 288 | }
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| 289 |
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| 290 | /* zero b and copy the parameters over */
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| 291 | {
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| 292 | register mp_digit *tmpa, *tmpb;
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| 293 |
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| 294 | /* pointer aliases */
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| 295 |
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| 296 | /* source */
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| 297 | tmpa = a->dp;
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| 298 |
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| 299 | /* destination */
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| 300 | tmpb = b->dp;
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| 301 |
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| 302 | /* copy all the digits */
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| 303 | for (n = 0; n < a->used; n++) {
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| 304 | *tmpb++ = *tmpa++;
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| 305 | }
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| 306 |
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| 307 | /* clear high digits */
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| 308 | for (; n < b->used; n++) {
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| 309 | *tmpb++ = 0;
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| 310 | }
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| 311 | }
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| 312 |
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| 313 | /* copy used count and sign */
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| 314 | b->used = a->used;
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| 315 | b->sign = a->sign;
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| 316 | return MP_OKAY;
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| 317 | }
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| 318 |
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| 319 |
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| 320 | /* grow as required */
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| 321 | int mp_grow (mp_int * a, int size)
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| 322 | {
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| 323 | int i;
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| 324 | mp_digit *tmp;
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| 325 |
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| 326 | /* if the alloc size is smaller alloc more ram */
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| 327 | if (a->alloc < size) {
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| 328 | /* ensure there are always at least MP_PREC digits extra on top */
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| 329 | size += (MP_PREC * 2) - (size % MP_PREC);
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| 330 |
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| 331 | /* reallocate the array a->dp
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| 332 | *
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| 333 | * We store the return in a temporary variable
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| 334 | * in case the operation failed we don't want
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| 335 | * to overwrite the dp member of a.
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| 336 | */
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| 337 | tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size, 0,
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| 338 | DYNAMIC_TYPE_BIGINT);
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| 339 | if (tmp == NULL) {
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| 340 | /* reallocation failed but "a" is still valid [can be freed] */
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| 341 | return MP_MEM;
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| 342 | }
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| 343 |
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| 344 | /* reallocation succeeded so set a->dp */
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| 345 | a->dp = tmp;
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| 346 |
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| 347 | /* zero excess digits */
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| 348 | i = a->alloc;
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| 349 | a->alloc = size;
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| 350 | for (; i < a->alloc; i++) {
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| 351 | a->dp[i] = 0;
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| 352 | }
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| 353 | }
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| 354 | return MP_OKAY;
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| 355 | }
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| 356 |
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| 357 |
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| 358 | /* shift right by a certain bit count (store quotient in c, optional
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| 359 | remainder in d) */
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| 360 | int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
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| 361 | {
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| 362 | int D, res;
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| 363 | mp_int t;
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| 364 |
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| 365 |
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| 366 | /* if the shift count is <= 0 then we do no work */
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| 367 | if (b <= 0) {
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| 368 | res = mp_copy (a, c);
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| 369 | if (d != NULL) {
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| 370 | mp_zero (d);
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| 371 | }
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| 372 | return res;
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| 373 | }
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| 374 |
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| 375 | if ((res = mp_init (&t)) != MP_OKAY) {
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| 376 | return res;
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| 377 | }
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| 378 |
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| 379 | /* get the remainder */
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| 380 | if (d != NULL) {
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| 381 | if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
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| 382 | mp_clear (&t);
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| 383 | return res;
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| 384 | }
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| 385 | }
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| 386 |
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| 387 | /* copy */
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| 388 | if ((res = mp_copy (a, c)) != MP_OKAY) {
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| 389 | mp_clear (&t);
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| 390 | return res;
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| 391 | }
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| 392 |
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| 393 | /* shift by as many digits in the bit count */
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| 394 | if (b >= (int)DIGIT_BIT) {
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| 395 | mp_rshd (c, b / DIGIT_BIT);
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| 396 | }
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| 397 |
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| 398 | /* shift any bit count < DIGIT_BIT */
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| 399 | D = (b % DIGIT_BIT);
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| 400 | if (D != 0) {
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| 401 | mp_rshb(c, D);
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| 402 | }
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| 403 | mp_clamp (c);
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| 404 | if (d != NULL) {
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| 405 | mp_exch (&t, d);
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| 406 | }
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| 407 | mp_clear (&t);
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| 408 | return MP_OKAY;
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| 409 | }
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| 410 |
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| 411 |
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| 412 | /* set to zero */
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| 413 | void mp_zero (mp_int * a)
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| 414 | {
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| 415 | int n;
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| 416 | mp_digit *tmp;
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| 417 |
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| 418 | a->sign = MP_ZPOS;
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| 419 | a->used = 0;
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| 420 |
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| 421 | tmp = a->dp;
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| 422 | for (n = 0; n < a->alloc; n++) {
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| 423 | *tmp++ = 0;
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| 424 | }
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| 425 | }
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| 426 |
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| 427 |
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| 428 | /* trim unused digits
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| 429 | *
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| 430 | * This is used to ensure that leading zero digits are
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| 431 | * trimed and the leading "used" digit will be non-zero
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| 432 | * Typically very fast. Also fixes the sign if there
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| 433 | * are no more leading digits
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| 434 | */
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| 435 | void
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| 436 | mp_clamp (mp_int * a)
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| 437 | {
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| 438 | /* decrease used while the most significant digit is
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| 439 | * zero.
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| 440 | */
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| 441 | while (a->used > 0 && a->dp[a->used - 1] == 0) {
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| 442 | --(a->used);
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| 443 | }
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| 444 |
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| 445 | /* reset the sign flag if used == 0 */
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| 446 | if (a->used == 0) {
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| 447 | a->sign = MP_ZPOS;
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| 448 | }
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| 449 | }
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| 450 |
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| 451 |
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| 452 | /* swap the elements of two integers, for cases where you can't simply swap the
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| 453 | * mp_int pointers around
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| 454 | */
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| 455 | void
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| 456 | mp_exch (mp_int * a, mp_int * b)
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| 457 | {
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| 458 | mp_int t;
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| 459 |
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| 460 | t = *a;
|
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| 461 | *a = *b;
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| 462 | *b = t;
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| 463 | }
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| 464 |
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| 465 |
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| 466 | /* shift right a certain number of bits */
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| 467 | void mp_rshb (mp_int *c, int x)
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| 468 | {
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| 469 | register mp_digit *tmpc, mask, shift;
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| 470 | mp_digit r, rr;
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| 471 | mp_digit D = x;
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| 472 |
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| 473 | /* mask */
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| 474 | mask = (((mp_digit)1) << D) - 1;
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| 475 |
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| 476 | /* shift for lsb */
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| 477 | shift = DIGIT_BIT - D;
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| 478 |
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| 479 | /* alias */
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| 480 | tmpc = c->dp + (c->used - 1);
|
---|
| 481 |
|
---|
| 482 | /* carry */
|
---|
| 483 | r = 0;
|
---|
| 484 | for (x = c->used - 1; x >= 0; x--) {
|
---|
| 485 | /* get the lower bits of this word in a temp */
|
---|
| 486 | rr = *tmpc & mask;
|
---|
| 487 |
|
---|
| 488 | /* shift the current word and mix in the carry bits from previous word */
|
---|
| 489 | *tmpc = (*tmpc >> D) | (r << shift);
|
---|
| 490 | --tmpc;
|
---|
| 491 |
|
---|
| 492 | /* set the carry to the carry bits of the current word found above */
|
---|
| 493 | r = rr;
|
---|
| 494 | }
|
---|
| 495 | }
|
---|
| 496 |
|
---|
| 497 |
|
---|
| 498 | /* shift right a certain amount of digits */
|
---|
| 499 | void mp_rshd (mp_int * a, int b)
|
---|
| 500 | {
|
---|
| 501 | int x;
|
---|
| 502 |
|
---|
| 503 | /* if b <= 0 then ignore it */
|
---|
| 504 | if (b <= 0) {
|
---|
| 505 | return;
|
---|
| 506 | }
|
---|
| 507 |
|
---|
| 508 | /* if b > used then simply zero it and return */
|
---|
| 509 | if (a->used <= b) {
|
---|
| 510 | mp_zero (a);
|
---|
| 511 | return;
|
---|
| 512 | }
|
---|
| 513 |
|
---|
| 514 | {
|
---|
| 515 | register mp_digit *bottom, *top;
|
---|
| 516 |
|
---|
| 517 | /* shift the digits down */
|
---|
| 518 |
|
---|
| 519 | /* bottom */
|
---|
| 520 | bottom = a->dp;
|
---|
| 521 |
|
---|
| 522 | /* top [offset into digits] */
|
---|
| 523 | top = a->dp + b;
|
---|
| 524 |
|
---|
| 525 | /* this is implemented as a sliding window where
|
---|
| 526 | * the window is b-digits long and digits from
|
---|
| 527 | * the top of the window are copied to the bottom
|
---|
| 528 | *
|
---|
| 529 | * e.g.
|
---|
| 530 |
|
---|
| 531 | b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
|
---|
| 532 | /\ | ---->
|
---|
| 533 | \-------------------/ ---->
|
---|
| 534 | */
|
---|
| 535 | for (x = 0; x < (a->used - b); x++) {
|
---|
| 536 | *bottom++ = *top++;
|
---|
| 537 | }
|
---|
| 538 |
|
---|
| 539 | /* zero the top digits */
|
---|
| 540 | for (; x < a->used; x++) {
|
---|
| 541 | *bottom++ = 0;
|
---|
| 542 | }
|
---|
| 543 | }
|
---|
| 544 |
|
---|
| 545 | /* remove excess digits */
|
---|
| 546 | a->used -= b;
|
---|
| 547 | }
|
---|
| 548 |
|
---|
| 549 |
|
---|
| 550 | /* calc a value mod 2**b */
|
---|
| 551 | int
|
---|
| 552 | mp_mod_2d (mp_int * a, int b, mp_int * c)
|
---|
| 553 | {
|
---|
| 554 | int x, res;
|
---|
| 555 |
|
---|
| 556 | /* if b is <= 0 then zero the int */
|
---|
| 557 | if (b <= 0) {
|
---|
| 558 | mp_zero (c);
|
---|
| 559 | return MP_OKAY;
|
---|
| 560 | }
|
---|
| 561 |
|
---|
| 562 | /* if the modulus is larger than the value than return */
|
---|
| 563 | if (b >= (int) (a->used * DIGIT_BIT)) {
|
---|
| 564 | res = mp_copy (a, c);
|
---|
| 565 | return res;
|
---|
| 566 | }
|
---|
| 567 |
|
---|
| 568 | /* copy */
|
---|
| 569 | if ((res = mp_copy (a, c)) != MP_OKAY) {
|
---|
| 570 | return res;
|
---|
| 571 | }
|
---|
| 572 |
|
---|
| 573 | /* zero digits above the last digit of the modulus */
|
---|
| 574 | for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
|
---|
| 575 | c->dp[x] = 0;
|
---|
| 576 | }
|
---|
| 577 | /* clear the digit that is not completely outside/inside the modulus */
|
---|
| 578 | c->dp[b / DIGIT_BIT] &= (mp_digit) ((((mp_digit) 1) <<
|
---|
| 579 | (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
|
---|
| 580 | mp_clamp (c);
|
---|
| 581 | return MP_OKAY;
|
---|
| 582 | }
|
---|
| 583 |
|
---|
| 584 |
|
---|
| 585 | /* reads a unsigned char array, assumes the msb is stored first [big endian] */
|
---|
| 586 | int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
|
---|
| 587 | {
|
---|
| 588 | int res;
|
---|
| 589 |
|
---|
| 590 | /* make sure there are at least two digits */
|
---|
| 591 | if (a->alloc < 2) {
|
---|
| 592 | if ((res = mp_grow(a, 2)) != MP_OKAY) {
|
---|
| 593 | return res;
|
---|
| 594 | }
|
---|
| 595 | }
|
---|
| 596 |
|
---|
| 597 | /* zero the int */
|
---|
| 598 | mp_zero (a);
|
---|
| 599 |
|
---|
| 600 | /* read the bytes in */
|
---|
| 601 | while (c-- > 0) {
|
---|
| 602 | if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
|
---|
| 603 | return res;
|
---|
| 604 | }
|
---|
| 605 |
|
---|
| 606 | #ifndef MP_8BIT
|
---|
| 607 | a->dp[0] |= *b++;
|
---|
| 608 | a->used += 1;
|
---|
| 609 | #else
|
---|
| 610 | a->dp[0] = (*b & MP_MASK);
|
---|
| 611 | a->dp[1] |= ((*b++ >> 7U) & 1);
|
---|
| 612 | a->used += 2;
|
---|
| 613 | #endif
|
---|
| 614 | }
|
---|
| 615 | mp_clamp (a);
|
---|
| 616 | return MP_OKAY;
|
---|
| 617 | }
|
---|
| 618 |
|
---|
| 619 |
|
---|
| 620 | /* shift left by a certain bit count */
|
---|
| 621 | int mp_mul_2d (mp_int * a, int b, mp_int * c)
|
---|
| 622 | {
|
---|
| 623 | mp_digit d;
|
---|
| 624 | int res;
|
---|
| 625 |
|
---|
| 626 | /* copy */
|
---|
| 627 | if (a != c) {
|
---|
| 628 | if ((res = mp_copy (a, c)) != MP_OKAY) {
|
---|
| 629 | return res;
|
---|
| 630 | }
|
---|
| 631 | }
|
---|
| 632 |
|
---|
| 633 | if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
|
---|
| 634 | if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
|
---|
| 635 | return res;
|
---|
| 636 | }
|
---|
| 637 | }
|
---|
| 638 |
|
---|
| 639 | /* shift by as many digits in the bit count */
|
---|
| 640 | if (b >= (int)DIGIT_BIT) {
|
---|
| 641 | if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
|
---|
| 642 | return res;
|
---|
| 643 | }
|
---|
| 644 | }
|
---|
| 645 |
|
---|
| 646 | /* shift any bit count < DIGIT_BIT */
|
---|
| 647 | d = (mp_digit) (b % DIGIT_BIT);
|
---|
| 648 | if (d != 0) {
|
---|
| 649 | register mp_digit *tmpc, shift, mask, r, rr;
|
---|
| 650 | register int x;
|
---|
| 651 |
|
---|
| 652 | /* bitmask for carries */
|
---|
| 653 | mask = (((mp_digit)1) << d) - 1;
|
---|
| 654 |
|
---|
| 655 | /* shift for msbs */
|
---|
| 656 | shift = DIGIT_BIT - d;
|
---|
| 657 |
|
---|
| 658 | /* alias */
|
---|
| 659 | tmpc = c->dp;
|
---|
| 660 |
|
---|
| 661 | /* carry */
|
---|
| 662 | r = 0;
|
---|
| 663 | for (x = 0; x < c->used; x++) {
|
---|
| 664 | /* get the higher bits of the current word */
|
---|
| 665 | rr = (*tmpc >> shift) & mask;
|
---|
| 666 |
|
---|
| 667 | /* shift the current word and OR in the carry */
|
---|
| 668 | *tmpc = ((*tmpc << d) | r) & MP_MASK;
|
---|
| 669 | ++tmpc;
|
---|
| 670 |
|
---|
| 671 | /* set the carry to the carry bits of the current word */
|
---|
| 672 | r = rr;
|
---|
| 673 | }
|
---|
| 674 |
|
---|
| 675 | /* set final carry */
|
---|
| 676 | if (r != 0) {
|
---|
| 677 | c->dp[(c->used)++] = r;
|
---|
| 678 | }
|
---|
| 679 | }
|
---|
| 680 | mp_clamp (c);
|
---|
| 681 | return MP_OKAY;
|
---|
| 682 | }
|
---|
| 683 |
|
---|
| 684 |
|
---|
| 685 | /* shift left a certain amount of digits */
|
---|
| 686 | int mp_lshd (mp_int * a, int b)
|
---|
| 687 | {
|
---|
| 688 | int x, res;
|
---|
| 689 |
|
---|
| 690 | /* if its less than zero return */
|
---|
| 691 | if (b <= 0) {
|
---|
| 692 | return MP_OKAY;
|
---|
| 693 | }
|
---|
| 694 |
|
---|
| 695 | /* grow to fit the new digits */
|
---|
| 696 | if (a->alloc < a->used + b) {
|
---|
| 697 | if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
|
---|
| 698 | return res;
|
---|
| 699 | }
|
---|
| 700 | }
|
---|
| 701 |
|
---|
| 702 | {
|
---|
| 703 | register mp_digit *top, *bottom;
|
---|
| 704 |
|
---|
| 705 | /* increment the used by the shift amount then copy upwards */
|
---|
| 706 | a->used += b;
|
---|
| 707 |
|
---|
| 708 | /* top */
|
---|
| 709 | top = a->dp + a->used - 1;
|
---|
| 710 |
|
---|
| 711 | /* base */
|
---|
| 712 | bottom = a->dp + a->used - 1 - b;
|
---|
| 713 |
|
---|
| 714 | /* much like mp_rshd this is implemented using a sliding window
|
---|
| 715 | * except the window goes the otherway around. Copying from
|
---|
| 716 | * the bottom to the top. see bn_mp_rshd.c for more info.
|
---|
| 717 | */
|
---|
| 718 | for (x = a->used - 1; x >= b; x--) {
|
---|
| 719 | *top-- = *bottom--;
|
---|
| 720 | }
|
---|
| 721 |
|
---|
| 722 | /* zero the lower digits */
|
---|
| 723 | top = a->dp;
|
---|
| 724 | for (x = 0; x < b; x++) {
|
---|
| 725 | *top++ = 0;
|
---|
| 726 | }
|
---|
| 727 | }
|
---|
| 728 | return MP_OKAY;
|
---|
| 729 | }
|
---|
| 730 |
|
---|
| 731 |
|
---|
| 732 | /* this is a shell function that calls either the normal or Montgomery
|
---|
| 733 | * exptmod functions. Originally the call to the montgomery code was
|
---|
| 734 | * embedded in the normal function but that wasted alot of stack space
|
---|
| 735 | * for nothing (since 99% of the time the Montgomery code would be called)
|
---|
| 736 | */
|
---|
| 737 | int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
|
---|
| 738 | {
|
---|
| 739 | int dr;
|
---|
| 740 |
|
---|
| 741 | /* modulus P must be positive */
|
---|
| 742 | if (P->sign == MP_NEG) {
|
---|
| 743 | return MP_VAL;
|
---|
| 744 | }
|
---|
| 745 |
|
---|
| 746 | /* if exponent X is negative we have to recurse */
|
---|
| 747 | if (X->sign == MP_NEG) {
|
---|
| 748 | #ifdef BN_MP_INVMOD_C
|
---|
| 749 | mp_int tmpG, tmpX;
|
---|
| 750 | int err;
|
---|
| 751 |
|
---|
| 752 | /* first compute 1/G mod P */
|
---|
| 753 | if ((err = mp_init(&tmpG)) != MP_OKAY) {
|
---|
| 754 | return err;
|
---|
| 755 | }
|
---|
| 756 | if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
|
---|
| 757 | mp_clear(&tmpG);
|
---|
| 758 | return err;
|
---|
| 759 | }
|
---|
| 760 |
|
---|
| 761 | /* now get |X| */
|
---|
| 762 | if ((err = mp_init(&tmpX)) != MP_OKAY) {
|
---|
| 763 | mp_clear(&tmpG);
|
---|
| 764 | return err;
|
---|
| 765 | }
|
---|
| 766 | if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
|
---|
| 767 | mp_clear(&tmpG);
|
---|
| 768 | mp_clear(&tmpX);
|
---|
| 769 | return err;
|
---|
| 770 | }
|
---|
| 771 |
|
---|
| 772 | /* and now compute (1/G)**|X| instead of G**X [X < 0] */
|
---|
| 773 | err = mp_exptmod(&tmpG, &tmpX, P, Y);
|
---|
| 774 | mp_clear(&tmpG);
|
---|
| 775 | mp_clear(&tmpX);
|
---|
| 776 | return err;
|
---|
| 777 | #else
|
---|
| 778 | /* no invmod */
|
---|
| 779 | return MP_VAL;
|
---|
| 780 | #endif
|
---|
| 781 | }
|
---|
| 782 |
|
---|
| 783 | /* modified diminished radix reduction */
|
---|
| 784 | #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && \
|
---|
| 785 | defined(BN_S_MP_EXPTMOD_C)
|
---|
| 786 | if (mp_reduce_is_2k_l(P) == MP_YES) {
|
---|
| 787 | return s_mp_exptmod(G, X, P, Y, 1);
|
---|
| 788 | }
|
---|
| 789 | #endif
|
---|
| 790 |
|
---|
| 791 | #ifdef BN_MP_DR_IS_MODULUS_C
|
---|
| 792 | /* is it a DR modulus? */
|
---|
| 793 | dr = mp_dr_is_modulus(P);
|
---|
| 794 | #else
|
---|
| 795 | /* default to no */
|
---|
| 796 | dr = 0;
|
---|
| 797 | #endif
|
---|
| 798 |
|
---|
| 799 | #ifdef BN_MP_REDUCE_IS_2K_C
|
---|
| 800 | /* if not, is it a unrestricted DR modulus? */
|
---|
| 801 | if (dr == 0) {
|
---|
| 802 | dr = mp_reduce_is_2k(P) << 1;
|
---|
| 803 | }
|
---|
| 804 | #endif
|
---|
| 805 |
|
---|
| 806 | /* if the modulus is odd or dr != 0 use the montgomery method */
|
---|
| 807 | #ifdef BN_MP_EXPTMOD_FAST_C
|
---|
| 808 | if (mp_isodd (P) == 1 || dr != 0) {
|
---|
| 809 | return mp_exptmod_fast (G, X, P, Y, dr);
|
---|
| 810 | } else {
|
---|
| 811 | #endif
|
---|
| 812 | #ifdef BN_S_MP_EXPTMOD_C
|
---|
| 813 | /* otherwise use the generic Barrett reduction technique */
|
---|
| 814 | return s_mp_exptmod (G, X, P, Y, 0);
|
---|
| 815 | #else
|
---|
| 816 | /* no exptmod for evens */
|
---|
| 817 | return MP_VAL;
|
---|
| 818 | #endif
|
---|
| 819 | #ifdef BN_MP_EXPTMOD_FAST_C
|
---|
| 820 | }
|
---|
| 821 | #endif
|
---|
| 822 | }
|
---|
| 823 |
|
---|
| 824 |
|
---|
| 825 | /* b = |a|
|
---|
| 826 | *
|
---|
| 827 | * Simple function copies the input and fixes the sign to positive
|
---|
| 828 | */
|
---|
| 829 | int
|
---|
| 830 | mp_abs (mp_int * a, mp_int * b)
|
---|
| 831 | {
|
---|
| 832 | int res;
|
---|
| 833 |
|
---|
| 834 | /* copy a to b */
|
---|
| 835 | if (a != b) {
|
---|
| 836 | if ((res = mp_copy (a, b)) != MP_OKAY) {
|
---|
| 837 | return res;
|
---|
| 838 | }
|
---|
| 839 | }
|
---|
| 840 |
|
---|
| 841 | /* force the sign of b to positive */
|
---|
| 842 | b->sign = MP_ZPOS;
|
---|
| 843 |
|
---|
| 844 | return MP_OKAY;
|
---|
| 845 | }
|
---|
| 846 |
|
---|
| 847 |
|
---|
| 848 | /* hac 14.61, pp608 */
|
---|
| 849 | int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 850 | {
|
---|
| 851 | /* b cannot be negative */
|
---|
| 852 | if (b->sign == MP_NEG || mp_iszero(b) == 1) {
|
---|
| 853 | return MP_VAL;
|
---|
| 854 | }
|
---|
| 855 |
|
---|
| 856 | #ifdef BN_FAST_MP_INVMOD_C
|
---|
| 857 | /* if the modulus is odd we can use a faster routine instead */
|
---|
| 858 | if (mp_isodd (b) == 1) {
|
---|
| 859 | return fast_mp_invmod (a, b, c);
|
---|
| 860 | }
|
---|
| 861 | #endif
|
---|
| 862 |
|
---|
| 863 | #ifdef BN_MP_INVMOD_SLOW_C
|
---|
| 864 | return mp_invmod_slow(a, b, c);
|
---|
| 865 | #endif
|
---|
| 866 | }
|
---|
| 867 |
|
---|
| 868 |
|
---|
| 869 | /* computes the modular inverse via binary extended euclidean algorithm,
|
---|
| 870 | * that is c = 1/a mod b
|
---|
| 871 | *
|
---|
| 872 | * Based on slow invmod except this is optimized for the case where b is
|
---|
| 873 | * odd as per HAC Note 14.64 on pp. 610
|
---|
| 874 | */
|
---|
| 875 | int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 876 | {
|
---|
| 877 | mp_int x, y, u, v, B, D;
|
---|
| 878 | int res, neg, loop_check = 0;
|
---|
| 879 |
|
---|
| 880 | /* 2. [modified] b must be odd */
|
---|
| 881 | if (mp_iseven (b) == 1) {
|
---|
| 882 | return MP_VAL;
|
---|
| 883 | }
|
---|
| 884 |
|
---|
| 885 | /* init all our temps */
|
---|
| 886 | if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D)) != MP_OKAY) {
|
---|
| 887 | return res;
|
---|
| 888 | }
|
---|
| 889 |
|
---|
| 890 | /* x == modulus, y == value to invert */
|
---|
| 891 | if ((res = mp_copy (b, &x)) != MP_OKAY) {
|
---|
| 892 | goto LBL_ERR;
|
---|
| 893 | }
|
---|
| 894 |
|
---|
| 895 | /* we need y = |a| */
|
---|
| 896 | if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
|
---|
| 897 | goto LBL_ERR;
|
---|
| 898 | }
|
---|
| 899 |
|
---|
| 900 | /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
---|
| 901 | if ((res = mp_copy (&x, &u)) != MP_OKAY) {
|
---|
| 902 | goto LBL_ERR;
|
---|
| 903 | }
|
---|
| 904 | if ((res = mp_copy (&y, &v)) != MP_OKAY) {
|
---|
| 905 | goto LBL_ERR;
|
---|
| 906 | }
|
---|
| 907 | mp_set (&D, 1);
|
---|
| 908 |
|
---|
| 909 | top:
|
---|
| 910 | /* 4. while u is even do */
|
---|
| 911 | while (mp_iseven (&u) == 1) {
|
---|
| 912 | /* 4.1 u = u/2 */
|
---|
| 913 | if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
|
---|
| 914 | goto LBL_ERR;
|
---|
| 915 | }
|
---|
| 916 | /* 4.2 if B is odd then */
|
---|
| 917 | if (mp_isodd (&B) == 1) {
|
---|
| 918 | if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
|
---|
| 919 | goto LBL_ERR;
|
---|
| 920 | }
|
---|
| 921 | }
|
---|
| 922 | /* B = B/2 */
|
---|
| 923 | if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
|
---|
| 924 | goto LBL_ERR;
|
---|
| 925 | }
|
---|
| 926 | }
|
---|
| 927 |
|
---|
| 928 | /* 5. while v is even do */
|
---|
| 929 | while (mp_iseven (&v) == 1) {
|
---|
| 930 | /* 5.1 v = v/2 */
|
---|
| 931 | if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
|
---|
| 932 | goto LBL_ERR;
|
---|
| 933 | }
|
---|
| 934 | /* 5.2 if D is odd then */
|
---|
| 935 | if (mp_isodd (&D) == 1) {
|
---|
| 936 | /* D = (D-x)/2 */
|
---|
| 937 | if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
|
---|
| 938 | goto LBL_ERR;
|
---|
| 939 | }
|
---|
| 940 | }
|
---|
| 941 | /* D = D/2 */
|
---|
| 942 | if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
|
---|
| 943 | goto LBL_ERR;
|
---|
| 944 | }
|
---|
| 945 | }
|
---|
| 946 |
|
---|
| 947 | /* 6. if u >= v then */
|
---|
| 948 | if (mp_cmp (&u, &v) != MP_LT) {
|
---|
| 949 | /* u = u - v, B = B - D */
|
---|
| 950 | if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
|
---|
| 951 | goto LBL_ERR;
|
---|
| 952 | }
|
---|
| 953 |
|
---|
| 954 | if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
|
---|
| 955 | goto LBL_ERR;
|
---|
| 956 | }
|
---|
| 957 | } else {
|
---|
| 958 | /* v - v - u, D = D - B */
|
---|
| 959 | if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
|
---|
| 960 | goto LBL_ERR;
|
---|
| 961 | }
|
---|
| 962 |
|
---|
| 963 | if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
|
---|
| 964 | goto LBL_ERR;
|
---|
| 965 | }
|
---|
| 966 | }
|
---|
| 967 |
|
---|
| 968 | /* if not zero goto step 4 */
|
---|
| 969 | if (mp_iszero (&u) == 0) {
|
---|
| 970 | if (++loop_check > 4096) {
|
---|
| 971 | res = MP_VAL;
|
---|
| 972 | goto LBL_ERR;
|
---|
| 973 | }
|
---|
| 974 | goto top;
|
---|
| 975 | }
|
---|
| 976 |
|
---|
| 977 | /* now a = C, b = D, gcd == g*v */
|
---|
| 978 |
|
---|
| 979 | /* if v != 1 then there is no inverse */
|
---|
| 980 | if (mp_cmp_d (&v, 1) != MP_EQ) {
|
---|
| 981 | res = MP_VAL;
|
---|
| 982 | goto LBL_ERR;
|
---|
| 983 | }
|
---|
| 984 |
|
---|
| 985 | /* b is now the inverse */
|
---|
| 986 | neg = a->sign;
|
---|
| 987 | while (D.sign == MP_NEG) {
|
---|
| 988 | if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
|
---|
| 989 | goto LBL_ERR;
|
---|
| 990 | }
|
---|
| 991 | }
|
---|
| 992 | /* too big */
|
---|
| 993 | while (mp_cmp_mag(&D, b) != MP_LT) {
|
---|
| 994 | if ((res = mp_sub(&D, b, &D)) != MP_OKAY) {
|
---|
| 995 | goto LBL_ERR;
|
---|
| 996 | }
|
---|
| 997 | }
|
---|
| 998 | mp_exch (&D, c);
|
---|
| 999 | c->sign = neg;
|
---|
| 1000 | res = MP_OKAY;
|
---|
| 1001 |
|
---|
| 1002 | LBL_ERR:mp_clear(&x);
|
---|
| 1003 | mp_clear(&y);
|
---|
| 1004 | mp_clear(&u);
|
---|
| 1005 | mp_clear(&v);
|
---|
| 1006 | mp_clear(&B);
|
---|
| 1007 | mp_clear(&D);
|
---|
| 1008 | return res;
|
---|
| 1009 | }
|
---|
| 1010 |
|
---|
| 1011 |
|
---|
| 1012 | /* hac 14.61, pp608 */
|
---|
| 1013 | int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1014 | {
|
---|
| 1015 | mp_int x, y, u, v, A, B, C, D;
|
---|
| 1016 | int res;
|
---|
| 1017 |
|
---|
| 1018 | /* b cannot be negative */
|
---|
| 1019 | if (b->sign == MP_NEG || mp_iszero(b) == 1) {
|
---|
| 1020 | return MP_VAL;
|
---|
| 1021 | }
|
---|
| 1022 |
|
---|
| 1023 | /* init temps */
|
---|
| 1024 | if ((res = mp_init_multi(&x, &y, &u, &v,
|
---|
| 1025 | &A, &B)) != MP_OKAY) {
|
---|
| 1026 | return res;
|
---|
| 1027 | }
|
---|
| 1028 |
|
---|
| 1029 | /* init rest of tmps temps */
|
---|
| 1030 | if ((res = mp_init_multi(&C, &D, 0, 0, 0, 0)) != MP_OKAY) {
|
---|
| 1031 | return res;
|
---|
| 1032 | }
|
---|
| 1033 |
|
---|
| 1034 | /* x = a, y = b */
|
---|
| 1035 | if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
|
---|
| 1036 | goto LBL_ERR;
|
---|
| 1037 | }
|
---|
| 1038 | if ((res = mp_copy (b, &y)) != MP_OKAY) {
|
---|
| 1039 | goto LBL_ERR;
|
---|
| 1040 | }
|
---|
| 1041 |
|
---|
| 1042 | /* 2. [modified] if x,y are both even then return an error! */
|
---|
| 1043 | if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
|
---|
| 1044 | res = MP_VAL;
|
---|
| 1045 | goto LBL_ERR;
|
---|
| 1046 | }
|
---|
| 1047 |
|
---|
| 1048 | /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
---|
| 1049 | if ((res = mp_copy (&x, &u)) != MP_OKAY) {
|
---|
| 1050 | goto LBL_ERR;
|
---|
| 1051 | }
|
---|
| 1052 | if ((res = mp_copy (&y, &v)) != MP_OKAY) {
|
---|
| 1053 | goto LBL_ERR;
|
---|
| 1054 | }
|
---|
| 1055 | mp_set (&A, 1);
|
---|
| 1056 | mp_set (&D, 1);
|
---|
| 1057 |
|
---|
| 1058 | top:
|
---|
| 1059 | /* 4. while u is even do */
|
---|
| 1060 | while (mp_iseven (&u) == 1) {
|
---|
| 1061 | /* 4.1 u = u/2 */
|
---|
| 1062 | if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
|
---|
| 1063 | goto LBL_ERR;
|
---|
| 1064 | }
|
---|
| 1065 | /* 4.2 if A or B is odd then */
|
---|
| 1066 | if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
|
---|
| 1067 | /* A = (A+y)/2, B = (B-x)/2 */
|
---|
| 1068 | if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
|
---|
| 1069 | goto LBL_ERR;
|
---|
| 1070 | }
|
---|
| 1071 | if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
|
---|
| 1072 | goto LBL_ERR;
|
---|
| 1073 | }
|
---|
| 1074 | }
|
---|
| 1075 | /* A = A/2, B = B/2 */
|
---|
| 1076 | if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
|
---|
| 1077 | goto LBL_ERR;
|
---|
| 1078 | }
|
---|
| 1079 | if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
|
---|
| 1080 | goto LBL_ERR;
|
---|
| 1081 | }
|
---|
| 1082 | }
|
---|
| 1083 |
|
---|
| 1084 | /* 5. while v is even do */
|
---|
| 1085 | while (mp_iseven (&v) == 1) {
|
---|
| 1086 | /* 5.1 v = v/2 */
|
---|
| 1087 | if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
|
---|
| 1088 | goto LBL_ERR;
|
---|
| 1089 | }
|
---|
| 1090 | /* 5.2 if C or D is odd then */
|
---|
| 1091 | if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
|
---|
| 1092 | /* C = (C+y)/2, D = (D-x)/2 */
|
---|
| 1093 | if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
|
---|
| 1094 | goto LBL_ERR;
|
---|
| 1095 | }
|
---|
| 1096 | if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
|
---|
| 1097 | goto LBL_ERR;
|
---|
| 1098 | }
|
---|
| 1099 | }
|
---|
| 1100 | /* C = C/2, D = D/2 */
|
---|
| 1101 | if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
|
---|
| 1102 | goto LBL_ERR;
|
---|
| 1103 | }
|
---|
| 1104 | if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
|
---|
| 1105 | goto LBL_ERR;
|
---|
| 1106 | }
|
---|
| 1107 | }
|
---|
| 1108 |
|
---|
| 1109 | /* 6. if u >= v then */
|
---|
| 1110 | if (mp_cmp (&u, &v) != MP_LT) {
|
---|
| 1111 | /* u = u - v, A = A - C, B = B - D */
|
---|
| 1112 | if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
|
---|
| 1113 | goto LBL_ERR;
|
---|
| 1114 | }
|
---|
| 1115 |
|
---|
| 1116 | if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
|
---|
| 1117 | goto LBL_ERR;
|
---|
| 1118 | }
|
---|
| 1119 |
|
---|
| 1120 | if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
|
---|
| 1121 | goto LBL_ERR;
|
---|
| 1122 | }
|
---|
| 1123 | } else {
|
---|
| 1124 | /* v - v - u, C = C - A, D = D - B */
|
---|
| 1125 | if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
|
---|
| 1126 | goto LBL_ERR;
|
---|
| 1127 | }
|
---|
| 1128 |
|
---|
| 1129 | if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
|
---|
| 1130 | goto LBL_ERR;
|
---|
| 1131 | }
|
---|
| 1132 |
|
---|
| 1133 | if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
|
---|
| 1134 | goto LBL_ERR;
|
---|
| 1135 | }
|
---|
| 1136 | }
|
---|
| 1137 |
|
---|
| 1138 | /* if not zero goto step 4 */
|
---|
| 1139 | if (mp_iszero (&u) == 0)
|
---|
| 1140 | goto top;
|
---|
| 1141 |
|
---|
| 1142 | /* now a = C, b = D, gcd == g*v */
|
---|
| 1143 |
|
---|
| 1144 | /* if v != 1 then there is no inverse */
|
---|
| 1145 | if (mp_cmp_d (&v, 1) != MP_EQ) {
|
---|
| 1146 | res = MP_VAL;
|
---|
| 1147 | goto LBL_ERR;
|
---|
| 1148 | }
|
---|
| 1149 |
|
---|
| 1150 | /* if its too low */
|
---|
| 1151 | while (mp_cmp_d(&C, 0) == MP_LT) {
|
---|
| 1152 | if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
|
---|
| 1153 | goto LBL_ERR;
|
---|
| 1154 | }
|
---|
| 1155 | }
|
---|
| 1156 |
|
---|
| 1157 | /* too big */
|
---|
| 1158 | while (mp_cmp_mag(&C, b) != MP_LT) {
|
---|
| 1159 | if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
|
---|
| 1160 | goto LBL_ERR;
|
---|
| 1161 | }
|
---|
| 1162 | }
|
---|
| 1163 |
|
---|
| 1164 | /* C is now the inverse */
|
---|
| 1165 | mp_exch (&C, c);
|
---|
| 1166 | res = MP_OKAY;
|
---|
| 1167 | LBL_ERR:mp_clear(&x);
|
---|
| 1168 | mp_clear(&y);
|
---|
| 1169 | mp_clear(&u);
|
---|
| 1170 | mp_clear(&v);
|
---|
| 1171 | mp_clear(&A);
|
---|
| 1172 | mp_clear(&B);
|
---|
| 1173 | mp_clear(&C);
|
---|
| 1174 | mp_clear(&D);
|
---|
| 1175 | return res;
|
---|
| 1176 | }
|
---|
| 1177 |
|
---|
| 1178 |
|
---|
| 1179 | /* compare maginitude of two ints (unsigned) */
|
---|
| 1180 | int mp_cmp_mag (mp_int * a, mp_int * b)
|
---|
| 1181 | {
|
---|
| 1182 | int n;
|
---|
| 1183 | mp_digit *tmpa, *tmpb;
|
---|
| 1184 |
|
---|
| 1185 | /* compare based on # of non-zero digits */
|
---|
| 1186 | if (a->used > b->used) {
|
---|
| 1187 | return MP_GT;
|
---|
| 1188 | }
|
---|
| 1189 |
|
---|
| 1190 | if (a->used < b->used) {
|
---|
| 1191 | return MP_LT;
|
---|
| 1192 | }
|
---|
| 1193 |
|
---|
| 1194 | /* alias for a */
|
---|
| 1195 | tmpa = a->dp + (a->used - 1);
|
---|
| 1196 |
|
---|
| 1197 | /* alias for b */
|
---|
| 1198 | tmpb = b->dp + (a->used - 1);
|
---|
| 1199 |
|
---|
| 1200 | /* compare based on digits */
|
---|
| 1201 | for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
|
---|
| 1202 | if (*tmpa > *tmpb) {
|
---|
| 1203 | return MP_GT;
|
---|
| 1204 | }
|
---|
| 1205 |
|
---|
| 1206 | if (*tmpa < *tmpb) {
|
---|
| 1207 | return MP_LT;
|
---|
| 1208 | }
|
---|
| 1209 | }
|
---|
| 1210 | return MP_EQ;
|
---|
| 1211 | }
|
---|
| 1212 |
|
---|
| 1213 |
|
---|
| 1214 | /* compare two ints (signed)*/
|
---|
| 1215 | int
|
---|
| 1216 | mp_cmp (mp_int * a, mp_int * b)
|
---|
| 1217 | {
|
---|
| 1218 | /* compare based on sign */
|
---|
| 1219 | if (a->sign != b->sign) {
|
---|
| 1220 | if (a->sign == MP_NEG) {
|
---|
| 1221 | return MP_LT;
|
---|
| 1222 | } else {
|
---|
| 1223 | return MP_GT;
|
---|
| 1224 | }
|
---|
| 1225 | }
|
---|
| 1226 |
|
---|
| 1227 | /* compare digits */
|
---|
| 1228 | if (a->sign == MP_NEG) {
|
---|
| 1229 | /* if negative compare opposite direction */
|
---|
| 1230 | return mp_cmp_mag(b, a);
|
---|
| 1231 | } else {
|
---|
| 1232 | return mp_cmp_mag(a, b);
|
---|
| 1233 | }
|
---|
| 1234 | }
|
---|
| 1235 |
|
---|
| 1236 |
|
---|
| 1237 | /* compare a digit */
|
---|
| 1238 | int mp_cmp_d(mp_int * a, mp_digit b)
|
---|
| 1239 | {
|
---|
| 1240 | /* compare based on sign */
|
---|
| 1241 | if (a->sign == MP_NEG) {
|
---|
| 1242 | return MP_LT;
|
---|
| 1243 | }
|
---|
| 1244 |
|
---|
| 1245 | /* compare based on magnitude */
|
---|
| 1246 | if (a->used > 1) {
|
---|
| 1247 | return MP_GT;
|
---|
| 1248 | }
|
---|
| 1249 |
|
---|
| 1250 | /* compare the only digit of a to b */
|
---|
| 1251 | if (a->dp[0] > b) {
|
---|
| 1252 | return MP_GT;
|
---|
| 1253 | } else if (a->dp[0] < b) {
|
---|
| 1254 | return MP_LT;
|
---|
| 1255 | } else {
|
---|
| 1256 | return MP_EQ;
|
---|
| 1257 | }
|
---|
| 1258 | }
|
---|
| 1259 |
|
---|
| 1260 |
|
---|
| 1261 | /* set to a digit */
|
---|
| 1262 | void mp_set (mp_int * a, mp_digit b)
|
---|
| 1263 | {
|
---|
| 1264 | mp_zero (a);
|
---|
| 1265 | a->dp[0] = b & MP_MASK;
|
---|
| 1266 | a->used = (a->dp[0] != 0) ? 1 : 0;
|
---|
| 1267 | }
|
---|
| 1268 |
|
---|
| 1269 | /* chek if a bit is set */
|
---|
| 1270 | int mp_is_bit_set (mp_int *a, mp_digit b)
|
---|
| 1271 | {
|
---|
| 1272 | if ((mp_digit)a->used < b/DIGIT_BIT)
|
---|
| 1273 | return 0;
|
---|
| 1274 |
|
---|
| 1275 | return (int)((a->dp[b/DIGIT_BIT] >> b%DIGIT_BIT) & (mp_digit)1);
|
---|
| 1276 | }
|
---|
| 1277 |
|
---|
| 1278 | /* c = a mod b, 0 <= c < b */
|
---|
| 1279 | int
|
---|
| 1280 | mp_mod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1281 | {
|
---|
| 1282 | mp_int t;
|
---|
| 1283 | int res;
|
---|
| 1284 |
|
---|
| 1285 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
| 1286 | return res;
|
---|
| 1287 | }
|
---|
| 1288 |
|
---|
| 1289 | if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
|
---|
| 1290 | mp_clear (&t);
|
---|
| 1291 | return res;
|
---|
| 1292 | }
|
---|
| 1293 |
|
---|
| 1294 | if (t.sign != b->sign) {
|
---|
| 1295 | res = mp_add (b, &t, c);
|
---|
| 1296 | } else {
|
---|
| 1297 | res = MP_OKAY;
|
---|
| 1298 | mp_exch (&t, c);
|
---|
| 1299 | }
|
---|
| 1300 |
|
---|
| 1301 | mp_clear (&t);
|
---|
| 1302 | return res;
|
---|
| 1303 | }
|
---|
| 1304 |
|
---|
| 1305 |
|
---|
| 1306 | /* slower bit-bang division... also smaller */
|
---|
| 1307 | int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
|
---|
| 1308 | {
|
---|
| 1309 | mp_int ta, tb, tq, q;
|
---|
| 1310 | int res, n, n2;
|
---|
| 1311 |
|
---|
| 1312 | /* is divisor zero ? */
|
---|
| 1313 | if (mp_iszero (b) == 1) {
|
---|
| 1314 | return MP_VAL;
|
---|
| 1315 | }
|
---|
| 1316 |
|
---|
| 1317 | /* if a < b then q=0, r = a */
|
---|
| 1318 | if (mp_cmp_mag (a, b) == MP_LT) {
|
---|
| 1319 | if (d != NULL) {
|
---|
| 1320 | res = mp_copy (a, d);
|
---|
| 1321 | } else {
|
---|
| 1322 | res = MP_OKAY;
|
---|
| 1323 | }
|
---|
| 1324 | if (c != NULL) {
|
---|
| 1325 | mp_zero (c);
|
---|
| 1326 | }
|
---|
| 1327 | return res;
|
---|
| 1328 | }
|
---|
| 1329 |
|
---|
| 1330 | /* init our temps */
|
---|
| 1331 | if ((res = mp_init_multi(&ta, &tb, &tq, &q, 0, 0)) != MP_OKAY) {
|
---|
| 1332 | return res;
|
---|
| 1333 | }
|
---|
| 1334 |
|
---|
| 1335 |
|
---|
| 1336 | mp_set(&tq, 1);
|
---|
| 1337 | n = mp_count_bits(a) - mp_count_bits(b);
|
---|
| 1338 | if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
|
---|
| 1339 | ((res = mp_abs(b, &tb)) != MP_OKAY) ||
|
---|
| 1340 | ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
|
---|
| 1341 | ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
|
---|
| 1342 | goto LBL_ERR;
|
---|
| 1343 | }
|
---|
| 1344 |
|
---|
| 1345 | while (n-- >= 0) {
|
---|
| 1346 | if (mp_cmp(&tb, &ta) != MP_GT) {
|
---|
| 1347 | if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
|
---|
| 1348 | ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
|
---|
| 1349 | goto LBL_ERR;
|
---|
| 1350 | }
|
---|
| 1351 | }
|
---|
| 1352 | if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
|
---|
| 1353 | ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
|
---|
| 1354 | goto LBL_ERR;
|
---|
| 1355 | }
|
---|
| 1356 | }
|
---|
| 1357 |
|
---|
| 1358 | /* now q == quotient and ta == remainder */
|
---|
| 1359 | n = a->sign;
|
---|
| 1360 | n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
|
---|
| 1361 | if (c != NULL) {
|
---|
| 1362 | mp_exch(c, &q);
|
---|
| 1363 | c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
|
---|
| 1364 | }
|
---|
| 1365 | if (d != NULL) {
|
---|
| 1366 | mp_exch(d, &ta);
|
---|
| 1367 | d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
|
---|
| 1368 | }
|
---|
| 1369 | LBL_ERR:
|
---|
| 1370 | mp_clear(&ta);
|
---|
| 1371 | mp_clear(&tb);
|
---|
| 1372 | mp_clear(&tq);
|
---|
| 1373 | mp_clear(&q);
|
---|
| 1374 | return res;
|
---|
| 1375 | }
|
---|
| 1376 |
|
---|
| 1377 |
|
---|
| 1378 | /* b = a/2 */
|
---|
| 1379 | int mp_div_2(mp_int * a, mp_int * b)
|
---|
| 1380 | {
|
---|
| 1381 | int x, res, oldused;
|
---|
| 1382 |
|
---|
| 1383 | /* copy */
|
---|
| 1384 | if (b->alloc < a->used) {
|
---|
| 1385 | if ((res = mp_grow (b, a->used)) != MP_OKAY) {
|
---|
| 1386 | return res;
|
---|
| 1387 | }
|
---|
| 1388 | }
|
---|
| 1389 |
|
---|
| 1390 | oldused = b->used;
|
---|
| 1391 | b->used = a->used;
|
---|
| 1392 | {
|
---|
| 1393 | register mp_digit r, rr, *tmpa, *tmpb;
|
---|
| 1394 |
|
---|
| 1395 | /* source alias */
|
---|
| 1396 | tmpa = a->dp + b->used - 1;
|
---|
| 1397 |
|
---|
| 1398 | /* dest alias */
|
---|
| 1399 | tmpb = b->dp + b->used - 1;
|
---|
| 1400 |
|
---|
| 1401 | /* carry */
|
---|
| 1402 | r = 0;
|
---|
| 1403 | for (x = b->used - 1; x >= 0; x--) {
|
---|
| 1404 | /* get the carry for the next iteration */
|
---|
| 1405 | rr = *tmpa & 1;
|
---|
| 1406 |
|
---|
| 1407 | /* shift the current digit, add in carry and store */
|
---|
| 1408 | *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
|
---|
| 1409 |
|
---|
| 1410 | /* forward carry to next iteration */
|
---|
| 1411 | r = rr;
|
---|
| 1412 | }
|
---|
| 1413 |
|
---|
| 1414 | /* zero excess digits */
|
---|
| 1415 | tmpb = b->dp + b->used;
|
---|
| 1416 | for (x = b->used; x < oldused; x++) {
|
---|
| 1417 | *tmpb++ = 0;
|
---|
| 1418 | }
|
---|
| 1419 | }
|
---|
| 1420 | b->sign = a->sign;
|
---|
| 1421 | mp_clamp (b);
|
---|
| 1422 | return MP_OKAY;
|
---|
| 1423 | }
|
---|
| 1424 |
|
---|
| 1425 |
|
---|
| 1426 | /* high level addition (handles signs) */
|
---|
| 1427 | int mp_add (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1428 | {
|
---|
| 1429 | int sa, sb, res;
|
---|
| 1430 |
|
---|
| 1431 | /* get sign of both inputs */
|
---|
| 1432 | sa = a->sign;
|
---|
| 1433 | sb = b->sign;
|
---|
| 1434 |
|
---|
| 1435 | /* handle two cases, not four */
|
---|
| 1436 | if (sa == sb) {
|
---|
| 1437 | /* both positive or both negative */
|
---|
| 1438 | /* add their magnitudes, copy the sign */
|
---|
| 1439 | c->sign = sa;
|
---|
| 1440 | res = s_mp_add (a, b, c);
|
---|
| 1441 | } else {
|
---|
| 1442 | /* one positive, the other negative */
|
---|
| 1443 | /* subtract the one with the greater magnitude from */
|
---|
| 1444 | /* the one of the lesser magnitude. The result gets */
|
---|
| 1445 | /* the sign of the one with the greater magnitude. */
|
---|
| 1446 | if (mp_cmp_mag (a, b) == MP_LT) {
|
---|
| 1447 | c->sign = sb;
|
---|
| 1448 | res = s_mp_sub (b, a, c);
|
---|
| 1449 | } else {
|
---|
| 1450 | c->sign = sa;
|
---|
| 1451 | res = s_mp_sub (a, b, c);
|
---|
| 1452 | }
|
---|
| 1453 | }
|
---|
| 1454 | return res;
|
---|
| 1455 | }
|
---|
| 1456 |
|
---|
| 1457 |
|
---|
| 1458 | /* low level addition, based on HAC pp.594, Algorithm 14.7 */
|
---|
| 1459 | int
|
---|
| 1460 | s_mp_add (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1461 | {
|
---|
| 1462 | mp_int *x;
|
---|
| 1463 | int olduse, res, min, max;
|
---|
| 1464 |
|
---|
| 1465 | /* find sizes, we let |a| <= |b| which means we have to sort
|
---|
| 1466 | * them. "x" will point to the input with the most digits
|
---|
| 1467 | */
|
---|
| 1468 | if (a->used > b->used) {
|
---|
| 1469 | min = b->used;
|
---|
| 1470 | max = a->used;
|
---|
| 1471 | x = a;
|
---|
| 1472 | } else {
|
---|
| 1473 | min = a->used;
|
---|
| 1474 | max = b->used;
|
---|
| 1475 | x = b;
|
---|
| 1476 | }
|
---|
| 1477 |
|
---|
| 1478 | /* init result */
|
---|
| 1479 | if (c->alloc < max + 1) {
|
---|
| 1480 | if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
|
---|
| 1481 | return res;
|
---|
| 1482 | }
|
---|
| 1483 | }
|
---|
| 1484 |
|
---|
| 1485 | /* get old used digit count and set new one */
|
---|
| 1486 | olduse = c->used;
|
---|
| 1487 | c->used = max + 1;
|
---|
| 1488 |
|
---|
| 1489 | {
|
---|
| 1490 | register mp_digit u, *tmpa, *tmpb, *tmpc;
|
---|
| 1491 | register int i;
|
---|
| 1492 |
|
---|
| 1493 | /* alias for digit pointers */
|
---|
| 1494 |
|
---|
| 1495 | /* first input */
|
---|
| 1496 | tmpa = a->dp;
|
---|
| 1497 |
|
---|
| 1498 | /* second input */
|
---|
| 1499 | tmpb = b->dp;
|
---|
| 1500 |
|
---|
| 1501 | /* destination */
|
---|
| 1502 | tmpc = c->dp;
|
---|
| 1503 |
|
---|
| 1504 | /* zero the carry */
|
---|
| 1505 | u = 0;
|
---|
| 1506 | for (i = 0; i < min; i++) {
|
---|
| 1507 | /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
|
---|
| 1508 | *tmpc = *tmpa++ + *tmpb++ + u;
|
---|
| 1509 |
|
---|
| 1510 | /* U = carry bit of T[i] */
|
---|
| 1511 | u = *tmpc >> ((mp_digit)DIGIT_BIT);
|
---|
| 1512 |
|
---|
| 1513 | /* take away carry bit from T[i] */
|
---|
| 1514 | *tmpc++ &= MP_MASK;
|
---|
| 1515 | }
|
---|
| 1516 |
|
---|
| 1517 | /* now copy higher words if any, that is in A+B
|
---|
| 1518 | * if A or B has more digits add those in
|
---|
| 1519 | */
|
---|
| 1520 | if (min != max) {
|
---|
| 1521 | for (; i < max; i++) {
|
---|
| 1522 | /* T[i] = X[i] + U */
|
---|
| 1523 | *tmpc = x->dp[i] + u;
|
---|
| 1524 |
|
---|
| 1525 | /* U = carry bit of T[i] */
|
---|
| 1526 | u = *tmpc >> ((mp_digit)DIGIT_BIT);
|
---|
| 1527 |
|
---|
| 1528 | /* take away carry bit from T[i] */
|
---|
| 1529 | *tmpc++ &= MP_MASK;
|
---|
| 1530 | }
|
---|
| 1531 | }
|
---|
| 1532 |
|
---|
| 1533 | /* add carry */
|
---|
| 1534 | *tmpc++ = u;
|
---|
| 1535 |
|
---|
| 1536 | /* clear digits above oldused */
|
---|
| 1537 | for (i = c->used; i < olduse; i++) {
|
---|
| 1538 | *tmpc++ = 0;
|
---|
| 1539 | }
|
---|
| 1540 | }
|
---|
| 1541 |
|
---|
| 1542 | mp_clamp (c);
|
---|
| 1543 | return MP_OKAY;
|
---|
| 1544 | }
|
---|
| 1545 |
|
---|
| 1546 |
|
---|
| 1547 | /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
|
---|
| 1548 | int
|
---|
| 1549 | s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1550 | {
|
---|
| 1551 | int olduse, res, min, max;
|
---|
| 1552 |
|
---|
| 1553 | /* find sizes */
|
---|
| 1554 | min = b->used;
|
---|
| 1555 | max = a->used;
|
---|
| 1556 |
|
---|
| 1557 | /* init result */
|
---|
| 1558 | if (c->alloc < max) {
|
---|
| 1559 | if ((res = mp_grow (c, max)) != MP_OKAY) {
|
---|
| 1560 | return res;
|
---|
| 1561 | }
|
---|
| 1562 | }
|
---|
| 1563 | olduse = c->used;
|
---|
| 1564 | c->used = max;
|
---|
| 1565 |
|
---|
| 1566 | {
|
---|
| 1567 | register mp_digit u, *tmpa, *tmpb, *tmpc;
|
---|
| 1568 | register int i;
|
---|
| 1569 |
|
---|
| 1570 | /* alias for digit pointers */
|
---|
| 1571 | tmpa = a->dp;
|
---|
| 1572 | tmpb = b->dp;
|
---|
| 1573 | tmpc = c->dp;
|
---|
| 1574 |
|
---|
| 1575 | /* set carry to zero */
|
---|
| 1576 | u = 0;
|
---|
| 1577 | for (i = 0; i < min; i++) {
|
---|
| 1578 | /* T[i] = A[i] - B[i] - U */
|
---|
| 1579 | *tmpc = *tmpa++ - *tmpb++ - u;
|
---|
| 1580 |
|
---|
| 1581 | /* U = carry bit of T[i]
|
---|
| 1582 | * Note this saves performing an AND operation since
|
---|
| 1583 | * if a carry does occur it will propagate all the way to the
|
---|
| 1584 | * MSB. As a result a single shift is enough to get the carry
|
---|
| 1585 | */
|
---|
| 1586 | u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
|
---|
| 1587 |
|
---|
| 1588 | /* Clear carry from T[i] */
|
---|
| 1589 | *tmpc++ &= MP_MASK;
|
---|
| 1590 | }
|
---|
| 1591 |
|
---|
| 1592 | /* now copy higher words if any, e.g. if A has more digits than B */
|
---|
| 1593 | for (; i < max; i++) {
|
---|
| 1594 | /* T[i] = A[i] - U */
|
---|
| 1595 | *tmpc = *tmpa++ - u;
|
---|
| 1596 |
|
---|
| 1597 | /* U = carry bit of T[i] */
|
---|
| 1598 | u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
|
---|
| 1599 |
|
---|
| 1600 | /* Clear carry from T[i] */
|
---|
| 1601 | *tmpc++ &= MP_MASK;
|
---|
| 1602 | }
|
---|
| 1603 |
|
---|
| 1604 | /* clear digits above used (since we may not have grown result above) */
|
---|
| 1605 | for (i = c->used; i < olduse; i++) {
|
---|
| 1606 | *tmpc++ = 0;
|
---|
| 1607 | }
|
---|
| 1608 | }
|
---|
| 1609 |
|
---|
| 1610 | mp_clamp (c);
|
---|
| 1611 | return MP_OKAY;
|
---|
| 1612 | }
|
---|
| 1613 |
|
---|
| 1614 |
|
---|
| 1615 | /* high level subtraction (handles signs) */
|
---|
| 1616 | int
|
---|
| 1617 | mp_sub (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1618 | {
|
---|
| 1619 | int sa, sb, res;
|
---|
| 1620 |
|
---|
| 1621 | sa = a->sign;
|
---|
| 1622 | sb = b->sign;
|
---|
| 1623 |
|
---|
| 1624 | if (sa != sb) {
|
---|
| 1625 | /* subtract a negative from a positive, OR */
|
---|
| 1626 | /* subtract a positive from a negative. */
|
---|
| 1627 | /* In either case, ADD their magnitudes, */
|
---|
| 1628 | /* and use the sign of the first number. */
|
---|
| 1629 | c->sign = sa;
|
---|
| 1630 | res = s_mp_add (a, b, c);
|
---|
| 1631 | } else {
|
---|
| 1632 | /* subtract a positive from a positive, OR */
|
---|
| 1633 | /* subtract a negative from a negative. */
|
---|
| 1634 | /* First, take the difference between their */
|
---|
| 1635 | /* magnitudes, then... */
|
---|
| 1636 | if (mp_cmp_mag (a, b) != MP_LT) {
|
---|
| 1637 | /* Copy the sign from the first */
|
---|
| 1638 | c->sign = sa;
|
---|
| 1639 | /* The first has a larger or equal magnitude */
|
---|
| 1640 | res = s_mp_sub (a, b, c);
|
---|
| 1641 | } else {
|
---|
| 1642 | /* The result has the *opposite* sign from */
|
---|
| 1643 | /* the first number. */
|
---|
| 1644 | c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
|
---|
| 1645 | /* The second has a larger magnitude */
|
---|
| 1646 | res = s_mp_sub (b, a, c);
|
---|
| 1647 | }
|
---|
| 1648 | }
|
---|
| 1649 | return res;
|
---|
| 1650 | }
|
---|
| 1651 |
|
---|
| 1652 |
|
---|
| 1653 | /* determines if reduce_2k_l can be used */
|
---|
| 1654 | int mp_reduce_is_2k_l(mp_int *a)
|
---|
| 1655 | {
|
---|
| 1656 | int ix, iy;
|
---|
| 1657 |
|
---|
| 1658 | if (a->used == 0) {
|
---|
| 1659 | return MP_NO;
|
---|
| 1660 | } else if (a->used == 1) {
|
---|
| 1661 | return MP_YES;
|
---|
| 1662 | } else if (a->used > 1) {
|
---|
| 1663 | /* if more than half of the digits are -1 we're sold */
|
---|
| 1664 | for (iy = ix = 0; ix < a->used; ix++) {
|
---|
| 1665 | if (a->dp[ix] == MP_MASK) {
|
---|
| 1666 | ++iy;
|
---|
| 1667 | }
|
---|
| 1668 | }
|
---|
| 1669 | return (iy >= (a->used/2)) ? MP_YES : MP_NO;
|
---|
| 1670 |
|
---|
| 1671 | }
|
---|
| 1672 | return MP_NO;
|
---|
| 1673 | }
|
---|
| 1674 |
|
---|
| 1675 |
|
---|
| 1676 | /* determines if mp_reduce_2k can be used */
|
---|
| 1677 | int mp_reduce_is_2k(mp_int *a)
|
---|
| 1678 | {
|
---|
| 1679 | int ix, iy, iw;
|
---|
| 1680 | mp_digit iz;
|
---|
| 1681 |
|
---|
| 1682 | if (a->used == 0) {
|
---|
| 1683 | return MP_NO;
|
---|
| 1684 | } else if (a->used == 1) {
|
---|
| 1685 | return MP_YES;
|
---|
| 1686 | } else if (a->used > 1) {
|
---|
| 1687 | iy = mp_count_bits(a);
|
---|
| 1688 | iz = 1;
|
---|
| 1689 | iw = 1;
|
---|
| 1690 |
|
---|
| 1691 | /* Test every bit from the second digit up, must be 1 */
|
---|
| 1692 | for (ix = DIGIT_BIT; ix < iy; ix++) {
|
---|
| 1693 | if ((a->dp[iw] & iz) == 0) {
|
---|
| 1694 | return MP_NO;
|
---|
| 1695 | }
|
---|
| 1696 | iz <<= 1;
|
---|
| 1697 | if (iz > (mp_digit)MP_MASK) {
|
---|
| 1698 | ++iw;
|
---|
| 1699 | iz = 1;
|
---|
| 1700 | }
|
---|
| 1701 | }
|
---|
| 1702 | }
|
---|
| 1703 | return MP_YES;
|
---|
| 1704 | }
|
---|
| 1705 |
|
---|
| 1706 |
|
---|
| 1707 | /* determines if a number is a valid DR modulus */
|
---|
| 1708 | int mp_dr_is_modulus(mp_int *a)
|
---|
| 1709 | {
|
---|
| 1710 | int ix;
|
---|
| 1711 |
|
---|
| 1712 | /* must be at least two digits */
|
---|
| 1713 | if (a->used < 2) {
|
---|
| 1714 | return 0;
|
---|
| 1715 | }
|
---|
| 1716 |
|
---|
| 1717 | /* must be of the form b**k - a [a <= b] so all
|
---|
| 1718 | * but the first digit must be equal to -1 (mod b).
|
---|
| 1719 | */
|
---|
| 1720 | for (ix = 1; ix < a->used; ix++) {
|
---|
| 1721 | if (a->dp[ix] != MP_MASK) {
|
---|
| 1722 | return 0;
|
---|
| 1723 | }
|
---|
| 1724 | }
|
---|
| 1725 | return 1;
|
---|
| 1726 | }
|
---|
| 1727 |
|
---|
| 1728 |
|
---|
| 1729 | /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
|
---|
| 1730 | *
|
---|
| 1731 | * Uses a left-to-right k-ary sliding window to compute the modular
|
---|
| 1732 | * exponentiation.
|
---|
| 1733 | * The value of k changes based on the size of the exponent.
|
---|
| 1734 | *
|
---|
| 1735 | * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
|
---|
| 1736 | */
|
---|
| 1737 |
|
---|
| 1738 | #ifdef MP_LOW_MEM
|
---|
| 1739 | #define TAB_SIZE 32
|
---|
| 1740 | #else
|
---|
| 1741 | #define TAB_SIZE 256
|
---|
| 1742 | #endif
|
---|
| 1743 |
|
---|
| 1744 | int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y,
|
---|
| 1745 | int redmode)
|
---|
| 1746 | {
|
---|
| 1747 | mp_int res;
|
---|
| 1748 | mp_digit buf, mp;
|
---|
| 1749 | int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
---|
| 1750 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 1751 | mp_int* M = NULL;
|
---|
| 1752 | #else
|
---|
| 1753 | mp_int M[TAB_SIZE];
|
---|
| 1754 | #endif
|
---|
| 1755 | /* use a pointer to the reduction algorithm. This allows us to use
|
---|
| 1756 | * one of many reduction algorithms without modding the guts of
|
---|
| 1757 | * the code with if statements everywhere.
|
---|
| 1758 | */
|
---|
| 1759 | int (*redux)(mp_int*,mp_int*,mp_digit);
|
---|
| 1760 |
|
---|
| 1761 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 1762 | M = (mp_int*) XMALLOC(sizeof(mp_int) * TAB_SIZE, NULL,
|
---|
| 1763 | DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 1764 | if (M == NULL)
|
---|
| 1765 | return MP_MEM;
|
---|
| 1766 | #endif
|
---|
| 1767 |
|
---|
| 1768 | /* find window size */
|
---|
| 1769 | x = mp_count_bits (X);
|
---|
| 1770 | if (x <= 7) {
|
---|
| 1771 | winsize = 2;
|
---|
| 1772 | } else if (x <= 36) {
|
---|
| 1773 | winsize = 3;
|
---|
| 1774 | } else if (x <= 140) {
|
---|
| 1775 | winsize = 4;
|
---|
| 1776 | } else if (x <= 450) {
|
---|
| 1777 | winsize = 5;
|
---|
| 1778 | } else if (x <= 1303) {
|
---|
| 1779 | winsize = 6;
|
---|
| 1780 | } else if (x <= 3529) {
|
---|
| 1781 | winsize = 7;
|
---|
| 1782 | } else {
|
---|
| 1783 | winsize = 8;
|
---|
| 1784 | }
|
---|
| 1785 |
|
---|
| 1786 | #ifdef MP_LOW_MEM
|
---|
| 1787 | if (winsize > 5) {
|
---|
| 1788 | winsize = 5;
|
---|
| 1789 | }
|
---|
| 1790 | #endif
|
---|
| 1791 |
|
---|
| 1792 | /* init M array */
|
---|
| 1793 | /* init first cell */
|
---|
| 1794 | if ((err = mp_init(&M[1])) != MP_OKAY) {
|
---|
| 1795 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 1796 | XFREE(M, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 1797 | #endif
|
---|
| 1798 |
|
---|
| 1799 | return err;
|
---|
| 1800 | }
|
---|
| 1801 |
|
---|
| 1802 | /* now init the second half of the array */
|
---|
| 1803 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 1804 | if ((err = mp_init(&M[x])) != MP_OKAY) {
|
---|
| 1805 | for (y = 1<<(winsize-1); y < x; y++) {
|
---|
| 1806 | mp_clear (&M[y]);
|
---|
| 1807 | }
|
---|
| 1808 | mp_clear(&M[1]);
|
---|
| 1809 |
|
---|
| 1810 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 1811 | XFREE(M, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 1812 | #endif
|
---|
| 1813 |
|
---|
| 1814 | return err;
|
---|
| 1815 | }
|
---|
| 1816 | }
|
---|
| 1817 |
|
---|
| 1818 | /* determine and setup reduction code */
|
---|
| 1819 | if (redmode == 0) {
|
---|
| 1820 | #ifdef BN_MP_MONTGOMERY_SETUP_C
|
---|
| 1821 | /* now setup montgomery */
|
---|
| 1822 | if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
|
---|
| 1823 | goto LBL_M;
|
---|
| 1824 | }
|
---|
| 1825 | #else
|
---|
| 1826 | err = MP_VAL;
|
---|
| 1827 | goto LBL_M;
|
---|
| 1828 | #endif
|
---|
| 1829 |
|
---|
| 1830 | /* automatically pick the comba one if available (saves quite a few
|
---|
| 1831 | calls/ifs) */
|
---|
| 1832 | #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
|
---|
| 1833 | if (((P->used * 2 + 1) < MP_WARRAY) &&
|
---|
| 1834 | P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
| 1835 | redux = fast_mp_montgomery_reduce;
|
---|
| 1836 | } else
|
---|
| 1837 | #endif
|
---|
| 1838 | {
|
---|
| 1839 | #ifdef BN_MP_MONTGOMERY_REDUCE_C
|
---|
| 1840 | /* use slower baseline Montgomery method */
|
---|
| 1841 | redux = mp_montgomery_reduce;
|
---|
| 1842 | #else
|
---|
| 1843 | err = MP_VAL;
|
---|
| 1844 | goto LBL_M;
|
---|
| 1845 | #endif
|
---|
| 1846 | }
|
---|
| 1847 | } else if (redmode == 1) {
|
---|
| 1848 | #if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
|
---|
| 1849 | /* setup DR reduction for moduli of the form B**k - b */
|
---|
| 1850 | mp_dr_setup(P, &mp);
|
---|
| 1851 | redux = mp_dr_reduce;
|
---|
| 1852 | #else
|
---|
| 1853 | err = MP_VAL;
|
---|
| 1854 | goto LBL_M;
|
---|
| 1855 | #endif
|
---|
| 1856 | } else {
|
---|
| 1857 | #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
|
---|
| 1858 | /* setup DR reduction for moduli of the form 2**k - b */
|
---|
| 1859 | if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
|
---|
| 1860 | goto LBL_M;
|
---|
| 1861 | }
|
---|
| 1862 | redux = mp_reduce_2k;
|
---|
| 1863 | #else
|
---|
| 1864 | err = MP_VAL;
|
---|
| 1865 | goto LBL_M;
|
---|
| 1866 | #endif
|
---|
| 1867 | }
|
---|
| 1868 |
|
---|
| 1869 | /* setup result */
|
---|
| 1870 | if ((err = mp_init (&res)) != MP_OKAY) {
|
---|
| 1871 | goto LBL_M;
|
---|
| 1872 | }
|
---|
| 1873 |
|
---|
| 1874 | /* create M table
|
---|
| 1875 | *
|
---|
| 1876 |
|
---|
| 1877 | *
|
---|
| 1878 | * The first half of the table is not computed though accept for M[0] and M[1]
|
---|
| 1879 | */
|
---|
| 1880 |
|
---|
| 1881 | if (redmode == 0) {
|
---|
| 1882 | #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
|
---|
| 1883 | /* now we need R mod m */
|
---|
| 1884 | if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
|
---|
| 1885 | goto LBL_RES;
|
---|
| 1886 | }
|
---|
| 1887 | #else
|
---|
| 1888 | err = MP_VAL;
|
---|
| 1889 | goto LBL_RES;
|
---|
| 1890 | #endif
|
---|
| 1891 |
|
---|
| 1892 | /* now set M[1] to G * R mod m */
|
---|
| 1893 | if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
|
---|
| 1894 | goto LBL_RES;
|
---|
| 1895 | }
|
---|
| 1896 | } else {
|
---|
| 1897 | mp_set(&res, 1);
|
---|
| 1898 | if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
|
---|
| 1899 | goto LBL_RES;
|
---|
| 1900 | }
|
---|
| 1901 | }
|
---|
| 1902 |
|
---|
| 1903 | /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times*/
|
---|
| 1904 | if ((err = mp_copy (&M[1], &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 1905 | goto LBL_RES;
|
---|
| 1906 | }
|
---|
| 1907 |
|
---|
| 1908 | for (x = 0; x < (winsize - 1); x++) {
|
---|
| 1909 | if ((err = mp_sqr (&M[(mp_digit)(1 << (winsize - 1))],
|
---|
| 1910 | &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 1911 | goto LBL_RES;
|
---|
| 1912 | }
|
---|
| 1913 | if ((err = redux (&M[(mp_digit)(1 << (winsize - 1))], P, mp)) != MP_OKAY) {
|
---|
| 1914 | goto LBL_RES;
|
---|
| 1915 | }
|
---|
| 1916 | }
|
---|
| 1917 |
|
---|
| 1918 | /* create upper table */
|
---|
| 1919 | for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
---|
| 1920 | if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
---|
| 1921 | goto LBL_RES;
|
---|
| 1922 | }
|
---|
| 1923 | if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
|
---|
| 1924 | goto LBL_RES;
|
---|
| 1925 | }
|
---|
| 1926 | }
|
---|
| 1927 |
|
---|
| 1928 | /* set initial mode and bit cnt */
|
---|
| 1929 | mode = 0;
|
---|
| 1930 | bitcnt = 1;
|
---|
| 1931 | buf = 0;
|
---|
| 1932 | digidx = X->used - 1;
|
---|
| 1933 | bitcpy = 0;
|
---|
| 1934 | bitbuf = 0;
|
---|
| 1935 |
|
---|
| 1936 | for (;;) {
|
---|
| 1937 | /* grab next digit as required */
|
---|
| 1938 | if (--bitcnt == 0) {
|
---|
| 1939 | /* if digidx == -1 we are out of digits so break */
|
---|
| 1940 | if (digidx == -1) {
|
---|
| 1941 | break;
|
---|
| 1942 | }
|
---|
| 1943 | /* read next digit and reset bitcnt */
|
---|
| 1944 | buf = X->dp[digidx--];
|
---|
| 1945 | bitcnt = (int)DIGIT_BIT;
|
---|
| 1946 | }
|
---|
| 1947 |
|
---|
| 1948 | /* grab the next msb from the exponent */
|
---|
| 1949 | y = (int)(buf >> (DIGIT_BIT - 1)) & 1;
|
---|
| 1950 | buf <<= (mp_digit)1;
|
---|
| 1951 |
|
---|
| 1952 | /* if the bit is zero and mode == 0 then we ignore it
|
---|
| 1953 | * These represent the leading zero bits before the first 1 bit
|
---|
| 1954 | * in the exponent. Technically this opt is not required but it
|
---|
| 1955 | * does lower the # of trivial squaring/reductions used
|
---|
| 1956 | */
|
---|
| 1957 | if (mode == 0 && y == 0) {
|
---|
| 1958 | continue;
|
---|
| 1959 | }
|
---|
| 1960 |
|
---|
| 1961 | /* if the bit is zero and mode == 1 then we square */
|
---|
| 1962 | if (mode == 1 && y == 0) {
|
---|
| 1963 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 1964 | goto LBL_RES;
|
---|
| 1965 | }
|
---|
| 1966 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 1967 | goto LBL_RES;
|
---|
| 1968 | }
|
---|
| 1969 | continue;
|
---|
| 1970 | }
|
---|
| 1971 |
|
---|
| 1972 | /* else we add it to the window */
|
---|
| 1973 | bitbuf |= (y << (winsize - ++bitcpy));
|
---|
| 1974 | mode = 2;
|
---|
| 1975 |
|
---|
| 1976 | if (bitcpy == winsize) {
|
---|
| 1977 | /* ok window is filled so square as required and multiply */
|
---|
| 1978 | /* square first */
|
---|
| 1979 | for (x = 0; x < winsize; x++) {
|
---|
| 1980 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 1981 | goto LBL_RES;
|
---|
| 1982 | }
|
---|
| 1983 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 1984 | goto LBL_RES;
|
---|
| 1985 | }
|
---|
| 1986 | }
|
---|
| 1987 |
|
---|
| 1988 | /* then multiply */
|
---|
| 1989 | if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
---|
| 1990 | goto LBL_RES;
|
---|
| 1991 | }
|
---|
| 1992 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 1993 | goto LBL_RES;
|
---|
| 1994 | }
|
---|
| 1995 |
|
---|
| 1996 | /* empty window and reset */
|
---|
| 1997 | bitcpy = 0;
|
---|
| 1998 | bitbuf = 0;
|
---|
| 1999 | mode = 1;
|
---|
| 2000 | }
|
---|
| 2001 | }
|
---|
| 2002 |
|
---|
| 2003 | /* if bits remain then square/multiply */
|
---|
| 2004 | if (mode == 2 && bitcpy > 0) {
|
---|
| 2005 | /* square then multiply if the bit is set */
|
---|
| 2006 | for (x = 0; x < bitcpy; x++) {
|
---|
| 2007 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 2008 | goto LBL_RES;
|
---|
| 2009 | }
|
---|
| 2010 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2011 | goto LBL_RES;
|
---|
| 2012 | }
|
---|
| 2013 |
|
---|
| 2014 | /* get next bit of the window */
|
---|
| 2015 | bitbuf <<= 1;
|
---|
| 2016 | if ((bitbuf & (1 << winsize)) != 0) {
|
---|
| 2017 | /* then multiply */
|
---|
| 2018 | if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
|
---|
| 2019 | goto LBL_RES;
|
---|
| 2020 | }
|
---|
| 2021 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2022 | goto LBL_RES;
|
---|
| 2023 | }
|
---|
| 2024 | }
|
---|
| 2025 | }
|
---|
| 2026 | }
|
---|
| 2027 |
|
---|
| 2028 | if (redmode == 0) {
|
---|
| 2029 | /* fixup result if Montgomery reduction is used
|
---|
| 2030 | * recall that any value in a Montgomery system is
|
---|
| 2031 | * actually multiplied by R mod n. So we have
|
---|
| 2032 | * to reduce one more time to cancel out the factor
|
---|
| 2033 | * of R.
|
---|
| 2034 | */
|
---|
| 2035 | if ((err = redux(&res, P, mp)) != MP_OKAY) {
|
---|
| 2036 | goto LBL_RES;
|
---|
| 2037 | }
|
---|
| 2038 | }
|
---|
| 2039 |
|
---|
| 2040 | /* swap res with Y */
|
---|
| 2041 | mp_exch (&res, Y);
|
---|
| 2042 | err = MP_OKAY;
|
---|
| 2043 | LBL_RES:mp_clear (&res);
|
---|
| 2044 | LBL_M:
|
---|
| 2045 | mp_clear(&M[1]);
|
---|
| 2046 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 2047 | mp_clear (&M[x]);
|
---|
| 2048 | }
|
---|
| 2049 |
|
---|
| 2050 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2051 | XFREE(M, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 2052 | #endif
|
---|
| 2053 |
|
---|
| 2054 | return err;
|
---|
| 2055 | }
|
---|
| 2056 |
|
---|
| 2057 |
|
---|
| 2058 | /* setups the montgomery reduction stuff */
|
---|
| 2059 | int
|
---|
| 2060 | mp_montgomery_setup (mp_int * n, mp_digit * rho)
|
---|
| 2061 | {
|
---|
| 2062 | mp_digit x, b;
|
---|
| 2063 |
|
---|
| 2064 | /* fast inversion mod 2**k
|
---|
| 2065 | *
|
---|
| 2066 | * Based on the fact that
|
---|
| 2067 | *
|
---|
| 2068 | * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
|
---|
| 2069 | * => 2*X*A - X*X*A*A = 1
|
---|
| 2070 | * => 2*(1) - (1) = 1
|
---|
| 2071 | */
|
---|
| 2072 | b = n->dp[0];
|
---|
| 2073 |
|
---|
| 2074 | if ((b & 1) == 0) {
|
---|
| 2075 | return MP_VAL;
|
---|
| 2076 | }
|
---|
| 2077 |
|
---|
| 2078 | x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
|
---|
| 2079 | x *= 2 - b * x; /* here x*a==1 mod 2**8 */
|
---|
| 2080 | #if !defined(MP_8BIT)
|
---|
| 2081 | x *= 2 - b * x; /* here x*a==1 mod 2**16 */
|
---|
| 2082 | #endif
|
---|
| 2083 | #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
|
---|
| 2084 | x *= 2 - b * x; /* here x*a==1 mod 2**32 */
|
---|
| 2085 | #endif
|
---|
| 2086 | #ifdef MP_64BIT
|
---|
| 2087 | x *= 2 - b * x; /* here x*a==1 mod 2**64 */
|
---|
| 2088 | #endif
|
---|
| 2089 |
|
---|
| 2090 | /* rho = -1/m mod b */
|
---|
| 2091 | /* TAO, switched mp_word casts to mp_digit to shut up compiler */
|
---|
| 2092 | *rho = (((mp_digit)1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK;
|
---|
| 2093 |
|
---|
| 2094 | return MP_OKAY;
|
---|
| 2095 | }
|
---|
| 2096 |
|
---|
| 2097 |
|
---|
| 2098 | /* computes xR**-1 == x (mod N) via Montgomery Reduction
|
---|
| 2099 | *
|
---|
| 2100 | * This is an optimized implementation of montgomery_reduce
|
---|
| 2101 | * which uses the comba method to quickly calculate the columns of the
|
---|
| 2102 | * reduction.
|
---|
| 2103 | *
|
---|
| 2104 | * Based on Algorithm 14.32 on pp.601 of HAC.
|
---|
| 2105 | */
|
---|
| 2106 | int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
|
---|
| 2107 | {
|
---|
| 2108 | int ix, res, olduse;
|
---|
| 2109 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2110 | mp_word* W; /* uses dynamic memory and slower */
|
---|
| 2111 | #else
|
---|
| 2112 | mp_word W[MP_WARRAY];
|
---|
| 2113 | #endif
|
---|
| 2114 |
|
---|
| 2115 | /* get old used count */
|
---|
| 2116 | olduse = x->used;
|
---|
| 2117 |
|
---|
| 2118 | /* grow a as required */
|
---|
| 2119 | if (x->alloc < n->used + 1) {
|
---|
| 2120 | if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
|
---|
| 2121 | return res;
|
---|
| 2122 | }
|
---|
| 2123 | }
|
---|
| 2124 |
|
---|
| 2125 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2126 | W = (mp_word*)XMALLOC(sizeof(mp_word) * MP_WARRAY, 0, DYNAMIC_TYPE_BIGINT);
|
---|
| 2127 | if (W == NULL)
|
---|
| 2128 | return MP_MEM;
|
---|
| 2129 | #endif
|
---|
| 2130 |
|
---|
| 2131 | /* first we have to get the digits of the input into
|
---|
| 2132 | * an array of double precision words W[...]
|
---|
| 2133 | */
|
---|
| 2134 | {
|
---|
| 2135 | register mp_word *_W;
|
---|
| 2136 | register mp_digit *tmpx;
|
---|
| 2137 |
|
---|
| 2138 | /* alias for the W[] array */
|
---|
| 2139 | _W = W;
|
---|
| 2140 |
|
---|
| 2141 | /* alias for the digits of x*/
|
---|
| 2142 | tmpx = x->dp;
|
---|
| 2143 |
|
---|
| 2144 | /* copy the digits of a into W[0..a->used-1] */
|
---|
| 2145 | for (ix = 0; ix < x->used; ix++) {
|
---|
| 2146 | *_W++ = *tmpx++;
|
---|
| 2147 | }
|
---|
| 2148 |
|
---|
| 2149 | /* zero the high words of W[a->used..m->used*2] */
|
---|
| 2150 | for (; ix < n->used * 2 + 1; ix++) {
|
---|
| 2151 | *_W++ = 0;
|
---|
| 2152 | }
|
---|
| 2153 | }
|
---|
| 2154 |
|
---|
| 2155 | /* now we proceed to zero successive digits
|
---|
| 2156 | * from the least significant upwards
|
---|
| 2157 | */
|
---|
| 2158 | for (ix = 0; ix < n->used; ix++) {
|
---|
| 2159 | /* mu = ai * m' mod b
|
---|
| 2160 | *
|
---|
| 2161 | * We avoid a double precision multiplication (which isn't required)
|
---|
| 2162 | * by casting the value down to a mp_digit. Note this requires
|
---|
| 2163 | * that W[ix-1] have the carry cleared (see after the inner loop)
|
---|
| 2164 | */
|
---|
| 2165 | register mp_digit mu;
|
---|
| 2166 | mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
|
---|
| 2167 |
|
---|
| 2168 | /* a = a + mu * m * b**i
|
---|
| 2169 | *
|
---|
| 2170 | * This is computed in place and on the fly. The multiplication
|
---|
| 2171 | * by b**i is handled by offseting which columns the results
|
---|
| 2172 | * are added to.
|
---|
| 2173 | *
|
---|
| 2174 | * Note the comba method normally doesn't handle carries in the
|
---|
| 2175 | * inner loop In this case we fix the carry from the previous
|
---|
| 2176 | * column since the Montgomery reduction requires digits of the
|
---|
| 2177 | * result (so far) [see above] to work. This is
|
---|
| 2178 | * handled by fixing up one carry after the inner loop. The
|
---|
| 2179 | * carry fixups are done in order so after these loops the
|
---|
| 2180 | * first m->used words of W[] have the carries fixed
|
---|
| 2181 | */
|
---|
| 2182 | {
|
---|
| 2183 | register int iy;
|
---|
| 2184 | register mp_digit *tmpn;
|
---|
| 2185 | register mp_word *_W;
|
---|
| 2186 |
|
---|
| 2187 | /* alias for the digits of the modulus */
|
---|
| 2188 | tmpn = n->dp;
|
---|
| 2189 |
|
---|
| 2190 | /* Alias for the columns set by an offset of ix */
|
---|
| 2191 | _W = W + ix;
|
---|
| 2192 |
|
---|
| 2193 | /* inner loop */
|
---|
| 2194 | for (iy = 0; iy < n->used; iy++) {
|
---|
| 2195 | *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
|
---|
| 2196 | }
|
---|
| 2197 | }
|
---|
| 2198 |
|
---|
| 2199 | /* now fix carry for next digit, W[ix+1] */
|
---|
| 2200 | W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
|
---|
| 2201 | }
|
---|
| 2202 |
|
---|
| 2203 | /* now we have to propagate the carries and
|
---|
| 2204 | * shift the words downward [all those least
|
---|
| 2205 | * significant digits we zeroed].
|
---|
| 2206 | */
|
---|
| 2207 | {
|
---|
| 2208 | register mp_digit *tmpx;
|
---|
| 2209 | register mp_word *_W, *_W1;
|
---|
| 2210 |
|
---|
| 2211 | /* nox fix rest of carries */
|
---|
| 2212 |
|
---|
| 2213 | /* alias for current word */
|
---|
| 2214 | _W1 = W + ix;
|
---|
| 2215 |
|
---|
| 2216 | /* alias for next word, where the carry goes */
|
---|
| 2217 | _W = W + ++ix;
|
---|
| 2218 |
|
---|
| 2219 | for (; ix <= n->used * 2 + 1; ix++) {
|
---|
| 2220 | *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
|
---|
| 2221 | }
|
---|
| 2222 |
|
---|
| 2223 | /* copy out, A = A/b**n
|
---|
| 2224 | *
|
---|
| 2225 | * The result is A/b**n but instead of converting from an
|
---|
| 2226 | * array of mp_word to mp_digit than calling mp_rshd
|
---|
| 2227 | * we just copy them in the right order
|
---|
| 2228 | */
|
---|
| 2229 |
|
---|
| 2230 | /* alias for destination word */
|
---|
| 2231 | tmpx = x->dp;
|
---|
| 2232 |
|
---|
| 2233 | /* alias for shifted double precision result */
|
---|
| 2234 | _W = W + n->used;
|
---|
| 2235 |
|
---|
| 2236 | for (ix = 0; ix < n->used + 1; ix++) {
|
---|
| 2237 | *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
|
---|
| 2238 | }
|
---|
| 2239 |
|
---|
| 2240 | /* zero oldused digits, if the input a was larger than
|
---|
| 2241 | * m->used+1 we'll have to clear the digits
|
---|
| 2242 | */
|
---|
| 2243 | for (; ix < olduse; ix++) {
|
---|
| 2244 | *tmpx++ = 0;
|
---|
| 2245 | }
|
---|
| 2246 | }
|
---|
| 2247 |
|
---|
| 2248 | /* set the max used and clamp */
|
---|
| 2249 | x->used = n->used + 1;
|
---|
| 2250 | mp_clamp (x);
|
---|
| 2251 |
|
---|
| 2252 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2253 | XFREE(W, 0, DYNAMIC_TYPE_BIGINT);
|
---|
| 2254 | #endif
|
---|
| 2255 |
|
---|
| 2256 | /* if A >= m then A = A - m */
|
---|
| 2257 | if (mp_cmp_mag (x, n) != MP_LT) {
|
---|
| 2258 | return s_mp_sub (x, n, x);
|
---|
| 2259 | }
|
---|
| 2260 | return MP_OKAY;
|
---|
| 2261 | }
|
---|
| 2262 |
|
---|
| 2263 |
|
---|
| 2264 | /* computes xR**-1 == x (mod N) via Montgomery Reduction */
|
---|
| 2265 | int
|
---|
| 2266 | mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
|
---|
| 2267 | {
|
---|
| 2268 | int ix, res, digs;
|
---|
| 2269 | mp_digit mu;
|
---|
| 2270 |
|
---|
| 2271 | /* can the fast reduction [comba] method be used?
|
---|
| 2272 | *
|
---|
| 2273 | * Note that unlike in mul you're safely allowed *less*
|
---|
| 2274 | * than the available columns [255 per default] since carries
|
---|
| 2275 | * are fixed up in the inner loop.
|
---|
| 2276 | */
|
---|
| 2277 | digs = n->used * 2 + 1;
|
---|
| 2278 | if ((digs < MP_WARRAY) &&
|
---|
| 2279 | n->used <
|
---|
| 2280 | (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
| 2281 | return fast_mp_montgomery_reduce (x, n, rho);
|
---|
| 2282 | }
|
---|
| 2283 |
|
---|
| 2284 | /* grow the input as required */
|
---|
| 2285 | if (x->alloc < digs) {
|
---|
| 2286 | if ((res = mp_grow (x, digs)) != MP_OKAY) {
|
---|
| 2287 | return res;
|
---|
| 2288 | }
|
---|
| 2289 | }
|
---|
| 2290 | x->used = digs;
|
---|
| 2291 |
|
---|
| 2292 | for (ix = 0; ix < n->used; ix++) {
|
---|
| 2293 | /* mu = ai * rho mod b
|
---|
| 2294 | *
|
---|
| 2295 | * The value of rho must be precalculated via
|
---|
| 2296 | * montgomery_setup() such that
|
---|
| 2297 | * it equals -1/n0 mod b this allows the
|
---|
| 2298 | * following inner loop to reduce the
|
---|
| 2299 | * input one digit at a time
|
---|
| 2300 | */
|
---|
| 2301 | mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
|
---|
| 2302 |
|
---|
| 2303 | /* a = a + mu * m * b**i */
|
---|
| 2304 | {
|
---|
| 2305 | register int iy;
|
---|
| 2306 | register mp_digit *tmpn, *tmpx, u;
|
---|
| 2307 | register mp_word r;
|
---|
| 2308 |
|
---|
| 2309 | /* alias for digits of the modulus */
|
---|
| 2310 | tmpn = n->dp;
|
---|
| 2311 |
|
---|
| 2312 | /* alias for the digits of x [the input] */
|
---|
| 2313 | tmpx = x->dp + ix;
|
---|
| 2314 |
|
---|
| 2315 | /* set the carry to zero */
|
---|
| 2316 | u = 0;
|
---|
| 2317 |
|
---|
| 2318 | /* Multiply and add in place */
|
---|
| 2319 | for (iy = 0; iy < n->used; iy++) {
|
---|
| 2320 | /* compute product and sum */
|
---|
| 2321 | r = ((mp_word)mu) * ((mp_word)*tmpn++) +
|
---|
| 2322 | ((mp_word) u) + ((mp_word) * tmpx);
|
---|
| 2323 |
|
---|
| 2324 | /* get carry */
|
---|
| 2325 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 2326 |
|
---|
| 2327 | /* fix digit */
|
---|
| 2328 | *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
|
---|
| 2329 | }
|
---|
| 2330 | /* At this point the ix'th digit of x should be zero */
|
---|
| 2331 |
|
---|
| 2332 |
|
---|
| 2333 | /* propagate carries upwards as required*/
|
---|
| 2334 | while (u) {
|
---|
| 2335 | *tmpx += u;
|
---|
| 2336 | u = *tmpx >> DIGIT_BIT;
|
---|
| 2337 | *tmpx++ &= MP_MASK;
|
---|
| 2338 | }
|
---|
| 2339 | }
|
---|
| 2340 | }
|
---|
| 2341 |
|
---|
| 2342 | /* at this point the n.used'th least
|
---|
| 2343 | * significant digits of x are all zero
|
---|
| 2344 | * which means we can shift x to the
|
---|
| 2345 | * right by n.used digits and the
|
---|
| 2346 | * residue is unchanged.
|
---|
| 2347 | */
|
---|
| 2348 |
|
---|
| 2349 | /* x = x/b**n.used */
|
---|
| 2350 | mp_clamp(x);
|
---|
| 2351 | mp_rshd (x, n->used);
|
---|
| 2352 |
|
---|
| 2353 | /* if x >= n then x = x - n */
|
---|
| 2354 | if (mp_cmp_mag (x, n) != MP_LT) {
|
---|
| 2355 | return s_mp_sub (x, n, x);
|
---|
| 2356 | }
|
---|
| 2357 |
|
---|
| 2358 | return MP_OKAY;
|
---|
| 2359 | }
|
---|
| 2360 |
|
---|
| 2361 |
|
---|
| 2362 | /* determines the setup value */
|
---|
| 2363 | void mp_dr_setup(mp_int *a, mp_digit *d)
|
---|
| 2364 | {
|
---|
| 2365 | /* the casts are required if DIGIT_BIT is one less than
|
---|
| 2366 | * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
|
---|
| 2367 | */
|
---|
| 2368 | *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
|
---|
| 2369 | ((mp_word)a->dp[0]));
|
---|
| 2370 | }
|
---|
| 2371 |
|
---|
| 2372 |
|
---|
| 2373 | /* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
|
---|
| 2374 | *
|
---|
| 2375 | * Based on algorithm from the paper
|
---|
| 2376 | *
|
---|
| 2377 | * "Generating Efficient Primes for Discrete Log Cryptosystems"
|
---|
| 2378 | * Chae Hoon Lim, Pil Joong Lee,
|
---|
| 2379 | * POSTECH Information Research Laboratories
|
---|
| 2380 | *
|
---|
| 2381 | * The modulus must be of a special format [see manual]
|
---|
| 2382 | *
|
---|
| 2383 | * Has been modified to use algorithm 7.10 from the LTM book instead
|
---|
| 2384 | *
|
---|
| 2385 | * Input x must be in the range 0 <= x <= (n-1)**2
|
---|
| 2386 | */
|
---|
| 2387 | int
|
---|
| 2388 | mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
|
---|
| 2389 | {
|
---|
| 2390 | int err, i, m;
|
---|
| 2391 | mp_word r;
|
---|
| 2392 | mp_digit mu, *tmpx1, *tmpx2;
|
---|
| 2393 |
|
---|
| 2394 | /* m = digits in modulus */
|
---|
| 2395 | m = n->used;
|
---|
| 2396 |
|
---|
| 2397 | /* ensure that "x" has at least 2m digits */
|
---|
| 2398 | if (x->alloc < m + m) {
|
---|
| 2399 | if ((err = mp_grow (x, m + m)) != MP_OKAY) {
|
---|
| 2400 | return err;
|
---|
| 2401 | }
|
---|
| 2402 | }
|
---|
| 2403 |
|
---|
| 2404 | /* top of loop, this is where the code resumes if
|
---|
| 2405 | * another reduction pass is required.
|
---|
| 2406 | */
|
---|
| 2407 | top:
|
---|
| 2408 | /* aliases for digits */
|
---|
| 2409 | /* alias for lower half of x */
|
---|
| 2410 | tmpx1 = x->dp;
|
---|
| 2411 |
|
---|
| 2412 | /* alias for upper half of x, or x/B**m */
|
---|
| 2413 | tmpx2 = x->dp + m;
|
---|
| 2414 |
|
---|
| 2415 | /* set carry to zero */
|
---|
| 2416 | mu = 0;
|
---|
| 2417 |
|
---|
| 2418 | /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
|
---|
| 2419 | for (i = 0; i < m; i++) {
|
---|
| 2420 | r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
|
---|
| 2421 | *tmpx1++ = (mp_digit)(r & MP_MASK);
|
---|
| 2422 | mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
|
---|
| 2423 | }
|
---|
| 2424 |
|
---|
| 2425 | /* set final carry */
|
---|
| 2426 | *tmpx1++ = mu;
|
---|
| 2427 |
|
---|
| 2428 | /* zero words above m */
|
---|
| 2429 | for (i = m + 1; i < x->used; i++) {
|
---|
| 2430 | *tmpx1++ = 0;
|
---|
| 2431 | }
|
---|
| 2432 |
|
---|
| 2433 | /* clamp, sub and return */
|
---|
| 2434 | mp_clamp (x);
|
---|
| 2435 |
|
---|
| 2436 | /* if x >= n then subtract and reduce again
|
---|
| 2437 | * Each successive "recursion" makes the input smaller and smaller.
|
---|
| 2438 | */
|
---|
| 2439 | if (mp_cmp_mag (x, n) != MP_LT) {
|
---|
| 2440 | s_mp_sub(x, n, x);
|
---|
| 2441 | goto top;
|
---|
| 2442 | }
|
---|
| 2443 | return MP_OKAY;
|
---|
| 2444 | }
|
---|
| 2445 |
|
---|
| 2446 |
|
---|
| 2447 | /* reduces a modulo n where n is of the form 2**p - d */
|
---|
| 2448 | int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
|
---|
| 2449 | {
|
---|
| 2450 | mp_int q;
|
---|
| 2451 | int p, res;
|
---|
| 2452 |
|
---|
| 2453 | if ((res = mp_init(&q)) != MP_OKAY) {
|
---|
| 2454 | return res;
|
---|
| 2455 | }
|
---|
| 2456 |
|
---|
| 2457 | p = mp_count_bits(n);
|
---|
| 2458 | top:
|
---|
| 2459 | /* q = a/2**p, a = a mod 2**p */
|
---|
| 2460 | if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
|
---|
| 2461 | goto ERR;
|
---|
| 2462 | }
|
---|
| 2463 |
|
---|
| 2464 | if (d != 1) {
|
---|
| 2465 | /* q = q * d */
|
---|
| 2466 | if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
|
---|
| 2467 | goto ERR;
|
---|
| 2468 | }
|
---|
| 2469 | }
|
---|
| 2470 |
|
---|
| 2471 | /* a = a + q */
|
---|
| 2472 | if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
|
---|
| 2473 | goto ERR;
|
---|
| 2474 | }
|
---|
| 2475 |
|
---|
| 2476 | if (mp_cmp_mag(a, n) != MP_LT) {
|
---|
| 2477 | s_mp_sub(a, n, a);
|
---|
| 2478 | goto top;
|
---|
| 2479 | }
|
---|
| 2480 |
|
---|
| 2481 | ERR:
|
---|
| 2482 | mp_clear(&q);
|
---|
| 2483 | return res;
|
---|
| 2484 | }
|
---|
| 2485 |
|
---|
| 2486 |
|
---|
| 2487 | /* determines the setup value */
|
---|
| 2488 | int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
|
---|
| 2489 | {
|
---|
| 2490 | int res, p;
|
---|
| 2491 | mp_int tmp;
|
---|
| 2492 |
|
---|
| 2493 | if ((res = mp_init(&tmp)) != MP_OKAY) {
|
---|
| 2494 | return res;
|
---|
| 2495 | }
|
---|
| 2496 |
|
---|
| 2497 | p = mp_count_bits(a);
|
---|
| 2498 | if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
|
---|
| 2499 | mp_clear(&tmp);
|
---|
| 2500 | return res;
|
---|
| 2501 | }
|
---|
| 2502 |
|
---|
| 2503 | if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
|
---|
| 2504 | mp_clear(&tmp);
|
---|
| 2505 | return res;
|
---|
| 2506 | }
|
---|
| 2507 |
|
---|
| 2508 | *d = tmp.dp[0];
|
---|
| 2509 | mp_clear(&tmp);
|
---|
| 2510 | return MP_OKAY;
|
---|
| 2511 | }
|
---|
| 2512 |
|
---|
| 2513 |
|
---|
| 2514 | /* set the b bit of a */
|
---|
| 2515 | int
|
---|
| 2516 | mp_set_bit (mp_int * a, int b)
|
---|
| 2517 | {
|
---|
| 2518 | int i = b / DIGIT_BIT, res;
|
---|
| 2519 |
|
---|
| 2520 | if (a->used < (int)(i + 1)) {
|
---|
| 2521 | /* grow a to accomodate the single bit */
|
---|
| 2522 | if ((res = mp_grow (a, i + 1)) != MP_OKAY) {
|
---|
| 2523 | return res;
|
---|
| 2524 | }
|
---|
| 2525 |
|
---|
| 2526 | /* set the used count of where the bit will go */
|
---|
| 2527 | a->used = (int)(i + 1);
|
---|
| 2528 | }
|
---|
| 2529 |
|
---|
| 2530 | /* put the single bit in its place */
|
---|
| 2531 | a->dp[i] |= ((mp_digit)1) << (b % DIGIT_BIT);
|
---|
| 2532 |
|
---|
| 2533 | return MP_OKAY;
|
---|
| 2534 | }
|
---|
| 2535 |
|
---|
| 2536 | /* computes a = 2**b
|
---|
| 2537 | *
|
---|
| 2538 | * Simple algorithm which zeroes the int, set the required bit
|
---|
| 2539 | */
|
---|
| 2540 | int
|
---|
| 2541 | mp_2expt (mp_int * a, int b)
|
---|
| 2542 | {
|
---|
| 2543 | /* zero a as per default */
|
---|
| 2544 | mp_zero (a);
|
---|
| 2545 |
|
---|
| 2546 | return mp_set_bit(a, b);
|
---|
| 2547 | }
|
---|
| 2548 |
|
---|
| 2549 | /* multiply by a digit */
|
---|
| 2550 | int
|
---|
| 2551 | mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
|
---|
| 2552 | {
|
---|
| 2553 | mp_digit u, *tmpa, *tmpc;
|
---|
| 2554 | mp_word r;
|
---|
| 2555 | int ix, res, olduse;
|
---|
| 2556 |
|
---|
| 2557 | /* make sure c is big enough to hold a*b */
|
---|
| 2558 | if (c->alloc < a->used + 1) {
|
---|
| 2559 | if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
|
---|
| 2560 | return res;
|
---|
| 2561 | }
|
---|
| 2562 | }
|
---|
| 2563 |
|
---|
| 2564 | /* get the original destinations used count */
|
---|
| 2565 | olduse = c->used;
|
---|
| 2566 |
|
---|
| 2567 | /* set the sign */
|
---|
| 2568 | c->sign = a->sign;
|
---|
| 2569 |
|
---|
| 2570 | /* alias for a->dp [source] */
|
---|
| 2571 | tmpa = a->dp;
|
---|
| 2572 |
|
---|
| 2573 | /* alias for c->dp [dest] */
|
---|
| 2574 | tmpc = c->dp;
|
---|
| 2575 |
|
---|
| 2576 | /* zero carry */
|
---|
| 2577 | u = 0;
|
---|
| 2578 |
|
---|
| 2579 | /* compute columns */
|
---|
| 2580 | for (ix = 0; ix < a->used; ix++) {
|
---|
| 2581 | /* compute product and carry sum for this term */
|
---|
| 2582 | r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
|
---|
| 2583 |
|
---|
| 2584 | /* mask off higher bits to get a single digit */
|
---|
| 2585 | *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 2586 |
|
---|
| 2587 | /* send carry into next iteration */
|
---|
| 2588 | u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
---|
| 2589 | }
|
---|
| 2590 |
|
---|
| 2591 | /* store final carry [if any] and increment ix offset */
|
---|
| 2592 | *tmpc++ = u;
|
---|
| 2593 | ++ix;
|
---|
| 2594 |
|
---|
| 2595 | /* now zero digits above the top */
|
---|
| 2596 | while (ix++ < olduse) {
|
---|
| 2597 | *tmpc++ = 0;
|
---|
| 2598 | }
|
---|
| 2599 |
|
---|
| 2600 | /* set used count */
|
---|
| 2601 | c->used = a->used + 1;
|
---|
| 2602 | mp_clamp(c);
|
---|
| 2603 |
|
---|
| 2604 | return MP_OKAY;
|
---|
| 2605 | }
|
---|
| 2606 |
|
---|
| 2607 |
|
---|
| 2608 | /* d = a * b (mod c) */
|
---|
| 2609 | int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
|
---|
| 2610 | {
|
---|
| 2611 | int res;
|
---|
| 2612 | mp_int t;
|
---|
| 2613 |
|
---|
| 2614 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
| 2615 | return res;
|
---|
| 2616 | }
|
---|
| 2617 |
|
---|
| 2618 | if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
|
---|
| 2619 | mp_clear (&t);
|
---|
| 2620 | return res;
|
---|
| 2621 | }
|
---|
| 2622 | res = mp_mod (&t, c, d);
|
---|
| 2623 | mp_clear (&t);
|
---|
| 2624 | return res;
|
---|
| 2625 | }
|
---|
| 2626 |
|
---|
| 2627 |
|
---|
| 2628 | /* computes b = a*a */
|
---|
| 2629 | int
|
---|
| 2630 | mp_sqr (mp_int * a, mp_int * b)
|
---|
| 2631 | {
|
---|
| 2632 | int res;
|
---|
| 2633 |
|
---|
| 2634 | {
|
---|
| 2635 | #ifdef BN_FAST_S_MP_SQR_C
|
---|
| 2636 | /* can we use the fast comba multiplier? */
|
---|
| 2637 | if ((a->used * 2 + 1) < MP_WARRAY &&
|
---|
| 2638 | a->used <
|
---|
| 2639 | (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
|
---|
| 2640 | res = fast_s_mp_sqr (a, b);
|
---|
| 2641 | } else
|
---|
| 2642 | #endif
|
---|
| 2643 | #ifdef BN_S_MP_SQR_C
|
---|
| 2644 | res = s_mp_sqr (a, b);
|
---|
| 2645 | #else
|
---|
| 2646 | res = MP_VAL;
|
---|
| 2647 | #endif
|
---|
| 2648 | }
|
---|
| 2649 | b->sign = MP_ZPOS;
|
---|
| 2650 | return res;
|
---|
| 2651 | }
|
---|
| 2652 |
|
---|
| 2653 |
|
---|
| 2654 | /* high level multiplication (handles sign) */
|
---|
| 2655 | int mp_mul (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 2656 | {
|
---|
| 2657 | int res, neg;
|
---|
| 2658 | neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
|
---|
| 2659 |
|
---|
| 2660 | {
|
---|
| 2661 | /* can we use the fast multiplier?
|
---|
| 2662 | *
|
---|
| 2663 | * The fast multiplier can be used if the output will
|
---|
| 2664 | * have less than MP_WARRAY digits and the number of
|
---|
| 2665 | * digits won't affect carry propagation
|
---|
| 2666 | */
|
---|
| 2667 | int digs = a->used + b->used + 1;
|
---|
| 2668 |
|
---|
| 2669 | #ifdef BN_FAST_S_MP_MUL_DIGS_C
|
---|
| 2670 | if ((digs < MP_WARRAY) &&
|
---|
| 2671 | MIN(a->used, b->used) <=
|
---|
| 2672 | (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
| 2673 | res = fast_s_mp_mul_digs (a, b, c, digs);
|
---|
| 2674 | } else
|
---|
| 2675 | #endif
|
---|
| 2676 | #ifdef BN_S_MP_MUL_DIGS_C
|
---|
| 2677 | res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
|
---|
| 2678 | #else
|
---|
| 2679 | res = MP_VAL;
|
---|
| 2680 | #endif
|
---|
| 2681 |
|
---|
| 2682 | }
|
---|
| 2683 | c->sign = (c->used > 0) ? neg : MP_ZPOS;
|
---|
| 2684 | return res;
|
---|
| 2685 | }
|
---|
| 2686 |
|
---|
| 2687 |
|
---|
| 2688 | /* b = a*2 */
|
---|
| 2689 | int mp_mul_2(mp_int * a, mp_int * b)
|
---|
| 2690 | {
|
---|
| 2691 | int x, res, oldused;
|
---|
| 2692 |
|
---|
| 2693 | /* grow to accomodate result */
|
---|
| 2694 | if (b->alloc < a->used + 1) {
|
---|
| 2695 | if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
|
---|
| 2696 | return res;
|
---|
| 2697 | }
|
---|
| 2698 | }
|
---|
| 2699 |
|
---|
| 2700 | oldused = b->used;
|
---|
| 2701 | b->used = a->used;
|
---|
| 2702 |
|
---|
| 2703 | {
|
---|
| 2704 | register mp_digit r, rr, *tmpa, *tmpb;
|
---|
| 2705 |
|
---|
| 2706 | /* alias for source */
|
---|
| 2707 | tmpa = a->dp;
|
---|
| 2708 |
|
---|
| 2709 | /* alias for dest */
|
---|
| 2710 | tmpb = b->dp;
|
---|
| 2711 |
|
---|
| 2712 | /* carry */
|
---|
| 2713 | r = 0;
|
---|
| 2714 | for (x = 0; x < a->used; x++) {
|
---|
| 2715 |
|
---|
| 2716 | /* get what will be the *next* carry bit from the
|
---|
| 2717 | * MSB of the current digit
|
---|
| 2718 | */
|
---|
| 2719 | rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
|
---|
| 2720 |
|
---|
| 2721 | /* now shift up this digit, add in the carry [from the previous] */
|
---|
| 2722 | *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
|
---|
| 2723 |
|
---|
| 2724 | /* copy the carry that would be from the source
|
---|
| 2725 | * digit into the next iteration
|
---|
| 2726 | */
|
---|
| 2727 | r = rr;
|
---|
| 2728 | }
|
---|
| 2729 |
|
---|
| 2730 | /* new leading digit? */
|
---|
| 2731 | if (r != 0) {
|
---|
| 2732 | /* add a MSB which is always 1 at this point */
|
---|
| 2733 | *tmpb = 1;
|
---|
| 2734 | ++(b->used);
|
---|
| 2735 | }
|
---|
| 2736 |
|
---|
| 2737 | /* now zero any excess digits on the destination
|
---|
| 2738 | * that we didn't write to
|
---|
| 2739 | */
|
---|
| 2740 | tmpb = b->dp + b->used;
|
---|
| 2741 | for (x = b->used; x < oldused; x++) {
|
---|
| 2742 | *tmpb++ = 0;
|
---|
| 2743 | }
|
---|
| 2744 | }
|
---|
| 2745 | b->sign = a->sign;
|
---|
| 2746 | return MP_OKAY;
|
---|
| 2747 | }
|
---|
| 2748 |
|
---|
| 2749 |
|
---|
| 2750 | /* divide by three (based on routine from MPI and the GMP manual) */
|
---|
| 2751 | int
|
---|
| 2752 | mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
|
---|
| 2753 | {
|
---|
| 2754 | mp_int q;
|
---|
| 2755 | mp_word w, t;
|
---|
| 2756 | mp_digit b;
|
---|
| 2757 | int res, ix;
|
---|
| 2758 |
|
---|
| 2759 | /* b = 2**DIGIT_BIT / 3 */
|
---|
| 2760 | b = (mp_digit) ( (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3) );
|
---|
| 2761 |
|
---|
| 2762 | if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
|
---|
| 2763 | return res;
|
---|
| 2764 | }
|
---|
| 2765 |
|
---|
| 2766 | q.used = a->used;
|
---|
| 2767 | q.sign = a->sign;
|
---|
| 2768 | w = 0;
|
---|
| 2769 | for (ix = a->used - 1; ix >= 0; ix--) {
|
---|
| 2770 | w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
|
---|
| 2771 |
|
---|
| 2772 | if (w >= 3) {
|
---|
| 2773 | /* multiply w by [1/3] */
|
---|
| 2774 | t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
|
---|
| 2775 |
|
---|
| 2776 | /* now subtract 3 * [w/3] from w, to get the remainder */
|
---|
| 2777 | w -= t+t+t;
|
---|
| 2778 |
|
---|
| 2779 | /* fixup the remainder as required since
|
---|
| 2780 | * the optimization is not exact.
|
---|
| 2781 | */
|
---|
| 2782 | while (w >= 3) {
|
---|
| 2783 | t += 1;
|
---|
| 2784 | w -= 3;
|
---|
| 2785 | }
|
---|
| 2786 | } else {
|
---|
| 2787 | t = 0;
|
---|
| 2788 | }
|
---|
| 2789 | q.dp[ix] = (mp_digit)t;
|
---|
| 2790 | }
|
---|
| 2791 |
|
---|
| 2792 | /* [optional] store the remainder */
|
---|
| 2793 | if (d != NULL) {
|
---|
| 2794 | *d = (mp_digit)w;
|
---|
| 2795 | }
|
---|
| 2796 |
|
---|
| 2797 | /* [optional] store the quotient */
|
---|
| 2798 | if (c != NULL) {
|
---|
| 2799 | mp_clamp(&q);
|
---|
| 2800 | mp_exch(&q, c);
|
---|
| 2801 | }
|
---|
| 2802 | mp_clear(&q);
|
---|
| 2803 |
|
---|
| 2804 | return res;
|
---|
| 2805 | }
|
---|
| 2806 |
|
---|
| 2807 |
|
---|
| 2808 | /* init an mp_init for a given size */
|
---|
| 2809 | int mp_init_size (mp_int * a, int size)
|
---|
| 2810 | {
|
---|
| 2811 | int x;
|
---|
| 2812 |
|
---|
| 2813 | /* pad size so there are always extra digits */
|
---|
| 2814 | size += (MP_PREC * 2) - (size % MP_PREC);
|
---|
| 2815 |
|
---|
| 2816 | /* alloc mem */
|
---|
| 2817 | a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size, 0,
|
---|
| 2818 | DYNAMIC_TYPE_BIGINT);
|
---|
| 2819 | if (a->dp == NULL) {
|
---|
| 2820 | return MP_MEM;
|
---|
| 2821 | }
|
---|
| 2822 |
|
---|
| 2823 | /* set the members */
|
---|
| 2824 | a->used = 0;
|
---|
| 2825 | a->alloc = size;
|
---|
| 2826 | a->sign = MP_ZPOS;
|
---|
| 2827 |
|
---|
| 2828 | /* zero the digits */
|
---|
| 2829 | for (x = 0; x < size; x++) {
|
---|
| 2830 | a->dp[x] = 0;
|
---|
| 2831 | }
|
---|
| 2832 |
|
---|
| 2833 | return MP_OKAY;
|
---|
| 2834 | }
|
---|
| 2835 |
|
---|
| 2836 |
|
---|
| 2837 | /* the jist of squaring...
|
---|
| 2838 | * you do like mult except the offset of the tmpx [one that
|
---|
| 2839 | * starts closer to zero] can't equal the offset of tmpy.
|
---|
| 2840 | * So basically you set up iy like before then you min it with
|
---|
| 2841 | * (ty-tx) so that it never happens. You double all those
|
---|
| 2842 | * you add in the inner loop
|
---|
| 2843 |
|
---|
| 2844 | After that loop you do the squares and add them in.
|
---|
| 2845 | */
|
---|
| 2846 |
|
---|
| 2847 | int fast_s_mp_sqr (mp_int * a, mp_int * b)
|
---|
| 2848 | {
|
---|
| 2849 | int olduse, res, pa, ix, iz;
|
---|
| 2850 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2851 | mp_digit* W; /* uses dynamic memory and slower */
|
---|
| 2852 | #else
|
---|
| 2853 | mp_digit W[MP_WARRAY];
|
---|
| 2854 | #endif
|
---|
| 2855 | mp_digit *tmpx;
|
---|
| 2856 | mp_word W1;
|
---|
| 2857 |
|
---|
| 2858 | /* grow the destination as required */
|
---|
| 2859 | pa = a->used + a->used;
|
---|
| 2860 | if (b->alloc < pa) {
|
---|
| 2861 | if ((res = mp_grow (b, pa)) != MP_OKAY) {
|
---|
| 2862 | return res;
|
---|
| 2863 | }
|
---|
| 2864 | }
|
---|
| 2865 |
|
---|
| 2866 | if (pa > MP_WARRAY)
|
---|
| 2867 | return MP_RANGE; /* TAO range check */
|
---|
| 2868 |
|
---|
| 2869 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2870 | W = (mp_digit*)XMALLOC(sizeof(mp_digit) * MP_WARRAY, 0, DYNAMIC_TYPE_BIGINT);
|
---|
| 2871 | if (W == NULL)
|
---|
| 2872 | return MP_MEM;
|
---|
| 2873 | #endif
|
---|
| 2874 |
|
---|
| 2875 | /* number of output digits to produce */
|
---|
| 2876 | W1 = 0;
|
---|
| 2877 | for (ix = 0; ix < pa; ix++) {
|
---|
| 2878 | int tx, ty, iy;
|
---|
| 2879 | mp_word _W;
|
---|
| 2880 | mp_digit *tmpy;
|
---|
| 2881 |
|
---|
| 2882 | /* clear counter */
|
---|
| 2883 | _W = 0;
|
---|
| 2884 |
|
---|
| 2885 | /* get offsets into the two bignums */
|
---|
| 2886 | ty = MIN(a->used-1, ix);
|
---|
| 2887 | tx = ix - ty;
|
---|
| 2888 |
|
---|
| 2889 | /* setup temp aliases */
|
---|
| 2890 | tmpx = a->dp + tx;
|
---|
| 2891 | tmpy = a->dp + ty;
|
---|
| 2892 |
|
---|
| 2893 | /* this is the number of times the loop will iterrate, essentially
|
---|
| 2894 | while (tx++ < a->used && ty-- >= 0) { ... }
|
---|
| 2895 | */
|
---|
| 2896 | iy = MIN(a->used-tx, ty+1);
|
---|
| 2897 |
|
---|
| 2898 | /* now for squaring tx can never equal ty
|
---|
| 2899 | * we halve the distance since they approach at a rate of 2x
|
---|
| 2900 | * and we have to round because odd cases need to be executed
|
---|
| 2901 | */
|
---|
| 2902 | iy = MIN(iy, (ty-tx+1)>>1);
|
---|
| 2903 |
|
---|
| 2904 | /* execute loop */
|
---|
| 2905 | for (iz = 0; iz < iy; iz++) {
|
---|
| 2906 | _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
---|
| 2907 | }
|
---|
| 2908 |
|
---|
| 2909 | /* double the inner product and add carry */
|
---|
| 2910 | _W = _W + _W + W1;
|
---|
| 2911 |
|
---|
| 2912 | /* even columns have the square term in them */
|
---|
| 2913 | if ((ix&1) == 0) {
|
---|
| 2914 | _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
|
---|
| 2915 | }
|
---|
| 2916 |
|
---|
| 2917 | /* store it */
|
---|
| 2918 | W[ix] = (mp_digit)(_W & MP_MASK);
|
---|
| 2919 |
|
---|
| 2920 | /* make next carry */
|
---|
| 2921 | W1 = _W >> ((mp_word)DIGIT_BIT);
|
---|
| 2922 | }
|
---|
| 2923 |
|
---|
| 2924 | /* setup dest */
|
---|
| 2925 | olduse = b->used;
|
---|
| 2926 | b->used = a->used+a->used;
|
---|
| 2927 |
|
---|
| 2928 | {
|
---|
| 2929 | mp_digit *tmpb;
|
---|
| 2930 | tmpb = b->dp;
|
---|
| 2931 | for (ix = 0; ix < pa; ix++) {
|
---|
| 2932 | *tmpb++ = W[ix] & MP_MASK;
|
---|
| 2933 | }
|
---|
| 2934 |
|
---|
| 2935 | /* clear unused digits [that existed in the old copy of c] */
|
---|
| 2936 | for (; ix < olduse; ix++) {
|
---|
| 2937 | *tmpb++ = 0;
|
---|
| 2938 | }
|
---|
| 2939 | }
|
---|
| 2940 | mp_clamp (b);
|
---|
| 2941 |
|
---|
| 2942 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2943 | XFREE(W, 0, DYNAMIC_TYPE_BIGINT);
|
---|
| 2944 | #endif
|
---|
| 2945 |
|
---|
| 2946 | return MP_OKAY;
|
---|
| 2947 | }
|
---|
| 2948 |
|
---|
| 2949 |
|
---|
| 2950 | /* Fast (comba) multiplier
|
---|
| 2951 | *
|
---|
| 2952 | * This is the fast column-array [comba] multiplier. It is
|
---|
| 2953 | * designed to compute the columns of the product first
|
---|
| 2954 | * then handle the carries afterwards. This has the effect
|
---|
| 2955 | * of making the nested loops that compute the columns very
|
---|
| 2956 | * simple and schedulable on super-scalar processors.
|
---|
| 2957 | *
|
---|
| 2958 | * This has been modified to produce a variable number of
|
---|
| 2959 | * digits of output so if say only a half-product is required
|
---|
| 2960 | * you don't have to compute the upper half (a feature
|
---|
| 2961 | * required for fast Barrett reduction).
|
---|
| 2962 | *
|
---|
| 2963 | * Based on Algorithm 14.12 on pp.595 of HAC.
|
---|
| 2964 | *
|
---|
| 2965 | */
|
---|
| 2966 | int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 2967 | {
|
---|
| 2968 | int olduse, res, pa, ix, iz;
|
---|
| 2969 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2970 | mp_digit* W; /* uses dynamic memory and slower */
|
---|
| 2971 | #else
|
---|
| 2972 | mp_digit W[MP_WARRAY];
|
---|
| 2973 | #endif
|
---|
| 2974 | register mp_word _W;
|
---|
| 2975 |
|
---|
| 2976 | /* grow the destination as required */
|
---|
| 2977 | if (c->alloc < digs) {
|
---|
| 2978 | if ((res = mp_grow (c, digs)) != MP_OKAY) {
|
---|
| 2979 | return res;
|
---|
| 2980 | }
|
---|
| 2981 | }
|
---|
| 2982 |
|
---|
| 2983 | /* number of output digits to produce */
|
---|
| 2984 | pa = MIN(digs, a->used + b->used);
|
---|
| 2985 | if (pa > MP_WARRAY)
|
---|
| 2986 | return MP_RANGE; /* TAO range check */
|
---|
| 2987 |
|
---|
| 2988 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2989 | W = (mp_digit*)XMALLOC(sizeof(mp_digit) * MP_WARRAY, 0, DYNAMIC_TYPE_BIGINT);
|
---|
| 2990 | if (W == NULL)
|
---|
| 2991 | return MP_MEM;
|
---|
| 2992 | #endif
|
---|
| 2993 |
|
---|
| 2994 | /* clear the carry */
|
---|
| 2995 | _W = 0;
|
---|
| 2996 | for (ix = 0; ix < pa; ix++) {
|
---|
| 2997 | int tx, ty;
|
---|
| 2998 | int iy;
|
---|
| 2999 | mp_digit *tmpx, *tmpy;
|
---|
| 3000 |
|
---|
| 3001 | /* get offsets into the two bignums */
|
---|
| 3002 | ty = MIN(b->used-1, ix);
|
---|
| 3003 | tx = ix - ty;
|
---|
| 3004 |
|
---|
| 3005 | /* setup temp aliases */
|
---|
| 3006 | tmpx = a->dp + tx;
|
---|
| 3007 | tmpy = b->dp + ty;
|
---|
| 3008 |
|
---|
| 3009 | /* this is the number of times the loop will iterrate, essentially
|
---|
| 3010 | while (tx++ < a->used && ty-- >= 0) { ... }
|
---|
| 3011 | */
|
---|
| 3012 | iy = MIN(a->used-tx, ty+1);
|
---|
| 3013 |
|
---|
| 3014 | /* execute loop */
|
---|
| 3015 | for (iz = 0; iz < iy; ++iz) {
|
---|
| 3016 | _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
---|
| 3017 |
|
---|
| 3018 | }
|
---|
| 3019 |
|
---|
| 3020 | /* store term */
|
---|
| 3021 | W[ix] = ((mp_digit)_W) & MP_MASK;
|
---|
| 3022 |
|
---|
| 3023 | /* make next carry */
|
---|
| 3024 | _W = _W >> ((mp_word)DIGIT_BIT);
|
---|
| 3025 | }
|
---|
| 3026 |
|
---|
| 3027 | /* setup dest */
|
---|
| 3028 | olduse = c->used;
|
---|
| 3029 | c->used = pa;
|
---|
| 3030 |
|
---|
| 3031 | {
|
---|
| 3032 | register mp_digit *tmpc;
|
---|
| 3033 | tmpc = c->dp;
|
---|
| 3034 | for (ix = 0; ix < pa+1; ix++) {
|
---|
| 3035 | /* now extract the previous digit [below the carry] */
|
---|
| 3036 | *tmpc++ = W[ix];
|
---|
| 3037 | }
|
---|
| 3038 |
|
---|
| 3039 | /* clear unused digits [that existed in the old copy of c] */
|
---|
| 3040 | for (; ix < olduse; ix++) {
|
---|
| 3041 | *tmpc++ = 0;
|
---|
| 3042 | }
|
---|
| 3043 | }
|
---|
| 3044 | mp_clamp (c);
|
---|
| 3045 |
|
---|
| 3046 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3047 | XFREE(W, 0, DYNAMIC_TYPE_BIGINT);
|
---|
| 3048 | #endif
|
---|
| 3049 |
|
---|
| 3050 | return MP_OKAY;
|
---|
| 3051 | }
|
---|
| 3052 |
|
---|
| 3053 |
|
---|
| 3054 | /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
|
---|
| 3055 | int s_mp_sqr (mp_int * a, mp_int * b)
|
---|
| 3056 | {
|
---|
| 3057 | mp_int t;
|
---|
| 3058 | int res, ix, iy, pa;
|
---|
| 3059 | mp_word r;
|
---|
| 3060 | mp_digit u, tmpx, *tmpt;
|
---|
| 3061 |
|
---|
| 3062 | pa = a->used;
|
---|
| 3063 | if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
|
---|
| 3064 | return res;
|
---|
| 3065 | }
|
---|
| 3066 |
|
---|
| 3067 | /* default used is maximum possible size */
|
---|
| 3068 | t.used = 2*pa + 1;
|
---|
| 3069 |
|
---|
| 3070 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3071 | /* first calculate the digit at 2*ix */
|
---|
| 3072 | /* calculate double precision result */
|
---|
| 3073 | r = ((mp_word) t.dp[2*ix]) +
|
---|
| 3074 | ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
|
---|
| 3075 |
|
---|
| 3076 | /* store lower part in result */
|
---|
| 3077 | t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3078 |
|
---|
| 3079 | /* get the carry */
|
---|
| 3080 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 3081 |
|
---|
| 3082 | /* left hand side of A[ix] * A[iy] */
|
---|
| 3083 | tmpx = a->dp[ix];
|
---|
| 3084 |
|
---|
| 3085 | /* alias for where to store the results */
|
---|
| 3086 | tmpt = t.dp + (2*ix + 1);
|
---|
| 3087 |
|
---|
| 3088 | for (iy = ix + 1; iy < pa; iy++) {
|
---|
| 3089 | /* first calculate the product */
|
---|
| 3090 | r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
|
---|
| 3091 |
|
---|
| 3092 | /* now calculate the double precision result, note we use
|
---|
| 3093 | * addition instead of *2 since it's easier to optimize
|
---|
| 3094 | */
|
---|
| 3095 | r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
|
---|
| 3096 |
|
---|
| 3097 | /* store lower part */
|
---|
| 3098 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3099 |
|
---|
| 3100 | /* get carry */
|
---|
| 3101 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 3102 | }
|
---|
| 3103 | /* propagate upwards */
|
---|
| 3104 | while (u != ((mp_digit) 0)) {
|
---|
| 3105 | r = ((mp_word) *tmpt) + ((mp_word) u);
|
---|
| 3106 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3107 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 3108 | }
|
---|
| 3109 | }
|
---|
| 3110 |
|
---|
| 3111 | mp_clamp (&t);
|
---|
| 3112 | mp_exch (&t, b);
|
---|
| 3113 | mp_clear (&t);
|
---|
| 3114 | return MP_OKAY;
|
---|
| 3115 | }
|
---|
| 3116 |
|
---|
| 3117 |
|
---|
| 3118 | /* multiplies |a| * |b| and only computes upto digs digits of result
|
---|
| 3119 | * HAC pp. 595, Algorithm 14.12 Modified so you can control how
|
---|
| 3120 | * many digits of output are created.
|
---|
| 3121 | */
|
---|
| 3122 | int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 3123 | {
|
---|
| 3124 | mp_int t;
|
---|
| 3125 | int res, pa, pb, ix, iy;
|
---|
| 3126 | mp_digit u;
|
---|
| 3127 | mp_word r;
|
---|
| 3128 | mp_digit tmpx, *tmpt, *tmpy;
|
---|
| 3129 |
|
---|
| 3130 | /* can we use the fast multiplier? */
|
---|
| 3131 | if (((digs) < MP_WARRAY) &&
|
---|
| 3132 | MIN (a->used, b->used) <
|
---|
| 3133 | (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
| 3134 | return fast_s_mp_mul_digs (a, b, c, digs);
|
---|
| 3135 | }
|
---|
| 3136 |
|
---|
| 3137 | if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
|
---|
| 3138 | return res;
|
---|
| 3139 | }
|
---|
| 3140 | t.used = digs;
|
---|
| 3141 |
|
---|
| 3142 | /* compute the digits of the product directly */
|
---|
| 3143 | pa = a->used;
|
---|
| 3144 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3145 | /* set the carry to zero */
|
---|
| 3146 | u = 0;
|
---|
| 3147 |
|
---|
| 3148 | /* limit ourselves to making digs digits of output */
|
---|
| 3149 | pb = MIN (b->used, digs - ix);
|
---|
| 3150 |
|
---|
| 3151 | /* setup some aliases */
|
---|
| 3152 | /* copy of the digit from a used within the nested loop */
|
---|
| 3153 | tmpx = a->dp[ix];
|
---|
| 3154 |
|
---|
| 3155 | /* an alias for the destination shifted ix places */
|
---|
| 3156 | tmpt = t.dp + ix;
|
---|
| 3157 |
|
---|
| 3158 | /* an alias for the digits of b */
|
---|
| 3159 | tmpy = b->dp;
|
---|
| 3160 |
|
---|
| 3161 | /* compute the columns of the output and propagate the carry */
|
---|
| 3162 | for (iy = 0; iy < pb; iy++) {
|
---|
| 3163 | /* compute the column as a mp_word */
|
---|
| 3164 | r = ((mp_word)*tmpt) +
|
---|
| 3165 | ((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
---|
| 3166 | ((mp_word) u);
|
---|
| 3167 |
|
---|
| 3168 | /* the new column is the lower part of the result */
|
---|
| 3169 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3170 |
|
---|
| 3171 | /* get the carry word from the result */
|
---|
| 3172 | u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
---|
| 3173 | }
|
---|
| 3174 | /* set carry if it is placed below digs */
|
---|
| 3175 | if (ix + iy < digs) {
|
---|
| 3176 | *tmpt = u;
|
---|
| 3177 | }
|
---|
| 3178 | }
|
---|
| 3179 |
|
---|
| 3180 | mp_clamp (&t);
|
---|
| 3181 | mp_exch (&t, c);
|
---|
| 3182 |
|
---|
| 3183 | mp_clear (&t);
|
---|
| 3184 | return MP_OKAY;
|
---|
| 3185 | }
|
---|
| 3186 |
|
---|
| 3187 |
|
---|
| 3188 | /*
|
---|
| 3189 | * shifts with subtractions when the result is greater than b.
|
---|
| 3190 | *
|
---|
| 3191 | * The method is slightly modified to shift B unconditionally upto just under
|
---|
| 3192 | * the leading bit of b. This saves alot of multiple precision shifting.
|
---|
| 3193 | */
|
---|
| 3194 | int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
|
---|
| 3195 | {
|
---|
| 3196 | int x, bits, res;
|
---|
| 3197 |
|
---|
| 3198 | /* how many bits of last digit does b use */
|
---|
| 3199 | bits = mp_count_bits (b) % DIGIT_BIT;
|
---|
| 3200 |
|
---|
| 3201 | if (b->used > 1) {
|
---|
| 3202 | if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1))
|
---|
| 3203 | != MP_OKAY) {
|
---|
| 3204 | return res;
|
---|
| 3205 | }
|
---|
| 3206 | } else {
|
---|
| 3207 | mp_set(a, 1);
|
---|
| 3208 | bits = 1;
|
---|
| 3209 | }
|
---|
| 3210 |
|
---|
| 3211 |
|
---|
| 3212 | /* now compute C = A * B mod b */
|
---|
| 3213 | for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
|
---|
| 3214 | if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
|
---|
| 3215 | return res;
|
---|
| 3216 | }
|
---|
| 3217 | if (mp_cmp_mag (a, b) != MP_LT) {
|
---|
| 3218 | if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
|
---|
| 3219 | return res;
|
---|
| 3220 | }
|
---|
| 3221 | }
|
---|
| 3222 | }
|
---|
| 3223 |
|
---|
| 3224 | return MP_OKAY;
|
---|
| 3225 | }
|
---|
| 3226 |
|
---|
| 3227 |
|
---|
| 3228 | #ifdef MP_LOW_MEM
|
---|
| 3229 | #define TAB_SIZE 32
|
---|
| 3230 | #else
|
---|
| 3231 | #define TAB_SIZE 256
|
---|
| 3232 | #endif
|
---|
| 3233 |
|
---|
| 3234 | int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
|
---|
| 3235 | {
|
---|
| 3236 | mp_int M[TAB_SIZE], res, mu;
|
---|
| 3237 | mp_digit buf;
|
---|
| 3238 | int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
---|
| 3239 | int (*redux)(mp_int*,mp_int*,mp_int*);
|
---|
| 3240 |
|
---|
| 3241 | /* find window size */
|
---|
| 3242 | x = mp_count_bits (X);
|
---|
| 3243 | if (x <= 7) {
|
---|
| 3244 | winsize = 2;
|
---|
| 3245 | } else if (x <= 36) {
|
---|
| 3246 | winsize = 3;
|
---|
| 3247 | } else if (x <= 140) {
|
---|
| 3248 | winsize = 4;
|
---|
| 3249 | } else if (x <= 450) {
|
---|
| 3250 | winsize = 5;
|
---|
| 3251 | } else if (x <= 1303) {
|
---|
| 3252 | winsize = 6;
|
---|
| 3253 | } else if (x <= 3529) {
|
---|
| 3254 | winsize = 7;
|
---|
| 3255 | } else {
|
---|
| 3256 | winsize = 8;
|
---|
| 3257 | }
|
---|
| 3258 |
|
---|
| 3259 | #ifdef MP_LOW_MEM
|
---|
| 3260 | if (winsize > 5) {
|
---|
| 3261 | winsize = 5;
|
---|
| 3262 | }
|
---|
| 3263 | #endif
|
---|
| 3264 |
|
---|
| 3265 | /* init M array */
|
---|
| 3266 | /* init first cell */
|
---|
| 3267 | if ((err = mp_init(&M[1])) != MP_OKAY) {
|
---|
| 3268 | return err;
|
---|
| 3269 | }
|
---|
| 3270 |
|
---|
| 3271 | /* now init the second half of the array */
|
---|
| 3272 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 3273 | if ((err = mp_init(&M[x])) != MP_OKAY) {
|
---|
| 3274 | for (y = 1<<(winsize-1); y < x; y++) {
|
---|
| 3275 | mp_clear (&M[y]);
|
---|
| 3276 | }
|
---|
| 3277 | mp_clear(&M[1]);
|
---|
| 3278 | return err;
|
---|
| 3279 | }
|
---|
| 3280 | }
|
---|
| 3281 |
|
---|
| 3282 | /* create mu, used for Barrett reduction */
|
---|
| 3283 | if ((err = mp_init (&mu)) != MP_OKAY) {
|
---|
| 3284 | goto LBL_M;
|
---|
| 3285 | }
|
---|
| 3286 |
|
---|
| 3287 | if (redmode == 0) {
|
---|
| 3288 | if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
|
---|
| 3289 | goto LBL_MU;
|
---|
| 3290 | }
|
---|
| 3291 | redux = mp_reduce;
|
---|
| 3292 | } else {
|
---|
| 3293 | if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
|
---|
| 3294 | goto LBL_MU;
|
---|
| 3295 | }
|
---|
| 3296 | redux = mp_reduce_2k_l;
|
---|
| 3297 | }
|
---|
| 3298 |
|
---|
| 3299 | /* create M table
|
---|
| 3300 | *
|
---|
| 3301 | * The M table contains powers of the base,
|
---|
| 3302 | * e.g. M[x] = G**x mod P
|
---|
| 3303 | *
|
---|
| 3304 | * The first half of the table is not
|
---|
| 3305 | * computed though accept for M[0] and M[1]
|
---|
| 3306 | */
|
---|
| 3307 | if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
|
---|
| 3308 | goto LBL_MU;
|
---|
| 3309 | }
|
---|
| 3310 |
|
---|
| 3311 | /* compute the value at M[1<<(winsize-1)] by squaring
|
---|
| 3312 | * M[1] (winsize-1) times
|
---|
| 3313 | */
|
---|
| 3314 | if ((err = mp_copy (&M[1], &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 3315 | goto LBL_MU;
|
---|
| 3316 | }
|
---|
| 3317 |
|
---|
| 3318 | for (x = 0; x < (winsize - 1); x++) {
|
---|
| 3319 | /* square it */
|
---|
| 3320 | if ((err = mp_sqr (&M[(mp_digit)(1 << (winsize - 1))],
|
---|
| 3321 | &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 3322 | goto LBL_MU;
|
---|
| 3323 | }
|
---|
| 3324 |
|
---|
| 3325 | /* reduce modulo P */
|
---|
| 3326 | if ((err = redux (&M[(mp_digit)(1 << (winsize - 1))], P, &mu)) != MP_OKAY) {
|
---|
| 3327 | goto LBL_MU;
|
---|
| 3328 | }
|
---|
| 3329 | }
|
---|
| 3330 |
|
---|
| 3331 | /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
|
---|
| 3332 | * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
|
---|
| 3333 | */
|
---|
| 3334 | for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
---|
| 3335 | if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
---|
| 3336 | goto LBL_MU;
|
---|
| 3337 | }
|
---|
| 3338 | if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
|
---|
| 3339 | goto LBL_MU;
|
---|
| 3340 | }
|
---|
| 3341 | }
|
---|
| 3342 |
|
---|
| 3343 | /* setup result */
|
---|
| 3344 | if ((err = mp_init (&res)) != MP_OKAY) {
|
---|
| 3345 | goto LBL_MU;
|
---|
| 3346 | }
|
---|
| 3347 | mp_set (&res, 1);
|
---|
| 3348 |
|
---|
| 3349 | /* set initial mode and bit cnt */
|
---|
| 3350 | mode = 0;
|
---|
| 3351 | bitcnt = 1;
|
---|
| 3352 | buf = 0;
|
---|
| 3353 | digidx = X->used - 1;
|
---|
| 3354 | bitcpy = 0;
|
---|
| 3355 | bitbuf = 0;
|
---|
| 3356 |
|
---|
| 3357 | for (;;) {
|
---|
| 3358 | /* grab next digit as required */
|
---|
| 3359 | if (--bitcnt == 0) {
|
---|
| 3360 | /* if digidx == -1 we are out of digits */
|
---|
| 3361 | if (digidx == -1) {
|
---|
| 3362 | break;
|
---|
| 3363 | }
|
---|
| 3364 | /* read next digit and reset the bitcnt */
|
---|
| 3365 | buf = X->dp[digidx--];
|
---|
| 3366 | bitcnt = (int) DIGIT_BIT;
|
---|
| 3367 | }
|
---|
| 3368 |
|
---|
| 3369 | /* grab the next msb from the exponent */
|
---|
| 3370 | y = (int)(buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
|
---|
| 3371 | buf <<= (mp_digit)1;
|
---|
| 3372 |
|
---|
| 3373 | /* if the bit is zero and mode == 0 then we ignore it
|
---|
| 3374 | * These represent the leading zero bits before the first 1 bit
|
---|
| 3375 | * in the exponent. Technically this opt is not required but it
|
---|
| 3376 | * does lower the # of trivial squaring/reductions used
|
---|
| 3377 | */
|
---|
| 3378 | if (mode == 0 && y == 0) {
|
---|
| 3379 | continue;
|
---|
| 3380 | }
|
---|
| 3381 |
|
---|
| 3382 | /* if the bit is zero and mode == 1 then we square */
|
---|
| 3383 | if (mode == 1 && y == 0) {
|
---|
| 3384 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 3385 | goto LBL_RES;
|
---|
| 3386 | }
|
---|
| 3387 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3388 | goto LBL_RES;
|
---|
| 3389 | }
|
---|
| 3390 | continue;
|
---|
| 3391 | }
|
---|
| 3392 |
|
---|
| 3393 | /* else we add it to the window */
|
---|
| 3394 | bitbuf |= (y << (winsize - ++bitcpy));
|
---|
| 3395 | mode = 2;
|
---|
| 3396 |
|
---|
| 3397 | if (bitcpy == winsize) {
|
---|
| 3398 | /* ok window is filled so square as required and multiply */
|
---|
| 3399 | /* square first */
|
---|
| 3400 | for (x = 0; x < winsize; x++) {
|
---|
| 3401 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 3402 | goto LBL_RES;
|
---|
| 3403 | }
|
---|
| 3404 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3405 | goto LBL_RES;
|
---|
| 3406 | }
|
---|
| 3407 | }
|
---|
| 3408 |
|
---|
| 3409 | /* then multiply */
|
---|
| 3410 | if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
---|
| 3411 | goto LBL_RES;
|
---|
| 3412 | }
|
---|
| 3413 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3414 | goto LBL_RES;
|
---|
| 3415 | }
|
---|
| 3416 |
|
---|
| 3417 | /* empty window and reset */
|
---|
| 3418 | bitcpy = 0;
|
---|
| 3419 | bitbuf = 0;
|
---|
| 3420 | mode = 1;
|
---|
| 3421 | }
|
---|
| 3422 | }
|
---|
| 3423 |
|
---|
| 3424 | /* if bits remain then square/multiply */
|
---|
| 3425 | if (mode == 2 && bitcpy > 0) {
|
---|
| 3426 | /* square then multiply if the bit is set */
|
---|
| 3427 | for (x = 0; x < bitcpy; x++) {
|
---|
| 3428 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 3429 | goto LBL_RES;
|
---|
| 3430 | }
|
---|
| 3431 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3432 | goto LBL_RES;
|
---|
| 3433 | }
|
---|
| 3434 |
|
---|
| 3435 | bitbuf <<= 1;
|
---|
| 3436 | if ((bitbuf & (1 << winsize)) != 0) {
|
---|
| 3437 | /* then multiply */
|
---|
| 3438 | if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
|
---|
| 3439 | goto LBL_RES;
|
---|
| 3440 | }
|
---|
| 3441 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3442 | goto LBL_RES;
|
---|
| 3443 | }
|
---|
| 3444 | }
|
---|
| 3445 | }
|
---|
| 3446 | }
|
---|
| 3447 |
|
---|
| 3448 | mp_exch (&res, Y);
|
---|
| 3449 | err = MP_OKAY;
|
---|
| 3450 | LBL_RES:mp_clear (&res);
|
---|
| 3451 | LBL_MU:mp_clear (&mu);
|
---|
| 3452 | LBL_M:
|
---|
| 3453 | mp_clear(&M[1]);
|
---|
| 3454 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 3455 | mp_clear (&M[x]);
|
---|
| 3456 | }
|
---|
| 3457 | return err;
|
---|
| 3458 | }
|
---|
| 3459 |
|
---|
| 3460 |
|
---|
| 3461 | /* pre-calculate the value required for Barrett reduction
|
---|
| 3462 | * For a given modulus "b" it calulates the value required in "a"
|
---|
| 3463 | */
|
---|
| 3464 | int mp_reduce_setup (mp_int * a, mp_int * b)
|
---|
| 3465 | {
|
---|
| 3466 | int res;
|
---|
| 3467 |
|
---|
| 3468 | if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
|
---|
| 3469 | return res;
|
---|
| 3470 | }
|
---|
| 3471 | return mp_div (a, b, a, NULL);
|
---|
| 3472 | }
|
---|
| 3473 |
|
---|
| 3474 |
|
---|
| 3475 | /* reduces x mod m, assumes 0 < x < m**2, mu is
|
---|
| 3476 | * precomputed via mp_reduce_setup.
|
---|
| 3477 | * From HAC pp.604 Algorithm 14.42
|
---|
| 3478 | */
|
---|
| 3479 | int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
|
---|
| 3480 | {
|
---|
| 3481 | mp_int q;
|
---|
| 3482 | int res, um = m->used;
|
---|
| 3483 |
|
---|
| 3484 | /* q = x */
|
---|
| 3485 | if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
|
---|
| 3486 | return res;
|
---|
| 3487 | }
|
---|
| 3488 |
|
---|
| 3489 | /* q1 = x / b**(k-1) */
|
---|
| 3490 | mp_rshd (&q, um - 1);
|
---|
| 3491 |
|
---|
| 3492 | /* according to HAC this optimization is ok */
|
---|
| 3493 | if (((mp_word) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
|
---|
| 3494 | if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
|
---|
| 3495 | goto CLEANUP;
|
---|
| 3496 | }
|
---|
| 3497 | } else {
|
---|
| 3498 | #ifdef BN_S_MP_MUL_HIGH_DIGS_C
|
---|
| 3499 | if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
|
---|
| 3500 | goto CLEANUP;
|
---|
| 3501 | }
|
---|
| 3502 | #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
|
---|
| 3503 | if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
|
---|
| 3504 | goto CLEANUP;
|
---|
| 3505 | }
|
---|
| 3506 | #else
|
---|
| 3507 | {
|
---|
| 3508 | res = MP_VAL;
|
---|
| 3509 | goto CLEANUP;
|
---|
| 3510 | }
|
---|
| 3511 | #endif
|
---|
| 3512 | }
|
---|
| 3513 |
|
---|
| 3514 | /* q3 = q2 / b**(k+1) */
|
---|
| 3515 | mp_rshd (&q, um + 1);
|
---|
| 3516 |
|
---|
| 3517 | /* x = x mod b**(k+1), quick (no division) */
|
---|
| 3518 | if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
|
---|
| 3519 | goto CLEANUP;
|
---|
| 3520 | }
|
---|
| 3521 |
|
---|
| 3522 | /* q = q * m mod b**(k+1), quick (no division) */
|
---|
| 3523 | if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
|
---|
| 3524 | goto CLEANUP;
|
---|
| 3525 | }
|
---|
| 3526 |
|
---|
| 3527 | /* x = x - q */
|
---|
| 3528 | if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
|
---|
| 3529 | goto CLEANUP;
|
---|
| 3530 | }
|
---|
| 3531 |
|
---|
| 3532 | /* If x < 0, add b**(k+1) to it */
|
---|
| 3533 | if (mp_cmp_d (x, 0) == MP_LT) {
|
---|
| 3534 | mp_set (&q, 1);
|
---|
| 3535 | if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
|
---|
| 3536 | goto CLEANUP;
|
---|
| 3537 | if ((res = mp_add (x, &q, x)) != MP_OKAY)
|
---|
| 3538 | goto CLEANUP;
|
---|
| 3539 | }
|
---|
| 3540 |
|
---|
| 3541 | /* Back off if it's too big */
|
---|
| 3542 | while (mp_cmp (x, m) != MP_LT) {
|
---|
| 3543 | if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
|
---|
| 3544 | goto CLEANUP;
|
---|
| 3545 | }
|
---|
| 3546 | }
|
---|
| 3547 |
|
---|
| 3548 | CLEANUP:
|
---|
| 3549 | mp_clear (&q);
|
---|
| 3550 |
|
---|
| 3551 | return res;
|
---|
| 3552 | }
|
---|
| 3553 |
|
---|
| 3554 |
|
---|
| 3555 | /* reduces a modulo n where n is of the form 2**p - d
|
---|
| 3556 | This differs from reduce_2k since "d" can be larger
|
---|
| 3557 | than a single digit.
|
---|
| 3558 | */
|
---|
| 3559 | int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
|
---|
| 3560 | {
|
---|
| 3561 | mp_int q;
|
---|
| 3562 | int p, res;
|
---|
| 3563 |
|
---|
| 3564 | if ((res = mp_init(&q)) != MP_OKAY) {
|
---|
| 3565 | return res;
|
---|
| 3566 | }
|
---|
| 3567 |
|
---|
| 3568 | p = mp_count_bits(n);
|
---|
| 3569 | top:
|
---|
| 3570 | /* q = a/2**p, a = a mod 2**p */
|
---|
| 3571 | if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
|
---|
| 3572 | goto ERR;
|
---|
| 3573 | }
|
---|
| 3574 |
|
---|
| 3575 | /* q = q * d */
|
---|
| 3576 | if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
|
---|
| 3577 | goto ERR;
|
---|
| 3578 | }
|
---|
| 3579 |
|
---|
| 3580 | /* a = a + q */
|
---|
| 3581 | if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
|
---|
| 3582 | goto ERR;
|
---|
| 3583 | }
|
---|
| 3584 |
|
---|
| 3585 | if (mp_cmp_mag(a, n) != MP_LT) {
|
---|
| 3586 | s_mp_sub(a, n, a);
|
---|
| 3587 | goto top;
|
---|
| 3588 | }
|
---|
| 3589 |
|
---|
| 3590 | ERR:
|
---|
| 3591 | mp_clear(&q);
|
---|
| 3592 | return res;
|
---|
| 3593 | }
|
---|
| 3594 |
|
---|
| 3595 |
|
---|
| 3596 | /* determines the setup value */
|
---|
| 3597 | int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
|
---|
| 3598 | {
|
---|
| 3599 | int res;
|
---|
| 3600 | mp_int tmp;
|
---|
| 3601 |
|
---|
| 3602 | if ((res = mp_init(&tmp)) != MP_OKAY) {
|
---|
| 3603 | return res;
|
---|
| 3604 | }
|
---|
| 3605 |
|
---|
| 3606 | if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
|
---|
| 3607 | goto ERR;
|
---|
| 3608 | }
|
---|
| 3609 |
|
---|
| 3610 | if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
|
---|
| 3611 | goto ERR;
|
---|
| 3612 | }
|
---|
| 3613 |
|
---|
| 3614 | ERR:
|
---|
| 3615 | mp_clear(&tmp);
|
---|
| 3616 | return res;
|
---|
| 3617 | }
|
---|
| 3618 |
|
---|
| 3619 |
|
---|
| 3620 | /* multiplies |a| * |b| and does not compute the lower digs digits
|
---|
| 3621 | * [meant to get the higher part of the product]
|
---|
| 3622 | */
|
---|
| 3623 | int
|
---|
| 3624 | s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 3625 | {
|
---|
| 3626 | mp_int t;
|
---|
| 3627 | int res, pa, pb, ix, iy;
|
---|
| 3628 | mp_digit u;
|
---|
| 3629 | mp_word r;
|
---|
| 3630 | mp_digit tmpx, *tmpt, *tmpy;
|
---|
| 3631 |
|
---|
| 3632 | /* can we use the fast multiplier? */
|
---|
| 3633 | #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
|
---|
| 3634 | if (((a->used + b->used + 1) < MP_WARRAY)
|
---|
| 3635 | && MIN (a->used, b->used) <
|
---|
| 3636 | (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
| 3637 | return fast_s_mp_mul_high_digs (a, b, c, digs);
|
---|
| 3638 | }
|
---|
| 3639 | #endif
|
---|
| 3640 |
|
---|
| 3641 | if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
|
---|
| 3642 | return res;
|
---|
| 3643 | }
|
---|
| 3644 | t.used = a->used + b->used + 1;
|
---|
| 3645 |
|
---|
| 3646 | pa = a->used;
|
---|
| 3647 | pb = b->used;
|
---|
| 3648 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3649 | /* clear the carry */
|
---|
| 3650 | u = 0;
|
---|
| 3651 |
|
---|
| 3652 | /* left hand side of A[ix] * B[iy] */
|
---|
| 3653 | tmpx = a->dp[ix];
|
---|
| 3654 |
|
---|
| 3655 | /* alias to the address of where the digits will be stored */
|
---|
| 3656 | tmpt = &(t.dp[digs]);
|
---|
| 3657 |
|
---|
| 3658 | /* alias for where to read the right hand side from */
|
---|
| 3659 | tmpy = b->dp + (digs - ix);
|
---|
| 3660 |
|
---|
| 3661 | for (iy = digs - ix; iy < pb; iy++) {
|
---|
| 3662 | /* calculate the double precision result */
|
---|
| 3663 | r = ((mp_word)*tmpt) +
|
---|
| 3664 | ((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
---|
| 3665 | ((mp_word) u);
|
---|
| 3666 |
|
---|
| 3667 | /* get the lower part */
|
---|
| 3668 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3669 |
|
---|
| 3670 | /* carry the carry */
|
---|
| 3671 | u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
---|
| 3672 | }
|
---|
| 3673 | *tmpt = u;
|
---|
| 3674 | }
|
---|
| 3675 | mp_clamp (&t);
|
---|
| 3676 | mp_exch (&t, c);
|
---|
| 3677 | mp_clear (&t);
|
---|
| 3678 | return MP_OKAY;
|
---|
| 3679 | }
|
---|
| 3680 |
|
---|
| 3681 |
|
---|
| 3682 | /* this is a modified version of fast_s_mul_digs that only produces
|
---|
| 3683 | * output digits *above* digs. See the comments for fast_s_mul_digs
|
---|
| 3684 | * to see how it works.
|
---|
| 3685 | *
|
---|
| 3686 | * This is used in the Barrett reduction since for one of the multiplications
|
---|
| 3687 | * only the higher digits were needed. This essentially halves the work.
|
---|
| 3688 | *
|
---|
| 3689 | * Based on Algorithm 14.12 on pp.595 of HAC.
|
---|
| 3690 | */
|
---|
| 3691 | int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 3692 | {
|
---|
| 3693 | int olduse, res, pa, ix, iz;
|
---|
| 3694 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3695 | mp_digit* W; /* uses dynamic memory and slower */
|
---|
| 3696 | #else
|
---|
| 3697 | mp_digit W[MP_WARRAY];
|
---|
| 3698 | #endif
|
---|
| 3699 | mp_word _W;
|
---|
| 3700 |
|
---|
| 3701 | /* grow the destination as required */
|
---|
| 3702 | pa = a->used + b->used;
|
---|
| 3703 | if (c->alloc < pa) {
|
---|
| 3704 | if ((res = mp_grow (c, pa)) != MP_OKAY) {
|
---|
| 3705 | return res;
|
---|
| 3706 | }
|
---|
| 3707 | }
|
---|
| 3708 |
|
---|
| 3709 | if (pa > MP_WARRAY)
|
---|
| 3710 | return MP_RANGE; /* TAO range check */
|
---|
| 3711 |
|
---|
| 3712 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3713 | W = (mp_digit*)XMALLOC(sizeof(mp_digit) * MP_WARRAY, 0, DYNAMIC_TYPE_BIGINT);
|
---|
| 3714 | if (W == NULL)
|
---|
| 3715 | return MP_MEM;
|
---|
| 3716 | #endif
|
---|
| 3717 |
|
---|
| 3718 | /* number of output digits to produce */
|
---|
| 3719 | pa = a->used + b->used;
|
---|
| 3720 | _W = 0;
|
---|
| 3721 | for (ix = digs; ix < pa; ix++) {
|
---|
| 3722 | int tx, ty, iy;
|
---|
| 3723 | mp_digit *tmpx, *tmpy;
|
---|
| 3724 |
|
---|
| 3725 | /* get offsets into the two bignums */
|
---|
| 3726 | ty = MIN(b->used-1, ix);
|
---|
| 3727 | tx = ix - ty;
|
---|
| 3728 |
|
---|
| 3729 | /* setup temp aliases */
|
---|
| 3730 | tmpx = a->dp + tx;
|
---|
| 3731 | tmpy = b->dp + ty;
|
---|
| 3732 |
|
---|
| 3733 | /* this is the number of times the loop will iterrate, essentially its
|
---|
| 3734 | while (tx++ < a->used && ty-- >= 0) { ... }
|
---|
| 3735 | */
|
---|
| 3736 | iy = MIN(a->used-tx, ty+1);
|
---|
| 3737 |
|
---|
| 3738 | /* execute loop */
|
---|
| 3739 | for (iz = 0; iz < iy; iz++) {
|
---|
| 3740 | _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
---|
| 3741 | }
|
---|
| 3742 |
|
---|
| 3743 | /* store term */
|
---|
| 3744 | W[ix] = ((mp_digit)_W) & MP_MASK;
|
---|
| 3745 |
|
---|
| 3746 | /* make next carry */
|
---|
| 3747 | _W = _W >> ((mp_word)DIGIT_BIT);
|
---|
| 3748 | }
|
---|
| 3749 |
|
---|
| 3750 | /* setup dest */
|
---|
| 3751 | olduse = c->used;
|
---|
| 3752 | c->used = pa;
|
---|
| 3753 |
|
---|
| 3754 | {
|
---|
| 3755 | register mp_digit *tmpc;
|
---|
| 3756 |
|
---|
| 3757 | tmpc = c->dp + digs;
|
---|
| 3758 | for (ix = digs; ix <= pa; ix++) {
|
---|
| 3759 | /* now extract the previous digit [below the carry] */
|
---|
| 3760 | *tmpc++ = W[ix];
|
---|
| 3761 | }
|
---|
| 3762 |
|
---|
| 3763 | /* clear unused digits [that existed in the old copy of c] */
|
---|
| 3764 | for (; ix < olduse; ix++) {
|
---|
| 3765 | *tmpc++ = 0;
|
---|
| 3766 | }
|
---|
| 3767 | }
|
---|
| 3768 | mp_clamp (c);
|
---|
| 3769 |
|
---|
| 3770 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3771 | XFREE(W, 0, DYNAMIC_TYPE_BIGINT);
|
---|
| 3772 | #endif
|
---|
| 3773 |
|
---|
| 3774 | return MP_OKAY;
|
---|
| 3775 | }
|
---|
| 3776 |
|
---|
| 3777 |
|
---|
| 3778 | /* set a 32-bit const */
|
---|
| 3779 | int mp_set_int (mp_int * a, unsigned long b)
|
---|
| 3780 | {
|
---|
| 3781 | int x, res;
|
---|
| 3782 |
|
---|
| 3783 | mp_zero (a);
|
---|
| 3784 |
|
---|
| 3785 | /* set four bits at a time */
|
---|
| 3786 | for (x = 0; x < 8; x++) {
|
---|
| 3787 | /* shift the number up four bits */
|
---|
| 3788 | if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) {
|
---|
| 3789 | return res;
|
---|
| 3790 | }
|
---|
| 3791 |
|
---|
| 3792 | /* OR in the top four bits of the source */
|
---|
| 3793 | a->dp[0] |= (b >> 28) & 15;
|
---|
| 3794 |
|
---|
| 3795 | /* shift the source up to the next four bits */
|
---|
| 3796 | b <<= 4;
|
---|
| 3797 |
|
---|
| 3798 | /* ensure that digits are not clamped off */
|
---|
| 3799 | a->used += 1;
|
---|
| 3800 | }
|
---|
| 3801 | mp_clamp (a);
|
---|
| 3802 | return MP_OKAY;
|
---|
| 3803 | }
|
---|
| 3804 |
|
---|
| 3805 |
|
---|
| 3806 | #if defined(WOLFSSL_KEY_GEN) || defined(HAVE_ECC)
|
---|
| 3807 |
|
---|
| 3808 | /* c = a * a (mod b) */
|
---|
| 3809 | int mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 3810 | {
|
---|
| 3811 | int res;
|
---|
| 3812 | mp_int t;
|
---|
| 3813 |
|
---|
| 3814 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
| 3815 | return res;
|
---|
| 3816 | }
|
---|
| 3817 |
|
---|
| 3818 | if ((res = mp_sqr (a, &t)) != MP_OKAY) {
|
---|
| 3819 | mp_clear (&t);
|
---|
| 3820 | return res;
|
---|
| 3821 | }
|
---|
| 3822 | res = mp_mod (&t, b, c);
|
---|
| 3823 | mp_clear (&t);
|
---|
| 3824 | return res;
|
---|
| 3825 | }
|
---|
| 3826 |
|
---|
| 3827 | #endif
|
---|
| 3828 |
|
---|
| 3829 |
|
---|
| 3830 | #if defined(HAVE_ECC) || !defined(NO_PWDBASED) || defined(WOLFSSL_SNIFFER) || \
|
---|
| 3831 | defined(WOLFSSL_HAVE_WOLFSCEP) || defined(WOLFSSL_KEY_GEN)
|
---|
| 3832 |
|
---|
| 3833 | /* single digit addition */
|
---|
| 3834 | int mp_add_d (mp_int* a, mp_digit b, mp_int* c)
|
---|
| 3835 | {
|
---|
| 3836 | int res, ix, oldused;
|
---|
| 3837 | mp_digit *tmpa, *tmpc, mu;
|
---|
| 3838 |
|
---|
| 3839 | /* grow c as required */
|
---|
| 3840 | if (c->alloc < a->used + 1) {
|
---|
| 3841 | if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
---|
| 3842 | return res;
|
---|
| 3843 | }
|
---|
| 3844 | }
|
---|
| 3845 |
|
---|
| 3846 | /* if a is negative and |a| >= b, call c = |a| - b */
|
---|
| 3847 | if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
|
---|
| 3848 | /* temporarily fix sign of a */
|
---|
| 3849 | a->sign = MP_ZPOS;
|
---|
| 3850 |
|
---|
| 3851 | /* c = |a| - b */
|
---|
| 3852 | res = mp_sub_d(a, b, c);
|
---|
| 3853 |
|
---|
| 3854 | /* fix sign */
|
---|
| 3855 | a->sign = c->sign = MP_NEG;
|
---|
| 3856 |
|
---|
| 3857 | /* clamp */
|
---|
| 3858 | mp_clamp(c);
|
---|
| 3859 |
|
---|
| 3860 | return res;
|
---|
| 3861 | }
|
---|
| 3862 |
|
---|
| 3863 | /* old number of used digits in c */
|
---|
| 3864 | oldused = c->used;
|
---|
| 3865 |
|
---|
| 3866 | /* sign always positive */
|
---|
| 3867 | c->sign = MP_ZPOS;
|
---|
| 3868 |
|
---|
| 3869 | /* source alias */
|
---|
| 3870 | tmpa = a->dp;
|
---|
| 3871 |
|
---|
| 3872 | /* destination alias */
|
---|
| 3873 | tmpc = c->dp;
|
---|
| 3874 |
|
---|
| 3875 | /* if a is positive */
|
---|
| 3876 | if (a->sign == MP_ZPOS) {
|
---|
| 3877 | /* add digit, after this we're propagating
|
---|
| 3878 | * the carry.
|
---|
| 3879 | */
|
---|
| 3880 | *tmpc = *tmpa++ + b;
|
---|
| 3881 | mu = *tmpc >> DIGIT_BIT;
|
---|
| 3882 | *tmpc++ &= MP_MASK;
|
---|
| 3883 |
|
---|
| 3884 | /* now handle rest of the digits */
|
---|
| 3885 | for (ix = 1; ix < a->used; ix++) {
|
---|
| 3886 | *tmpc = *tmpa++ + mu;
|
---|
| 3887 | mu = *tmpc >> DIGIT_BIT;
|
---|
| 3888 | *tmpc++ &= MP_MASK;
|
---|
| 3889 | }
|
---|
| 3890 | /* set final carry */
|
---|
| 3891 | if (ix < c->alloc) {
|
---|
| 3892 | ix++;
|
---|
| 3893 | *tmpc++ = mu;
|
---|
| 3894 | }
|
---|
| 3895 |
|
---|
| 3896 | /* setup size */
|
---|
| 3897 | c->used = a->used + 1;
|
---|
| 3898 | } else {
|
---|
| 3899 | /* a was negative and |a| < b */
|
---|
| 3900 | c->used = 1;
|
---|
| 3901 |
|
---|
| 3902 | /* the result is a single digit */
|
---|
| 3903 | if (a->used == 1) {
|
---|
| 3904 | *tmpc++ = b - a->dp[0];
|
---|
| 3905 | } else {
|
---|
| 3906 | *tmpc++ = b;
|
---|
| 3907 | }
|
---|
| 3908 |
|
---|
| 3909 | /* setup count so the clearing of oldused
|
---|
| 3910 | * can fall through correctly
|
---|
| 3911 | */
|
---|
| 3912 | ix = 1;
|
---|
| 3913 | }
|
---|
| 3914 |
|
---|
| 3915 | /* now zero to oldused */
|
---|
| 3916 | while (ix++ < oldused) {
|
---|
| 3917 | *tmpc++ = 0;
|
---|
| 3918 | }
|
---|
| 3919 | mp_clamp(c);
|
---|
| 3920 |
|
---|
| 3921 | return MP_OKAY;
|
---|
| 3922 | }
|
---|
| 3923 |
|
---|
| 3924 |
|
---|
| 3925 | /* single digit subtraction */
|
---|
| 3926 | int mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
|
---|
| 3927 | {
|
---|
| 3928 | mp_digit *tmpa, *tmpc, mu;
|
---|
| 3929 | int res, ix, oldused;
|
---|
| 3930 |
|
---|
| 3931 | /* grow c as required */
|
---|
| 3932 | if (c->alloc < a->used + 1) {
|
---|
| 3933 | if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
---|
| 3934 | return res;
|
---|
| 3935 | }
|
---|
| 3936 | }
|
---|
| 3937 |
|
---|
| 3938 | /* if a is negative just do an unsigned
|
---|
| 3939 | * addition [with fudged signs]
|
---|
| 3940 | */
|
---|
| 3941 | if (a->sign == MP_NEG) {
|
---|
| 3942 | a->sign = MP_ZPOS;
|
---|
| 3943 | res = mp_add_d(a, b, c);
|
---|
| 3944 | a->sign = c->sign = MP_NEG;
|
---|
| 3945 |
|
---|
| 3946 | /* clamp */
|
---|
| 3947 | mp_clamp(c);
|
---|
| 3948 |
|
---|
| 3949 | return res;
|
---|
| 3950 | }
|
---|
| 3951 |
|
---|
| 3952 | /* setup regs */
|
---|
| 3953 | oldused = c->used;
|
---|
| 3954 | tmpa = a->dp;
|
---|
| 3955 | tmpc = c->dp;
|
---|
| 3956 |
|
---|
| 3957 | /* if a <= b simply fix the single digit */
|
---|
| 3958 | if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
|
---|
| 3959 | if (a->used == 1) {
|
---|
| 3960 | *tmpc++ = b - *tmpa;
|
---|
| 3961 | } else {
|
---|
| 3962 | *tmpc++ = b;
|
---|
| 3963 | }
|
---|
| 3964 | ix = 1;
|
---|
| 3965 |
|
---|
| 3966 | /* negative/1digit */
|
---|
| 3967 | c->sign = MP_NEG;
|
---|
| 3968 | c->used = 1;
|
---|
| 3969 | } else {
|
---|
| 3970 | /* positive/size */
|
---|
| 3971 | c->sign = MP_ZPOS;
|
---|
| 3972 | c->used = a->used;
|
---|
| 3973 |
|
---|
| 3974 | /* subtract first digit */
|
---|
| 3975 | *tmpc = *tmpa++ - b;
|
---|
| 3976 | mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
|
---|
| 3977 | *tmpc++ &= MP_MASK;
|
---|
| 3978 |
|
---|
| 3979 | /* handle rest of the digits */
|
---|
| 3980 | for (ix = 1; ix < a->used; ix++) {
|
---|
| 3981 | *tmpc = *tmpa++ - mu;
|
---|
| 3982 | mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
|
---|
| 3983 | *tmpc++ &= MP_MASK;
|
---|
| 3984 | }
|
---|
| 3985 | }
|
---|
| 3986 |
|
---|
| 3987 | /* zero excess digits */
|
---|
| 3988 | while (ix++ < oldused) {
|
---|
| 3989 | *tmpc++ = 0;
|
---|
| 3990 | }
|
---|
| 3991 | mp_clamp(c);
|
---|
| 3992 | return MP_OKAY;
|
---|
| 3993 | }
|
---|
| 3994 |
|
---|
| 3995 | #endif /* defined(HAVE_ECC) || !defined(NO_PWDBASED) */
|
---|
| 3996 |
|
---|
| 3997 |
|
---|
| 3998 | #if defined(WOLFSSL_KEY_GEN) || defined(HAVE_COMP_KEY) || defined(HAVE_ECC)
|
---|
| 3999 |
|
---|
| 4000 | static const int lnz[16] = {
|
---|
| 4001 | 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
|
---|
| 4002 | };
|
---|
| 4003 |
|
---|
| 4004 | /* Counts the number of lsbs which are zero before the first zero bit */
|
---|
| 4005 | int mp_cnt_lsb(mp_int *a)
|
---|
| 4006 | {
|
---|
| 4007 | int x;
|
---|
| 4008 | mp_digit q, qq;
|
---|
| 4009 |
|
---|
| 4010 | /* easy out */
|
---|
| 4011 | if (mp_iszero(a) == 1) {
|
---|
| 4012 | return 0;
|
---|
| 4013 | }
|
---|
| 4014 |
|
---|
| 4015 | /* scan lower digits until non-zero */
|
---|
| 4016 | for (x = 0; x < a->used && a->dp[x] == 0; x++);
|
---|
| 4017 | q = a->dp[x];
|
---|
| 4018 | x *= DIGIT_BIT;
|
---|
| 4019 |
|
---|
| 4020 | /* now scan this digit until a 1 is found */
|
---|
| 4021 | if ((q & 1) == 0) {
|
---|
| 4022 | do {
|
---|
| 4023 | qq = q & 15;
|
---|
| 4024 | x += lnz[qq];
|
---|
| 4025 | q >>= 4;
|
---|
| 4026 | } while (qq == 0);
|
---|
| 4027 | }
|
---|
| 4028 | return x;
|
---|
| 4029 | }
|
---|
| 4030 |
|
---|
| 4031 |
|
---|
| 4032 |
|
---|
| 4033 |
|
---|
| 4034 | static int s_is_power_of_two(mp_digit b, int *p)
|
---|
| 4035 | {
|
---|
| 4036 | int x;
|
---|
| 4037 |
|
---|
| 4038 | /* fast return if no power of two */
|
---|
| 4039 | if ((b==0) || (b & (b-1))) {
|
---|
| 4040 | return 0;
|
---|
| 4041 | }
|
---|
| 4042 |
|
---|
| 4043 | for (x = 0; x < DIGIT_BIT; x++) {
|
---|
| 4044 | if (b == (((mp_digit)1)<<x)) {
|
---|
| 4045 | *p = x;
|
---|
| 4046 | return 1;
|
---|
| 4047 | }
|
---|
| 4048 | }
|
---|
| 4049 | return 0;
|
---|
| 4050 | }
|
---|
| 4051 |
|
---|
| 4052 | /* single digit division (based on routine from MPI) */
|
---|
| 4053 | static int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
|
---|
| 4054 | {
|
---|
| 4055 | mp_int q;
|
---|
| 4056 | mp_word w;
|
---|
| 4057 | mp_digit t;
|
---|
| 4058 | int res = MP_OKAY, ix;
|
---|
| 4059 |
|
---|
| 4060 | /* cannot divide by zero */
|
---|
| 4061 | if (b == 0) {
|
---|
| 4062 | return MP_VAL;
|
---|
| 4063 | }
|
---|
| 4064 |
|
---|
| 4065 | /* quick outs */
|
---|
| 4066 | if (b == 1 || mp_iszero(a) == 1) {
|
---|
| 4067 | if (d != NULL) {
|
---|
| 4068 | *d = 0;
|
---|
| 4069 | }
|
---|
| 4070 | if (c != NULL) {
|
---|
| 4071 | return mp_copy(a, c);
|
---|
| 4072 | }
|
---|
| 4073 | return MP_OKAY;
|
---|
| 4074 | }
|
---|
| 4075 |
|
---|
| 4076 | /* power of two ? */
|
---|
| 4077 | if (s_is_power_of_two(b, &ix) == 1) {
|
---|
| 4078 | if (d != NULL) {
|
---|
| 4079 | *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
|
---|
| 4080 | }
|
---|
| 4081 | if (c != NULL) {
|
---|
| 4082 | return mp_div_2d(a, ix, c, NULL);
|
---|
| 4083 | }
|
---|
| 4084 | return MP_OKAY;
|
---|
| 4085 | }
|
---|
| 4086 |
|
---|
| 4087 | #ifdef BN_MP_DIV_3_C
|
---|
| 4088 | /* three? */
|
---|
| 4089 | if (b == 3) {
|
---|
| 4090 | return mp_div_3(a, c, d);
|
---|
| 4091 | }
|
---|
| 4092 | #endif
|
---|
| 4093 |
|
---|
| 4094 | /* no easy answer [c'est la vie]. Just division */
|
---|
| 4095 | if (c != NULL) {
|
---|
| 4096 | if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
|
---|
| 4097 | return res;
|
---|
| 4098 | }
|
---|
| 4099 |
|
---|
| 4100 | q.used = a->used;
|
---|
| 4101 | q.sign = a->sign;
|
---|
| 4102 | }
|
---|
| 4103 |
|
---|
| 4104 | w = 0;
|
---|
| 4105 | for (ix = a->used - 1; ix >= 0; ix--) {
|
---|
| 4106 | w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
|
---|
| 4107 |
|
---|
| 4108 | if (w >= b) {
|
---|
| 4109 | t = (mp_digit)(w / b);
|
---|
| 4110 | w -= ((mp_word)t) * ((mp_word)b);
|
---|
| 4111 | } else {
|
---|
| 4112 | t = 0;
|
---|
| 4113 | }
|
---|
| 4114 | if (c != NULL)
|
---|
| 4115 | q.dp[ix] = (mp_digit)t;
|
---|
| 4116 | }
|
---|
| 4117 |
|
---|
| 4118 | if (d != NULL) {
|
---|
| 4119 | *d = (mp_digit)w;
|
---|
| 4120 | }
|
---|
| 4121 |
|
---|
| 4122 | if (c != NULL) {
|
---|
| 4123 | mp_clamp(&q);
|
---|
| 4124 | mp_exch(&q, c);
|
---|
| 4125 | mp_clear(&q);
|
---|
| 4126 | }
|
---|
| 4127 |
|
---|
| 4128 | return res;
|
---|
| 4129 | }
|
---|
| 4130 |
|
---|
| 4131 |
|
---|
| 4132 | int mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
|
---|
| 4133 | {
|
---|
| 4134 | return mp_div_d(a, b, NULL, c);
|
---|
| 4135 | }
|
---|
| 4136 |
|
---|
| 4137 | #endif /* defined(WOLFSSL_KEY_GEN)||defined(HAVE_COMP_KEY)||defined(HAVE_ECC) */
|
---|
| 4138 |
|
---|
| 4139 | #ifdef WOLFSSL_KEY_GEN
|
---|
| 4140 |
|
---|
| 4141 | const mp_digit ltm_prime_tab[] = {
|
---|
| 4142 | 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
|
---|
| 4143 | 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
|
---|
| 4144 | 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
|
---|
| 4145 | 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
|
---|
| 4146 | #ifndef MP_8BIT
|
---|
| 4147 | 0x0083,
|
---|
| 4148 | 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
|
---|
| 4149 | 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
|
---|
| 4150 | 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
|
---|
| 4151 | 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
|
---|
| 4152 |
|
---|
| 4153 | 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
|
---|
| 4154 | 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
|
---|
| 4155 | 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
|
---|
| 4156 | 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
|
---|
| 4157 | 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
|
---|
| 4158 | 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
|
---|
| 4159 | 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
|
---|
| 4160 | 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
|
---|
| 4161 |
|
---|
| 4162 | 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
|
---|
| 4163 | 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
|
---|
| 4164 | 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
|
---|
| 4165 | 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
|
---|
| 4166 | 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
|
---|
| 4167 | 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
|
---|
| 4168 | 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
|
---|
| 4169 | 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
|
---|
| 4170 |
|
---|
| 4171 | 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
|
---|
| 4172 | 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
|
---|
| 4173 | 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
|
---|
| 4174 | 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
|
---|
| 4175 | 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
|
---|
| 4176 | 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
|
---|
| 4177 | 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
|
---|
| 4178 | 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
|
---|
| 4179 | #endif
|
---|
| 4180 | };
|
---|
| 4181 |
|
---|
| 4182 |
|
---|
| 4183 | /* Miller-Rabin test of "a" to the base of "b" as described in
|
---|
| 4184 | * HAC pp. 139 Algorithm 4.24
|
---|
| 4185 | *
|
---|
| 4186 | * Sets result to 0 if definitely composite or 1 if probably prime.
|
---|
| 4187 | * Randomly the chance of error is no more than 1/4 and often
|
---|
| 4188 | * very much lower.
|
---|
| 4189 | */
|
---|
| 4190 | static int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
|
---|
| 4191 | {
|
---|
| 4192 | mp_int n1, y, r;
|
---|
| 4193 | int s, j, err;
|
---|
| 4194 |
|
---|
| 4195 | /* default */
|
---|
| 4196 | *result = MP_NO;
|
---|
| 4197 |
|
---|
| 4198 | /* ensure b > 1 */
|
---|
| 4199 | if (mp_cmp_d(b, 1) != MP_GT) {
|
---|
| 4200 | return MP_VAL;
|
---|
| 4201 | }
|
---|
| 4202 |
|
---|
| 4203 | /* get n1 = a - 1 */
|
---|
| 4204 | if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
|
---|
| 4205 | return err;
|
---|
| 4206 | }
|
---|
| 4207 | if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
|
---|
| 4208 | goto LBL_N1;
|
---|
| 4209 | }
|
---|
| 4210 |
|
---|
| 4211 | /* set 2**s * r = n1 */
|
---|
| 4212 | if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
|
---|
| 4213 | goto LBL_N1;
|
---|
| 4214 | }
|
---|
| 4215 |
|
---|
| 4216 | /* count the number of least significant bits
|
---|
| 4217 | * which are zero
|
---|
| 4218 | */
|
---|
| 4219 | s = mp_cnt_lsb(&r);
|
---|
| 4220 |
|
---|
| 4221 | /* now divide n - 1 by 2**s */
|
---|
| 4222 | if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
|
---|
| 4223 | goto LBL_R;
|
---|
| 4224 | }
|
---|
| 4225 |
|
---|
| 4226 | /* compute y = b**r mod a */
|
---|
| 4227 | if ((err = mp_init (&y)) != MP_OKAY) {
|
---|
| 4228 | goto LBL_R;
|
---|
| 4229 | }
|
---|
| 4230 | if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
|
---|
| 4231 | goto LBL_Y;
|
---|
| 4232 | }
|
---|
| 4233 |
|
---|
| 4234 | /* if y != 1 and y != n1 do */
|
---|
| 4235 | if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
|
---|
| 4236 | j = 1;
|
---|
| 4237 | /* while j <= s-1 and y != n1 */
|
---|
| 4238 | while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
|
---|
| 4239 | if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
|
---|
| 4240 | goto LBL_Y;
|
---|
| 4241 | }
|
---|
| 4242 |
|
---|
| 4243 | /* if y == 1 then composite */
|
---|
| 4244 | if (mp_cmp_d (&y, 1) == MP_EQ) {
|
---|
| 4245 | goto LBL_Y;
|
---|
| 4246 | }
|
---|
| 4247 |
|
---|
| 4248 | ++j;
|
---|
| 4249 | }
|
---|
| 4250 |
|
---|
| 4251 | /* if y != n1 then composite */
|
---|
| 4252 | if (mp_cmp (&y, &n1) != MP_EQ) {
|
---|
| 4253 | goto LBL_Y;
|
---|
| 4254 | }
|
---|
| 4255 | }
|
---|
| 4256 |
|
---|
| 4257 | /* probably prime now */
|
---|
| 4258 | *result = MP_YES;
|
---|
| 4259 | LBL_Y:mp_clear (&y);
|
---|
| 4260 | LBL_R:mp_clear (&r);
|
---|
| 4261 | LBL_N1:mp_clear (&n1);
|
---|
| 4262 | return err;
|
---|
| 4263 | }
|
---|
| 4264 |
|
---|
| 4265 |
|
---|
| 4266 | /* determines if an integers is divisible by one
|
---|
| 4267 | * of the first PRIME_SIZE primes or not
|
---|
| 4268 | *
|
---|
| 4269 | * sets result to 0 if not, 1 if yes
|
---|
| 4270 | */
|
---|
| 4271 | static int mp_prime_is_divisible (mp_int * a, int *result)
|
---|
| 4272 | {
|
---|
| 4273 | int err, ix;
|
---|
| 4274 | mp_digit res;
|
---|
| 4275 |
|
---|
| 4276 | /* default to not */
|
---|
| 4277 | *result = MP_NO;
|
---|
| 4278 |
|
---|
| 4279 | for (ix = 0; ix < PRIME_SIZE; ix++) {
|
---|
| 4280 | /* what is a mod LBL_prime_tab[ix] */
|
---|
| 4281 | if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
|
---|
| 4282 | return err;
|
---|
| 4283 | }
|
---|
| 4284 |
|
---|
| 4285 | /* is the residue zero? */
|
---|
| 4286 | if (res == 0) {
|
---|
| 4287 | *result = MP_YES;
|
---|
| 4288 | return MP_OKAY;
|
---|
| 4289 | }
|
---|
| 4290 | }
|
---|
| 4291 |
|
---|
| 4292 | return MP_OKAY;
|
---|
| 4293 | }
|
---|
| 4294 |
|
---|
| 4295 | static const int USE_BBS = 1;
|
---|
| 4296 |
|
---|
| 4297 | int mp_rand_prime(mp_int* N, int len, WC_RNG* rng, void* heap)
|
---|
| 4298 | {
|
---|
| 4299 | int err, res, type;
|
---|
| 4300 | byte* buf;
|
---|
| 4301 |
|
---|
| 4302 | if (N == NULL || rng == NULL)
|
---|
| 4303 | return MP_VAL;
|
---|
| 4304 |
|
---|
| 4305 | /* get type */
|
---|
| 4306 | if (len < 0) {
|
---|
| 4307 | type = USE_BBS;
|
---|
| 4308 | len = -len;
|
---|
| 4309 | } else {
|
---|
| 4310 | type = 0;
|
---|
| 4311 | }
|
---|
| 4312 |
|
---|
| 4313 | /* allow sizes between 2 and 512 bytes for a prime size */
|
---|
| 4314 | if (len < 2 || len > 512) {
|
---|
| 4315 | return MP_VAL;
|
---|
| 4316 | }
|
---|
| 4317 |
|
---|
| 4318 | /* allocate buffer to work with */
|
---|
| 4319 | buf = (byte*)XMALLOC(len, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4320 | if (buf == NULL) {
|
---|
| 4321 | return MP_MEM;
|
---|
| 4322 | }
|
---|
| 4323 | XMEMSET(buf, 0, len);
|
---|
| 4324 |
|
---|
| 4325 | do {
|
---|
| 4326 | #ifdef SHOW_GEN
|
---|
| 4327 | printf(".");
|
---|
| 4328 | fflush(stdout);
|
---|
| 4329 | #endif
|
---|
| 4330 | /* generate value */
|
---|
| 4331 | err = wc_RNG_GenerateBlock(rng, buf, len);
|
---|
| 4332 | if (err != 0) {
|
---|
| 4333 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4334 | return err;
|
---|
| 4335 | }
|
---|
| 4336 |
|
---|
| 4337 | /* munge bits */
|
---|
| 4338 | buf[0] |= 0x80 | 0x40;
|
---|
| 4339 | buf[len-1] |= 0x01 | ((type & USE_BBS) ? 0x02 : 0x00);
|
---|
| 4340 |
|
---|
| 4341 | /* load value */
|
---|
| 4342 | if ((err = mp_read_unsigned_bin(N, buf, len)) != MP_OKAY) {
|
---|
| 4343 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4344 | return err;
|
---|
| 4345 | }
|
---|
| 4346 |
|
---|
| 4347 | /* test */
|
---|
| 4348 | if ((err = mp_prime_is_prime(N, 8, &res)) != MP_OKAY) {
|
---|
| 4349 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4350 | return err;
|
---|
| 4351 | }
|
---|
| 4352 | } while (res == MP_NO);
|
---|
| 4353 |
|
---|
| 4354 | XMEMSET(buf, 0, len);
|
---|
| 4355 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4356 |
|
---|
| 4357 | return MP_OKAY;
|
---|
| 4358 | }
|
---|
| 4359 |
|
---|
| 4360 | /*
|
---|
| 4361 | * Sets result to 1 if probably prime, 0 otherwise
|
---|
| 4362 | */
|
---|
| 4363 | int mp_prime_is_prime (mp_int * a, int t, int *result)
|
---|
| 4364 | {
|
---|
| 4365 | mp_int b;
|
---|
| 4366 | int ix, err, res;
|
---|
| 4367 |
|
---|
| 4368 | /* default to no */
|
---|
| 4369 | *result = MP_NO;
|
---|
| 4370 |
|
---|
| 4371 | /* valid value of t? */
|
---|
| 4372 | if (t <= 0 || t > PRIME_SIZE) {
|
---|
| 4373 | return MP_VAL;
|
---|
| 4374 | }
|
---|
| 4375 |
|
---|
| 4376 | /* is the input equal to one of the primes in the table? */
|
---|
| 4377 | for (ix = 0; ix < PRIME_SIZE; ix++) {
|
---|
| 4378 | if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
|
---|
| 4379 | *result = 1;
|
---|
| 4380 | return MP_OKAY;
|
---|
| 4381 | }
|
---|
| 4382 | }
|
---|
| 4383 |
|
---|
| 4384 | /* first perform trial division */
|
---|
| 4385 | if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
|
---|
| 4386 | return err;
|
---|
| 4387 | }
|
---|
| 4388 |
|
---|
| 4389 | /* return if it was trivially divisible */
|
---|
| 4390 | if (res == MP_YES) {
|
---|
| 4391 | return MP_OKAY;
|
---|
| 4392 | }
|
---|
| 4393 |
|
---|
| 4394 | /* now perform the miller-rabin rounds */
|
---|
| 4395 | if ((err = mp_init (&b)) != MP_OKAY) {
|
---|
| 4396 | return err;
|
---|
| 4397 | }
|
---|
| 4398 |
|
---|
| 4399 | for (ix = 0; ix < t; ix++) {
|
---|
| 4400 | /* set the prime */
|
---|
| 4401 | mp_set (&b, ltm_prime_tab[ix]);
|
---|
| 4402 |
|
---|
| 4403 | if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
|
---|
| 4404 | goto LBL_B;
|
---|
| 4405 | }
|
---|
| 4406 |
|
---|
| 4407 | if (res == MP_NO) {
|
---|
| 4408 | goto LBL_B;
|
---|
| 4409 | }
|
---|
| 4410 | }
|
---|
| 4411 |
|
---|
| 4412 | /* passed the test */
|
---|
| 4413 | *result = MP_YES;
|
---|
| 4414 | LBL_B:mp_clear (&b);
|
---|
| 4415 | return err;
|
---|
| 4416 | }
|
---|
| 4417 |
|
---|
| 4418 |
|
---|
| 4419 | /* computes least common multiple as |a*b|/(a, b) */
|
---|
| 4420 | int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 4421 | {
|
---|
| 4422 | int res;
|
---|
| 4423 | mp_int t1, t2;
|
---|
| 4424 |
|
---|
| 4425 |
|
---|
| 4426 | if ((res = mp_init_multi (&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
|
---|
| 4427 | return res;
|
---|
| 4428 | }
|
---|
| 4429 |
|
---|
| 4430 | /* t1 = get the GCD of the two inputs */
|
---|
| 4431 | if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
|
---|
| 4432 | goto LBL_T;
|
---|
| 4433 | }
|
---|
| 4434 |
|
---|
| 4435 | /* divide the smallest by the GCD */
|
---|
| 4436 | if (mp_cmp_mag(a, b) == MP_LT) {
|
---|
| 4437 | /* store quotient in t2 such that t2 * b is the LCM */
|
---|
| 4438 | if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
|
---|
| 4439 | goto LBL_T;
|
---|
| 4440 | }
|
---|
| 4441 | res = mp_mul(b, &t2, c);
|
---|
| 4442 | } else {
|
---|
| 4443 | /* store quotient in t2 such that t2 * a is the LCM */
|
---|
| 4444 | if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
|
---|
| 4445 | goto LBL_T;
|
---|
| 4446 | }
|
---|
| 4447 | res = mp_mul(a, &t2, c);
|
---|
| 4448 | }
|
---|
| 4449 |
|
---|
| 4450 | /* fix the sign to positive */
|
---|
| 4451 | c->sign = MP_ZPOS;
|
---|
| 4452 |
|
---|
| 4453 | LBL_T:
|
---|
| 4454 | mp_clear(&t1);
|
---|
| 4455 | mp_clear(&t2);
|
---|
| 4456 | return res;
|
---|
| 4457 | }
|
---|
| 4458 |
|
---|
| 4459 |
|
---|
| 4460 |
|
---|
| 4461 | /* Greatest Common Divisor using the binary method */
|
---|
| 4462 | int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 4463 | {
|
---|
| 4464 | mp_int u, v;
|
---|
| 4465 | int k, u_lsb, v_lsb, res;
|
---|
| 4466 |
|
---|
| 4467 | /* either zero than gcd is the largest */
|
---|
| 4468 | if (mp_iszero (a) == MP_YES) {
|
---|
| 4469 | return mp_abs (b, c);
|
---|
| 4470 | }
|
---|
| 4471 | if (mp_iszero (b) == MP_YES) {
|
---|
| 4472 | return mp_abs (a, c);
|
---|
| 4473 | }
|
---|
| 4474 |
|
---|
| 4475 | /* get copies of a and b we can modify */
|
---|
| 4476 | if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
|
---|
| 4477 | return res;
|
---|
| 4478 | }
|
---|
| 4479 |
|
---|
| 4480 | if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
|
---|
| 4481 | goto LBL_U;
|
---|
| 4482 | }
|
---|
| 4483 |
|
---|
| 4484 | /* must be positive for the remainder of the algorithm */
|
---|
| 4485 | u.sign = v.sign = MP_ZPOS;
|
---|
| 4486 |
|
---|
| 4487 | /* B1. Find the common power of two for u and v */
|
---|
| 4488 | u_lsb = mp_cnt_lsb(&u);
|
---|
| 4489 | v_lsb = mp_cnt_lsb(&v);
|
---|
| 4490 | k = MIN(u_lsb, v_lsb);
|
---|
| 4491 |
|
---|
| 4492 | if (k > 0) {
|
---|
| 4493 | /* divide the power of two out */
|
---|
| 4494 | if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
|
---|
| 4495 | goto LBL_V;
|
---|
| 4496 | }
|
---|
| 4497 |
|
---|
| 4498 | if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
|
---|
| 4499 | goto LBL_V;
|
---|
| 4500 | }
|
---|
| 4501 | }
|
---|
| 4502 |
|
---|
| 4503 | /* divide any remaining factors of two out */
|
---|
| 4504 | if (u_lsb != k) {
|
---|
| 4505 | if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
|
---|
| 4506 | goto LBL_V;
|
---|
| 4507 | }
|
---|
| 4508 | }
|
---|
| 4509 |
|
---|
| 4510 | if (v_lsb != k) {
|
---|
| 4511 | if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
|
---|
| 4512 | goto LBL_V;
|
---|
| 4513 | }
|
---|
| 4514 | }
|
---|
| 4515 |
|
---|
| 4516 | while (mp_iszero(&v) == 0) {
|
---|
| 4517 | /* make sure v is the largest */
|
---|
| 4518 | if (mp_cmp_mag(&u, &v) == MP_GT) {
|
---|
| 4519 | /* swap u and v to make sure v is >= u */
|
---|
| 4520 | mp_exch(&u, &v);
|
---|
| 4521 | }
|
---|
| 4522 |
|
---|
| 4523 | /* subtract smallest from largest */
|
---|
| 4524 | if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
|
---|
| 4525 | goto LBL_V;
|
---|
| 4526 | }
|
---|
| 4527 |
|
---|
| 4528 | /* Divide out all factors of two */
|
---|
| 4529 | if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
|
---|
| 4530 | goto LBL_V;
|
---|
| 4531 | }
|
---|
| 4532 | }
|
---|
| 4533 |
|
---|
| 4534 | /* multiply by 2**k which we divided out at the beginning */
|
---|
| 4535 | if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
|
---|
| 4536 | goto LBL_V;
|
---|
| 4537 | }
|
---|
| 4538 | c->sign = MP_ZPOS;
|
---|
| 4539 | res = MP_OKAY;
|
---|
| 4540 | LBL_V:mp_clear (&u);
|
---|
| 4541 | LBL_U:mp_clear (&v);
|
---|
| 4542 | return res;
|
---|
| 4543 | }
|
---|
| 4544 |
|
---|
| 4545 | #endif /* WOLFSSL_KEY_GEN */
|
---|
| 4546 |
|
---|
| 4547 |
|
---|
| 4548 | #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN) || defined(HAVE_COMP_KEY)
|
---|
| 4549 |
|
---|
| 4550 | /* chars used in radix conversions */
|
---|
| 4551 | const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ\
|
---|
| 4552 | abcdefghijklmnopqrstuvwxyz+/";
|
---|
| 4553 | #endif
|
---|
| 4554 |
|
---|
| 4555 | #ifdef HAVE_ECC
|
---|
| 4556 | /* read a string [ASCII] in a given radix */
|
---|
| 4557 | int mp_read_radix (mp_int * a, const char *str, int radix)
|
---|
| 4558 | {
|
---|
| 4559 | int y, res, neg;
|
---|
| 4560 | char ch;
|
---|
| 4561 |
|
---|
| 4562 | /* zero the digit bignum */
|
---|
| 4563 | mp_zero(a);
|
---|
| 4564 |
|
---|
| 4565 | /* make sure the radix is ok */
|
---|
| 4566 | if (radix < 2 || radix > 64) {
|
---|
| 4567 | return MP_VAL;
|
---|
| 4568 | }
|
---|
| 4569 |
|
---|
| 4570 | /* if the leading digit is a
|
---|
| 4571 | * minus set the sign to negative.
|
---|
| 4572 | */
|
---|
| 4573 | if (*str == '-') {
|
---|
| 4574 | ++str;
|
---|
| 4575 | neg = MP_NEG;
|
---|
| 4576 | } else {
|
---|
| 4577 | neg = MP_ZPOS;
|
---|
| 4578 | }
|
---|
| 4579 |
|
---|
| 4580 | /* set the integer to the default of zero */
|
---|
| 4581 | mp_zero (a);
|
---|
| 4582 |
|
---|
| 4583 | /* process each digit of the string */
|
---|
| 4584 | while (*str) {
|
---|
| 4585 | /* if the radix < 36 the conversion is case insensitive
|
---|
| 4586 | * this allows numbers like 1AB and 1ab to represent the same value
|
---|
| 4587 | * [e.g. in hex]
|
---|
| 4588 | */
|
---|
| 4589 | ch = (char) ((radix < 36) ? XTOUPPER((unsigned char)*str) : *str);
|
---|
| 4590 | for (y = 0; y < 64; y++) {
|
---|
| 4591 | if (ch == mp_s_rmap[y]) {
|
---|
| 4592 | break;
|
---|
| 4593 | }
|
---|
| 4594 | }
|
---|
| 4595 |
|
---|
| 4596 | /* if the char was found in the map
|
---|
| 4597 | * and is less than the given radix add it
|
---|
| 4598 | * to the number, otherwise exit the loop.
|
---|
| 4599 | */
|
---|
| 4600 | if (y < radix) {
|
---|
| 4601 | if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
|
---|
| 4602 | return res;
|
---|
| 4603 | }
|
---|
| 4604 | if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
|
---|
| 4605 | return res;
|
---|
| 4606 | }
|
---|
| 4607 | } else {
|
---|
| 4608 | break;
|
---|
| 4609 | }
|
---|
| 4610 | ++str;
|
---|
| 4611 | }
|
---|
| 4612 |
|
---|
| 4613 | /* set the sign only if a != 0 */
|
---|
| 4614 | if (mp_iszero(a) != 1) {
|
---|
| 4615 | a->sign = neg;
|
---|
| 4616 | }
|
---|
| 4617 | return MP_OKAY;
|
---|
| 4618 | }
|
---|
| 4619 | #endif /* HAVE_ECC */
|
---|
| 4620 |
|
---|
| 4621 | #if defined(WOLFSSL_KEY_GEN) || defined(HAVE_COMP_KEY)
|
---|
| 4622 |
|
---|
| 4623 | /* returns size of ASCII representation */
|
---|
| 4624 | int mp_radix_size (mp_int *a, int radix, int *size)
|
---|
| 4625 | {
|
---|
| 4626 | int res, digs;
|
---|
| 4627 | mp_int t;
|
---|
| 4628 | mp_digit d;
|
---|
| 4629 |
|
---|
| 4630 | *size = 0;
|
---|
| 4631 |
|
---|
| 4632 | /* special case for binary */
|
---|
| 4633 | if (radix == 2) {
|
---|
| 4634 | *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
|
---|
| 4635 | return MP_OKAY;
|
---|
| 4636 | }
|
---|
| 4637 |
|
---|
| 4638 | /* make sure the radix is in range */
|
---|
| 4639 | if (radix < 2 || radix > 64) {
|
---|
| 4640 | return MP_VAL;
|
---|
| 4641 | }
|
---|
| 4642 |
|
---|
| 4643 | if (mp_iszero(a) == MP_YES) {
|
---|
| 4644 | *size = 2;
|
---|
| 4645 | return MP_OKAY;
|
---|
| 4646 | }
|
---|
| 4647 |
|
---|
| 4648 | /* digs is the digit count */
|
---|
| 4649 | digs = 0;
|
---|
| 4650 |
|
---|
| 4651 | /* if it's negative add one for the sign */
|
---|
| 4652 | if (a->sign == MP_NEG) {
|
---|
| 4653 | ++digs;
|
---|
| 4654 | }
|
---|
| 4655 |
|
---|
| 4656 | /* init a copy of the input */
|
---|
| 4657 | if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
|
---|
| 4658 | return res;
|
---|
| 4659 | }
|
---|
| 4660 |
|
---|
| 4661 | /* force temp to positive */
|
---|
| 4662 | t.sign = MP_ZPOS;
|
---|
| 4663 |
|
---|
| 4664 | /* fetch out all of the digits */
|
---|
| 4665 | while (mp_iszero (&t) == MP_NO) {
|
---|
| 4666 | if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
|
---|
| 4667 | mp_clear (&t);
|
---|
| 4668 | return res;
|
---|
| 4669 | }
|
---|
| 4670 | ++digs;
|
---|
| 4671 | }
|
---|
| 4672 | mp_clear (&t);
|
---|
| 4673 |
|
---|
| 4674 | /* return digs + 1, the 1 is for the NULL byte that would be required. */
|
---|
| 4675 | *size = digs + 1;
|
---|
| 4676 | return MP_OKAY;
|
---|
| 4677 | }
|
---|
| 4678 |
|
---|
| 4679 | /* stores a bignum as a ASCII string in a given radix (2..64) */
|
---|
| 4680 | int mp_toradix (mp_int *a, char *str, int radix)
|
---|
| 4681 | {
|
---|
| 4682 | int res, digs;
|
---|
| 4683 | mp_int t;
|
---|
| 4684 | mp_digit d;
|
---|
| 4685 | char *_s = str;
|
---|
| 4686 |
|
---|
| 4687 | /* check range of the radix */
|
---|
| 4688 | if (radix < 2 || radix > 64) {
|
---|
| 4689 | return MP_VAL;
|
---|
| 4690 | }
|
---|
| 4691 |
|
---|
| 4692 | /* quick out if its zero */
|
---|
| 4693 | if (mp_iszero(a) == 1) {
|
---|
| 4694 | *str++ = '0';
|
---|
| 4695 | *str = '\0';
|
---|
| 4696 | return MP_OKAY;
|
---|
| 4697 | }
|
---|
| 4698 |
|
---|
| 4699 | if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
|
---|
| 4700 | return res;
|
---|
| 4701 | }
|
---|
| 4702 |
|
---|
| 4703 | /* if it is negative output a - */
|
---|
| 4704 | if (t.sign == MP_NEG) {
|
---|
| 4705 | ++_s;
|
---|
| 4706 | *str++ = '-';
|
---|
| 4707 | t.sign = MP_ZPOS;
|
---|
| 4708 | }
|
---|
| 4709 |
|
---|
| 4710 | digs = 0;
|
---|
| 4711 | while (mp_iszero (&t) == 0) {
|
---|
| 4712 | if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
|
---|
| 4713 | mp_clear (&t);
|
---|
| 4714 | return res;
|
---|
| 4715 | }
|
---|
| 4716 | *str++ = mp_s_rmap[d];
|
---|
| 4717 | ++digs;
|
---|
| 4718 | }
|
---|
| 4719 |
|
---|
| 4720 | /* reverse the digits of the string. In this case _s points
|
---|
| 4721 | * to the first digit [exluding the sign] of the number]
|
---|
| 4722 | */
|
---|
| 4723 | bn_reverse ((unsigned char *)_s, digs);
|
---|
| 4724 |
|
---|
| 4725 | /* append a NULL so the string is properly terminated */
|
---|
| 4726 | *str = '\0';
|
---|
| 4727 |
|
---|
| 4728 | mp_clear (&t);
|
---|
| 4729 | return MP_OKAY;
|
---|
| 4730 | }
|
---|
| 4731 |
|
---|
| 4732 | #endif /* defined(WOLFSSL_KEY_GEN) || defined(HAVE_COMP_KEY) */
|
---|
| 4733 |
|
---|
| 4734 | #endif /* USE_FAST_MATH */
|
---|
| 4735 |
|
---|
| 4736 | #endif /* NO_BIG_INT */
|
---|
| 4737 |
|
---|