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annotate tommath.h @ 154:b4c6e7f276e9 libtomcrypt

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Makefile.in: don't compile things we don't need
author Matt Johnston <matt@ucc.asn.au>
date Mon, 20 Dec 2004 14:46:40 +0000
parents d7da3b1e1540
children
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1 /* LibTomMath, multiple-precision integer library -- Tom St Denis
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2 *
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3 * LibTomMath is a library that provides multiple-precision
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4 * integer arithmetic as well as number theoretic functionality.
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5 *
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6 * The library was designed directly after the MPI library by
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7 * Michael Fromberger but has been written from scratch with
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8 * additional optimizations in place.
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9 *
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10 * The library is free for all purposes without any express
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11 * guarantee it works.
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12 *
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13 * Tom St Denis, [email protected], http://math.libtomcrypt.org
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14 */
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15 #ifndef BN_H_
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16 #define BN_H_
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17
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18 #include <stdio.h>
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19 #include <string.h>
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20 #include <stdlib.h>
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21 #include <ctype.h>
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22 #include <limits.h>
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23
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24 #define NO_LTM_TOOM 1
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25
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26 #undef MIN
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27 #define MIN(x,y) ((x)<(y)?(x):(y))
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28 #undef MAX
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29 #define MAX(x,y) ((x)>(y)?(x):(y))
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30
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31 #ifdef __cplusplus
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32 extern "C" {
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33
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34 /* C++ compilers don't like assigning void * to mp_digit * */
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35 #define OPT_CAST(x) (x *)
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36
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37 #else
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38
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39 /* C on the other hand doesn't care */
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40 #define OPT_CAST(x)
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41
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42 #endif
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43
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44 /* some default configurations.
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45 *
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46 * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
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47 * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
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48 *
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49 * At the very least a mp_digit must be able to hold 7 bits
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50 * [any size beyond that is ok provided it doesn't overflow the data type]
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51 */
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52 #ifdef MP_8BIT
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53 typedef unsigned char mp_digit;
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54 typedef unsigned short mp_word;
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55 #elif defined(MP_16BIT)
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56 typedef unsigned short mp_digit;
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57 typedef unsigned long mp_word;
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58 #elif defined(MP_64BIT)
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59 /* for GCC only on supported platforms */
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60 #ifndef CRYPT
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61 typedef unsigned long long ulong64;
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62 typedef signed long long long64;
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63 #endif
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64
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65 typedef ulong64 mp_digit;
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66 typedef unsigned long mp_word __attribute__ ((mode(TI)));
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67
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68 #define DIGIT_BIT 60
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69 #else
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70 /* this is the default case, 28-bit digits */
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71
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72 /* this is to make porting into LibTomCrypt easier :-) */
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73 #ifndef CRYPT
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74 #if defined(_MSC_VER) || defined(__BORLANDC__)
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75 typedef unsigned __int64 ulong64;
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76 typedef signed __int64 long64;
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77 #else
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78 typedef unsigned long long ulong64;
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79 typedef signed long long long64;
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80 #endif
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81 #endif
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82
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83 typedef unsigned long mp_digit;
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84 typedef ulong64 mp_word;
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85
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86 #ifdef MP_31BIT
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87 /* this is an extension that uses 31-bit digits */
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88 #define DIGIT_BIT 31
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89 #else
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90 /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
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91 #define DIGIT_BIT 28
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92 #define MP_28BIT
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93 #endif
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94 #endif
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95
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96 /* define heap macros */
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97 #ifndef CRYPT
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98 /* default to libc stuff */
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99 #ifndef XMALLOC
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100 #define XMALLOC malloc
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101 #define XFREE free
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102 #define XREALLOC realloc
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103 #define XCALLOC calloc
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104 #else
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105 /* prototypes for our heap functions */
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106 extern void *XMALLOC(size_t n);
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107 extern void *REALLOC(void *p, size_t n);
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108 extern void *XCALLOC(size_t n, size_t s);
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109 extern void XFREE(void *p);
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110 #endif
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111 #endif
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112
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113
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114 /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
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115 #ifndef DIGIT_BIT
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116 #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */
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117 #endif
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118
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119 #define MP_DIGIT_BIT DIGIT_BIT
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120 #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
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121 #define MP_DIGIT_MAX MP_MASK
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122
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123 /* equalities */
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124 #define MP_LT -1 /* less than */
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125 #define MP_EQ 0 /* equal to */
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126 #define MP_GT 1 /* greater than */
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127
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128 #define MP_ZPOS 0 /* positive integer */
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129 #define MP_NEG 1 /* negative */
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130
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131 #define MP_OKAY 0 /* ok result */
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132 #define MP_MEM -2 /* out of mem */
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133 #define MP_VAL -3 /* invalid input */
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134 #define MP_RANGE MP_VAL
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135
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136 #define MP_YES 1 /* yes response */
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137 #define MP_NO 0 /* no response */
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138
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139 /* Primality generation flags */
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140 #define LTM_PRIME_BBS 0x0001 /* BBS style prime */
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141 #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
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142 #define LTM_PRIME_2MSB_OFF 0x0004 /* force 2nd MSB to 0 */
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143 #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
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144
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145 typedef int mp_err;
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146
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147 /* you'll have to tune these... */
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148 extern int KARATSUBA_MUL_CUTOFF,
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149 KARATSUBA_SQR_CUTOFF,
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150 TOOM_MUL_CUTOFF,
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151 TOOM_SQR_CUTOFF;
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152
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153 /* define this to use lower memory usage routines (exptmods mostly) */
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154 /* #define MP_LOW_MEM */
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155
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156 /* default precision */
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157 #ifndef MP_PREC
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158 #ifdef MP_LOW_MEM
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159 #define MP_PREC 64 /* default digits of precision */
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160 #else
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161 #define MP_PREC 8 /* default digits of precision */
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162 #endif
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163 #endif
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164
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165 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
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166 #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
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167
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168 /* the infamous mp_int structure */
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169 typedef struct {
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170 int used, alloc, sign;
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171 mp_digit *dp;
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172 } mp_int;
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173
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174 /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
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175 typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
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176
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177
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178 #define USED(m) ((m)->used)
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179 #define DIGIT(m,k) ((m)->dp[(k)])
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180 #define SIGN(m) ((m)->sign)
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181
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182 /* error code to char* string */
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183 char *mp_error_to_string(int code);
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184
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185 /* ---> init and deinit bignum functions <--- */
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186 /* init a bignum */
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187 int mp_init(mp_int *a);
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188
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189 /* free a bignum */
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190 void mp_clear(mp_int *a);
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191
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192 /* init a null terminated series of arguments */
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193 int mp_init_multi(mp_int *mp, ...);
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194
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195 /* clear a null terminated series of arguments */
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196 void mp_clear_multi(mp_int *mp, ...);
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197
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198 /* exchange two ints */
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199 void mp_exch(mp_int *a, mp_int *b);
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200
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201 /* shrink ram required for a bignum */
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202 int mp_shrink(mp_int *a);
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203
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204 /* grow an int to a given size */
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205 int mp_grow(mp_int *a, int size);
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206
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207 /* init to a given number of digits */
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208 int mp_init_size(mp_int *a, int size);
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209
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210 /* ---> Basic Manipulations <--- */
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211 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
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212 #define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
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213 #define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
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214
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215 /* set to zero */
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216 void mp_zero(mp_int *a);
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217
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218 /* set to a digit */
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219 void mp_set(mp_int *a, mp_digit b);
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220
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221 /* set a 32-bit const */
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222 int mp_set_int(mp_int *a, unsigned long b);
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223
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224 /* get a 32-bit value */
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225 unsigned long mp_get_int(mp_int * a);
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226
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227 /* initialize and set a digit */
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228 int mp_init_set (mp_int * a, mp_digit b);
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229
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230 /* initialize and set 32-bit value */
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231 int mp_init_set_int (mp_int * a, unsigned long b);
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232
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233 /* copy, b = a */
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234 int mp_copy(mp_int *a, mp_int *b);
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235
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236 /* inits and copies, a = b */
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237 int mp_init_copy(mp_int *a, mp_int *b);
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238
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239 /* trim unused digits */
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240 void mp_clamp(mp_int *a);
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241
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242 /* ---> digit manipulation <--- */
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243
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244 /* right shift by "b" digits */
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245 void mp_rshd(mp_int *a, int b);
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246
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247 /* left shift by "b" digits */
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248 int mp_lshd(mp_int *a, int b);
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249
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250 /* c = a / 2**b */
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251 int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d);
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252
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253 /* b = a/2 */
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254 int mp_div_2(mp_int *a, mp_int *b);
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255
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256 /* c = a * 2**b */
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257 int mp_mul_2d(mp_int *a, int b, mp_int *c);
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258
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259 /* b = a*2 */
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260 int mp_mul_2(mp_int *a, mp_int *b);
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261
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262 /* c = a mod 2**d */
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263 int mp_mod_2d(mp_int *a, int b, mp_int *c);
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264
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265 /* computes a = 2**b */
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266 int mp_2expt(mp_int *a, int b);
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267
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268 /* Counts the number of lsbs which are zero before the first zero bit */
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269 int mp_cnt_lsb(mp_int *a);
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270
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271 /* I Love Earth! */
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272
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273 /* makes a pseudo-random int of a given size */
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274 int mp_rand(mp_int *a, int digits);
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275
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276 /* ---> binary operations <--- */
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277 /* c = a XOR b */
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278 int mp_xor(mp_int *a, mp_int *b, mp_int *c);
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279
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280 /* c = a OR b */
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281 int mp_or(mp_int *a, mp_int *b, mp_int *c);
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282
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283 /* c = a AND b */
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284 int mp_and(mp_int *a, mp_int *b, mp_int *c);
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285
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286 /* ---> Basic arithmetic <--- */
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287
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288 /* b = -a */
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289 int mp_neg(mp_int *a, mp_int *b);
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290
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291 /* b = |a| */
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292 int mp_abs(mp_int *a, mp_int *b);
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293
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294 /* compare a to b */
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295 int mp_cmp(mp_int *a, mp_int *b);
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296
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297 /* compare |a| to |b| */
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298 int mp_cmp_mag(mp_int *a, mp_int *b);
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299
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300 /* c = a + b */
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301 int mp_add(mp_int *a, mp_int *b, mp_int *c);
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302
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303 /* c = a - b */
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304 int mp_sub(mp_int *a, mp_int *b, mp_int *c);
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305
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306 /* c = a * b */
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307 int mp_mul(mp_int *a, mp_int *b, mp_int *c);
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308
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309 /* b = a*a */
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310 int mp_sqr(mp_int *a, mp_int *b);
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311
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312 /* a/b => cb + d == a */
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313 int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
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314
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315 /* c = a mod b, 0 <= c < b */
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316 int mp_mod(mp_int *a, mp_int *b, mp_int *c);
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317
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318 /* ---> single digit functions <--- */
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319
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320 /* compare against a single digit */
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321 int mp_cmp_d(mp_int *a, mp_digit b);
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322
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323 /* c = a + b */
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324 int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
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325
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326 /* c = a - b */
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327 int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
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328
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329 /* c = a * b */
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330 int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
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331
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332 /* a/b => cb + d == a */
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333 int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
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334
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335 /* a/3 => 3c + d == a */
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336 int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
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337
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338 /* c = a**b */
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339 int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
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340
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341 /* c = a mod b, 0 <= c < b */
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342 int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
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343
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344 /* ---> number theory <--- */
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345
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346 /* d = a + b (mod c) */
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347 int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
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348
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349 /* d = a - b (mod c) */
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350 int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
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351
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352 /* d = a * b (mod c) */
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353 int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
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354
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355 /* c = a * a (mod b) */
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356 int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);
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357
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358 /* c = 1/a (mod b) */
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359 int mp_invmod(mp_int *a, mp_int *b, mp_int *c);
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360
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361 /* c = (a, b) */
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362 int mp_gcd(mp_int *a, mp_int *b, mp_int *c);
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363
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364 /* produces value such that U1*a + U2*b = U3 */
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365 int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
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366
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367 /* c = [a, b] or (a*b)/(a, b) */
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368 int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
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369
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370 /* finds one of the b'th root of a, such that |c|**b <= |a|
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371 *
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372 * returns error if a < 0 and b is even
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373 */
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374 int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
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375
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376 /* special sqrt algo */
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377 int mp_sqrt(mp_int *arg, mp_int *ret);
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378
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379 /* is number a square? */
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380 int mp_is_square(mp_int *arg, int *ret);
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381
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382 /* computes the jacobi c = (a | n) (or Legendre if b is prime) */
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383 int mp_jacobi(mp_int *a, mp_int *n, int *c);
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384
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385 /* used to setup the Barrett reduction for a given modulus b */
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386 int mp_reduce_setup(mp_int *a, mp_int *b);
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387
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388 /* Barrett Reduction, computes a (mod b) with a precomputed value c
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389 *
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390 * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
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391 * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
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392 */
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393 int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
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394
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395 /* setups the montgomery reduction */
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396 int mp_montgomery_setup(mp_int *a, mp_digit *mp);
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397
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398 /* computes a = B**n mod b without division or multiplication useful for
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399 * normalizing numbers in a Montgomery system.
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400 */
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401 int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
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402
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403 /* computes x/R == x (mod N) via Montgomery Reduction */
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404 int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
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405
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406 /* returns 1 if a is a valid DR modulus */
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407 int mp_dr_is_modulus(mp_int *a);
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408
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409 /* sets the value of "d" required for mp_dr_reduce */
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410 void mp_dr_setup(mp_int *a, mp_digit *d);
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411
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412 /* reduces a modulo b using the Diminished Radix method */
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413 int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
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414
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415 /* returns true if a can be reduced with mp_reduce_2k */
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416 int mp_reduce_is_2k(mp_int *a);
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417
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418 /* determines k value for 2k reduction */
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419 int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
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420
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421 /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
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422 int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
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423
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424 /* d = a**b (mod c) */
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425 int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
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426
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427 /* ---> Primes <--- */
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428
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429 /* number of primes */
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430 #ifdef MP_8BIT
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431 #define PRIME_SIZE 31
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432 #else
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433 #define PRIME_SIZE 256
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434 #endif
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435
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436 /* table of first PRIME_SIZE primes */
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437 extern const mp_digit __prime_tab[];
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438
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439 /* result=1 if a is divisible by one of the first PRIME_SIZE primes */
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440 int mp_prime_is_divisible(mp_int *a, int *result);
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441
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442 /* performs one Fermat test of "a" using base "b".
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443 * Sets result to 0 if composite or 1 if probable prime
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444 */
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445 int mp_prime_fermat(mp_int *a, mp_int *b, int *result);
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446
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447 /* performs one Miller-Rabin test of "a" using base "b".
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448 * Sets result to 0 if composite or 1 if probable prime
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449 */
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450 int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
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451
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452 /* This gives [for a given bit size] the number of trials required
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453 * such that Miller-Rabin gives a prob of failure lower than 2^-96
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454 */
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455 int mp_prime_rabin_miller_trials(int size);
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456
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457 /* performs t rounds of Miller-Rabin on "a" using the first
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458 * t prime bases. Also performs an initial sieve of trial
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459 * division. Determines if "a" is prime with probability
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460 * of error no more than (1/4)**t.
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461 *
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462 * Sets result to 1 if probably prime, 0 otherwise
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463 */
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464 int mp_prime_is_prime(mp_int *a, int t, int *result);
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465
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466 /* finds the next prime after the number "a" using "t" trials
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467 * of Miller-Rabin.
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468 *
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469 * bbs_style = 1 means the prime must be congruent to 3 mod 4
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470 */
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471 int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
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472
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473 /* makes a truly random prime of a given size (bytes),
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474 * call with bbs = 1 if you want it to be congruent to 3 mod 4
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475 *
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476 * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
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477 * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
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478 * so it can be NULL
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479 *
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480 * The prime generated will be larger than 2^(8*size).
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481 */
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482 #define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)
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483
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484 /* makes a truly random prime of a given size (bits),
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485 *
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486 * Flags are as follows:
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487 *
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488 * LTM_PRIME_BBS - make prime congruent to 3 mod 4
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489 * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
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490 * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
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491 * LTM_PRIME_2MSB_ON - make the 2nd highest bit one
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492 *
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493 * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
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494 * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
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495 * so it can be NULL
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496 *
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497 */
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498 int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat);
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499
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500 /* ---> radix conversion <--- */
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501 int mp_count_bits(mp_int *a);
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502
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503 int mp_unsigned_bin_size(mp_int *a);
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504 int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
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505 int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
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506
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507 int mp_signed_bin_size(mp_int *a);
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508 int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
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509 int mp_to_signed_bin(mp_int *a, unsigned char *b);
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510
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511 int mp_read_radix(mp_int *a, char *str, int radix);
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512 int mp_toradix(mp_int *a, char *str, int radix);
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513 int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
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514 int mp_radix_size(mp_int *a, int radix, int *size);
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515
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516 int mp_fread(mp_int *a, int radix, FILE *stream);
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517 int mp_fwrite(mp_int *a, int radix, FILE *stream);
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518
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519 #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
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520 #define mp_raw_size(mp) mp_signed_bin_size(mp)
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521 #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
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522 #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
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523 #define mp_mag_size(mp) mp_unsigned_bin_size(mp)
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524 #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
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525
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526 #define mp_tobinary(M, S) mp_toradix((M), (S), 2)
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527 #define mp_tooctal(M, S) mp_toradix((M), (S), 8)
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528 #define mp_todecimal(M, S) mp_toradix((M), (S), 10)
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529 #define mp_tohex(M, S) mp_toradix((M), (S), 16)
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530
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531 /* lowlevel functions, do not call! */
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532 int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
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533 int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
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534 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
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535 int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
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536 int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
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537 int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
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538 int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
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539 int fast_s_mp_sqr(mp_int *a, mp_int *b);
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540 int s_mp_sqr(mp_int *a, mp_int *b);
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541 int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
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542 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
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543 int mp_karatsuba_sqr(mp_int *a, mp_int *b);
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544 int mp_toom_sqr(mp_int *a, mp_int *b);
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545 int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
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546 int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
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547 int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
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548 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
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549 void bn_reverse(unsigned char *s, int len);
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550
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551 extern const char *mp_s_rmap;
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552
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553 #ifdef __cplusplus
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554 }
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555 #endif
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556
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557 #endif
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558