Mercurial > dropbear
annotate libtommath/bn_mp_exptmod_fast.c @ 1656:a36e545fb43d
Prime-related bugfixes (#81)
* Merge pull request #180 from czurnieden/isprimeerror
Fixed bug in mp_prime_isprime
(cherry picked from commit f3ff7064f3301a2fc11b84d389fd67769862d437)
* do 2 MR rounds for numbers >=2048bits
* back-port modified mp_prime_next_prime()
author | Steffen Jaeckel <s@jaeckel.eu> |
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date | Tue, 17 Sep 2019 16:11:09 +0200 |
parents | f52919ffd3b1 |
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rev | line source |
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1 #include "tommath_private.h" |
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2 #ifdef BN_MP_EXPTMOD_FAST_C |
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
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4 * |
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5 * LibTomMath is a library that provides multiple-precision |
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6 * integer arithmetic as well as number theoretic functionality. |
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7 * |
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8 * The library was designed directly after the MPI library by |
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9 * Michael Fromberger but has been written from scratch with |
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10 * additional optimizations in place. |
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11 * |
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12 * SPDX-License-Identifier: Unlicense |
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13 */ |
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14 |
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15 /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 |
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16 * |
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17 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation. |
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18 * The value of k changes based on the size of the exponent. |
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19 * |
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20 * Uses Montgomery or Diminished Radix reduction [whichever appropriate] |
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21 */ |
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22 |
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23 #ifdef MP_LOW_MEM |
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24 # define TAB_SIZE 32 |
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25 #else |
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26 # define TAB_SIZE 256 |
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27 #endif |
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28 |
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29 int mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) |
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30 { |
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31 mp_int M[TAB_SIZE], res; |
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32 mp_digit buf, mp; |
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33 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; |
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34 |
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35 /* use a pointer to the reduction algorithm. This allows us to use |
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36 * one of many reduction algorithms without modding the guts of |
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37 * the code with if statements everywhere. |
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38 */ |
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39 int (*redux)(mp_int *x, const mp_int *n, mp_digit rho); |
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40 |
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41 /* find window size */ |
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42 x = mp_count_bits(X); |
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43 if (x <= 7) { |
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44 winsize = 2; |
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45 } else if (x <= 36) { |
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46 winsize = 3; |
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47 } else if (x <= 140) { |
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48 winsize = 4; |
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49 } else if (x <= 450) { |
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50 winsize = 5; |
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51 } else if (x <= 1303) { |
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52 winsize = 6; |
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53 } else if (x <= 3529) { |
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54 winsize = 7; |
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55 } else { |
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56 winsize = 8; |
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57 } |
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58 |
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59 #ifdef MP_LOW_MEM |
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60 if (winsize > 5) { |
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61 winsize = 5; |
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62 } |
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63 #endif |
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64 |
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65 /* init M array */ |
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66 /* init first cell */ |
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67 if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) { |
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68 return err; |
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69 } |
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70 |
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71 /* now init the second half of the array */ |
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72 for (x = 1<<(winsize-1); x < (1 << winsize); x++) { |
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73 if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) { |
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74 for (y = 1<<(winsize-1); y < x; y++) { |
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75 mp_clear(&M[y]); |
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76 } |
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77 mp_clear(&M[1]); |
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78 return err; |
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79 } |
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80 } |
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81 |
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82 /* determine and setup reduction code */ |
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83 if (redmode == 0) { |
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84 #ifdef BN_MP_MONTGOMERY_SETUP_C |
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85 /* now setup montgomery */ |
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86 if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) { |
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87 goto LBL_M; |
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88 } |
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89 #else |
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90 err = MP_VAL; |
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91 goto LBL_M; |
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92 #endif |
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93 |
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94 /* automatically pick the comba one if available (saves quite a few calls/ifs) */ |
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95 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C |
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96 if ((((P->used * 2) + 1) < (int)MP_WARRAY) && |
1436 | 97 (P->used < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) { |
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98 redux = fast_mp_montgomery_reduce; |
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99 } else |
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100 #endif |
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101 { |
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102 #ifdef BN_MP_MONTGOMERY_REDUCE_C |
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103 /* use slower baseline Montgomery method */ |
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104 redux = mp_montgomery_reduce; |
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105 #else |
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106 err = MP_VAL; |
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107 goto LBL_M; |
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108 #endif |
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109 } |
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110 } else if (redmode == 1) { |
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111 #if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C) |
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112 /* setup DR reduction for moduli of the form B**k - b */ |
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113 mp_dr_setup(P, &mp); |
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114 redux = mp_dr_reduce; |
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115 #else |
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116 err = MP_VAL; |
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117 goto LBL_M; |
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118 #endif |
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119 } else { |
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120 #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C) |
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121 /* setup DR reduction for moduli of the form 2**k - b */ |
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122 if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) { |
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123 goto LBL_M; |
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124 } |
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125 redux = mp_reduce_2k; |
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126 #else |
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127 err = MP_VAL; |
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128 goto LBL_M; |
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129 #endif |
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130 } |
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131 |
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132 /* setup result */ |
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133 if ((err = mp_init_size(&res, P->alloc)) != MP_OKAY) { |
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134 goto LBL_M; |
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135 } |
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136 |
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137 /* create M table |
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138 * |
284
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139 |
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140 * |
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141 * The first half of the table is not computed though accept for M[0] and M[1] |
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142 */ |
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143 |
1655
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144 if (redmode == 0) { |
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145 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C |
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146 /* now we need R mod m */ |
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147 if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) { |
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148 goto LBL_RES; |
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149 } |
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150 |
1655
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151 /* now set M[1] to G * R mod m */ |
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152 if ((err = mp_mulmod(G, &res, P, &M[1])) != MP_OKAY) { |
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153 goto LBL_RES; |
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154 } |
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155 #else |
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156 err = MP_VAL; |
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157 goto LBL_RES; |
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158 #endif |
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159 } else { |
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160 mp_set(&res, 1uL); |
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161 if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) { |
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162 goto LBL_RES; |
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163 } |
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164 } |
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165 |
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166 /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */ |
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167 if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) { |
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168 goto LBL_RES; |
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169 } |
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170 |
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171 for (x = 0; x < (winsize - 1); x++) { |
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172 if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) { |
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173 goto LBL_RES; |
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174 } |
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175 if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, mp)) != MP_OKAY) { |
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176 goto LBL_RES; |
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177 } |
1655
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178 } |
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179 |
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180 /* create upper table */ |
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181 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { |
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182 if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) { |
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183 goto LBL_RES; |
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184 } |
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185 if ((err = redux(&M[x], P, mp)) != MP_OKAY) { |
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186 goto LBL_RES; |
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187 } |
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188 } |
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189 |
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190 /* set initial mode and bit cnt */ |
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191 mode = 0; |
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192 bitcnt = 1; |
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193 buf = 0; |
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194 digidx = X->used - 1; |
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195 bitcpy = 0; |
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196 bitbuf = 0; |
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197 |
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198 for (;;) { |
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199 /* grab next digit as required */ |
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200 if (--bitcnt == 0) { |
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201 /* if digidx == -1 we are out of digits so break */ |
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202 if (digidx == -1) { |
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203 break; |
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204 } |
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205 /* read next digit and reset bitcnt */ |
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206 buf = X->dp[digidx--]; |
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207 bitcnt = (int)DIGIT_BIT; |
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208 } |
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209 |
1655
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210 /* grab the next msb from the exponent */ |
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211 y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1; |
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212 buf <<= (mp_digit)1; |
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213 |
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214 /* if the bit is zero and mode == 0 then we ignore it |
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215 * These represent the leading zero bits before the first 1 bit |
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216 * in the exponent. Technically this opt is not required but it |
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217 * does lower the # of trivial squaring/reductions used |
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218 */ |
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219 if ((mode == 0) && (y == 0)) { |
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220 continue; |
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221 } |
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222 |
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223 /* if the bit is zero and mode == 1 then we square */ |
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224 if ((mode == 1) && (y == 0)) { |
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225 if ((err = mp_sqr(&res, &res)) != MP_OKAY) { |
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226 goto LBL_RES; |
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227 } |
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228 if ((err = redux(&res, P, mp)) != MP_OKAY) { |
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229 goto LBL_RES; |
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230 } |
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231 continue; |
284
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232 } |
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233 |
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234 /* else we add it to the window */ |
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235 bitbuf |= (y << (winsize - ++bitcpy)); |
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236 mode = 2; |
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237 |
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238 if (bitcpy == winsize) { |
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239 /* ok window is filled so square as required and multiply */ |
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240 /* square first */ |
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241 for (x = 0; x < winsize; x++) { |
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242 if ((err = mp_sqr(&res, &res)) != MP_OKAY) { |
f52919ffd3b1
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243 goto LBL_RES; |
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244 } |
f52919ffd3b1
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245 if ((err = redux(&res, P, mp)) != MP_OKAY) { |
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246 goto LBL_RES; |
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247 } |
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248 } |
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249 |
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250 /* then multiply */ |
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251 if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) { |
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252 goto LBL_RES; |
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253 } |
f52919ffd3b1
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254 if ((err = redux(&res, P, mp)) != MP_OKAY) { |
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255 goto LBL_RES; |
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|
256 } |
f52919ffd3b1
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257 |
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258 /* empty window and reset */ |
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259 bitcpy = 0; |
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260 bitbuf = 0; |
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261 mode = 1; |
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|
262 } |
f52919ffd3b1
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|
263 } |
284
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264 |
1655
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|
265 /* if bits remain then square/multiply */ |
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266 if ((mode == 2) && (bitcpy > 0)) { |
f52919ffd3b1
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267 /* square then multiply if the bit is set */ |
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|
268 for (x = 0; x < bitcpy; x++) { |
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269 if ((err = mp_sqr(&res, &res)) != MP_OKAY) { |
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270 goto LBL_RES; |
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|
271 } |
f52919ffd3b1
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272 if ((err = redux(&res, P, mp)) != MP_OKAY) { |
f52919ffd3b1
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|
273 goto LBL_RES; |
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274 } |
284
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275 |
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276 /* get next bit of the window */ |
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277 bitbuf <<= 1; |
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278 if ((bitbuf & (1 << winsize)) != 0) { |
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279 /* then multiply */ |
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280 if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) { |
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281 goto LBL_RES; |
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282 } |
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283 if ((err = redux(&res, P, mp)) != MP_OKAY) { |
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284 goto LBL_RES; |
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285 } |
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286 } |
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287 } |
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288 } |
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289 |
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290 if (redmode == 0) { |
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291 /* fixup result if Montgomery reduction is used |
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292 * recall that any value in a Montgomery system is |
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293 * actually multiplied by R mod n. So we have |
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294 * to reduce one more time to cancel out the factor |
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295 * of R. |
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296 */ |
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297 if ((err = redux(&res, P, mp)) != MP_OKAY) { |
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298 goto LBL_RES; |
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299 } |
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300 } |
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301 |
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302 /* swap res with Y */ |
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303 mp_exch(&res, Y); |
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304 err = MP_OKAY; |
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305 LBL_RES: |
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306 mp_clear(&res); |
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307 LBL_M: |
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308 mp_clear(&M[1]); |
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309 for (x = 1<<(winsize-1); x < (1 << winsize); x++) { |
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310 mp_clear(&M[x]); |
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311 } |
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312 return err; |
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313 } |
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314 #endif |
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315 |
389
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316 |
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317 /* ref: HEAD -> master, tag: v1.1.0 */ |
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318 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */ |
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319 /* commit time: 2019-01-28 20:32:32 +0100 */ |