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1 /* |
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2 mpi.c |
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3 |
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4 by Michael J. Fromberger <[email protected]> |
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5 Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved |
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6 |
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7 Arbitrary precision integer arithmetic library |
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8 |
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9 $Id: mpi.c,v 1.1.1.1 2003/05/19 04:01:19 matt Exp $ |
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10 */ |
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11 |
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12 #include "mpi.h" |
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13 #include <stdlib.h> |
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14 #include <string.h> |
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15 #include <ctype.h> |
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16 |
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17 #if MP_DEBUG |
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18 #include <stdio.h> |
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19 |
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20 #define DIAG(T,V) {fprintf(stderr,T);mp_print(V,stderr);fputc('\n',stderr);} |
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21 #else |
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22 #define DIAG(T,V) |
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23 #endif |
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24 |
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25 /* |
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26 If MP_LOGTAB is not defined, use the math library to compute the |
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27 logarithms on the fly. Otherwise, use the static table below. |
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28 Pick which works best for your system. |
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29 */ |
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30 #if MP_LOGTAB |
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31 |
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32 /* {{{ s_logv_2[] - log table for 2 in various bases */ |
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33 |
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34 /* |
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35 A table of the logs of 2 for various bases (the 0 and 1 entries of |
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36 this table are meaningless and should not be referenced). |
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37 |
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38 This table is used to compute output lengths for the mp_toradix() |
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39 function. Since a number n in radix r takes up about log_r(n) |
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40 digits, we estimate the output size by taking the least integer |
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41 greater than log_r(n), where: |
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42 |
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43 log_r(n) = log_2(n) * log_r(2) |
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44 |
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45 This table, therefore, is a table of log_r(2) for 2 <= r <= 36, |
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46 which are the output bases supported. |
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47 */ |
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48 |
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49 #include "logtab.h" |
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50 |
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51 /* }}} */ |
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52 #define LOG_V_2(R) s_logv_2[(R)] |
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53 |
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54 #else |
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55 |
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56 #include <math.h> |
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57 #define LOG_V_2(R) (log(2.0)/log(R)) |
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58 |
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59 #endif |
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60 |
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61 /* Default precision for newly created mp_int's */ |
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62 static unsigned int s_mp_defprec = MP_DEFPREC; |
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63 |
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64 /* {{{ Digit arithmetic macros */ |
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65 |
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66 /* |
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67 When adding and multiplying digits, the results can be larger than |
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68 can be contained in an mp_digit. Thus, an mp_word is used. These |
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69 macros mask off the upper and lower digits of the mp_word (the |
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70 mp_word may be more than 2 mp_digits wide, but we only concern |
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71 ourselves with the low-order 2 mp_digits) |
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72 |
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73 If your mp_word DOES have more than 2 mp_digits, you need to |
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74 uncomment the first line, and comment out the second. |
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75 */ |
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76 |
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77 /* #define CARRYOUT(W) (((W)>>DIGIT_BIT)&MP_DIGIT_MAX) */ |
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78 #define CARRYOUT(W) ((W)>>DIGIT_BIT) |
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79 #define ACCUM(W) ((W)&MP_DIGIT_MAX) |
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80 |
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81 /* }}} */ |
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82 |
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83 /* {{{ Comparison constants */ |
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84 |
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85 #define MP_LT -1 |
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86 #define MP_EQ 0 |
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87 #define MP_GT 1 |
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88 |
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89 /* }}} */ |
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90 |
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91 /* {{{ Constant strings */ |
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92 |
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93 /* Constant strings returned by mp_strerror() */ |
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94 static const char *mp_err_string[] = { |
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95 "unknown result code", /* say what? */ |
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96 "boolean true", /* MP_OKAY, MP_YES */ |
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97 "boolean false", /* MP_NO */ |
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98 "out of memory", /* MP_MEM */ |
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99 "argument out of range", /* MP_RANGE */ |
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100 "invalid input parameter", /* MP_BADARG */ |
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101 "result is undefined" /* MP_UNDEF */ |
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102 }; |
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103 |
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104 /* Value to digit maps for radix conversion */ |
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105 |
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106 /* s_dmap_1 - standard digits and letters */ |
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107 static const char *s_dmap_1 = |
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108 "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; |
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109 |
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110 #if 0 |
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111 /* s_dmap_2 - base64 ordering for digits */ |
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112 static const char *s_dmap_2 = |
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113 "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"; |
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114 #endif |
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115 |
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116 /* }}} */ |
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117 |
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118 /* {{{ Static function declarations */ |
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119 |
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120 /* |
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121 If MP_MACRO is false, these will be defined as actual functions; |
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122 otherwise, suitable macro definitions will be used. This works |
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123 around the fact that ANSI C89 doesn't support an 'inline' keyword |
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124 (although I hear C9x will ... about bloody time). At present, the |
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125 macro definitions are identical to the function bodies, but they'll |
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126 expand in place, instead of generating a function call. |
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127 |
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128 I chose these particular functions to be made into macros because |
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129 some profiling showed they are called a lot on a typical workload, |
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130 and yet they are primarily housekeeping. |
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131 */ |
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132 #if MP_MACRO == 0 |
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133 void s_mp_setz(mp_digit *dp, mp_size count); /* zero digits */ |
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134 void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count); /* copy */ |
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135 void *s_mp_alloc(size_t nb, size_t ni); /* general allocator */ |
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136 void s_mp_free(void *ptr); /* general free function */ |
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137 #else |
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138 |
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139 /* Even if these are defined as macros, we need to respect the settings |
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140 of the MP_MEMSET and MP_MEMCPY configuration options... |
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141 */ |
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142 #if MP_MEMSET == 0 |
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143 #define s_mp_setz(dp, count) \ |
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144 {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=0;} |
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145 #else |
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146 #define s_mp_setz(dp, count) memset(dp, 0, (count) * sizeof(mp_digit)) |
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147 #endif /* MP_MEMSET */ |
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148 |
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149 #if MP_MEMCPY == 0 |
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150 #define s_mp_copy(sp, dp, count) \ |
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151 {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=(sp)[ix];} |
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152 #else |
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153 #define s_mp_copy(sp, dp, count) memcpy(dp, sp, (count) * sizeof(mp_digit)) |
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154 #endif /* MP_MEMCPY */ |
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155 |
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156 #define s_mp_alloc(nb, ni) calloc(nb, ni) |
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157 #define s_mp_free(ptr) {if(ptr) free(ptr);} |
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158 #endif /* MP_MACRO */ |
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159 |
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160 mp_err s_mp_grow(mp_int *mp, mp_size min); /* increase allocated size */ |
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161 mp_err s_mp_pad(mp_int *mp, mp_size min); /* left pad with zeroes */ |
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162 |
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163 void s_mp_clamp(mp_int *mp); /* clip leading zeroes */ |
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164 |
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165 void s_mp_exch(mp_int *a, mp_int *b); /* swap a and b in place */ |
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166 |
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167 mp_err s_mp_lshd(mp_int *mp, mp_size p); /* left-shift by p digits */ |
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168 void s_mp_rshd(mp_int *mp, mp_size p); /* right-shift by p digits */ |
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169 void s_mp_div_2d(mp_int *mp, mp_digit d); /* divide by 2^d in place */ |
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170 void s_mp_mod_2d(mp_int *mp, mp_digit d); /* modulo 2^d in place */ |
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171 mp_err s_mp_mul_2d(mp_int *mp, mp_digit d); /* multiply by 2^d in place*/ |
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172 void s_mp_div_2(mp_int *mp); /* divide by 2 in place */ |
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173 mp_err s_mp_mul_2(mp_int *mp); /* multiply by 2 in place */ |
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174 mp_digit s_mp_norm(mp_int *a, mp_int *b); /* normalize for division */ |
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175 mp_err s_mp_add_d(mp_int *mp, mp_digit d); /* unsigned digit addition */ |
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176 mp_err s_mp_sub_d(mp_int *mp, mp_digit d); /* unsigned digit subtract */ |
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177 mp_err s_mp_mul_d(mp_int *mp, mp_digit d); /* unsigned digit multiply */ |
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178 mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r); |
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179 /* unsigned digit divide */ |
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180 mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu); |
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181 /* Barrett reduction */ |
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182 mp_err s_mp_add(mp_int *a, mp_int *b); /* magnitude addition */ |
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183 mp_err s_mp_sub(mp_int *a, mp_int *b); /* magnitude subtract */ |
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184 mp_err s_mp_mul(mp_int *a, mp_int *b); /* magnitude multiply */ |
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185 #if 0 |
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186 void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len); |
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187 /* multiply buffers in place */ |
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188 #endif |
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189 #if MP_SQUARE |
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190 mp_err s_mp_sqr(mp_int *a); /* magnitude square */ |
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191 #else |
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192 #define s_mp_sqr(a) s_mp_mul(a, a) |
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193 #endif |
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194 mp_err s_mp_div(mp_int *a, mp_int *b); /* magnitude divide */ |
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195 mp_err s_mp_2expt(mp_int *a, mp_digit k); /* a = 2^k */ |
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196 int s_mp_cmp(mp_int *a, mp_int *b); /* magnitude comparison */ |
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197 int s_mp_cmp_d(mp_int *a, mp_digit d); /* magnitude digit compare */ |
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198 int s_mp_ispow2(mp_int *v); /* is v a power of 2? */ |
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199 int s_mp_ispow2d(mp_digit d); /* is d a power of 2? */ |
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200 |
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201 int s_mp_tovalue(char ch, int r); /* convert ch to value */ |
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202 char s_mp_todigit(int val, int r, int low); /* convert val to digit */ |
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203 int s_mp_outlen(int bits, int r); /* output length in bytes */ |
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204 |
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205 /* }}} */ |
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206 |
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207 /* {{{ Default precision manipulation */ |
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208 |
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209 unsigned int mp_get_prec(void) |
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210 { |
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211 return s_mp_defprec; |
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212 |
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213 } /* end mp_get_prec() */ |
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214 |
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215 void mp_set_prec(unsigned int prec) |
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216 { |
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217 if(prec == 0) |
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218 s_mp_defprec = MP_DEFPREC; |
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219 else |
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220 s_mp_defprec = prec; |
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221 |
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222 } /* end mp_set_prec() */ |
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223 |
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224 /* }}} */ |
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225 |
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226 /*------------------------------------------------------------------------*/ |
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227 /* {{{ mp_init(mp) */ |
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228 |
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229 /* |
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230 mp_init(mp) |
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231 |
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232 Initialize a new zero-valued mp_int. Returns MP_OKAY if successful, |
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233 MP_MEM if memory could not be allocated for the structure. |
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234 */ |
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235 |
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236 mp_err mp_init(mp_int *mp) |
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237 { |
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238 return mp_init_size(mp, s_mp_defprec); |
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239 |
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240 } /* end mp_init() */ |
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241 |
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242 /* }}} */ |
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243 |
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244 /* {{{ mp_init_array(mp[], count) */ |
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245 |
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246 mp_err mp_init_array(mp_int mp[], int count) |
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247 { |
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248 mp_err res; |
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249 int pos; |
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250 |
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251 ARGCHK(mp !=NULL && count > 0, MP_BADARG); |
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252 |
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253 for(pos = 0; pos < count; ++pos) { |
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254 if((res = mp_init(&mp[pos])) != MP_OKAY) |
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255 goto CLEANUP; |
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256 } |
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257 |
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258 return MP_OKAY; |
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259 |
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260 CLEANUP: |
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261 while(--pos >= 0) |
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262 mp_clear(&mp[pos]); |
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263 |
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264 return res; |
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265 |
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266 } /* end mp_init_array() */ |
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267 |
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268 /* }}} */ |
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269 |
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270 /* {{{ mp_init_size(mp, prec) */ |
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271 |
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272 /* |
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273 mp_init_size(mp, prec) |
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274 |
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275 Initialize a new zero-valued mp_int with at least the given |
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276 precision; returns MP_OKAY if successful, or MP_MEM if memory could |
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277 not be allocated for the structure. |
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278 */ |
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279 |
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280 mp_err mp_init_size(mp_int *mp, mp_size prec) |
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281 { |
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282 ARGCHK(mp != NULL && prec > 0, MP_BADARG); |
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283 |
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284 if((DIGITS(mp) = s_mp_alloc(prec, sizeof(mp_digit))) == NULL) |
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285 return MP_MEM; |
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286 |
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287 SIGN(mp) = MP_ZPOS; |
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288 USED(mp) = 1; |
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289 ALLOC(mp) = prec; |
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290 |
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291 return MP_OKAY; |
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292 |
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293 } /* end mp_init_size() */ |
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294 |
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295 /* }}} */ |
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296 |
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297 /* {{{ mp_init_copy(mp, from) */ |
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298 |
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299 /* |
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300 mp_init_copy(mp, from) |
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301 |
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302 Initialize mp as an exact copy of from. Returns MP_OKAY if |
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303 successful, MP_MEM if memory could not be allocated for the new |
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304 structure. |
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305 */ |
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306 |
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307 mp_err mp_init_copy(mp_int *mp, mp_int *from) |
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308 { |
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309 ARGCHK(mp != NULL && from != NULL, MP_BADARG); |
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310 |
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311 if(mp == from) |
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312 return MP_OKAY; |
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313 |
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314 if((DIGITS(mp) = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL) |
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315 return MP_MEM; |
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316 |
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317 s_mp_copy(DIGITS(from), DIGITS(mp), USED(from)); |
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318 USED(mp) = USED(from); |
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319 ALLOC(mp) = USED(from); |
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320 SIGN(mp) = SIGN(from); |
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321 |
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322 return MP_OKAY; |
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323 |
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324 } /* end mp_init_copy() */ |
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325 |
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326 /* }}} */ |
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327 |
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328 /* {{{ mp_copy(from, to) */ |
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329 |
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330 /* |
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331 mp_copy(from, to) |
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332 |
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333 Copies the mp_int 'from' to the mp_int 'to'. It is presumed that |
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334 'to' has already been initialized (if not, use mp_init_copy() |
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335 instead). If 'from' and 'to' are identical, nothing happens. |
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336 */ |
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337 |
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338 mp_err mp_copy(mp_int *from, mp_int *to) |
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339 { |
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340 ARGCHK(from != NULL && to != NULL, MP_BADARG); |
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341 |
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342 if(from == to) |
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343 return MP_OKAY; |
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344 |
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345 { /* copy */ |
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346 mp_digit *tmp; |
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347 |
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348 /* |
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349 If the allocated buffer in 'to' already has enough space to hold |
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350 all the used digits of 'from', we'll re-use it to avoid hitting |
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351 the memory allocater more than necessary; otherwise, we'd have |
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352 to grow anyway, so we just allocate a hunk and make the copy as |
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353 usual |
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354 */ |
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355 if(ALLOC(to) >= USED(from)) { |
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356 s_mp_setz(DIGITS(to) + USED(from), ALLOC(to) - USED(from)); |
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357 s_mp_copy(DIGITS(from), DIGITS(to), USED(from)); |
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358 |
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359 } else { |
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360 if((tmp = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL) |
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361 return MP_MEM; |
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362 |
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363 s_mp_copy(DIGITS(from), tmp, USED(from)); |
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364 |
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365 if(DIGITS(to) != NULL) { |
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366 #if MP_CRYPTO |
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367 s_mp_setz(DIGITS(to), ALLOC(to)); |
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368 #endif |
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369 s_mp_free(DIGITS(to)); |
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370 } |
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371 |
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372 DIGITS(to) = tmp; |
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373 ALLOC(to) = USED(from); |
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374 } |
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375 |
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376 /* Copy the precision and sign from the original */ |
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377 USED(to) = USED(from); |
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378 SIGN(to) = SIGN(from); |
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379 } /* end copy */ |
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380 |
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381 return MP_OKAY; |
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382 |
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383 } /* end mp_copy() */ |
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384 |
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385 /* }}} */ |
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386 |
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387 /* {{{ mp_exch(mp1, mp2) */ |
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388 |
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389 /* |
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390 mp_exch(mp1, mp2) |
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391 |
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392 Exchange mp1 and mp2 without allocating any intermediate memory |
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393 (well, unless you count the stack space needed for this call and the |
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394 locals it creates...). This cannot fail. |
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395 */ |
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396 |
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397 void mp_exch(mp_int *mp1, mp_int *mp2) |
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398 { |
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399 #if MP_ARGCHK == 2 |
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400 assert(mp1 != NULL && mp2 != NULL); |
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401 #else |
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402 if(mp1 == NULL || mp2 == NULL) |
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403 return; |
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404 #endif |
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405 |
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406 s_mp_exch(mp1, mp2); |
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407 |
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408 } /* end mp_exch() */ |
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409 |
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410 /* }}} */ |
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411 |
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412 /* {{{ mp_clear(mp) */ |
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413 |
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414 /* |
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415 mp_clear(mp) |
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416 |
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417 Release the storage used by an mp_int, and void its fields so that |
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418 if someone calls mp_clear() again for the same int later, we won't |
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419 get tollchocked. |
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420 */ |
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421 |
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422 void mp_clear(mp_int *mp) |
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423 { |
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424 if(mp == NULL) |
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425 return; |
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426 |
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427 if(DIGITS(mp) != NULL) { |
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428 #if MP_CRYPTO |
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429 s_mp_setz(DIGITS(mp), ALLOC(mp)); |
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430 #endif |
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431 s_mp_free(DIGITS(mp)); |
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432 DIGITS(mp) = NULL; |
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433 } |
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434 |
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435 USED(mp) = 0; |
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436 ALLOC(mp) = 0; |
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437 |
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438 } /* end mp_clear() */ |
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439 |
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440 /* }}} */ |
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441 |
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442 /* {{{ mp_clear_array(mp[], count) */ |
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443 |
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444 void mp_clear_array(mp_int mp[], int count) |
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445 { |
|
|
446 ARGCHK(mp != NULL && count > 0, MP_BADARG); |
|
|
447 |
|
|
448 while(--count >= 0) |
|
|
449 mp_clear(&mp[count]); |
|
|
450 |
|
|
451 } /* end mp_clear_array() */ |
|
|
452 |
|
|
453 /* }}} */ |
|
|
454 |
|
|
455 /* {{{ mp_zero(mp) */ |
|
|
456 |
|
|
457 /* |
|
|
458 mp_zero(mp) |
|
|
459 |
|
|
460 Set mp to zero. Does not change the allocated size of the structure, |
|
|
461 and therefore cannot fail (except on a bad argument, which we ignore) |
|
|
462 */ |
|
|
463 void mp_zero(mp_int *mp) |
|
|
464 { |
|
|
465 if(mp == NULL) |
|
|
466 return; |
|
|
467 |
|
|
468 s_mp_setz(DIGITS(mp), ALLOC(mp)); |
|
|
469 USED(mp) = 1; |
|
|
470 SIGN(mp) = MP_ZPOS; |
|
|
471 |
|
|
472 } /* end mp_zero() */ |
|
|
473 |
|
|
474 /* }}} */ |
|
|
475 |
|
|
476 /* {{{ mp_set(mp, d) */ |
|
|
477 |
|
|
478 void mp_set(mp_int *mp, mp_digit d) |
|
|
479 { |
|
|
480 if(mp == NULL) |
|
|
481 return; |
|
|
482 |
|
|
483 mp_zero(mp); |
|
|
484 DIGIT(mp, 0) = d; |
|
|
485 |
|
|
486 } /* end mp_set() */ |
|
|
487 |
|
|
488 /* }}} */ |
|
|
489 |
|
|
490 /* {{{ mp_set_int(mp, z) */ |
|
|
491 |
|
|
492 mp_err mp_set_int(mp_int *mp, long z) |
|
|
493 { |
|
|
494 int ix; |
|
|
495 unsigned long v = abs(z); |
|
|
496 mp_err res; |
|
|
497 |
|
|
498 ARGCHK(mp != NULL, MP_BADARG); |
|
|
499 |
|
|
500 mp_zero(mp); |
|
|
501 if(z == 0) |
|
|
502 return MP_OKAY; /* shortcut for zero */ |
|
|
503 |
|
|
504 for(ix = sizeof(long) - 1; ix >= 0; ix--) { |
|
|
505 |
|
|
506 if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY) |
|
|
507 return res; |
|
|
508 |
|
|
509 res = s_mp_add_d(mp, |
|
|
510 (mp_digit)((v >> (ix * CHAR_BIT)) & UCHAR_MAX)); |
|
|
511 if(res != MP_OKAY) |
|
|
512 return res; |
|
|
513 |
|
|
514 } |
|
|
515 |
|
|
516 if(z < 0) |
|
|
517 SIGN(mp) = MP_NEG; |
|
|
518 |
|
|
519 return MP_OKAY; |
|
|
520 |
|
|
521 } /* end mp_set_int() */ |
|
|
522 |
|
|
523 /* }}} */ |
|
|
524 |
|
|
525 /*------------------------------------------------------------------------*/ |
|
|
526 /* {{{ Digit arithmetic */ |
|
|
527 |
|
|
528 /* {{{ mp_add_d(a, d, b) */ |
|
|
529 |
|
|
530 /* |
|
|
531 mp_add_d(a, d, b) |
|
|
532 |
|
|
533 Compute the sum b = a + d, for a single digit d. Respects the sign of |
|
|
534 its primary addend (single digits are unsigned anyway). |
|
|
535 */ |
|
|
536 |
|
|
537 mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b) |
|
|
538 { |
|
|
539 mp_err res = MP_OKAY; |
|
|
540 |
|
|
541 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
|
|
542 |
|
|
543 if((res = mp_copy(a, b)) != MP_OKAY) |
|
|
544 return res; |
|
|
545 |
|
|
546 if(SIGN(b) == MP_ZPOS) { |
|
|
547 res = s_mp_add_d(b, d); |
|
|
548 } else if(s_mp_cmp_d(b, d) >= 0) { |
|
|
549 res = s_mp_sub_d(b, d); |
|
|
550 } else { |
|
|
551 SIGN(b) = MP_ZPOS; |
|
|
552 |
|
|
553 DIGIT(b, 0) = d - DIGIT(b, 0); |
|
|
554 } |
|
|
555 |
|
|
556 return res; |
|
|
557 |
|
|
558 } /* end mp_add_d() */ |
|
|
559 |
|
|
560 /* }}} */ |
|
|
561 |
|
|
562 /* {{{ mp_sub_d(a, d, b) */ |
|
|
563 |
|
|
564 /* |
|
|
565 mp_sub_d(a, d, b) |
|
|
566 |
|
|
567 Compute the difference b = a - d, for a single digit d. Respects the |
|
|
568 sign of its subtrahend (single digits are unsigned anyway). |
|
|
569 */ |
|
|
570 |
|
|
571 mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b) |
|
|
572 { |
|
|
573 mp_err res; |
|
|
574 |
|
|
575 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
|
|
576 |
|
|
577 if((res = mp_copy(a, b)) != MP_OKAY) |
|
|
578 return res; |
|
|
579 |
|
|
580 if(SIGN(b) == MP_NEG) { |
|
|
581 if((res = s_mp_add_d(b, d)) != MP_OKAY) |
|
|
582 return res; |
|
|
583 |
|
|
584 } else if(s_mp_cmp_d(b, d) >= 0) { |
|
|
585 if((res = s_mp_sub_d(b, d)) != MP_OKAY) |
|
|
586 return res; |
|
|
587 |
|
|
588 } else { |
|
|
589 mp_neg(b, b); |
|
|
590 |
|
|
591 DIGIT(b, 0) = d - DIGIT(b, 0); |
|
|
592 SIGN(b) = MP_NEG; |
|
|
593 } |
|
|
594 |
|
|
595 if(s_mp_cmp_d(b, 0) == 0) |
|
|
596 SIGN(b) = MP_ZPOS; |
|
|
597 |
|
|
598 return MP_OKAY; |
|
|
599 |
|
|
600 } /* end mp_sub_d() */ |
|
|
601 |
|
|
602 /* }}} */ |
|
|
603 |
|
|
604 /* {{{ mp_mul_d(a, d, b) */ |
|
|
605 |
|
|
606 /* |
|
|
607 mp_mul_d(a, d, b) |
|
|
608 |
|
|
609 Compute the product b = a * d, for a single digit d. Respects the sign |
|
|
610 of its multiplicand (single digits are unsigned anyway) |
|
|
611 */ |
|
|
612 |
|
|
613 mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b) |
|
|
614 { |
|
|
615 mp_err res; |
|
|
616 |
|
|
617 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
|
|
618 |
|
|
619 if(d == 0) { |
|
|
620 mp_zero(b); |
|
|
621 return MP_OKAY; |
|
|
622 } |
|
|
623 |
|
|
624 if((res = mp_copy(a, b)) != MP_OKAY) |
|
|
625 return res; |
|
|
626 |
|
|
627 res = s_mp_mul_d(b, d); |
|
|
628 |
|
|
629 return res; |
|
|
630 |
|
|
631 } /* end mp_mul_d() */ |
|
|
632 |
|
|
633 /* }}} */ |
|
|
634 |
|
|
635 /* {{{ mp_mul_2(a, c) */ |
|
|
636 |
|
|
637 mp_err mp_mul_2(mp_int *a, mp_int *c) |
|
|
638 { |
|
|
639 mp_err res; |
|
|
640 |
|
|
641 ARGCHK(a != NULL && c != NULL, MP_BADARG); |
|
|
642 |
|
|
643 if((res = mp_copy(a, c)) != MP_OKAY) |
|
|
644 return res; |
|
|
645 |
|
|
646 return s_mp_mul_2(c); |
|
|
647 |
|
|
648 } /* end mp_mul_2() */ |
|
|
649 |
|
|
650 /* }}} */ |
|
|
651 |
|
|
652 /* {{{ mp_div_d(a, d, q, r) */ |
|
|
653 |
|
|
654 /* |
|
|
655 mp_div_d(a, d, q, r) |
|
|
656 |
|
|
657 Compute the quotient q = a / d and remainder r = a mod d, for a |
|
|
658 single digit d. Respects the sign of its divisor (single digits are |
|
|
659 unsigned anyway). |
|
|
660 */ |
|
|
661 |
|
|
662 mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r) |
|
|
663 { |
|
|
664 mp_err res; |
|
|
665 mp_digit rem; |
|
|
666 int pow; |
|
|
667 |
|
|
668 ARGCHK(a != NULL, MP_BADARG); |
|
|
669 |
|
|
670 if(d == 0) |
|
|
671 return MP_RANGE; |
|
|
672 |
|
|
673 /* Shortcut for powers of two ... */ |
|
|
674 if((pow = s_mp_ispow2d(d)) >= 0) { |
|
|
675 mp_digit mask; |
|
|
676 |
|
|
677 mask = (1 << pow) - 1; |
|
|
678 rem = DIGIT(a, 0) & mask; |
|
|
679 |
|
|
680 if(q) { |
|
|
681 mp_copy(a, q); |
|
|
682 s_mp_div_2d(q, pow); |
|
|
683 } |
|
|
684 |
|
|
685 if(r) |
|
|
686 *r = rem; |
|
|
687 |
|
|
688 return MP_OKAY; |
|
|
689 } |
|
|
690 |
|
|
691 /* |
|
|
692 If the quotient is actually going to be returned, we'll try to |
|
|
693 avoid hitting the memory allocator by copying the dividend into it |
|
|
694 and doing the division there. This can't be any _worse_ than |
|
|
695 always copying, and will sometimes be better (since it won't make |
|
|
696 another copy) |
|
|
697 |
|
|
698 If it's not going to be returned, we need to allocate a temporary |
|
|
699 to hold the quotient, which will just be discarded. |
|
|
700 */ |
|
|
701 if(q) { |
|
|
702 if((res = mp_copy(a, q)) != MP_OKAY) |
|
|
703 return res; |
|
|
704 |
|
|
705 res = s_mp_div_d(q, d, &rem); |
|
|
706 if(s_mp_cmp_d(q, 0) == MP_EQ) |
|
|
707 SIGN(q) = MP_ZPOS; |
|
|
708 |
|
|
709 } else { |
|
|
710 mp_int qp; |
|
|
711 |
|
|
712 if((res = mp_init_copy(&qp, a)) != MP_OKAY) |
|
|
713 return res; |
|
|
714 |
|
|
715 res = s_mp_div_d(&qp, d, &rem); |
|
|
716 if(s_mp_cmp_d(&qp, 0) == 0) |
|
|
717 SIGN(&qp) = MP_ZPOS; |
|
|
718 |
|
|
719 mp_clear(&qp); |
|
|
720 } |
|
|
721 |
|
|
722 if(r) |
|
|
723 *r = rem; |
|
|
724 |
|
|
725 return res; |
|
|
726 |
|
|
727 } /* end mp_div_d() */ |
|
|
728 |
|
|
729 /* }}} */ |
|
|
730 |
|
|
731 /* {{{ mp_div_2(a, c) */ |
|
|
732 |
|
|
733 /* |
|
|
734 mp_div_2(a, c) |
|
|
735 |
|
|
736 Compute c = a / 2, disregarding the remainder. |
|
|
737 */ |
|
|
738 |
|
|
739 mp_err mp_div_2(mp_int *a, mp_int *c) |
|
|
740 { |
|
|
741 mp_err res; |
|
|
742 |
|
|
743 ARGCHK(a != NULL && c != NULL, MP_BADARG); |
|
|
744 |
|
|
745 if((res = mp_copy(a, c)) != MP_OKAY) |
|
|
746 return res; |
|
|
747 |
|
|
748 s_mp_div_2(c); |
|
|
749 |
|
|
750 return MP_OKAY; |
|
|
751 |
|
|
752 } /* end mp_div_2() */ |
|
|
753 |
|
|
754 /* }}} */ |
|
|
755 |
|
|
756 /* {{{ mp_expt_d(a, d, b) */ |
|
|
757 |
|
|
758 mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c) |
|
|
759 { |
|
|
760 mp_int s, x; |
|
|
761 mp_err res; |
|
|
762 |
|
|
763 ARGCHK(a != NULL && c != NULL, MP_BADARG); |
|
|
764 |
|
|
765 if((res = mp_init(&s)) != MP_OKAY) |
|
|
766 return res; |
|
|
767 if((res = mp_init_copy(&x, a)) != MP_OKAY) |
|
|
768 goto X; |
|
|
769 |
|
|
770 DIGIT(&s, 0) = 1; |
|
|
771 |
|
|
772 while(d != 0) { |
|
|
773 if(d & 1) { |
|
|
774 if((res = s_mp_mul(&s, &x)) != MP_OKAY) |
|
|
775 goto CLEANUP; |
|
|
776 } |
|
|
777 |
|
|
778 d >>= 1; |
|
|
779 |
|
|
780 if((res = s_mp_sqr(&x)) != MP_OKAY) |
|
|
781 goto CLEANUP; |
|
|
782 } |
|
|
783 |
|
|
784 s_mp_exch(&s, c); |
|
|
785 |
|
|
786 CLEANUP: |
|
|
787 mp_clear(&x); |
|
|
788 X: |
|
|
789 mp_clear(&s); |
|
|
790 |
|
|
791 return res; |
|
|
792 |
|
|
793 } /* end mp_expt_d() */ |
|
|
794 |
|
|
795 /* }}} */ |
|
|
796 |
|
|
797 /* }}} */ |
|
|
798 |
|
|
799 /*------------------------------------------------------------------------*/ |
|
|
800 /* {{{ Full arithmetic */ |
|
|
801 |
|
|
802 /* {{{ mp_abs(a, b) */ |
|
|
803 |
|
|
804 /* |
|
|
805 mp_abs(a, b) |
|
|
806 |
|
|
807 Compute b = |a|. 'a' and 'b' may be identical. |
|
|
808 */ |
|
|
809 |
|
|
810 mp_err mp_abs(mp_int *a, mp_int *b) |
|
|
811 { |
|
|
812 mp_err res; |
|
|
813 |
|
|
814 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
|
|
815 |
|
|
816 if((res = mp_copy(a, b)) != MP_OKAY) |
|
|
817 return res; |
|
|
818 |
|
|
819 SIGN(b) = MP_ZPOS; |
|
|
820 |
|
|
821 return MP_OKAY; |
|
|
822 |
|
|
823 } /* end mp_abs() */ |
|
|
824 |
|
|
825 /* }}} */ |
|
|
826 |
|
|
827 /* {{{ mp_neg(a, b) */ |
|
|
828 |
|
|
829 /* |
|
|
830 mp_neg(a, b) |
|
|
831 |
|
|
832 Compute b = -a. 'a' and 'b' may be identical. |
|
|
833 */ |
|
|
834 |
|
|
835 mp_err mp_neg(mp_int *a, mp_int *b) |
|
|
836 { |
|
|
837 mp_err res; |
|
|
838 |
|
|
839 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
|
|
840 |
|
|
841 if((res = mp_copy(a, b)) != MP_OKAY) |
|
|
842 return res; |
|
|
843 |
|
|
844 if(s_mp_cmp_d(b, 0) == MP_EQ) |
|
|
845 SIGN(b) = MP_ZPOS; |
|
|
846 else |
|
|
847 SIGN(b) = (SIGN(b) == MP_NEG) ? MP_ZPOS : MP_NEG; |
|
|
848 |
|
|
849 return MP_OKAY; |
|
|
850 |
|
|
851 } /* end mp_neg() */ |
|
|
852 |
|
|
853 /* }}} */ |
|
|
854 |
|
|
855 /* {{{ mp_add(a, b, c) */ |
|
|
856 |
|
|
857 /* |
|
|
858 mp_add(a, b, c) |
|
|
859 |
|
|
860 Compute c = a + b. All parameters may be identical. |
|
|
861 */ |
|
|
862 |
|
|
863 mp_err mp_add(mp_int *a, mp_int *b, mp_int *c) |
|
|
864 { |
|
|
865 mp_err res; |
|
|
866 int cmp; |
|
|
867 |
|
|
868 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); |
|
|
869 |
|
|
870 if(SIGN(a) == SIGN(b)) { /* same sign: add values, keep sign */ |
|
|
871 |
|
|
872 /* Commutativity of addition lets us do this in either order, |
|
|
873 so we avoid having to use a temporary even if the result |
|
|
874 is supposed to replace the output |
|
|
875 */ |
|
|
876 if(c == b) { |
|
|
877 if((res = s_mp_add(c, a)) != MP_OKAY) |
|
|
878 return res; |
|
|
879 } else { |
|
|
880 if(c != a && (res = mp_copy(a, c)) != MP_OKAY) |
|
|
881 return res; |
|
|
882 |
|
|
883 if((res = s_mp_add(c, b)) != MP_OKAY) |
|
|
884 return res; |
|
|
885 } |
|
|
886 |
|
|
887 } else if((cmp = s_mp_cmp(a, b)) > 0) { /* different sign: a > b */ |
|
|
888 |
|
|
889 /* If the output is going to be clobbered, we will use a temporary |
|
|
890 variable; otherwise, we'll do it without touching the memory |
|
|
891 allocator at all, if possible |
|
|
892 */ |
|
|
893 if(c == b) { |
|
|
894 mp_int tmp; |
|
|
895 |
|
|
896 if((res = mp_init_copy(&tmp, a)) != MP_OKAY) |
|
|
897 return res; |
|
|
898 if((res = s_mp_sub(&tmp, b)) != MP_OKAY) { |
|
|
899 mp_clear(&tmp); |
|
|
900 return res; |
|
|
901 } |
|
|
902 |
|
|
903 s_mp_exch(&tmp, c); |
|
|
904 mp_clear(&tmp); |
|
|
905 |
|
|
906 } else { |
|
|
907 |
|
|
908 if(c != a && (res = mp_copy(a, c)) != MP_OKAY) |
|
|
909 return res; |
|
|
910 if((res = s_mp_sub(c, b)) != MP_OKAY) |
|
|
911 return res; |
|
|
912 |
|
|
913 } |
|
|
914 |
|
|
915 } else if(cmp == 0) { /* different sign, a == b */ |
|
|
916 |
|
|
917 mp_zero(c); |
|
|
918 return MP_OKAY; |
|
|
919 |
|
|
920 } else { /* different sign: a < b */ |
|
|
921 |
|
|
922 /* See above... */ |
|
|
923 if(c == a) { |
|
|
924 mp_int tmp; |
|
|
925 |
|
|
926 if((res = mp_init_copy(&tmp, b)) != MP_OKAY) |
|
|
927 return res; |
|
|
928 if((res = s_mp_sub(&tmp, a)) != MP_OKAY) { |
|
|
929 mp_clear(&tmp); |
|
|
930 return res; |
|
|
931 } |
|
|
932 |
|
|
933 s_mp_exch(&tmp, c); |
|
|
934 mp_clear(&tmp); |
|
|
935 |
|
|
936 } else { |
|
|
937 |
|
|
938 if(c != b && (res = mp_copy(b, c)) != MP_OKAY) |
|
|
939 return res; |
|
|
940 if((res = s_mp_sub(c, a)) != MP_OKAY) |
|
|
941 return res; |
|
|
942 |
|
|
943 } |
|
|
944 } |
|
|
945 |
|
|
946 if(USED(c) == 1 && DIGIT(c, 0) == 0) |
|
|
947 SIGN(c) = MP_ZPOS; |
|
|
948 |
|
|
949 return MP_OKAY; |
|
|
950 |
|
|
951 } /* end mp_add() */ |
|
|
952 |
|
|
953 /* }}} */ |
|
|
954 |
|
|
955 /* {{{ mp_sub(a, b, c) */ |
|
|
956 |
|
|
957 /* |
|
|
958 mp_sub(a, b, c) |
|
|
959 |
|
|
960 Compute c = a - b. All parameters may be identical. |
|
|
961 */ |
|
|
962 |
|
|
963 mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c) |
|
|
964 { |
|
|
965 mp_err res; |
|
|
966 int cmp; |
|
|
967 |
|
|
968 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); |
|
|
969 |
|
|
970 if(SIGN(a) != SIGN(b)) { |
|
|
971 if(c == a) { |
|
|
972 if((res = s_mp_add(c, b)) != MP_OKAY) |
|
|
973 return res; |
|
|
974 } else { |
|
|
975 if(c != b && ((res = mp_copy(b, c)) != MP_OKAY)) |
|
|
976 return res; |
|
|
977 if((res = s_mp_add(c, a)) != MP_OKAY) |
|
|
978 return res; |
|
|
979 SIGN(c) = SIGN(a); |
|
|
980 } |
|
|
981 |
|
|
982 } else if((cmp = s_mp_cmp(a, b)) > 0) { /* Same sign, a > b */ |
|
|
983 if(c == b) { |
|
|
984 mp_int tmp; |
|
|
985 |
|
|
986 if((res = mp_init_copy(&tmp, a)) != MP_OKAY) |
|
|
987 return res; |
|
|
988 if((res = s_mp_sub(&tmp, b)) != MP_OKAY) { |
|
|
989 mp_clear(&tmp); |
|
|
990 return res; |
|
|
991 } |
|
|
992 s_mp_exch(&tmp, c); |
|
|
993 mp_clear(&tmp); |
|
|
994 |
|
|
995 } else { |
|
|
996 if(c != a && ((res = mp_copy(a, c)) != MP_OKAY)) |
|
|
997 return res; |
|
|
998 |
|
|
999 if((res = s_mp_sub(c, b)) != MP_OKAY) |
|
|
1000 return res; |
|
|
1001 } |
|
|
1002 |
|
|
1003 } else if(cmp == 0) { /* Same sign, equal magnitude */ |
|
|
1004 mp_zero(c); |
|
|
1005 return MP_OKAY; |
|
|
1006 |
|
|
1007 } else { /* Same sign, b > a */ |
|
|
1008 if(c == a) { |
|
|
1009 mp_int tmp; |
|
|
1010 |
|
|
1011 if((res = mp_init_copy(&tmp, b)) != MP_OKAY) |
|
|
1012 return res; |
|
|
1013 |
|
|
1014 if((res = s_mp_sub(&tmp, a)) != MP_OKAY) { |
|
|
1015 mp_clear(&tmp); |
|
|
1016 return res; |
|
|
1017 } |
|
|
1018 s_mp_exch(&tmp, c); |
|
|
1019 mp_clear(&tmp); |
|
|
1020 |
|
|
1021 } else { |
|
|
1022 if(c != b && ((res = mp_copy(b, c)) != MP_OKAY)) |
|
|
1023 return res; |
|
|
1024 |
|
|
1025 if((res = s_mp_sub(c, a)) != MP_OKAY) |
|
|
1026 return res; |
|
|
1027 } |
|
|
1028 |
|
|
1029 SIGN(c) = !SIGN(b); |
|
|
1030 } |
|
|
1031 |
|
|
1032 if(USED(c) == 1 && DIGIT(c, 0) == 0) |
|
|
1033 SIGN(c) = MP_ZPOS; |
|
|
1034 |
|
|
1035 return MP_OKAY; |
|
|
1036 |
|
|
1037 } /* end mp_sub() */ |
|
|
1038 |
|
|
1039 /* }}} */ |
|
|
1040 |
|
|
1041 /* {{{ mp_mul(a, b, c) */ |
|
|
1042 |
|
|
1043 /* |
|
|
1044 mp_mul(a, b, c) |
|
|
1045 |
|
|
1046 Compute c = a * b. All parameters may be identical. |
|
|
1047 */ |
|
|
1048 |
|
|
1049 mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c) |
|
|
1050 { |
|
|
1051 mp_err res; |
|
|
1052 mp_sign sgn; |
|
|
1053 |
|
|
1054 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); |
|
|
1055 |
|
|
1056 sgn = (SIGN(a) == SIGN(b)) ? MP_ZPOS : MP_NEG; |
|
|
1057 |
|
|
1058 if(c == b) { |
|
|
1059 if((res = s_mp_mul(c, a)) != MP_OKAY) |
|
|
1060 return res; |
|
|
1061 |
|
|
1062 } else { |
|
|
1063 if((res = mp_copy(a, c)) != MP_OKAY) |
|
|
1064 return res; |
|
|
1065 |
|
|
1066 if((res = s_mp_mul(c, b)) != MP_OKAY) |
|
|
1067 return res; |
|
|
1068 } |
|
|
1069 |
|
|
1070 if(sgn == MP_ZPOS || s_mp_cmp_d(c, 0) == MP_EQ) |
|
|
1071 SIGN(c) = MP_ZPOS; |
|
|
1072 else |
|
|
1073 SIGN(c) = sgn; |
|
|
1074 |
|
|
1075 return MP_OKAY; |
|
|
1076 |
|
|
1077 } /* end mp_mul() */ |
|
|
1078 |
|
|
1079 /* }}} */ |
|
|
1080 |
|
|
1081 /* {{{ mp_mul_2d(a, d, c) */ |
|
|
1082 |
|
|
1083 /* |
|
|
1084 mp_mul_2d(a, d, c) |
|
|
1085 |
|
|
1086 Compute c = a * 2^d. a may be the same as c. |
|
|
1087 */ |
|
|
1088 |
|
|
1089 mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c) |
|
|
1090 { |
|
|
1091 mp_err res; |
|
|
1092 |
|
|
1093 ARGCHK(a != NULL && c != NULL, MP_BADARG); |
|
|
1094 |
|
|
1095 if((res = mp_copy(a, c)) != MP_OKAY) |
|
|
1096 return res; |
|
|
1097 |
|
|
1098 if(d == 0) |
|
|
1099 return MP_OKAY; |
|
|
1100 |
|
|
1101 return s_mp_mul_2d(c, d); |
|
|
1102 |
|
|
1103 } /* end mp_mul() */ |
|
|
1104 |
|
|
1105 /* }}} */ |
|
|
1106 |
|
|
1107 /* {{{ mp_sqr(a, b) */ |
|
|
1108 |
|
|
1109 #if MP_SQUARE |
|
|
1110 mp_err mp_sqr(mp_int *a, mp_int *b) |
|
|
1111 { |
|
|
1112 mp_err res; |
|
|
1113 |
|
|
1114 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
|
|
1115 |
|
|
1116 if((res = mp_copy(a, b)) != MP_OKAY) |
|
|
1117 return res; |
|
|
1118 |
|
|
1119 if((res = s_mp_sqr(b)) != MP_OKAY) |
|
|
1120 return res; |
|
|
1121 |
|
|
1122 SIGN(b) = MP_ZPOS; |
|
|
1123 |
|
|
1124 return MP_OKAY; |
|
|
1125 |
|
|
1126 } /* end mp_sqr() */ |
|
|
1127 #endif |
|
|
1128 |
|
|
1129 /* }}} */ |
|
|
1130 |
|
|
1131 /* {{{ mp_div(a, b, q, r) */ |
|
|
1132 |
|
|
1133 /* |
|
|
1134 mp_div(a, b, q, r) |
|
|
1135 |
|
|
1136 Compute q = a / b and r = a mod b. Input parameters may be re-used |
|
|
1137 as output parameters. If q or r is NULL, that portion of the |
|
|
1138 computation will be discarded (although it will still be computed) |
|
|
1139 |
|
|
1140 Pay no attention to the hacker behind the curtain. |
|
|
1141 */ |
|
|
1142 |
|
|
1143 mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r) |
|
|
1144 { |
|
|
1145 mp_err res; |
|
|
1146 mp_int qtmp, rtmp; |
|
|
1147 int cmp; |
|
|
1148 |
|
|
1149 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
|
|
1150 |
|
|
1151 if(mp_cmp_z(b) == MP_EQ) |
|
|
1152 return MP_RANGE; |
|
|
1153 |
|
|
1154 /* If a <= b, we can compute the solution without division, and |
|
|
1155 avoid any memory allocation |
|
|
1156 */ |
|
|
1157 if((cmp = s_mp_cmp(a, b)) < 0) { |
|
|
1158 if(r) { |
|
|
1159 if((res = mp_copy(a, r)) != MP_OKAY) |
|
|
1160 return res; |
|
|
1161 } |
|
|
1162 |
|
|
1163 if(q) |
|
|
1164 mp_zero(q); |
|
|
1165 |
|
|
1166 return MP_OKAY; |
|
|
1167 |
|
|
1168 } else if(cmp == 0) { |
|
|
1169 |
|
|
1170 /* Set quotient to 1, with appropriate sign */ |
|
|
1171 if(q) { |
|
|
1172 int qneg = (SIGN(a) != SIGN(b)); |
|
|
1173 |
|
|
1174 mp_set(q, 1); |
|
|
1175 if(qneg) |
|
|
1176 SIGN(q) = MP_NEG; |
|
|
1177 } |
|
|
1178 |
|
|
1179 if(r) |
|
|
1180 mp_zero(r); |
|
|
1181 |
|
|
1182 return MP_OKAY; |
|
|
1183 } |
|
|
1184 |
|
|
1185 /* If we get here, it means we actually have to do some division */ |
|
|
1186 |
|
|
1187 /* Set up some temporaries... */ |
|
|
1188 if((res = mp_init_copy(&qtmp, a)) != MP_OKAY) |
|
|
1189 return res; |
|
|
1190 if((res = mp_init_copy(&rtmp, b)) != MP_OKAY) |
|
|
1191 goto CLEANUP; |
|
|
1192 |
|
|
1193 if((res = s_mp_div(&qtmp, &rtmp)) != MP_OKAY) |
|
|
1194 goto CLEANUP; |
|
|
1195 |
|
|
1196 /* Compute the signs for the output */ |
|
|
1197 SIGN(&rtmp) = SIGN(a); /* Sr = Sa */ |
|
|
1198 if(SIGN(a) == SIGN(b)) |
|
|
1199 SIGN(&qtmp) = MP_ZPOS; /* Sq = MP_ZPOS if Sa = Sb */ |
|
|
1200 else |
|
|
1201 SIGN(&qtmp) = MP_NEG; /* Sq = MP_NEG if Sa != Sb */ |
|
|
1202 |
|
|
1203 if(s_mp_cmp_d(&qtmp, 0) == MP_EQ) |
|
|
1204 SIGN(&qtmp) = MP_ZPOS; |
|
|
1205 if(s_mp_cmp_d(&rtmp, 0) == MP_EQ) |
|
|
1206 SIGN(&rtmp) = MP_ZPOS; |
|
|
1207 |
|
|
1208 /* Copy output, if it is needed */ |
|
|
1209 if(q) |
|
|
1210 s_mp_exch(&qtmp, q); |
|
|
1211 |
|
|
1212 if(r) |
|
|
1213 s_mp_exch(&rtmp, r); |
|
|
1214 |
|
|
1215 CLEANUP: |
|
|
1216 mp_clear(&rtmp); |
|
|
1217 mp_clear(&qtmp); |
|
|
1218 |
|
|
1219 return res; |
|
|
1220 |
|
|
1221 } /* end mp_div() */ |
|
|
1222 |
|
|
1223 /* }}} */ |
|
|
1224 |
|
|
1225 /* {{{ mp_div_2d(a, d, q, r) */ |
|
|
1226 |
|
|
1227 mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r) |
|
|
1228 { |
|
|
1229 mp_err res; |
|
|
1230 |
|
|
1231 ARGCHK(a != NULL, MP_BADARG); |
|
|
1232 |
|
|
1233 if(q) { |
|
|
1234 if((res = mp_copy(a, q)) != MP_OKAY) |
|
|
1235 return res; |
|
|
1236 |
|
|
1237 s_mp_div_2d(q, d); |
|
|
1238 } |
|
|
1239 |
|
|
1240 if(r) { |
|
|
1241 if((res = mp_copy(a, r)) != MP_OKAY) |
|
|
1242 return res; |
|
|
1243 |
|
|
1244 s_mp_mod_2d(r, d); |
|
|
1245 } |
|
|
1246 |
|
|
1247 return MP_OKAY; |
|
|
1248 |
|
|
1249 } /* end mp_div_2d() */ |
|
|
1250 |
|
|
1251 /* }}} */ |
|
|
1252 |
|
|
1253 /* {{{ mp_expt(a, b, c) */ |
|
|
1254 |
|
|
1255 /* |
|
|
1256 mp_expt(a, b, c) |
|
|
1257 |
|
|
1258 Compute c = a ** b, that is, raise a to the b power. Uses a |
|
|
1259 standard iterative square-and-multiply technique. |
|
|
1260 */ |
|
|
1261 |
|
|
1262 mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c) |
|
|
1263 { |
|
|
1264 mp_int s, x; |
|
|
1265 mp_err res; |
|
|
1266 mp_digit d; |
|
|
1267 int dig, bit; |
|
|
1268 |
|
|
1269 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); |
|
|
1270 |
|
|
1271 if(mp_cmp_z(b) < 0) |
|
|
1272 return MP_RANGE; |
|
|
1273 |
|
|
1274 if((res = mp_init(&s)) != MP_OKAY) |
|
|
1275 return res; |
|
|
1276 |
|
|
1277 mp_set(&s, 1); |
|
|
1278 |
|
|
1279 if((res = mp_init_copy(&x, a)) != MP_OKAY) |
|
|
1280 goto X; |
|
|
1281 |
|
|
1282 /* Loop over low-order digits in ascending order */ |
|
|
1283 for(dig = 0; dig < (USED(b) - 1); dig++) { |
|
|
1284 d = DIGIT(b, dig); |
|
|
1285 |
|
|
1286 /* Loop over bits of each non-maximal digit */ |
|
|
1287 for(bit = 0; bit < DIGIT_BIT; bit++) { |
|
|
1288 if(d & 1) { |
|
|
1289 if((res = s_mp_mul(&s, &x)) != MP_OKAY) |
|
|
1290 goto CLEANUP; |
|
|
1291 } |
|
|
1292 |
|
|
1293 d >>= 1; |
|
|
1294 |
|
|
1295 if((res = s_mp_sqr(&x)) != MP_OKAY) |
|
|
1296 goto CLEANUP; |
|
|
1297 } |
|
|
1298 } |
|
|
1299 |
|
|
1300 /* Consider now the last digit... */ |
|
|
1301 d = DIGIT(b, dig); |
|
|
1302 |
|
|
1303 while(d) { |
|
|
1304 if(d & 1) { |
|
|
1305 if((res = s_mp_mul(&s, &x)) != MP_OKAY) |
|
|
1306 goto CLEANUP; |
|
|
1307 } |
|
|
1308 |
|
|
1309 d >>= 1; |
|
|
1310 |
|
|
1311 if((res = s_mp_sqr(&x)) != MP_OKAY) |
|
|
1312 goto CLEANUP; |
|
|
1313 } |
|
|
1314 |
|
|
1315 if(mp_iseven(b)) |
|
|
1316 SIGN(&s) = SIGN(a); |
|
|
1317 |
|
|
1318 res = mp_copy(&s, c); |
|
|
1319 |
|
|
1320 CLEANUP: |
|
|
1321 mp_clear(&x); |
|
|
1322 X: |
|
|
1323 mp_clear(&s); |
|
|
1324 |
|
|
1325 return res; |
|
|
1326 |
|
|
1327 } /* end mp_expt() */ |
|
|
1328 |
|
|
1329 /* }}} */ |
|
|
1330 |
|
|
1331 /* {{{ mp_2expt(a, k) */ |
|
|
1332 |
|
|
1333 /* Compute a = 2^k */ |
|
|
1334 |
|
|
1335 mp_err mp_2expt(mp_int *a, mp_digit k) |
|
|
1336 { |
|
|
1337 ARGCHK(a != NULL, MP_BADARG); |
|
|
1338 |
|
|
1339 return s_mp_2expt(a, k); |
|
|
1340 |
|
|
1341 } /* end mp_2expt() */ |
|
|
1342 |
|
|
1343 /* }}} */ |
|
|
1344 |
|
|
1345 /* {{{ mp_mod(a, m, c) */ |
|
|
1346 |
|
|
1347 /* |
|
|
1348 mp_mod(a, m, c) |
|
|
1349 |
|
|
1350 Compute c = a (mod m). Result will always be 0 <= c < m. |
|
|
1351 */ |
|
|
1352 |
|
|
1353 mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c) |
|
|
1354 { |
|
|
1355 mp_err res; |
|
|
1356 int mag; |
|
|
1357 |
|
|
1358 ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG); |
|
|
1359 |
|
|
1360 if(SIGN(m) == MP_NEG) |
|
|
1361 return MP_RANGE; |
|
|
1362 |
|
|
1363 /* |
|
|
1364 If |a| > m, we need to divide to get the remainder and take the |
|
|
1365 absolute value. |
|
|
1366 |
|
|
1367 If |a| < m, we don't need to do any division, just copy and adjust |
|
|
1368 the sign (if a is negative). |
|
|
1369 |
|
|
1370 If |a| == m, we can simply set the result to zero. |
|
|
1371 |
|
|
1372 This order is intended to minimize the average path length of the |
|
|
1373 comparison chain on common workloads -- the most frequent cases are |
|
|
1374 that |a| != m, so we do those first. |
|
|
1375 */ |
|
|
1376 if((mag = s_mp_cmp(a, m)) > 0) { |
|
|
1377 if((res = mp_div(a, m, NULL, c)) != MP_OKAY) |
|
|
1378 return res; |
|
|
1379 |
|
|
1380 if(SIGN(c) == MP_NEG) { |
|
|
1381 if((res = mp_add(c, m, c)) != MP_OKAY) |
|
|
1382 return res; |
|
|
1383 } |
|
|
1384 |
|
|
1385 } else if(mag < 0) { |
|
|
1386 if((res = mp_copy(a, c)) != MP_OKAY) |
|
|
1387 return res; |
|
|
1388 |
|
|
1389 if(mp_cmp_z(a) < 0) { |
|
|
1390 if((res = mp_add(c, m, c)) != MP_OKAY) |
|
|
1391 return res; |
|
|
1392 |
|
|
1393 } |
|
|
1394 |
|
|
1395 } else { |
|
|
1396 mp_zero(c); |
|
|
1397 |
|
|
1398 } |
|
|
1399 |
|
|
1400 return MP_OKAY; |
|
|
1401 |
|
|
1402 } /* end mp_mod() */ |
|
|
1403 |
|
|
1404 /* }}} */ |
|
|
1405 |
|
|
1406 /* {{{ mp_mod_d(a, d, c) */ |
|
|
1407 |
|
|
1408 /* |
|
|
1409 mp_mod_d(a, d, c) |
|
|
1410 |
|
|
1411 Compute c = a (mod d). Result will always be 0 <= c < d |
|
|
1412 */ |
|
|
1413 mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c) |
|
|
1414 { |
|
|
1415 mp_err res; |
|
|
1416 mp_digit rem; |
|
|
1417 |
|
|
1418 ARGCHK(a != NULL && c != NULL, MP_BADARG); |
|
|
1419 |
|
|
1420 if(s_mp_cmp_d(a, d) > 0) { |
|
|
1421 if((res = mp_div_d(a, d, NULL, &rem)) != MP_OKAY) |
|
|
1422 return res; |
|
|
1423 |
|
|
1424 } else { |
|
|
1425 if(SIGN(a) == MP_NEG) |
|
|
1426 rem = d - DIGIT(a, 0); |
|
|
1427 else |
|
|
1428 rem = DIGIT(a, 0); |
|
|
1429 } |
|
|
1430 |
|
|
1431 if(c) |
|
|
1432 *c = rem; |
|
|
1433 |
|
|
1434 return MP_OKAY; |
|
|
1435 |
|
|
1436 } /* end mp_mod_d() */ |
|
|
1437 |
|
|
1438 /* }}} */ |
|
|
1439 |
|
|
1440 /* {{{ mp_sqrt(a, b) */ |
|
|
1441 |
|
|
1442 /* |
|
|
1443 mp_sqrt(a, b) |
|
|
1444 |
|
|
1445 Compute the integer square root of a, and store the result in b. |
|
|
1446 Uses an integer-arithmetic version of Newton's iterative linear |
|
|
1447 approximation technique to determine this value; the result has the |
|
|
1448 following two properties: |
|
|
1449 |
|
|
1450 b^2 <= a |
|
|
1451 (b+1)^2 >= a |
|
|
1452 |
|
|
1453 It is a range error to pass a negative value. |
|
|
1454 */ |
|
|
1455 mp_err mp_sqrt(mp_int *a, mp_int *b) |
|
|
1456 { |
|
|
1457 mp_int x, t; |
|
|
1458 mp_err res; |
|
|
1459 |
|
|
1460 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
|
|
1461 |
|
|
1462 /* Cannot take square root of a negative value */ |
|
|
1463 if(SIGN(a) == MP_NEG) |
|
|
1464 return MP_RANGE; |
|
|
1465 |
|
|
1466 /* Special cases for zero and one, trivial */ |
|
|
1467 if(mp_cmp_d(a, 0) == MP_EQ || mp_cmp_d(a, 1) == MP_EQ) |
|
|
1468 return mp_copy(a, b); |
|
|
1469 |
|
|
1470 /* Initialize the temporaries we'll use below */ |
|
|
1471 if((res = mp_init_size(&t, USED(a))) != MP_OKAY) |
|
|
1472 return res; |
|
|
1473 |
|
|
1474 /* Compute an initial guess for the iteration as a itself */ |
|
|
1475 if((res = mp_init_copy(&x, a)) != MP_OKAY) |
|
|
1476 goto X; |
|
|
1477 |
|
|
1478 s_mp_rshd(&x, (USED(&x)/2)+1); |
|
|
1479 mp_add_d(&x, 1, &x); |
|
|
1480 |
|
|
1481 for(;;) { |
|
|
1482 /* t = (x * x) - a */ |
|
|
1483 mp_copy(&x, &t); /* can't fail, t is big enough for original x */ |
|
|
1484 if((res = mp_sqr(&t, &t)) != MP_OKAY || |
|
|
1485 (res = mp_sub(&t, a, &t)) != MP_OKAY) |
|
|
1486 goto CLEANUP; |
|
|
1487 |
|
|
1488 /* t = t / 2x */ |
|
|
1489 s_mp_mul_2(&x); |
|
|
1490 if((res = mp_div(&t, &x, &t, NULL)) != MP_OKAY) |
|
|
1491 goto CLEANUP; |
|
|
1492 s_mp_div_2(&x); |
|
|
1493 |
|
|
1494 /* Terminate the loop, if the quotient is zero */ |
|
|
1495 if(mp_cmp_z(&t) == MP_EQ) |
|
|
1496 break; |
|
|
1497 |
|
|
1498 /* x = x - t */ |
|
|
1499 if((res = mp_sub(&x, &t, &x)) != MP_OKAY) |
|
|
1500 goto CLEANUP; |
|
|
1501 |
|
|
1502 } |
|
|
1503 |
|
|
1504 /* Copy result to output parameter */ |
|
|
1505 mp_sub_d(&x, 1, &x); |
|
|
1506 s_mp_exch(&x, b); |
|
|
1507 |
|
|
1508 CLEANUP: |
|
|
1509 mp_clear(&x); |
|
|
1510 X: |
|
|
1511 mp_clear(&t); |
|
|
1512 |
|
|
1513 return res; |
|
|
1514 |
|
|
1515 } /* end mp_sqrt() */ |
|
|
1516 |
|
|
1517 /* }}} */ |
|
|
1518 |
|
|
1519 /* }}} */ |
|
|
1520 |
|
|
1521 /*------------------------------------------------------------------------*/ |
|
|
1522 /* {{{ Modular arithmetic */ |
|
|
1523 |
|
|
1524 #if MP_MODARITH |
|
|
1525 /* {{{ mp_addmod(a, b, m, c) */ |
|
|
1526 |
|
|
1527 /* |
|
|
1528 mp_addmod(a, b, m, c) |
|
|
1529 |
|
|
1530 Compute c = (a + b) mod m |
|
|
1531 */ |
|
|
1532 |
|
|
1533 mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) |
|
|
1534 { |
|
|
1535 mp_err res; |
|
|
1536 |
|
|
1537 ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG); |
|
|
1538 |
|
|
1539 if((res = mp_add(a, b, c)) != MP_OKAY) |
|
|
1540 return res; |
|
|
1541 if((res = mp_mod(c, m, c)) != MP_OKAY) |
|
|
1542 return res; |
|
|
1543 |
|
|
1544 return MP_OKAY; |
|
|
1545 |
|
|
1546 } |
|
|
1547 |
|
|
1548 /* }}} */ |
|
|
1549 |
|
|
1550 /* {{{ mp_submod(a, b, m, c) */ |
|
|
1551 |
|
|
1552 /* |
|
|
1553 mp_submod(a, b, m, c) |
|
|
1554 |
|
|
1555 Compute c = (a - b) mod m |
|
|
1556 */ |
|
|
1557 |
|
|
1558 mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) |
|
|
1559 { |
|
|
1560 mp_err res; |
|
|
1561 |
|
|
1562 ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG); |
|
|
1563 |
|
|
1564 if((res = mp_sub(a, b, c)) != MP_OKAY) |
|
|
1565 return res; |
|
|
1566 if((res = mp_mod(c, m, c)) != MP_OKAY) |
|
|
1567 return res; |
|
|
1568 |
|
|
1569 return MP_OKAY; |
|
|
1570 |
|
|
1571 } |
|
|
1572 |
|
|
1573 /* }}} */ |
|
|
1574 |
|
|
1575 /* {{{ mp_mulmod(a, b, m, c) */ |
|
|
1576 |
|
|
1577 /* |
|
|
1578 mp_mulmod(a, b, m, c) |
|
|
1579 |
|
|
1580 Compute c = (a * b) mod m |
|
|
1581 */ |
|
|
1582 |
|
|
1583 mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) |
|
|
1584 { |
|
|
1585 mp_err res; |
|
|
1586 |
|
|
1587 ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG); |
|
|
1588 |
|
|
1589 if((res = mp_mul(a, b, c)) != MP_OKAY) |
|
|
1590 return res; |
|
|
1591 if((res = mp_mod(c, m, c)) != MP_OKAY) |
|
|
1592 return res; |
|
|
1593 |
|
|
1594 return MP_OKAY; |
|
|
1595 |
|
|
1596 } |
|
|
1597 |
|
|
1598 /* }}} */ |
|
|
1599 |
|
|
1600 /* {{{ mp_sqrmod(a, m, c) */ |
|
|
1601 |
|
|
1602 #if MP_SQUARE |
|
|
1603 mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c) |
|
|
1604 { |
|
|
1605 mp_err res; |
|
|
1606 |
|
|
1607 ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG); |
|
|
1608 |
|
|
1609 if((res = mp_sqr(a, c)) != MP_OKAY) |
|
|
1610 return res; |
|
|
1611 if((res = mp_mod(c, m, c)) != MP_OKAY) |
|
|
1612 return res; |
|
|
1613 |
|
|
1614 return MP_OKAY; |
|
|
1615 |
|
|
1616 } /* end mp_sqrmod() */ |
|
|
1617 #endif |
|
|
1618 |
|
|
1619 /* }}} */ |
|
|
1620 |
|
|
1621 /* {{{ mp_exptmod(a, b, m, c) */ |
|
|
1622 |
|
|
1623 /* |
|
|
1624 mp_exptmod(a, b, m, c) |
|
|
1625 |
|
|
1626 Compute c = (a ** b) mod m. Uses a standard square-and-multiply |
|
|
1627 method with modular reductions at each step. (This is basically the |
|
|
1628 same code as mp_expt(), except for the addition of the reductions) |
|
|
1629 |
|
|
1630 The modular reductions are done using Barrett's algorithm (see |
|
|
1631 s_mp_reduce() below for details) |
|
|
1632 */ |
|
|
1633 |
|
|
1634 mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) |
|
|
1635 { |
|
|
1636 mp_int s, x, mu; |
|
|
1637 mp_err res; |
|
|
1638 mp_digit d, *db = DIGITS(b); |
|
|
1639 mp_size ub = USED(b); |
|
|
1640 int dig, bit; |
|
|
1641 |
|
|
1642 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); |
|
|
1643 |
|
|
1644 if(mp_cmp_z(b) < 0 || mp_cmp_z(m) <= 0) |
|
|
1645 return MP_RANGE; |
|
|
1646 |
|
|
1647 if((res = mp_init(&s)) != MP_OKAY) |
|
|
1648 return res; |
|
|
1649 if((res = mp_init_copy(&x, a)) != MP_OKAY) |
|
|
1650 goto X; |
|
|
1651 if((res = mp_mod(&x, m, &x)) != MP_OKAY || |
|
|
1652 (res = mp_init(&mu)) != MP_OKAY) |
|
|
1653 goto MU; |
|
|
1654 |
|
|
1655 mp_set(&s, 1); |
|
|
1656 |
|
|
1657 /* mu = b^2k / m */ |
|
|
1658 s_mp_add_d(&mu, 1); |
|
|
1659 s_mp_lshd(&mu, 2 * USED(m)); |
|
|
1660 if((res = mp_div(&mu, m, &mu, NULL)) != MP_OKAY) |
|
|
1661 goto CLEANUP; |
|
|
1662 |
|
|
1663 /* Loop over digits of b in ascending order, except highest order */ |
|
|
1664 for(dig = 0; dig < (ub - 1); dig++) { |
|
|
1665 d = *db++; |
|
|
1666 |
|
|
1667 /* Loop over the bits of the lower-order digits */ |
|
|
1668 for(bit = 0; bit < DIGIT_BIT; bit++) { |
|
|
1669 if(d & 1) { |
|
|
1670 if((res = s_mp_mul(&s, &x)) != MP_OKAY) |
|
|
1671 goto CLEANUP; |
|
|
1672 if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY) |
|
|
1673 goto CLEANUP; |
|
|
1674 } |
|
|
1675 |
|
|
1676 d >>= 1; |
|
|
1677 |
|
|
1678 if((res = s_mp_sqr(&x)) != MP_OKAY) |
|
|
1679 goto CLEANUP; |
|
|
1680 if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY) |
|
|
1681 goto CLEANUP; |
|
|
1682 } |
|
|
1683 } |
|
|
1684 |
|
|
1685 /* Now do the last digit... */ |
|
|
1686 d = *db; |
|
|
1687 |
|
|
1688 while(d) { |
|
|
1689 if(d & 1) { |
|
|
1690 if((res = s_mp_mul(&s, &x)) != MP_OKAY) |
|
|
1691 goto CLEANUP; |
|
|
1692 if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY) |
|
|
1693 goto CLEANUP; |
|
|
1694 } |
|
|
1695 |
|
|
1696 d >>= 1; |
|
|
1697 |
|
|
1698 if((res = s_mp_sqr(&x)) != MP_OKAY) |
|
|
1699 goto CLEANUP; |
|
|
1700 if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY) |
|
|
1701 goto CLEANUP; |
|
|
1702 } |
|
|
1703 |
|
|
1704 s_mp_exch(&s, c); |
|
|
1705 |
|
|
1706 CLEANUP: |
|
|
1707 mp_clear(&mu); |
|
|
1708 MU: |
|
|
1709 mp_clear(&x); |
|
|
1710 X: |
|
|
1711 mp_clear(&s); |
|
|
1712 |
|
|
1713 return res; |
|
|
1714 |
|
|
1715 } /* end mp_exptmod() */ |
|
|
1716 |
|
|
1717 /* }}} */ |
|
|
1718 |
|
|
1719 /* {{{ mp_exptmod_d(a, d, m, c) */ |
|
|
1720 |
|
|
1721 mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c) |
|
|
1722 { |
|
|
1723 mp_int s, x; |
|
|
1724 mp_err res; |
|
|
1725 |
|
|
1726 ARGCHK(a != NULL && c != NULL, MP_BADARG); |
|
|
1727 |
|
|
1728 if((res = mp_init(&s)) != MP_OKAY) |
|
|
1729 return res; |
|
|
1730 if((res = mp_init_copy(&x, a)) != MP_OKAY) |
|
|
1731 goto X; |
|
|
1732 |
|
|
1733 mp_set(&s, 1); |
|
|
1734 |
|
|
1735 while(d != 0) { |
|
|
1736 if(d & 1) { |
|
|
1737 if((res = s_mp_mul(&s, &x)) != MP_OKAY || |
|
|
1738 (res = mp_mod(&s, m, &s)) != MP_OKAY) |
|
|
1739 goto CLEANUP; |
|
|
1740 } |
|
|
1741 |
|
|
1742 d /= 2; |
|
|
1743 |
|
|
1744 if((res = s_mp_sqr(&x)) != MP_OKAY || |
|
|
1745 (res = mp_mod(&x, m, &x)) != MP_OKAY) |
|
|
1746 goto CLEANUP; |
|
|
1747 } |
|
|
1748 |
|
|
1749 s_mp_exch(&s, c); |
|
|
1750 |
|
|
1751 CLEANUP: |
|
|
1752 mp_clear(&x); |
|
|
1753 X: |
|
|
1754 mp_clear(&s); |
|
|
1755 |
|
|
1756 return res; |
|
|
1757 |
|
|
1758 } /* end mp_exptmod_d() */ |
|
|
1759 |
|
|
1760 /* }}} */ |
|
|
1761 #endif /* if MP_MODARITH */ |
|
|
1762 |
|
|
1763 /* }}} */ |
|
|
1764 |
|
|
1765 /*------------------------------------------------------------------------*/ |
|
|
1766 /* {{{ Comparison functions */ |
|
|
1767 |
|
|
1768 /* {{{ mp_cmp_z(a) */ |
|
|
1769 |
|
|
1770 /* |
|
|
1771 mp_cmp_z(a) |
|
|
1772 |
|
|
1773 Compare a <=> 0. Returns <0 if a<0, 0 if a=0, >0 if a>0. |
|
|
1774 */ |
|
|
1775 |
|
|
1776 int mp_cmp_z(mp_int *a) |
|
|
1777 { |
|
|
1778 if(SIGN(a) == MP_NEG) |
|
|
1779 return MP_LT; |
|
|
1780 else if(USED(a) == 1 && DIGIT(a, 0) == 0) |
|
|
1781 return MP_EQ; |
|
|
1782 else |
|
|
1783 return MP_GT; |
|
|
1784 |
|
|
1785 } /* end mp_cmp_z() */ |
|
|
1786 |
|
|
1787 /* }}} */ |
|
|
1788 |
|
|
1789 /* {{{ mp_cmp_d(a, d) */ |
|
|
1790 |
|
|
1791 /* |
|
|
1792 mp_cmp_d(a, d) |
|
|
1793 |
|
|
1794 Compare a <=> d. Returns <0 if a<d, 0 if a=d, >0 if a>d |
|
|
1795 */ |
|
|
1796 |
|
|
1797 int mp_cmp_d(mp_int *a, mp_digit d) |
|
|
1798 { |
|
|
1799 ARGCHK(a != NULL, MP_EQ); |
|
|
1800 |
|
|
1801 if(SIGN(a) == MP_NEG) |
|
|
1802 return MP_LT; |
|
|
1803 |
|
|
1804 return s_mp_cmp_d(a, d); |
|
|
1805 |
|
|
1806 } /* end mp_cmp_d() */ |
|
|
1807 |
|
|
1808 /* }}} */ |
|
|
1809 |
|
|
1810 /* {{{ mp_cmp(a, b) */ |
|
|
1811 |
|
|
1812 int mp_cmp(mp_int *a, mp_int *b) |
|
|
1813 { |
|
|
1814 ARGCHK(a != NULL && b != NULL, MP_EQ); |
|
|
1815 |
|
|
1816 if(SIGN(a) == SIGN(b)) { |
|
|
1817 int mag; |
|
|
1818 |
|
|
1819 if((mag = s_mp_cmp(a, b)) == MP_EQ) |
|
|
1820 return MP_EQ; |
|
|
1821 |
|
|
1822 if(SIGN(a) == MP_ZPOS) |
|
|
1823 return mag; |
|
|
1824 else |
|
|
1825 return -mag; |
|
|
1826 |
|
|
1827 } else if(SIGN(a) == MP_ZPOS) { |
|
|
1828 return MP_GT; |
|
|
1829 } else { |
|
|
1830 return MP_LT; |
|
|
1831 } |
|
|
1832 |
|
|
1833 } /* end mp_cmp() */ |
|
|
1834 |
|
|
1835 /* }}} */ |
|
|
1836 |
|
|
1837 /* {{{ mp_cmp_mag(a, b) */ |
|
|
1838 |
|
|
1839 /* |
|
|
1840 mp_cmp_mag(a, b) |
|
|
1841 |
|
|
1842 Compares |a| <=> |b|, and returns an appropriate comparison result |
|
|
1843 */ |
|
|
1844 |
|
|
1845 int mp_cmp_mag(mp_int *a, mp_int *b) |
|
|
1846 { |
|
|
1847 ARGCHK(a != NULL && b != NULL, MP_EQ); |
|
|
1848 |
|
|
1849 return s_mp_cmp(a, b); |
|
|
1850 |
|
|
1851 } /* end mp_cmp_mag() */ |
|
|
1852 |
|
|
1853 /* }}} */ |
|
|
1854 |
|
|
1855 /* {{{ mp_cmp_int(a, z) */ |
|
|
1856 |
|
|
1857 /* |
|
|
1858 This just converts z to an mp_int, and uses the existing comparison |
|
|
1859 routines. This is sort of inefficient, but it's not clear to me how |
|
|
1860 frequently this wil get used anyway. For small positive constants, |
|
|
1861 you can always use mp_cmp_d(), and for zero, there is mp_cmp_z(). |
|
|
1862 */ |
|
|
1863 int mp_cmp_int(mp_int *a, long z) |
|
|
1864 { |
|
|
1865 mp_int tmp; |
|
|
1866 int out; |
|
|
1867 |
|
|
1868 ARGCHK(a != NULL, MP_EQ); |
|
|
1869 |
|
|
1870 mp_init(&tmp); mp_set_int(&tmp, z); |
|
|
1871 out = mp_cmp(a, &tmp); |
|
|
1872 mp_clear(&tmp); |
|
|
1873 |
|
|
1874 return out; |
|
|
1875 |
|
|
1876 } /* end mp_cmp_int() */ |
|
|
1877 |
|
|
1878 /* }}} */ |
|
|
1879 |
|
|
1880 /* {{{ mp_isodd(a) */ |
|
|
1881 |
|
|
1882 /* |
|
|
1883 mp_isodd(a) |
|
|
1884 |
|
|
1885 Returns a true (non-zero) value if a is odd, false (zero) otherwise. |
|
|
1886 */ |
|
|
1887 int mp_isodd(mp_int *a) |
|
|
1888 { |
|
|
1889 ARGCHK(a != NULL, 0); |
|
|
1890 |
|
|
1891 return (DIGIT(a, 0) & 1); |
|
|
1892 |
|
|
1893 } /* end mp_isodd() */ |
|
|
1894 |
|
|
1895 /* }}} */ |
|
|
1896 |
|
|
1897 /* {{{ mp_iseven(a) */ |
|
|
1898 |
|
|
1899 int mp_iseven(mp_int *a) |
|
|
1900 { |
|
|
1901 return !mp_isodd(a); |
|
|
1902 |
|
|
1903 } /* end mp_iseven() */ |
|
|
1904 |
|
|
1905 /* }}} */ |
|
|
1906 |
|
|
1907 /* }}} */ |
|
|
1908 |
|
|
1909 /*------------------------------------------------------------------------*/ |
|
|
1910 /* {{{ Number theoretic functions */ |
|
|
1911 |
|
|
1912 #if MP_NUMTH |
|
|
1913 /* {{{ mp_gcd(a, b, c) */ |
|
|
1914 |
|
|
1915 /* |
|
|
1916 Like the old mp_gcd() function, except computes the GCD using the |
|
|
1917 binary algorithm due to Josef Stein in 1961 (via Knuth). |
|
|
1918 */ |
|
|
1919 mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c) |
|
|
1920 { |
|
|
1921 mp_err res; |
|
|
1922 mp_int u, v, t; |
|
|
1923 mp_size k = 0; |
|
|
1924 |
|
|
1925 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); |
|
|
1926 |
|
|
1927 if(mp_cmp_z(a) == MP_EQ && mp_cmp_z(b) == MP_EQ) |
|
|
1928 return MP_RANGE; |
|
|
1929 if(mp_cmp_z(a) == MP_EQ) { |
|
|
1930 return mp_copy(b, c); |
|
|
1931 } else if(mp_cmp_z(b) == MP_EQ) { |
|
|
1932 return mp_copy(a, c); |
|
|
1933 } |
|
|
1934 |
|
|
1935 if((res = mp_init(&t)) != MP_OKAY) |
|
|
1936 return res; |
|
|
1937 if((res = mp_init_copy(&u, a)) != MP_OKAY) |
|
|
1938 goto U; |
|
|
1939 if((res = mp_init_copy(&v, b)) != MP_OKAY) |
|
|
1940 goto V; |
|
|
1941 |
|
|
1942 SIGN(&u) = MP_ZPOS; |
|
|
1943 SIGN(&v) = MP_ZPOS; |
|
|
1944 |
|
|
1945 /* Divide out common factors of 2 until at least 1 of a, b is even */ |
|
|
1946 while(mp_iseven(&u) && mp_iseven(&v)) { |
|
|
1947 s_mp_div_2(&u); |
|
|
1948 s_mp_div_2(&v); |
|
|
1949 ++k; |
|
|
1950 } |
|
|
1951 |
|
|
1952 /* Initialize t */ |
|
|
1953 if(mp_isodd(&u)) { |
|
|
1954 if((res = mp_copy(&v, &t)) != MP_OKAY) |
|
|
1955 goto CLEANUP; |
|
|
1956 |
|
|
1957 /* t = -v */ |
|
|
1958 if(SIGN(&v) == MP_ZPOS) |
|
|
1959 SIGN(&t) = MP_NEG; |
|
|
1960 else |
|
|
1961 SIGN(&t) = MP_ZPOS; |
|
|
1962 |
|
|
1963 } else { |
|
|
1964 if((res = mp_copy(&u, &t)) != MP_OKAY) |
|
|
1965 goto CLEANUP; |
|
|
1966 |
|
|
1967 } |
|
|
1968 |
|
|
1969 for(;;) { |
|
|
1970 while(mp_iseven(&t)) { |
|
|
1971 s_mp_div_2(&t); |
|
|
1972 } |
|
|
1973 |
|
|
1974 if(mp_cmp_z(&t) == MP_GT) { |
|
|
1975 if((res = mp_copy(&t, &u)) != MP_OKAY) |
|
|
1976 goto CLEANUP; |
|
|
1977 |
|
|
1978 } else { |
|
|
1979 if((res = mp_copy(&t, &v)) != MP_OKAY) |
|
|
1980 goto CLEANUP; |
|
|
1981 |
|
|
1982 /* v = -t */ |
|
|
1983 if(SIGN(&t) == MP_ZPOS) |
|
|
1984 SIGN(&v) = MP_NEG; |
|
|
1985 else |
|
|
1986 SIGN(&v) = MP_ZPOS; |
|
|
1987 } |
|
|
1988 |
|
|
1989 if((res = mp_sub(&u, &v, &t)) != MP_OKAY) |
|
|
1990 goto CLEANUP; |
|
|
1991 |
|
|
1992 if(s_mp_cmp_d(&t, 0) == MP_EQ) |
|
|
1993 break; |
|
|
1994 } |
|
|
1995 |
|
|
1996 s_mp_2expt(&v, k); /* v = 2^k */ |
|
|
1997 res = mp_mul(&u, &v, c); /* c = u * v */ |
|
|
1998 |
|
|
1999 CLEANUP: |
|
|
2000 mp_clear(&v); |
|
|
2001 V: |
|
|
2002 mp_clear(&u); |
|
|
2003 U: |
|
|
2004 mp_clear(&t); |
|
|
2005 |
|
|
2006 return res; |
|
|
2007 |
|
|
2008 } /* end mp_bgcd() */ |
|
|
2009 |
|
|
2010 /* }}} */ |
|
|
2011 |
|
|
2012 /* {{{ mp_lcm(a, b, c) */ |
|
|
2013 |
|
|
2014 /* We compute the least common multiple using the rule: |
|
|
2015 |
|
|
2016 ab = [a, b](a, b) |
|
|
2017 |
|
|
2018 ... by computing the product, and dividing out the gcd. |
|
|
2019 */ |
|
|
2020 |
|
|
2021 mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c) |
|
|
2022 { |
|
|
2023 mp_int gcd, prod; |
|
|
2024 mp_err res; |
|
|
2025 |
|
|
2026 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); |
|
|
2027 |
|
|
2028 /* Set up temporaries */ |
|
|
2029 if((res = mp_init(&gcd)) != MP_OKAY) |
|
|
2030 return res; |
|
|
2031 if((res = mp_init(&prod)) != MP_OKAY) |
|
|
2032 goto GCD; |
|
|
2033 |
|
|
2034 if((res = mp_mul(a, b, &prod)) != MP_OKAY) |
|
|
2035 goto CLEANUP; |
|
|
2036 if((res = mp_gcd(a, b, &gcd)) != MP_OKAY) |
|
|
2037 goto CLEANUP; |
|
|
2038 |
|
|
2039 res = mp_div(&prod, &gcd, c, NULL); |
|
|
2040 |
|
|
2041 CLEANUP: |
|
|
2042 mp_clear(&prod); |
|
|
2043 GCD: |
|
|
2044 mp_clear(&gcd); |
|
|
2045 |
|
|
2046 return res; |
|
|
2047 |
|
|
2048 } /* end mp_lcm() */ |
|
|
2049 |
|
|
2050 /* }}} */ |
|
|
2051 |
|
|
2052 /* {{{ mp_xgcd(a, b, g, x, y) */ |
|
|
2053 |
|
|
2054 /* |
|
|
2055 mp_xgcd(a, b, g, x, y) |
|
|
2056 |
|
|
2057 Compute g = (a, b) and values x and y satisfying Bezout's identity |
|
|
2058 (that is, ax + by = g). This uses the extended binary GCD algorithm |
|
|
2059 based on the Stein algorithm used for mp_gcd() |
|
|
2060 */ |
|
|
2061 |
|
|
2062 mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y) |
|
|
2063 { |
|
|
2064 mp_int gx, xc, yc, u, v, A, B, C, D; |
|
|
2065 mp_int *clean[9]; |
|
|
2066 mp_err res; |
|
|
2067 int last = -1; |
|
|
2068 |
|
|
2069 if(mp_cmp_z(b) == 0) |
|
|
2070 return MP_RANGE; |
|
|
2071 |
|
|
2072 /* Initialize all these variables we need */ |
|
|
2073 if((res = mp_init(&u)) != MP_OKAY) goto CLEANUP; |
|
|
2074 clean[++last] = &u; |
|
|
2075 if((res = mp_init(&v)) != MP_OKAY) goto CLEANUP; |
|
|
2076 clean[++last] = &v; |
|
|
2077 if((res = mp_init(&gx)) != MP_OKAY) goto CLEANUP; |
|
|
2078 clean[++last] = &gx; |
|
|
2079 if((res = mp_init(&A)) != MP_OKAY) goto CLEANUP; |
|
|
2080 clean[++last] = &A; |
|
|
2081 if((res = mp_init(&B)) != MP_OKAY) goto CLEANUP; |
|
|
2082 clean[++last] = &B; |
|
|
2083 if((res = mp_init(&C)) != MP_OKAY) goto CLEANUP; |
|
|
2084 clean[++last] = &C; |
|
|
2085 if((res = mp_init(&D)) != MP_OKAY) goto CLEANUP; |
|
|
2086 clean[++last] = &D; |
|
|
2087 if((res = mp_init_copy(&xc, a)) != MP_OKAY) goto CLEANUP; |
|
|
2088 clean[++last] = &xc; |
|
|
2089 mp_abs(&xc, &xc); |
|
|
2090 if((res = mp_init_copy(&yc, b)) != MP_OKAY) goto CLEANUP; |
|
|
2091 clean[++last] = &yc; |
|
|
2092 mp_abs(&yc, &yc); |
|
|
2093 |
|
|
2094 mp_set(&gx, 1); |
|
|
2095 |
|
|
2096 /* Divide by two until at least one of them is even */ |
|
|
2097 while(mp_iseven(&xc) && mp_iseven(&yc)) { |
|
|
2098 s_mp_div_2(&xc); |
|
|
2099 s_mp_div_2(&yc); |
|
|
2100 if((res = s_mp_mul_2(&gx)) != MP_OKAY) |
|
|
2101 goto CLEANUP; |
|
|
2102 } |
|
|
2103 |
|
|
2104 mp_copy(&xc, &u); |
|
|
2105 mp_copy(&yc, &v); |
|
|
2106 mp_set(&A, 1); mp_set(&D, 1); |
|
|
2107 |
|
|
2108 /* Loop through binary GCD algorithm */ |
|
|
2109 for(;;) { |
|
|
2110 while(mp_iseven(&u)) { |
|
|
2111 s_mp_div_2(&u); |
|
|
2112 |
|
|
2113 if(mp_iseven(&A) && mp_iseven(&B)) { |
|
|
2114 s_mp_div_2(&A); s_mp_div_2(&B); |
|
|
2115 } else { |
|
|
2116 if((res = mp_add(&A, &yc, &A)) != MP_OKAY) goto CLEANUP; |
|
|
2117 s_mp_div_2(&A); |
|
|
2118 if((res = mp_sub(&B, &xc, &B)) != MP_OKAY) goto CLEANUP; |
|
|
2119 s_mp_div_2(&B); |
|
|
2120 } |
|
|
2121 } |
|
|
2122 |
|
|
2123 while(mp_iseven(&v)) { |
|
|
2124 s_mp_div_2(&v); |
|
|
2125 |
|
|
2126 if(mp_iseven(&C) && mp_iseven(&D)) { |
|
|
2127 s_mp_div_2(&C); s_mp_div_2(&D); |
|
|
2128 } else { |
|
|
2129 if((res = mp_add(&C, &yc, &C)) != MP_OKAY) goto CLEANUP; |
|
|
2130 s_mp_div_2(&C); |
|
|
2131 if((res = mp_sub(&D, &xc, &D)) != MP_OKAY) goto CLEANUP; |
|
|
2132 s_mp_div_2(&D); |
|
|
2133 } |
|
|
2134 } |
|
|
2135 |
|
|
2136 if(mp_cmp(&u, &v) >= 0) { |
|
|
2137 if((res = mp_sub(&u, &v, &u)) != MP_OKAY) goto CLEANUP; |
|
|
2138 if((res = mp_sub(&A, &C, &A)) != MP_OKAY) goto CLEANUP; |
|
|
2139 if((res = mp_sub(&B, &D, &B)) != MP_OKAY) goto CLEANUP; |
|
|
2140 |
|
|
2141 } else { |
|
|
2142 if((res = mp_sub(&v, &u, &v)) != MP_OKAY) goto CLEANUP; |
|
|
2143 if((res = mp_sub(&C, &A, &C)) != MP_OKAY) goto CLEANUP; |
|
|
2144 if((res = mp_sub(&D, &B, &D)) != MP_OKAY) goto CLEANUP; |
|
|
2145 |
|
|
2146 } |
|
|
2147 |
|
|
2148 /* If we're done, copy results to output */ |
|
|
2149 if(mp_cmp_z(&u) == 0) { |
|
|
2150 if(x) |
|
|
2151 if((res = mp_copy(&C, x)) != MP_OKAY) goto CLEANUP; |
|
|
2152 |
|
|
2153 if(y) |
|
|
2154 if((res = mp_copy(&D, y)) != MP_OKAY) goto CLEANUP; |
|
|
2155 |
|
|
2156 if(g) |
|
|
2157 if((res = mp_mul(&gx, &v, g)) != MP_OKAY) goto CLEANUP; |
|
|
2158 |
|
|
2159 break; |
|
|
2160 } |
|
|
2161 } |
|
|
2162 |
|
|
2163 CLEANUP: |
|
|
2164 while(last >= 0) |
|
|
2165 mp_clear(clean[last--]); |
|
|
2166 |
|
|
2167 return res; |
|
|
2168 |
|
|
2169 } /* end mp_xgcd() */ |
|
|
2170 |
|
|
2171 /* }}} */ |
|
|
2172 |
|
|
2173 /* {{{ mp_invmod(a, m, c) */ |
|
|
2174 |
|
|
2175 /* |
|
|
2176 mp_invmod(a, m, c) |
|
|
2177 |
|
|
2178 Compute c = a^-1 (mod m), if there is an inverse for a (mod m). |
|
|
2179 This is equivalent to the question of whether (a, m) = 1. If not, |
|
|
2180 MP_UNDEF is returned, and there is no inverse. |
|
|
2181 */ |
|
|
2182 |
|
|
2183 mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c) |
|
|
2184 { |
|
|
2185 mp_int g, x; |
|
|
2186 mp_err res; |
|
|
2187 |
|
|
2188 ARGCHK(a && m && c, MP_BADARG); |
|
|
2189 |
|
|
2190 if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0) |
|
|
2191 return MP_RANGE; |
|
|
2192 |
|
|
2193 if((res = mp_init(&g)) != MP_OKAY) |
|
|
2194 return res; |
|
|
2195 if((res = mp_init(&x)) != MP_OKAY) |
|
|
2196 goto X; |
|
|
2197 |
|
|
2198 if((res = mp_xgcd(a, m, &g, &x, NULL)) != MP_OKAY) |
|
|
2199 goto CLEANUP; |
|
|
2200 |
|
|
2201 if(mp_cmp_d(&g, 1) != MP_EQ) { |
|
|
2202 res = MP_UNDEF; |
|
|
2203 goto CLEANUP; |
|
|
2204 } |
|
|
2205 |
|
|
2206 res = mp_mod(&x, m, c); |
|
|
2207 SIGN(c) = SIGN(a); |
|
|
2208 |
|
|
2209 CLEANUP: |
|
|
2210 mp_clear(&x); |
|
|
2211 X: |
|
|
2212 mp_clear(&g); |
|
|
2213 |
|
|
2214 return res; |
|
|
2215 |
|
|
2216 } /* end mp_invmod() */ |
|
|
2217 |
|
|
2218 /* }}} */ |
|
|
2219 #endif /* if MP_NUMTH */ |
|
|
2220 |
|
|
2221 /* }}} */ |
|
|
2222 |
|
|
2223 /*------------------------------------------------------------------------*/ |
|
|
2224 /* {{{ mp_print(mp, ofp) */ |
|
|
2225 |
|
|
2226 #if MP_IOFUNC |
|
|
2227 /* |
|
|
2228 mp_print(mp, ofp) |
|
|
2229 |
|
|
2230 Print a textual representation of the given mp_int on the output |
|
|
2231 stream 'ofp'. Output is generated using the internal radix. |
|
|
2232 */ |
|
|
2233 |
|
|
2234 void mp_print(mp_int *mp, FILE *ofp) |
|
|
2235 { |
|
|
2236 int ix; |
|
|
2237 |
|
|
2238 if(mp == NULL || ofp == NULL) |
|
|
2239 return; |
|
|
2240 |
|
|
2241 fputc((SIGN(mp) == MP_NEG) ? '-' : '+', ofp); |
|
|
2242 |
|
|
2243 for(ix = USED(mp) - 1; ix >= 0; ix--) { |
|
|
2244 fprintf(ofp, DIGIT_FMT, DIGIT(mp, ix)); |
|
|
2245 } |
|
|
2246 |
|
|
2247 } /* end mp_print() */ |
|
|
2248 |
|
|
2249 #endif /* if MP_IOFUNC */ |
|
|
2250 |
|
|
2251 /* }}} */ |
|
|
2252 |
|
|
2253 /*------------------------------------------------------------------------*/ |
|
|
2254 /* {{{ More I/O Functions */ |
|
|
2255 |
|
|
2256 /* {{{ mp_read_signed_bin(mp, str, len) */ |
|
|
2257 |
|
|
2258 /* |
|
|
2259 mp_read_signed_bin(mp, str, len) |
|
|
2260 |
|
|
2261 Read in a raw value (base 256) into the given mp_int |
|
|
2262 */ |
|
|
2263 |
|
|
2264 mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len) |
|
|
2265 { |
|
|
2266 mp_err res; |
|
|
2267 |
|
|
2268 ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG); |
|
|
2269 |
|
|
2270 if((res = mp_read_unsigned_bin(mp, str + 1, len - 1)) == MP_OKAY) { |
|
|
2271 /* Get sign from first byte */ |
|
|
2272 if(str[0]) |
|
|
2273 SIGN(mp) = MP_NEG; |
|
|
2274 else |
|
|
2275 SIGN(mp) = MP_ZPOS; |
|
|
2276 } |
|
|
2277 |
|
|
2278 return res; |
|
|
2279 |
|
|
2280 } /* end mp_read_signed_bin() */ |
|
|
2281 |
|
|
2282 /* }}} */ |
|
|
2283 |
|
|
2284 /* {{{ mp_signed_bin_size(mp) */ |
|
|
2285 |
|
|
2286 int mp_signed_bin_size(mp_int *mp) |
|
|
2287 { |
|
|
2288 ARGCHK(mp != NULL, 0); |
|
|
2289 |
|
|
2290 return mp_unsigned_bin_size(mp) + 1; |
|
|
2291 |
|
|
2292 } /* end mp_signed_bin_size() */ |
|
|
2293 |
|
|
2294 /* }}} */ |
|
|
2295 |
|
|
2296 /* {{{ mp_to_signed_bin(mp, str) */ |
|
|
2297 |
|
|
2298 mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str) |
|
|
2299 { |
|
|
2300 ARGCHK(mp != NULL && str != NULL, MP_BADARG); |
|
|
2301 |
|
|
2302 /* Caller responsible for allocating enough memory (use mp_raw_size(mp)) */ |
|
|
2303 str[0] = (char)SIGN(mp); |
|
|
2304 |
|
|
2305 return mp_to_unsigned_bin(mp, str + 1); |
|
|
2306 |
|
|
2307 } /* end mp_to_signed_bin() */ |
|
|
2308 |
|
|
2309 /* }}} */ |
|
|
2310 |
|
|
2311 /* {{{ mp_read_unsigned_bin(mp, str, len) */ |
|
|
2312 |
|
|
2313 /* |
|
|
2314 mp_read_unsigned_bin(mp, str, len) |
|
|
2315 |
|
|
2316 Read in an unsigned value (base 256) into the given mp_int |
|
|
2317 */ |
|
|
2318 |
|
|
2319 mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len) |
|
|
2320 { |
|
|
2321 int ix; |
|
|
2322 mp_err res; |
|
|
2323 |
|
|
2324 ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG); |
|
|
2325 |
|
|
2326 mp_zero(mp); |
|
|
2327 |
|
|
2328 for(ix = 0; ix < len; ix++) { |
|
|
2329 if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY) |
|
|
2330 return res; |
|
|
2331 |
|
|
2332 if((res = mp_add_d(mp, str[ix], mp)) != MP_OKAY) |
|
|
2333 return res; |
|
|
2334 } |
|
|
2335 |
|
|
2336 return MP_OKAY; |
|
|
2337 |
|
|
2338 } /* end mp_read_unsigned_bin() */ |
|
|
2339 |
|
|
2340 /* }}} */ |
|
|
2341 |
|
|
2342 /* {{{ mp_unsigned_bin_size(mp) */ |
|
|
2343 |
|
|
2344 int mp_unsigned_bin_size(mp_int *mp) |
|
|
2345 { |
|
|
2346 mp_digit topdig; |
|
|
2347 int count; |
|
|
2348 |
|
|
2349 ARGCHK(mp != NULL, 0); |
|
|
2350 |
|
|
2351 /* Special case for the value zero */ |
|
|
2352 if(USED(mp) == 1 && DIGIT(mp, 0) == 0) |
|
|
2353 return 1; |
|
|
2354 |
|
|
2355 count = (USED(mp) - 1) * sizeof(mp_digit); |
|
|
2356 topdig = DIGIT(mp, USED(mp) - 1); |
|
|
2357 |
|
|
2358 while(topdig != 0) { |
|
|
2359 ++count; |
|
|
2360 topdig >>= CHAR_BIT; |
|
|
2361 } |
|
|
2362 |
|
|
2363 return count; |
|
|
2364 |
|
|
2365 } /* end mp_unsigned_bin_size() */ |
|
|
2366 |
|
|
2367 /* }}} */ |
|
|
2368 |
|
|
2369 /* {{{ mp_to_unsigned_bin(mp, str) */ |
|
|
2370 |
|
|
2371 mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str) |
|
|
2372 { |
|
|
2373 mp_digit *dp, *end, d; |
|
|
2374 unsigned char *spos; |
|
|
2375 |
|
|
2376 ARGCHK(mp != NULL && str != NULL, MP_BADARG); |
|
|
2377 |
|
|
2378 dp = DIGITS(mp); |
|
|
2379 end = dp + USED(mp) - 1; |
|
|
2380 spos = str; |
|
|
2381 |
|
|
2382 /* Special case for zero, quick test */ |
|
|
2383 if(dp == end && *dp == 0) { |
|
|
2384 *str = '\0'; |
|
|
2385 return MP_OKAY; |
|
|
2386 } |
|
|
2387 |
|
|
2388 /* Generate digits in reverse order */ |
|
|
2389 while(dp < end) { |
|
|
2390 int ix; |
|
|
2391 |
|
|
2392 d = *dp; |
|
|
2393 for(ix = 0; ix < sizeof(mp_digit); ++ix) { |
|
|
2394 *spos = d & UCHAR_MAX; |
|
|
2395 d >>= CHAR_BIT; |
|
|
2396 ++spos; |
|
|
2397 } |
|
|
2398 |
|
|
2399 ++dp; |
|
|
2400 } |
|
|
2401 |
|
|
2402 /* Now handle last digit specially, high order zeroes are not written */ |
|
|
2403 d = *end; |
|
|
2404 while(d != 0) { |
|
|
2405 *spos = d & UCHAR_MAX; |
|
|
2406 d >>= CHAR_BIT; |
|
|
2407 ++spos; |
|
|
2408 } |
|
|
2409 |
|
|
2410 /* Reverse everything to get digits in the correct order */ |
|
|
2411 while(--spos > str) { |
|
|
2412 unsigned char t = *str; |
|
|
2413 *str = *spos; |
|
|
2414 *spos = t; |
|
|
2415 |
|
|
2416 ++str; |
|
|
2417 } |
|
|
2418 |
|
|
2419 return MP_OKAY; |
|
|
2420 |
|
|
2421 } /* end mp_to_unsigned_bin() */ |
|
|
2422 |
|
|
2423 /* }}} */ |
|
|
2424 |
|
|
2425 /* {{{ mp_count_bits(mp) */ |
|
|
2426 |
|
|
2427 int mp_count_bits(mp_int *mp) |
|
|
2428 { |
|
|
2429 int len; |
|
|
2430 mp_digit d; |
|
|
2431 |
|
|
2432 ARGCHK(mp != NULL, MP_BADARG); |
|
|
2433 |
|
|
2434 len = DIGIT_BIT * (USED(mp) - 1); |
|
|
2435 d = DIGIT(mp, USED(mp) - 1); |
|
|
2436 |
|
|
2437 while(d != 0) { |
|
|
2438 ++len; |
|
|
2439 d >>= 1; |
|
|
2440 } |
|
|
2441 |
|
|
2442 return len; |
|
|
2443 |
|
|
2444 } /* end mp_count_bits() */ |
|
|
2445 |
|
|
2446 /* }}} */ |
|
|
2447 |
|
|
2448 /* {{{ mp_read_radix(mp, str, radix) */ |
|
|
2449 |
|
|
2450 /* |
|
|
2451 mp_read_radix(mp, str, radix) |
|
|
2452 |
|
|
2453 Read an integer from the given string, and set mp to the resulting |
|
|
2454 value. The input is presumed to be in base 10. Leading non-digit |
|
|
2455 characters are ignored, and the function reads until a non-digit |
|
|
2456 character or the end of the string. |
|
|
2457 */ |
|
|
2458 |
|
|
2459 mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix) |
|
|
2460 { |
|
|
2461 int ix = 0, val = 0; |
|
|
2462 mp_err res; |
|
|
2463 mp_sign sig = MP_ZPOS; |
|
|
2464 |
|
|
2465 ARGCHK(mp != NULL && str != NULL && radix >= 2 && radix <= MAX_RADIX, |
|
|
2466 MP_BADARG); |
|
|
2467 |
|
|
2468 mp_zero(mp); |
|
|
2469 |
|
|
2470 /* Skip leading non-digit characters until a digit or '-' or '+' */ |
|
|
2471 while(str[ix] && |
|
|
2472 (s_mp_tovalue(str[ix], radix) < 0) && |
|
|
2473 str[ix] != '-' && |
|
|
2474 str[ix] != '+') { |
|
|
2475 ++ix; |
|
|
2476 } |
|
|
2477 |
|
|
2478 if(str[ix] == '-') { |
|
|
2479 sig = MP_NEG; |
|
|
2480 ++ix; |
|
|
2481 } else if(str[ix] == '+') { |
|
|
2482 sig = MP_ZPOS; /* this is the default anyway... */ |
|
|
2483 ++ix; |
|
|
2484 } |
|
|
2485 |
|
|
2486 while((val = s_mp_tovalue(str[ix], radix)) >= 0) { |
|
|
2487 if((res = s_mp_mul_d(mp, radix)) != MP_OKAY) |
|
|
2488 return res; |
|
|
2489 if((res = s_mp_add_d(mp, val)) != MP_OKAY) |
|
|
2490 return res; |
|
|
2491 ++ix; |
|
|
2492 } |
|
|
2493 |
|
|
2494 if(s_mp_cmp_d(mp, 0) == MP_EQ) |
|
|
2495 SIGN(mp) = MP_ZPOS; |
|
|
2496 else |
|
|
2497 SIGN(mp) = sig; |
|
|
2498 |
|
|
2499 return MP_OKAY; |
|
|
2500 |
|
|
2501 } /* end mp_read_radix() */ |
|
|
2502 |
|
|
2503 /* }}} */ |
|
|
2504 |
|
|
2505 /* {{{ mp_radix_size(mp, radix) */ |
|
|
2506 |
|
|
2507 int mp_radix_size(mp_int *mp, int radix) |
|
|
2508 { |
|
|
2509 int len; |
|
|
2510 ARGCHK(mp != NULL, 0); |
|
|
2511 |
|
|
2512 len = s_mp_outlen(mp_count_bits(mp), radix) + 1; /* for NUL terminator */ |
|
|
2513 |
|
|
2514 if(mp_cmp_z(mp) < 0) |
|
|
2515 ++len; /* for sign */ |
|
|
2516 |
|
|
2517 return len; |
|
|
2518 |
|
|
2519 } /* end mp_radix_size() */ |
|
|
2520 |
|
|
2521 /* }}} */ |
|
|
2522 |
|
|
2523 /* {{{ mp_value_radix_size(num, qty, radix) */ |
|
|
2524 |
|
|
2525 /* num = number of digits |
|
|
2526 qty = number of bits per digit |
|
|
2527 radix = target base |
|
|
2528 |
|
|
2529 Return the number of digits in the specified radix that would be |
|
|
2530 needed to express 'num' digits of 'qty' bits each. |
|
|
2531 */ |
|
|
2532 int mp_value_radix_size(int num, int qty, int radix) |
|
|
2533 { |
|
|
2534 ARGCHK(num >= 0 && qty > 0 && radix >= 2 && radix <= MAX_RADIX, 0); |
|
|
2535 |
|
|
2536 return s_mp_outlen(num * qty, radix); |
|
|
2537 |
|
|
2538 } /* end mp_value_radix_size() */ |
|
|
2539 |
|
|
2540 /* }}} */ |
|
|
2541 |
|
|
2542 /* {{{ mp_toradix(mp, str, radix) */ |
|
|
2543 |
|
|
2544 mp_err mp_toradix(mp_int *mp, unsigned char *str, int radix) |
|
|
2545 { |
|
|
2546 int ix, pos = 0; |
|
|
2547 |
|
|
2548 ARGCHK(mp != NULL && str != NULL, MP_BADARG); |
|
|
2549 ARGCHK(radix > 1 && radix <= MAX_RADIX, MP_RANGE); |
|
|
2550 |
|
|
2551 if(mp_cmp_z(mp) == MP_EQ) { |
|
|
2552 str[0] = '0'; |
|
|
2553 str[1] = '\0'; |
|
|
2554 } else { |
|
|
2555 mp_err res; |
|
|
2556 mp_int tmp; |
|
|
2557 mp_sign sgn; |
|
|
2558 mp_digit rem, rdx = (mp_digit)radix; |
|
|
2559 char ch; |
|
|
2560 |
|
|
2561 if((res = mp_init_copy(&tmp, mp)) != MP_OKAY) |
|
|
2562 return res; |
|
|
2563 |
|
|
2564 /* Save sign for later, and take absolute value */ |
|
|
2565 sgn = SIGN(&tmp); SIGN(&tmp) = MP_ZPOS; |
|
|
2566 |
|
|
2567 /* Generate output digits in reverse order */ |
|
|
2568 while(mp_cmp_z(&tmp) != 0) { |
|
|
2569 if((res = s_mp_div_d(&tmp, rdx, &rem)) != MP_OKAY) { |
|
|
2570 mp_clear(&tmp); |
|
|
2571 return res; |
|
|
2572 } |
|
|
2573 |
|
|
2574 /* Generate digits, use capital letters */ |
|
|
2575 ch = s_mp_todigit(rem, radix, 0); |
|
|
2576 |
|
|
2577 str[pos++] = ch; |
|
|
2578 } |
|
|
2579 |
|
|
2580 /* Add - sign if original value was negative */ |
|
|
2581 if(sgn == MP_NEG) |
|
|
2582 str[pos++] = '-'; |
|
|
2583 |
|
|
2584 /* Add trailing NUL to end the string */ |
|
|
2585 str[pos--] = '\0'; |
|
|
2586 |
|
|
2587 /* Reverse the digits and sign indicator */ |
|
|
2588 ix = 0; |
|
|
2589 while(ix < pos) { |
|
|
2590 char tmp = str[ix]; |
|
|
2591 |
|
|
2592 str[ix] = str[pos]; |
|
|
2593 str[pos] = tmp; |
|
|
2594 ++ix; |
|
|
2595 --pos; |
|
|
2596 } |
|
|
2597 |
|
|
2598 mp_clear(&tmp); |
|
|
2599 } |
|
|
2600 |
|
|
2601 return MP_OKAY; |
|
|
2602 |
|
|
2603 } /* end mp_toradix() */ |
|
|
2604 |
|
|
2605 /* }}} */ |
|
|
2606 |
|
|
2607 /* {{{ mp_char2value(ch, r) */ |
|
|
2608 |
|
|
2609 int mp_char2value(char ch, int r) |
|
|
2610 { |
|
|
2611 return s_mp_tovalue(ch, r); |
|
|
2612 |
|
|
2613 } /* end mp_tovalue() */ |
|
|
2614 |
|
|
2615 /* }}} */ |
|
|
2616 |
|
|
2617 /* }}} */ |
|
|
2618 |
|
|
2619 /* {{{ mp_strerror(ec) */ |
|
|
2620 |
|
|
2621 /* |
|
|
2622 mp_strerror(ec) |
|
|
2623 |
|
|
2624 Return a string describing the meaning of error code 'ec'. The |
|
|
2625 string returned is allocated in static memory, so the caller should |
|
|
2626 not attempt to modify or free the memory associated with this |
|
|
2627 string. |
|
|
2628 */ |
|
|
2629 const char *mp_strerror(mp_err ec) |
|
|
2630 { |
|
|
2631 int aec = (ec < 0) ? -ec : ec; |
|
|
2632 |
|
|
2633 /* Code values are negative, so the senses of these comparisons |
|
|
2634 are accurate */ |
|
|
2635 if(ec < MP_LAST_CODE || ec > MP_OKAY) { |
|
|
2636 return mp_err_string[0]; /* unknown error code */ |
|
|
2637 } else { |
|
|
2638 return mp_err_string[aec + 1]; |
|
|
2639 } |
|
|
2640 |
|
|
2641 } /* end mp_strerror() */ |
|
|
2642 |
|
|
2643 /* }}} */ |
|
|
2644 |
|
|
2645 /*========================================================================*/ |
|
|
2646 /*------------------------------------------------------------------------*/ |
|
|
2647 /* Static function definitions (internal use only) */ |
|
|
2648 |
|
|
2649 /* {{{ Memory management */ |
|
|
2650 |
|
|
2651 /* {{{ s_mp_grow(mp, min) */ |
|
|
2652 |
|
|
2653 /* Make sure there are at least 'min' digits allocated to mp */ |
|
|
2654 mp_err s_mp_grow(mp_int *mp, mp_size min) |
|
|
2655 { |
|
|
2656 if(min > ALLOC(mp)) { |
|
|
2657 mp_digit *tmp; |
|
|
2658 |
|
|
2659 /* Set min to next nearest default precision block size */ |
|
|
2660 min = ((min + (s_mp_defprec - 1)) / s_mp_defprec) * s_mp_defprec; |
|
|
2661 |
|
|
2662 if((tmp = s_mp_alloc(min, sizeof(mp_digit))) == NULL) |
|
|
2663 return MP_MEM; |
|
|
2664 |
|
|
2665 s_mp_copy(DIGITS(mp), tmp, USED(mp)); |
|
|
2666 |
|
|
2667 #if MP_CRYPTO |
|
|
2668 s_mp_setz(DIGITS(mp), ALLOC(mp)); |
|
|
2669 #endif |
|
|
2670 s_mp_free(DIGITS(mp)); |
|
|
2671 DIGITS(mp) = tmp; |
|
|
2672 ALLOC(mp) = min; |
|
|
2673 } |
|
|
2674 |
|
|
2675 return MP_OKAY; |
|
|
2676 |
|
|
2677 } /* end s_mp_grow() */ |
|
|
2678 |
|
|
2679 /* }}} */ |
|
|
2680 |
|
|
2681 /* {{{ s_mp_pad(mp, min) */ |
|
|
2682 |
|
|
2683 /* Make sure the used size of mp is at least 'min', growing if needed */ |
|
|
2684 mp_err s_mp_pad(mp_int *mp, mp_size min) |
|
|
2685 { |
|
|
2686 if(min > USED(mp)) { |
|
|
2687 mp_err res; |
|
|
2688 |
|
|
2689 /* Make sure there is room to increase precision */ |
|
|
2690 if(min > ALLOC(mp) && (res = s_mp_grow(mp, min)) != MP_OKAY) |
|
|
2691 return res; |
|
|
2692 |
|
|
2693 /* Increase precision; should already be 0-filled */ |
|
|
2694 USED(mp) = min; |
|
|
2695 } |
|
|
2696 |
|
|
2697 return MP_OKAY; |
|
|
2698 |
|
|
2699 } /* end s_mp_pad() */ |
|
|
2700 |
|
|
2701 /* }}} */ |
|
|
2702 |
|
|
2703 /* {{{ s_mp_setz(dp, count) */ |
|
|
2704 |
|
|
2705 #if MP_MACRO == 0 |
|
|
2706 /* Set 'count' digits pointed to by dp to be zeroes */ |
|
|
2707 void s_mp_setz(mp_digit *dp, mp_size count) |
|
|
2708 { |
|
|
2709 #if MP_MEMSET == 0 |
|
|
2710 int ix; |
|
|
2711 |
|
|
2712 for(ix = 0; ix < count; ix++) |
|
|
2713 dp[ix] = 0; |
|
|
2714 #else |
|
|
2715 memset(dp, 0, count * sizeof(mp_digit)); |
|
|
2716 #endif |
|
|
2717 |
|
|
2718 } /* end s_mp_setz() */ |
|
|
2719 #endif |
|
|
2720 |
|
|
2721 /* }}} */ |
|
|
2722 |
|
|
2723 /* {{{ s_mp_copy(sp, dp, count) */ |
|
|
2724 |
|
|
2725 #if MP_MACRO == 0 |
|
|
2726 /* Copy 'count' digits from sp to dp */ |
|
|
2727 void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count) |
|
|
2728 { |
|
|
2729 #if MP_MEMCPY == 0 |
|
|
2730 int ix; |
|
|
2731 |
|
|
2732 for(ix = 0; ix < count; ix++) |
|
|
2733 dp[ix] = sp[ix]; |
|
|
2734 #else |
|
|
2735 memcpy(dp, sp, count * sizeof(mp_digit)); |
|
|
2736 #endif |
|
|
2737 |
|
|
2738 } /* end s_mp_copy() */ |
|
|
2739 #endif |
|
|
2740 |
|
|
2741 /* }}} */ |
|
|
2742 |
|
|
2743 /* {{{ s_mp_alloc(nb, ni) */ |
|
|
2744 |
|
|
2745 #if MP_MACRO == 0 |
|
|
2746 /* Allocate ni records of nb bytes each, and return a pointer to that */ |
|
|
2747 void *s_mp_alloc(size_t nb, size_t ni) |
|
|
2748 { |
|
|
2749 return calloc(nb, ni); |
|
|
2750 |
|
|
2751 } /* end s_mp_alloc() */ |
|
|
2752 #endif |
|
|
2753 |
|
|
2754 /* }}} */ |
|
|
2755 |
|
|
2756 /* {{{ s_mp_free(ptr) */ |
|
|
2757 |
|
|
2758 #if MP_MACRO == 0 |
|
|
2759 /* Free the memory pointed to by ptr */ |
|
|
2760 void s_mp_free(void *ptr) |
|
|
2761 { |
|
|
2762 if(ptr) |
|
|
2763 free(ptr); |
|
|
2764 |
|
|
2765 } /* end s_mp_free() */ |
|
|
2766 #endif |
|
|
2767 |
|
|
2768 /* }}} */ |
|
|
2769 |
|
|
2770 /* {{{ s_mp_clamp(mp) */ |
|
|
2771 |
|
|
2772 /* Remove leading zeroes from the given value */ |
|
|
2773 void s_mp_clamp(mp_int *mp) |
|
|
2774 { |
|
|
2775 mp_size du = USED(mp); |
|
|
2776 mp_digit *zp = DIGITS(mp) + du - 1; |
|
|
2777 |
|
|
2778 while(du > 1 && !*zp--) |
|
|
2779 --du; |
|
|
2780 |
|
|
2781 USED(mp) = du; |
|
|
2782 |
|
|
2783 } /* end s_mp_clamp() */ |
|
|
2784 |
|
|
2785 |
|
|
2786 /* }}} */ |
|
|
2787 |
|
|
2788 /* {{{ s_mp_exch(a, b) */ |
|
|
2789 |
|
|
2790 /* Exchange the data for a and b; (b, a) = (a, b) */ |
|
|
2791 void s_mp_exch(mp_int *a, mp_int *b) |
|
|
2792 { |
|
|
2793 mp_int tmp; |
|
|
2794 |
|
|
2795 tmp = *a; |
|
|
2796 *a = *b; |
|
|
2797 *b = tmp; |
|
|
2798 |
|
|
2799 } /* end s_mp_exch() */ |
|
|
2800 |
|
|
2801 /* }}} */ |
|
|
2802 |
|
|
2803 /* }}} */ |
|
|
2804 |
|
|
2805 /* {{{ Arithmetic helpers */ |
|
|
2806 |
|
|
2807 /* {{{ s_mp_lshd(mp, p) */ |
|
|
2808 |
|
|
2809 /* |
|
|
2810 Shift mp leftward by p digits, growing if needed, and zero-filling |
|
|
2811 the in-shifted digits at the right end. This is a convenient |
|
|
2812 alternative to multiplication by powers of the radix |
|
|
2813 */ |
|
|
2814 |
|
|
2815 mp_err s_mp_lshd(mp_int *mp, mp_size p) |
|
|
2816 { |
|
|
2817 mp_err res; |
|
|
2818 mp_size pos; |
|
|
2819 mp_digit *dp; |
|
|
2820 int ix; |
|
|
2821 |
|
|
2822 if(p == 0) |
|
|
2823 return MP_OKAY; |
|
|
2824 |
|
|
2825 if((res = s_mp_pad(mp, USED(mp) + p)) != MP_OKAY) |
|
|
2826 return res; |
|
|
2827 |
|
|
2828 pos = USED(mp) - 1; |
|
|
2829 dp = DIGITS(mp); |
|
|
2830 |
|
|
2831 /* Shift all the significant figures over as needed */ |
|
|
2832 for(ix = pos - p; ix >= 0; ix--) |
|
|
2833 dp[ix + p] = dp[ix]; |
|
|
2834 |
|
|
2835 /* Fill the bottom digits with zeroes */ |
|
|
2836 for(ix = 0; ix < p; ix++) |
|
|
2837 dp[ix] = 0; |
|
|
2838 |
|
|
2839 return MP_OKAY; |
|
|
2840 |
|
|
2841 } /* end s_mp_lshd() */ |
|
|
2842 |
|
|
2843 /* }}} */ |
|
|
2844 |
|
|
2845 /* {{{ s_mp_rshd(mp, p) */ |
|
|
2846 |
|
|
2847 /* |
|
|
2848 Shift mp rightward by p digits. Maintains the invariant that |
|
|
2849 digits above the precision are all zero. Digits shifted off the |
|
|
2850 end are lost. Cannot fail. |
|
|
2851 */ |
|
|
2852 |
|
|
2853 void s_mp_rshd(mp_int *mp, mp_size p) |
|
|
2854 { |
|
|
2855 mp_size ix; |
|
|
2856 mp_digit *dp; |
|
|
2857 |
|
|
2858 if(p == 0) |
|
|
2859 return; |
|
|
2860 |
|
|
2861 /* Shortcut when all digits are to be shifted off */ |
|
|
2862 if(p >= USED(mp)) { |
|
|
2863 s_mp_setz(DIGITS(mp), ALLOC(mp)); |
|
|
2864 USED(mp) = 1; |
|
|
2865 SIGN(mp) = MP_ZPOS; |
|
|
2866 return; |
|
|
2867 } |
|
|
2868 |
|
|
2869 /* Shift all the significant figures over as needed */ |
|
|
2870 dp = DIGITS(mp); |
|
|
2871 for(ix = p; ix < USED(mp); ix++) |
|
|
2872 dp[ix - p] = dp[ix]; |
|
|
2873 |
|
|
2874 /* Fill the top digits with zeroes */ |
|
|
2875 ix -= p; |
|
|
2876 while(ix < USED(mp)) |
|
|
2877 dp[ix++] = 0; |
|
|
2878 |
|
|
2879 /* Strip off any leading zeroes */ |
|
|
2880 s_mp_clamp(mp); |
|
|
2881 |
|
|
2882 } /* end s_mp_rshd() */ |
|
|
2883 |
|
|
2884 /* }}} */ |
|
|
2885 |
|
|
2886 /* {{{ s_mp_div_2(mp) */ |
|
|
2887 |
|
|
2888 /* Divide by two -- take advantage of radix properties to do it fast */ |
|
|
2889 void s_mp_div_2(mp_int *mp) |
|
|
2890 { |
|
|
2891 s_mp_div_2d(mp, 1); |
|
|
2892 |
|
|
2893 } /* end s_mp_div_2() */ |
|
|
2894 |
|
|
2895 /* }}} */ |
|
|
2896 |
|
|
2897 /* {{{ s_mp_mul_2(mp) */ |
|
|
2898 |
|
|
2899 mp_err s_mp_mul_2(mp_int *mp) |
|
|
2900 { |
|
|
2901 int ix; |
|
|
2902 mp_digit kin = 0, kout, *dp = DIGITS(mp); |
|
|
2903 mp_err res; |
|
|
2904 |
|
|
2905 /* Shift digits leftward by 1 bit */ |
|
|
2906 for(ix = 0; ix < USED(mp); ix++) { |
|
|
2907 kout = (dp[ix] >> (DIGIT_BIT - 1)) & 1; |
|
|
2908 dp[ix] = (dp[ix] << 1) | kin; |
|
|
2909 |
|
|
2910 kin = kout; |
|
|
2911 } |
|
|
2912 |
|
|
2913 /* Deal with rollover from last digit */ |
|
|
2914 if(kin) { |
|
|
2915 if(ix >= ALLOC(mp)) { |
|
|
2916 if((res = s_mp_grow(mp, ALLOC(mp) + 1)) != MP_OKAY) |
|
|
2917 return res; |
|
|
2918 dp = DIGITS(mp); |
|
|
2919 } |
|
|
2920 |
|
|
2921 dp[ix] = kin; |
|
|
2922 USED(mp) += 1; |
|
|
2923 } |
|
|
2924 |
|
|
2925 return MP_OKAY; |
|
|
2926 |
|
|
2927 } /* end s_mp_mul_2() */ |
|
|
2928 |
|
|
2929 /* }}} */ |
|
|
2930 |
|
|
2931 /* {{{ s_mp_mod_2d(mp, d) */ |
|
|
2932 |
|
|
2933 /* |
|
|
2934 Remainder the integer by 2^d, where d is a number of bits. This |
|
|
2935 amounts to a bitwise AND of the value, and does not require the full |
|
|
2936 division code |
|
|
2937 */ |
|
|
2938 void s_mp_mod_2d(mp_int *mp, mp_digit d) |
|
|
2939 { |
|
|
2940 unsigned int ndig = (d / DIGIT_BIT), nbit = (d % DIGIT_BIT); |
|
|
2941 unsigned int ix; |
|
|
2942 mp_digit dmask, *dp = DIGITS(mp); |
|
|
2943 |
|
|
2944 if(ndig >= USED(mp)) |
|
|
2945 return; |
|
|
2946 |
|
|
2947 /* Flush all the bits above 2^d in its digit */ |
|
|
2948 dmask = (1 << nbit) - 1; |
|
|
2949 dp[ndig] &= dmask; |
|
|
2950 |
|
|
2951 /* Flush all digits above the one with 2^d in it */ |
|
|
2952 for(ix = ndig + 1; ix < USED(mp); ix++) |
|
|
2953 dp[ix] = 0; |
|
|
2954 |
|
|
2955 s_mp_clamp(mp); |
|
|
2956 |
|
|
2957 } /* end s_mp_mod_2d() */ |
|
|
2958 |
|
|
2959 /* }}} */ |
|
|
2960 |
|
|
2961 /* {{{ s_mp_mul_2d(mp, d) */ |
|
|
2962 |
|
|
2963 /* |
|
|
2964 Multiply by the integer 2^d, where d is a number of bits. This |
|
|
2965 amounts to a bitwise shift of the value, and does not require the |
|
|
2966 full multiplication code. |
|
|
2967 */ |
|
|
2968 mp_err s_mp_mul_2d(mp_int *mp, mp_digit d) |
|
|
2969 { |
|
|
2970 mp_err res; |
|
|
2971 mp_digit save, next, mask, *dp; |
|
|
2972 mp_size used; |
|
|
2973 int ix; |
|
|
2974 |
|
|
2975 if((res = s_mp_lshd(mp, d / DIGIT_BIT)) != MP_OKAY) |
|
|
2976 return res; |
|
|
2977 |
|
|
2978 dp = DIGITS(mp); used = USED(mp); |
|
|
2979 d %= DIGIT_BIT; |
|
|
2980 |
|
|
2981 mask = (1 << d) - 1; |
|
|
2982 |
|
|
2983 /* If the shift requires another digit, make sure we've got one to |
|
|
2984 work with */ |
|
|
2985 if((dp[used - 1] >> (DIGIT_BIT - d)) & mask) { |
|
|
2986 if((res = s_mp_grow(mp, used + 1)) != MP_OKAY) |
|
|
2987 return res; |
|
|
2988 dp = DIGITS(mp); |
|
|
2989 } |
|
|
2990 |
|
|
2991 /* Do the shifting... */ |
|
|
2992 save = 0; |
|
|
2993 for(ix = 0; ix < used; ix++) { |
|
|
2994 next = (dp[ix] >> (DIGIT_BIT - d)) & mask; |
|
|
2995 dp[ix] = (dp[ix] << d) | save; |
|
|
2996 save = next; |
|
|
2997 } |
|
|
2998 |
|
|
2999 /* If, at this point, we have a nonzero carryout into the next |
|
|
3000 digit, we'll increase the size by one digit, and store it... |
|
|
3001 */ |
|
|
3002 if(save) { |
|
|
3003 dp[used] = save; |
|
|
3004 USED(mp) += 1; |
|
|
3005 } |
|
|
3006 |
|
|
3007 s_mp_clamp(mp); |
|
|
3008 return MP_OKAY; |
|
|
3009 |
|
|
3010 } /* end s_mp_mul_2d() */ |
|
|
3011 |
|
|
3012 /* }}} */ |
|
|
3013 |
|
|
3014 /* {{{ s_mp_div_2d(mp, d) */ |
|
|
3015 |
|
|
3016 /* |
|
|
3017 Divide the integer by 2^d, where d is a number of bits. This |
|
|
3018 amounts to a bitwise shift of the value, and does not require the |
|
|
3019 full division code (used in Barrett reduction, see below) |
|
|
3020 */ |
|
|
3021 void s_mp_div_2d(mp_int *mp, mp_digit d) |
|
|
3022 { |
|
|
3023 int ix; |
|
|
3024 mp_digit save, next, mask, *dp = DIGITS(mp); |
|
|
3025 |
|
|
3026 s_mp_rshd(mp, d / DIGIT_BIT); |
|
|
3027 d %= DIGIT_BIT; |
|
|
3028 |
|
|
3029 mask = (1 << d) - 1; |
|
|
3030 |
|
|
3031 save = 0; |
|
|
3032 for(ix = USED(mp) - 1; ix >= 0; ix--) { |
|
|
3033 next = dp[ix] & mask; |
|
|
3034 dp[ix] = (dp[ix] >> d) | (save << (DIGIT_BIT - d)); |
|
|
3035 save = next; |
|
|
3036 } |
|
|
3037 |
|
|
3038 s_mp_clamp(mp); |
|
|
3039 |
|
|
3040 } /* end s_mp_div_2d() */ |
|
|
3041 |
|
|
3042 /* }}} */ |
|
|
3043 |
|
|
3044 /* {{{ s_mp_norm(a, b) */ |
|
|
3045 |
|
|
3046 /* |
|
|
3047 s_mp_norm(a, b) |
|
|
3048 |
|
|
3049 Normalize a and b for division, where b is the divisor. In order |
|
|
3050 that we might make good guesses for quotient digits, we want the |
|
|
3051 leading digit of b to be at least half the radix, which we |
|
|
3052 accomplish by multiplying a and b by a constant. This constant is |
|
|
3053 returned (so that it can be divided back out of the remainder at the |
|
|
3054 end of the division process). |
|
|
3055 |
|
|
3056 We multiply by the smallest power of 2 that gives us a leading digit |
|
|
3057 at least half the radix. By choosing a power of 2, we simplify the |
|
|
3058 multiplication and division steps to simple shifts. |
|
|
3059 */ |
|
|
3060 mp_digit s_mp_norm(mp_int *a, mp_int *b) |
|
|
3061 { |
|
|
3062 mp_digit t, d = 0; |
|
|
3063 |
|
|
3064 t = DIGIT(b, USED(b) - 1); |
|
|
3065 while(t < (RADIX / 2)) { |
|
|
3066 t <<= 1; |
|
|
3067 ++d; |
|
|
3068 } |
|
|
3069 |
|
|
3070 if(d != 0) { |
|
|
3071 s_mp_mul_2d(a, d); |
|
|
3072 s_mp_mul_2d(b, d); |
|
|
3073 } |
|
|
3074 |
|
|
3075 return d; |
|
|
3076 |
|
|
3077 } /* end s_mp_norm() */ |
|
|
3078 |
|
|
3079 /* }}} */ |
|
|
3080 |
|
|
3081 /* }}} */ |
|
|
3082 |
|
|
3083 /* {{{ Primitive digit arithmetic */ |
|
|
3084 |
|
|
3085 /* {{{ s_mp_add_d(mp, d) */ |
|
|
3086 |
|
|
3087 /* Add d to |mp| in place */ |
|
|
3088 mp_err s_mp_add_d(mp_int *mp, mp_digit d) /* unsigned digit addition */ |
|
|
3089 { |
|
|
3090 mp_word w, k = 0; |
|
|
3091 mp_size ix = 1, used = USED(mp); |
|
|
3092 mp_digit *dp = DIGITS(mp); |
|
|
3093 |
|
|
3094 w = dp[0] + d; |
|
|
3095 dp[0] = ACCUM(w); |
|
|
3096 k = CARRYOUT(w); |
|
|
3097 |
|
|
3098 while(ix < used && k) { |
|
|
3099 w = dp[ix] + k; |
|
|
3100 dp[ix] = ACCUM(w); |
|
|
3101 k = CARRYOUT(w); |
|
|
3102 ++ix; |
|
|
3103 } |
|
|
3104 |
|
|
3105 if(k != 0) { |
|
|
3106 mp_err res; |
|
|
3107 |
|
|
3108 if((res = s_mp_pad(mp, USED(mp) + 1)) != MP_OKAY) |
|
|
3109 return res; |
|
|
3110 |
|
|
3111 DIGIT(mp, ix) = k; |
|
|
3112 } |
|
|
3113 |
|
|
3114 return MP_OKAY; |
|
|
3115 |
|
|
3116 } /* end s_mp_add_d() */ |
|
|
3117 |
|
|
3118 /* }}} */ |
|
|
3119 |
|
|
3120 /* {{{ s_mp_sub_d(mp, d) */ |
|
|
3121 |
|
|
3122 /* Subtract d from |mp| in place, assumes |mp| > d */ |
|
|
3123 mp_err s_mp_sub_d(mp_int *mp, mp_digit d) /* unsigned digit subtract */ |
|
|
3124 { |
|
|
3125 mp_word w, b = 0; |
|
|
3126 mp_size ix = 1, used = USED(mp); |
|
|
3127 mp_digit *dp = DIGITS(mp); |
|
|
3128 |
|
|
3129 /* Compute initial subtraction */ |
|
|
3130 w = (RADIX + dp[0]) - d; |
|
|
3131 b = CARRYOUT(w) ? 0 : 1; |
|
|
3132 dp[0] = ACCUM(w); |
|
|
3133 |
|
|
3134 /* Propagate borrows leftward */ |
|
|
3135 while(b && ix < used) { |
|
|
3136 w = (RADIX + dp[ix]) - b; |
|
|
3137 b = CARRYOUT(w) ? 0 : 1; |
|
|
3138 dp[ix] = ACCUM(w); |
|
|
3139 ++ix; |
|
|
3140 } |
|
|
3141 |
|
|
3142 /* Remove leading zeroes */ |
|
|
3143 s_mp_clamp(mp); |
|
|
3144 |
|
|
3145 /* If we have a borrow out, it's a violation of the input invariant */ |
|
|
3146 if(b) |
|
|
3147 return MP_RANGE; |
|
|
3148 else |
|
|
3149 return MP_OKAY; |
|
|
3150 |
|
|
3151 } /* end s_mp_sub_d() */ |
|
|
3152 |
|
|
3153 /* }}} */ |
|
|
3154 |
|
|
3155 /* {{{ s_mp_mul_d(a, d) */ |
|
|
3156 |
|
|
3157 /* Compute a = a * d, single digit multiplication */ |
|
|
3158 mp_err s_mp_mul_d(mp_int *a, mp_digit d) |
|
|
3159 { |
|
|
3160 mp_word w, k = 0; |
|
|
3161 mp_size ix, max; |
|
|
3162 mp_err res; |
|
|
3163 mp_digit *dp = DIGITS(a); |
|
|
3164 |
|
|
3165 /* |
|
|
3166 Single-digit multiplication will increase the precision of the |
|
|
3167 output by at most one digit. However, we can detect when this |
|
|
3168 will happen -- if the high-order digit of a, times d, gives a |
|
|
3169 two-digit result, then the precision of the result will increase; |
|
|
3170 otherwise it won't. We use this fact to avoid calling s_mp_pad() |
|
|
3171 unless absolutely necessary. |
|
|
3172 */ |
|
|
3173 max = USED(a); |
|
|
3174 w = dp[max - 1] * d; |
|
|
3175 if(CARRYOUT(w) != 0) { |
|
|
3176 if((res = s_mp_pad(a, max + 1)) != MP_OKAY) |
|
|
3177 return res; |
|
|
3178 dp = DIGITS(a); |
|
|
3179 } |
|
|
3180 |
|
|
3181 for(ix = 0; ix < max; ix++) { |
|
|
3182 w = (dp[ix] * d) + k; |
|
|
3183 dp[ix] = ACCUM(w); |
|
|
3184 k = CARRYOUT(w); |
|
|
3185 } |
|
|
3186 |
|
|
3187 /* If there is a precision increase, take care of it here; the above |
|
|
3188 test guarantees we have enough storage to do this safely. |
|
|
3189 */ |
|
|
3190 if(k) { |
|
|
3191 dp[max] = k; |
|
|
3192 USED(a) = max + 1; |
|
|
3193 } |
|
|
3194 |
|
|
3195 s_mp_clamp(a); |
|
|
3196 |
|
|
3197 return MP_OKAY; |
|
|
3198 |
|
|
3199 } /* end s_mp_mul_d() */ |
|
|
3200 |
|
|
3201 /* }}} */ |
|
|
3202 |
|
|
3203 /* {{{ s_mp_div_d(mp, d, r) */ |
|
|
3204 |
|
|
3205 /* |
|
|
3206 s_mp_div_d(mp, d, r) |
|
|
3207 |
|
|
3208 Compute the quotient mp = mp / d and remainder r = mp mod d, for a |
|
|
3209 single digit d. If r is null, the remainder will be discarded. |
|
|
3210 */ |
|
|
3211 |
|
|
3212 mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r) |
|
|
3213 { |
|
|
3214 mp_word w = 0, t; |
|
|
3215 mp_int quot; |
|
|
3216 mp_err res; |
|
|
3217 mp_digit *dp = DIGITS(mp), *qp; |
|
|
3218 int ix; |
|
|
3219 |
|
|
3220 if(d == 0) |
|
|
3221 return MP_RANGE; |
|
|
3222 |
|
|
3223 /* Make room for the quotient */ |
|
|
3224 if((res = mp_init_size(", USED(mp))) != MP_OKAY) |
|
|
3225 return res; |
|
|
3226 |
|
|
3227 USED(") = USED(mp); /* so clamping will work below */ |
|
|
3228 qp = DIGITS("); |
|
|
3229 |
|
|
3230 /* Divide without subtraction */ |
|
|
3231 for(ix = USED(mp) - 1; ix >= 0; ix--) { |
|
|
3232 w = (w << DIGIT_BIT) | dp[ix]; |
|
|
3233 |
|
|
3234 if(w >= d) { |
|
|
3235 t = w / d; |
|
|
3236 w = w % d; |
|
|
3237 } else { |
|
|
3238 t = 0; |
|
|
3239 } |
|
|
3240 |
|
|
3241 qp[ix] = t; |
|
|
3242 } |
|
|
3243 |
|
|
3244 /* Deliver the remainder, if desired */ |
|
|
3245 if(r) |
|
|
3246 *r = w; |
|
|
3247 |
|
|
3248 s_mp_clamp("); |
|
|
3249 mp_exch(", mp); |
|
|
3250 mp_clear("); |
|
|
3251 |
|
|
3252 return MP_OKAY; |
|
|
3253 |
|
|
3254 } /* end s_mp_div_d() */ |
|
|
3255 |
|
|
3256 /* }}} */ |
|
|
3257 |
|
|
3258 /* }}} */ |
|
|
3259 |
|
|
3260 /* {{{ Primitive full arithmetic */ |
|
|
3261 |
|
|
3262 /* {{{ s_mp_add(a, b) */ |
|
|
3263 |
|
|
3264 /* Compute a = |a| + |b| */ |
|
|
3265 mp_err s_mp_add(mp_int *a, mp_int *b) /* magnitude addition */ |
|
|
3266 { |
|
|
3267 mp_word w = 0; |
|
|
3268 mp_digit *pa, *pb; |
|
|
3269 mp_size ix, used = USED(b); |
|
|
3270 mp_err res; |
|
|
3271 |
|
|
3272 /* Make sure a has enough precision for the output value */ |
|
|
3273 if((used > USED(a)) && (res = s_mp_pad(a, used)) != MP_OKAY) |
|
|
3274 return res; |
|
|
3275 |
|
|
3276 /* |
|
|
3277 Add up all digits up to the precision of b. If b had initially |
|
|
3278 the same precision as a, or greater, we took care of it by the |
|
|
3279 padding step above, so there is no problem. If b had initially |
|
|
3280 less precision, we'll have to make sure the carry out is duly |
|
|
3281 propagated upward among the higher-order digits of the sum. |
|
|
3282 */ |
|
|
3283 pa = DIGITS(a); |
|
|
3284 pb = DIGITS(b); |
|
|
3285 for(ix = 0; ix < used; ++ix) { |
|
|
3286 w += *pa + *pb++; |
|
|
3287 *pa++ = ACCUM(w); |
|
|
3288 w = CARRYOUT(w); |
|
|
3289 } |
|
|
3290 |
|
|
3291 /* If we run out of 'b' digits before we're actually done, make |
|
|
3292 sure the carries get propagated upward... |
|
|
3293 */ |
|
|
3294 used = USED(a); |
|
|
3295 while(w && ix < used) { |
|
|
3296 w += *pa; |
|
|
3297 *pa++ = ACCUM(w); |
|
|
3298 w = CARRYOUT(w); |
|
|
3299 ++ix; |
|
|
3300 } |
|
|
3301 |
|
|
3302 /* If there's an overall carry out, increase precision and include |
|
|
3303 it. We could have done this initially, but why touch the memory |
|
|
3304 allocator unless we're sure we have to? |
|
|
3305 */ |
|
|
3306 if(w) { |
|
|
3307 if((res = s_mp_pad(a, used + 1)) != MP_OKAY) |
|
|
3308 return res; |
|
|
3309 |
|
|
3310 DIGIT(a, ix) = w; /* pa may not be valid after s_mp_pad() call */ |
|
|
3311 } |
|
|
3312 |
|
|
3313 return MP_OKAY; |
|
|
3314 |
|
|
3315 } /* end s_mp_add() */ |
|
|
3316 |
|
|
3317 /* }}} */ |
|
|
3318 |
|
|
3319 /* {{{ s_mp_sub(a, b) */ |
|
|
3320 |
|
|
3321 /* Compute a = |a| - |b|, assumes |a| >= |b| */ |
|
|
3322 mp_err s_mp_sub(mp_int *a, mp_int *b) /* magnitude subtract */ |
|
|
3323 { |
|
|
3324 mp_word w = 0; |
|
|
3325 mp_digit *pa, *pb; |
|
|
3326 mp_size ix, used = USED(b); |
|
|
3327 |
|
|
3328 /* |
|
|
3329 Subtract and propagate borrow. Up to the precision of b, this |
|
|
3330 accounts for the digits of b; after that, we just make sure the |
|
|
3331 carries get to the right place. This saves having to pad b out to |
|
|
3332 the precision of a just to make the loops work right... |
|
|
3333 */ |
|
|
3334 pa = DIGITS(a); |
|
|
3335 pb = DIGITS(b); |
|
|
3336 |
|
|
3337 for(ix = 0; ix < used; ++ix) { |
|
|
3338 w = (RADIX + *pa) - w - *pb++; |
|
|
3339 *pa++ = ACCUM(w); |
|
|
3340 w = CARRYOUT(w) ? 0 : 1; |
|
|
3341 } |
|
|
3342 |
|
|
3343 used = USED(a); |
|
|
3344 while(ix < used) { |
|
|
3345 w = RADIX + *pa - w; |
|
|
3346 *pa++ = ACCUM(w); |
|
|
3347 w = CARRYOUT(w) ? 0 : 1; |
|
|
3348 ++ix; |
|
|
3349 } |
|
|
3350 |
|
|
3351 /* Clobber any leading zeroes we created */ |
|
|
3352 s_mp_clamp(a); |
|
|
3353 |
|
|
3354 /* |
|
|
3355 If there was a borrow out, then |b| > |a| in violation |
|
|
3356 of our input invariant. We've already done the work, |
|
|
3357 but we'll at least complain about it... |
|
|
3358 */ |
|
|
3359 if(w) |
|
|
3360 return MP_RANGE; |
|
|
3361 else |
|
|
3362 return MP_OKAY; |
|
|
3363 |
|
|
3364 } /* end s_mp_sub() */ |
|
|
3365 |
|
|
3366 /* }}} */ |
|
|
3367 |
|
|
3368 mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu) |
|
|
3369 { |
|
|
3370 mp_int q; |
|
|
3371 mp_err res; |
|
|
3372 mp_size um = USED(m); |
|
|
3373 |
|
|
3374 if((res = mp_init_copy(&q, x)) != MP_OKAY) |
|
|
3375 return res; |
|
|
3376 |
|
|
3377 s_mp_rshd(&q, um - 1); /* q1 = x / b^(k-1) */ |
|
|
3378 s_mp_mul(&q, mu); /* q2 = q1 * mu */ |
|
|
3379 s_mp_rshd(&q, um + 1); /* q3 = q2 / b^(k+1) */ |
|
|
3380 |
|
|
3381 /* x = x mod b^(k+1), quick (no division) */ |
|
|
3382 s_mp_mod_2d(x, (mp_digit)(DIGIT_BIT * (um + 1))); |
|
|
3383 |
|
|
3384 /* q = q * m mod b^(k+1), quick (no division), uses the short multiplier */ |
|
|
3385 #ifndef SHRT_MUL |
|
|
3386 s_mp_mul(&q, m); |
|
|
3387 s_mp_mod_2d(&q, (mp_digit)(DIGIT_BIT * (um + 1))); |
|
|
3388 #else |
|
|
3389 s_mp_mul_dig(&q, m, um + 1); |
|
|
3390 #endif |
|
|
3391 |
|
|
3392 /* x = x - q */ |
|
|
3393 if((res = mp_sub(x, &q, x)) != MP_OKAY) |
|
|
3394 goto CLEANUP; |
|
|
3395 |
|
|
3396 /* If x < 0, add b^(k+1) to it */ |
|
|
3397 if(mp_cmp_z(x) < 0) { |
|
|
3398 mp_set(&q, 1); |
|
|
3399 if((res = s_mp_lshd(&q, um + 1)) != MP_OKAY) |
|
|
3400 goto CLEANUP; |
|
|
3401 if((res = mp_add(x, &q, x)) != MP_OKAY) |
|
|
3402 goto CLEANUP; |
|
|
3403 } |
|
|
3404 |
|
|
3405 /* Back off if it's too big */ |
|
|
3406 while(mp_cmp(x, m) >= 0) { |
|
|
3407 if((res = s_mp_sub(x, m)) != MP_OKAY) |
|
|
3408 break; |
|
|
3409 } |
|
|
3410 |
|
|
3411 CLEANUP: |
|
|
3412 mp_clear(&q); |
|
|
3413 |
|
|
3414 return res; |
|
|
3415 |
|
|
3416 } /* end s_mp_reduce() */ |
|
|
3417 |
|
|
3418 |
|
|
3419 |
|
|
3420 /* {{{ s_mp_mul(a, b) */ |
|
|
3421 |
|
|
3422 /* Compute a = |a| * |b| */ |
|
|
3423 mp_err s_mp_mul(mp_int *a, mp_int *b) |
|
|
3424 { |
|
|
3425 mp_word w, k = 0; |
|
|
3426 mp_int tmp; |
|
|
3427 mp_err res; |
|
|
3428 mp_size ix, jx, ua = USED(a), ub = USED(b); |
|
|
3429 mp_digit *pa, *pb, *pt, *pbt; |
|
|
3430 |
|
|
3431 if((res = mp_init_size(&tmp, ua + ub)) != MP_OKAY) |
|
|
3432 return res; |
|
|
3433 |
|
|
3434 /* This has the effect of left-padding with zeroes... */ |
|
|
3435 USED(&tmp) = ua + ub; |
|
|
3436 |
|
|
3437 /* We're going to need the base value each iteration */ |
|
|
3438 pbt = DIGITS(&tmp); |
|
|
3439 |
|
|
3440 /* Outer loop: Digits of b */ |
|
|
3441 |
|
|
3442 pb = DIGITS(b); |
|
|
3443 for(ix = 0; ix < ub; ++ix, ++pb) { |
|
|
3444 if(*pb == 0) |
|
|
3445 continue; |
|
|
3446 |
|
|
3447 /* Inner product: Digits of a */ |
|
|
3448 pa = DIGITS(a); |
|
|
3449 for(jx = 0; jx < ua; ++jx, ++pa) { |
|
|
3450 pt = pbt + ix + jx; |
|
|
3451 w = *pb * *pa + k + *pt; |
|
|
3452 *pt = ACCUM(w); |
|
|
3453 k = CARRYOUT(w); |
|
|
3454 } |
|
|
3455 |
|
|
3456 pbt[ix + jx] = k; |
|
|
3457 k = 0; |
|
|
3458 } |
|
|
3459 |
|
|
3460 s_mp_clamp(&tmp); |
|
|
3461 s_mp_exch(&tmp, a); |
|
|
3462 |
|
|
3463 mp_clear(&tmp); |
|
|
3464 |
|
|
3465 return MP_OKAY; |
|
|
3466 |
|
|
3467 } /* end s_mp_mul() */ |
|
|
3468 |
|
|
3469 /* }}} */ |
|
|
3470 |
|
|
3471 /* {{{ s_mp_kmul(a, b, out, len) */ |
|
|
3472 |
|
|
3473 #if 0 |
|
|
3474 void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len) |
|
|
3475 { |
|
|
3476 mp_word w, k = 0; |
|
|
3477 mp_size ix, jx; |
|
|
3478 mp_digit *pa, *pt; |
|
|
3479 |
|
|
3480 for(ix = 0; ix < len; ++ix, ++b) { |
|
|
3481 if(*b == 0) |
|
|
3482 continue; |
|
|
3483 |
|
|
3484 pa = a; |
|
|
3485 for(jx = 0; jx < len; ++jx, ++pa) { |
|
|
3486 pt = out + ix + jx; |
|
|
3487 w = *b * *pa + k + *pt; |
|
|
3488 *pt = ACCUM(w); |
|
|
3489 k = CARRYOUT(w); |
|
|
3490 } |
|
|
3491 |
|
|
3492 out[ix + jx] = k; |
|
|
3493 k = 0; |
|
|
3494 } |
|
|
3495 |
|
|
3496 } /* end s_mp_kmul() */ |
|
|
3497 #endif |
|
|
3498 |
|
|
3499 /* }}} */ |
|
|
3500 |
|
|
3501 /* {{{ s_mp_sqr(a) */ |
|
|
3502 |
|
|
3503 /* |
|
|
3504 Computes the square of a, in place. This can be done more |
|
|
3505 efficiently than a general multiplication, because many of the |
|
|
3506 computation steps are redundant when squaring. The inner product |
|
|
3507 step is a bit more complicated, but we save a fair number of |
|
|
3508 iterations of the multiplication loop. |
|
|
3509 */ |
|
|
3510 #if MP_SQUARE |
|
|
3511 mp_err s_mp_sqr(mp_int *a) |
|
|
3512 { |
|
|
3513 mp_word w, k = 0; |
|
|
3514 mp_int tmp; |
|
|
3515 mp_err res; |
|
|
3516 mp_size ix, jx, kx, used = USED(a); |
|
|
3517 mp_digit *pa1, *pa2, *pt, *pbt; |
|
|
3518 |
|
|
3519 if((res = mp_init_size(&tmp, 2 * used)) != MP_OKAY) |
|
|
3520 return res; |
|
|
3521 |
|
|
3522 /* Left-pad with zeroes */ |
|
|
3523 USED(&tmp) = 2 * used; |
|
|
3524 |
|
|
3525 /* We need the base value each time through the loop */ |
|
|
3526 pbt = DIGITS(&tmp); |
|
|
3527 |
|
|
3528 pa1 = DIGITS(a); |
|
|
3529 for(ix = 0; ix < used; ++ix, ++pa1) { |
|
|
3530 if(*pa1 == 0) |
|
|
3531 continue; |
|
|
3532 |
|
|
3533 w = DIGIT(&tmp, ix + ix) + (*pa1 * *pa1); |
|
|
3534 |
|
|
3535 pbt[ix + ix] = ACCUM(w); |
|
|
3536 k = CARRYOUT(w); |
|
|
3537 |
|
|
3538 /* |
|
|
3539 The inner product is computed as: |
|
|
3540 |
|
|
3541 (C, S) = t[i,j] + 2 a[i] a[j] + C |
|
|
3542 |
|
|
3543 This can overflow what can be represented in an mp_word, and |
|
|
3544 since C arithmetic does not provide any way to check for |
|
|
3545 overflow, we have to check explicitly for overflow conditions |
|
|
3546 before they happen. |
|
|
3547 */ |
|
|
3548 for(jx = ix + 1, pa2 = DIGITS(a) + jx; jx < used; ++jx, ++pa2) { |
|
|
3549 mp_word u = 0, v; |
|
|
3550 |
|
|
3551 /* Store this in a temporary to avoid indirections later */ |
|
|
3552 pt = pbt + ix + jx; |
|
|
3553 |
|
|
3554 /* Compute the multiplicative step */ |
|
|
3555 w = *pa1 * *pa2; |
|
|
3556 |
|
|
3557 /* If w is more than half MP_WORD_MAX, the doubling will |
|
|
3558 overflow, and we need to record a carry out into the next |
|
|
3559 word */ |
|
|
3560 u = (w >> (MP_WORD_BIT - 1)) & 1; |
|
|
3561 |
|
|
3562 /* Double what we've got, overflow will be ignored as defined |
|
|
3563 for C arithmetic (we've already noted if it is to occur) |
|
|
3564 */ |
|
|
3565 w *= 2; |
|
|
3566 |
|
|
3567 /* Compute the additive step */ |
|
|
3568 v = *pt + k; |
|
|
3569 |
|
|
3570 /* If we do not already have an overflow carry, check to see |
|
|
3571 if the addition will cause one, and set the carry out if so |
|
|
3572 */ |
|
|
3573 u |= ((MP_WORD_MAX - v) < w); |
|
|
3574 |
|
|
3575 /* Add in the rest, again ignoring overflow */ |
|
|
3576 w += v; |
|
|
3577 |
|
|
3578 /* Set the i,j digit of the output */ |
|
|
3579 *pt = ACCUM(w); |
|
|
3580 |
|
|
3581 /* Save carry information for the next iteration of the loop. |
|
|
3582 This is why k must be an mp_word, instead of an mp_digit */ |
|
|
3583 k = CARRYOUT(w) | (u << DIGIT_BIT); |
|
|
3584 |
|
|
3585 } /* for(jx ...) */ |
|
|
3586 |
|
|
3587 /* Set the last digit in the cycle and reset the carry */ |
|
|
3588 k = DIGIT(&tmp, ix + jx) + k; |
|
|
3589 pbt[ix + jx] = ACCUM(k); |
|
|
3590 k = CARRYOUT(k); |
|
|
3591 |
|
|
3592 /* If we are carrying out, propagate the carry to the next digit |
|
|
3593 in the output. This may cascade, so we have to be somewhat |
|
|
3594 circumspect -- but we will have enough precision in the output |
|
|
3595 that we won't overflow |
|
|
3596 */ |
|
|
3597 kx = 1; |
|
|
3598 while(k) { |
|
|
3599 k = pbt[ix + jx + kx] + 1; |
|
|
3600 pbt[ix + jx + kx] = ACCUM(k); |
|
|
3601 k = CARRYOUT(k); |
|
|
3602 ++kx; |
|
|
3603 } |
|
|
3604 } /* for(ix ...) */ |
|
|
3605 |
|
|
3606 s_mp_clamp(&tmp); |
|
|
3607 s_mp_exch(&tmp, a); |
|
|
3608 |
|
|
3609 mp_clear(&tmp); |
|
|
3610 |
|
|
3611 return MP_OKAY; |
|
|
3612 |
|
|
3613 } /* end s_mp_sqr() */ |
|
|
3614 #endif |
|
|
3615 |
|
|
3616 /* }}} */ |
|
|
3617 |
|
|
3618 /* {{{ s_mp_div(a, b) */ |
|
|
3619 |
|
|
3620 /* |
|
|
3621 s_mp_div(a, b) |
|
|
3622 |
|
|
3623 Compute a = a / b and b = a mod b. Assumes b > a. |
|
|
3624 */ |
|
|
3625 |
|
|
3626 mp_err s_mp_div(mp_int *a, mp_int *b) |
|
|
3627 { |
|
|
3628 mp_int quot, rem, t; |
|
|
3629 mp_word q; |
|
|
3630 mp_err res; |
|
|
3631 mp_digit d; |
|
|
3632 int ix; |
|
|
3633 |
|
|
3634 if(mp_cmp_z(b) == 0) |
|
|
3635 return MP_RANGE; |
|
|
3636 |
|
|
3637 /* Shortcut if b is power of two */ |
|
|
3638 if((ix = s_mp_ispow2(b)) >= 0) { |
|
|
3639 mp_copy(a, b); /* need this for remainder */ |
|
|
3640 s_mp_div_2d(a, (mp_digit)ix); |
|
|
3641 s_mp_mod_2d(b, (mp_digit)ix); |
|
|
3642 |
|
|
3643 return MP_OKAY; |
|
|
3644 } |
|
|
3645 |
|
|
3646 /* Allocate space to store the quotient */ |
|
|
3647 if((res = mp_init_size(", USED(a))) != MP_OKAY) |
|
|
3648 return res; |
|
|
3649 |
|
|
3650 /* A working temporary for division */ |
|
|
3651 if((res = mp_init_size(&t, USED(a))) != MP_OKAY) |
|
|
3652 goto T; |
|
|
3653 |
|
|
3654 /* Allocate space for the remainder */ |
|
|
3655 if((res = mp_init_size(&rem, USED(a))) != MP_OKAY) |
|
|
3656 goto REM; |
|
|
3657 |
|
|
3658 /* Normalize to optimize guessing */ |
|
|
3659 d = s_mp_norm(a, b); |
|
|
3660 |
|
|
3661 /* Perform the division itself...woo! */ |
|
|
3662 ix = USED(a) - 1; |
|
|
3663 |
|
|
3664 while(ix >= 0) { |
|
|
3665 /* Find a partial substring of a which is at least b */ |
|
|
3666 while(s_mp_cmp(&rem, b) < 0 && ix >= 0) { |
|
|
3667 if((res = s_mp_lshd(&rem, 1)) != MP_OKAY) |
|
|
3668 goto CLEANUP; |
|
|
3669 |
|
|
3670 if((res = s_mp_lshd(", 1)) != MP_OKAY) |
|
|
3671 goto CLEANUP; |
|
|
3672 |
|
|
3673 DIGIT(&rem, 0) = DIGIT(a, ix); |
|
|
3674 s_mp_clamp(&rem); |
|
|
3675 --ix; |
|
|
3676 } |
|
|
3677 |
|
|
3678 /* If we didn't find one, we're finished dividing */ |
|
|
3679 if(s_mp_cmp(&rem, b) < 0) |
|
|
3680 break; |
|
|
3681 |
|
|
3682 /* Compute a guess for the next quotient digit */ |
|
|
3683 q = DIGIT(&rem, USED(&rem) - 1); |
|
|
3684 if(q <= DIGIT(b, USED(b) - 1) && USED(&rem) > 1) |
|
|
3685 q = (q << DIGIT_BIT) | DIGIT(&rem, USED(&rem) - 2); |
|
|
3686 |
|
|
3687 q /= DIGIT(b, USED(b) - 1); |
|
|
3688 |
|
|
3689 /* The guess can be as much as RADIX + 1 */ |
|
|
3690 if(q >= RADIX) |
|
|
3691 q = RADIX - 1; |
|
|
3692 |
|
|
3693 /* See what that multiplies out to */ |
|
|
3694 mp_copy(b, &t); |
|
|
3695 if((res = s_mp_mul_d(&t, q)) != MP_OKAY) |
|
|
3696 goto CLEANUP; |
|
|
3697 |
|
|
3698 /* |
|
|
3699 If it's too big, back it off. We should not have to do this |
|
|
3700 more than once, or, in rare cases, twice. Knuth describes a |
|
|
3701 method by which this could be reduced to a maximum of once, but |
|
|
3702 I didn't implement that here. |
|
|
3703 */ |
|
|
3704 while(s_mp_cmp(&t, &rem) > 0) { |
|
|
3705 --q; |
|
|
3706 s_mp_sub(&t, b); |
|
|
3707 } |
|
|
3708 |
|
|
3709 /* At this point, q should be the right next digit */ |
|
|
3710 if((res = s_mp_sub(&rem, &t)) != MP_OKAY) |
|
|
3711 goto CLEANUP; |
|
|
3712 |
|
|
3713 /* |
|
|
3714 Include the digit in the quotient. We allocated enough memory |
|
|
3715 for any quotient we could ever possibly get, so we should not |
|
|
3716 have to check for failures here |
|
|
3717 */ |
|
|
3718 DIGIT(", 0) = q; |
|
|
3719 } |
|
|
3720 |
|
|
3721 /* Denormalize remainder */ |
|
|
3722 if(d != 0) |
|
|
3723 s_mp_div_2d(&rem, d); |
|
|
3724 |
|
|
3725 s_mp_clamp("); |
|
|
3726 s_mp_clamp(&rem); |
|
|
3727 |
|
|
3728 /* Copy quotient back to output */ |
|
|
3729 s_mp_exch(", a); |
|
|
3730 |
|
|
3731 /* Copy remainder back to output */ |
|
|
3732 s_mp_exch(&rem, b); |
|
|
3733 |
|
|
3734 CLEANUP: |
|
|
3735 mp_clear(&rem); |
|
|
3736 REM: |
|
|
3737 mp_clear(&t); |
|
|
3738 T: |
|
|
3739 mp_clear("); |
|
|
3740 |
|
|
3741 return res; |
|
|
3742 |
|
|
3743 } /* end s_mp_div() */ |
|
|
3744 |
|
|
3745 /* }}} */ |
|
|
3746 |
|
|
3747 /* {{{ s_mp_2expt(a, k) */ |
|
|
3748 |
|
|
3749 mp_err s_mp_2expt(mp_int *a, mp_digit k) |
|
|
3750 { |
|
|
3751 mp_err res; |
|
|
3752 mp_size dig, bit; |
|
|
3753 |
|
|
3754 dig = k / DIGIT_BIT; |
|
|
3755 bit = k % DIGIT_BIT; |
|
|
3756 |
|
|
3757 mp_zero(a); |
|
|
3758 if((res = s_mp_pad(a, dig + 1)) != MP_OKAY) |
|
|
3759 return res; |
|
|
3760 |
|
|
3761 DIGIT(a, dig) |= (1 << bit); |
|
|
3762 |
|
|
3763 return MP_OKAY; |
|
|
3764 |
|
|
3765 } /* end s_mp_2expt() */ |
|
|
3766 |
|
|
3767 /* }}} */ |
|
|
3768 |
|
|
3769 |
|
|
3770 /* }}} */ |
|
|
3771 |
|
|
3772 /* }}} */ |
|
|
3773 |
|
|
3774 /* {{{ Primitive comparisons */ |
|
|
3775 |
|
|
3776 /* {{{ s_mp_cmp(a, b) */ |
|
|
3777 |
|
|
3778 /* Compare |a| <=> |b|, return 0 if equal, <0 if a<b, >0 if a>b */ |
|
|
3779 int s_mp_cmp(mp_int *a, mp_int *b) |
|
|
3780 { |
|
|
3781 mp_size ua = USED(a), ub = USED(b); |
|
|
3782 |
|
|
3783 if(ua > ub) |
|
|
3784 return MP_GT; |
|
|
3785 else if(ua < ub) |
|
|
3786 return MP_LT; |
|
|
3787 else { |
|
|
3788 int ix = ua - 1; |
|
|
3789 mp_digit *ap = DIGITS(a) + ix, *bp = DIGITS(b) + ix; |
|
|
3790 |
|
|
3791 while(ix >= 0) { |
|
|
3792 if(*ap > *bp) |
|
|
3793 return MP_GT; |
|
|
3794 else if(*ap < *bp) |
|
|
3795 return MP_LT; |
|
|
3796 |
|
|
3797 --ap; --bp; --ix; |
|
|
3798 } |
|
|
3799 |
|
|
3800 return MP_EQ; |
|
|
3801 } |
|
|
3802 |
|
|
3803 } /* end s_mp_cmp() */ |
|
|
3804 |
|
|
3805 /* }}} */ |
|
|
3806 |
|
|
3807 /* {{{ s_mp_cmp_d(a, d) */ |
|
|
3808 |
|
|
3809 /* Compare |a| <=> d, return 0 if equal, <0 if a<d, >0 if a>d */ |
|
|
3810 int s_mp_cmp_d(mp_int *a, mp_digit d) |
|
|
3811 { |
|
|
3812 mp_size ua = USED(a); |
|
|
3813 mp_digit *ap = DIGITS(a); |
|
|
3814 |
|
|
3815 if(ua > 1) |
|
|
3816 return MP_GT; |
|
|
3817 |
|
|
3818 if(*ap < d) |
|
|
3819 return MP_LT; |
|
|
3820 else if(*ap > d) |
|
|
3821 return MP_GT; |
|
|
3822 else |
|
|
3823 return MP_EQ; |
|
|
3824 |
|
|
3825 } /* end s_mp_cmp_d() */ |
|
|
3826 |
|
|
3827 /* }}} */ |
|
|
3828 |
|
|
3829 /* {{{ s_mp_ispow2(v) */ |
|
|
3830 |
|
|
3831 /* |
|
|
3832 Returns -1 if the value is not a power of two; otherwise, it returns |
|
|
3833 k such that v = 2^k, i.e. lg(v). |
|
|
3834 */ |
|
|
3835 int s_mp_ispow2(mp_int *v) |
|
|
3836 { |
|
|
3837 mp_digit d, *dp; |
|
|
3838 mp_size uv = USED(v); |
|
|
3839 int extra = 0, ix; |
|
|
3840 |
|
|
3841 d = DIGIT(v, uv - 1); /* most significant digit of v */ |
|
|
3842 |
|
|
3843 while(d && ((d & 1) == 0)) { |
|
|
3844 d >>= 1; |
|
|
3845 ++extra; |
|
|
3846 } |
|
|
3847 |
|
|
3848 if(d == 1) { |
|
|
3849 ix = uv - 2; |
|
|
3850 dp = DIGITS(v) + ix; |
|
|
3851 |
|
|
3852 while(ix >= 0) { |
|
|
3853 if(*dp) |
|
|
3854 return -1; /* not a power of two */ |
|
|
3855 |
|
|
3856 --dp; --ix; |
|
|
3857 } |
|
|
3858 |
|
|
3859 return ((uv - 1) * DIGIT_BIT) + extra; |
|
|
3860 } |
|
|
3861 |
|
|
3862 return -1; |
|
|
3863 |
|
|
3864 } /* end s_mp_ispow2() */ |
|
|
3865 |
|
|
3866 /* }}} */ |
|
|
3867 |
|
|
3868 /* {{{ s_mp_ispow2d(d) */ |
|
|
3869 |
|
|
3870 int s_mp_ispow2d(mp_digit d) |
|
|
3871 { |
|
|
3872 int pow = 0; |
|
|
3873 |
|
|
3874 while((d & 1) == 0) { |
|
|
3875 ++pow; d >>= 1; |
|
|
3876 } |
|
|
3877 |
|
|
3878 if(d == 1) |
|
|
3879 return pow; |
|
|
3880 |
|
|
3881 return -1; |
|
|
3882 |
|
|
3883 } /* end s_mp_ispow2d() */ |
|
|
3884 |
|
|
3885 /* }}} */ |
|
|
3886 |
|
|
3887 /* }}} */ |
|
|
3888 |
|
|
3889 /* {{{ Primitive I/O helpers */ |
|
|
3890 |
|
|
3891 /* {{{ s_mp_tovalue(ch, r) */ |
|
|
3892 |
|
|
3893 /* |
|
|
3894 Convert the given character to its digit value, in the given radix. |
|
|
3895 If the given character is not understood in the given radix, -1 is |
|
|
3896 returned. Otherwise the digit's numeric value is returned. |
|
|
3897 |
|
|
3898 The results will be odd if you use a radix < 2 or > 62, you are |
|
|
3899 expected to know what you're up to. |
|
|
3900 */ |
|
|
3901 int s_mp_tovalue(char ch, int r) |
|
|
3902 { |
|
|
3903 int val, xch; |
|
|
3904 |
|
|
3905 if(r > 36) |
|
|
3906 xch = ch; |
|
|
3907 else |
|
|
3908 xch = toupper(ch); |
|
|
3909 |
|
|
3910 if(isdigit(xch)) |
|
|
3911 val = xch - '0'; |
|
|
3912 else if(isupper(xch)) |
|
|
3913 val = xch - 'A' + 10; |
|
|
3914 else if(islower(xch)) |
|
|
3915 val = xch - 'a' + 36; |
|
|
3916 else if(xch == '+') |
|
|
3917 val = 62; |
|
|
3918 else if(xch == '/') |
|
|
3919 val = 63; |
|
|
3920 else |
|
|
3921 return -1; |
|
|
3922 |
|
|
3923 if(val < 0 || val >= r) |
|
|
3924 return -1; |
|
|
3925 |
|
|
3926 return val; |
|
|
3927 |
|
|
3928 } /* end s_mp_tovalue() */ |
|
|
3929 |
|
|
3930 /* }}} */ |
|
|
3931 |
|
|
3932 /* {{{ s_mp_todigit(val, r, low) */ |
|
|
3933 |
|
|
3934 /* |
|
|
3935 Convert val to a radix-r digit, if possible. If val is out of range |
|
|
3936 for r, returns zero. Otherwise, returns an ASCII character denoting |
|
|
3937 the value in the given radix. |
|
|
3938 |
|
|
3939 The results may be odd if you use a radix < 2 or > 64, you are |
|
|
3940 expected to know what you're doing. |
|
|
3941 */ |
|
|
3942 |
|
|
3943 char s_mp_todigit(int val, int r, int low) |
|
|
3944 { |
|
|
3945 char ch; |
|
|
3946 |
|
|
3947 if(val < 0 || val >= r) |
|
|
3948 return 0; |
|
|
3949 |
|
|
3950 ch = s_dmap_1[val]; |
|
|
3951 |
|
|
3952 if(r <= 36 && low) |
|
|
3953 ch = tolower(ch); |
|
|
3954 |
|
|
3955 return ch; |
|
|
3956 |
|
|
3957 } /* end s_mp_todigit() */ |
|
|
3958 |
|
|
3959 /* }}} */ |
|
|
3960 |
|
|
3961 /* {{{ s_mp_outlen(bits, radix) */ |
|
|
3962 |
|
|
3963 /* |
|
|
3964 Return an estimate for how long a string is needed to hold a radix |
|
|
3965 r representation of a number with 'bits' significant bits. |
|
|
3966 |
|
|
3967 Does not include space for a sign or a NUL terminator. |
|
|
3968 */ |
|
|
3969 int s_mp_outlen(int bits, int r) |
|
|
3970 { |
|
|
3971 return (int)((double)bits * LOG_V_2(r)); |
|
|
3972 |
|
|
3973 } /* end s_mp_outlen() */ |
|
|
3974 |
|
|
3975 /* }}} */ |
|
|
3976 |
|
|
3977 /* }}} */ |
|
|
3978 |
|
|
3979 /*------------------------------------------------------------------------*/ |
|
|
3980 /* HERE THERE BE DRAGONS */ |
|
|
3981 /* crc==4242132123, version==2, Sat Feb 02 06:43:52 2002 */ |
