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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 /* finds the next prime after the number "a" using "t" trials |
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18 * of Miller-Rabin. |
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19 * |
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20 * bbs_style = 1 means the prime must be congruent to 3 mod 4 |
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21 */ |
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22 int mp_prime_next_prime(mp_int *a, int t, int bbs_style) |
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23 { |
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24 int err, res, x, y; |
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25 mp_digit res_tab[PRIME_SIZE], step, kstep; |
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26 mp_int b; |
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27 |
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28 /* ensure t is valid */ |
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29 if (t <= 0 || t > PRIME_SIZE) { |
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30 return MP_VAL; |
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31 } |
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32 |
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33 /* force positive */ |
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34 a->sign = MP_ZPOS; |
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35 |
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36 /* simple algo if a is less than the largest prime in the table */ |
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37 if (mp_cmp_d(a, __prime_tab[PRIME_SIZE-1]) == MP_LT) { |
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38 /* find which prime it is bigger than */ |
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39 for (x = PRIME_SIZE - 2; x >= 0; x--) { |
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40 if (mp_cmp_d(a, __prime_tab[x]) != MP_LT) { |
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41 if (bbs_style == 1) { |
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42 /* ok we found a prime smaller or |
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43 * equal [so the next is larger] |
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44 * |
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45 * however, the prime must be |
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46 * congruent to 3 mod 4 |
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47 */ |
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48 if ((__prime_tab[x + 1] & 3) != 3) { |
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49 /* scan upwards for a prime congruent to 3 mod 4 */ |
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50 for (y = x + 1; y < PRIME_SIZE; y++) { |
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51 if ((__prime_tab[y] & 3) == 3) { |
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52 mp_set(a, __prime_tab[y]); |
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53 return MP_OKAY; |
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54 } |
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55 } |
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56 } |
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57 } else { |
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58 mp_set(a, __prime_tab[x + 1]); |
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59 return MP_OKAY; |
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60 } |
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61 } |
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62 } |
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63 /* at this point a maybe 1 */ |
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64 if (mp_cmp_d(a, 1) == MP_EQ) { |
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65 mp_set(a, 2); |
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66 return MP_OKAY; |
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67 } |
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68 /* fall through to the sieve */ |
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69 } |
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70 |
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71 /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */ |
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72 if (bbs_style == 1) { |
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73 kstep = 4; |
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74 } else { |
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75 kstep = 2; |
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76 } |
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77 |
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78 /* at this point we will use a combination of a sieve and Miller-Rabin */ |
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79 |
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80 if (bbs_style == 1) { |
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81 /* if a mod 4 != 3 subtract the correct value to make it so */ |
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82 if ((a->dp[0] & 3) != 3) { |
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83 if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; }; |
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84 } |
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85 } else { |
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86 if (mp_iseven(a) == 1) { |
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87 /* force odd */ |
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88 if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { |
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89 return err; |
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90 } |
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91 } |
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92 } |
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93 |
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94 /* generate the restable */ |
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95 for (x = 1; x < PRIME_SIZE; x++) { |
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96 if ((err = mp_mod_d(a, __prime_tab[x], res_tab + x)) != MP_OKAY) { |
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97 return err; |
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98 } |
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99 } |
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100 |
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101 /* init temp used for Miller-Rabin Testing */ |
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102 if ((err = mp_init(&b)) != MP_OKAY) { |
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103 return err; |
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104 } |
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105 |
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106 for (;;) { |
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107 /* skip to the next non-trivially divisible candidate */ |
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108 step = 0; |
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109 do { |
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110 /* y == 1 if any residue was zero [e.g. cannot be prime] */ |
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111 y = 0; |
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112 |
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113 /* increase step to next candidate */ |
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114 step += kstep; |
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115 |
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116 /* compute the new residue without using division */ |
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117 for (x = 1; x < PRIME_SIZE; x++) { |
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118 /* add the step to each residue */ |
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119 res_tab[x] += kstep; |
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120 |
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121 /* subtract the modulus [instead of using division] */ |
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122 if (res_tab[x] >= __prime_tab[x]) { |
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123 res_tab[x] -= __prime_tab[x]; |
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124 } |
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125 |
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126 /* set flag if zero */ |
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127 if (res_tab[x] == 0) { |
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128 y = 1; |
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129 } |
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130 } |
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131 } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep)); |
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132 |
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133 /* add the step */ |
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134 if ((err = mp_add_d(a, step, a)) != MP_OKAY) { |
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135 goto __ERR; |
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136 } |
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137 |
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138 /* if didn't pass sieve and step == MAX then skip test */ |
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139 if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) { |
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140 continue; |
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141 } |
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142 |
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143 /* is this prime? */ |
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144 for (x = 0; x < t; x++) { |
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145 mp_set(&b, __prime_tab[t]); |
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146 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { |
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147 goto __ERR; |
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148 } |
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149 if (res == MP_NO) { |
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150 break; |
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151 } |
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152 } |
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153 |
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154 if (res == MP_YES) { |
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155 break; |
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156 } |
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157 } |
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158 |
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159 err = MP_OKAY; |
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160 __ERR: |
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161 mp_clear(&b); |
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162 return err; |
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163 } |
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164 |
