Mercurial > dropbear
annotate libtommath/bn_mp_exptmod_fast.c @ 1659:d32bcb5c557d
Add Ed25519 support (#91)
* Add support for Ed25519 as a public key type
Ed25519 is a elliptic curve signature scheme that offers
better security than ECDSA and DSA and good performance. It may be
used for both user and host keys.
OpenSSH key import and fuzzer are not supported yet.
Initially inspired by Peter Szabo.
* Add curve25519 and ed25519 fuzzers
* Add import and export of Ed25519 keys
author | Vladislav Grishenko <themiron@users.noreply.github.com> |
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date | Wed, 11 Mar 2020 21:09:45 +0500 |
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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 |
1655
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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 |
1655
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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 */ |
284
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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; |
284
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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) { |
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243 goto LBL_RES; |
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244 } |
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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)) { |
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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) { |
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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 */ |