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1 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
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2 * |
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3 * LibTomMath is a library that provides multiple-precision |
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4 * integer arithmetic as well as number theoretic functionality. |
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5 * |
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6 * The library was designed directly after the MPI library by |
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7 * Michael Fromberger but has been written from scratch with |
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8 * additional optimizations in place. |
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9 * |
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10 * The library is free for all purposes without any express |
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11 * guarantee it works. |
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12 * |
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13 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
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14 */ |
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15 #include <tommath.h> |
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16 |
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17 #ifdef MP_LOW_MEM |
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18 #define TAB_SIZE 32 |
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19 #else |
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20 #define TAB_SIZE 256 |
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21 #endif |
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22 |
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23 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) |
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24 { |
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25 mp_int M[TAB_SIZE], res, mu; |
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26 mp_digit buf; |
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27 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; |
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28 |
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29 /* find window size */ |
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30 x = mp_count_bits (X); |
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31 if (x <= 7) { |
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32 winsize = 2; |
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33 } else if (x <= 36) { |
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34 winsize = 3; |
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35 } else if (x <= 140) { |
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36 winsize = 4; |
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37 } else if (x <= 450) { |
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38 winsize = 5; |
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39 } else if (x <= 1303) { |
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40 winsize = 6; |
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41 } else if (x <= 3529) { |
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42 winsize = 7; |
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43 } else { |
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44 winsize = 8; |
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45 } |
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46 |
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47 #ifdef MP_LOW_MEM |
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48 if (winsize > 5) { |
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49 winsize = 5; |
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50 } |
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51 #endif |
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52 |
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53 /* init M array */ |
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54 /* init first cell */ |
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55 if ((err = mp_init(&M[1])) != MP_OKAY) { |
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56 return err; |
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57 } |
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58 |
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59 /* now init the second half of the array */ |
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60 for (x = 1<<(winsize-1); x < (1 << winsize); x++) { |
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61 if ((err = mp_init(&M[x])) != MP_OKAY) { |
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62 for (y = 1<<(winsize-1); y < x; y++) { |
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63 mp_clear (&M[y]); |
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64 } |
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65 mp_clear(&M[1]); |
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66 return err; |
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67 } |
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68 } |
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69 |
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70 /* create mu, used for Barrett reduction */ |
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71 if ((err = mp_init (&mu)) != MP_OKAY) { |
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72 goto __M; |
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73 } |
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74 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) { |
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75 goto __MU; |
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76 } |
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77 |
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78 /* create M table |
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79 * |
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80 * The M table contains powers of the base, |
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81 * e.g. M[x] = G**x mod P |
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82 * |
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83 * The first half of the table is not |
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84 * computed though accept for M[0] and M[1] |
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85 */ |
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86 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) { |
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87 goto __MU; |
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88 } |
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89 |
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90 /* compute the value at M[1<<(winsize-1)] by squaring |
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91 * M[1] (winsize-1) times |
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92 */ |
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93 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { |
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94 goto __MU; |
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95 } |
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96 |
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97 for (x = 0; x < (winsize - 1); x++) { |
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98 if ((err = mp_sqr (&M[1 << (winsize - 1)], |
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99 &M[1 << (winsize - 1)])) != MP_OKAY) { |
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100 goto __MU; |
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101 } |
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102 if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) { |
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103 goto __MU; |
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104 } |
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105 } |
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106 |
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107 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) |
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108 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) |
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109 */ |
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110 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { |
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111 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) { |
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112 goto __MU; |
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113 } |
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114 if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) { |
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115 goto __MU; |
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116 } |
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117 } |
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118 |
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119 /* setup result */ |
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120 if ((err = mp_init (&res)) != MP_OKAY) { |
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121 goto __MU; |
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122 } |
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123 mp_set (&res, 1); |
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124 |
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125 /* set initial mode and bit cnt */ |
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126 mode = 0; |
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127 bitcnt = 1; |
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128 buf = 0; |
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129 digidx = X->used - 1; |
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130 bitcpy = 0; |
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131 bitbuf = 0; |
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132 |
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133 for (;;) { |
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134 /* grab next digit as required */ |
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135 if (--bitcnt == 0) { |
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136 /* if digidx == -1 we are out of digits */ |
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137 if (digidx == -1) { |
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138 break; |
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139 } |
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140 /* read next digit and reset the bitcnt */ |
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141 buf = X->dp[digidx--]; |
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142 bitcnt = (int) DIGIT_BIT; |
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143 } |
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144 |
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145 /* grab the next msb from the exponent */ |
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146 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1; |
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147 buf <<= (mp_digit)1; |
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148 |
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149 /* if the bit is zero and mode == 0 then we ignore it |
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150 * These represent the leading zero bits before the first 1 bit |
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151 * in the exponent. Technically this opt is not required but it |
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152 * does lower the # of trivial squaring/reductions used |
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153 */ |
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154 if (mode == 0 && y == 0) { |
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155 continue; |
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156 } |
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157 |
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158 /* if the bit is zero and mode == 1 then we square */ |
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159 if (mode == 1 && y == 0) { |
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160 if ((err = mp_sqr (&res, &res)) != MP_OKAY) { |
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161 goto __RES; |
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162 } |
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163 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { |
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164 goto __RES; |
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165 } |
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166 continue; |
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167 } |
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168 |
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169 /* else we add it to the window */ |
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170 bitbuf |= (y << (winsize - ++bitcpy)); |
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171 mode = 2; |
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172 |
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173 if (bitcpy == winsize) { |
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174 /* ok window is filled so square as required and multiply */ |
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175 /* square first */ |
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176 for (x = 0; x < winsize; x++) { |
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177 if ((err = mp_sqr (&res, &res)) != MP_OKAY) { |
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178 goto __RES; |
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179 } |
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180 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { |
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181 goto __RES; |
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182 } |
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183 } |
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184 |
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185 /* then multiply */ |
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186 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { |
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187 goto __RES; |
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188 } |
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189 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { |
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190 goto __RES; |
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191 } |
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192 |
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193 /* empty window and reset */ |
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194 bitcpy = 0; |
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195 bitbuf = 0; |
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196 mode = 1; |
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197 } |
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198 } |
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199 |
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200 /* if bits remain then square/multiply */ |
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201 if (mode == 2 && bitcpy > 0) { |
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202 /* square then multiply if the bit is set */ |
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203 for (x = 0; x < bitcpy; x++) { |
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204 if ((err = mp_sqr (&res, &res)) != MP_OKAY) { |
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205 goto __RES; |
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206 } |
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207 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { |
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208 goto __RES; |
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209 } |
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210 |
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211 bitbuf <<= 1; |
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212 if ((bitbuf & (1 << winsize)) != 0) { |
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213 /* then multiply */ |
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214 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { |
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215 goto __RES; |
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216 } |
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217 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { |
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218 goto __RES; |
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219 } |
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220 } |
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221 } |
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222 } |
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223 |
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224 mp_exch (&res, Y); |
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225 err = MP_OKAY; |
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226 __RES:mp_clear (&res); |
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227 __MU:mp_clear (&mu); |
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228 __M: |
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229 mp_clear(&M[1]); |
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230 for (x = 1<<(winsize-1); x < (1 << winsize); x++) { |
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231 mp_clear (&M[x]); |
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232 } |
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233 return err; |
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234 } |
