Mercurial > dropbear
annotate libtommath/bn_mp_prime_is_prime.c @ 1704:d384bc2e5af3
Don't warn when SO_PRIORITY fails
author | Matt Johnston <matt@ucc.asn.au> |
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date | Thu, 28 May 2020 23:26:34 +0800 |
parents | 1051e4eea25a |
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1 #include "tommath_private.h" |
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2 #ifdef BN_MP_PRIME_IS_PRIME_C |
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis */ |
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4 /* SPDX-License-Identifier: Unlicense */ |
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5 |
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6 /* portable integer log of two with small footprint */ |
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7 static unsigned int s_floor_ilog2(int value) |
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8 { |
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9 unsigned int r = 0; |
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10 while ((value >>= 1) != 0) { |
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11 r++; |
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12 } |
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13 return r; |
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14 } |
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15 |
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16 |
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17 mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result) |
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18 { |
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19 mp_int b; |
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20 int ix, p_max = 0, size_a, len; |
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21 mp_bool res; |
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22 mp_err err; |
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23 unsigned int fips_rand, mask; |
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24 |
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25 /* default to no */ |
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26 *result = MP_NO; |
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27 |
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28 /* Some shortcuts */ |
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29 /* N > 3 */ |
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30 if (a->used == 1) { |
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31 if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) { |
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32 *result = MP_NO; |
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33 return MP_OKAY; |
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34 } |
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35 if (a->dp[0] == 2u) { |
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36 *result = MP_YES; |
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37 return MP_OKAY; |
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38 } |
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39 } |
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40 |
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41 /* N must be odd */ |
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42 if (MP_IS_EVEN(a)) { |
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43 return MP_OKAY; |
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44 } |
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45 /* N is not a perfect square: floor(sqrt(N))^2 != N */ |
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46 if ((err = mp_is_square(a, &res)) != MP_OKAY) { |
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47 return err; |
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48 } |
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49 if (res != MP_NO) { |
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50 return MP_OKAY; |
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51 } |
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52 |
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53 /* is the input equal to one of the primes in the table? */ |
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54 for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) { |
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55 if (mp_cmp_d(a, s_mp_prime_tab[ix]) == MP_EQ) { |
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56 *result = MP_YES; |
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57 return MP_OKAY; |
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58 } |
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59 } |
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60 #ifdef MP_8BIT |
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61 /* The search in the loop above was exhaustive in this case */ |
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62 if ((a->used == 1) && (PRIVATE_MP_PRIME_TAB_SIZE >= 31)) { |
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63 return MP_OKAY; |
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64 } |
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65 #endif |
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66 |
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67 /* first perform trial division */ |
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68 if ((err = s_mp_prime_is_divisible(a, &res)) != MP_OKAY) { |
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69 return err; |
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70 } |
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71 |
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72 /* return if it was trivially divisible */ |
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73 if (res == MP_YES) { |
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74 return MP_OKAY; |
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75 } |
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76 |
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77 /* |
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78 Run the Miller-Rabin test with base 2 for the BPSW test. |
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79 */ |
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80 if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) { |
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81 return err; |
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82 } |
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83 |
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84 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { |
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85 goto LBL_B; |
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86 } |
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87 if (res == MP_NO) { |
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88 goto LBL_B; |
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89 } |
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90 /* |
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91 Rumours have it that Mathematica does a second M-R test with base 3. |
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92 Other rumours have it that their strong L-S test is slightly different. |
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93 It does not hurt, though, beside a bit of extra runtime. |
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94 */ |
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95 b.dp[0]++; |
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96 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { |
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97 goto LBL_B; |
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98 } |
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99 if (res == MP_NO) { |
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100 goto LBL_B; |
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101 } |
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102 |
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103 /* |
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104 * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite |
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105 * slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with |
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106 * bases 2, 3 and t random bases. |
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107 */ |
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108 #ifndef LTM_USE_ONLY_MR |
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109 if (t >= 0) { |
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110 /* |
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111 * Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for |
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112 * MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit |
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113 * integers but the necesssary analysis is on the todo-list). |
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114 */ |
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115 #if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST) |
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116 err = mp_prime_frobenius_underwood(a, &res); |
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117 if ((err != MP_OKAY) && (err != MP_ITER)) { |
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118 goto LBL_B; |
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119 } |
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120 if (res == MP_NO) { |
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121 goto LBL_B; |
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122 } |
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123 #else |
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124 if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) { |
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125 goto LBL_B; |
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126 } |
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127 if (res == MP_NO) { |
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128 goto LBL_B; |
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129 } |
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130 #endif |
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131 } |
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132 #endif |
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133 |
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134 /* run at least one Miller-Rabin test with a random base */ |
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135 if (t == 0) { |
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136 t = 1; |
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137 } |
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138 |
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139 /* |
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140 Only recommended if the input range is known to be < 3317044064679887385961981 |
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141 |
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142 It uses the bases necessary for a deterministic M-R test if the input is |
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143 smaller than 3317044064679887385961981 |
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144 The caller has to check the size. |
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145 TODO: can be made a bit finer grained but comparing is not free. |
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146 */ |
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147 if (t < 0) { |
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148 /* |
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149 Sorenson, Jonathan; Webster, Jonathan (2015). |
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150 "Strong Pseudoprimes to Twelve Prime Bases". |
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151 */ |
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152 /* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */ |
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153 if ((err = mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) { |
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154 goto LBL_B; |
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155 } |
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156 |
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157 if (mp_cmp(a, &b) == MP_LT) { |
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158 p_max = 12; |
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159 } else { |
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160 /* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */ |
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161 if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) { |
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162 goto LBL_B; |
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163 } |
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164 |
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165 if (mp_cmp(a, &b) == MP_LT) { |
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166 p_max = 13; |
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167 } else { |
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168 err = MP_VAL; |
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169 goto LBL_B; |
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170 } |
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171 } |
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172 |
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173 /* we did bases 2 and 3 already, skip them */ |
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174 for (ix = 2; ix < p_max; ix++) { |
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175 mp_set(&b, s_mp_prime_tab[ix]); |
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176 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { |
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177 goto LBL_B; |
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178 } |
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179 if (res == MP_NO) { |
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180 goto LBL_B; |
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181 } |
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182 } |
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183 } |
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184 /* |
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185 Do "t" M-R tests with random bases between 3 and "a". |
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186 See Fips 186.4 p. 126ff |
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187 */ |
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188 else if (t > 0) { |
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189 /* |
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190 * The mp_digit's have a defined bit-size but the size of the |
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191 * array a.dp is a simple 'int' and this library can not assume full |
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192 * compliance to the current C-standard (ISO/IEC 9899:2011) because |
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193 * it gets used for small embeded processors, too. Some of those MCUs |
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194 * have compilers that one cannot call standard compliant by any means. |
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195 * Hence the ugly type-fiddling in the following code. |
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196 */ |
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197 size_a = mp_count_bits(a); |
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198 mask = (1u << s_floor_ilog2(size_a)) - 1u; |
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199 /* |
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200 Assuming the General Rieman hypothesis (never thought to write that in a |
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201 comment) the upper bound can be lowered to 2*(log a)^2. |
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202 E. Bach, "Explicit bounds for primality testing and related problems," |
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203 Math. Comp. 55 (1990), 355-380. |
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204 |
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205 size_a = (size_a/10) * 7; |
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206 len = 2 * (size_a * size_a); |
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207 |
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208 E.g.: a number of size 2^2048 would be reduced to the upper limit |
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209 |
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210 floor(2048/10)*7 = 1428 |
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211 2 * 1428^2 = 4078368 |
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212 |
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213 (would have been ~4030331.9962 with floats and natural log instead) |
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214 That number is smaller than 2^28, the default bit-size of mp_digit. |
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215 */ |
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216 |
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217 /* |
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218 How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame |
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219 does exactly 1. In words: one. Look at the end of _GMP_is_prime() in |
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220 Math-Prime-Util-GMP-0.50/primality.c if you do not believe it. |
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221 |
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222 The function mp_rand() goes to some length to use a cryptographically |
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223 good PRNG. That also means that the chance to always get the same base |
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224 in the loop is non-zero, although very low. |
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225 If the BPSW test and/or the addtional Frobenious test have been |
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226 performed instead of just the Miller-Rabin test with the bases 2 and 3, |
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227 a single extra test should suffice, so such a very unlikely event |
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228 will not do much harm. |
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229 |
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230 To preemptivly answer the dangling question: no, a witness does not |
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231 need to be prime. |
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232 */ |
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233 for (ix = 0; ix < t; ix++) { |
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234 /* mp_rand() guarantees the first digit to be non-zero */ |
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235 if ((err = mp_rand(&b, 1)) != MP_OKAY) { |
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236 goto LBL_B; |
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237 } |
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238 /* |
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239 * Reduce digit before casting because mp_digit might be bigger than |
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240 * an unsigned int and "mask" on the other side is most probably not. |
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241 */ |
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242 fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask); |
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243 #ifdef MP_8BIT |
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244 /* |
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245 * One 8-bit digit is too small, so concatenate two if the size of |
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246 * unsigned int allows for it. |
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247 */ |
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248 if ((MP_SIZEOF_BITS(unsigned int)/2) >= MP_SIZEOF_BITS(mp_digit)) { |
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249 if ((err = mp_rand(&b, 1)) != MP_OKAY) { |
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250 goto LBL_B; |
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251 } |
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252 fips_rand <<= MP_SIZEOF_BITS(mp_digit); |
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253 fips_rand |= (unsigned int) b.dp[0]; |
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254 fips_rand &= mask; |
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255 } |
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256 #endif |
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257 if (fips_rand > (unsigned int)(INT_MAX - MP_DIGIT_BIT)) { |
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258 len = INT_MAX / MP_DIGIT_BIT; |
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259 } else { |
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260 len = (((int)fips_rand + MP_DIGIT_BIT) / MP_DIGIT_BIT); |
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261 } |
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262 /* Unlikely. */ |
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263 if (len < 0) { |
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264 ix--; |
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265 continue; |
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266 } |
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267 /* |
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268 * As mentioned above, one 8-bit digit is too small and |
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269 * although it can only happen in the unlikely case that |
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270 * an "unsigned int" is smaller than 16 bit a simple test |
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271 * is cheap and the correction even cheaper. |
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272 */ |
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273 #ifdef MP_8BIT |
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274 /* All "a" < 2^8 have been caught before */ |
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275 if (len == 1) { |
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276 len++; |
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277 } |
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278 #endif |
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279 if ((err = mp_rand(&b, len)) != MP_OKAY) { |
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280 goto LBL_B; |
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281 } |
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282 /* |
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283 * That number might got too big and the witness has to be |
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284 * smaller than "a" |
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285 */ |
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286 len = mp_count_bits(&b); |
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287 if (len >= size_a) { |
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288 len = (len - size_a) + 1; |
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289 if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) { |
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290 goto LBL_B; |
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291 } |
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292 } |
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293 /* Although the chance for b <= 3 is miniscule, try again. */ |
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294 if (mp_cmp_d(&b, 3uL) != MP_GT) { |
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295 ix--; |
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296 continue; |
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297 } |
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298 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { |
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299 goto LBL_B; |
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300 } |
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301 if (res == MP_NO) { |
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302 goto LBL_B; |
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303 } |
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304 } |
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305 } |
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306 |
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307 /* passed the test */ |
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308 *result = MP_YES; |
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309 LBL_B: |
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310 mp_clear(&b); |
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311 return err; |
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312 } |
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313 |
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314 #endif |