[388] | 1 | /* integer.c
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| 2 | *
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| 3 | * Copyright (C) 2006-2017 wolfSSL Inc.
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| 4 | *
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| 5 | * This file is part of wolfSSL.
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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 02110-1335, 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 | /*
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| 25 | * Based on public domain LibTomMath 0.38 by Tom St Denis, tomstdenis@iahu.ca,
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| 26 | * http://math.libtomcrypt.com
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| 27 | */
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| 28 |
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| 29 |
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| 30 | #ifdef HAVE_CONFIG_H
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| 31 | #include <config.h>
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| 32 | #endif
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| 33 |
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| 34 | /* in case user set USE_FAST_MATH there */
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| 35 | #include <wolfssl/wolfcrypt/settings.h>
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| 36 |
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| 37 | #ifdef NO_INLINE
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| 38 | #include <wolfssl/wolfcrypt/misc.h>
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| 39 | #else
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| 40 | #define WOLFSSL_MISC_INCLUDED
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| 41 | #include <wolfcrypt/src/misc.c>
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| 42 | #endif
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| 43 |
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| 44 | #ifndef NO_BIG_INT
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| 45 |
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| 46 | #ifndef USE_FAST_MATH
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| 47 |
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| 48 | #ifndef WOLFSSL_SP_MATH
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| 49 |
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| 50 | #include <wolfssl/wolfcrypt/integer.h>
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| 51 |
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| 52 | #if defined(FREESCALE_LTC_TFM)
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| 53 | #include <wolfssl/wolfcrypt/port/nxp/ksdk_port.h>
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| 54 | #endif
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| 55 | #ifdef WOLFSSL_DEBUG_MATH
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| 56 | #include <stdio.h>
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| 57 | #endif
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| 58 |
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| 59 | #ifndef NO_WOLFSSL_SMALL_STACK
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| 60 | #ifndef WOLFSSL_SMALL_STACK
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| 61 | #define WOLFSSL_SMALL_STACK
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| 62 | #endif
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| 63 | #endif
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| 64 |
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| 65 | #ifdef SHOW_GEN
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| 66 | #if defined(FREESCALE_MQX) || defined(FREESCALE_KSDK_MQX)
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| 67 | #if MQX_USE_IO_OLD
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| 68 | #include <fio.h>
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| 69 | #else
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| 70 | #include <nio.h>
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| 71 | #endif
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| 72 | #else
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| 73 | #include <stdio.h>
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| 74 | #endif
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| 75 | #endif
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| 76 |
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| 77 | /* reverse an array, used for radix code */
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| 78 | static void
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| 79 | bn_reverse (unsigned char *s, int len)
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| 80 | {
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| 81 | int ix, iy;
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| 82 | unsigned char t;
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| 83 |
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| 84 | ix = 0;
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| 85 | iy = len - 1;
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| 86 | while (ix < iy) {
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| 87 | t = s[ix];
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| 88 | s[ix] = s[iy];
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| 89 | s[iy] = t;
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| 90 | ++ix;
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| 91 | --iy;
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| 92 | }
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| 93 | }
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| 94 |
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| 95 | /* math settings check */
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| 96 | word32 CheckRunTimeSettings(void)
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| 97 | {
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| 98 | return CTC_SETTINGS;
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| 99 | }
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| 100 |
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| 101 |
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| 102 | /* handle up to 6 inits */
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| 103 | int mp_init_multi(mp_int* a, mp_int* b, mp_int* c, mp_int* d, mp_int* e,
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| 104 | mp_int* f)
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| 105 | {
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| 106 | int res = MP_OKAY;
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| 107 |
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| 108 | if (a) XMEMSET(a, 0, sizeof(mp_int));
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| 109 | if (b) XMEMSET(b, 0, sizeof(mp_int));
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| 110 | if (c) XMEMSET(c, 0, sizeof(mp_int));
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| 111 | if (d) XMEMSET(d, 0, sizeof(mp_int));
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| 112 | if (e) XMEMSET(e, 0, sizeof(mp_int));
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| 113 | if (f) XMEMSET(f, 0, sizeof(mp_int));
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| 114 |
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| 115 | if (a && ((res = mp_init(a)) != MP_OKAY))
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| 116 | return res;
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| 117 |
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| 118 | if (b && ((res = mp_init(b)) != MP_OKAY)) {
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| 119 | mp_clear(a);
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| 120 | return res;
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| 121 | }
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| 122 |
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| 123 | if (c && ((res = mp_init(c)) != MP_OKAY)) {
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| 124 | mp_clear(a); mp_clear(b);
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| 125 | return res;
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| 126 | }
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| 127 |
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| 128 | if (d && ((res = mp_init(d)) != MP_OKAY)) {
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| 129 | mp_clear(a); mp_clear(b); mp_clear(c);
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| 130 | return res;
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| 131 | }
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| 132 |
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| 133 | if (e && ((res = mp_init(e)) != MP_OKAY)) {
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| 134 | mp_clear(a); mp_clear(b); mp_clear(c); mp_clear(d);
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| 135 | return res;
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| 136 | }
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| 137 |
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| 138 | if (f && ((res = mp_init(f)) != MP_OKAY)) {
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| 139 | mp_clear(a); mp_clear(b); mp_clear(c); mp_clear(d); mp_clear(e);
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| 140 | return res;
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| 141 | }
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| 142 |
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| 143 | return res;
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| 144 | }
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| 145 |
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| 146 |
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| 147 | /* init a new mp_int */
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| 148 | int mp_init (mp_int * a)
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| 149 | {
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| 150 | /* Safeguard against passing in a null pointer */
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| 151 | if (a == NULL)
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| 152 | return MP_VAL;
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| 153 |
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| 154 | /* defer allocation until mp_grow */
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| 155 | a->dp = NULL;
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| 156 |
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| 157 | /* set the used to zero, allocated digits to the default precision
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| 158 | * and sign to positive */
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| 159 | a->used = 0;
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| 160 | a->alloc = 0;
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| 161 | a->sign = MP_ZPOS;
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| 162 | #ifdef HAVE_WOLF_BIGINT
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| 163 | wc_bigint_init(&a->raw);
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| 164 | #endif
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| 165 |
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| 166 | return MP_OKAY;
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| 167 | }
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| 168 |
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| 169 |
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| 170 | /* clear one (frees) */
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| 171 | void mp_clear (mp_int * a)
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| 172 | {
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| 173 | int i;
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| 174 |
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| 175 | if (a == NULL)
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| 176 | return;
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| 177 |
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| 178 | /* only do anything if a hasn't been freed previously */
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| 179 | if (a->dp != NULL) {
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| 180 | /* first zero the digits */
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| 181 | for (i = 0; i < a->used; i++) {
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| 182 | a->dp[i] = 0;
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| 183 | }
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| 184 |
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| 185 | /* free ram */
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| 186 | mp_free(a);
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| 187 |
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| 188 | /* reset members to make debugging easier */
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| 189 | a->alloc = a->used = 0;
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| 190 | a->sign = MP_ZPOS;
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| 191 | }
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| 192 | }
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| 193 |
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| 194 | void mp_free (mp_int * a)
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| 195 | {
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| 196 | /* only do anything if a hasn't been freed previously */
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| 197 | if (a->dp != NULL) {
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| 198 | /* free ram */
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| 199 | XFREE(a->dp, 0, DYNAMIC_TYPE_BIGINT);
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| 200 | a->dp = NULL;
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| 201 | }
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| 202 |
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| 203 | #ifdef HAVE_WOLF_BIGINT
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| 204 | wc_bigint_free(&a->raw);
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| 205 | #endif
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| 206 | }
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| 207 |
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| 208 | void mp_forcezero(mp_int * a)
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| 209 | {
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| 210 | if (a == NULL)
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| 211 | return;
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| 212 |
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| 213 | /* only do anything if a hasn't been freed previously */
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| 214 | if (a->dp != NULL) {
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| 215 | /* force zero the used digits */
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| 216 | ForceZero(a->dp, a->used * sizeof(mp_digit));
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| 217 | #ifdef HAVE_WOLF_BIGINT
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| 218 | wc_bigint_zero(&a->raw);
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| 219 | #endif
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| 220 | /* free ram */
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| 221 | mp_free(a);
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| 222 |
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| 223 | /* reset members to make debugging easier */
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| 224 | a->alloc = a->used = 0;
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| 225 | a->sign = MP_ZPOS;
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| 226 | }
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| 227 |
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| 228 | a->sign = MP_ZPOS;
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| 229 | a->used = 0;
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| 230 | }
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| 231 |
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| 232 |
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| 233 | /* get the size for an unsigned equivalent */
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| 234 | int mp_unsigned_bin_size (mp_int * a)
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| 235 | {
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| 236 | int size = mp_count_bits (a);
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| 237 | return (size / 8 + ((size & 7) != 0 ? 1 : 0));
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| 238 | }
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| 239 |
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| 240 |
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| 241 | /* returns the number of bits in an int */
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| 242 | int mp_count_bits (mp_int * a)
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| 243 | {
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| 244 | int r;
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| 245 | mp_digit q;
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| 246 |
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| 247 | /* shortcut */
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| 248 | if (a->used == 0) {
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| 249 | return 0;
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| 250 | }
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| 251 |
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| 252 | /* get number of digits and add that */
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| 253 | r = (a->used - 1) * DIGIT_BIT;
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| 254 |
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| 255 | /* take the last digit and count the bits in it */
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| 256 | q = a->dp[a->used - 1];
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| 257 | while (q > ((mp_digit) 0)) {
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| 258 | ++r;
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| 259 | q >>= ((mp_digit) 1);
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| 260 | }
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| 261 | return r;
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| 262 | }
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| 263 |
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| 264 |
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| 265 | int mp_leading_bit (mp_int * a)
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| 266 | {
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| 267 | int bit = 0;
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| 268 | mp_int t;
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| 269 |
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| 270 | if (mp_init_copy(&t, a) != MP_OKAY)
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| 271 | return 0;
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| 272 |
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| 273 | while (mp_iszero(&t) == MP_NO) {
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| 274 | #ifndef MP_8BIT
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| 275 | bit = (t.dp[0] & 0x80) != 0;
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| 276 | #else
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| 277 | bit = (t.dp[0] | ((t.dp[1] & 0x01) << 7)) & 0x80 != 0;
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| 278 | #endif
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| 279 | if (mp_div_2d (&t, 8, &t, NULL) != MP_OKAY)
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| 280 | break;
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| 281 | }
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| 282 | mp_clear(&t);
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| 283 | return bit;
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| 284 | }
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| 285 |
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| 286 | int mp_to_unsigned_bin_at_pos(int x, mp_int *t, unsigned char *b)
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| 287 | {
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| 288 | int res = 0;
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| 289 | while (mp_iszero(t) == MP_NO) {
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| 290 | #ifndef MP_8BIT
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| 291 | b[x++] = (unsigned char) (t->dp[0] & 255);
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| 292 | #else
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| 293 | b[x++] = (unsigned char) (t->dp[0] | ((t->dp[1] & 0x01) << 7));
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| 294 | #endif
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| 295 | if ((res = mp_div_2d (t, 8, t, NULL)) != MP_OKAY) {
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| 296 | return res;
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| 297 | }
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| 298 | res = x;
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| 299 | }
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| 300 | return res;
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| 301 | }
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| 302 |
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| 303 | /* store in unsigned [big endian] format */
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| 304 | int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
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| 305 | {
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| 306 | int x, res;
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| 307 | mp_int t;
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| 308 |
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| 309 | if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
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| 310 | return res;
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| 311 | }
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| 312 |
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| 313 | x = mp_to_unsigned_bin_at_pos(0, &t, b);
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| 314 | if (x < 0) {
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| 315 | mp_clear(&t);
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| 316 | return x;
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| 317 | }
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| 318 |
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| 319 | bn_reverse (b, x);
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| 320 | mp_clear (&t);
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| 321 | return res;
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| 322 | }
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| 323 |
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| 324 | int mp_to_unsigned_bin_len(mp_int * a, unsigned char *b, int c)
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| 325 | {
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| 326 | int i, len;
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| 327 |
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| 328 | len = mp_unsigned_bin_size(a);
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| 329 |
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| 330 | /* pad front w/ zeros to match length */
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| 331 | for (i = 0; i < c - len; i++)
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| 332 | b[i] = 0x00;
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| 333 | return mp_to_unsigned_bin(a, b + i);
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| 334 | }
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| 335 |
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| 336 | /* creates "a" then copies b into it */
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| 337 | int mp_init_copy (mp_int * a, mp_int * b)
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| 338 | {
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| 339 | int res;
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| 340 |
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| 341 | if ((res = mp_init_size (a, b->used)) != MP_OKAY) {
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| 342 | return res;
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| 343 | }
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| 344 |
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| 345 | if((res = mp_copy (b, a)) != MP_OKAY) {
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| 346 | mp_clear(a);
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| 347 | }
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| 348 |
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| 349 | return res;
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| 350 | }
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| 351 |
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| 352 |
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| 353 | /* copy, b = a */
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| 354 | int mp_copy (mp_int * a, mp_int * b)
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| 355 | {
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| 356 | int res, n;
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| 357 |
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| 358 | /* Safeguard against passing in a null pointer */
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| 359 | if (a == NULL || b == NULL)
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| 360 | return MP_VAL;
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| 361 |
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| 362 | /* if dst == src do nothing */
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| 363 | if (a == b) {
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| 364 | return MP_OKAY;
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| 365 | }
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| 366 |
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| 367 | /* grow dest */
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| 368 | if (b->alloc < a->used || b->alloc == 0) {
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| 369 | if ((res = mp_grow (b, a->used)) != MP_OKAY) {
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| 370 | return res;
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| 371 | }
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| 372 | }
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| 373 |
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| 374 | /* zero b and copy the parameters over */
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| 375 | {
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| 376 | mp_digit *tmpa, *tmpb;
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| 377 |
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| 378 | /* pointer aliases */
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| 379 |
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| 380 | /* source */
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| 381 | tmpa = a->dp;
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| 382 |
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| 383 | /* destination */
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| 384 | tmpb = b->dp;
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| 385 |
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| 386 | /* copy all the digits */
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| 387 | for (n = 0; n < a->used; n++) {
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| 388 | *tmpb++ = *tmpa++;
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| 389 | }
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| 390 |
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| 391 | /* clear high digits */
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| 392 | for (; n < b->used && b->dp; n++) {
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| 393 | *tmpb++ = 0;
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| 394 | }
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| 395 | }
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| 396 |
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| 397 | /* copy used count and sign */
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| 398 | b->used = a->used;
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| 399 | b->sign = a->sign;
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| 400 | return MP_OKAY;
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| 401 | }
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| 402 |
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| 403 |
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| 404 | /* grow as required */
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| 405 | int mp_grow (mp_int * a, int size)
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| 406 | {
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| 407 | int i;
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| 408 | mp_digit *tmp;
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| 409 |
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| 410 | /* if the alloc size is smaller alloc more ram */
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| 411 | if (a->alloc < size || size == 0) {
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| 412 | /* ensure there are always at least MP_PREC digits extra on top */
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| 413 | size += (MP_PREC * 2) - (size % MP_PREC);
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| 414 |
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| 415 | /* reallocate the array a->dp
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| 416 | *
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| 417 | * We store the return in a temporary variable
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| 418 | * in case the operation failed we don't want
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| 419 | * to overwrite the dp member of a.
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| 420 | */
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| 421 | tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size, NULL,
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| 422 | DYNAMIC_TYPE_BIGINT);
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| 423 | if (tmp == NULL) {
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| 424 | /* reallocation failed but "a" is still valid [can be freed] */
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| 425 | return MP_MEM;
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| 426 | }
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| 427 |
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| 428 | /* reallocation succeeded so set a->dp */
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| 429 | a->dp = tmp;
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| 430 |
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| 431 | /* zero excess digits */
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| 432 | i = a->alloc;
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| 433 | a->alloc = size;
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| 434 | for (; i < a->alloc; i++) {
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| 435 | a->dp[i] = 0;
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| 436 | }
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| 437 | }
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| 438 | return MP_OKAY;
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| 439 | }
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| 440 |
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| 441 |
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| 442 | /* shift right by a certain bit count (store quotient in c, optional
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| 443 | remainder in d) */
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| 444 | int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
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| 445 | {
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| 446 | int D, res;
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| 447 | mp_int t;
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| 448 |
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| 449 |
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| 450 | /* if the shift count is <= 0 then we do no work */
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| 451 | if (b <= 0) {
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| 452 | res = mp_copy (a, c);
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| 453 | if (d != NULL) {
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| 454 | mp_zero (d);
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| 455 | }
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| 456 | return res;
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| 457 | }
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| 458 |
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| 459 | if ((res = mp_init (&t)) != MP_OKAY) {
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| 460 | return res;
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| 461 | }
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| 462 |
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| 463 | /* get the remainder */
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| 464 | if (d != NULL) {
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| 465 | if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
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| 466 | mp_clear (&t);
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| 467 | return res;
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| 468 | }
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| 469 | }
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| 470 |
|
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| 471 | /* copy */
|
---|
| 472 | if ((res = mp_copy (a, c)) != MP_OKAY) {
|
---|
| 473 | mp_clear (&t);
|
---|
| 474 | return res;
|
---|
| 475 | }
|
---|
| 476 |
|
---|
| 477 | /* shift by as many digits in the bit count */
|
---|
| 478 | if (b >= (int)DIGIT_BIT) {
|
---|
| 479 | mp_rshd (c, b / DIGIT_BIT);
|
---|
| 480 | }
|
---|
| 481 |
|
---|
| 482 | /* shift any bit count < DIGIT_BIT */
|
---|
| 483 | D = (b % DIGIT_BIT);
|
---|
| 484 | if (D != 0) {
|
---|
| 485 | mp_rshb(c, D);
|
---|
| 486 | }
|
---|
| 487 | mp_clamp (c);
|
---|
| 488 | if (d != NULL) {
|
---|
| 489 | mp_exch (&t, d);
|
---|
| 490 | }
|
---|
| 491 | mp_clear (&t);
|
---|
| 492 | return MP_OKAY;
|
---|
| 493 | }
|
---|
| 494 |
|
---|
| 495 |
|
---|
| 496 | /* set to zero */
|
---|
| 497 | void mp_zero (mp_int * a)
|
---|
| 498 | {
|
---|
| 499 | int n;
|
---|
| 500 | mp_digit *tmp;
|
---|
| 501 |
|
---|
| 502 | if (a == NULL)
|
---|
| 503 | return;
|
---|
| 504 |
|
---|
| 505 | a->sign = MP_ZPOS;
|
---|
| 506 | a->used = 0;
|
---|
| 507 |
|
---|
| 508 | tmp = a->dp;
|
---|
| 509 | for (n = 0; n < a->alloc; n++) {
|
---|
| 510 | *tmp++ = 0;
|
---|
| 511 | }
|
---|
| 512 | }
|
---|
| 513 |
|
---|
| 514 |
|
---|
| 515 | /* trim unused digits
|
---|
| 516 | *
|
---|
| 517 | * This is used to ensure that leading zero digits are
|
---|
| 518 | * trimmed and the leading "used" digit will be non-zero
|
---|
| 519 | * Typically very fast. Also fixes the sign if there
|
---|
| 520 | * are no more leading digits
|
---|
| 521 | */
|
---|
| 522 | void mp_clamp (mp_int * a)
|
---|
| 523 | {
|
---|
| 524 | /* decrease used while the most significant digit is
|
---|
| 525 | * zero.
|
---|
| 526 | */
|
---|
| 527 | while (a->used > 0 && a->dp[a->used - 1] == 0) {
|
---|
| 528 | --(a->used);
|
---|
| 529 | }
|
---|
| 530 |
|
---|
| 531 | /* reset the sign flag if used == 0 */
|
---|
| 532 | if (a->used == 0) {
|
---|
| 533 | a->sign = MP_ZPOS;
|
---|
| 534 | }
|
---|
| 535 | }
|
---|
| 536 |
|
---|
| 537 |
|
---|
| 538 | /* swap the elements of two integers, for cases where you can't simply swap the
|
---|
| 539 | * mp_int pointers around
|
---|
| 540 | */
|
---|
| 541 | void mp_exch (mp_int * a, mp_int * b)
|
---|
| 542 | {
|
---|
| 543 | mp_int t;
|
---|
| 544 |
|
---|
| 545 | t = *a;
|
---|
| 546 | *a = *b;
|
---|
| 547 | *b = t;
|
---|
| 548 | }
|
---|
| 549 |
|
---|
| 550 |
|
---|
| 551 | /* shift right a certain number of bits */
|
---|
| 552 | void mp_rshb (mp_int *c, int x)
|
---|
| 553 | {
|
---|
| 554 | mp_digit *tmpc, mask, shift;
|
---|
| 555 | mp_digit r, rr;
|
---|
| 556 | mp_digit D = x;
|
---|
| 557 |
|
---|
| 558 | /* mask */
|
---|
| 559 | mask = (((mp_digit)1) << D) - 1;
|
---|
| 560 |
|
---|
| 561 | /* shift for lsb */
|
---|
| 562 | shift = DIGIT_BIT - D;
|
---|
| 563 |
|
---|
| 564 | /* alias */
|
---|
| 565 | tmpc = c->dp + (c->used - 1);
|
---|
| 566 |
|
---|
| 567 | /* carry */
|
---|
| 568 | r = 0;
|
---|
| 569 | for (x = c->used - 1; x >= 0; x--) {
|
---|
| 570 | /* get the lower bits of this word in a temp */
|
---|
| 571 | rr = *tmpc & mask;
|
---|
| 572 |
|
---|
| 573 | /* shift the current word and mix in the carry bits from previous word */
|
---|
| 574 | *tmpc = (*tmpc >> D) | (r << shift);
|
---|
| 575 | --tmpc;
|
---|
| 576 |
|
---|
| 577 | /* set the carry to the carry bits of the current word found above */
|
---|
| 578 | r = rr;
|
---|
| 579 | }
|
---|
| 580 | mp_clamp(c);
|
---|
| 581 | }
|
---|
| 582 |
|
---|
| 583 |
|
---|
| 584 | /* shift right a certain amount of digits */
|
---|
| 585 | void mp_rshd (mp_int * a, int b)
|
---|
| 586 | {
|
---|
| 587 | int x;
|
---|
| 588 |
|
---|
| 589 | /* if b <= 0 then ignore it */
|
---|
| 590 | if (b <= 0) {
|
---|
| 591 | return;
|
---|
| 592 | }
|
---|
| 593 |
|
---|
| 594 | /* if b > used then simply zero it and return */
|
---|
| 595 | if (a->used <= b) {
|
---|
| 596 | mp_zero (a);
|
---|
| 597 | return;
|
---|
| 598 | }
|
---|
| 599 |
|
---|
| 600 | {
|
---|
| 601 | mp_digit *bottom, *top;
|
---|
| 602 |
|
---|
| 603 | /* shift the digits down */
|
---|
| 604 |
|
---|
| 605 | /* bottom */
|
---|
| 606 | bottom = a->dp;
|
---|
| 607 |
|
---|
| 608 | /* top [offset into digits] */
|
---|
| 609 | top = a->dp + b;
|
---|
| 610 |
|
---|
| 611 | /* this is implemented as a sliding window where
|
---|
| 612 | * the window is b-digits long and digits from
|
---|
| 613 | * the top of the window are copied to the bottom
|
---|
| 614 | *
|
---|
| 615 | * e.g.
|
---|
| 616 |
|
---|
| 617 | b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
|
---|
| 618 | /\ | ---->
|
---|
| 619 | \-------------------/ ---->
|
---|
| 620 | */
|
---|
| 621 | for (x = 0; x < (a->used - b); x++) {
|
---|
| 622 | *bottom++ = *top++;
|
---|
| 623 | }
|
---|
| 624 |
|
---|
| 625 | /* zero the top digits */
|
---|
| 626 | for (; x < a->used; x++) {
|
---|
| 627 | *bottom++ = 0;
|
---|
| 628 | }
|
---|
| 629 | }
|
---|
| 630 |
|
---|
| 631 | /* remove excess digits */
|
---|
| 632 | a->used -= b;
|
---|
| 633 | }
|
---|
| 634 |
|
---|
| 635 |
|
---|
| 636 | /* calc a value mod 2**b */
|
---|
| 637 | int mp_mod_2d (mp_int * a, int b, mp_int * c)
|
---|
| 638 | {
|
---|
| 639 | int x, res;
|
---|
| 640 |
|
---|
| 641 | /* if b is <= 0 then zero the int */
|
---|
| 642 | if (b <= 0) {
|
---|
| 643 | mp_zero (c);
|
---|
| 644 | return MP_OKAY;
|
---|
| 645 | }
|
---|
| 646 |
|
---|
| 647 | /* if the modulus is larger than the value than return */
|
---|
| 648 | if (b >= (int) (a->used * DIGIT_BIT)) {
|
---|
| 649 | res = mp_copy (a, c);
|
---|
| 650 | return res;
|
---|
| 651 | }
|
---|
| 652 |
|
---|
| 653 | /* copy */
|
---|
| 654 | if ((res = mp_copy (a, c)) != MP_OKAY) {
|
---|
| 655 | return res;
|
---|
| 656 | }
|
---|
| 657 |
|
---|
| 658 | /* zero digits above the last digit of the modulus */
|
---|
| 659 | for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
|
---|
| 660 | c->dp[x] = 0;
|
---|
| 661 | }
|
---|
| 662 | /* clear the digit that is not completely outside/inside the modulus */
|
---|
| 663 | c->dp[b / DIGIT_BIT] &= (mp_digit) ((((mp_digit) 1) <<
|
---|
| 664 | (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
|
---|
| 665 | mp_clamp (c);
|
---|
| 666 | return MP_OKAY;
|
---|
| 667 | }
|
---|
| 668 |
|
---|
| 669 |
|
---|
| 670 | /* reads a unsigned char array, assumes the msb is stored first [big endian] */
|
---|
| 671 | int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
|
---|
| 672 | {
|
---|
| 673 | int res;
|
---|
| 674 |
|
---|
| 675 | /* make sure there are at least two digits */
|
---|
| 676 | if (a->alloc < 2) {
|
---|
| 677 | if ((res = mp_grow(a, 2)) != MP_OKAY) {
|
---|
| 678 | return res;
|
---|
| 679 | }
|
---|
| 680 | }
|
---|
| 681 |
|
---|
| 682 | /* zero the int */
|
---|
| 683 | mp_zero (a);
|
---|
| 684 |
|
---|
| 685 | /* read the bytes in */
|
---|
| 686 | while (c-- > 0) {
|
---|
| 687 | if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
|
---|
| 688 | return res;
|
---|
| 689 | }
|
---|
| 690 |
|
---|
| 691 | #ifndef MP_8BIT
|
---|
| 692 | a->dp[0] |= *b++;
|
---|
| 693 | a->used += 1;
|
---|
| 694 | #else
|
---|
| 695 | a->dp[0] = (*b & MP_MASK);
|
---|
| 696 | a->dp[1] |= ((*b++ >> 7U) & 1);
|
---|
| 697 | a->used += 2;
|
---|
| 698 | #endif
|
---|
| 699 | }
|
---|
| 700 | mp_clamp (a);
|
---|
| 701 | return MP_OKAY;
|
---|
| 702 | }
|
---|
| 703 |
|
---|
| 704 |
|
---|
| 705 | /* shift left by a certain bit count */
|
---|
| 706 | int mp_mul_2d (mp_int * a, int b, mp_int * c)
|
---|
| 707 | {
|
---|
| 708 | mp_digit d;
|
---|
| 709 | int res;
|
---|
| 710 |
|
---|
| 711 | /* copy */
|
---|
| 712 | if (a != c) {
|
---|
| 713 | if ((res = mp_copy (a, c)) != MP_OKAY) {
|
---|
| 714 | return res;
|
---|
| 715 | }
|
---|
| 716 | }
|
---|
| 717 |
|
---|
| 718 | if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
|
---|
| 719 | if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
|
---|
| 720 | return res;
|
---|
| 721 | }
|
---|
| 722 | }
|
---|
| 723 |
|
---|
| 724 | /* shift by as many digits in the bit count */
|
---|
| 725 | if (b >= (int)DIGIT_BIT) {
|
---|
| 726 | if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
|
---|
| 727 | return res;
|
---|
| 728 | }
|
---|
| 729 | }
|
---|
| 730 |
|
---|
| 731 | /* shift any bit count < DIGIT_BIT */
|
---|
| 732 | d = (mp_digit) (b % DIGIT_BIT);
|
---|
| 733 | if (d != 0) {
|
---|
| 734 | mp_digit *tmpc, shift, mask, r, rr;
|
---|
| 735 | int x;
|
---|
| 736 |
|
---|
| 737 | /* bitmask for carries */
|
---|
| 738 | mask = (((mp_digit)1) << d) - 1;
|
---|
| 739 |
|
---|
| 740 | /* shift for msbs */
|
---|
| 741 | shift = DIGIT_BIT - d;
|
---|
| 742 |
|
---|
| 743 | /* alias */
|
---|
| 744 | tmpc = c->dp;
|
---|
| 745 |
|
---|
| 746 | /* carry */
|
---|
| 747 | r = 0;
|
---|
| 748 | for (x = 0; x < c->used; x++) {
|
---|
| 749 | /* get the higher bits of the current word */
|
---|
| 750 | rr = (*tmpc >> shift) & mask;
|
---|
| 751 |
|
---|
| 752 | /* shift the current word and OR in the carry */
|
---|
| 753 | *tmpc = (mp_digit)(((*tmpc << d) | r) & MP_MASK);
|
---|
| 754 | ++tmpc;
|
---|
| 755 |
|
---|
| 756 | /* set the carry to the carry bits of the current word */
|
---|
| 757 | r = rr;
|
---|
| 758 | }
|
---|
| 759 |
|
---|
| 760 | /* set final carry */
|
---|
| 761 | if (r != 0) {
|
---|
| 762 | c->dp[(c->used)++] = r;
|
---|
| 763 | }
|
---|
| 764 | }
|
---|
| 765 | mp_clamp (c);
|
---|
| 766 | return MP_OKAY;
|
---|
| 767 | }
|
---|
| 768 |
|
---|
| 769 |
|
---|
| 770 | /* shift left a certain amount of digits */
|
---|
| 771 | int mp_lshd (mp_int * a, int b)
|
---|
| 772 | {
|
---|
| 773 | int x, res;
|
---|
| 774 |
|
---|
| 775 | /* if its less than zero return */
|
---|
| 776 | if (b <= 0) {
|
---|
| 777 | return MP_OKAY;
|
---|
| 778 | }
|
---|
| 779 |
|
---|
| 780 | /* grow to fit the new digits */
|
---|
| 781 | if (a->alloc < a->used + b) {
|
---|
| 782 | if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
|
---|
| 783 | return res;
|
---|
| 784 | }
|
---|
| 785 | }
|
---|
| 786 |
|
---|
| 787 | {
|
---|
| 788 | mp_digit *top, *bottom;
|
---|
| 789 |
|
---|
| 790 | /* increment the used by the shift amount then copy upwards */
|
---|
| 791 | a->used += b;
|
---|
| 792 |
|
---|
| 793 | /* top */
|
---|
| 794 | top = a->dp + a->used - 1;
|
---|
| 795 |
|
---|
| 796 | /* base */
|
---|
| 797 | bottom = a->dp + a->used - 1 - b;
|
---|
| 798 |
|
---|
| 799 | /* much like mp_rshd this is implemented using a sliding window
|
---|
| 800 | * except the window goes the other way around. Copying from
|
---|
| 801 | * the bottom to the top. see bn_mp_rshd.c for more info.
|
---|
| 802 | */
|
---|
| 803 | for (x = a->used - 1; x >= b; x--) {
|
---|
| 804 | *top-- = *bottom--;
|
---|
| 805 | }
|
---|
| 806 |
|
---|
| 807 | /* zero the lower digits */
|
---|
| 808 | top = a->dp;
|
---|
| 809 | for (x = 0; x < b; x++) {
|
---|
| 810 | *top++ = 0;
|
---|
| 811 | }
|
---|
| 812 | }
|
---|
| 813 | return MP_OKAY;
|
---|
| 814 | }
|
---|
| 815 |
|
---|
| 816 |
|
---|
| 817 | /* this is a shell function that calls either the normal or Montgomery
|
---|
| 818 | * exptmod functions. Originally the call to the montgomery code was
|
---|
| 819 | * embedded in the normal function but that wasted a lot of stack space
|
---|
| 820 | * for nothing (since 99% of the time the Montgomery code would be called)
|
---|
| 821 | */
|
---|
| 822 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 823 | int wolfcrypt_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
|
---|
| 824 | #else
|
---|
| 825 | int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
|
---|
| 826 | #endif
|
---|
| 827 | {
|
---|
| 828 | int dr;
|
---|
| 829 |
|
---|
| 830 | /* modulus P must be positive */
|
---|
| 831 | if (P->sign == MP_NEG) {
|
---|
| 832 | return MP_VAL;
|
---|
| 833 | }
|
---|
| 834 |
|
---|
| 835 | /* if exponent X is negative we have to recurse */
|
---|
| 836 | if (X->sign == MP_NEG) {
|
---|
| 837 | #ifdef BN_MP_INVMOD_C
|
---|
| 838 | mp_int tmpG, tmpX;
|
---|
| 839 | int err;
|
---|
| 840 |
|
---|
| 841 | /* first compute 1/G mod P */
|
---|
| 842 | if ((err = mp_init(&tmpG)) != MP_OKAY) {
|
---|
| 843 | return err;
|
---|
| 844 | }
|
---|
| 845 | if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
|
---|
| 846 | mp_clear(&tmpG);
|
---|
| 847 | return err;
|
---|
| 848 | }
|
---|
| 849 |
|
---|
| 850 | /* now get |X| */
|
---|
| 851 | if ((err = mp_init(&tmpX)) != MP_OKAY) {
|
---|
| 852 | mp_clear(&tmpG);
|
---|
| 853 | return err;
|
---|
| 854 | }
|
---|
| 855 | if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
|
---|
| 856 | mp_clear(&tmpG);
|
---|
| 857 | mp_clear(&tmpX);
|
---|
| 858 | return err;
|
---|
| 859 | }
|
---|
| 860 |
|
---|
| 861 | /* and now compute (1/G)**|X| instead of G**X [X < 0] */
|
---|
| 862 | err = mp_exptmod(&tmpG, &tmpX, P, Y);
|
---|
| 863 | mp_clear(&tmpG);
|
---|
| 864 | mp_clear(&tmpX);
|
---|
| 865 | return err;
|
---|
| 866 | #else
|
---|
| 867 | /* no invmod */
|
---|
| 868 | return MP_VAL;
|
---|
| 869 | #endif
|
---|
| 870 | }
|
---|
| 871 |
|
---|
| 872 | /* modified diminished radix reduction */
|
---|
| 873 | #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && \
|
---|
| 874 | defined(BN_S_MP_EXPTMOD_C)
|
---|
| 875 | if (mp_reduce_is_2k_l(P) == MP_YES) {
|
---|
| 876 | return s_mp_exptmod(G, X, P, Y, 1);
|
---|
| 877 | }
|
---|
| 878 | #endif
|
---|
| 879 |
|
---|
| 880 | #ifdef BN_MP_DR_IS_MODULUS_C
|
---|
| 881 | /* is it a DR modulus? */
|
---|
| 882 | dr = mp_dr_is_modulus(P);
|
---|
| 883 | #else
|
---|
| 884 | /* default to no */
|
---|
| 885 | dr = 0;
|
---|
| 886 | #endif
|
---|
| 887 |
|
---|
| 888 | #ifdef BN_MP_REDUCE_IS_2K_C
|
---|
| 889 | /* if not, is it a unrestricted DR modulus? */
|
---|
| 890 | if (dr == 0) {
|
---|
| 891 | dr = mp_reduce_is_2k(P) << 1;
|
---|
| 892 | }
|
---|
| 893 | #endif
|
---|
| 894 |
|
---|
| 895 | /* if the modulus is odd or dr != 0 use the montgomery method */
|
---|
| 896 | #ifdef BN_MP_EXPTMOD_FAST_C
|
---|
| 897 | if (mp_isodd (P) == MP_YES || dr != 0) {
|
---|
| 898 | return mp_exptmod_fast (G, X, P, Y, dr);
|
---|
| 899 | } else {
|
---|
| 900 | #endif
|
---|
| 901 | #ifdef BN_S_MP_EXPTMOD_C
|
---|
| 902 | /* otherwise use the generic Barrett reduction technique */
|
---|
| 903 | return s_mp_exptmod (G, X, P, Y, 0);
|
---|
| 904 | #else
|
---|
| 905 | /* no exptmod for evens */
|
---|
| 906 | return MP_VAL;
|
---|
| 907 | #endif
|
---|
| 908 | #ifdef BN_MP_EXPTMOD_FAST_C
|
---|
| 909 | }
|
---|
| 910 | #endif
|
---|
| 911 | }
|
---|
| 912 |
|
---|
| 913 |
|
---|
| 914 | /* b = |a|
|
---|
| 915 | *
|
---|
| 916 | * Simple function copies the input and fixes the sign to positive
|
---|
| 917 | */
|
---|
| 918 | int mp_abs (mp_int * a, mp_int * b)
|
---|
| 919 | {
|
---|
| 920 | int res;
|
---|
| 921 |
|
---|
| 922 | /* copy a to b */
|
---|
| 923 | if (a != b) {
|
---|
| 924 | if ((res = mp_copy (a, b)) != MP_OKAY) {
|
---|
| 925 | return res;
|
---|
| 926 | }
|
---|
| 927 | }
|
---|
| 928 |
|
---|
| 929 | /* force the sign of b to positive */
|
---|
| 930 | b->sign = MP_ZPOS;
|
---|
| 931 |
|
---|
| 932 | return MP_OKAY;
|
---|
| 933 | }
|
---|
| 934 |
|
---|
| 935 |
|
---|
| 936 | /* hac 14.61, pp608 */
|
---|
| 937 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 938 | int wolfcrypt_mp_invmod(mp_int * a, mp_int * b, mp_int * c)
|
---|
| 939 | #else
|
---|
| 940 | int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 941 | #endif
|
---|
| 942 | {
|
---|
| 943 | /* b cannot be negative */
|
---|
| 944 | if (b->sign == MP_NEG || mp_iszero(b) == MP_YES) {
|
---|
| 945 | return MP_VAL;
|
---|
| 946 | }
|
---|
| 947 |
|
---|
| 948 | #ifdef BN_FAST_MP_INVMOD_C
|
---|
| 949 | /* if the modulus is odd we can use a faster routine instead */
|
---|
| 950 | if ((mp_isodd(b) == MP_YES) && (mp_cmp_d(b, 1) != MP_EQ)) {
|
---|
| 951 | return fast_mp_invmod (a, b, c);
|
---|
| 952 | }
|
---|
| 953 | #endif
|
---|
| 954 |
|
---|
| 955 | #ifdef BN_MP_INVMOD_SLOW_C
|
---|
| 956 | return mp_invmod_slow(a, b, c);
|
---|
| 957 | #else
|
---|
| 958 | return MP_VAL;
|
---|
| 959 | #endif
|
---|
| 960 | }
|
---|
| 961 |
|
---|
| 962 |
|
---|
| 963 | /* computes the modular inverse via binary extended euclidean algorithm,
|
---|
| 964 | * that is c = 1/a mod b
|
---|
| 965 | *
|
---|
| 966 | * Based on slow invmod except this is optimized for the case where b is
|
---|
| 967 | * odd as per HAC Note 14.64 on pp. 610
|
---|
| 968 | */
|
---|
| 969 | int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 970 | {
|
---|
| 971 | mp_int x, y, u, v, B, D;
|
---|
| 972 | int res, neg, loop_check = 0;
|
---|
| 973 |
|
---|
| 974 | /* 2. [modified] b must be odd */
|
---|
| 975 | if (mp_iseven (b) == MP_YES) {
|
---|
| 976 | return MP_VAL;
|
---|
| 977 | }
|
---|
| 978 |
|
---|
| 979 | /* init all our temps */
|
---|
| 980 | if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D)) != MP_OKAY) {
|
---|
| 981 | return res;
|
---|
| 982 | }
|
---|
| 983 |
|
---|
| 984 | /* x == modulus, y == value to invert */
|
---|
| 985 | if ((res = mp_copy (b, &x)) != MP_OKAY) {
|
---|
| 986 | goto LBL_ERR;
|
---|
| 987 | }
|
---|
| 988 |
|
---|
| 989 | /* we need y = |a| */
|
---|
| 990 | if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
|
---|
| 991 | goto LBL_ERR;
|
---|
| 992 | }
|
---|
| 993 |
|
---|
| 994 | /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
---|
| 995 | if ((res = mp_copy (&x, &u)) != MP_OKAY) {
|
---|
| 996 | goto LBL_ERR;
|
---|
| 997 | }
|
---|
| 998 | if ((res = mp_copy (&y, &v)) != MP_OKAY) {
|
---|
| 999 | goto LBL_ERR;
|
---|
| 1000 | }
|
---|
| 1001 | if ((res = mp_set (&D, 1)) != MP_OKAY) {
|
---|
| 1002 | goto LBL_ERR;
|
---|
| 1003 | }
|
---|
| 1004 |
|
---|
| 1005 | top:
|
---|
| 1006 | /* 4. while u is even do */
|
---|
| 1007 | while (mp_iseven (&u) == MP_YES) {
|
---|
| 1008 | /* 4.1 u = u/2 */
|
---|
| 1009 | if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
|
---|
| 1010 | goto LBL_ERR;
|
---|
| 1011 | }
|
---|
| 1012 | /* 4.2 if B is odd then */
|
---|
| 1013 | if (mp_isodd (&B) == MP_YES) {
|
---|
| 1014 | if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
|
---|
| 1015 | goto LBL_ERR;
|
---|
| 1016 | }
|
---|
| 1017 | }
|
---|
| 1018 | /* B = B/2 */
|
---|
| 1019 | if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
|
---|
| 1020 | goto LBL_ERR;
|
---|
| 1021 | }
|
---|
| 1022 | }
|
---|
| 1023 |
|
---|
| 1024 | /* 5. while v is even do */
|
---|
| 1025 | while (mp_iseven (&v) == MP_YES) {
|
---|
| 1026 | /* 5.1 v = v/2 */
|
---|
| 1027 | if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
|
---|
| 1028 | goto LBL_ERR;
|
---|
| 1029 | }
|
---|
| 1030 | /* 5.2 if D is odd then */
|
---|
| 1031 | if (mp_isodd (&D) == MP_YES) {
|
---|
| 1032 | /* D = (D-x)/2 */
|
---|
| 1033 | if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
|
---|
| 1034 | goto LBL_ERR;
|
---|
| 1035 | }
|
---|
| 1036 | }
|
---|
| 1037 | /* D = D/2 */
|
---|
| 1038 | if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
|
---|
| 1039 | goto LBL_ERR;
|
---|
| 1040 | }
|
---|
| 1041 | }
|
---|
| 1042 |
|
---|
| 1043 | /* 6. if u >= v then */
|
---|
| 1044 | if (mp_cmp (&u, &v) != MP_LT) {
|
---|
| 1045 | /* u = u - v, B = B - D */
|
---|
| 1046 | if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
|
---|
| 1047 | goto LBL_ERR;
|
---|
| 1048 | }
|
---|
| 1049 |
|
---|
| 1050 | if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
|
---|
| 1051 | goto LBL_ERR;
|
---|
| 1052 | }
|
---|
| 1053 | } else {
|
---|
| 1054 | /* v - v - u, D = D - B */
|
---|
| 1055 | if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
|
---|
| 1056 | goto LBL_ERR;
|
---|
| 1057 | }
|
---|
| 1058 |
|
---|
| 1059 | if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
|
---|
| 1060 | goto LBL_ERR;
|
---|
| 1061 | }
|
---|
| 1062 | }
|
---|
| 1063 |
|
---|
| 1064 | /* if not zero goto step 4 */
|
---|
| 1065 | if (mp_iszero (&u) == MP_NO) {
|
---|
| 1066 | if (++loop_check > MAX_INVMOD_SZ) {
|
---|
| 1067 | res = MP_VAL;
|
---|
| 1068 | goto LBL_ERR;
|
---|
| 1069 | }
|
---|
| 1070 | goto top;
|
---|
| 1071 | }
|
---|
| 1072 |
|
---|
| 1073 | /* now a = C, b = D, gcd == g*v */
|
---|
| 1074 |
|
---|
| 1075 | /* if v != 1 then there is no inverse */
|
---|
| 1076 | if (mp_cmp_d (&v, 1) != MP_EQ) {
|
---|
| 1077 | res = MP_VAL;
|
---|
| 1078 | goto LBL_ERR;
|
---|
| 1079 | }
|
---|
| 1080 |
|
---|
| 1081 | /* b is now the inverse */
|
---|
| 1082 | neg = a->sign;
|
---|
| 1083 | while (D.sign == MP_NEG) {
|
---|
| 1084 | if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
|
---|
| 1085 | goto LBL_ERR;
|
---|
| 1086 | }
|
---|
| 1087 | }
|
---|
| 1088 | /* too big */
|
---|
| 1089 | while (mp_cmp_mag(&D, b) != MP_LT) {
|
---|
| 1090 | if ((res = mp_sub(&D, b, &D)) != MP_OKAY) {
|
---|
| 1091 | goto LBL_ERR;
|
---|
| 1092 | }
|
---|
| 1093 | }
|
---|
| 1094 | mp_exch (&D, c);
|
---|
| 1095 | c->sign = neg;
|
---|
| 1096 | res = MP_OKAY;
|
---|
| 1097 |
|
---|
| 1098 | LBL_ERR:mp_clear(&x);
|
---|
| 1099 | mp_clear(&y);
|
---|
| 1100 | mp_clear(&u);
|
---|
| 1101 | mp_clear(&v);
|
---|
| 1102 | mp_clear(&B);
|
---|
| 1103 | mp_clear(&D);
|
---|
| 1104 | return res;
|
---|
| 1105 | }
|
---|
| 1106 |
|
---|
| 1107 |
|
---|
| 1108 | /* hac 14.61, pp608 */
|
---|
| 1109 | int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1110 | {
|
---|
| 1111 | mp_int x, y, u, v, A, B, C, D;
|
---|
| 1112 | int res;
|
---|
| 1113 |
|
---|
| 1114 | /* b cannot be negative */
|
---|
| 1115 | if (b->sign == MP_NEG || mp_iszero(b) == MP_YES) {
|
---|
| 1116 | return MP_VAL;
|
---|
| 1117 | }
|
---|
| 1118 |
|
---|
| 1119 | /* init temps */
|
---|
| 1120 | if ((res = mp_init_multi(&x, &y, &u, &v,
|
---|
| 1121 | &A, &B)) != MP_OKAY) {
|
---|
| 1122 | return res;
|
---|
| 1123 | }
|
---|
| 1124 |
|
---|
| 1125 | /* init rest of tmps temps */
|
---|
| 1126 | if ((res = mp_init_multi(&C, &D, 0, 0, 0, 0)) != MP_OKAY) {
|
---|
| 1127 | mp_clear(&x);
|
---|
| 1128 | mp_clear(&y);
|
---|
| 1129 | mp_clear(&u);
|
---|
| 1130 | mp_clear(&v);
|
---|
| 1131 | mp_clear(&A);
|
---|
| 1132 | mp_clear(&B);
|
---|
| 1133 | return res;
|
---|
| 1134 | }
|
---|
| 1135 |
|
---|
| 1136 | /* x = a, y = b */
|
---|
| 1137 | if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
|
---|
| 1138 | goto LBL_ERR;
|
---|
| 1139 | }
|
---|
| 1140 | if ((res = mp_copy (b, &y)) != MP_OKAY) {
|
---|
| 1141 | goto LBL_ERR;
|
---|
| 1142 | }
|
---|
| 1143 |
|
---|
| 1144 | /* 2. [modified] if x,y are both even then return an error! */
|
---|
| 1145 | if (mp_iseven (&x) == MP_YES && mp_iseven (&y) == MP_YES) {
|
---|
| 1146 | res = MP_VAL;
|
---|
| 1147 | goto LBL_ERR;
|
---|
| 1148 | }
|
---|
| 1149 |
|
---|
| 1150 | /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
---|
| 1151 | if ((res = mp_copy (&x, &u)) != MP_OKAY) {
|
---|
| 1152 | goto LBL_ERR;
|
---|
| 1153 | }
|
---|
| 1154 | if ((res = mp_copy (&y, &v)) != MP_OKAY) {
|
---|
| 1155 | goto LBL_ERR;
|
---|
| 1156 | }
|
---|
| 1157 | if ((res = mp_set (&A, 1)) != MP_OKAY) {
|
---|
| 1158 | goto LBL_ERR;
|
---|
| 1159 | }
|
---|
| 1160 | if ((res = mp_set (&D, 1)) != MP_OKAY) {
|
---|
| 1161 | goto LBL_ERR;
|
---|
| 1162 | }
|
---|
| 1163 |
|
---|
| 1164 | top:
|
---|
| 1165 | /* 4. while u is even do */
|
---|
| 1166 | while (mp_iseven (&u) == MP_YES) {
|
---|
| 1167 | /* 4.1 u = u/2 */
|
---|
| 1168 | if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
|
---|
| 1169 | goto LBL_ERR;
|
---|
| 1170 | }
|
---|
| 1171 | /* 4.2 if A or B is odd then */
|
---|
| 1172 | if (mp_isodd (&A) == MP_YES || mp_isodd (&B) == MP_YES) {
|
---|
| 1173 | /* A = (A+y)/2, B = (B-x)/2 */
|
---|
| 1174 | if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
|
---|
| 1175 | goto LBL_ERR;
|
---|
| 1176 | }
|
---|
| 1177 | if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
|
---|
| 1178 | goto LBL_ERR;
|
---|
| 1179 | }
|
---|
| 1180 | }
|
---|
| 1181 | /* A = A/2, B = B/2 */
|
---|
| 1182 | if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
|
---|
| 1183 | goto LBL_ERR;
|
---|
| 1184 | }
|
---|
| 1185 | if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
|
---|
| 1186 | goto LBL_ERR;
|
---|
| 1187 | }
|
---|
| 1188 | }
|
---|
| 1189 |
|
---|
| 1190 | /* 5. while v is even do */
|
---|
| 1191 | while (mp_iseven (&v) == MP_YES) {
|
---|
| 1192 | /* 5.1 v = v/2 */
|
---|
| 1193 | if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
|
---|
| 1194 | goto LBL_ERR;
|
---|
| 1195 | }
|
---|
| 1196 | /* 5.2 if C or D is odd then */
|
---|
| 1197 | if (mp_isodd (&C) == MP_YES || mp_isodd (&D) == MP_YES) {
|
---|
| 1198 | /* C = (C+y)/2, D = (D-x)/2 */
|
---|
| 1199 | if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
|
---|
| 1200 | goto LBL_ERR;
|
---|
| 1201 | }
|
---|
| 1202 | if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
|
---|
| 1203 | goto LBL_ERR;
|
---|
| 1204 | }
|
---|
| 1205 | }
|
---|
| 1206 | /* C = C/2, D = D/2 */
|
---|
| 1207 | if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
|
---|
| 1208 | goto LBL_ERR;
|
---|
| 1209 | }
|
---|
| 1210 | if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
|
---|
| 1211 | goto LBL_ERR;
|
---|
| 1212 | }
|
---|
| 1213 | }
|
---|
| 1214 |
|
---|
| 1215 | /* 6. if u >= v then */
|
---|
| 1216 | if (mp_cmp (&u, &v) != MP_LT) {
|
---|
| 1217 | /* u = u - v, A = A - C, B = B - D */
|
---|
| 1218 | if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
|
---|
| 1219 | goto LBL_ERR;
|
---|
| 1220 | }
|
---|
| 1221 |
|
---|
| 1222 | if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
|
---|
| 1223 | goto LBL_ERR;
|
---|
| 1224 | }
|
---|
| 1225 |
|
---|
| 1226 | if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
|
---|
| 1227 | goto LBL_ERR;
|
---|
| 1228 | }
|
---|
| 1229 | } else {
|
---|
| 1230 | /* v - v - u, C = C - A, D = D - B */
|
---|
| 1231 | if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
|
---|
| 1232 | goto LBL_ERR;
|
---|
| 1233 | }
|
---|
| 1234 |
|
---|
| 1235 | if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
|
---|
| 1236 | goto LBL_ERR;
|
---|
| 1237 | }
|
---|
| 1238 |
|
---|
| 1239 | if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
|
---|
| 1240 | goto LBL_ERR;
|
---|
| 1241 | }
|
---|
| 1242 | }
|
---|
| 1243 |
|
---|
| 1244 | /* if not zero goto step 4 */
|
---|
| 1245 | if (mp_iszero (&u) == MP_NO)
|
---|
| 1246 | goto top;
|
---|
| 1247 |
|
---|
| 1248 | /* now a = C, b = D, gcd == g*v */
|
---|
| 1249 |
|
---|
| 1250 | /* if v != 1 then there is no inverse */
|
---|
| 1251 | if (mp_cmp_d (&v, 1) != MP_EQ) {
|
---|
| 1252 | res = MP_VAL;
|
---|
| 1253 | goto LBL_ERR;
|
---|
| 1254 | }
|
---|
| 1255 |
|
---|
| 1256 | /* if its too low */
|
---|
| 1257 | while (mp_cmp_d(&C, 0) == MP_LT) {
|
---|
| 1258 | if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
|
---|
| 1259 | goto LBL_ERR;
|
---|
| 1260 | }
|
---|
| 1261 | }
|
---|
| 1262 |
|
---|
| 1263 | /* too big */
|
---|
| 1264 | while (mp_cmp_mag(&C, b) != MP_LT) {
|
---|
| 1265 | if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
|
---|
| 1266 | goto LBL_ERR;
|
---|
| 1267 | }
|
---|
| 1268 | }
|
---|
| 1269 |
|
---|
| 1270 | /* C is now the inverse */
|
---|
| 1271 | mp_exch (&C, c);
|
---|
| 1272 | res = MP_OKAY;
|
---|
| 1273 | LBL_ERR:mp_clear(&x);
|
---|
| 1274 | mp_clear(&y);
|
---|
| 1275 | mp_clear(&u);
|
---|
| 1276 | mp_clear(&v);
|
---|
| 1277 | mp_clear(&A);
|
---|
| 1278 | mp_clear(&B);
|
---|
| 1279 | mp_clear(&C);
|
---|
| 1280 | mp_clear(&D);
|
---|
| 1281 | return res;
|
---|
| 1282 | }
|
---|
| 1283 |
|
---|
| 1284 |
|
---|
| 1285 | /* compare magnitude of two ints (unsigned) */
|
---|
| 1286 | int mp_cmp_mag (mp_int * a, mp_int * b)
|
---|
| 1287 | {
|
---|
| 1288 | int n;
|
---|
| 1289 | mp_digit *tmpa, *tmpb;
|
---|
| 1290 |
|
---|
| 1291 | /* compare based on # of non-zero digits */
|
---|
| 1292 | if (a->used > b->used) {
|
---|
| 1293 | return MP_GT;
|
---|
| 1294 | }
|
---|
| 1295 |
|
---|
| 1296 | if (a->used < b->used) {
|
---|
| 1297 | return MP_LT;
|
---|
| 1298 | }
|
---|
| 1299 |
|
---|
| 1300 | /* alias for a */
|
---|
| 1301 | tmpa = a->dp + (a->used - 1);
|
---|
| 1302 |
|
---|
| 1303 | /* alias for b */
|
---|
| 1304 | tmpb = b->dp + (a->used - 1);
|
---|
| 1305 |
|
---|
| 1306 | /* compare based on digits */
|
---|
| 1307 | for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
|
---|
| 1308 | if (*tmpa > *tmpb) {
|
---|
| 1309 | return MP_GT;
|
---|
| 1310 | }
|
---|
| 1311 |
|
---|
| 1312 | if (*tmpa < *tmpb) {
|
---|
| 1313 | return MP_LT;
|
---|
| 1314 | }
|
---|
| 1315 | }
|
---|
| 1316 | return MP_EQ;
|
---|
| 1317 | }
|
---|
| 1318 |
|
---|
| 1319 |
|
---|
| 1320 | /* compare two ints (signed)*/
|
---|
| 1321 | int mp_cmp (mp_int * a, mp_int * b)
|
---|
| 1322 | {
|
---|
| 1323 | /* compare based on sign */
|
---|
| 1324 | if (a->sign != b->sign) {
|
---|
| 1325 | if (a->sign == MP_NEG) {
|
---|
| 1326 | return MP_LT;
|
---|
| 1327 | } else {
|
---|
| 1328 | return MP_GT;
|
---|
| 1329 | }
|
---|
| 1330 | }
|
---|
| 1331 |
|
---|
| 1332 | /* compare digits */
|
---|
| 1333 | if (a->sign == MP_NEG) {
|
---|
| 1334 | /* if negative compare opposite direction */
|
---|
| 1335 | return mp_cmp_mag(b, a);
|
---|
| 1336 | } else {
|
---|
| 1337 | return mp_cmp_mag(a, b);
|
---|
| 1338 | }
|
---|
| 1339 | }
|
---|
| 1340 |
|
---|
| 1341 |
|
---|
| 1342 | /* compare a digit */
|
---|
| 1343 | int mp_cmp_d(mp_int * a, mp_digit b)
|
---|
| 1344 | {
|
---|
| 1345 | /* special case for zero*/
|
---|
| 1346 | if (a->used == 0 && b == 0)
|
---|
| 1347 | return MP_EQ;
|
---|
| 1348 |
|
---|
| 1349 | /* compare based on sign */
|
---|
| 1350 | if ((b && a->used == 0) || a->sign == MP_NEG) {
|
---|
| 1351 | return MP_LT;
|
---|
| 1352 | }
|
---|
| 1353 |
|
---|
| 1354 | /* compare based on magnitude */
|
---|
| 1355 | if (a->used > 1) {
|
---|
| 1356 | return MP_GT;
|
---|
| 1357 | }
|
---|
| 1358 |
|
---|
| 1359 | /* compare the only digit of a to b */
|
---|
| 1360 | if (a->dp[0] > b) {
|
---|
| 1361 | return MP_GT;
|
---|
| 1362 | } else if (a->dp[0] < b) {
|
---|
| 1363 | return MP_LT;
|
---|
| 1364 | } else {
|
---|
| 1365 | return MP_EQ;
|
---|
| 1366 | }
|
---|
| 1367 | }
|
---|
| 1368 |
|
---|
| 1369 |
|
---|
| 1370 | /* set to a digit */
|
---|
| 1371 | int mp_set (mp_int * a, mp_digit b)
|
---|
| 1372 | {
|
---|
| 1373 | int res;
|
---|
| 1374 | mp_zero (a);
|
---|
| 1375 | res = mp_grow (a, 1);
|
---|
| 1376 | if (res == MP_OKAY) {
|
---|
| 1377 | a->dp[0] = (mp_digit)(b & MP_MASK);
|
---|
| 1378 | a->used = (a->dp[0] != 0) ? 1 : 0;
|
---|
| 1379 | }
|
---|
| 1380 | return res;
|
---|
| 1381 | }
|
---|
| 1382 |
|
---|
| 1383 | /* chek if a bit is set */
|
---|
| 1384 | int mp_is_bit_set (mp_int *a, mp_digit b)
|
---|
| 1385 | {
|
---|
| 1386 | if ((mp_digit)a->used < b/DIGIT_BIT)
|
---|
| 1387 | return 0;
|
---|
| 1388 |
|
---|
| 1389 | return (int)((a->dp[b/DIGIT_BIT] >> b%DIGIT_BIT) & (mp_digit)1);
|
---|
| 1390 | }
|
---|
| 1391 |
|
---|
| 1392 | /* c = a mod b, 0 <= c < b */
|
---|
| 1393 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 1394 | int wolfcrypt_mp_mod(mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1395 | #else
|
---|
| 1396 | int mp_mod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1397 | #endif
|
---|
| 1398 | {
|
---|
| 1399 | mp_int t;
|
---|
| 1400 | int res;
|
---|
| 1401 |
|
---|
| 1402 | if ((res = mp_init_size (&t, b->used)) != MP_OKAY) {
|
---|
| 1403 | return res;
|
---|
| 1404 | }
|
---|
| 1405 |
|
---|
| 1406 | if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
|
---|
| 1407 | mp_clear (&t);
|
---|
| 1408 | return res;
|
---|
| 1409 | }
|
---|
| 1410 |
|
---|
| 1411 | if ((mp_iszero(&t) != MP_NO) || (t.sign == b->sign)) {
|
---|
| 1412 | res = MP_OKAY;
|
---|
| 1413 | mp_exch (&t, c);
|
---|
| 1414 | } else {
|
---|
| 1415 | res = mp_add (b, &t, c);
|
---|
| 1416 | }
|
---|
| 1417 |
|
---|
| 1418 | mp_clear (&t);
|
---|
| 1419 | return res;
|
---|
| 1420 | }
|
---|
| 1421 |
|
---|
| 1422 |
|
---|
| 1423 | /* slower bit-bang division... also smaller */
|
---|
| 1424 | int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
|
---|
| 1425 | {
|
---|
| 1426 | mp_int ta, tb, tq, q;
|
---|
| 1427 | int res, n, n2;
|
---|
| 1428 |
|
---|
| 1429 | /* is divisor zero ? */
|
---|
| 1430 | if (mp_iszero (b) == MP_YES) {
|
---|
| 1431 | return MP_VAL;
|
---|
| 1432 | }
|
---|
| 1433 |
|
---|
| 1434 | /* if a < b then q=0, r = a */
|
---|
| 1435 | if (mp_cmp_mag (a, b) == MP_LT) {
|
---|
| 1436 | if (d != NULL) {
|
---|
| 1437 | res = mp_copy (a, d);
|
---|
| 1438 | } else {
|
---|
| 1439 | res = MP_OKAY;
|
---|
| 1440 | }
|
---|
| 1441 | if (c != NULL) {
|
---|
| 1442 | mp_zero (c);
|
---|
| 1443 | }
|
---|
| 1444 | return res;
|
---|
| 1445 | }
|
---|
| 1446 |
|
---|
| 1447 | /* init our temps */
|
---|
| 1448 | if ((res = mp_init_multi(&ta, &tb, &tq, &q, 0, 0)) != MP_OKAY) {
|
---|
| 1449 | return res;
|
---|
| 1450 | }
|
---|
| 1451 |
|
---|
| 1452 | if ((res = mp_set(&tq, 1)) != MP_OKAY) {
|
---|
| 1453 | return res;
|
---|
| 1454 | }
|
---|
| 1455 | n = mp_count_bits(a) - mp_count_bits(b);
|
---|
| 1456 | if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
|
---|
| 1457 | ((res = mp_abs(b, &tb)) != MP_OKAY) ||
|
---|
| 1458 | ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
|
---|
| 1459 | ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
|
---|
| 1460 | goto LBL_ERR;
|
---|
| 1461 | }
|
---|
| 1462 |
|
---|
| 1463 | while (n-- >= 0) {
|
---|
| 1464 | if (mp_cmp(&tb, &ta) != MP_GT) {
|
---|
| 1465 | if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
|
---|
| 1466 | ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
|
---|
| 1467 | goto LBL_ERR;
|
---|
| 1468 | }
|
---|
| 1469 | }
|
---|
| 1470 | if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
|
---|
| 1471 | ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
|
---|
| 1472 | goto LBL_ERR;
|
---|
| 1473 | }
|
---|
| 1474 | }
|
---|
| 1475 |
|
---|
| 1476 | /* now q == quotient and ta == remainder */
|
---|
| 1477 | n = a->sign;
|
---|
| 1478 | n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
|
---|
| 1479 | if (c != NULL) {
|
---|
| 1480 | mp_exch(c, &q);
|
---|
| 1481 | c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
|
---|
| 1482 | }
|
---|
| 1483 | if (d != NULL) {
|
---|
| 1484 | mp_exch(d, &ta);
|
---|
| 1485 | d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
|
---|
| 1486 | }
|
---|
| 1487 | LBL_ERR:
|
---|
| 1488 | mp_clear(&ta);
|
---|
| 1489 | mp_clear(&tb);
|
---|
| 1490 | mp_clear(&tq);
|
---|
| 1491 | mp_clear(&q);
|
---|
| 1492 | return res;
|
---|
| 1493 | }
|
---|
| 1494 |
|
---|
| 1495 |
|
---|
| 1496 | /* b = a/2 */
|
---|
| 1497 | int mp_div_2(mp_int * a, mp_int * b)
|
---|
| 1498 | {
|
---|
| 1499 | int x, res, oldused;
|
---|
| 1500 |
|
---|
| 1501 | /* copy */
|
---|
| 1502 | if (b->alloc < a->used) {
|
---|
| 1503 | if ((res = mp_grow (b, a->used)) != MP_OKAY) {
|
---|
| 1504 | return res;
|
---|
| 1505 | }
|
---|
| 1506 | }
|
---|
| 1507 |
|
---|
| 1508 | oldused = b->used;
|
---|
| 1509 | b->used = a->used;
|
---|
| 1510 | {
|
---|
| 1511 | mp_digit r, rr, *tmpa, *tmpb;
|
---|
| 1512 |
|
---|
| 1513 | /* source alias */
|
---|
| 1514 | tmpa = a->dp + b->used - 1;
|
---|
| 1515 |
|
---|
| 1516 | /* dest alias */
|
---|
| 1517 | tmpb = b->dp + b->used - 1;
|
---|
| 1518 |
|
---|
| 1519 | /* carry */
|
---|
| 1520 | r = 0;
|
---|
| 1521 | for (x = b->used - 1; x >= 0; x--) {
|
---|
| 1522 | /* get the carry for the next iteration */
|
---|
| 1523 | rr = *tmpa & 1;
|
---|
| 1524 |
|
---|
| 1525 | /* shift the current digit, add in carry and store */
|
---|
| 1526 | *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
|
---|
| 1527 |
|
---|
| 1528 | /* forward carry to next iteration */
|
---|
| 1529 | r = rr;
|
---|
| 1530 | }
|
---|
| 1531 |
|
---|
| 1532 | /* zero excess digits */
|
---|
| 1533 | tmpb = b->dp + b->used;
|
---|
| 1534 | for (x = b->used; x < oldused; x++) {
|
---|
| 1535 | *tmpb++ = 0;
|
---|
| 1536 | }
|
---|
| 1537 | }
|
---|
| 1538 | b->sign = a->sign;
|
---|
| 1539 | mp_clamp (b);
|
---|
| 1540 | return MP_OKAY;
|
---|
| 1541 | }
|
---|
| 1542 |
|
---|
| 1543 |
|
---|
| 1544 | /* high level addition (handles signs) */
|
---|
| 1545 | int mp_add (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1546 | {
|
---|
| 1547 | int sa, sb, res;
|
---|
| 1548 |
|
---|
| 1549 | /* get sign of both inputs */
|
---|
| 1550 | sa = a->sign;
|
---|
| 1551 | sb = b->sign;
|
---|
| 1552 |
|
---|
| 1553 | /* handle two cases, not four */
|
---|
| 1554 | if (sa == sb) {
|
---|
| 1555 | /* both positive or both negative */
|
---|
| 1556 | /* add their magnitudes, copy the sign */
|
---|
| 1557 | c->sign = sa;
|
---|
| 1558 | res = s_mp_add (a, b, c);
|
---|
| 1559 | } else {
|
---|
| 1560 | /* one positive, the other negative */
|
---|
| 1561 | /* subtract the one with the greater magnitude from */
|
---|
| 1562 | /* the one of the lesser magnitude. The result gets */
|
---|
| 1563 | /* the sign of the one with the greater magnitude. */
|
---|
| 1564 | if (mp_cmp_mag (a, b) == MP_LT) {
|
---|
| 1565 | c->sign = sb;
|
---|
| 1566 | res = s_mp_sub (b, a, c);
|
---|
| 1567 | } else {
|
---|
| 1568 | c->sign = sa;
|
---|
| 1569 | res = s_mp_sub (a, b, c);
|
---|
| 1570 | }
|
---|
| 1571 | }
|
---|
| 1572 | return res;
|
---|
| 1573 | }
|
---|
| 1574 |
|
---|
| 1575 |
|
---|
| 1576 | /* low level addition, based on HAC pp.594, Algorithm 14.7 */
|
---|
| 1577 | int s_mp_add (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1578 | {
|
---|
| 1579 | mp_int *x;
|
---|
| 1580 | int olduse, res, min_ab, max_ab;
|
---|
| 1581 |
|
---|
| 1582 | /* find sizes, we let |a| <= |b| which means we have to sort
|
---|
| 1583 | * them. "x" will point to the input with the most digits
|
---|
| 1584 | */
|
---|
| 1585 | if (a->used > b->used) {
|
---|
| 1586 | min_ab = b->used;
|
---|
| 1587 | max_ab = a->used;
|
---|
| 1588 | x = a;
|
---|
| 1589 | } else {
|
---|
| 1590 | min_ab = a->used;
|
---|
| 1591 | max_ab = b->used;
|
---|
| 1592 | x = b;
|
---|
| 1593 | }
|
---|
| 1594 |
|
---|
| 1595 | /* init result */
|
---|
| 1596 | if (c->alloc < max_ab + 1) {
|
---|
| 1597 | if ((res = mp_grow (c, max_ab + 1)) != MP_OKAY) {
|
---|
| 1598 | return res;
|
---|
| 1599 | }
|
---|
| 1600 | }
|
---|
| 1601 |
|
---|
| 1602 | /* get old used digit count and set new one */
|
---|
| 1603 | olduse = c->used;
|
---|
| 1604 | c->used = max_ab + 1;
|
---|
| 1605 |
|
---|
| 1606 | {
|
---|
| 1607 | mp_digit u, *tmpa, *tmpb, *tmpc;
|
---|
| 1608 | int i;
|
---|
| 1609 |
|
---|
| 1610 | /* alias for digit pointers */
|
---|
| 1611 |
|
---|
| 1612 | /* first input */
|
---|
| 1613 | tmpa = a->dp;
|
---|
| 1614 |
|
---|
| 1615 | /* second input */
|
---|
| 1616 | tmpb = b->dp;
|
---|
| 1617 |
|
---|
| 1618 | /* destination */
|
---|
| 1619 | tmpc = c->dp;
|
---|
| 1620 |
|
---|
| 1621 | /* zero the carry */
|
---|
| 1622 | u = 0;
|
---|
| 1623 | for (i = 0; i < min_ab; i++) {
|
---|
| 1624 | /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
|
---|
| 1625 | *tmpc = *tmpa++ + *tmpb++ + u;
|
---|
| 1626 |
|
---|
| 1627 | /* U = carry bit of T[i] */
|
---|
| 1628 | u = *tmpc >> ((mp_digit)DIGIT_BIT);
|
---|
| 1629 |
|
---|
| 1630 | /* take away carry bit from T[i] */
|
---|
| 1631 | *tmpc++ &= MP_MASK;
|
---|
| 1632 | }
|
---|
| 1633 |
|
---|
| 1634 | /* now copy higher words if any, that is in A+B
|
---|
| 1635 | * if A or B has more digits add those in
|
---|
| 1636 | */
|
---|
| 1637 | if (min_ab != max_ab) {
|
---|
| 1638 | for (; i < max_ab; i++) {
|
---|
| 1639 | /* T[i] = X[i] + U */
|
---|
| 1640 | *tmpc = x->dp[i] + u;
|
---|
| 1641 |
|
---|
| 1642 | /* U = carry bit of T[i] */
|
---|
| 1643 | u = *tmpc >> ((mp_digit)DIGIT_BIT);
|
---|
| 1644 |
|
---|
| 1645 | /* take away carry bit from T[i] */
|
---|
| 1646 | *tmpc++ &= MP_MASK;
|
---|
| 1647 | }
|
---|
| 1648 | }
|
---|
| 1649 |
|
---|
| 1650 | /* add carry */
|
---|
| 1651 | *tmpc++ = u;
|
---|
| 1652 |
|
---|
| 1653 | /* clear digits above olduse */
|
---|
| 1654 | for (i = c->used; i < olduse; i++) {
|
---|
| 1655 | *tmpc++ = 0;
|
---|
| 1656 | }
|
---|
| 1657 | }
|
---|
| 1658 |
|
---|
| 1659 | mp_clamp (c);
|
---|
| 1660 | return MP_OKAY;
|
---|
| 1661 | }
|
---|
| 1662 |
|
---|
| 1663 |
|
---|
| 1664 | /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
|
---|
| 1665 | int s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1666 | {
|
---|
| 1667 | int olduse, res, min_b, max_a;
|
---|
| 1668 |
|
---|
| 1669 | /* find sizes */
|
---|
| 1670 | min_b = b->used;
|
---|
| 1671 | max_a = a->used;
|
---|
| 1672 |
|
---|
| 1673 | /* init result */
|
---|
| 1674 | if (c->alloc < max_a) {
|
---|
| 1675 | if ((res = mp_grow (c, max_a)) != MP_OKAY) {
|
---|
| 1676 | return res;
|
---|
| 1677 | }
|
---|
| 1678 | }
|
---|
| 1679 |
|
---|
| 1680 | /* sanity check on destination */
|
---|
| 1681 | if (c->dp == NULL)
|
---|
| 1682 | return MP_VAL;
|
---|
| 1683 |
|
---|
| 1684 | olduse = c->used;
|
---|
| 1685 | c->used = max_a;
|
---|
| 1686 |
|
---|
| 1687 | {
|
---|
| 1688 | mp_digit u, *tmpa, *tmpb, *tmpc;
|
---|
| 1689 | int i;
|
---|
| 1690 |
|
---|
| 1691 | /* alias for digit pointers */
|
---|
| 1692 | tmpa = a->dp;
|
---|
| 1693 | tmpb = b->dp;
|
---|
| 1694 | tmpc = c->dp;
|
---|
| 1695 |
|
---|
| 1696 | /* set carry to zero */
|
---|
| 1697 | u = 0;
|
---|
| 1698 | for (i = 0; i < min_b; i++) {
|
---|
| 1699 | /* T[i] = A[i] - B[i] - U */
|
---|
| 1700 | *tmpc = *tmpa++ - *tmpb++ - u;
|
---|
| 1701 |
|
---|
| 1702 | /* U = carry bit of T[i]
|
---|
| 1703 | * Note this saves performing an AND operation since
|
---|
| 1704 | * if a carry does occur it will propagate all the way to the
|
---|
| 1705 | * MSB. As a result a single shift is enough to get the carry
|
---|
| 1706 | */
|
---|
| 1707 | u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
|
---|
| 1708 |
|
---|
| 1709 | /* Clear carry from T[i] */
|
---|
| 1710 | *tmpc++ &= MP_MASK;
|
---|
| 1711 | }
|
---|
| 1712 |
|
---|
| 1713 | /* now copy higher words if any, e.g. if A has more digits than B */
|
---|
| 1714 | for (; i < max_a; i++) {
|
---|
| 1715 | /* T[i] = A[i] - U */
|
---|
| 1716 | *tmpc = *tmpa++ - u;
|
---|
| 1717 |
|
---|
| 1718 | /* U = carry bit of T[i] */
|
---|
| 1719 | u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
|
---|
| 1720 |
|
---|
| 1721 | /* Clear carry from T[i] */
|
---|
| 1722 | *tmpc++ &= MP_MASK;
|
---|
| 1723 | }
|
---|
| 1724 |
|
---|
| 1725 | /* clear digits above used (since we may not have grown result above) */
|
---|
| 1726 | for (i = c->used; i < olduse; i++) {
|
---|
| 1727 | *tmpc++ = 0;
|
---|
| 1728 | }
|
---|
| 1729 | }
|
---|
| 1730 |
|
---|
| 1731 | mp_clamp (c);
|
---|
| 1732 | return MP_OKAY;
|
---|
| 1733 | }
|
---|
| 1734 |
|
---|
| 1735 |
|
---|
| 1736 | /* high level subtraction (handles signs) */
|
---|
| 1737 | int mp_sub (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1738 | {
|
---|
| 1739 | int sa, sb, res;
|
---|
| 1740 |
|
---|
| 1741 | sa = a->sign;
|
---|
| 1742 | sb = b->sign;
|
---|
| 1743 |
|
---|
| 1744 | if (sa != sb) {
|
---|
| 1745 | /* subtract a negative from a positive, OR */
|
---|
| 1746 | /* subtract a positive from a negative. */
|
---|
| 1747 | /* In either case, ADD their magnitudes, */
|
---|
| 1748 | /* and use the sign of the first number. */
|
---|
| 1749 | c->sign = sa;
|
---|
| 1750 | res = s_mp_add (a, b, c);
|
---|
| 1751 | } else {
|
---|
| 1752 | /* subtract a positive from a positive, OR */
|
---|
| 1753 | /* subtract a negative from a negative. */
|
---|
| 1754 | /* First, take the difference between their */
|
---|
| 1755 | /* magnitudes, then... */
|
---|
| 1756 | if (mp_cmp_mag (a, b) != MP_LT) {
|
---|
| 1757 | /* Copy the sign from the first */
|
---|
| 1758 | c->sign = sa;
|
---|
| 1759 | /* The first has a larger or equal magnitude */
|
---|
| 1760 | res = s_mp_sub (a, b, c);
|
---|
| 1761 | } else {
|
---|
| 1762 | /* The result has the *opposite* sign from */
|
---|
| 1763 | /* the first number. */
|
---|
| 1764 | c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
|
---|
| 1765 | /* The second has a larger magnitude */
|
---|
| 1766 | res = s_mp_sub (b, a, c);
|
---|
| 1767 | }
|
---|
| 1768 | }
|
---|
| 1769 | return res;
|
---|
| 1770 | }
|
---|
| 1771 |
|
---|
| 1772 |
|
---|
| 1773 | /* determines if reduce_2k_l can be used */
|
---|
| 1774 | int mp_reduce_is_2k_l(mp_int *a)
|
---|
| 1775 | {
|
---|
| 1776 | int ix, iy;
|
---|
| 1777 |
|
---|
| 1778 | if (a->used == 0) {
|
---|
| 1779 | return MP_NO;
|
---|
| 1780 | } else if (a->used == 1) {
|
---|
| 1781 | return MP_YES;
|
---|
| 1782 | } else if (a->used > 1) {
|
---|
| 1783 | /* if more than half of the digits are -1 we're sold */
|
---|
| 1784 | for (iy = ix = 0; ix < a->used; ix++) {
|
---|
| 1785 | if (a->dp[ix] == MP_MASK) {
|
---|
| 1786 | ++iy;
|
---|
| 1787 | }
|
---|
| 1788 | }
|
---|
| 1789 | return (iy >= (a->used/2)) ? MP_YES : MP_NO;
|
---|
| 1790 |
|
---|
| 1791 | }
|
---|
| 1792 | return MP_NO;
|
---|
| 1793 | }
|
---|
| 1794 |
|
---|
| 1795 |
|
---|
| 1796 | /* determines if mp_reduce_2k can be used */
|
---|
| 1797 | int mp_reduce_is_2k(mp_int *a)
|
---|
| 1798 | {
|
---|
| 1799 | int ix, iy, iw;
|
---|
| 1800 | mp_digit iz;
|
---|
| 1801 |
|
---|
| 1802 | if (a->used == 0) {
|
---|
| 1803 | return MP_NO;
|
---|
| 1804 | } else if (a->used == 1) {
|
---|
| 1805 | return MP_YES;
|
---|
| 1806 | } else if (a->used > 1) {
|
---|
| 1807 | iy = mp_count_bits(a);
|
---|
| 1808 | iz = 1;
|
---|
| 1809 | iw = 1;
|
---|
| 1810 |
|
---|
| 1811 | /* Test every bit from the second digit up, must be 1 */
|
---|
| 1812 | for (ix = DIGIT_BIT; ix < iy; ix++) {
|
---|
| 1813 | if ((a->dp[iw] & iz) == 0) {
|
---|
| 1814 | return MP_NO;
|
---|
| 1815 | }
|
---|
| 1816 | iz <<= 1;
|
---|
| 1817 | if (iz > (mp_digit)MP_MASK) {
|
---|
| 1818 | ++iw;
|
---|
| 1819 | iz = 1;
|
---|
| 1820 | }
|
---|
| 1821 | }
|
---|
| 1822 | }
|
---|
| 1823 | return MP_YES;
|
---|
| 1824 | }
|
---|
| 1825 |
|
---|
| 1826 |
|
---|
| 1827 | /* determines if a number is a valid DR modulus */
|
---|
| 1828 | int mp_dr_is_modulus(mp_int *a)
|
---|
| 1829 | {
|
---|
| 1830 | int ix;
|
---|
| 1831 |
|
---|
| 1832 | /* must be at least two digits */
|
---|
| 1833 | if (a->used < 2) {
|
---|
| 1834 | return 0;
|
---|
| 1835 | }
|
---|
| 1836 |
|
---|
| 1837 | /* must be of the form b**k - a [a <= b] so all
|
---|
| 1838 | * but the first digit must be equal to -1 (mod b).
|
---|
| 1839 | */
|
---|
| 1840 | for (ix = 1; ix < a->used; ix++) {
|
---|
| 1841 | if (a->dp[ix] != MP_MASK) {
|
---|
| 1842 | return 0;
|
---|
| 1843 | }
|
---|
| 1844 | }
|
---|
| 1845 | return 1;
|
---|
| 1846 | }
|
---|
| 1847 |
|
---|
| 1848 |
|
---|
| 1849 | /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
|
---|
| 1850 | *
|
---|
| 1851 | * Uses a left-to-right k-ary sliding window to compute the modular
|
---|
| 1852 | * exponentiation.
|
---|
| 1853 | * The value of k changes based on the size of the exponent.
|
---|
| 1854 | *
|
---|
| 1855 | * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
|
---|
| 1856 | */
|
---|
| 1857 |
|
---|
| 1858 | #ifdef MP_LOW_MEM
|
---|
| 1859 | #define TAB_SIZE 32
|
---|
| 1860 | #else
|
---|
| 1861 | #define TAB_SIZE 256
|
---|
| 1862 | #endif
|
---|
| 1863 |
|
---|
| 1864 | int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y,
|
---|
| 1865 | int redmode)
|
---|
| 1866 | {
|
---|
| 1867 | mp_int res;
|
---|
| 1868 | mp_digit buf, mp;
|
---|
| 1869 | int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
---|
| 1870 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 1871 | mp_int* M = NULL;
|
---|
| 1872 | #else
|
---|
| 1873 | mp_int M[TAB_SIZE];
|
---|
| 1874 | #endif
|
---|
| 1875 | /* use a pointer to the reduction algorithm. This allows us to use
|
---|
| 1876 | * one of many reduction algorithms without modding the guts of
|
---|
| 1877 | * the code with if statements everywhere.
|
---|
| 1878 | */
|
---|
| 1879 | int (*redux)(mp_int*,mp_int*,mp_digit);
|
---|
| 1880 |
|
---|
| 1881 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 1882 | M = (mp_int*) XMALLOC(sizeof(mp_int) * TAB_SIZE, NULL,
|
---|
| 1883 | DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 1884 | if (M == NULL)
|
---|
| 1885 | return MP_MEM;
|
---|
| 1886 | #endif
|
---|
| 1887 |
|
---|
| 1888 | /* find window size */
|
---|
| 1889 | x = mp_count_bits (X);
|
---|
| 1890 | if (x <= 7) {
|
---|
| 1891 | winsize = 2;
|
---|
| 1892 | } else if (x <= 36) {
|
---|
| 1893 | winsize = 3;
|
---|
| 1894 | } else if (x <= 140) {
|
---|
| 1895 | winsize = 4;
|
---|
| 1896 | } else if (x <= 450) {
|
---|
| 1897 | winsize = 5;
|
---|
| 1898 | } else if (x <= 1303) {
|
---|
| 1899 | winsize = 6;
|
---|
| 1900 | } else if (x <= 3529) {
|
---|
| 1901 | winsize = 7;
|
---|
| 1902 | } else {
|
---|
| 1903 | winsize = 8;
|
---|
| 1904 | }
|
---|
| 1905 |
|
---|
| 1906 | #ifdef MP_LOW_MEM
|
---|
| 1907 | if (winsize > 5) {
|
---|
| 1908 | winsize = 5;
|
---|
| 1909 | }
|
---|
| 1910 | #endif
|
---|
| 1911 |
|
---|
| 1912 | /* init M array */
|
---|
| 1913 | /* init first cell */
|
---|
| 1914 | if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) {
|
---|
| 1915 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 1916 | XFREE(M, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 1917 | #endif
|
---|
| 1918 |
|
---|
| 1919 | return err;
|
---|
| 1920 | }
|
---|
| 1921 |
|
---|
| 1922 | /* now init the second half of the array */
|
---|
| 1923 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 1924 | if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) {
|
---|
| 1925 | for (y = 1<<(winsize-1); y < x; y++) {
|
---|
| 1926 | mp_clear (&M[y]);
|
---|
| 1927 | }
|
---|
| 1928 | mp_clear(&M[1]);
|
---|
| 1929 |
|
---|
| 1930 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 1931 | XFREE(M, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 1932 | #endif
|
---|
| 1933 |
|
---|
| 1934 | return err;
|
---|
| 1935 | }
|
---|
| 1936 | }
|
---|
| 1937 |
|
---|
| 1938 | /* determine and setup reduction code */
|
---|
| 1939 | if (redmode == 0) {
|
---|
| 1940 | #ifdef BN_MP_MONTGOMERY_SETUP_C
|
---|
| 1941 | /* now setup montgomery */
|
---|
| 1942 | if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
|
---|
| 1943 | goto LBL_M;
|
---|
| 1944 | }
|
---|
| 1945 | #else
|
---|
| 1946 | err = MP_VAL;
|
---|
| 1947 | goto LBL_M;
|
---|
| 1948 | #endif
|
---|
| 1949 |
|
---|
| 1950 | /* automatically pick the comba one if available (saves quite a few
|
---|
| 1951 | calls/ifs) */
|
---|
| 1952 | #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
|
---|
| 1953 | if (((P->used * 2 + 1) < MP_WARRAY) &&
|
---|
| 1954 | P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
| 1955 | redux = fast_mp_montgomery_reduce;
|
---|
| 1956 | } else
|
---|
| 1957 | #endif
|
---|
| 1958 | {
|
---|
| 1959 | #ifdef BN_MP_MONTGOMERY_REDUCE_C
|
---|
| 1960 | /* use slower baseline Montgomery method */
|
---|
| 1961 | redux = mp_montgomery_reduce;
|
---|
| 1962 | #else
|
---|
| 1963 | err = MP_VAL;
|
---|
| 1964 | goto LBL_M;
|
---|
| 1965 | #endif
|
---|
| 1966 | }
|
---|
| 1967 | } else if (redmode == 1) {
|
---|
| 1968 | #if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
|
---|
| 1969 | /* setup DR reduction for moduli of the form B**k - b */
|
---|
| 1970 | mp_dr_setup(P, &mp);
|
---|
| 1971 | redux = mp_dr_reduce;
|
---|
| 1972 | #else
|
---|
| 1973 | err = MP_VAL;
|
---|
| 1974 | goto LBL_M;
|
---|
| 1975 | #endif
|
---|
| 1976 | } else {
|
---|
| 1977 | #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
|
---|
| 1978 | /* setup DR reduction for moduli of the form 2**k - b */
|
---|
| 1979 | if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
|
---|
| 1980 | goto LBL_M;
|
---|
| 1981 | }
|
---|
| 1982 | redux = mp_reduce_2k;
|
---|
| 1983 | #else
|
---|
| 1984 | err = MP_VAL;
|
---|
| 1985 | goto LBL_M;
|
---|
| 1986 | #endif
|
---|
| 1987 | }
|
---|
| 1988 |
|
---|
| 1989 | /* setup result */
|
---|
| 1990 | if ((err = mp_init_size (&res, P->alloc)) != MP_OKAY) {
|
---|
| 1991 | goto LBL_M;
|
---|
| 1992 | }
|
---|
| 1993 |
|
---|
| 1994 | /* create M table
|
---|
| 1995 | *
|
---|
| 1996 |
|
---|
| 1997 | *
|
---|
| 1998 | * The first half of the table is not computed though accept for M[0] and M[1]
|
---|
| 1999 | */
|
---|
| 2000 |
|
---|
| 2001 | if (redmode == 0) {
|
---|
| 2002 | #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
|
---|
| 2003 | /* now we need R mod m */
|
---|
| 2004 | if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
|
---|
| 2005 | goto LBL_RES;
|
---|
| 2006 | }
|
---|
| 2007 |
|
---|
| 2008 | /* now set M[1] to G * R mod m */
|
---|
| 2009 | if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
|
---|
| 2010 | goto LBL_RES;
|
---|
| 2011 | }
|
---|
| 2012 | #else
|
---|
| 2013 | err = MP_VAL;
|
---|
| 2014 | goto LBL_RES;
|
---|
| 2015 | #endif
|
---|
| 2016 | } else {
|
---|
| 2017 | if ((err = mp_set(&res, 1)) != MP_OKAY) {
|
---|
| 2018 | goto LBL_RES;
|
---|
| 2019 | }
|
---|
| 2020 | if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
|
---|
| 2021 | goto LBL_RES;
|
---|
| 2022 | }
|
---|
| 2023 | }
|
---|
| 2024 |
|
---|
| 2025 | /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times*/
|
---|
| 2026 | if ((err = mp_copy (&M[1], &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 2027 | goto LBL_RES;
|
---|
| 2028 | }
|
---|
| 2029 |
|
---|
| 2030 | for (x = 0; x < (winsize - 1); x++) {
|
---|
| 2031 | if ((err = mp_sqr (&M[(mp_digit)(1 << (winsize - 1))],
|
---|
| 2032 | &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 2033 | goto LBL_RES;
|
---|
| 2034 | }
|
---|
| 2035 | if ((err = redux (&M[(mp_digit)(1 << (winsize - 1))], P, mp)) != MP_OKAY) {
|
---|
| 2036 | goto LBL_RES;
|
---|
| 2037 | }
|
---|
| 2038 | }
|
---|
| 2039 |
|
---|
| 2040 | /* create upper table */
|
---|
| 2041 | for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
---|
| 2042 | if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
---|
| 2043 | goto LBL_RES;
|
---|
| 2044 | }
|
---|
| 2045 | if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
|
---|
| 2046 | goto LBL_RES;
|
---|
| 2047 | }
|
---|
| 2048 | }
|
---|
| 2049 |
|
---|
| 2050 | /* set initial mode and bit cnt */
|
---|
| 2051 | mode = 0;
|
---|
| 2052 | bitcnt = 1;
|
---|
| 2053 | buf = 0;
|
---|
| 2054 | digidx = X->used - 1;
|
---|
| 2055 | bitcpy = 0;
|
---|
| 2056 | bitbuf = 0;
|
---|
| 2057 |
|
---|
| 2058 | for (;;) {
|
---|
| 2059 | /* grab next digit as required */
|
---|
| 2060 | if (--bitcnt == 0) {
|
---|
| 2061 | /* if digidx == -1 we are out of digits so break */
|
---|
| 2062 | if (digidx == -1) {
|
---|
| 2063 | break;
|
---|
| 2064 | }
|
---|
| 2065 | /* read next digit and reset bitcnt */
|
---|
| 2066 | buf = X->dp[digidx--];
|
---|
| 2067 | bitcnt = (int)DIGIT_BIT;
|
---|
| 2068 | }
|
---|
| 2069 |
|
---|
| 2070 | /* grab the next msb from the exponent */
|
---|
| 2071 | y = (int)(buf >> (DIGIT_BIT - 1)) & 1;
|
---|
| 2072 | buf <<= (mp_digit)1;
|
---|
| 2073 |
|
---|
| 2074 | /* if the bit is zero and mode == 0 then we ignore it
|
---|
| 2075 | * These represent the leading zero bits before the first 1 bit
|
---|
| 2076 | * in the exponent. Technically this opt is not required but it
|
---|
| 2077 | * does lower the # of trivial squaring/reductions used
|
---|
| 2078 | */
|
---|
| 2079 | if (mode == 0 && y == 0) {
|
---|
| 2080 | continue;
|
---|
| 2081 | }
|
---|
| 2082 |
|
---|
| 2083 | /* if the bit is zero and mode == 1 then we square */
|
---|
| 2084 | if (mode == 1 && y == 0) {
|
---|
| 2085 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 2086 | goto LBL_RES;
|
---|
| 2087 | }
|
---|
| 2088 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2089 | goto LBL_RES;
|
---|
| 2090 | }
|
---|
| 2091 | continue;
|
---|
| 2092 | }
|
---|
| 2093 |
|
---|
| 2094 | /* else we add it to the window */
|
---|
| 2095 | bitbuf |= (y << (winsize - ++bitcpy));
|
---|
| 2096 | mode = 2;
|
---|
| 2097 |
|
---|
| 2098 | if (bitcpy == winsize) {
|
---|
| 2099 | /* ok window is filled so square as required and multiply */
|
---|
| 2100 | /* square first */
|
---|
| 2101 | for (x = 0; x < winsize; x++) {
|
---|
| 2102 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 2103 | goto LBL_RES;
|
---|
| 2104 | }
|
---|
| 2105 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2106 | goto LBL_RES;
|
---|
| 2107 | }
|
---|
| 2108 | }
|
---|
| 2109 |
|
---|
| 2110 | /* then multiply */
|
---|
| 2111 | if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
---|
| 2112 | goto LBL_RES;
|
---|
| 2113 | }
|
---|
| 2114 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2115 | goto LBL_RES;
|
---|
| 2116 | }
|
---|
| 2117 |
|
---|
| 2118 | /* empty window and reset */
|
---|
| 2119 | bitcpy = 0;
|
---|
| 2120 | bitbuf = 0;
|
---|
| 2121 | mode = 1;
|
---|
| 2122 | }
|
---|
| 2123 | }
|
---|
| 2124 |
|
---|
| 2125 | /* if bits remain then square/multiply */
|
---|
| 2126 | if (mode == 2 && bitcpy > 0) {
|
---|
| 2127 | /* square then multiply if the bit is set */
|
---|
| 2128 | for (x = 0; x < bitcpy; x++) {
|
---|
| 2129 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 2130 | goto LBL_RES;
|
---|
| 2131 | }
|
---|
| 2132 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2133 | goto LBL_RES;
|
---|
| 2134 | }
|
---|
| 2135 |
|
---|
| 2136 | /* get next bit of the window */
|
---|
| 2137 | bitbuf <<= 1;
|
---|
| 2138 | if ((bitbuf & (1 << winsize)) != 0) {
|
---|
| 2139 | /* then multiply */
|
---|
| 2140 | if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
|
---|
| 2141 | goto LBL_RES;
|
---|
| 2142 | }
|
---|
| 2143 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2144 | goto LBL_RES;
|
---|
| 2145 | }
|
---|
| 2146 | }
|
---|
| 2147 | }
|
---|
| 2148 | }
|
---|
| 2149 |
|
---|
| 2150 | if (redmode == 0) {
|
---|
| 2151 | /* fixup result if Montgomery reduction is used
|
---|
| 2152 | * recall that any value in a Montgomery system is
|
---|
| 2153 | * actually multiplied by R mod n. So we have
|
---|
| 2154 | * to reduce one more time to cancel out the factor
|
---|
| 2155 | * of R.
|
---|
| 2156 | */
|
---|
| 2157 | if ((err = redux(&res, P, mp)) != MP_OKAY) {
|
---|
| 2158 | goto LBL_RES;
|
---|
| 2159 | }
|
---|
| 2160 | }
|
---|
| 2161 |
|
---|
| 2162 | /* swap res with Y */
|
---|
| 2163 | mp_exch (&res, Y);
|
---|
| 2164 | err = MP_OKAY;
|
---|
| 2165 | LBL_RES:mp_clear (&res);
|
---|
| 2166 | LBL_M:
|
---|
| 2167 | mp_clear(&M[1]);
|
---|
| 2168 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 2169 | mp_clear (&M[x]);
|
---|
| 2170 | }
|
---|
| 2171 |
|
---|
| 2172 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2173 | XFREE(M, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 2174 | #endif
|
---|
| 2175 |
|
---|
| 2176 | return err;
|
---|
| 2177 | }
|
---|
| 2178 |
|
---|
| 2179 |
|
---|
| 2180 | /* setups the montgomery reduction stuff */
|
---|
| 2181 | int mp_montgomery_setup (mp_int * n, mp_digit * rho)
|
---|
| 2182 | {
|
---|
| 2183 | mp_digit x, b;
|
---|
| 2184 |
|
---|
| 2185 | /* fast inversion mod 2**k
|
---|
| 2186 | *
|
---|
| 2187 | * Based on the fact that
|
---|
| 2188 | *
|
---|
| 2189 | * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
|
---|
| 2190 | * => 2*X*A - X*X*A*A = 1
|
---|
| 2191 | * => 2*(1) - (1) = 1
|
---|
| 2192 | */
|
---|
| 2193 | b = n->dp[0];
|
---|
| 2194 |
|
---|
| 2195 | if ((b & 1) == 0) {
|
---|
| 2196 | return MP_VAL;
|
---|
| 2197 | }
|
---|
| 2198 |
|
---|
| 2199 | x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
|
---|
| 2200 | x *= 2 - b * x; /* here x*a==1 mod 2**8 */
|
---|
| 2201 | #if !defined(MP_8BIT)
|
---|
| 2202 | x *= 2 - b * x; /* here x*a==1 mod 2**16 */
|
---|
| 2203 | #endif
|
---|
| 2204 | #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
|
---|
| 2205 | x *= 2 - b * x; /* here x*a==1 mod 2**32 */
|
---|
| 2206 | #endif
|
---|
| 2207 | #ifdef MP_64BIT
|
---|
| 2208 | x *= 2 - b * x; /* here x*a==1 mod 2**64 */
|
---|
| 2209 | #endif
|
---|
| 2210 |
|
---|
| 2211 | /* rho = -1/m mod b */
|
---|
| 2212 | /* TAO, switched mp_word casts to mp_digit to shut up compiler */
|
---|
| 2213 | *rho = (mp_digit)((((mp_digit)1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK);
|
---|
| 2214 |
|
---|
| 2215 | return MP_OKAY;
|
---|
| 2216 | }
|
---|
| 2217 |
|
---|
| 2218 |
|
---|
| 2219 | /* computes xR**-1 == x (mod N) via Montgomery Reduction
|
---|
| 2220 | *
|
---|
| 2221 | * This is an optimized implementation of montgomery_reduce
|
---|
| 2222 | * which uses the comba method to quickly calculate the columns of the
|
---|
| 2223 | * reduction.
|
---|
| 2224 | *
|
---|
| 2225 | * Based on Algorithm 14.32 on pp.601 of HAC.
|
---|
| 2226 | */
|
---|
| 2227 | int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
|
---|
| 2228 | {
|
---|
| 2229 | int ix, res, olduse;
|
---|
| 2230 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2231 | mp_word* W; /* uses dynamic memory and slower */
|
---|
| 2232 | #else
|
---|
| 2233 | mp_word W[MP_WARRAY];
|
---|
| 2234 | #endif
|
---|
| 2235 |
|
---|
| 2236 | /* get old used count */
|
---|
| 2237 | olduse = x->used;
|
---|
| 2238 |
|
---|
| 2239 | /* grow a as required */
|
---|
| 2240 | if (x->alloc < n->used + 1) {
|
---|
| 2241 | if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
|
---|
| 2242 | return res;
|
---|
| 2243 | }
|
---|
| 2244 | }
|
---|
| 2245 |
|
---|
| 2246 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2247 | W = (mp_word*)XMALLOC(sizeof(mp_word) * MP_WARRAY, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 2248 | if (W == NULL)
|
---|
| 2249 | return MP_MEM;
|
---|
| 2250 | #endif
|
---|
| 2251 |
|
---|
| 2252 | /* first we have to get the digits of the input into
|
---|
| 2253 | * an array of double precision words W[...]
|
---|
| 2254 | */
|
---|
| 2255 | {
|
---|
| 2256 | mp_word *_W;
|
---|
| 2257 | mp_digit *tmpx;
|
---|
| 2258 |
|
---|
| 2259 | /* alias for the W[] array */
|
---|
| 2260 | _W = W;
|
---|
| 2261 |
|
---|
| 2262 | /* alias for the digits of x*/
|
---|
| 2263 | tmpx = x->dp;
|
---|
| 2264 |
|
---|
| 2265 | /* copy the digits of a into W[0..a->used-1] */
|
---|
| 2266 | for (ix = 0; ix < x->used; ix++) {
|
---|
| 2267 | *_W++ = *tmpx++;
|
---|
| 2268 | }
|
---|
| 2269 |
|
---|
| 2270 | /* zero the high words of W[a->used..m->used*2] */
|
---|
| 2271 | for (; ix < n->used * 2 + 1; ix++) {
|
---|
| 2272 | *_W++ = 0;
|
---|
| 2273 | }
|
---|
| 2274 | }
|
---|
| 2275 |
|
---|
| 2276 | /* now we proceed to zero successive digits
|
---|
| 2277 | * from the least significant upwards
|
---|
| 2278 | */
|
---|
| 2279 | for (ix = 0; ix < n->used; ix++) {
|
---|
| 2280 | /* mu = ai * m' mod b
|
---|
| 2281 | *
|
---|
| 2282 | * We avoid a double precision multiplication (which isn't required)
|
---|
| 2283 | * by casting the value down to a mp_digit. Note this requires
|
---|
| 2284 | * that W[ix-1] have the carry cleared (see after the inner loop)
|
---|
| 2285 | */
|
---|
| 2286 | mp_digit mu;
|
---|
| 2287 | mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
|
---|
| 2288 |
|
---|
| 2289 | /* a = a + mu * m * b**i
|
---|
| 2290 | *
|
---|
| 2291 | * This is computed in place and on the fly. The multiplication
|
---|
| 2292 | * by b**i is handled by offseting which columns the results
|
---|
| 2293 | * are added to.
|
---|
| 2294 | *
|
---|
| 2295 | * Note the comba method normally doesn't handle carries in the
|
---|
| 2296 | * inner loop In this case we fix the carry from the previous
|
---|
| 2297 | * column since the Montgomery reduction requires digits of the
|
---|
| 2298 | * result (so far) [see above] to work. This is
|
---|
| 2299 | * handled by fixing up one carry after the inner loop. The
|
---|
| 2300 | * carry fixups are done in order so after these loops the
|
---|
| 2301 | * first m->used words of W[] have the carries fixed
|
---|
| 2302 | */
|
---|
| 2303 | {
|
---|
| 2304 | int iy;
|
---|
| 2305 | mp_digit *tmpn;
|
---|
| 2306 | mp_word *_W;
|
---|
| 2307 |
|
---|
| 2308 | /* alias for the digits of the modulus */
|
---|
| 2309 | tmpn = n->dp;
|
---|
| 2310 |
|
---|
| 2311 | /* Alias for the columns set by an offset of ix */
|
---|
| 2312 | _W = W + ix;
|
---|
| 2313 |
|
---|
| 2314 | /* inner loop */
|
---|
| 2315 | for (iy = 0; iy < n->used; iy++) {
|
---|
| 2316 | *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
|
---|
| 2317 | }
|
---|
| 2318 | }
|
---|
| 2319 |
|
---|
| 2320 | /* now fix carry for next digit, W[ix+1] */
|
---|
| 2321 | W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
|
---|
| 2322 | }
|
---|
| 2323 |
|
---|
| 2324 | /* now we have to propagate the carries and
|
---|
| 2325 | * shift the words downward [all those least
|
---|
| 2326 | * significant digits we zeroed].
|
---|
| 2327 | */
|
---|
| 2328 | {
|
---|
| 2329 | mp_digit *tmpx;
|
---|
| 2330 | mp_word *_W, *_W1;
|
---|
| 2331 |
|
---|
| 2332 | /* nox fix rest of carries */
|
---|
| 2333 |
|
---|
| 2334 | /* alias for current word */
|
---|
| 2335 | _W1 = W + ix;
|
---|
| 2336 |
|
---|
| 2337 | /* alias for next word, where the carry goes */
|
---|
| 2338 | _W = W + ++ix;
|
---|
| 2339 |
|
---|
| 2340 | for (; ix <= n->used * 2 + 1; ix++) {
|
---|
| 2341 | *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
|
---|
| 2342 | }
|
---|
| 2343 |
|
---|
| 2344 | /* copy out, A = A/b**n
|
---|
| 2345 | *
|
---|
| 2346 | * The result is A/b**n but instead of converting from an
|
---|
| 2347 | * array of mp_word to mp_digit than calling mp_rshd
|
---|
| 2348 | * we just copy them in the right order
|
---|
| 2349 | */
|
---|
| 2350 |
|
---|
| 2351 | /* alias for destination word */
|
---|
| 2352 | tmpx = x->dp;
|
---|
| 2353 |
|
---|
| 2354 | /* alias for shifted double precision result */
|
---|
| 2355 | _W = W + n->used;
|
---|
| 2356 |
|
---|
| 2357 | for (ix = 0; ix < n->used + 1; ix++) {
|
---|
| 2358 | *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
|
---|
| 2359 | }
|
---|
| 2360 |
|
---|
| 2361 | /* zero olduse digits, if the input a was larger than
|
---|
| 2362 | * m->used+1 we'll have to clear the digits
|
---|
| 2363 | */
|
---|
| 2364 | for (; ix < olduse; ix++) {
|
---|
| 2365 | *tmpx++ = 0;
|
---|
| 2366 | }
|
---|
| 2367 | }
|
---|
| 2368 |
|
---|
| 2369 | /* set the max used and clamp */
|
---|
| 2370 | x->used = n->used + 1;
|
---|
| 2371 | mp_clamp (x);
|
---|
| 2372 |
|
---|
| 2373 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2374 | XFREE(W, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 2375 | #endif
|
---|
| 2376 |
|
---|
| 2377 | /* if A >= m then A = A - m */
|
---|
| 2378 | if (mp_cmp_mag (x, n) != MP_LT) {
|
---|
| 2379 | return s_mp_sub (x, n, x);
|
---|
| 2380 | }
|
---|
| 2381 | return MP_OKAY;
|
---|
| 2382 | }
|
---|
| 2383 |
|
---|
| 2384 |
|
---|
| 2385 | /* computes xR**-1 == x (mod N) via Montgomery Reduction */
|
---|
| 2386 | int mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
|
---|
| 2387 | {
|
---|
| 2388 | int ix, res, digs;
|
---|
| 2389 | mp_digit mu;
|
---|
| 2390 |
|
---|
| 2391 | /* can the fast reduction [comba] method be used?
|
---|
| 2392 | *
|
---|
| 2393 | * Note that unlike in mul you're safely allowed *less*
|
---|
| 2394 | * than the available columns [255 per default] since carries
|
---|
| 2395 | * are fixed up in the inner loop.
|
---|
| 2396 | */
|
---|
| 2397 | digs = n->used * 2 + 1;
|
---|
| 2398 | if ((digs < MP_WARRAY) &&
|
---|
| 2399 | n->used <
|
---|
| 2400 | (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
| 2401 | return fast_mp_montgomery_reduce (x, n, rho);
|
---|
| 2402 | }
|
---|
| 2403 |
|
---|
| 2404 | /* grow the input as required */
|
---|
| 2405 | if (x->alloc < digs) {
|
---|
| 2406 | if ((res = mp_grow (x, digs)) != MP_OKAY) {
|
---|
| 2407 | return res;
|
---|
| 2408 | }
|
---|
| 2409 | }
|
---|
| 2410 | x->used = digs;
|
---|
| 2411 |
|
---|
| 2412 | for (ix = 0; ix < n->used; ix++) {
|
---|
| 2413 | /* mu = ai * rho mod b
|
---|
| 2414 | *
|
---|
| 2415 | * The value of rho must be precalculated via
|
---|
| 2416 | * montgomery_setup() such that
|
---|
| 2417 | * it equals -1/n0 mod b this allows the
|
---|
| 2418 | * following inner loop to reduce the
|
---|
| 2419 | * input one digit at a time
|
---|
| 2420 | */
|
---|
| 2421 | mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
|
---|
| 2422 |
|
---|
| 2423 | /* a = a + mu * m * b**i */
|
---|
| 2424 | {
|
---|
| 2425 | int iy;
|
---|
| 2426 | mp_digit *tmpn, *tmpx, u;
|
---|
| 2427 | mp_word r;
|
---|
| 2428 |
|
---|
| 2429 | /* alias for digits of the modulus */
|
---|
| 2430 | tmpn = n->dp;
|
---|
| 2431 |
|
---|
| 2432 | /* alias for the digits of x [the input] */
|
---|
| 2433 | tmpx = x->dp + ix;
|
---|
| 2434 |
|
---|
| 2435 | /* set the carry to zero */
|
---|
| 2436 | u = 0;
|
---|
| 2437 |
|
---|
| 2438 | /* Multiply and add in place */
|
---|
| 2439 | for (iy = 0; iy < n->used; iy++) {
|
---|
| 2440 | /* compute product and sum */
|
---|
| 2441 | r = ((mp_word)mu) * ((mp_word)*tmpn++) +
|
---|
| 2442 | ((mp_word) u) + ((mp_word) * tmpx);
|
---|
| 2443 |
|
---|
| 2444 | /* get carry */
|
---|
| 2445 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 2446 |
|
---|
| 2447 | /* fix digit */
|
---|
| 2448 | *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
|
---|
| 2449 | }
|
---|
| 2450 | /* At this point the ix'th digit of x should be zero */
|
---|
| 2451 |
|
---|
| 2452 |
|
---|
| 2453 | /* propagate carries upwards as required*/
|
---|
| 2454 | while (u) {
|
---|
| 2455 | *tmpx += u;
|
---|
| 2456 | u = *tmpx >> DIGIT_BIT;
|
---|
| 2457 | *tmpx++ &= MP_MASK;
|
---|
| 2458 | }
|
---|
| 2459 | }
|
---|
| 2460 | }
|
---|
| 2461 |
|
---|
| 2462 | /* at this point the n.used'th least
|
---|
| 2463 | * significant digits of x are all zero
|
---|
| 2464 | * which means we can shift x to the
|
---|
| 2465 | * right by n.used digits and the
|
---|
| 2466 | * residue is unchanged.
|
---|
| 2467 | */
|
---|
| 2468 |
|
---|
| 2469 | /* x = x/b**n.used */
|
---|
| 2470 | mp_clamp(x);
|
---|
| 2471 | mp_rshd (x, n->used);
|
---|
| 2472 |
|
---|
| 2473 | /* if x >= n then x = x - n */
|
---|
| 2474 | if (mp_cmp_mag (x, n) != MP_LT) {
|
---|
| 2475 | return s_mp_sub (x, n, x);
|
---|
| 2476 | }
|
---|
| 2477 |
|
---|
| 2478 | return MP_OKAY;
|
---|
| 2479 | }
|
---|
| 2480 |
|
---|
| 2481 |
|
---|
| 2482 | /* determines the setup value */
|
---|
| 2483 | void mp_dr_setup(mp_int *a, mp_digit *d)
|
---|
| 2484 | {
|
---|
| 2485 | /* the casts are required if DIGIT_BIT is one less than
|
---|
| 2486 | * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
|
---|
| 2487 | */
|
---|
| 2488 | *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
|
---|
| 2489 | ((mp_word)a->dp[0]));
|
---|
| 2490 | }
|
---|
| 2491 |
|
---|
| 2492 |
|
---|
| 2493 | /* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
|
---|
| 2494 | *
|
---|
| 2495 | * Based on algorithm from the paper
|
---|
| 2496 | *
|
---|
| 2497 | * "Generating Efficient Primes for Discrete Log Cryptosystems"
|
---|
| 2498 | * Chae Hoon Lim, Pil Joong Lee,
|
---|
| 2499 | * POSTECH Information Research Laboratories
|
---|
| 2500 | *
|
---|
| 2501 | * The modulus must be of a special format [see manual]
|
---|
| 2502 | *
|
---|
| 2503 | * Has been modified to use algorithm 7.10 from the LTM book instead
|
---|
| 2504 | *
|
---|
| 2505 | * Input x must be in the range 0 <= x <= (n-1)**2
|
---|
| 2506 | */
|
---|
| 2507 | int mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
|
---|
| 2508 | {
|
---|
| 2509 | int err, i, m;
|
---|
| 2510 | mp_word r;
|
---|
| 2511 | mp_digit mu, *tmpx1, *tmpx2;
|
---|
| 2512 |
|
---|
| 2513 | /* m = digits in modulus */
|
---|
| 2514 | m = n->used;
|
---|
| 2515 |
|
---|
| 2516 | /* ensure that "x" has at least 2m digits */
|
---|
| 2517 | if (x->alloc < m + m) {
|
---|
| 2518 | if ((err = mp_grow (x, m + m)) != MP_OKAY) {
|
---|
| 2519 | return err;
|
---|
| 2520 | }
|
---|
| 2521 | }
|
---|
| 2522 |
|
---|
| 2523 | /* top of loop, this is where the code resumes if
|
---|
| 2524 | * another reduction pass is required.
|
---|
| 2525 | */
|
---|
| 2526 | top:
|
---|
| 2527 | /* aliases for digits */
|
---|
| 2528 | /* alias for lower half of x */
|
---|
| 2529 | tmpx1 = x->dp;
|
---|
| 2530 |
|
---|
| 2531 | /* alias for upper half of x, or x/B**m */
|
---|
| 2532 | tmpx2 = x->dp + m;
|
---|
| 2533 |
|
---|
| 2534 | /* set carry to zero */
|
---|
| 2535 | mu = 0;
|
---|
| 2536 |
|
---|
| 2537 | /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
|
---|
| 2538 | for (i = 0; i < m; i++) {
|
---|
| 2539 | r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
|
---|
| 2540 | *tmpx1++ = (mp_digit)(r & MP_MASK);
|
---|
| 2541 | mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
|
---|
| 2542 | }
|
---|
| 2543 |
|
---|
| 2544 | /* set final carry */
|
---|
| 2545 | *tmpx1++ = mu;
|
---|
| 2546 |
|
---|
| 2547 | /* zero words above m */
|
---|
| 2548 | for (i = m + 1; i < x->used; i++) {
|
---|
| 2549 | *tmpx1++ = 0;
|
---|
| 2550 | }
|
---|
| 2551 |
|
---|
| 2552 | /* clamp, sub and return */
|
---|
| 2553 | mp_clamp (x);
|
---|
| 2554 |
|
---|
| 2555 | /* if x >= n then subtract and reduce again
|
---|
| 2556 | * Each successive "recursion" makes the input smaller and smaller.
|
---|
| 2557 | */
|
---|
| 2558 | if (mp_cmp_mag (x, n) != MP_LT) {
|
---|
| 2559 | if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
|
---|
| 2560 | return err;
|
---|
| 2561 | }
|
---|
| 2562 | goto top;
|
---|
| 2563 | }
|
---|
| 2564 | return MP_OKAY;
|
---|
| 2565 | }
|
---|
| 2566 |
|
---|
| 2567 |
|
---|
| 2568 | /* reduces a modulo n where n is of the form 2**p - d */
|
---|
| 2569 | int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
|
---|
| 2570 | {
|
---|
| 2571 | mp_int q;
|
---|
| 2572 | int p, res;
|
---|
| 2573 |
|
---|
| 2574 | if ((res = mp_init(&q)) != MP_OKAY) {
|
---|
| 2575 | return res;
|
---|
| 2576 | }
|
---|
| 2577 |
|
---|
| 2578 | p = mp_count_bits(n);
|
---|
| 2579 | top:
|
---|
| 2580 | /* q = a/2**p, a = a mod 2**p */
|
---|
| 2581 | if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
|
---|
| 2582 | goto ERR;
|
---|
| 2583 | }
|
---|
| 2584 |
|
---|
| 2585 | if (d != 1) {
|
---|
| 2586 | /* q = q * d */
|
---|
| 2587 | if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
|
---|
| 2588 | goto ERR;
|
---|
| 2589 | }
|
---|
| 2590 | }
|
---|
| 2591 |
|
---|
| 2592 | /* a = a + q */
|
---|
| 2593 | if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
|
---|
| 2594 | goto ERR;
|
---|
| 2595 | }
|
---|
| 2596 |
|
---|
| 2597 | if (mp_cmp_mag(a, n) != MP_LT) {
|
---|
| 2598 | if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
|
---|
| 2599 | goto ERR;
|
---|
| 2600 | }
|
---|
| 2601 | goto top;
|
---|
| 2602 | }
|
---|
| 2603 |
|
---|
| 2604 | ERR:
|
---|
| 2605 | mp_clear(&q);
|
---|
| 2606 | return res;
|
---|
| 2607 | }
|
---|
| 2608 |
|
---|
| 2609 |
|
---|
| 2610 | /* determines the setup value */
|
---|
| 2611 | int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
|
---|
| 2612 | {
|
---|
| 2613 | int res, p;
|
---|
| 2614 | mp_int tmp;
|
---|
| 2615 |
|
---|
| 2616 | if ((res = mp_init(&tmp)) != MP_OKAY) {
|
---|
| 2617 | return res;
|
---|
| 2618 | }
|
---|
| 2619 |
|
---|
| 2620 | p = mp_count_bits(a);
|
---|
| 2621 | if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
|
---|
| 2622 | mp_clear(&tmp);
|
---|
| 2623 | return res;
|
---|
| 2624 | }
|
---|
| 2625 |
|
---|
| 2626 | if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
|
---|
| 2627 | mp_clear(&tmp);
|
---|
| 2628 | return res;
|
---|
| 2629 | }
|
---|
| 2630 |
|
---|
| 2631 | *d = tmp.dp[0];
|
---|
| 2632 | mp_clear(&tmp);
|
---|
| 2633 | return MP_OKAY;
|
---|
| 2634 | }
|
---|
| 2635 |
|
---|
| 2636 |
|
---|
| 2637 | /* set the b bit of a */
|
---|
| 2638 | int mp_set_bit (mp_int * a, int b)
|
---|
| 2639 | {
|
---|
| 2640 | int i = b / DIGIT_BIT, res;
|
---|
| 2641 |
|
---|
| 2642 | if (a->used < (int)(i + 1)) {
|
---|
| 2643 | /* grow a to accommodate the single bit */
|
---|
| 2644 | if ((res = mp_grow (a, i + 1)) != MP_OKAY) {
|
---|
| 2645 | return res;
|
---|
| 2646 | }
|
---|
| 2647 |
|
---|
| 2648 | /* set the used count of where the bit will go */
|
---|
| 2649 | a->used = (int)(i + 1);
|
---|
| 2650 | }
|
---|
| 2651 |
|
---|
| 2652 | /* put the single bit in its place */
|
---|
| 2653 | a->dp[i] |= ((mp_digit)1) << (b % DIGIT_BIT);
|
---|
| 2654 |
|
---|
| 2655 | return MP_OKAY;
|
---|
| 2656 | }
|
---|
| 2657 |
|
---|
| 2658 | /* computes a = 2**b
|
---|
| 2659 | *
|
---|
| 2660 | * Simple algorithm which zeros the int, set the required bit
|
---|
| 2661 | */
|
---|
| 2662 | int mp_2expt (mp_int * a, int b)
|
---|
| 2663 | {
|
---|
| 2664 | /* zero a as per default */
|
---|
| 2665 | mp_zero (a);
|
---|
| 2666 |
|
---|
| 2667 | return mp_set_bit(a, b);
|
---|
| 2668 | }
|
---|
| 2669 |
|
---|
| 2670 | /* multiply by a digit */
|
---|
| 2671 | int mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
|
---|
| 2672 | {
|
---|
| 2673 | mp_digit u, *tmpa, *tmpc;
|
---|
| 2674 | mp_word r;
|
---|
| 2675 | int ix, res, olduse;
|
---|
| 2676 |
|
---|
| 2677 | /* make sure c is big enough to hold a*b */
|
---|
| 2678 | if (c->alloc < a->used + 1) {
|
---|
| 2679 | if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
|
---|
| 2680 | return res;
|
---|
| 2681 | }
|
---|
| 2682 | }
|
---|
| 2683 |
|
---|
| 2684 | /* get the original destinations used count */
|
---|
| 2685 | olduse = c->used;
|
---|
| 2686 |
|
---|
| 2687 | /* set the sign */
|
---|
| 2688 | c->sign = a->sign;
|
---|
| 2689 |
|
---|
| 2690 | /* alias for a->dp [source] */
|
---|
| 2691 | tmpa = a->dp;
|
---|
| 2692 |
|
---|
| 2693 | /* alias for c->dp [dest] */
|
---|
| 2694 | tmpc = c->dp;
|
---|
| 2695 |
|
---|
| 2696 | /* zero carry */
|
---|
| 2697 | u = 0;
|
---|
| 2698 |
|
---|
| 2699 | /* compute columns */
|
---|
| 2700 | for (ix = 0; ix < a->used; ix++) {
|
---|
| 2701 | /* compute product and carry sum for this term */
|
---|
| 2702 | r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
|
---|
| 2703 |
|
---|
| 2704 | /* mask off higher bits to get a single digit */
|
---|
| 2705 | *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 2706 |
|
---|
| 2707 | /* send carry into next iteration */
|
---|
| 2708 | u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
---|
| 2709 | }
|
---|
| 2710 |
|
---|
| 2711 | /* store final carry [if any] and increment ix offset */
|
---|
| 2712 | *tmpc++ = u;
|
---|
| 2713 | ++ix;
|
---|
| 2714 |
|
---|
| 2715 | /* now zero digits above the top */
|
---|
| 2716 | while (ix++ < olduse) {
|
---|
| 2717 | *tmpc++ = 0;
|
---|
| 2718 | }
|
---|
| 2719 |
|
---|
| 2720 | /* set used count */
|
---|
| 2721 | c->used = a->used + 1;
|
---|
| 2722 | mp_clamp(c);
|
---|
| 2723 |
|
---|
| 2724 | return MP_OKAY;
|
---|
| 2725 | }
|
---|
| 2726 |
|
---|
| 2727 |
|
---|
| 2728 | /* d = a * b (mod c) */
|
---|
| 2729 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 2730 | int wolfcrypt_mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d)
|
---|
| 2731 | #else
|
---|
| 2732 | int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
|
---|
| 2733 | #endif
|
---|
| 2734 | {
|
---|
| 2735 | int res;
|
---|
| 2736 | mp_int t;
|
---|
| 2737 |
|
---|
| 2738 | if ((res = mp_init_size (&t, c->used)) != MP_OKAY) {
|
---|
| 2739 | return res;
|
---|
| 2740 | }
|
---|
| 2741 |
|
---|
| 2742 | res = mp_mul (a, b, &t);
|
---|
| 2743 | if (res == MP_OKAY) {
|
---|
| 2744 | res = mp_mod (&t, c, d);
|
---|
| 2745 | }
|
---|
| 2746 |
|
---|
| 2747 | mp_clear (&t);
|
---|
| 2748 | return res;
|
---|
| 2749 | }
|
---|
| 2750 |
|
---|
| 2751 |
|
---|
| 2752 | /* d = a - b (mod c) */
|
---|
| 2753 | int mp_submod(mp_int* a, mp_int* b, mp_int* c, mp_int* d)
|
---|
| 2754 | {
|
---|
| 2755 | int res;
|
---|
| 2756 | mp_int t;
|
---|
| 2757 |
|
---|
| 2758 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
| 2759 | return res;
|
---|
| 2760 | }
|
---|
| 2761 |
|
---|
| 2762 | res = mp_sub (a, b, &t);
|
---|
| 2763 | if (res == MP_OKAY) {
|
---|
| 2764 | res = mp_mod (&t, c, d);
|
---|
| 2765 | }
|
---|
| 2766 |
|
---|
| 2767 | mp_clear (&t);
|
---|
| 2768 |
|
---|
| 2769 | return res;
|
---|
| 2770 | }
|
---|
| 2771 |
|
---|
| 2772 | /* d = a + b (mod c) */
|
---|
| 2773 | int mp_addmod(mp_int* a, mp_int* b, mp_int* c, mp_int* d)
|
---|
| 2774 | {
|
---|
| 2775 | int res;
|
---|
| 2776 | mp_int t;
|
---|
| 2777 |
|
---|
| 2778 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
| 2779 | return res;
|
---|
| 2780 | }
|
---|
| 2781 |
|
---|
| 2782 | res = mp_add (a, b, &t);
|
---|
| 2783 | if (res == MP_OKAY) {
|
---|
| 2784 | res = mp_mod (&t, c, d);
|
---|
| 2785 | }
|
---|
| 2786 |
|
---|
| 2787 | mp_clear (&t);
|
---|
| 2788 |
|
---|
| 2789 | return res;
|
---|
| 2790 | }
|
---|
| 2791 |
|
---|
| 2792 | /* computes b = a*a */
|
---|
| 2793 | int mp_sqr (mp_int * a, mp_int * b)
|
---|
| 2794 | {
|
---|
| 2795 | int res;
|
---|
| 2796 |
|
---|
| 2797 | {
|
---|
| 2798 | #ifdef BN_FAST_S_MP_SQR_C
|
---|
| 2799 | /* can we use the fast comba multiplier? */
|
---|
| 2800 | if ((a->used * 2 + 1) < MP_WARRAY &&
|
---|
| 2801 | a->used <
|
---|
| 2802 | (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
|
---|
| 2803 | res = fast_s_mp_sqr (a, b);
|
---|
| 2804 | } else
|
---|
| 2805 | #endif
|
---|
| 2806 | #ifdef BN_S_MP_SQR_C
|
---|
| 2807 | res = s_mp_sqr (a, b);
|
---|
| 2808 | #else
|
---|
| 2809 | res = MP_VAL;
|
---|
| 2810 | #endif
|
---|
| 2811 | }
|
---|
| 2812 | b->sign = MP_ZPOS;
|
---|
| 2813 | return res;
|
---|
| 2814 | }
|
---|
| 2815 |
|
---|
| 2816 |
|
---|
| 2817 | /* high level multiplication (handles sign) */
|
---|
| 2818 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 2819 | int wolfcrypt_mp_mul(mp_int *a, mp_int *b, mp_int *c)
|
---|
| 2820 | #else
|
---|
| 2821 | int mp_mul (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 2822 | #endif
|
---|
| 2823 | {
|
---|
| 2824 | int res, neg;
|
---|
| 2825 | neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
|
---|
| 2826 |
|
---|
| 2827 | {
|
---|
| 2828 | /* can we use the fast multiplier?
|
---|
| 2829 | *
|
---|
| 2830 | * The fast multiplier can be used if the output will
|
---|
| 2831 | * have less than MP_WARRAY digits and the number of
|
---|
| 2832 | * digits won't affect carry propagation
|
---|
| 2833 | */
|
---|
| 2834 | int digs = a->used + b->used + 1;
|
---|
| 2835 |
|
---|
| 2836 | #ifdef BN_FAST_S_MP_MUL_DIGS_C
|
---|
| 2837 | if ((digs < MP_WARRAY) &&
|
---|
| 2838 | MIN(a->used, b->used) <=
|
---|
| 2839 | (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
| 2840 | res = fast_s_mp_mul_digs (a, b, c, digs);
|
---|
| 2841 | } else
|
---|
| 2842 | #endif
|
---|
| 2843 | #ifdef BN_S_MP_MUL_DIGS_C
|
---|
| 2844 | res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
|
---|
| 2845 | #else
|
---|
| 2846 | res = MP_VAL;
|
---|
| 2847 | #endif
|
---|
| 2848 |
|
---|
| 2849 | }
|
---|
| 2850 | c->sign = (c->used > 0) ? neg : MP_ZPOS;
|
---|
| 2851 | return res;
|
---|
| 2852 | }
|
---|
| 2853 |
|
---|
| 2854 |
|
---|
| 2855 | /* b = a*2 */
|
---|
| 2856 | int mp_mul_2(mp_int * a, mp_int * b)
|
---|
| 2857 | {
|
---|
| 2858 | int x, res, oldused;
|
---|
| 2859 |
|
---|
| 2860 | /* grow to accommodate result */
|
---|
| 2861 | if (b->alloc < a->used + 1) {
|
---|
| 2862 | if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
|
---|
| 2863 | return res;
|
---|
| 2864 | }
|
---|
| 2865 | }
|
---|
| 2866 |
|
---|
| 2867 | oldused = b->used;
|
---|
| 2868 | b->used = a->used;
|
---|
| 2869 |
|
---|
| 2870 | {
|
---|
| 2871 | mp_digit r, rr, *tmpa, *tmpb;
|
---|
| 2872 |
|
---|
| 2873 | /* alias for source */
|
---|
| 2874 | tmpa = a->dp;
|
---|
| 2875 |
|
---|
| 2876 | /* alias for dest */
|
---|
| 2877 | tmpb = b->dp;
|
---|
| 2878 |
|
---|
| 2879 | /* carry */
|
---|
| 2880 | r = 0;
|
---|
| 2881 | for (x = 0; x < a->used; x++) {
|
---|
| 2882 |
|
---|
| 2883 | /* get what will be the *next* carry bit from the
|
---|
| 2884 | * MSB of the current digit
|
---|
| 2885 | */
|
---|
| 2886 | rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
|
---|
| 2887 |
|
---|
| 2888 | /* now shift up this digit, add in the carry [from the previous] */
|
---|
| 2889 | *tmpb++ = (mp_digit)(((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK);
|
---|
| 2890 |
|
---|
| 2891 | /* copy the carry that would be from the source
|
---|
| 2892 | * digit into the next iteration
|
---|
| 2893 | */
|
---|
| 2894 | r = rr;
|
---|
| 2895 | }
|
---|
| 2896 |
|
---|
| 2897 | /* new leading digit? */
|
---|
| 2898 | if (r != 0) {
|
---|
| 2899 | /* add a MSB which is always 1 at this point */
|
---|
| 2900 | *tmpb = 1;
|
---|
| 2901 | ++(b->used);
|
---|
| 2902 | }
|
---|
| 2903 |
|
---|
| 2904 | /* now zero any excess digits on the destination
|
---|
| 2905 | * that we didn't write to
|
---|
| 2906 | */
|
---|
| 2907 | tmpb = b->dp + b->used;
|
---|
| 2908 | for (x = b->used; x < oldused; x++) {
|
---|
| 2909 | *tmpb++ = 0;
|
---|
| 2910 | }
|
---|
| 2911 | }
|
---|
| 2912 | b->sign = a->sign;
|
---|
| 2913 | return MP_OKAY;
|
---|
| 2914 | }
|
---|
| 2915 |
|
---|
| 2916 |
|
---|
| 2917 | /* divide by three (based on routine from MPI and the GMP manual) */
|
---|
| 2918 | int mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
|
---|
| 2919 | {
|
---|
| 2920 | mp_int q;
|
---|
| 2921 | mp_word w, t;
|
---|
| 2922 | mp_digit b;
|
---|
| 2923 | int res, ix;
|
---|
| 2924 |
|
---|
| 2925 | /* b = 2**DIGIT_BIT / 3 */
|
---|
| 2926 | b = (mp_digit) ( (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3) );
|
---|
| 2927 |
|
---|
| 2928 | if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
|
---|
| 2929 | return res;
|
---|
| 2930 | }
|
---|
| 2931 |
|
---|
| 2932 | q.used = a->used;
|
---|
| 2933 | q.sign = a->sign;
|
---|
| 2934 | w = 0;
|
---|
| 2935 | for (ix = a->used - 1; ix >= 0; ix--) {
|
---|
| 2936 | w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
|
---|
| 2937 |
|
---|
| 2938 | if (w >= 3) {
|
---|
| 2939 | /* multiply w by [1/3] */
|
---|
| 2940 | t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
|
---|
| 2941 |
|
---|
| 2942 | /* now subtract 3 * [w/3] from w, to get the remainder */
|
---|
| 2943 | w -= t+t+t;
|
---|
| 2944 |
|
---|
| 2945 | /* fixup the remainder as required since
|
---|
| 2946 | * the optimization is not exact.
|
---|
| 2947 | */
|
---|
| 2948 | while (w >= 3) {
|
---|
| 2949 | t += 1;
|
---|
| 2950 | w -= 3;
|
---|
| 2951 | }
|
---|
| 2952 | } else {
|
---|
| 2953 | t = 0;
|
---|
| 2954 | }
|
---|
| 2955 | q.dp[ix] = (mp_digit)t;
|
---|
| 2956 | }
|
---|
| 2957 |
|
---|
| 2958 | /* [optional] store the remainder */
|
---|
| 2959 | if (d != NULL) {
|
---|
| 2960 | *d = (mp_digit)w;
|
---|
| 2961 | }
|
---|
| 2962 |
|
---|
| 2963 | /* [optional] store the quotient */
|
---|
| 2964 | if (c != NULL) {
|
---|
| 2965 | mp_clamp(&q);
|
---|
| 2966 | mp_exch(&q, c);
|
---|
| 2967 | }
|
---|
| 2968 | mp_clear(&q);
|
---|
| 2969 |
|
---|
| 2970 | return res;
|
---|
| 2971 | }
|
---|
| 2972 |
|
---|
| 2973 |
|
---|
| 2974 | /* init an mp_init for a given size */
|
---|
| 2975 | int mp_init_size (mp_int * a, int size)
|
---|
| 2976 | {
|
---|
| 2977 | int x;
|
---|
| 2978 |
|
---|
| 2979 | /* pad size so there are always extra digits */
|
---|
| 2980 | size += (MP_PREC * 2) - (size % MP_PREC);
|
---|
| 2981 |
|
---|
| 2982 | /* alloc mem */
|
---|
| 2983 | a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size, NULL,
|
---|
| 2984 | DYNAMIC_TYPE_BIGINT);
|
---|
| 2985 | if (a->dp == NULL) {
|
---|
| 2986 | return MP_MEM;
|
---|
| 2987 | }
|
---|
| 2988 |
|
---|
| 2989 | /* set the members */
|
---|
| 2990 | a->used = 0;
|
---|
| 2991 | a->alloc = size;
|
---|
| 2992 | a->sign = MP_ZPOS;
|
---|
| 2993 | #ifdef HAVE_WOLF_BIGINT
|
---|
| 2994 | wc_bigint_init(&a->raw);
|
---|
| 2995 | #endif
|
---|
| 2996 |
|
---|
| 2997 | /* zero the digits */
|
---|
| 2998 | for (x = 0; x < size; x++) {
|
---|
| 2999 | a->dp[x] = 0;
|
---|
| 3000 | }
|
---|
| 3001 |
|
---|
| 3002 | return MP_OKAY;
|
---|
| 3003 | }
|
---|
| 3004 |
|
---|
| 3005 |
|
---|
| 3006 | /* the jist of squaring...
|
---|
| 3007 | * you do like mult except the offset of the tmpx [one that
|
---|
| 3008 | * starts closer to zero] can't equal the offset of tmpy.
|
---|
| 3009 | * So basically you set up iy like before then you min it with
|
---|
| 3010 | * (ty-tx) so that it never happens. You double all those
|
---|
| 3011 | * you add in the inner loop
|
---|
| 3012 |
|
---|
| 3013 | After that loop you do the squares and add them in.
|
---|
| 3014 | */
|
---|
| 3015 |
|
---|
| 3016 | int fast_s_mp_sqr (mp_int * a, mp_int * b)
|
---|
| 3017 | {
|
---|
| 3018 | int olduse, res, pa, ix, iz;
|
---|
| 3019 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3020 | mp_digit* W; /* uses dynamic memory and slower */
|
---|
| 3021 | #else
|
---|
| 3022 | mp_digit W[MP_WARRAY];
|
---|
| 3023 | #endif
|
---|
| 3024 | mp_digit *tmpx;
|
---|
| 3025 | mp_word W1;
|
---|
| 3026 |
|
---|
| 3027 | /* grow the destination as required */
|
---|
| 3028 | pa = a->used + a->used;
|
---|
| 3029 | if (b->alloc < pa) {
|
---|
| 3030 | if ((res = mp_grow (b, pa)) != MP_OKAY) {
|
---|
| 3031 | return res;
|
---|
| 3032 | }
|
---|
| 3033 | }
|
---|
| 3034 |
|
---|
| 3035 | if (pa > MP_WARRAY)
|
---|
| 3036 | return MP_RANGE; /* TAO range check */
|
---|
| 3037 |
|
---|
| 3038 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3039 | W = (mp_digit*)XMALLOC(sizeof(mp_digit) * MP_WARRAY, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 3040 | if (W == NULL)
|
---|
| 3041 | return MP_MEM;
|
---|
| 3042 | #endif
|
---|
| 3043 |
|
---|
| 3044 | /* number of output digits to produce */
|
---|
| 3045 | W1 = 0;
|
---|
| 3046 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3047 | int tx, ty, iy;
|
---|
| 3048 | mp_word _W;
|
---|
| 3049 | mp_digit *tmpy;
|
---|
| 3050 |
|
---|
| 3051 | /* clear counter */
|
---|
| 3052 | _W = 0;
|
---|
| 3053 |
|
---|
| 3054 | /* get offsets into the two bignums */
|
---|
| 3055 | ty = MIN(a->used-1, ix);
|
---|
| 3056 | tx = ix - ty;
|
---|
| 3057 |
|
---|
| 3058 | /* setup temp aliases */
|
---|
| 3059 | tmpx = a->dp + tx;
|
---|
| 3060 | tmpy = a->dp + ty;
|
---|
| 3061 |
|
---|
| 3062 | /* this is the number of times the loop will iterate, essentially
|
---|
| 3063 | while (tx++ < a->used && ty-- >= 0) { ... }
|
---|
| 3064 | */
|
---|
| 3065 | iy = MIN(a->used-tx, ty+1);
|
---|
| 3066 |
|
---|
| 3067 | /* now for squaring tx can never equal ty
|
---|
| 3068 | * we halve the distance since they approach at a rate of 2x
|
---|
| 3069 | * and we have to round because odd cases need to be executed
|
---|
| 3070 | */
|
---|
| 3071 | iy = MIN(iy, (ty-tx+1)>>1);
|
---|
| 3072 |
|
---|
| 3073 | /* execute loop */
|
---|
| 3074 | for (iz = 0; iz < iy; iz++) {
|
---|
| 3075 | _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
---|
| 3076 | }
|
---|
| 3077 |
|
---|
| 3078 | /* double the inner product and add carry */
|
---|
| 3079 | _W = _W + _W + W1;
|
---|
| 3080 |
|
---|
| 3081 | /* even columns have the square term in them */
|
---|
| 3082 | if ((ix&1) == 0) {
|
---|
| 3083 | _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
|
---|
| 3084 | }
|
---|
| 3085 |
|
---|
| 3086 | /* store it */
|
---|
| 3087 | W[ix] = (mp_digit)(_W & MP_MASK);
|
---|
| 3088 |
|
---|
| 3089 | /* make next carry */
|
---|
| 3090 | W1 = _W >> ((mp_word)DIGIT_BIT);
|
---|
| 3091 | }
|
---|
| 3092 |
|
---|
| 3093 | /* setup dest */
|
---|
| 3094 | olduse = b->used;
|
---|
| 3095 | b->used = a->used+a->used;
|
---|
| 3096 |
|
---|
| 3097 | {
|
---|
| 3098 | mp_digit *tmpb;
|
---|
| 3099 | tmpb = b->dp;
|
---|
| 3100 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3101 | *tmpb++ = (mp_digit)(W[ix] & MP_MASK);
|
---|
| 3102 | }
|
---|
| 3103 |
|
---|
| 3104 | /* clear unused digits [that existed in the old copy of c] */
|
---|
| 3105 | for (; ix < olduse; ix++) {
|
---|
| 3106 | *tmpb++ = 0;
|
---|
| 3107 | }
|
---|
| 3108 | }
|
---|
| 3109 | mp_clamp (b);
|
---|
| 3110 |
|
---|
| 3111 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3112 | XFREE(W, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 3113 | #endif
|
---|
| 3114 |
|
---|
| 3115 | return MP_OKAY;
|
---|
| 3116 | }
|
---|
| 3117 |
|
---|
| 3118 |
|
---|
| 3119 | /* Fast (comba) multiplier
|
---|
| 3120 | *
|
---|
| 3121 | * This is the fast column-array [comba] multiplier. It is
|
---|
| 3122 | * designed to compute the columns of the product first
|
---|
| 3123 | * then handle the carries afterwards. This has the effect
|
---|
| 3124 | * of making the nested loops that compute the columns very
|
---|
| 3125 | * simple and schedulable on super-scalar processors.
|
---|
| 3126 | *
|
---|
| 3127 | * This has been modified to produce a variable number of
|
---|
| 3128 | * digits of output so if say only a half-product is required
|
---|
| 3129 | * you don't have to compute the upper half (a feature
|
---|
| 3130 | * required for fast Barrett reduction).
|
---|
| 3131 | *
|
---|
| 3132 | * Based on Algorithm 14.12 on pp.595 of HAC.
|
---|
| 3133 | *
|
---|
| 3134 | */
|
---|
| 3135 | int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 3136 | {
|
---|
| 3137 | int olduse, res, pa, ix, iz;
|
---|
| 3138 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3139 | mp_digit* W; /* uses dynamic memory and slower */
|
---|
| 3140 | #else
|
---|
| 3141 | mp_digit W[MP_WARRAY];
|
---|
| 3142 | #endif
|
---|
| 3143 | mp_word _W;
|
---|
| 3144 |
|
---|
| 3145 | /* grow the destination as required */
|
---|
| 3146 | if (c->alloc < digs) {
|
---|
| 3147 | if ((res = mp_grow (c, digs)) != MP_OKAY) {
|
---|
| 3148 | return res;
|
---|
| 3149 | }
|
---|
| 3150 | }
|
---|
| 3151 |
|
---|
| 3152 | /* number of output digits to produce */
|
---|
| 3153 | pa = MIN(digs, a->used + b->used);
|
---|
| 3154 | if (pa > MP_WARRAY)
|
---|
| 3155 | return MP_RANGE; /* TAO range check */
|
---|
| 3156 |
|
---|
| 3157 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3158 | W = (mp_digit*)XMALLOC(sizeof(mp_digit) * MP_WARRAY, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 3159 | if (W == NULL)
|
---|
| 3160 | return MP_MEM;
|
---|
| 3161 | #endif
|
---|
| 3162 |
|
---|
| 3163 | /* clear the carry */
|
---|
| 3164 | _W = 0;
|
---|
| 3165 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3166 | int tx, ty;
|
---|
| 3167 | int iy;
|
---|
| 3168 | mp_digit *tmpx, *tmpy;
|
---|
| 3169 |
|
---|
| 3170 | /* get offsets into the two bignums */
|
---|
| 3171 | ty = MIN(b->used-1, ix);
|
---|
| 3172 | tx = ix - ty;
|
---|
| 3173 |
|
---|
| 3174 | /* setup temp aliases */
|
---|
| 3175 | tmpx = a->dp + tx;
|
---|
| 3176 | tmpy = b->dp + ty;
|
---|
| 3177 |
|
---|
| 3178 | /* this is the number of times the loop will iterate, essentially
|
---|
| 3179 | while (tx++ < a->used && ty-- >= 0) { ... }
|
---|
| 3180 | */
|
---|
| 3181 | iy = MIN(a->used-tx, ty+1);
|
---|
| 3182 |
|
---|
| 3183 | /* execute loop */
|
---|
| 3184 | for (iz = 0; iz < iy; ++iz) {
|
---|
| 3185 | _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
---|
| 3186 |
|
---|
| 3187 | }
|
---|
| 3188 |
|
---|
| 3189 | /* store term */
|
---|
| 3190 | W[ix] = (mp_digit)(((mp_digit)_W) & MP_MASK);
|
---|
| 3191 |
|
---|
| 3192 | /* make next carry */
|
---|
| 3193 | _W = _W >> ((mp_word)DIGIT_BIT);
|
---|
| 3194 | }
|
---|
| 3195 |
|
---|
| 3196 | /* setup dest */
|
---|
| 3197 | olduse = c->used;
|
---|
| 3198 | c->used = pa;
|
---|
| 3199 |
|
---|
| 3200 | {
|
---|
| 3201 | mp_digit *tmpc;
|
---|
| 3202 | tmpc = c->dp;
|
---|
| 3203 | for (ix = 0; ix < pa; ix++) { /* JRB, +1 could read uninitialized data */
|
---|
| 3204 | /* now extract the previous digit [below the carry] */
|
---|
| 3205 | *tmpc++ = W[ix];
|
---|
| 3206 | }
|
---|
| 3207 |
|
---|
| 3208 | /* clear unused digits [that existed in the old copy of c] */
|
---|
| 3209 | for (; ix < olduse; ix++) {
|
---|
| 3210 | *tmpc++ = 0;
|
---|
| 3211 | }
|
---|
| 3212 | }
|
---|
| 3213 | mp_clamp (c);
|
---|
| 3214 |
|
---|
| 3215 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3216 | XFREE(W, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 3217 | #endif
|
---|
| 3218 |
|
---|
| 3219 | return MP_OKAY;
|
---|
| 3220 | }
|
---|
| 3221 |
|
---|
| 3222 |
|
---|
| 3223 | /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
|
---|
| 3224 | int s_mp_sqr (mp_int * a, mp_int * b)
|
---|
| 3225 | {
|
---|
| 3226 | mp_int t;
|
---|
| 3227 | int res, ix, iy, pa;
|
---|
| 3228 | mp_word r;
|
---|
| 3229 | mp_digit u, tmpx, *tmpt;
|
---|
| 3230 |
|
---|
| 3231 | pa = a->used;
|
---|
| 3232 | if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
|
---|
| 3233 | return res;
|
---|
| 3234 | }
|
---|
| 3235 |
|
---|
| 3236 | /* default used is maximum possible size */
|
---|
| 3237 | t.used = 2*pa + 1;
|
---|
| 3238 |
|
---|
| 3239 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3240 | /* first calculate the digit at 2*ix */
|
---|
| 3241 | /* calculate double precision result */
|
---|
| 3242 | r = ((mp_word) t.dp[2*ix]) +
|
---|
| 3243 | ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
|
---|
| 3244 |
|
---|
| 3245 | /* store lower part in result */
|
---|
| 3246 | t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3247 |
|
---|
| 3248 | /* get the carry */
|
---|
| 3249 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 3250 |
|
---|
| 3251 | /* left hand side of A[ix] * A[iy] */
|
---|
| 3252 | tmpx = a->dp[ix];
|
---|
| 3253 |
|
---|
| 3254 | /* alias for where to store the results */
|
---|
| 3255 | tmpt = t.dp + (2*ix + 1);
|
---|
| 3256 |
|
---|
| 3257 | for (iy = ix + 1; iy < pa; iy++) {
|
---|
| 3258 | /* first calculate the product */
|
---|
| 3259 | r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
|
---|
| 3260 |
|
---|
| 3261 | /* now calculate the double precision result, note we use
|
---|
| 3262 | * addition instead of *2 since it's easier to optimize
|
---|
| 3263 | */
|
---|
| 3264 | r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
|
---|
| 3265 |
|
---|
| 3266 | /* store lower part */
|
---|
| 3267 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3268 |
|
---|
| 3269 | /* get carry */
|
---|
| 3270 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 3271 | }
|
---|
| 3272 | /* propagate upwards */
|
---|
| 3273 | while (u != ((mp_digit) 0)) {
|
---|
| 3274 | r = ((mp_word) *tmpt) + ((mp_word) u);
|
---|
| 3275 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3276 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 3277 | }
|
---|
| 3278 | }
|
---|
| 3279 |
|
---|
| 3280 | mp_clamp (&t);
|
---|
| 3281 | mp_exch (&t, b);
|
---|
| 3282 | mp_clear (&t);
|
---|
| 3283 | return MP_OKAY;
|
---|
| 3284 | }
|
---|
| 3285 |
|
---|
| 3286 |
|
---|
| 3287 | /* multiplies |a| * |b| and only computes up to digs digits of result
|
---|
| 3288 | * HAC pp. 595, Algorithm 14.12 Modified so you can control how
|
---|
| 3289 | * many digits of output are created.
|
---|
| 3290 | */
|
---|
| 3291 | int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 3292 | {
|
---|
| 3293 | mp_int t;
|
---|
| 3294 | int res, pa, pb, ix, iy;
|
---|
| 3295 | mp_digit u;
|
---|
| 3296 | mp_word r;
|
---|
| 3297 | mp_digit tmpx, *tmpt, *tmpy;
|
---|
| 3298 |
|
---|
| 3299 | /* can we use the fast multiplier? */
|
---|
| 3300 | if (((digs) < MP_WARRAY) &&
|
---|
| 3301 | MIN (a->used, b->used) <
|
---|
| 3302 | (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
| 3303 | return fast_s_mp_mul_digs (a, b, c, digs);
|
---|
| 3304 | }
|
---|
| 3305 |
|
---|
| 3306 | if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
|
---|
| 3307 | return res;
|
---|
| 3308 | }
|
---|
| 3309 | t.used = digs;
|
---|
| 3310 |
|
---|
| 3311 | /* compute the digits of the product directly */
|
---|
| 3312 | pa = a->used;
|
---|
| 3313 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3314 | /* set the carry to zero */
|
---|
| 3315 | u = 0;
|
---|
| 3316 |
|
---|
| 3317 | /* limit ourselves to making digs digits of output */
|
---|
| 3318 | pb = MIN (b->used, digs - ix);
|
---|
| 3319 |
|
---|
| 3320 | /* setup some aliases */
|
---|
| 3321 | /* copy of the digit from a used within the nested loop */
|
---|
| 3322 | tmpx = a->dp[ix];
|
---|
| 3323 |
|
---|
| 3324 | /* an alias for the destination shifted ix places */
|
---|
| 3325 | tmpt = t.dp + ix;
|
---|
| 3326 |
|
---|
| 3327 | /* an alias for the digits of b */
|
---|
| 3328 | tmpy = b->dp;
|
---|
| 3329 |
|
---|
| 3330 | /* compute the columns of the output and propagate the carry */
|
---|
| 3331 | for (iy = 0; iy < pb; iy++) {
|
---|
| 3332 | /* compute the column as a mp_word */
|
---|
| 3333 | r = ((mp_word)*tmpt) +
|
---|
| 3334 | ((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
---|
| 3335 | ((mp_word) u);
|
---|
| 3336 |
|
---|
| 3337 | /* the new column is the lower part of the result */
|
---|
| 3338 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3339 |
|
---|
| 3340 | /* get the carry word from the result */
|
---|
| 3341 | u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
---|
| 3342 | }
|
---|
| 3343 | /* set carry if it is placed below digs */
|
---|
| 3344 | if (ix + iy < digs) {
|
---|
| 3345 | *tmpt = u;
|
---|
| 3346 | }
|
---|
| 3347 | }
|
---|
| 3348 |
|
---|
| 3349 | mp_clamp (&t);
|
---|
| 3350 | mp_exch (&t, c);
|
---|
| 3351 |
|
---|
| 3352 | mp_clear (&t);
|
---|
| 3353 | return MP_OKAY;
|
---|
| 3354 | }
|
---|
| 3355 |
|
---|
| 3356 |
|
---|
| 3357 | /*
|
---|
| 3358 | * shifts with subtractions when the result is greater than b.
|
---|
| 3359 | *
|
---|
| 3360 | * The method is slightly modified to shift B unconditionally up to just under
|
---|
| 3361 | * the leading bit of b. This saves a lot of multiple precision shifting.
|
---|
| 3362 | */
|
---|
| 3363 | int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
|
---|
| 3364 | {
|
---|
| 3365 | int x, bits, res;
|
---|
| 3366 |
|
---|
| 3367 | /* how many bits of last digit does b use */
|
---|
| 3368 | bits = mp_count_bits (b) % DIGIT_BIT;
|
---|
| 3369 |
|
---|
| 3370 | if (b->used > 1) {
|
---|
| 3371 | if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1))
|
---|
| 3372 | != MP_OKAY) {
|
---|
| 3373 | return res;
|
---|
| 3374 | }
|
---|
| 3375 | } else {
|
---|
| 3376 | if ((res = mp_set(a, 1)) != MP_OKAY) {
|
---|
| 3377 | return res;
|
---|
| 3378 | }
|
---|
| 3379 | bits = 1;
|
---|
| 3380 | }
|
---|
| 3381 |
|
---|
| 3382 | /* now compute C = A * B mod b */
|
---|
| 3383 | for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
|
---|
| 3384 | if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
|
---|
| 3385 | return res;
|
---|
| 3386 | }
|
---|
| 3387 | if (mp_cmp_mag (a, b) != MP_LT) {
|
---|
| 3388 | if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
|
---|
| 3389 | return res;
|
---|
| 3390 | }
|
---|
| 3391 | }
|
---|
| 3392 | }
|
---|
| 3393 |
|
---|
| 3394 | return MP_OKAY;
|
---|
| 3395 | }
|
---|
| 3396 |
|
---|
| 3397 |
|
---|
| 3398 | #ifdef MP_LOW_MEM
|
---|
| 3399 | #define TAB_SIZE 32
|
---|
| 3400 | #else
|
---|
| 3401 | #define TAB_SIZE 256
|
---|
| 3402 | #endif
|
---|
| 3403 |
|
---|
| 3404 | int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
|
---|
| 3405 | {
|
---|
| 3406 | mp_int M[TAB_SIZE], res, mu;
|
---|
| 3407 | mp_digit buf;
|
---|
| 3408 | int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
---|
| 3409 | int (*redux)(mp_int*,mp_int*,mp_int*);
|
---|
| 3410 |
|
---|
| 3411 | /* find window size */
|
---|
| 3412 | x = mp_count_bits (X);
|
---|
| 3413 | if (x <= 7) {
|
---|
| 3414 | winsize = 2;
|
---|
| 3415 | } else if (x <= 36) {
|
---|
| 3416 | winsize = 3;
|
---|
| 3417 | } else if (x <= 140) {
|
---|
| 3418 | winsize = 4;
|
---|
| 3419 | } else if (x <= 450) {
|
---|
| 3420 | winsize = 5;
|
---|
| 3421 | } else if (x <= 1303) {
|
---|
| 3422 | winsize = 6;
|
---|
| 3423 | } else if (x <= 3529) {
|
---|
| 3424 | winsize = 7;
|
---|
| 3425 | } else {
|
---|
| 3426 | winsize = 8;
|
---|
| 3427 | }
|
---|
| 3428 |
|
---|
| 3429 | #ifdef MP_LOW_MEM
|
---|
| 3430 | if (winsize > 5) {
|
---|
| 3431 | winsize = 5;
|
---|
| 3432 | }
|
---|
| 3433 | #endif
|
---|
| 3434 |
|
---|
| 3435 | /* init M array */
|
---|
| 3436 | /* init first cell */
|
---|
| 3437 | if ((err = mp_init(&M[1])) != MP_OKAY) {
|
---|
| 3438 | return err;
|
---|
| 3439 | }
|
---|
| 3440 |
|
---|
| 3441 | /* now init the second half of the array */
|
---|
| 3442 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 3443 | if ((err = mp_init(&M[x])) != MP_OKAY) {
|
---|
| 3444 | for (y = 1<<(winsize-1); y < x; y++) {
|
---|
| 3445 | mp_clear (&M[y]);
|
---|
| 3446 | }
|
---|
| 3447 | mp_clear(&M[1]);
|
---|
| 3448 | return err;
|
---|
| 3449 | }
|
---|
| 3450 | }
|
---|
| 3451 |
|
---|
| 3452 | /* create mu, used for Barrett reduction */
|
---|
| 3453 | if ((err = mp_init (&mu)) != MP_OKAY) {
|
---|
| 3454 | goto LBL_M;
|
---|
| 3455 | }
|
---|
| 3456 |
|
---|
| 3457 | if (redmode == 0) {
|
---|
| 3458 | if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
|
---|
| 3459 | goto LBL_MU;
|
---|
| 3460 | }
|
---|
| 3461 | redux = mp_reduce;
|
---|
| 3462 | } else {
|
---|
| 3463 | if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
|
---|
| 3464 | goto LBL_MU;
|
---|
| 3465 | }
|
---|
| 3466 | redux = mp_reduce_2k_l;
|
---|
| 3467 | }
|
---|
| 3468 |
|
---|
| 3469 | /* create M table
|
---|
| 3470 | *
|
---|
| 3471 | * The M table contains powers of the base,
|
---|
| 3472 | * e.g. M[x] = G**x mod P
|
---|
| 3473 | *
|
---|
| 3474 | * The first half of the table is not
|
---|
| 3475 | * computed though accept for M[0] and M[1]
|
---|
| 3476 | */
|
---|
| 3477 | if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
|
---|
| 3478 | goto LBL_MU;
|
---|
| 3479 | }
|
---|
| 3480 |
|
---|
| 3481 | /* compute the value at M[1<<(winsize-1)] by squaring
|
---|
| 3482 | * M[1] (winsize-1) times
|
---|
| 3483 | */
|
---|
| 3484 | if ((err = mp_copy (&M[1], &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 3485 | goto LBL_MU;
|
---|
| 3486 | }
|
---|
| 3487 |
|
---|
| 3488 | for (x = 0; x < (winsize - 1); x++) {
|
---|
| 3489 | /* square it */
|
---|
| 3490 | if ((err = mp_sqr (&M[(mp_digit)(1 << (winsize - 1))],
|
---|
| 3491 | &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 3492 | goto LBL_MU;
|
---|
| 3493 | }
|
---|
| 3494 |
|
---|
| 3495 | /* reduce modulo P */
|
---|
| 3496 | if ((err = redux (&M[(mp_digit)(1 << (winsize - 1))], P, &mu)) != MP_OKAY) {
|
---|
| 3497 | goto LBL_MU;
|
---|
| 3498 | }
|
---|
| 3499 | }
|
---|
| 3500 |
|
---|
| 3501 | /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
|
---|
| 3502 | * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
|
---|
| 3503 | */
|
---|
| 3504 | for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
---|
| 3505 | if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
---|
| 3506 | goto LBL_MU;
|
---|
| 3507 | }
|
---|
| 3508 | if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
|
---|
| 3509 | goto LBL_MU;
|
---|
| 3510 | }
|
---|
| 3511 | }
|
---|
| 3512 |
|
---|
| 3513 | /* setup result */
|
---|
| 3514 | if ((err = mp_init (&res)) != MP_OKAY) {
|
---|
| 3515 | goto LBL_MU;
|
---|
| 3516 | }
|
---|
| 3517 | if ((err = mp_set (&res, 1)) != MP_OKAY) {
|
---|
| 3518 | goto LBL_MU;
|
---|
| 3519 | }
|
---|
| 3520 |
|
---|
| 3521 | /* set initial mode and bit cnt */
|
---|
| 3522 | mode = 0;
|
---|
| 3523 | bitcnt = 1;
|
---|
| 3524 | buf = 0;
|
---|
| 3525 | digidx = X->used - 1;
|
---|
| 3526 | bitcpy = 0;
|
---|
| 3527 | bitbuf = 0;
|
---|
| 3528 |
|
---|
| 3529 | for (;;) {
|
---|
| 3530 | /* grab next digit as required */
|
---|
| 3531 | if (--bitcnt == 0) {
|
---|
| 3532 | /* if digidx == -1 we are out of digits */
|
---|
| 3533 | if (digidx == -1) {
|
---|
| 3534 | break;
|
---|
| 3535 | }
|
---|
| 3536 | /* read next digit and reset the bitcnt */
|
---|
| 3537 | buf = X->dp[digidx--];
|
---|
| 3538 | bitcnt = (int) DIGIT_BIT;
|
---|
| 3539 | }
|
---|
| 3540 |
|
---|
| 3541 | /* grab the next msb from the exponent */
|
---|
| 3542 | y = (int)(buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
|
---|
| 3543 | buf <<= (mp_digit)1;
|
---|
| 3544 |
|
---|
| 3545 | /* if the bit is zero and mode == 0 then we ignore it
|
---|
| 3546 | * These represent the leading zero bits before the first 1 bit
|
---|
| 3547 | * in the exponent. Technically this opt is not required but it
|
---|
| 3548 | * does lower the # of trivial squaring/reductions used
|
---|
| 3549 | */
|
---|
| 3550 | if (mode == 0 && y == 0) {
|
---|
| 3551 | continue;
|
---|
| 3552 | }
|
---|
| 3553 |
|
---|
| 3554 | /* if the bit is zero and mode == 1 then we square */
|
---|
| 3555 | if (mode == 1 && y == 0) {
|
---|
| 3556 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 3557 | goto LBL_RES;
|
---|
| 3558 | }
|
---|
| 3559 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3560 | goto LBL_RES;
|
---|
| 3561 | }
|
---|
| 3562 | continue;
|
---|
| 3563 | }
|
---|
| 3564 |
|
---|
| 3565 | /* else we add it to the window */
|
---|
| 3566 | bitbuf |= (y << (winsize - ++bitcpy));
|
---|
| 3567 | mode = 2;
|
---|
| 3568 |
|
---|
| 3569 | if (bitcpy == winsize) {
|
---|
| 3570 | /* ok window is filled so square as required and multiply */
|
---|
| 3571 | /* square first */
|
---|
| 3572 | for (x = 0; x < winsize; x++) {
|
---|
| 3573 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 3574 | goto LBL_RES;
|
---|
| 3575 | }
|
---|
| 3576 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3577 | goto LBL_RES;
|
---|
| 3578 | }
|
---|
| 3579 | }
|
---|
| 3580 |
|
---|
| 3581 | /* then multiply */
|
---|
| 3582 | if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
---|
| 3583 | goto LBL_RES;
|
---|
| 3584 | }
|
---|
| 3585 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3586 | goto LBL_RES;
|
---|
| 3587 | }
|
---|
| 3588 |
|
---|
| 3589 | /* empty window and reset */
|
---|
| 3590 | bitcpy = 0;
|
---|
| 3591 | bitbuf = 0;
|
---|
| 3592 | mode = 1;
|
---|
| 3593 | }
|
---|
| 3594 | }
|
---|
| 3595 |
|
---|
| 3596 | /* if bits remain then square/multiply */
|
---|
| 3597 | if (mode == 2 && bitcpy > 0) {
|
---|
| 3598 | /* square then multiply if the bit is set */
|
---|
| 3599 | for (x = 0; x < bitcpy; x++) {
|
---|
| 3600 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 3601 | goto LBL_RES;
|
---|
| 3602 | }
|
---|
| 3603 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3604 | goto LBL_RES;
|
---|
| 3605 | }
|
---|
| 3606 |
|
---|
| 3607 | bitbuf <<= 1;
|
---|
| 3608 | if ((bitbuf & (1 << winsize)) != 0) {
|
---|
| 3609 | /* then multiply */
|
---|
| 3610 | if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
|
---|
| 3611 | goto LBL_RES;
|
---|
| 3612 | }
|
---|
| 3613 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3614 | goto LBL_RES;
|
---|
| 3615 | }
|
---|
| 3616 | }
|
---|
| 3617 | }
|
---|
| 3618 | }
|
---|
| 3619 |
|
---|
| 3620 | mp_exch (&res, Y);
|
---|
| 3621 | err = MP_OKAY;
|
---|
| 3622 | LBL_RES:mp_clear (&res);
|
---|
| 3623 | LBL_MU:mp_clear (&mu);
|
---|
| 3624 | LBL_M:
|
---|
| 3625 | mp_clear(&M[1]);
|
---|
| 3626 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 3627 | mp_clear (&M[x]);
|
---|
| 3628 | }
|
---|
| 3629 | return err;
|
---|
| 3630 | }
|
---|
| 3631 |
|
---|
| 3632 |
|
---|
| 3633 | /* pre-calculate the value required for Barrett reduction
|
---|
| 3634 | * For a given modulus "b" it calculates the value required in "a"
|
---|
| 3635 | */
|
---|
| 3636 | int mp_reduce_setup (mp_int * a, mp_int * b)
|
---|
| 3637 | {
|
---|
| 3638 | int res;
|
---|
| 3639 |
|
---|
| 3640 | if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
|
---|
| 3641 | return res;
|
---|
| 3642 | }
|
---|
| 3643 | return mp_div (a, b, a, NULL);
|
---|
| 3644 | }
|
---|
| 3645 |
|
---|
| 3646 |
|
---|
| 3647 | /* reduces x mod m, assumes 0 < x < m**2, mu is
|
---|
| 3648 | * precomputed via mp_reduce_setup.
|
---|
| 3649 | * From HAC pp.604 Algorithm 14.42
|
---|
| 3650 | */
|
---|
| 3651 | int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
|
---|
| 3652 | {
|
---|
| 3653 | mp_int q;
|
---|
| 3654 | int res, um = m->used;
|
---|
| 3655 |
|
---|
| 3656 | /* q = x */
|
---|
| 3657 | if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
|
---|
| 3658 | return res;
|
---|
| 3659 | }
|
---|
| 3660 |
|
---|
| 3661 | /* q1 = x / b**(k-1) */
|
---|
| 3662 | mp_rshd (&q, um - 1);
|
---|
| 3663 |
|
---|
| 3664 | /* according to HAC this optimization is ok */
|
---|
| 3665 | if (((mp_word) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
|
---|
| 3666 | if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
|
---|
| 3667 | goto CLEANUP;
|
---|
| 3668 | }
|
---|
| 3669 | } else {
|
---|
| 3670 | #ifdef BN_S_MP_MUL_HIGH_DIGS_C
|
---|
| 3671 | if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
|
---|
| 3672 | goto CLEANUP;
|
---|
| 3673 | }
|
---|
| 3674 | #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
|
---|
| 3675 | if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
|
---|
| 3676 | goto CLEANUP;
|
---|
| 3677 | }
|
---|
| 3678 | #else
|
---|
| 3679 | {
|
---|
| 3680 | res = MP_VAL;
|
---|
| 3681 | goto CLEANUP;
|
---|
| 3682 | }
|
---|
| 3683 | #endif
|
---|
| 3684 | }
|
---|
| 3685 |
|
---|
| 3686 | /* q3 = q2 / b**(k+1) */
|
---|
| 3687 | mp_rshd (&q, um + 1);
|
---|
| 3688 |
|
---|
| 3689 | /* x = x mod b**(k+1), quick (no division) */
|
---|
| 3690 | if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
|
---|
| 3691 | goto CLEANUP;
|
---|
| 3692 | }
|
---|
| 3693 |
|
---|
| 3694 | /* q = q * m mod b**(k+1), quick (no division) */
|
---|
| 3695 | if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
|
---|
| 3696 | goto CLEANUP;
|
---|
| 3697 | }
|
---|
| 3698 |
|
---|
| 3699 | /* x = x - q */
|
---|
| 3700 | if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
|
---|
| 3701 | goto CLEANUP;
|
---|
| 3702 | }
|
---|
| 3703 |
|
---|
| 3704 | /* If x < 0, add b**(k+1) to it */
|
---|
| 3705 | if (mp_cmp_d (x, 0) == MP_LT) {
|
---|
| 3706 | if ((res = mp_set (&q, 1)) != MP_OKAY)
|
---|
| 3707 | goto CLEANUP;
|
---|
| 3708 | if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
|
---|
| 3709 | goto CLEANUP;
|
---|
| 3710 | if ((res = mp_add (x, &q, x)) != MP_OKAY)
|
---|
| 3711 | goto CLEANUP;
|
---|
| 3712 | }
|
---|
| 3713 |
|
---|
| 3714 | /* Back off if it's too big */
|
---|
| 3715 | while (mp_cmp (x, m) != MP_LT) {
|
---|
| 3716 | if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
|
---|
| 3717 | goto CLEANUP;
|
---|
| 3718 | }
|
---|
| 3719 | }
|
---|
| 3720 |
|
---|
| 3721 | CLEANUP:
|
---|
| 3722 | mp_clear (&q);
|
---|
| 3723 |
|
---|
| 3724 | return res;
|
---|
| 3725 | }
|
---|
| 3726 |
|
---|
| 3727 |
|
---|
| 3728 | /* reduces a modulo n where n is of the form 2**p - d
|
---|
| 3729 | This differs from reduce_2k since "d" can be larger
|
---|
| 3730 | than a single digit.
|
---|
| 3731 | */
|
---|
| 3732 | int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
|
---|
| 3733 | {
|
---|
| 3734 | mp_int q;
|
---|
| 3735 | int p, res;
|
---|
| 3736 |
|
---|
| 3737 | if ((res = mp_init(&q)) != MP_OKAY) {
|
---|
| 3738 | return res;
|
---|
| 3739 | }
|
---|
| 3740 |
|
---|
| 3741 | p = mp_count_bits(n);
|
---|
| 3742 | top:
|
---|
| 3743 | /* q = a/2**p, a = a mod 2**p */
|
---|
| 3744 | if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
|
---|
| 3745 | goto ERR;
|
---|
| 3746 | }
|
---|
| 3747 |
|
---|
| 3748 | /* q = q * d */
|
---|
| 3749 | if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
|
---|
| 3750 | goto ERR;
|
---|
| 3751 | }
|
---|
| 3752 |
|
---|
| 3753 | /* a = a + q */
|
---|
| 3754 | if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
|
---|
| 3755 | goto ERR;
|
---|
| 3756 | }
|
---|
| 3757 |
|
---|
| 3758 | if (mp_cmp_mag(a, n) != MP_LT) {
|
---|
| 3759 | if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
|
---|
| 3760 | goto ERR;
|
---|
| 3761 | }
|
---|
| 3762 | goto top;
|
---|
| 3763 | }
|
---|
| 3764 |
|
---|
| 3765 | ERR:
|
---|
| 3766 | mp_clear(&q);
|
---|
| 3767 | return res;
|
---|
| 3768 | }
|
---|
| 3769 |
|
---|
| 3770 |
|
---|
| 3771 | /* determines the setup value */
|
---|
| 3772 | int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
|
---|
| 3773 | {
|
---|
| 3774 | int res;
|
---|
| 3775 | mp_int tmp;
|
---|
| 3776 |
|
---|
| 3777 | if ((res = mp_init(&tmp)) != MP_OKAY) {
|
---|
| 3778 | return res;
|
---|
| 3779 | }
|
---|
| 3780 |
|
---|
| 3781 | if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
|
---|
| 3782 | goto ERR;
|
---|
| 3783 | }
|
---|
| 3784 |
|
---|
| 3785 | if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
|
---|
| 3786 | goto ERR;
|
---|
| 3787 | }
|
---|
| 3788 |
|
---|
| 3789 | ERR:
|
---|
| 3790 | mp_clear(&tmp);
|
---|
| 3791 | return res;
|
---|
| 3792 | }
|
---|
| 3793 |
|
---|
| 3794 |
|
---|
| 3795 | /* multiplies |a| * |b| and does not compute the lower digs digits
|
---|
| 3796 | * [meant to get the higher part of the product]
|
---|
| 3797 | */
|
---|
| 3798 | int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 3799 | {
|
---|
| 3800 | mp_int t;
|
---|
| 3801 | int res, pa, pb, ix, iy;
|
---|
| 3802 | mp_digit u;
|
---|
| 3803 | mp_word r;
|
---|
| 3804 | mp_digit tmpx, *tmpt, *tmpy;
|
---|
| 3805 |
|
---|
| 3806 | /* can we use the fast multiplier? */
|
---|
| 3807 | #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
|
---|
| 3808 | if (((a->used + b->used + 1) < MP_WARRAY)
|
---|
| 3809 | && MIN (a->used, b->used) <
|
---|
| 3810 | (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
| 3811 | return fast_s_mp_mul_high_digs (a, b, c, digs);
|
---|
| 3812 | }
|
---|
| 3813 | #endif
|
---|
| 3814 |
|
---|
| 3815 | if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
|
---|
| 3816 | return res;
|
---|
| 3817 | }
|
---|
| 3818 | t.used = a->used + b->used + 1;
|
---|
| 3819 |
|
---|
| 3820 | pa = a->used;
|
---|
| 3821 | pb = b->used;
|
---|
| 3822 | for (ix = 0; ix < pa && a->dp; ix++) {
|
---|
| 3823 | /* clear the carry */
|
---|
| 3824 | u = 0;
|
---|
| 3825 |
|
---|
| 3826 | /* left hand side of A[ix] * B[iy] */
|
---|
| 3827 | tmpx = a->dp[ix];
|
---|
| 3828 |
|
---|
| 3829 | /* alias to the address of where the digits will be stored */
|
---|
| 3830 | tmpt = &(t.dp[digs]);
|
---|
| 3831 |
|
---|
| 3832 | /* alias for where to read the right hand side from */
|
---|
| 3833 | tmpy = b->dp + (digs - ix);
|
---|
| 3834 |
|
---|
| 3835 | for (iy = digs - ix; iy < pb; iy++) {
|
---|
| 3836 | /* calculate the double precision result */
|
---|
| 3837 | r = ((mp_word)*tmpt) +
|
---|
| 3838 | ((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
---|
| 3839 | ((mp_word) u);
|
---|
| 3840 |
|
---|
| 3841 | /* get the lower part */
|
---|
| 3842 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3843 |
|
---|
| 3844 | /* carry the carry */
|
---|
| 3845 | u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
---|
| 3846 | }
|
---|
| 3847 | *tmpt = u;
|
---|
| 3848 | }
|
---|
| 3849 | mp_clamp (&t);
|
---|
| 3850 | mp_exch (&t, c);
|
---|
| 3851 | mp_clear (&t);
|
---|
| 3852 | return MP_OKAY;
|
---|
| 3853 | }
|
---|
| 3854 |
|
---|
| 3855 |
|
---|
| 3856 | /* this is a modified version of fast_s_mul_digs that only produces
|
---|
| 3857 | * output digits *above* digs. See the comments for fast_s_mul_digs
|
---|
| 3858 | * to see how it works.
|
---|
| 3859 | *
|
---|
| 3860 | * This is used in the Barrett reduction since for one of the multiplications
|
---|
| 3861 | * only the higher digits were needed. This essentially halves the work.
|
---|
| 3862 | *
|
---|
| 3863 | * Based on Algorithm 14.12 on pp.595 of HAC.
|
---|
| 3864 | */
|
---|
| 3865 | int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 3866 | {
|
---|
| 3867 | int olduse, res, pa, ix, iz;
|
---|
| 3868 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3869 | mp_digit* W; /* uses dynamic memory and slower */
|
---|
| 3870 | #else
|
---|
| 3871 | mp_digit W[MP_WARRAY];
|
---|
| 3872 | #endif
|
---|
| 3873 | mp_word _W;
|
---|
| 3874 |
|
---|
| 3875 | if (a->dp == NULL) { /* JRB, avoid reading uninitialized values */
|
---|
| 3876 | return MP_VAL;
|
---|
| 3877 | }
|
---|
| 3878 |
|
---|
| 3879 | /* grow the destination as required */
|
---|
| 3880 | pa = a->used + b->used;
|
---|
| 3881 | if (c->alloc < pa) {
|
---|
| 3882 | if ((res = mp_grow (c, pa)) != MP_OKAY) {
|
---|
| 3883 | return res;
|
---|
| 3884 | }
|
---|
| 3885 | }
|
---|
| 3886 |
|
---|
| 3887 | if (pa > MP_WARRAY)
|
---|
| 3888 | return MP_RANGE; /* TAO range check */
|
---|
| 3889 |
|
---|
| 3890 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3891 | W = (mp_digit*)XMALLOC(sizeof(mp_digit) * MP_WARRAY, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 3892 | if (W == NULL)
|
---|
| 3893 | return MP_MEM;
|
---|
| 3894 | #endif
|
---|
| 3895 |
|
---|
| 3896 | /* number of output digits to produce */
|
---|
| 3897 | pa = a->used + b->used;
|
---|
| 3898 | _W = 0;
|
---|
| 3899 | for (ix = digs; ix < pa; ix++) { /* JRB, have a->dp check at top of function*/
|
---|
| 3900 | int tx, ty, iy;
|
---|
| 3901 | mp_digit *tmpx, *tmpy;
|
---|
| 3902 |
|
---|
| 3903 | /* get offsets into the two bignums */
|
---|
| 3904 | ty = MIN(b->used-1, ix);
|
---|
| 3905 | tx = ix - ty;
|
---|
| 3906 |
|
---|
| 3907 | /* setup temp aliases */
|
---|
| 3908 | tmpx = a->dp + tx;
|
---|
| 3909 | tmpy = b->dp + ty;
|
---|
| 3910 |
|
---|
| 3911 | /* this is the number of times the loop will iterate, essentially its
|
---|
| 3912 | while (tx++ < a->used && ty-- >= 0) { ... }
|
---|
| 3913 | */
|
---|
| 3914 | iy = MIN(a->used-tx, ty+1);
|
---|
| 3915 |
|
---|
| 3916 | /* execute loop */
|
---|
| 3917 | for (iz = 0; iz < iy; iz++) {
|
---|
| 3918 | _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
---|
| 3919 | }
|
---|
| 3920 |
|
---|
| 3921 | /* store term */
|
---|
| 3922 | W[ix] = (mp_digit)(((mp_digit)_W) & MP_MASK);
|
---|
| 3923 |
|
---|
| 3924 | /* make next carry */
|
---|
| 3925 | _W = _W >> ((mp_word)DIGIT_BIT);
|
---|
| 3926 | }
|
---|
| 3927 |
|
---|
| 3928 | /* setup dest */
|
---|
| 3929 | olduse = c->used;
|
---|
| 3930 | c->used = pa;
|
---|
| 3931 |
|
---|
| 3932 | {
|
---|
| 3933 | mp_digit *tmpc;
|
---|
| 3934 |
|
---|
| 3935 | tmpc = c->dp + digs;
|
---|
| 3936 | for (ix = digs; ix < pa; ix++) { /* TAO, <= could potentially overwrite */
|
---|
| 3937 | /* now extract the previous digit [below the carry] */
|
---|
| 3938 | *tmpc++ = W[ix];
|
---|
| 3939 | }
|
---|
| 3940 |
|
---|
| 3941 | /* clear unused digits [that existed in the old copy of c] */
|
---|
| 3942 | for (; ix < olduse; ix++) {
|
---|
| 3943 | *tmpc++ = 0;
|
---|
| 3944 | }
|
---|
| 3945 | }
|
---|
| 3946 | mp_clamp (c);
|
---|
| 3947 |
|
---|
| 3948 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3949 | XFREE(W, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 3950 | #endif
|
---|
| 3951 |
|
---|
| 3952 | return MP_OKAY;
|
---|
| 3953 | }
|
---|
| 3954 |
|
---|
| 3955 |
|
---|
| 3956 | #ifndef MP_SET_CHUNK_BITS
|
---|
| 3957 | #define MP_SET_CHUNK_BITS 4
|
---|
| 3958 | #endif
|
---|
| 3959 | int mp_set_int (mp_int * a, unsigned long b)
|
---|
| 3960 | {
|
---|
| 3961 | int x, res;
|
---|
| 3962 |
|
---|
| 3963 | /* use direct mp_set if b is less than mp_digit max */
|
---|
| 3964 | if (b < MP_DIGIT_MAX) {
|
---|
| 3965 | return mp_set (a, (mp_digit)b);
|
---|
| 3966 | }
|
---|
| 3967 |
|
---|
| 3968 | mp_zero (a);
|
---|
| 3969 |
|
---|
| 3970 | /* set chunk bits at a time */
|
---|
| 3971 | for (x = 0; x < (int)(sizeof(b) * 8) / MP_SET_CHUNK_BITS; x++) {
|
---|
| 3972 | /* shift the number up chunk bits */
|
---|
| 3973 | if ((res = mp_mul_2d (a, MP_SET_CHUNK_BITS, a)) != MP_OKAY) {
|
---|
| 3974 | return res;
|
---|
| 3975 | }
|
---|
| 3976 |
|
---|
| 3977 | /* OR in the top bits of the source */
|
---|
| 3978 | a->dp[0] |= (b >> ((sizeof(b) * 8) - MP_SET_CHUNK_BITS)) &
|
---|
| 3979 | ((1 << MP_SET_CHUNK_BITS) - 1);
|
---|
| 3980 |
|
---|
| 3981 | /* shift the source up to the next chunk bits */
|
---|
| 3982 | b <<= MP_SET_CHUNK_BITS;
|
---|
| 3983 |
|
---|
| 3984 | /* ensure that digits are not clamped off */
|
---|
| 3985 | a->used += 1;
|
---|
| 3986 | }
|
---|
| 3987 | mp_clamp (a);
|
---|
| 3988 | return MP_OKAY;
|
---|
| 3989 | }
|
---|
| 3990 |
|
---|
| 3991 |
|
---|
| 3992 | #if defined(WOLFSSL_KEY_GEN) || defined(HAVE_ECC) || !defined(NO_RSA) || \
|
---|
| 3993 | !defined(NO_DSA) | !defined(NO_DH)
|
---|
| 3994 |
|
---|
| 3995 | /* c = a * a (mod b) */
|
---|
| 3996 | int mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 3997 | {
|
---|
| 3998 | int res;
|
---|
| 3999 | mp_int t;
|
---|
| 4000 |
|
---|
| 4001 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
| 4002 | return res;
|
---|
| 4003 | }
|
---|
| 4004 |
|
---|
| 4005 | if ((res = mp_sqr (a, &t)) != MP_OKAY) {
|
---|
| 4006 | mp_clear (&t);
|
---|
| 4007 | return res;
|
---|
| 4008 | }
|
---|
| 4009 | res = mp_mod (&t, b, c);
|
---|
| 4010 | mp_clear (&t);
|
---|
| 4011 | return res;
|
---|
| 4012 | }
|
---|
| 4013 |
|
---|
| 4014 | #endif
|
---|
| 4015 |
|
---|
| 4016 |
|
---|
| 4017 | #if defined(HAVE_ECC) || !defined(NO_PWDBASED) || defined(WOLFSSL_SNIFFER) || \
|
---|
| 4018 | defined(WOLFSSL_HAVE_WOLFSCEP) || defined(WOLFSSL_KEY_GEN) || \
|
---|
| 4019 | defined(OPENSSL_EXTRA) || defined(WC_RSA_BLINDING) || \
|
---|
| 4020 | (!defined(NO_RSA) && !defined(NO_RSA_BOUNDS_CHECK))
|
---|
| 4021 |
|
---|
| 4022 | /* single digit addition */
|
---|
| 4023 | int mp_add_d (mp_int* a, mp_digit b, mp_int* c)
|
---|
| 4024 | {
|
---|
| 4025 | int res, ix, oldused;
|
---|
| 4026 | mp_digit *tmpa, *tmpc, mu;
|
---|
| 4027 |
|
---|
| 4028 | /* grow c as required */
|
---|
| 4029 | if (c->alloc < a->used + 1) {
|
---|
| 4030 | if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
---|
| 4031 | return res;
|
---|
| 4032 | }
|
---|
| 4033 | }
|
---|
| 4034 |
|
---|
| 4035 | /* if a is negative and |a| >= b, call c = |a| - b */
|
---|
| 4036 | if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
|
---|
| 4037 | /* temporarily fix sign of a */
|
---|
| 4038 | a->sign = MP_ZPOS;
|
---|
| 4039 |
|
---|
| 4040 | /* c = |a| - b */
|
---|
| 4041 | res = mp_sub_d(a, b, c);
|
---|
| 4042 |
|
---|
| 4043 | /* fix sign */
|
---|
| 4044 | a->sign = c->sign = MP_NEG;
|
---|
| 4045 |
|
---|
| 4046 | /* clamp */
|
---|
| 4047 | mp_clamp(c);
|
---|
| 4048 |
|
---|
| 4049 | return res;
|
---|
| 4050 | }
|
---|
| 4051 |
|
---|
| 4052 | /* old number of used digits in c */
|
---|
| 4053 | oldused = c->used;
|
---|
| 4054 |
|
---|
| 4055 | /* sign always positive */
|
---|
| 4056 | c->sign = MP_ZPOS;
|
---|
| 4057 |
|
---|
| 4058 | /* source alias */
|
---|
| 4059 | tmpa = a->dp;
|
---|
| 4060 |
|
---|
| 4061 | /* destination alias */
|
---|
| 4062 | tmpc = c->dp;
|
---|
| 4063 |
|
---|
| 4064 | /* if a is positive */
|
---|
| 4065 | if (a->sign == MP_ZPOS) {
|
---|
| 4066 | /* add digit, after this we're propagating
|
---|
| 4067 | * the carry.
|
---|
| 4068 | */
|
---|
| 4069 | *tmpc = *tmpa++ + b;
|
---|
| 4070 | mu = *tmpc >> DIGIT_BIT;
|
---|
| 4071 | *tmpc++ &= MP_MASK;
|
---|
| 4072 |
|
---|
| 4073 | /* now handle rest of the digits */
|
---|
| 4074 | for (ix = 1; ix < a->used; ix++) {
|
---|
| 4075 | *tmpc = *tmpa++ + mu;
|
---|
| 4076 | mu = *tmpc >> DIGIT_BIT;
|
---|
| 4077 | *tmpc++ &= MP_MASK;
|
---|
| 4078 | }
|
---|
| 4079 | /* set final carry */
|
---|
| 4080 | if (ix < c->alloc) {
|
---|
| 4081 | ix++;
|
---|
| 4082 | *tmpc++ = mu;
|
---|
| 4083 | }
|
---|
| 4084 |
|
---|
| 4085 | /* setup size */
|
---|
| 4086 | c->used = a->used + 1;
|
---|
| 4087 | } else {
|
---|
| 4088 | /* a was negative and |a| < b */
|
---|
| 4089 | c->used = 1;
|
---|
| 4090 |
|
---|
| 4091 | /* the result is a single digit */
|
---|
| 4092 | if (a->used == 1) {
|
---|
| 4093 | *tmpc++ = b - a->dp[0];
|
---|
| 4094 | } else {
|
---|
| 4095 | *tmpc++ = b;
|
---|
| 4096 | }
|
---|
| 4097 |
|
---|
| 4098 | /* setup count so the clearing of oldused
|
---|
| 4099 | * can fall through correctly
|
---|
| 4100 | */
|
---|
| 4101 | ix = 1;
|
---|
| 4102 | }
|
---|
| 4103 |
|
---|
| 4104 | /* now zero to oldused */
|
---|
| 4105 | while (ix++ < oldused) {
|
---|
| 4106 | *tmpc++ = 0;
|
---|
| 4107 | }
|
---|
| 4108 | mp_clamp(c);
|
---|
| 4109 |
|
---|
| 4110 | return MP_OKAY;
|
---|
| 4111 | }
|
---|
| 4112 |
|
---|
| 4113 |
|
---|
| 4114 | /* single digit subtraction */
|
---|
| 4115 | int mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
|
---|
| 4116 | {
|
---|
| 4117 | mp_digit *tmpa, *tmpc, mu;
|
---|
| 4118 | int res, ix, oldused;
|
---|
| 4119 |
|
---|
| 4120 | /* grow c as required */
|
---|
| 4121 | if (c->alloc < a->used + 1) {
|
---|
| 4122 | if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
---|
| 4123 | return res;
|
---|
| 4124 | }
|
---|
| 4125 | }
|
---|
| 4126 |
|
---|
| 4127 | /* if a is negative just do an unsigned
|
---|
| 4128 | * addition [with fudged signs]
|
---|
| 4129 | */
|
---|
| 4130 | if (a->sign == MP_NEG) {
|
---|
| 4131 | a->sign = MP_ZPOS;
|
---|
| 4132 | res = mp_add_d(a, b, c);
|
---|
| 4133 | a->sign = c->sign = MP_NEG;
|
---|
| 4134 |
|
---|
| 4135 | /* clamp */
|
---|
| 4136 | mp_clamp(c);
|
---|
| 4137 |
|
---|
| 4138 | return res;
|
---|
| 4139 | }
|
---|
| 4140 |
|
---|
| 4141 | /* setup regs */
|
---|
| 4142 | oldused = c->used;
|
---|
| 4143 | tmpa = a->dp;
|
---|
| 4144 | tmpc = c->dp;
|
---|
| 4145 |
|
---|
| 4146 | /* if a <= b simply fix the single digit */
|
---|
| 4147 | if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
|
---|
| 4148 | if (a->used == 1) {
|
---|
| 4149 | *tmpc++ = b - *tmpa;
|
---|
| 4150 | } else {
|
---|
| 4151 | *tmpc++ = b;
|
---|
| 4152 | }
|
---|
| 4153 | ix = 1;
|
---|
| 4154 |
|
---|
| 4155 | /* negative/1digit */
|
---|
| 4156 | c->sign = MP_NEG;
|
---|
| 4157 | c->used = 1;
|
---|
| 4158 | } else {
|
---|
| 4159 | /* positive/size */
|
---|
| 4160 | c->sign = MP_ZPOS;
|
---|
| 4161 | c->used = a->used;
|
---|
| 4162 |
|
---|
| 4163 | /* subtract first digit */
|
---|
| 4164 | *tmpc = *tmpa++ - b;
|
---|
| 4165 | mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
|
---|
| 4166 | *tmpc++ &= MP_MASK;
|
---|
| 4167 |
|
---|
| 4168 | /* handle rest of the digits */
|
---|
| 4169 | for (ix = 1; ix < a->used; ix++) {
|
---|
| 4170 | *tmpc = *tmpa++ - mu;
|
---|
| 4171 | mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
|
---|
| 4172 | *tmpc++ &= MP_MASK;
|
---|
| 4173 | }
|
---|
| 4174 | }
|
---|
| 4175 |
|
---|
| 4176 | /* zero excess digits */
|
---|
| 4177 | while (ix++ < oldused) {
|
---|
| 4178 | *tmpc++ = 0;
|
---|
| 4179 | }
|
---|
| 4180 | mp_clamp(c);
|
---|
| 4181 | return MP_OKAY;
|
---|
| 4182 | }
|
---|
| 4183 |
|
---|
| 4184 | #endif /* defined(HAVE_ECC) || !defined(NO_PWDBASED) */
|
---|
| 4185 |
|
---|
| 4186 |
|
---|
| 4187 | #if defined(WOLFSSL_KEY_GEN) || defined(HAVE_COMP_KEY) || defined(HAVE_ECC) || \
|
---|
| 4188 | defined(DEBUG_WOLFSSL) || !defined(NO_RSA) || !defined(NO_DSA) || \
|
---|
| 4189 | !defined(NO_DH)
|
---|
| 4190 |
|
---|
| 4191 | static const int lnz[16] = {
|
---|
| 4192 | 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
|
---|
| 4193 | };
|
---|
| 4194 |
|
---|
| 4195 | /* Counts the number of lsbs which are zero before the first zero bit */
|
---|
| 4196 | int mp_cnt_lsb(mp_int *a)
|
---|
| 4197 | {
|
---|
| 4198 | int x;
|
---|
| 4199 | mp_digit q = 0, qq;
|
---|
| 4200 |
|
---|
| 4201 | /* easy out */
|
---|
| 4202 | if (mp_iszero(a) == MP_YES) {
|
---|
| 4203 | return 0;
|
---|
| 4204 | }
|
---|
| 4205 |
|
---|
| 4206 | /* scan lower digits until non-zero */
|
---|
| 4207 | for (x = 0; x < a->used && a->dp[x] == 0; x++) {}
|
---|
| 4208 | if (a->dp)
|
---|
| 4209 | q = a->dp[x];
|
---|
| 4210 | x *= DIGIT_BIT;
|
---|
| 4211 |
|
---|
| 4212 | /* now scan this digit until a 1 is found */
|
---|
| 4213 | if ((q & 1) == 0) {
|
---|
| 4214 | do {
|
---|
| 4215 | qq = q & 15;
|
---|
| 4216 | x += lnz[qq];
|
---|
| 4217 | q >>= 4;
|
---|
| 4218 | } while (qq == 0);
|
---|
| 4219 | }
|
---|
| 4220 | return x;
|
---|
| 4221 | }
|
---|
| 4222 |
|
---|
| 4223 |
|
---|
| 4224 |
|
---|
| 4225 |
|
---|
| 4226 | static int s_is_power_of_two(mp_digit b, int *p)
|
---|
| 4227 | {
|
---|
| 4228 | int x;
|
---|
| 4229 |
|
---|
| 4230 | /* fast return if no power of two */
|
---|
| 4231 | if ((b==0) || (b & (b-1))) {
|
---|
| 4232 | return 0;
|
---|
| 4233 | }
|
---|
| 4234 |
|
---|
| 4235 | for (x = 0; x < DIGIT_BIT; x++) {
|
---|
| 4236 | if (b == (((mp_digit)1)<<x)) {
|
---|
| 4237 | *p = x;
|
---|
| 4238 | return 1;
|
---|
| 4239 | }
|
---|
| 4240 | }
|
---|
| 4241 | return 0;
|
---|
| 4242 | }
|
---|
| 4243 |
|
---|
| 4244 | /* single digit division (based on routine from MPI) */
|
---|
| 4245 | static int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
|
---|
| 4246 | {
|
---|
| 4247 | mp_int q;
|
---|
| 4248 | mp_word w;
|
---|
| 4249 | mp_digit t;
|
---|
| 4250 | int res = MP_OKAY, ix;
|
---|
| 4251 |
|
---|
| 4252 | /* cannot divide by zero */
|
---|
| 4253 | if (b == 0) {
|
---|
| 4254 | return MP_VAL;
|
---|
| 4255 | }
|
---|
| 4256 |
|
---|
| 4257 | /* quick outs */
|
---|
| 4258 | if (b == 1 || mp_iszero(a) == MP_YES) {
|
---|
| 4259 | if (d != NULL) {
|
---|
| 4260 | *d = 0;
|
---|
| 4261 | }
|
---|
| 4262 | if (c != NULL) {
|
---|
| 4263 | return mp_copy(a, c);
|
---|
| 4264 | }
|
---|
| 4265 | return MP_OKAY;
|
---|
| 4266 | }
|
---|
| 4267 |
|
---|
| 4268 | /* power of two ? */
|
---|
| 4269 | if (s_is_power_of_two(b, &ix) == 1) {
|
---|
| 4270 | if (d != NULL) {
|
---|
| 4271 | *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
|
---|
| 4272 | }
|
---|
| 4273 | if (c != NULL) {
|
---|
| 4274 | return mp_div_2d(a, ix, c, NULL);
|
---|
| 4275 | }
|
---|
| 4276 | return MP_OKAY;
|
---|
| 4277 | }
|
---|
| 4278 |
|
---|
| 4279 | #ifdef BN_MP_DIV_3_C
|
---|
| 4280 | /* three? */
|
---|
| 4281 | if (b == 3) {
|
---|
| 4282 | return mp_div_3(a, c, d);
|
---|
| 4283 | }
|
---|
| 4284 | #endif
|
---|
| 4285 |
|
---|
| 4286 | /* no easy answer [c'est la vie]. Just division */
|
---|
| 4287 | if (c != NULL) {
|
---|
| 4288 | if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
|
---|
| 4289 | return res;
|
---|
| 4290 | }
|
---|
| 4291 |
|
---|
| 4292 | q.used = a->used;
|
---|
| 4293 | q.sign = a->sign;
|
---|
| 4294 | }
|
---|
| 4295 | else {
|
---|
| 4296 | if ((res = mp_init(&q)) != MP_OKAY) {
|
---|
| 4297 | return res;
|
---|
| 4298 | }
|
---|
| 4299 | }
|
---|
| 4300 |
|
---|
| 4301 |
|
---|
| 4302 | w = 0;
|
---|
| 4303 | for (ix = a->used - 1; ix >= 0; ix--) {
|
---|
| 4304 | w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
|
---|
| 4305 |
|
---|
| 4306 | if (w >= b) {
|
---|
| 4307 | t = (mp_digit)(w / b);
|
---|
| 4308 | w -= ((mp_word)t) * ((mp_word)b);
|
---|
| 4309 | } else {
|
---|
| 4310 | t = 0;
|
---|
| 4311 | }
|
---|
| 4312 | if (c != NULL)
|
---|
| 4313 | q.dp[ix] = (mp_digit)t;
|
---|
| 4314 | }
|
---|
| 4315 |
|
---|
| 4316 | if (d != NULL) {
|
---|
| 4317 | *d = (mp_digit)w;
|
---|
| 4318 | }
|
---|
| 4319 |
|
---|
| 4320 | if (c != NULL) {
|
---|
| 4321 | mp_clamp(&q);
|
---|
| 4322 | mp_exch(&q, c);
|
---|
| 4323 | }
|
---|
| 4324 | mp_clear(&q);
|
---|
| 4325 |
|
---|
| 4326 | return res;
|
---|
| 4327 | }
|
---|
| 4328 |
|
---|
| 4329 |
|
---|
| 4330 | int mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
|
---|
| 4331 | {
|
---|
| 4332 | return mp_div_d(a, b, NULL, c);
|
---|
| 4333 | }
|
---|
| 4334 |
|
---|
| 4335 | #endif /* WOLFSSL_KEY_GEN || HAVE_COMP_KEY || HAVE_ECC || DEBUG_WOLFSSL */
|
---|
| 4336 |
|
---|
| 4337 | #if defined(WOLFSSL_KEY_GEN) || !defined(NO_DH) || !defined(NO_DSA) || !defined(NO_RSA)
|
---|
| 4338 |
|
---|
| 4339 | const mp_digit ltm_prime_tab[PRIME_SIZE] = {
|
---|
| 4340 | 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
|
---|
| 4341 | 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
|
---|
| 4342 | 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
|
---|
| 4343 | 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
|
---|
| 4344 | #ifndef MP_8BIT
|
---|
| 4345 | 0x0083,
|
---|
| 4346 | 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
|
---|
| 4347 | 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
|
---|
| 4348 | 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
|
---|
| 4349 | 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
|
---|
| 4350 |
|
---|
| 4351 | 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
|
---|
| 4352 | 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
|
---|
| 4353 | 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
|
---|
| 4354 | 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
|
---|
| 4355 | 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
|
---|
| 4356 | 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
|
---|
| 4357 | 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
|
---|
| 4358 | 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
|
---|
| 4359 |
|
---|
| 4360 | 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
|
---|
| 4361 | 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
|
---|
| 4362 | 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
|
---|
| 4363 | 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
|
---|
| 4364 | 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
|
---|
| 4365 | 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
|
---|
| 4366 | 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
|
---|
| 4367 | 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
|
---|
| 4368 |
|
---|
| 4369 | 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
|
---|
| 4370 | 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
|
---|
| 4371 | 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
|
---|
| 4372 | 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
|
---|
| 4373 | 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
|
---|
| 4374 | 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
|
---|
| 4375 | 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
|
---|
| 4376 | 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
|
---|
| 4377 | #endif
|
---|
| 4378 | };
|
---|
| 4379 |
|
---|
| 4380 |
|
---|
| 4381 | /* Miller-Rabin test of "a" to the base of "b" as described in
|
---|
| 4382 | * HAC pp. 139 Algorithm 4.24
|
---|
| 4383 | *
|
---|
| 4384 | * Sets result to 0 if definitely composite or 1 if probably prime.
|
---|
| 4385 | * Randomly the chance of error is no more than 1/4 and often
|
---|
| 4386 | * very much lower.
|
---|
| 4387 | */
|
---|
| 4388 | static int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
|
---|
| 4389 | {
|
---|
| 4390 | mp_int n1, y, r;
|
---|
| 4391 | int s, j, err;
|
---|
| 4392 |
|
---|
| 4393 | /* default */
|
---|
| 4394 | *result = MP_NO;
|
---|
| 4395 |
|
---|
| 4396 | /* ensure b > 1 */
|
---|
| 4397 | if (mp_cmp_d(b, 1) != MP_GT) {
|
---|
| 4398 | return MP_VAL;
|
---|
| 4399 | }
|
---|
| 4400 |
|
---|
| 4401 | /* get n1 = a - 1 */
|
---|
| 4402 | if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
|
---|
| 4403 | return err;
|
---|
| 4404 | }
|
---|
| 4405 | if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
|
---|
| 4406 | goto LBL_N1;
|
---|
| 4407 | }
|
---|
| 4408 |
|
---|
| 4409 | /* set 2**s * r = n1 */
|
---|
| 4410 | if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
|
---|
| 4411 | goto LBL_N1;
|
---|
| 4412 | }
|
---|
| 4413 |
|
---|
| 4414 | /* count the number of least significant bits
|
---|
| 4415 | * which are zero
|
---|
| 4416 | */
|
---|
| 4417 | s = mp_cnt_lsb(&r);
|
---|
| 4418 |
|
---|
| 4419 | /* now divide n - 1 by 2**s */
|
---|
| 4420 | if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
|
---|
| 4421 | goto LBL_R;
|
---|
| 4422 | }
|
---|
| 4423 |
|
---|
| 4424 | /* compute y = b**r mod a */
|
---|
| 4425 | if ((err = mp_init (&y)) != MP_OKAY) {
|
---|
| 4426 | goto LBL_R;
|
---|
| 4427 | }
|
---|
| 4428 | if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
|
---|
| 4429 | goto LBL_Y;
|
---|
| 4430 | }
|
---|
| 4431 |
|
---|
| 4432 | /* if y != 1 and y != n1 do */
|
---|
| 4433 | if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
|
---|
| 4434 | j = 1;
|
---|
| 4435 | /* while j <= s-1 and y != n1 */
|
---|
| 4436 | while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
|
---|
| 4437 | if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
|
---|
| 4438 | goto LBL_Y;
|
---|
| 4439 | }
|
---|
| 4440 |
|
---|
| 4441 | /* if y == 1 then composite */
|
---|
| 4442 | if (mp_cmp_d (&y, 1) == MP_EQ) {
|
---|
| 4443 | goto LBL_Y;
|
---|
| 4444 | }
|
---|
| 4445 |
|
---|
| 4446 | ++j;
|
---|
| 4447 | }
|
---|
| 4448 |
|
---|
| 4449 | /* if y != n1 then composite */
|
---|
| 4450 | if (mp_cmp (&y, &n1) != MP_EQ) {
|
---|
| 4451 | goto LBL_Y;
|
---|
| 4452 | }
|
---|
| 4453 | }
|
---|
| 4454 |
|
---|
| 4455 | /* probably prime now */
|
---|
| 4456 | *result = MP_YES;
|
---|
| 4457 | LBL_Y:mp_clear (&y);
|
---|
| 4458 | LBL_R:mp_clear (&r);
|
---|
| 4459 | LBL_N1:mp_clear (&n1);
|
---|
| 4460 | return err;
|
---|
| 4461 | }
|
---|
| 4462 |
|
---|
| 4463 |
|
---|
| 4464 | /* determines if an integers is divisible by one
|
---|
| 4465 | * of the first PRIME_SIZE primes or not
|
---|
| 4466 | *
|
---|
| 4467 | * sets result to 0 if not, 1 if yes
|
---|
| 4468 | */
|
---|
| 4469 | static int mp_prime_is_divisible (mp_int * a, int *result)
|
---|
| 4470 | {
|
---|
| 4471 | int err, ix;
|
---|
| 4472 | mp_digit res;
|
---|
| 4473 |
|
---|
| 4474 | /* default to not */
|
---|
| 4475 | *result = MP_NO;
|
---|
| 4476 |
|
---|
| 4477 | for (ix = 0; ix < PRIME_SIZE; ix++) {
|
---|
| 4478 | /* what is a mod LBL_prime_tab[ix] */
|
---|
| 4479 | if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
|
---|
| 4480 | return err;
|
---|
| 4481 | }
|
---|
| 4482 |
|
---|
| 4483 | /* is the residue zero? */
|
---|
| 4484 | if (res == 0) {
|
---|
| 4485 | *result = MP_YES;
|
---|
| 4486 | return MP_OKAY;
|
---|
| 4487 | }
|
---|
| 4488 | }
|
---|
| 4489 |
|
---|
| 4490 | return MP_OKAY;
|
---|
| 4491 | }
|
---|
| 4492 |
|
---|
| 4493 | /*
|
---|
| 4494 | * Sets result to 1 if probably prime, 0 otherwise
|
---|
| 4495 | */
|
---|
| 4496 | int mp_prime_is_prime (mp_int * a, int t, int *result)
|
---|
| 4497 | {
|
---|
| 4498 | mp_int b;
|
---|
| 4499 | int ix, err, res;
|
---|
| 4500 |
|
---|
| 4501 | /* default to no */
|
---|
| 4502 | *result = MP_NO;
|
---|
| 4503 |
|
---|
| 4504 | /* valid value of t? */
|
---|
| 4505 | if (t <= 0 || t > PRIME_SIZE) {
|
---|
| 4506 | return MP_VAL;
|
---|
| 4507 | }
|
---|
| 4508 |
|
---|
| 4509 | /* is the input equal to one of the primes in the table? */
|
---|
| 4510 | for (ix = 0; ix < PRIME_SIZE; ix++) {
|
---|
| 4511 | if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
|
---|
| 4512 | *result = 1;
|
---|
| 4513 | return MP_OKAY;
|
---|
| 4514 | }
|
---|
| 4515 | }
|
---|
| 4516 |
|
---|
| 4517 | /* first perform trial division */
|
---|
| 4518 | if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
|
---|
| 4519 | return err;
|
---|
| 4520 | }
|
---|
| 4521 |
|
---|
| 4522 | /* return if it was trivially divisible */
|
---|
| 4523 | if (res == MP_YES) {
|
---|
| 4524 | return MP_OKAY;
|
---|
| 4525 | }
|
---|
| 4526 |
|
---|
| 4527 | /* now perform the miller-rabin rounds */
|
---|
| 4528 | if ((err = mp_init (&b)) != MP_OKAY) {
|
---|
| 4529 | return err;
|
---|
| 4530 | }
|
---|
| 4531 |
|
---|
| 4532 | for (ix = 0; ix < t; ix++) {
|
---|
| 4533 | /* set the prime */
|
---|
| 4534 | if ((err = mp_set (&b, ltm_prime_tab[ix])) != MP_OKAY) {
|
---|
| 4535 | goto LBL_B;
|
---|
| 4536 | }
|
---|
| 4537 |
|
---|
| 4538 | if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
|
---|
| 4539 | goto LBL_B;
|
---|
| 4540 | }
|
---|
| 4541 |
|
---|
| 4542 | if (res == MP_NO) {
|
---|
| 4543 | goto LBL_B;
|
---|
| 4544 | }
|
---|
| 4545 | }
|
---|
| 4546 |
|
---|
| 4547 | /* passed the test */
|
---|
| 4548 | *result = MP_YES;
|
---|
| 4549 | LBL_B:mp_clear (&b);
|
---|
| 4550 | return err;
|
---|
| 4551 | }
|
---|
| 4552 |
|
---|
| 4553 |
|
---|
| 4554 | /*
|
---|
| 4555 | * Sets result to 1 if probably prime, 0 otherwise
|
---|
| 4556 | */
|
---|
| 4557 | int mp_prime_is_prime_ex (mp_int * a, int t, int *result, WC_RNG *rng)
|
---|
| 4558 | {
|
---|
| 4559 | mp_int b, c;
|
---|
| 4560 | int ix, err, res;
|
---|
| 4561 | byte* base = NULL;
|
---|
| 4562 | word32 baseSz = 0;
|
---|
| 4563 |
|
---|
| 4564 | /* default to no */
|
---|
| 4565 | *result = MP_NO;
|
---|
| 4566 |
|
---|
| 4567 | /* valid value of t? */
|
---|
| 4568 | if (t <= 0 || t > PRIME_SIZE) {
|
---|
| 4569 | return MP_VAL;
|
---|
| 4570 | }
|
---|
| 4571 |
|
---|
| 4572 | /* is the input equal to one of the primes in the table? */
|
---|
| 4573 | for (ix = 0; ix < PRIME_SIZE; ix++) {
|
---|
| 4574 | if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
|
---|
| 4575 | *result = MP_YES;
|
---|
| 4576 | return MP_OKAY;
|
---|
| 4577 | }
|
---|
| 4578 | }
|
---|
| 4579 |
|
---|
| 4580 | /* first perform trial division */
|
---|
| 4581 | if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
|
---|
| 4582 | return err;
|
---|
| 4583 | }
|
---|
| 4584 |
|
---|
| 4585 | /* return if it was trivially divisible */
|
---|
| 4586 | if (res == MP_YES) {
|
---|
| 4587 | return MP_OKAY;
|
---|
| 4588 | }
|
---|
| 4589 |
|
---|
| 4590 | /* now perform the miller-rabin rounds */
|
---|
| 4591 | if ((err = mp_init (&b)) != MP_OKAY) {
|
---|
| 4592 | return err;
|
---|
| 4593 | }
|
---|
| 4594 | if ((err = mp_init (&c)) != MP_OKAY) {
|
---|
| 4595 | mp_clear(&b);
|
---|
| 4596 | return err;
|
---|
| 4597 | }
|
---|
| 4598 |
|
---|
| 4599 | baseSz = mp_count_bits(a);
|
---|
| 4600 | baseSz = (baseSz / 8) + ((baseSz % 8) ? 1 : 0);
|
---|
| 4601 |
|
---|
| 4602 | base = (byte*)XMALLOC(baseSz, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 4603 | if (base == NULL) {
|
---|
| 4604 | err = MP_MEM;
|
---|
| 4605 | goto LBL_B;
|
---|
| 4606 | }
|
---|
| 4607 |
|
---|
| 4608 | if ((err = mp_sub_d(a, 2, &c)) != MP_OKAY) {
|
---|
| 4609 | goto LBL_B;
|
---|
| 4610 | }
|
---|
| 4611 |
|
---|
| 4612 | /* now do a miller rabin with up to t random numbers, this should
|
---|
| 4613 | * give a (1/4)^t chance of a false prime. */
|
---|
| 4614 | for (ix = 0; ix < t; ix++) {
|
---|
| 4615 | /* Set a test candidate. */
|
---|
| 4616 | if ((err = wc_RNG_GenerateBlock(rng, base, baseSz)) != 0) {
|
---|
| 4617 | goto LBL_B;
|
---|
| 4618 | }
|
---|
| 4619 |
|
---|
| 4620 | if ((err = mp_read_unsigned_bin(&b, base, baseSz)) != MP_OKAY) {
|
---|
| 4621 | goto LBL_B;
|
---|
| 4622 | }
|
---|
| 4623 |
|
---|
| 4624 | if (mp_cmp_d(&b, 2) != MP_GT || mp_cmp(&b, &c) != MP_LT)
|
---|
| 4625 | continue;
|
---|
| 4626 |
|
---|
| 4627 | if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
|
---|
| 4628 | goto LBL_B;
|
---|
| 4629 | }
|
---|
| 4630 |
|
---|
| 4631 | if (res == MP_NO) {
|
---|
| 4632 | goto LBL_B;
|
---|
| 4633 | }
|
---|
| 4634 | }
|
---|
| 4635 |
|
---|
| 4636 | /* passed the test */
|
---|
| 4637 | *result = MP_YES;
|
---|
| 4638 | LBL_B:mp_clear (&b);
|
---|
| 4639 | mp_clear (&c);
|
---|
| 4640 | XFREE(base, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 4641 | return err;
|
---|
| 4642 | }
|
---|
| 4643 |
|
---|
| 4644 | #endif /* WOLFSSL_KEY_GEN NO_DH NO_DSA NO_RSA */
|
---|
| 4645 |
|
---|
| 4646 | #ifdef WOLFSSL_KEY_GEN
|
---|
| 4647 |
|
---|
| 4648 | static const int USE_BBS = 1;
|
---|
| 4649 |
|
---|
| 4650 | int mp_rand_prime(mp_int* N, int len, WC_RNG* rng, void* heap)
|
---|
| 4651 | {
|
---|
| 4652 | int err, res, type;
|
---|
| 4653 | byte* buf;
|
---|
| 4654 |
|
---|
| 4655 | if (N == NULL || rng == NULL)
|
---|
| 4656 | return MP_VAL;
|
---|
| 4657 |
|
---|
| 4658 | /* get type */
|
---|
| 4659 | if (len < 0) {
|
---|
| 4660 | type = USE_BBS;
|
---|
| 4661 | len = -len;
|
---|
| 4662 | } else {
|
---|
| 4663 | type = 0;
|
---|
| 4664 | }
|
---|
| 4665 |
|
---|
| 4666 | /* allow sizes between 2 and 512 bytes for a prime size */
|
---|
| 4667 | if (len < 2 || len > 512) {
|
---|
| 4668 | return MP_VAL;
|
---|
| 4669 | }
|
---|
| 4670 |
|
---|
| 4671 | /* allocate buffer to work with */
|
---|
| 4672 | buf = (byte*)XMALLOC(len, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4673 | if (buf == NULL) {
|
---|
| 4674 | return MP_MEM;
|
---|
| 4675 | }
|
---|
| 4676 | XMEMSET(buf, 0, len);
|
---|
| 4677 |
|
---|
| 4678 | do {
|
---|
| 4679 | #ifdef SHOW_GEN
|
---|
| 4680 | printf(".");
|
---|
| 4681 | fflush(stdout);
|
---|
| 4682 | #endif
|
---|
| 4683 | /* generate value */
|
---|
| 4684 | err = wc_RNG_GenerateBlock(rng, buf, len);
|
---|
| 4685 | if (err != 0) {
|
---|
| 4686 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4687 | return err;
|
---|
| 4688 | }
|
---|
| 4689 |
|
---|
| 4690 | /* munge bits */
|
---|
| 4691 | buf[0] |= 0x80 | 0x40;
|
---|
| 4692 | buf[len-1] |= 0x01 | ((type & USE_BBS) ? 0x02 : 0x00);
|
---|
| 4693 |
|
---|
| 4694 | /* load value */
|
---|
| 4695 | if ((err = mp_read_unsigned_bin(N, buf, len)) != MP_OKAY) {
|
---|
| 4696 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4697 | return err;
|
---|
| 4698 | }
|
---|
| 4699 |
|
---|
| 4700 | /* test */
|
---|
| 4701 | /* Running Miller-Rabin up to 3 times gives us a 2^{-80} chance
|
---|
| 4702 | * of a 1024-bit candidate being a false positive, when it is our
|
---|
| 4703 | * prime candidate. (Note 4.49 of Handbook of Applied Cryptography.)
|
---|
| 4704 | * Using 8 because we've always used 8. */
|
---|
| 4705 | if ((err = mp_prime_is_prime_ex(N, 8, &res, rng)) != MP_OKAY) {
|
---|
| 4706 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4707 | return err;
|
---|
| 4708 | }
|
---|
| 4709 | } while (res == MP_NO);
|
---|
| 4710 |
|
---|
| 4711 | XMEMSET(buf, 0, len);
|
---|
| 4712 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4713 |
|
---|
| 4714 | return MP_OKAY;
|
---|
| 4715 | }
|
---|
| 4716 |
|
---|
| 4717 |
|
---|
| 4718 | /* computes least common multiple as |a*b|/(a, b) */
|
---|
| 4719 | int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 4720 | {
|
---|
| 4721 | int res;
|
---|
| 4722 | mp_int t1, t2;
|
---|
| 4723 |
|
---|
| 4724 |
|
---|
| 4725 | if ((res = mp_init_multi (&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
|
---|
| 4726 | return res;
|
---|
| 4727 | }
|
---|
| 4728 |
|
---|
| 4729 | /* t1 = get the GCD of the two inputs */
|
---|
| 4730 | if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
|
---|
| 4731 | goto LBL_T;
|
---|
| 4732 | }
|
---|
| 4733 |
|
---|
| 4734 | /* divide the smallest by the GCD */
|
---|
| 4735 | if (mp_cmp_mag(a, b) == MP_LT) {
|
---|
| 4736 | /* store quotient in t2 such that t2 * b is the LCM */
|
---|
| 4737 | if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
|
---|
| 4738 | goto LBL_T;
|
---|
| 4739 | }
|
---|
| 4740 | res = mp_mul(b, &t2, c);
|
---|
| 4741 | } else {
|
---|
| 4742 | /* store quotient in t2 such that t2 * a is the LCM */
|
---|
| 4743 | if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
|
---|
| 4744 | goto LBL_T;
|
---|
| 4745 | }
|
---|
| 4746 | res = mp_mul(a, &t2, c);
|
---|
| 4747 | }
|
---|
| 4748 |
|
---|
| 4749 | /* fix the sign to positive */
|
---|
| 4750 | c->sign = MP_ZPOS;
|
---|
| 4751 |
|
---|
| 4752 | LBL_T:
|
---|
| 4753 | mp_clear(&t1);
|
---|
| 4754 | mp_clear(&t2);
|
---|
| 4755 | return res;
|
---|
| 4756 | }
|
---|
| 4757 |
|
---|
| 4758 |
|
---|
| 4759 |
|
---|
| 4760 | /* Greatest Common Divisor using the binary method */
|
---|
| 4761 | int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 4762 | {
|
---|
| 4763 | mp_int u, v;
|
---|
| 4764 | int k, u_lsb, v_lsb, res;
|
---|
| 4765 |
|
---|
| 4766 | /* either zero than gcd is the largest */
|
---|
| 4767 | if (mp_iszero (a) == MP_YES) {
|
---|
| 4768 | return mp_abs (b, c);
|
---|
| 4769 | }
|
---|
| 4770 | if (mp_iszero (b) == MP_YES) {
|
---|
| 4771 | return mp_abs (a, c);
|
---|
| 4772 | }
|
---|
| 4773 |
|
---|
| 4774 | /* get copies of a and b we can modify */
|
---|
| 4775 | if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
|
---|
| 4776 | return res;
|
---|
| 4777 | }
|
---|
| 4778 |
|
---|
| 4779 | if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
|
---|
| 4780 | goto LBL_U;
|
---|
| 4781 | }
|
---|
| 4782 |
|
---|
| 4783 | /* must be positive for the remainder of the algorithm */
|
---|
| 4784 | u.sign = v.sign = MP_ZPOS;
|
---|
| 4785 |
|
---|
| 4786 | /* B1. Find the common power of two for u and v */
|
---|
| 4787 | u_lsb = mp_cnt_lsb(&u);
|
---|
| 4788 | v_lsb = mp_cnt_lsb(&v);
|
---|
| 4789 | k = MIN(u_lsb, v_lsb);
|
---|
| 4790 |
|
---|
| 4791 | if (k > 0) {
|
---|
| 4792 | /* divide the power of two out */
|
---|
| 4793 | if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
|
---|
| 4794 | goto LBL_V;
|
---|
| 4795 | }
|
---|
| 4796 |
|
---|
| 4797 | if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
|
---|
| 4798 | goto LBL_V;
|
---|
| 4799 | }
|
---|
| 4800 | }
|
---|
| 4801 |
|
---|
| 4802 | /* divide any remaining factors of two out */
|
---|
| 4803 | if (u_lsb != k) {
|
---|
| 4804 | if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
|
---|
| 4805 | goto LBL_V;
|
---|
| 4806 | }
|
---|
| 4807 | }
|
---|
| 4808 |
|
---|
| 4809 | if (v_lsb != k) {
|
---|
| 4810 | if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
|
---|
| 4811 | goto LBL_V;
|
---|
| 4812 | }
|
---|
| 4813 | }
|
---|
| 4814 |
|
---|
| 4815 | while (mp_iszero(&v) == MP_NO) {
|
---|
| 4816 | /* make sure v is the largest */
|
---|
| 4817 | if (mp_cmp_mag(&u, &v) == MP_GT) {
|
---|
| 4818 | /* swap u and v to make sure v is >= u */
|
---|
| 4819 | mp_exch(&u, &v);
|
---|
| 4820 | }
|
---|
| 4821 |
|
---|
| 4822 | /* subtract smallest from largest */
|
---|
| 4823 | if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
|
---|
| 4824 | goto LBL_V;
|
---|
| 4825 | }
|
---|
| 4826 |
|
---|
| 4827 | /* Divide out all factors of two */
|
---|
| 4828 | if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
|
---|
| 4829 | goto LBL_V;
|
---|
| 4830 | }
|
---|
| 4831 | }
|
---|
| 4832 |
|
---|
| 4833 | /* multiply by 2**k which we divided out at the beginning */
|
---|
| 4834 | if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
|
---|
| 4835 | goto LBL_V;
|
---|
| 4836 | }
|
---|
| 4837 | c->sign = MP_ZPOS;
|
---|
| 4838 | res = MP_OKAY;
|
---|
| 4839 | LBL_V:mp_clear (&u);
|
---|
| 4840 | LBL_U:mp_clear (&v);
|
---|
| 4841 | return res;
|
---|
| 4842 | }
|
---|
| 4843 |
|
---|
| 4844 | #endif /* WOLFSSL_KEY_GEN */
|
---|
| 4845 |
|
---|
| 4846 |
|
---|
| 4847 | #if !defined(NO_DSA) || defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN) || \
|
---|
| 4848 | defined(HAVE_COMP_KEY) || defined(WOLFSSL_DEBUG_MATH) || \
|
---|
| 4849 | defined(DEBUG_WOLFSSL) || defined(OPENSSL_EXTRA)
|
---|
| 4850 |
|
---|
| 4851 | /* chars used in radix conversions */
|
---|
| 4852 | const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ\
|
---|
| 4853 | abcdefghijklmnopqrstuvwxyz+/";
|
---|
| 4854 | #endif
|
---|
| 4855 |
|
---|
| 4856 | #if !defined(NO_DSA) || defined(HAVE_ECC)
|
---|
| 4857 | /* read a string [ASCII] in a given radix */
|
---|
| 4858 | int mp_read_radix (mp_int * a, const char *str, int radix)
|
---|
| 4859 | {
|
---|
| 4860 | int y, res, neg;
|
---|
| 4861 | char ch;
|
---|
| 4862 |
|
---|
| 4863 | /* zero the digit bignum */
|
---|
| 4864 | mp_zero(a);
|
---|
| 4865 |
|
---|
| 4866 | /* make sure the radix is ok */
|
---|
| 4867 | if (radix < MP_RADIX_BIN || radix > MP_RADIX_MAX) {
|
---|
| 4868 | return MP_VAL;
|
---|
| 4869 | }
|
---|
| 4870 |
|
---|
| 4871 | /* if the leading digit is a
|
---|
| 4872 | * minus set the sign to negative.
|
---|
| 4873 | */
|
---|
| 4874 | if (*str == '-') {
|
---|
| 4875 | ++str;
|
---|
| 4876 | neg = MP_NEG;
|
---|
| 4877 | } else {
|
---|
| 4878 | neg = MP_ZPOS;
|
---|
| 4879 | }
|
---|
| 4880 |
|
---|
| 4881 | /* set the integer to the default of zero */
|
---|
| 4882 | mp_zero (a);
|
---|
| 4883 |
|
---|
| 4884 | /* process each digit of the string */
|
---|
| 4885 | while (*str != '\0') {
|
---|
| 4886 | /* if the radix <= 36 the conversion is case insensitive
|
---|
| 4887 | * this allows numbers like 1AB and 1ab to represent the same value
|
---|
| 4888 | * [e.g. in hex]
|
---|
| 4889 | */
|
---|
| 4890 | ch = (radix <= 36) ? (char)XTOUPPER((unsigned char)*str) : *str;
|
---|
| 4891 | for (y = 0; y < 64; y++) {
|
---|
| 4892 | if (ch == mp_s_rmap[y]) {
|
---|
| 4893 | break;
|
---|
| 4894 | }
|
---|
| 4895 | }
|
---|
| 4896 |
|
---|
| 4897 | /* if the char was found in the map
|
---|
| 4898 | * and is less than the given radix add it
|
---|
| 4899 | * to the number, otherwise exit the loop.
|
---|
| 4900 | */
|
---|
| 4901 | if (y < radix) {
|
---|
| 4902 | if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
|
---|
| 4903 | return res;
|
---|
| 4904 | }
|
---|
| 4905 | if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
|
---|
| 4906 | return res;
|
---|
| 4907 | }
|
---|
| 4908 | } else {
|
---|
| 4909 | break;
|
---|
| 4910 | }
|
---|
| 4911 | ++str;
|
---|
| 4912 | }
|
---|
| 4913 |
|
---|
| 4914 | /* if digit in isn't null term, then invalid character was found */
|
---|
| 4915 | if (*str != '\0') {
|
---|
| 4916 | mp_zero (a);
|
---|
| 4917 | return MP_VAL;
|
---|
| 4918 | }
|
---|
| 4919 |
|
---|
| 4920 | /* set the sign only if a != 0 */
|
---|
| 4921 | if (mp_iszero(a) != MP_YES) {
|
---|
| 4922 | a->sign = neg;
|
---|
| 4923 | }
|
---|
| 4924 | return MP_OKAY;
|
---|
| 4925 | }
|
---|
| 4926 | #endif /* !defined(NO_DSA) || defined(HAVE_ECC) */
|
---|
| 4927 |
|
---|
| 4928 | #ifdef WC_MP_TO_RADIX
|
---|
| 4929 |
|
---|
| 4930 | /* returns size of ASCII representation */
|
---|
| 4931 | int mp_radix_size (mp_int *a, int radix, int *size)
|
---|
| 4932 | {
|
---|
| 4933 | int res, digs;
|
---|
| 4934 | mp_int t;
|
---|
| 4935 | mp_digit d;
|
---|
| 4936 |
|
---|
| 4937 | *size = 0;
|
---|
| 4938 |
|
---|
| 4939 | /* special case for binary */
|
---|
| 4940 | if (radix == MP_RADIX_BIN) {
|
---|
| 4941 | *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
|
---|
| 4942 | return MP_OKAY;
|
---|
| 4943 | }
|
---|
| 4944 |
|
---|
| 4945 | /* make sure the radix is in range */
|
---|
| 4946 | if (radix < MP_RADIX_BIN || radix > MP_RADIX_MAX) {
|
---|
| 4947 | return MP_VAL;
|
---|
| 4948 | }
|
---|
| 4949 |
|
---|
| 4950 | if (mp_iszero(a) == MP_YES) {
|
---|
| 4951 | *size = 2;
|
---|
| 4952 | return MP_OKAY;
|
---|
| 4953 | }
|
---|
| 4954 |
|
---|
| 4955 | /* digs is the digit count */
|
---|
| 4956 | digs = 0;
|
---|
| 4957 |
|
---|
| 4958 | /* if it's negative add one for the sign */
|
---|
| 4959 | if (a->sign == MP_NEG) {
|
---|
| 4960 | ++digs;
|
---|
| 4961 | }
|
---|
| 4962 |
|
---|
| 4963 | /* init a copy of the input */
|
---|
| 4964 | if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
|
---|
| 4965 | return res;
|
---|
| 4966 | }
|
---|
| 4967 |
|
---|
| 4968 | /* force temp to positive */
|
---|
| 4969 | t.sign = MP_ZPOS;
|
---|
| 4970 |
|
---|
| 4971 | /* fetch out all of the digits */
|
---|
| 4972 | while (mp_iszero (&t) == MP_NO) {
|
---|
| 4973 | if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
|
---|
| 4974 | mp_clear (&t);
|
---|
| 4975 | return res;
|
---|
| 4976 | }
|
---|
| 4977 | ++digs;
|
---|
| 4978 | }
|
---|
| 4979 | mp_clear (&t);
|
---|
| 4980 |
|
---|
| 4981 | /* return digs + 1, the 1 is for the NULL byte that would be required. */
|
---|
| 4982 | *size = digs + 1;
|
---|
| 4983 | return MP_OKAY;
|
---|
| 4984 | }
|
---|
| 4985 |
|
---|
| 4986 | /* stores a bignum as a ASCII string in a given radix (2..64) */
|
---|
| 4987 | int mp_toradix (mp_int *a, char *str, int radix)
|
---|
| 4988 | {
|
---|
| 4989 | int res, digs;
|
---|
| 4990 | mp_int t;
|
---|
| 4991 | mp_digit d;
|
---|
| 4992 | char *_s = str;
|
---|
| 4993 |
|
---|
| 4994 | /* check range of the radix */
|
---|
| 4995 | if (radix < MP_RADIX_BIN || radix > MP_RADIX_MAX) {
|
---|
| 4996 | return MP_VAL;
|
---|
| 4997 | }
|
---|
| 4998 |
|
---|
| 4999 | /* quick out if its zero */
|
---|
| 5000 | if (mp_iszero(a) == MP_YES) {
|
---|
| 5001 | *str++ = '0';
|
---|
| 5002 | *str = '\0';
|
---|
| 5003 | return MP_OKAY;
|
---|
| 5004 | }
|
---|
| 5005 |
|
---|
| 5006 | if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
|
---|
| 5007 | return res;
|
---|
| 5008 | }
|
---|
| 5009 |
|
---|
| 5010 | /* if it is negative output a - */
|
---|
| 5011 | if (t.sign == MP_NEG) {
|
---|
| 5012 | ++_s;
|
---|
| 5013 | *str++ = '-';
|
---|
| 5014 | t.sign = MP_ZPOS;
|
---|
| 5015 | }
|
---|
| 5016 |
|
---|
| 5017 | digs = 0;
|
---|
| 5018 | while (mp_iszero (&t) == MP_NO) {
|
---|
| 5019 | if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
|
---|
| 5020 | mp_clear (&t);
|
---|
| 5021 | return res;
|
---|
| 5022 | }
|
---|
| 5023 | *str++ = mp_s_rmap[d];
|
---|
| 5024 | ++digs;
|
---|
| 5025 | }
|
---|
| 5026 |
|
---|
| 5027 | /* reverse the digits of the string. In this case _s points
|
---|
| 5028 | * to the first digit [excluding the sign] of the number]
|
---|
| 5029 | */
|
---|
| 5030 | bn_reverse ((unsigned char *)_s, digs);
|
---|
| 5031 |
|
---|
| 5032 | /* append a NULL so the string is properly terminated */
|
---|
| 5033 | *str = '\0';
|
---|
| 5034 |
|
---|
| 5035 | mp_clear (&t);
|
---|
| 5036 | return MP_OKAY;
|
---|
| 5037 | }
|
---|
| 5038 |
|
---|
| 5039 | #ifdef WOLFSSL_DEBUG_MATH
|
---|
| 5040 | void mp_dump(const char* desc, mp_int* a, byte verbose)
|
---|
| 5041 | {
|
---|
| 5042 | char *buffer;
|
---|
| 5043 | int size = a->alloc;
|
---|
| 5044 |
|
---|
| 5045 | buffer = (char*)XMALLOC(size * sizeof(mp_digit) * 2, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 5046 | if (buffer == NULL) {
|
---|
| 5047 | return;
|
---|
| 5048 | }
|
---|
| 5049 |
|
---|
| 5050 | printf("%s: ptr=%p, used=%d, sign=%d, size=%d, mpd=%d\n",
|
---|
| 5051 | desc, a, a->used, a->sign, size, (int)sizeof(mp_digit));
|
---|
| 5052 |
|
---|
| 5053 | mp_tohex(a, buffer);
|
---|
| 5054 | printf(" %s\n ", buffer);
|
---|
| 5055 |
|
---|
| 5056 | if (verbose) {
|
---|
| 5057 | int i;
|
---|
| 5058 | for(i=0; i<a->alloc * (int)sizeof(mp_digit); i++) {
|
---|
| 5059 | printf("%02x ", *(((byte*)a->dp) + i));
|
---|
| 5060 | }
|
---|
| 5061 | printf("\n");
|
---|
| 5062 | }
|
---|
| 5063 |
|
---|
| 5064 | XFREE(buffer, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 5065 | }
|
---|
| 5066 | #endif /* WOLFSSL_DEBUG_MATH */
|
---|
| 5067 |
|
---|
| 5068 | #endif /* WC_MP_TO_RADIX */
|
---|
| 5069 |
|
---|
| 5070 | #endif /* WOLFSSL_SP_MATH */
|
---|
| 5071 |
|
---|
| 5072 | #endif /* USE_FAST_MATH */
|
---|
| 5073 |
|
---|
| 5074 | #endif /* NO_BIG_INT */
|
---|
| 5075 |
|
---|