| 1 | /* integer.h
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| 2 | *
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| 3 | * Copyright (C) 2006-2020 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 | * Based on public domain LibTomMath 0.38 by Tom St Denis, tomstdenis@iahu.ca,
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| 25 | * http://math.libtomcrypt.com
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| 26 | */
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| 27 |
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| 28 |
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| 29 | #ifndef WOLF_CRYPT_INTEGER_H
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| 30 | #define WOLF_CRYPT_INTEGER_H
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| 31 |
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| 32 | /* may optionally use fast math instead, not yet supported on all platforms and
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| 33 | may not be faster on all
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| 34 | */
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| 35 | #include <wolfssl/wolfcrypt/types.h> /* will set MP_xxBIT if not default */
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| 36 | #ifdef WOLFSSL_SP_MATH
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| 37 | #include <wolfssl/wolfcrypt/sp_int.h>
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| 38 | #elif defined(USE_FAST_MATH)
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| 39 | #include <wolfssl/wolfcrypt/tfm.h>
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| 40 | #else
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| 41 |
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| 42 | #include <wolfssl/wolfcrypt/random.h>
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| 43 |
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| 44 | #ifndef CHAR_BIT
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| 45 | #include <limits.h>
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| 46 | #endif
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| 47 |
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| 48 | #include <wolfssl/wolfcrypt/mpi_class.h>
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| 49 |
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| 50 |
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| 51 | #ifdef __cplusplus
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| 52 | extern "C" {
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| 53 |
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| 54 | /* C++ compilers don't like assigning void * to mp_digit * */
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| 55 | #define OPT_CAST(x) (x *)
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| 56 |
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| 57 | #elif defined(_SH3)
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| 58 |
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| 59 | /* SuperH SH3 compiler doesn't like assigning voi* to mp_digit* */
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| 60 | #define OPT_CAST(x) (x *)
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| 61 |
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| 62 | #else
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| 63 |
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| 64 | /* C on the other hand doesn't care */
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| 65 | #define OPT_CAST(x)
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| 66 |
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| 67 | #endif /* __cplusplus */
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| 68 |
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| 69 |
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| 70 | /* detect 64-bit mode if possible */
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| 71 | #if defined(__x86_64__) && !(defined (_MSC_VER) && defined(__clang__))
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| 72 | #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
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| 73 | #define MP_64BIT
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| 74 | #endif
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| 75 | #endif
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| 76 | /* if intel compiler doesn't provide 128 bit type don't turn on 64bit */
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| 77 | #if defined(MP_64BIT) && defined(__INTEL_COMPILER) && !defined(HAVE___UINT128_T)
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| 78 | #undef MP_64BIT
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| 79 | #endif
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| 80 |
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| 81 |
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| 82 | /* allow user to define on mp_digit, mp_word, DIGIT_BIT types */
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| 83 | #ifndef WOLFSSL_BIGINT_TYPES
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| 84 |
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| 85 | /* some default configurations.
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| 86 | *
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| 87 | * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
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| 88 | * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
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| 89 | *
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| 90 | * At the very least a mp_digit must be able to hold 7 bits
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| 91 | * [any size beyond that is ok provided it doesn't overflow the data type]
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| 92 | */
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| 93 | #ifdef MP_8BIT
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| 94 | /* 8-bit */
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| 95 | typedef unsigned char mp_digit;
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| 96 | typedef unsigned short mp_word;
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| 97 | /* don't define DIGIT_BIT, so its calculated below */
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| 98 | #elif defined(MP_16BIT)
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| 99 | /* 16-bit */
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| 100 | typedef unsigned int mp_digit;
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| 101 | typedef unsigned long mp_word;
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| 102 | /* don't define DIGIT_BIT, so its calculated below */
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| 103 | #elif defined(NO_64BIT)
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| 104 | /* 32-bit forced to 16-bit */
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| 105 | typedef unsigned short mp_digit;
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| 106 | typedef unsigned int mp_word;
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| 107 | #define DIGIT_BIT 12
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| 108 | #elif defined(MP_64BIT)
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| 109 | /* 64-bit */
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| 110 | /* for GCC only on supported platforms */
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| 111 | typedef unsigned long long mp_digit; /* 64 bit type, 128 uses mode(TI) */
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| 112 | typedef unsigned long mp_word __attribute__ ((mode(TI)));
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| 113 | #define DIGIT_BIT 60
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| 114 | #else
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| 115 | /* 32-bit default case */
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| 116 |
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| 117 | #if defined(_MSC_VER) || defined(__BORLANDC__)
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| 118 | typedef unsigned __int64 ulong64;
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| 119 | #else
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| 120 | typedef unsigned long long ulong64;
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| 121 | #endif
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| 122 |
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| 123 | typedef unsigned int mp_digit; /* long could be 64 now, changed TAO */
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| 124 | typedef ulong64 mp_word;
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| 125 |
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| 126 | #ifdef MP_31BIT
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| 127 | /* this is an extension that uses 31-bit digits */
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| 128 | #define DIGIT_BIT 31
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| 129 | #else
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| 130 | /* default case is 28-bit digits, defines MP_28BIT as a handy test macro */
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| 131 | #define DIGIT_BIT 28
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| 132 | #define MP_28BIT
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| 133 | #endif
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| 134 | #endif
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| 135 |
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| 136 | #endif /* WOLFSSL_BIGINT_TYPES */
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| 137 |
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| 138 | /* otherwise the bits per digit is calculated automatically from the size of
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| 139 | a mp_digit */
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| 140 | #ifndef DIGIT_BIT
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| 141 | #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))
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| 142 | /* bits per digit */
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| 143 | #endif
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| 144 |
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| 145 | #define MP_DIGIT_BIT DIGIT_BIT
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| 146 | #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
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| 147 | #define MP_DIGIT_MAX MP_MASK
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| 148 |
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| 149 | /* equalities */
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| 150 | #define MP_LT -1 /* less than */
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| 151 | #define MP_EQ 0 /* equal to */
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| 152 | #define MP_GT 1 /* greater than */
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| 153 |
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| 154 | #define MP_ZPOS 0 /* positive integer */
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| 155 | #define MP_NEG 1 /* negative */
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| 156 |
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| 157 | #define MP_OKAY 0 /* ok result */
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| 158 | #define MP_MEM -2 /* out of mem */
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| 159 | #define MP_VAL -3 /* invalid input */
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| 160 | #define MP_NOT_INF -4 /* point not at infinity */
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| 161 | #define MP_RANGE MP_NOT_INF
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| 162 |
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| 163 | #define MP_YES 1 /* yes response */
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| 164 | #define MP_NO 0 /* no response */
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| 165 |
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| 166 | /* Primality generation flags */
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| 167 | #define LTM_PRIME_BBS 0x0001 /* BBS style prime */
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| 168 | #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
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| 169 | #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
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| 170 |
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| 171 | typedef int mp_err;
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| 172 |
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| 173 | /* define this to use lower memory usage routines (exptmods mostly) */
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| 174 | #define MP_LOW_MEM
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| 175 |
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| 176 | /* default precision */
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| 177 | #ifndef MP_PREC
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| 178 | #ifndef MP_LOW_MEM
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| 179 | #define MP_PREC 32 /* default digits of precision */
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| 180 | #else
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| 181 | #define MP_PREC 1 /* default digits of precision */
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| 182 | #endif
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| 183 | #endif
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| 184 |
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| 185 | /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD -
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| 186 | BITS_PER_DIGIT*2) */
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| 187 | #define MP_WARRAY ((mp_word)1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
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| 188 |
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| 189 | #ifdef HAVE_WOLF_BIGINT
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| 190 | /* raw big integer */
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| 191 | typedef struct WC_BIGINT {
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| 192 | byte* buf;
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| 193 | word32 len;
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| 194 | void* heap;
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| 195 | } WC_BIGINT;
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| 196 | #define WOLF_BIGINT_DEFINED
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| 197 | #endif
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| 198 |
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| 199 | /* the mp_int structure */
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| 200 | typedef struct mp_int {
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| 201 | int used, alloc, sign;
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| 202 | mp_digit *dp;
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| 203 |
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| 204 | #ifdef HAVE_WOLF_BIGINT
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| 205 | struct WC_BIGINT raw; /* unsigned binary (big endian) */
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| 206 | #endif
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| 207 | } mp_int;
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| 208 |
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| 209 | /* wolf big int and common functions */
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| 210 | #include <wolfssl/wolfcrypt/wolfmath.h>
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| 211 |
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| 212 |
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| 213 | /* callback for mp_prime_random, should fill dst with random bytes and return
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| 214 | how many read [up to len] */
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| 215 | typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
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| 216 |
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| 217 |
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| 218 | #define USED(m) ((m)->used)
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| 219 | #define DIGIT(m,k) ((m)->dp[(k)])
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| 220 | #define SIGN(m) ((m)->sign)
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| 221 |
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| 222 |
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| 223 | /* ---> Basic Manipulations <--- */
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| 224 | #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
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| 225 | #define mp_isone(a) \
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| 226 | (((((a)->used == 1)) && ((a)->dp[0] == 1u)) ? MP_YES : MP_NO)
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| 227 | #define mp_iseven(a) \
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| 228 | (((a)->used > 0 && (((a)->dp[0] & 1u) == 0u)) ? MP_YES : MP_NO)
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| 229 | #define mp_isodd(a) \
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| 230 | (((a)->used > 0 && (((a)->dp[0] & 1u) == 1u)) ? MP_YES : MP_NO)
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| 231 | #define mp_isneg(a) (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO)
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| 232 | #define mp_isword(a, w) \
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| 233 | ((((a)->used == 1) && ((a)->dp[0] == w)) || ((w == 0) && ((a)->used == 0)) \
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| 234 | ? MP_YES : MP_NO)
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| 235 |
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| 236 | /* number of primes */
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| 237 | #ifdef MP_8BIT
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| 238 | #define PRIME_SIZE 31
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| 239 | #else
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| 240 | #define PRIME_SIZE 256
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| 241 | #endif
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| 242 |
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| 243 | #ifndef MAX_INVMOD_SZ
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| 244 | #if defined(WOLFSSL_MYSQL_COMPATIBLE)
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| 245 | #define MAX_INVMOD_SZ 8192
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| 246 | #else
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| 247 | #define MAX_INVMOD_SZ 4096
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| 248 | #endif
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| 249 | #endif
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| 250 |
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| 251 | #define mp_prime_random(a, t, size, bbs, cb, dat) \
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| 252 | mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)
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| 253 |
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| 254 | #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
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| 255 | #define mp_raw_size(mp) mp_signed_bin_size(mp)
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| 256 | #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
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| 257 | #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
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| 258 | #define mp_mag_size(mp) mp_unsigned_bin_size(mp)
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| 259 | #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
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| 260 |
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| 261 | #define MP_RADIX_BIN 2
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| 262 | #define MP_RADIX_OCT 8
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| 263 | #define MP_RADIX_DEC 10
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| 264 | #define MP_RADIX_HEX 16
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| 265 | #define MP_RADIX_MAX 64
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| 266 |
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| 267 | #define mp_tobinary(M, S) mp_toradix((M), (S), MP_RADIX_BIN)
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| 268 | #define mp_tooctal(M, S) mp_toradix((M), (S), MP_RADIX_OCT)
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| 269 | #define mp_todecimal(M, S) mp_toradix((M), (S), MP_RADIX_DEC)
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| 270 | #define mp_tohex(M, S) mp_toradix((M), (S), MP_RADIX_HEX)
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| 271 |
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| 272 | #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
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| 273 |
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| 274 | #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN) || defined(HAVE_COMP_KEY) || \
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| 275 | defined(WOLFSSL_DEBUG_MATH) || defined(DEBUG_WOLFSSL)
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| 276 | extern const char *mp_s_rmap;
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| 277 | #endif
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| 278 |
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| 279 | /* 6 functions needed by Rsa */
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| 280 | MP_API int mp_init (mp_int * a);
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| 281 | MP_API void mp_clear (mp_int * a);
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| 282 | MP_API void mp_free (mp_int * a);
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| 283 | MP_API void mp_forcezero(mp_int * a);
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| 284 | MP_API int mp_unsigned_bin_size(mp_int * a);
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| 285 | MP_API int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c);
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| 286 | MP_API int mp_to_unsigned_bin_at_pos(int x, mp_int *t, unsigned char *b);
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| 287 | MP_API int mp_to_unsigned_bin (mp_int * a, unsigned char *b);
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| 288 | MP_API int mp_to_unsigned_bin_len(mp_int * a, unsigned char *b, int c);
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| 289 | MP_API int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
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| 290 | MP_API int mp_exptmod_ex (mp_int * G, mp_int * X, int digits, mp_int * P,
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| 291 | mp_int * Y);
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| 292 | /* end functions needed by Rsa */
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| 293 |
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| 294 | /* functions added to support above needed, removed TOOM and KARATSUBA */
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| 295 | MP_API int mp_count_bits (mp_int * a);
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| 296 | MP_API int mp_leading_bit (mp_int * a);
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| 297 | MP_API int mp_init_copy (mp_int * a, mp_int * b);
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| 298 | MP_API int mp_copy (mp_int * a, mp_int * b);
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| 299 | MP_API int mp_grow (mp_int * a, int size);
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| 300 | MP_API int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
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| 301 | MP_API void mp_zero (mp_int * a);
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| 302 | MP_API void mp_clamp (mp_int * a);
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| 303 | MP_API void mp_exch (mp_int * a, mp_int * b);
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| 304 | MP_API void mp_rshd (mp_int * a, int b);
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| 305 | MP_API void mp_rshb (mp_int * a, int b);
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| 306 | MP_API int mp_mod_2d (mp_int * a, int b, mp_int * c);
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| 307 | MP_API int mp_mul_2d (mp_int * a, int b, mp_int * c);
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| 308 | MP_API int mp_lshd (mp_int * a, int b);
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| 309 | MP_API int mp_abs (mp_int * a, mp_int * b);
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| 310 | MP_API int mp_invmod (mp_int * a, mp_int * b, mp_int * c);
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| 311 | int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c);
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| 312 | MP_API int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
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| 313 | MP_API int mp_cmp_mag (mp_int * a, mp_int * b);
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| 314 | MP_API int mp_cmp (mp_int * a, mp_int * b);
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| 315 | MP_API int mp_cmp_d(mp_int * a, mp_digit b);
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| 316 | MP_API int mp_set (mp_int * a, mp_digit b);
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| 317 | MP_API int mp_is_bit_set (mp_int * a, mp_digit b);
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| 318 | MP_API int mp_mod (mp_int * a, mp_int * b, mp_int * c);
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| 319 | MP_API int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
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| 320 | MP_API int mp_div_2(mp_int * a, mp_int * b);
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| 321 | MP_API int mp_add (mp_int * a, mp_int * b, mp_int * c);
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| 322 | int s_mp_add (mp_int * a, mp_int * b, mp_int * c);
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| 323 | int s_mp_sub (mp_int * a, mp_int * b, mp_int * c);
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| 324 | MP_API int mp_sub (mp_int * a, mp_int * b, mp_int * c);
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| 325 | MP_API int mp_reduce_is_2k_l(mp_int *a);
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| 326 | MP_API int mp_reduce_is_2k(mp_int *a);
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| 327 | MP_API int mp_dr_is_modulus(mp_int *a);
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| 328 | MP_API int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y,
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| 329 | int);
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| 330 | MP_API int mp_exptmod_base_2 (mp_int * X, mp_int * P, mp_int * Y);
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| 331 | #define mp_exptmod_nct(G,X,P,Y) mp_exptmod_fast(G,X,P,Y,0)
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| 332 | MP_API int mp_montgomery_setup (mp_int * n, mp_digit * rho);
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| 333 | int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho);
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| 334 | MP_API int mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho);
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| 335 | MP_API void mp_dr_setup(mp_int *a, mp_digit *d);
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| 336 | MP_API int mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k);
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| 337 | MP_API int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
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| 338 | int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
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| 339 | int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
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| 340 | MP_API int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
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| 341 | MP_API int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
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| 342 | MP_API int mp_reduce (mp_int * x, mp_int * m, mp_int * mu);
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| 343 | MP_API int mp_reduce_setup (mp_int * a, mp_int * b);
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| 344 | int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
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| 345 | MP_API int mp_montgomery_calc_normalization (mp_int * a, mp_int * b);
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| 346 | int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
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|---|
| 347 | int s_mp_sqr (mp_int * a, mp_int * b);
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|---|
| 348 | int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
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|---|
| 349 | int fast_s_mp_sqr (mp_int * a, mp_int * b);
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|---|
| 350 | MP_API int mp_init_size (mp_int * a, int size);
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|---|
| 351 | MP_API int mp_div_3 (mp_int * a, mp_int *c, mp_digit * d);
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|---|
| 352 | MP_API int mp_mul_2(mp_int * a, mp_int * b);
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|---|
| 353 | MP_API int mp_mul (mp_int * a, mp_int * b, mp_int * c);
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|---|
| 354 | MP_API int mp_sqr (mp_int * a, mp_int * b);
|
|---|
| 355 | MP_API int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
|
|---|
| 356 | MP_API int mp_submod (mp_int* a, mp_int* b, mp_int* c, mp_int* d);
|
|---|
| 357 | MP_API int mp_addmod (mp_int* a, mp_int* b, mp_int* c, mp_int* d);
|
|---|
| 358 | MP_API int mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
|
|---|
| 359 | MP_API int mp_2expt (mp_int * a, int b);
|
|---|
| 360 | MP_API int mp_set_bit (mp_int * a, int b);
|
|---|
| 361 | MP_API int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
|
|---|
| 362 | MP_API int mp_add_d (mp_int* a, mp_digit b, mp_int* c);
|
|---|
| 363 | MP_API int mp_set_int (mp_int * a, unsigned long b);
|
|---|
| 364 | MP_API int mp_sub_d (mp_int * a, mp_digit b, mp_int * c);
|
|---|
| 365 | /* end support added functions */
|
|---|
| 366 |
|
|---|
| 367 | /* added */
|
|---|
| 368 | MP_API int mp_init_multi(mp_int* a, mp_int* b, mp_int* c, mp_int* d, mp_int* e,
|
|---|
| 369 | mp_int* f);
|
|---|
| 370 | MP_API int mp_toradix (mp_int *a, char *str, int radix);
|
|---|
| 371 | MP_API int mp_radix_size (mp_int * a, int radix, int *size);
|
|---|
| 372 |
|
|---|
| 373 | #ifdef WOLFSSL_DEBUG_MATH
|
|---|
| 374 | MP_API void mp_dump(const char* desc, mp_int* a, byte verbose);
|
|---|
| 375 | #else
|
|---|
| 376 | #define mp_dump(desc, a, verbose)
|
|---|
| 377 | #endif
|
|---|
| 378 |
|
|---|
| 379 | #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN) || !defined(NO_RSA) || \
|
|---|
| 380 | !defined(NO_DSA) || !defined(NO_DH)
|
|---|
| 381 | MP_API int mp_sqrmod(mp_int* a, mp_int* b, mp_int* c);
|
|---|
| 382 | #endif
|
|---|
| 383 | #if !defined(NO_DSA) || defined(HAVE_ECC)
|
|---|
| 384 | MP_API int mp_read_radix(mp_int* a, const char* str, int radix);
|
|---|
| 385 | #endif
|
|---|
| 386 |
|
|---|
| 387 | #if defined(WOLFSSL_KEY_GEN) || !defined(NO_RSA) || !defined(NO_DSA) || !defined(NO_DH)
|
|---|
| 388 | MP_API int mp_prime_is_prime (mp_int * a, int t, int *result);
|
|---|
| 389 | MP_API int mp_prime_is_prime_ex (mp_int * a, int t, int *result, WC_RNG*);
|
|---|
| 390 | #endif /* WOLFSSL_KEY_GEN NO_RSA NO_DSA NO_DH */
|
|---|
| 391 | #ifdef WOLFSSL_KEY_GEN
|
|---|
| 392 | MP_API int mp_gcd (mp_int * a, mp_int * b, mp_int * c);
|
|---|
| 393 | MP_API int mp_lcm (mp_int * a, mp_int * b, mp_int * c);
|
|---|
| 394 | MP_API int mp_rand_prime(mp_int* N, int len, WC_RNG* rng, void* heap);
|
|---|
| 395 | #endif
|
|---|
| 396 |
|
|---|
| 397 | MP_API int mp_cnt_lsb(mp_int *a);
|
|---|
| 398 | MP_API int mp_mod_d(mp_int* a, mp_digit b, mp_digit* c);
|
|---|
| 399 |
|
|---|
| 400 |
|
|---|
| 401 | #ifdef __cplusplus
|
|---|
| 402 | }
|
|---|
| 403 | #endif
|
|---|
| 404 |
|
|---|
| 405 |
|
|---|
| 406 | #endif /* USE_FAST_MATH */
|
|---|
| 407 |
|
|---|
| 408 | #endif /* WOLF_CRYPT_INTEGER_H */
|
|---|
| 409 |
|
|---|
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