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, tomstdenis@gmail.com, http://math.libtomcrypt.com |
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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 <tclTomMathDecls.h> |
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19 | #ifndef MODULE_SCOPE |
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20 | #define MODULE_SCOPE extern |
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21 | #endif |
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22 | |
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23 | #include <stdio.h> |
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24 | #include <string.h> |
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25 | #include <stdlib.h> |
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26 | #include <ctype.h> |
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27 | #include <limits.h> |
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28 | |
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29 | #include <tommath_class.h> |
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30 | |
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31 | #ifndef MIN |
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32 | #define MIN(x,y) ((x)<(y)?(x):(y)) |
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33 | #endif |
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34 | |
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35 | #ifndef MAX |
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36 | #define MAX(x,y) ((x)>(y)?(x):(y)) |
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37 | #endif |
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38 | |
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39 | #ifdef __cplusplus |
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40 | extern "C" { |
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41 | |
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42 | /* C++ compilers don't like assigning void * to mp_digit * */ |
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43 | #define OPT_CAST(x) (x *) |
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44 | |
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45 | #else |
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46 | |
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47 | /* C on the other hand doesn't care */ |
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48 | #define OPT_CAST(x) |
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49 | |
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50 | #endif |
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51 | |
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52 | |
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53 | /* detect 64-bit mode if possible */ |
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54 | #if defined(NEVER) /* 128-bit ints fail in too many places */ |
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55 | #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT)) |
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56 | #define MP_64BIT |
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57 | #endif |
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58 | #endif |
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59 | |
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60 | /* some default configurations. |
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61 | * |
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62 | * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits |
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63 | * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits |
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64 | * |
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65 | * At the very least a mp_digit must be able to hold 7 bits |
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66 | * [any size beyond that is ok provided it doesn't overflow the data type] |
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67 | */ |
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68 | #ifdef MP_8BIT |
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69 | #ifndef MP_DIGIT_DECLARED |
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70 | typedef unsigned char mp_digit; |
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71 | #define MP_DIGIT_DECLARED |
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72 | #endif |
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73 | typedef unsigned short mp_word; |
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74 | #elif defined(MP_16BIT) |
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75 | #ifndef MP_DIGIT_DECLARED |
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76 | typedef unsigned short mp_digit; |
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77 | #define MP_DIGIT_DECLARED |
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78 | #endif |
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79 | typedef unsigned long mp_word; |
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80 | #elif defined(MP_64BIT) |
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81 | /* for GCC only on supported platforms */ |
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82 | #ifndef CRYPT |
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83 | typedef unsigned long long ulong64; |
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84 | typedef signed long long long64; |
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85 | #endif |
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86 | |
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87 | #ifndef MP_DIGIT_DECLARED |
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88 | typedef unsigned long mp_digit; |
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89 | #define MP_DIGIT_DECLARED |
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90 | #endif |
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91 | typedef unsigned long mp_word __attribute__ ((mode(TI))); |
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92 | |
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93 | #define DIGIT_BIT 60 |
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94 | #else |
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95 | /* this is the default case, 28-bit digits */ |
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96 | |
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97 | /* this is to make porting into LibTomCrypt easier :-) */ |
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98 | #ifndef CRYPT |
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99 | #if defined(_MSC_VER) || defined(__BORLANDC__) |
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100 | typedef unsigned __int64 ulong64; |
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101 | typedef signed __int64 long64; |
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102 | #else |
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103 | typedef unsigned long long ulong64; |
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104 | typedef signed long long long64; |
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105 | #endif |
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106 | #endif |
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107 | |
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108 | #ifndef MP_DIGIT_DECLARED |
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109 | typedef unsigned int mp_digit; |
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110 | #define MP_DIGIT_DECLARED |
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111 | #endif |
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112 | typedef ulong64 mp_word; |
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113 | |
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114 | #ifdef MP_31BIT |
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115 | /* this is an extension that uses 31-bit digits */ |
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116 | #define DIGIT_BIT 31 |
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117 | #else |
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118 | /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */ |
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119 | #define DIGIT_BIT 28 |
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120 | #define MP_28BIT |
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121 | #endif |
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122 | #endif |
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123 | |
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124 | /* define heap macros */ |
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125 | #if 0 /* these are macros in tclTomMathDecls.h */ |
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126 | #ifndef CRYPT |
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127 | /* default to libc stuff */ |
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128 | #ifndef XMALLOC |
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129 | #define XMALLOC malloc |
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130 | #define XFREE free |
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131 | #define XREALLOC realloc |
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132 | #define XCALLOC calloc |
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133 | #else |
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134 | /* prototypes for our heap functions */ |
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135 | extern void *XMALLOC(size_t n); |
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136 | extern void *XREALLOC(void *p, size_t n); |
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137 | extern void *XCALLOC(size_t n, size_t s); |
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138 | extern void XFREE(void *p); |
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139 | #endif |
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140 | #endif |
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141 | #endif |
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142 | |
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143 | |
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144 | /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ |
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145 | #ifndef DIGIT_BIT |
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146 | #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */ |
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147 | #endif |
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148 | |
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149 | #define MP_DIGIT_BIT DIGIT_BIT |
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150 | #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1)) |
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151 | #define MP_DIGIT_MAX MP_MASK |
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152 | |
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153 | /* equalities */ |
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154 | #define MP_LT -1 /* less than */ |
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155 | #define MP_EQ 0 /* equal to */ |
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156 | #define MP_GT 1 /* greater than */ |
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157 | |
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158 | #define MP_ZPOS 0 /* positive integer */ |
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159 | #define MP_NEG 1 /* negative */ |
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160 | |
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161 | #define MP_OKAY 0 /* ok result */ |
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162 | #define MP_MEM -2 /* out of mem */ |
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163 | #define MP_VAL -3 /* invalid input */ |
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164 | #define MP_RANGE MP_VAL |
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165 | |
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166 | #define MP_YES 1 /* yes response */ |
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167 | #define MP_NO 0 /* no response */ |
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168 | |
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169 | /* Primality generation flags */ |
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170 | #define LTM_PRIME_BBS 0x0001 /* BBS style prime */ |
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171 | #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ |
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172 | #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ |
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173 | |
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174 | typedef int mp_err; |
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175 | |
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176 | /* you'll have to tune these... */ |
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177 | #if defined(BUILD_tcl) || !defined(_WIN32) |
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178 | MODULE_SCOPE int KARATSUBA_MUL_CUTOFF, |
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179 | KARATSUBA_SQR_CUTOFF, |
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180 | TOOM_MUL_CUTOFF, |
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181 | TOOM_SQR_CUTOFF; |
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182 | #endif |
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183 | |
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184 | /* define this to use lower memory usage routines (exptmods mostly) */ |
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185 | /* #define MP_LOW_MEM */ |
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186 | |
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187 | /* default precision */ |
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188 | #ifndef MP_PREC |
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189 | #ifndef MP_LOW_MEM |
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190 | #define MP_PREC 32 /* default digits of precision */ |
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191 | #else |
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192 | #define MP_PREC 8 /* default digits of precision */ |
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193 | #endif |
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194 | #endif |
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195 | |
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196 | /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ |
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197 | #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1)) |
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198 | |
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199 | /* the infamous mp_int structure */ |
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200 | #ifndef MP_INT_DECLARED |
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201 | #define MP_INT_DECLARED |
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202 | typedef struct mp_int mp_int; |
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203 | #endif |
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204 | struct mp_int { |
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205 | int used, alloc, sign; |
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206 | mp_digit *dp; |
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207 | }; |
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208 | |
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209 | /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */ |
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210 | typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat); |
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211 | |
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212 | |
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213 | #define USED(m) ((m)->used) |
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214 | #define DIGIT(m,k) ((m)->dp[(k)]) |
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215 | #define SIGN(m) ((m)->sign) |
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216 | |
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217 | /* error code to char* string */ |
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218 | /* |
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219 | char *mp_error_to_string(int code); |
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220 | */ |
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221 | |
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222 | /* ---> init and deinit bignum functions <--- */ |
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223 | /* init a bignum */ |
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224 | /* |
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225 | int mp_init(mp_int *a); |
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226 | */ |
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227 | |
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228 | /* free a bignum */ |
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229 | /* |
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230 | void mp_clear(mp_int *a); |
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231 | */ |
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232 | |
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233 | /* init a null terminated series of arguments */ |
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234 | /* |
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235 | int mp_init_multi(mp_int *mp, ...); |
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236 | */ |
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237 | |
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238 | /* clear a null terminated series of arguments */ |
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239 | /* |
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240 | void mp_clear_multi(mp_int *mp, ...); |
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241 | */ |
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242 | |
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243 | /* exchange two ints */ |
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244 | /* |
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245 | void mp_exch(mp_int *a, mp_int *b); |
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246 | */ |
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247 | |
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248 | /* shrink ram required for a bignum */ |
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249 | /* |
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250 | int mp_shrink(mp_int *a); |
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251 | */ |
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252 | |
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253 | /* grow an int to a given size */ |
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254 | /* |
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255 | int mp_grow(mp_int *a, int size); |
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256 | */ |
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257 | |
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258 | /* init to a given number of digits */ |
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259 | /* |
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260 | int mp_init_size(mp_int *a, int size); |
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261 | */ |
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262 | |
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263 | /* ---> Basic Manipulations <--- */ |
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264 | #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO) |
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265 | #define mp_iseven(a) (((a)->used == 0 || (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO) |
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266 | #define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO) |
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267 | |
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268 | /* set to zero */ |
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269 | /* |
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270 | void mp_zero(mp_int *a); |
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271 | */ |
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272 | |
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273 | /* set to a digit */ |
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274 | /* |
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275 | void mp_set(mp_int *a, mp_digit b); |
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276 | */ |
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277 | |
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278 | /* set a 32-bit const */ |
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279 | /* |
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280 | int mp_set_int(mp_int *a, unsigned long b); |
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281 | */ |
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282 | |
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283 | /* get a 32-bit value */ |
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284 | unsigned long mp_get_int(mp_int * a); |
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285 | |
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286 | /* initialize and set a digit */ |
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287 | /* |
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288 | int mp_init_set (mp_int * a, mp_digit b); |
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289 | */ |
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290 | |
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291 | /* initialize and set 32-bit value */ |
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292 | /* |
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293 | int mp_init_set_int (mp_int * a, unsigned long b); |
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294 | */ |
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295 | |
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296 | /* copy, b = a */ |
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297 | /* |
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298 | int mp_copy(mp_int *a, mp_int *b); |
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299 | */ |
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300 | |
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301 | /* inits and copies, a = b */ |
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302 | /* |
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303 | int mp_init_copy(mp_int *a, mp_int *b); |
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304 | */ |
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305 | |
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306 | /* trim unused digits */ |
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307 | /* |
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308 | void mp_clamp(mp_int *a); |
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309 | */ |
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310 | |
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311 | /* ---> digit manipulation <--- */ |
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312 | |
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313 | /* right shift by "b" digits */ |
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314 | /* |
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315 | void mp_rshd(mp_int *a, int b); |
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316 | */ |
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317 | |
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318 | /* left shift by "b" digits */ |
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319 | /* |
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320 | int mp_lshd(mp_int *a, int b); |
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321 | */ |
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322 | |
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323 | /* c = a / 2**b */ |
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324 | /* |
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325 | int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d); |
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326 | */ |
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327 | |
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328 | /* b = a/2 */ |
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329 | /* |
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330 | int mp_div_2(mp_int *a, mp_int *b); |
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331 | */ |
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332 | |
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333 | /* c = a * 2**b */ |
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334 | /* |
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335 | int mp_mul_2d(mp_int *a, int b, mp_int *c); |
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336 | */ |
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337 | |
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338 | /* b = a*2 */ |
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339 | /* |
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340 | int mp_mul_2(mp_int *a, mp_int *b); |
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341 | */ |
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342 | |
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343 | /* c = a mod 2**d */ |
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344 | /* |
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345 | int mp_mod_2d(mp_int *a, int b, mp_int *c); |
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346 | */ |
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347 | |
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348 | /* computes a = 2**b */ |
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349 | /* |
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350 | int mp_2expt(mp_int *a, int b); |
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351 | */ |
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352 | |
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353 | /* Counts the number of lsbs which are zero before the first zero bit */ |
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354 | /* |
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355 | int mp_cnt_lsb(mp_int *a); |
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356 | */ |
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357 | |
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358 | /* I Love Earth! */ |
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359 | |
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360 | /* makes a pseudo-random int of a given size */ |
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361 | /* |
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362 | int mp_rand(mp_int *a, int digits); |
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363 | */ |
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364 | |
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365 | /* ---> binary operations <--- */ |
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366 | /* c = a XOR b */ |
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367 | /* |
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368 | int mp_xor(mp_int *a, mp_int *b, mp_int *c); |
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369 | */ |
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370 | |
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371 | /* c = a OR b */ |
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372 | /* |
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373 | int mp_or(mp_int *a, mp_int *b, mp_int *c); |
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374 | */ |
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375 | |
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376 | /* c = a AND b */ |
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377 | /* |
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378 | int mp_and(mp_int *a, mp_int *b, mp_int *c); |
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379 | */ |
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380 | |
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381 | /* ---> Basic arithmetic <--- */ |
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382 | |
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383 | /* b = -a */ |
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384 | /* |
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385 | int mp_neg(mp_int *a, mp_int *b); |
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386 | */ |
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387 | |
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388 | /* b = |a| */ |
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389 | /* |
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390 | int mp_abs(mp_int *a, mp_int *b); |
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391 | */ |
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392 | |
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393 | /* compare a to b */ |
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394 | /* |
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395 | int mp_cmp(mp_int *a, mp_int *b); |
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396 | */ |
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397 | |
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398 | /* compare |a| to |b| */ |
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399 | /* |
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400 | int mp_cmp_mag(mp_int *a, mp_int *b); |
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401 | */ |
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402 | |
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403 | /* c = a + b */ |
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404 | /* |
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405 | int mp_add(mp_int *a, mp_int *b, mp_int *c); |
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406 | */ |
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407 | |
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408 | /* c = a - b */ |
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409 | /* |
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410 | int mp_sub(mp_int *a, mp_int *b, mp_int *c); |
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411 | */ |
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412 | |
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413 | /* c = a * b */ |
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414 | /* |
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415 | int mp_mul(mp_int *a, mp_int *b, mp_int *c); |
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416 | */ |
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417 | |
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418 | /* b = a*a */ |
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419 | /* |
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420 | int mp_sqr(mp_int *a, mp_int *b); |
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421 | */ |
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422 | |
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423 | /* a/b => cb + d == a */ |
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424 | /* |
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425 | int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d); |
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426 | */ |
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427 | |
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428 | /* c = a mod b, 0 <= c < b */ |
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429 | /* |
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430 | int mp_mod(mp_int *a, mp_int *b, mp_int *c); |
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431 | */ |
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432 | |
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433 | /* ---> single digit functions <--- */ |
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434 | |
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435 | /* compare against a single digit */ |
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436 | /* |
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437 | int mp_cmp_d(mp_int *a, mp_digit b); |
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438 | */ |
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439 | |
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440 | /* c = a + b */ |
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441 | /* |
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442 | int mp_add_d(mp_int *a, mp_digit b, mp_int *c); |
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443 | */ |
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444 | |
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445 | /* c = a - b */ |
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446 | /* |
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447 | int mp_sub_d(mp_int *a, mp_digit b, mp_int *c); |
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448 | */ |
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449 | |
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450 | /* c = a * b */ |
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451 | /* |
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452 | int mp_mul_d(mp_int *a, mp_digit b, mp_int *c); |
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453 | */ |
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454 | |
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455 | /* a/b => cb + d == a */ |
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456 | /* |
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457 | int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d); |
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458 | */ |
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459 | |
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460 | /* a/3 => 3c + d == a */ |
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461 | /* |
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462 | int mp_div_3(mp_int *a, mp_int *c, mp_digit *d); |
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463 | */ |
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464 | |
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465 | /* c = a**b */ |
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466 | /* |
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467 | int mp_expt_d(mp_int *a, mp_digit b, mp_int *c); |
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468 | */ |
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469 | |
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470 | /* c = a mod b, 0 <= c < b */ |
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471 | /* |
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472 | int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c); |
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473 | */ |
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474 | |
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475 | /* ---> number theory <--- */ |
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476 | |
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477 | /* d = a + b (mod c) */ |
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478 | /* |
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479 | int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); |
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480 | */ |
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481 | |
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482 | /* d = a - b (mod c) */ |
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483 | /* |
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484 | int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); |
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485 | */ |
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486 | |
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487 | /* d = a * b (mod c) */ |
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488 | /* |
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489 | int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); |
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490 | */ |
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491 | |
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492 | /* c = a * a (mod b) */ |
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493 | /* |
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494 | int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c); |
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495 | */ |
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496 | |
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497 | /* c = 1/a (mod b) */ |
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498 | /* |
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499 | int mp_invmod(mp_int *a, mp_int *b, mp_int *c); |
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500 | */ |
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501 | |
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502 | /* c = (a, b) */ |
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503 | /* |
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504 | int mp_gcd(mp_int *a, mp_int *b, mp_int *c); |
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505 | */ |
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506 | |
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507 | /* produces value such that U1*a + U2*b = U3 */ |
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508 | /* |
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509 | int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3); |
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510 | */ |
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511 | |
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512 | /* c = [a, b] or (a*b)/(a, b) */ |
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513 | /* |
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514 | int mp_lcm(mp_int *a, mp_int *b, mp_int *c); |
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515 | */ |
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516 | |
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517 | /* finds one of the b'th root of a, such that |c|**b <= |a| |
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518 | * |
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519 | * returns error if a < 0 and b is even |
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520 | */ |
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521 | /* |
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522 | int mp_n_root(mp_int *a, mp_digit b, mp_int *c); |
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523 | */ |
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524 | |
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525 | /* special sqrt algo */ |
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526 | /* |
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527 | int mp_sqrt(mp_int *arg, mp_int *ret); |
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528 | */ |
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529 | |
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530 | /* is number a square? */ |
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531 | /* |
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532 | int mp_is_square(mp_int *arg, int *ret); |
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533 | */ |
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534 | |
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535 | /* computes the jacobi c = (a | n) (or Legendre if b is prime) */ |
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536 | /* |
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537 | int mp_jacobi(mp_int *a, mp_int *n, int *c); |
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538 | */ |
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539 | |
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540 | /* used to setup the Barrett reduction for a given modulus b */ |
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541 | /* |
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542 | int mp_reduce_setup(mp_int *a, mp_int *b); |
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543 | */ |
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544 | |
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545 | /* Barrett Reduction, computes a (mod b) with a precomputed value c |
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546 | * |
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547 | * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely |
---|
548 | * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code]. |
---|
549 | */ |
---|
550 | /* |
---|
551 | int mp_reduce(mp_int *a, mp_int *b, mp_int *c); |
---|
552 | */ |
---|
553 | |
---|
554 | /* setups the montgomery reduction */ |
---|
555 | /* |
---|
556 | int mp_montgomery_setup(mp_int *a, mp_digit *mp); |
---|
557 | */ |
---|
558 | |
---|
559 | /* computes a = B**n mod b without division or multiplication useful for |
---|
560 | * normalizing numbers in a Montgomery system. |
---|
561 | */ |
---|
562 | /* |
---|
563 | int mp_montgomery_calc_normalization(mp_int *a, mp_int *b); |
---|
564 | */ |
---|
565 | |
---|
566 | /* computes x/R == x (mod N) via Montgomery Reduction */ |
---|
567 | /* |
---|
568 | int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); |
---|
569 | */ |
---|
570 | |
---|
571 | /* returns 1 if a is a valid DR modulus */ |
---|
572 | /* |
---|
573 | int mp_dr_is_modulus(mp_int *a); |
---|
574 | */ |
---|
575 | |
---|
576 | /* sets the value of "d" required for mp_dr_reduce */ |
---|
577 | /* |
---|
578 | void mp_dr_setup(mp_int *a, mp_digit *d); |
---|
579 | */ |
---|
580 | |
---|
581 | /* reduces a modulo b using the Diminished Radix method */ |
---|
582 | /* |
---|
583 | int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp); |
---|
584 | */ |
---|
585 | |
---|
586 | /* returns true if a can be reduced with mp_reduce_2k */ |
---|
587 | /* |
---|
588 | int mp_reduce_is_2k(mp_int *a); |
---|
589 | */ |
---|
590 | |
---|
591 | /* determines k value for 2k reduction */ |
---|
592 | /* |
---|
593 | int mp_reduce_2k_setup(mp_int *a, mp_digit *d); |
---|
594 | */ |
---|
595 | |
---|
596 | /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ |
---|
597 | /* |
---|
598 | int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d); |
---|
599 | */ |
---|
600 | |
---|
601 | /* returns true if a can be reduced with mp_reduce_2k_l */ |
---|
602 | /* |
---|
603 | int mp_reduce_is_2k_l(mp_int *a); |
---|
604 | */ |
---|
605 | |
---|
606 | /* determines k value for 2k reduction */ |
---|
607 | /* |
---|
608 | int mp_reduce_2k_setup_l(mp_int *a, mp_int *d); |
---|
609 | */ |
---|
610 | |
---|
611 | /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ |
---|
612 | /* |
---|
613 | int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d); |
---|
614 | */ |
---|
615 | |
---|
616 | /* d = a**b (mod c) */ |
---|
617 | /* |
---|
618 | int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); |
---|
619 | */ |
---|
620 | |
---|
621 | /* ---> Primes <--- */ |
---|
622 | |
---|
623 | /* number of primes */ |
---|
624 | #ifdef MP_8BIT |
---|
625 | #define PRIME_SIZE 31 |
---|
626 | #else |
---|
627 | #define PRIME_SIZE 256 |
---|
628 | #endif |
---|
629 | |
---|
630 | /* table of first PRIME_SIZE primes */ |
---|
631 | #if defined(BUILD_tcl) || !defined(_WIN32) |
---|
632 | MODULE_SCOPE const mp_digit ltm_prime_tab[]; |
---|
633 | #endif |
---|
634 | |
---|
635 | /* result=1 if a is divisible by one of the first PRIME_SIZE primes */ |
---|
636 | /* |
---|
637 | int mp_prime_is_divisible(mp_int *a, int *result); |
---|
638 | */ |
---|
639 | |
---|
640 | /* performs one Fermat test of "a" using base "b". |
---|
641 | * Sets result to 0 if composite or 1 if probable prime |
---|
642 | */ |
---|
643 | /* |
---|
644 | int mp_prime_fermat(mp_int *a, mp_int *b, int *result); |
---|
645 | */ |
---|
646 | |
---|
647 | /* performs one Miller-Rabin test of "a" using base "b". |
---|
648 | * Sets result to 0 if composite or 1 if probable prime |
---|
649 | */ |
---|
650 | /* |
---|
651 | int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result); |
---|
652 | */ |
---|
653 | |
---|
654 | /* This gives [for a given bit size] the number of trials required |
---|
655 | * such that Miller-Rabin gives a prob of failure lower than 2^-96 |
---|
656 | */ |
---|
657 | /* |
---|
658 | int mp_prime_rabin_miller_trials(int size); |
---|
659 | */ |
---|
660 | |
---|
661 | /* performs t rounds of Miller-Rabin on "a" using the first |
---|
662 | * t prime bases. Also performs an initial sieve of trial |
---|
663 | * division. Determines if "a" is prime with probability |
---|
664 | * of error no more than (1/4)**t. |
---|
665 | * |
---|
666 | * Sets result to 1 if probably prime, 0 otherwise |
---|
667 | */ |
---|
668 | /* |
---|
669 | int mp_prime_is_prime(mp_int *a, int t, int *result); |
---|
670 | */ |
---|
671 | |
---|
672 | /* finds the next prime after the number "a" using "t" trials |
---|
673 | * of Miller-Rabin. |
---|
674 | * |
---|
675 | * bbs_style = 1 means the prime must be congruent to 3 mod 4 |
---|
676 | */ |
---|
677 | /* |
---|
678 | int mp_prime_next_prime(mp_int *a, int t, int bbs_style); |
---|
679 | */ |
---|
680 | |
---|
681 | /* makes a truly random prime of a given size (bytes), |
---|
682 | * call with bbs = 1 if you want it to be congruent to 3 mod 4 |
---|
683 | * |
---|
684 | * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can |
---|
685 | * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself |
---|
686 | * so it can be NULL |
---|
687 | * |
---|
688 | * The prime generated will be larger than 2^(8*size). |
---|
689 | */ |
---|
690 | #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) |
---|
691 | |
---|
692 | /* makes a truly random prime of a given size (bits), |
---|
693 | * |
---|
694 | * Flags are as follows: |
---|
695 | * |
---|
696 | * LTM_PRIME_BBS - make prime congruent to 3 mod 4 |
---|
697 | * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS) |
---|
698 | * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero |
---|
699 | * LTM_PRIME_2MSB_ON - make the 2nd highest bit one |
---|
700 | * |
---|
701 | * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can |
---|
702 | * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself |
---|
703 | * so it can be NULL |
---|
704 | * |
---|
705 | */ |
---|
706 | /* |
---|
707 | int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); |
---|
708 | */ |
---|
709 | |
---|
710 | /* ---> radix conversion <--- */ |
---|
711 | /* |
---|
712 | int mp_count_bits(mp_int *a); |
---|
713 | */ |
---|
714 | |
---|
715 | /* |
---|
716 | int mp_unsigned_bin_size(mp_int *a); |
---|
717 | */ |
---|
718 | /* |
---|
719 | int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); |
---|
720 | */ |
---|
721 | /* |
---|
722 | int mp_to_unsigned_bin(mp_int *a, unsigned char *b); |
---|
723 | */ |
---|
724 | /* |
---|
725 | int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); |
---|
726 | */ |
---|
727 | |
---|
728 | /* |
---|
729 | int mp_signed_bin_size(mp_int *a); |
---|
730 | */ |
---|
731 | /* |
---|
732 | int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); |
---|
733 | */ |
---|
734 | /* |
---|
735 | int mp_to_signed_bin(mp_int *a, unsigned char *b); |
---|
736 | */ |
---|
737 | /* |
---|
738 | int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); |
---|
739 | */ |
---|
740 | |
---|
741 | /* |
---|
742 | int mp_read_radix(mp_int *a, const char *str, int radix); |
---|
743 | */ |
---|
744 | /* |
---|
745 | int mp_toradix(mp_int *a, char *str, int radix); |
---|
746 | */ |
---|
747 | /* |
---|
748 | int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); |
---|
749 | */ |
---|
750 | /* |
---|
751 | int mp_radix_size(mp_int *a, int radix, int *size); |
---|
752 | */ |
---|
753 | |
---|
754 | /* |
---|
755 | int mp_fread(mp_int *a, int radix, FILE *stream); |
---|
756 | */ |
---|
757 | /* |
---|
758 | int mp_fwrite(mp_int *a, int radix, FILE *stream); |
---|
759 | */ |
---|
760 | |
---|
761 | #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len)) |
---|
762 | #define mp_raw_size(mp) mp_signed_bin_size(mp) |
---|
763 | #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str)) |
---|
764 | #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len)) |
---|
765 | #define mp_mag_size(mp) mp_unsigned_bin_size(mp) |
---|
766 | #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str)) |
---|
767 | |
---|
768 | #define mp_tobinary(M, S) mp_toradix((M), (S), 2) |
---|
769 | #define mp_tooctal(M, S) mp_toradix((M), (S), 8) |
---|
770 | #define mp_todecimal(M, S) mp_toradix((M), (S), 10) |
---|
771 | #define mp_tohex(M, S) mp_toradix((M), (S), 16) |
---|
772 | |
---|
773 | /* lowlevel functions, do not call! */ |
---|
774 | /* |
---|
775 | int s_mp_add(mp_int *a, mp_int *b, mp_int *c); |
---|
776 | */ |
---|
777 | /* |
---|
778 | int s_mp_sub(mp_int *a, mp_int *b, mp_int *c); |
---|
779 | */ |
---|
780 | #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) |
---|
781 | /* |
---|
782 | int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); |
---|
783 | */ |
---|
784 | /* |
---|
785 | int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); |
---|
786 | */ |
---|
787 | /* |
---|
788 | int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); |
---|
789 | */ |
---|
790 | /* |
---|
791 | int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); |
---|
792 | */ |
---|
793 | /* |
---|
794 | int fast_s_mp_sqr(mp_int *a, mp_int *b); |
---|
795 | */ |
---|
796 | /* |
---|
797 | int s_mp_sqr(mp_int *a, mp_int *b); |
---|
798 | */ |
---|
799 | /* |
---|
800 | int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c); |
---|
801 | */ |
---|
802 | /* |
---|
803 | int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c); |
---|
804 | */ |
---|
805 | /* |
---|
806 | int mp_karatsuba_sqr(mp_int *a, mp_int *b); |
---|
807 | */ |
---|
808 | /* |
---|
809 | int mp_toom_sqr(mp_int *a, mp_int *b); |
---|
810 | */ |
---|
811 | /* |
---|
812 | int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c); |
---|
813 | */ |
---|
814 | /* |
---|
815 | int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c); |
---|
816 | */ |
---|
817 | /* |
---|
818 | int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); |
---|
819 | */ |
---|
820 | /* |
---|
821 | int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode); |
---|
822 | */ |
---|
823 | /* |
---|
824 | int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode); |
---|
825 | */ |
---|
826 | /* |
---|
827 | void bn_reverse(unsigned char *s, int len); |
---|
828 | */ |
---|
829 | |
---|
830 | #if defined(BUILD_tcl) || !defined(_WIN32) |
---|
831 | MODULE_SCOPE const char *mp_s_rmap; |
---|
832 | #endif |
---|
833 | |
---|
834 | #ifdef __cplusplus |
---|
835 | } |
---|
836 | #endif |
---|
837 | |
---|
838 | #endif |
---|
839 | |
---|
840 | |
---|
841 | /* $Source: /cvsroot/tcl/tcl/generic/tclTomMath.h,v $ */ |
---|
842 | /* Based on Tom's version 1.8 */ |
---|
843 | /* $Revision: 1.10 $ */ |
---|
844 | /* $Date: 2007/02/14 17:59:21 $ */ |
---|
845 | |
---|