Mercurial > dropbear
annotate libtommath/bn_mp_prime_is_prime.c @ 1663:c795520269f9
Fallback for key gen without hard link support (#89)
Add a non-atomic fallback for key generation on platforms where link()
is not permitted (such as most stock Android installs) or on filesystems
without hard link support (such as FAT).
author | Matt Robinson <git@nerdoftheherd.com> |
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date | Sat, 14 Mar 2020 14:37:35 +0000 |
parents | a36e545fb43d |
children | 1051e4eea25a |
rev | line source |
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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 * |
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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 /* portable integer log of two with small footprint */ |
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16 static unsigned int s_floor_ilog2(int value) |
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17 { |
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18 unsigned int r = 0; |
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19 while ((value >>= 1) != 0) { |
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20 r++; |
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21 } |
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22 return r; |
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23 } |
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24 |
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25 |
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26 int mp_prime_is_prime(const mp_int *a, int t, int *result) |
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27 { |
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28 mp_int b; |
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29 int ix, err, res, p_max = 0, size_a, len; |
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30 unsigned int fips_rand, mask; |
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31 |
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32 /* default to no */ |
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33 *result = MP_NO; |
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34 |
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35 /* valid value of t? */ |
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36 if (t > PRIME_SIZE) { |
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37 return MP_VAL; |
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38 } |
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39 |
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40 /* Some shortcuts */ |
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41 /* N > 3 */ |
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42 if (a->used == 1) { |
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43 if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) { |
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44 *result = 0; |
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45 return MP_OKAY; |
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46 } |
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47 if (a->dp[0] == 2u) { |
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48 *result = 1; |
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49 return MP_OKAY; |
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50 } |
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51 } |
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52 |
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53 /* N must be odd */ |
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54 if (mp_iseven(a) == MP_YES) { |
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55 return MP_OKAY; |
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56 } |
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57 /* N is not a perfect square: floor(sqrt(N))^2 != N */ |
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58 if ((err = mp_is_square(a, &res)) != MP_OKAY) { |
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59 return err; |
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60 } |
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61 if (res != 0) { |
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62 return MP_OKAY; |
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63 } |
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64 |
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65 /* is the input equal to one of the primes in the table? */ |
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66 for (ix = 0; ix < PRIME_SIZE; ix++) { |
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67 if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) { |
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68 *result = MP_YES; |
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69 return MP_OKAY; |
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70 } |
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71 } |
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72 #ifdef MP_8BIT |
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73 /* The search in the loop above was exhaustive in this case */ |
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74 if ((a->used == 1) && (PRIME_SIZE >= 31)) { |
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75 return MP_OKAY; |
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76 } |
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77 #endif |
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78 |
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79 /* first perform trial division */ |
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80 if ((err = mp_prime_is_divisible(a, &res)) != MP_OKAY) { |
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81 return err; |
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82 } |
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83 |
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84 /* return if it was trivially divisible */ |
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85 if (res == MP_YES) { |
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86 return MP_OKAY; |
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87 } |
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88 |
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89 /* |
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90 Run the Miller-Rabin test with base 2 for the BPSW test. |
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91 */ |
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92 if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) { |
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93 return err; |
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94 } |
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95 |
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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 Rumours have it that Mathematica does a second M-R test with base 3. |
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104 Other rumours have it that their strong L-S test is slightly different. |
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105 It does not hurt, though, beside a bit of extra runtime. |
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106 */ |
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107 b.dp[0]++; |
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108 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { |
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109 goto LBL_B; |
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110 } |
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111 if (res == MP_NO) { |
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112 goto LBL_B; |
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113 } |
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114 |
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115 /* |
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116 * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite |
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117 * slow so if speed is an issue, define LTM_USE_FIPS_ONLY to use M-R tests with |
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118 * bases 2, 3 and t random bases. |
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119 */ |
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120 #ifndef LTM_USE_FIPS_ONLY |
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121 if (t >= 0) { |
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122 /* |
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123 * Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for |
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124 * MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit |
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125 * integers but the necesssary analysis is on the todo-list). |
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126 */ |
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127 #if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST) |
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128 err = mp_prime_frobenius_underwood(a, &res); |
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129 if ((err != MP_OKAY) && (err != MP_ITER)) { |
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130 goto LBL_B; |
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131 } |
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132 if (res == MP_NO) { |
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133 goto LBL_B; |
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134 } |
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135 #else |
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136 if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) { |
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137 goto LBL_B; |
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138 } |
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139 if (res == MP_NO) { |
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140 goto LBL_B; |
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141 } |
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142 #endif |
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143 } |
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144 #endif |
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145 |
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146 /* run at least one Miller-Rabin test with a random base */ |
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147 if (t == 0) { |
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148 t = 1; |
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149 } |
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150 |
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151 /* |
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152 abs(t) extra rounds of M-R to extend the range of primes it can find if t < 0. |
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153 Only recommended if the input range is known to be < 3317044064679887385961981 |
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154 |
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155 It uses the bases for a deterministic M-R test if input < 3317044064679887385961981 |
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156 The caller has to check the size. |
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157 |
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158 Not for cryptographic use because with known bases strong M-R pseudoprimes can |
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159 be constructed. Use at least one M-R test with a random base (t >= 1). |
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160 |
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161 The 1119 bit large number |
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162 |
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163 80383745745363949125707961434194210813883768828755814583748891752229742737653\ |
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164 33652186502336163960045457915042023603208766569966760987284043965408232928738\ |
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165 79185086916685732826776177102938969773947016708230428687109997439976544144845\ |
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166 34115587245063340927902227529622941498423068816854043264575340183297861112989\ |
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167 60644845216191652872597534901 |
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168 |
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169 has been constructed by F. Arnault (F. Arnault, "Rabin-Miller primality test: |
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170 composite numbers which pass it.", Mathematics of Computation, 1995, 64. Jg., |
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171 Nr. 209, S. 355-361), is a semiprime with the two factors |
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172 |
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173 40095821663949960541830645208454685300518816604113250877450620473800321707011\ |
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174 96242716223191597219733582163165085358166969145233813917169287527980445796800\ |
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175 452592031836601 |
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176 |
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177 20047910831974980270915322604227342650259408302056625438725310236900160853505\ |
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178 98121358111595798609866791081582542679083484572616906958584643763990222898400\ |
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179 226296015918301 |
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180 |
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181 and it is a strong pseudoprime to all forty-six prime M-R bases up to 200 |
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182 |
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183 It does not fail the strong Bailley-PSP test as implemented here, it is just |
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184 given as an example, if not the reason to use the BPSW-test instead of M-R-tests |
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185 with a sequence of primes 2...n. |
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186 |
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187 */ |
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188 if (t < 0) { |
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189 t = -t; |
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190 /* |
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191 Sorenson, Jonathan; Webster, Jonathan (2015). |
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192 "Strong Pseudoprimes to Twelve Prime Bases". |
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193 */ |
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194 /* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */ |
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195 if ((err = mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) { |
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196 goto LBL_B; |
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197 } |
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198 |
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199 if (mp_cmp(a, &b) == MP_LT) { |
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200 p_max = 12; |
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201 } else { |
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202 /* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */ |
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203 if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) { |
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204 goto LBL_B; |
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205 } |
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206 |
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207 if (mp_cmp(a, &b) == MP_LT) { |
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208 p_max = 13; |
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209 } else { |
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210 err = MP_VAL; |
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211 goto LBL_B; |
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212 } |
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213 } |
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214 |
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215 /* for compatibility with the current API (well, compatible within a sign's width) */ |
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216 if (p_max < t) { |
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217 p_max = t; |
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218 } |
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219 |
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220 if (p_max > PRIME_SIZE) { |
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221 err = MP_VAL; |
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222 goto LBL_B; |
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223 } |
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224 /* we did bases 2 and 3 already, skip them */ |
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225 for (ix = 2; ix < p_max; ix++) { |
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226 mp_set(&b, ltm_prime_tab[ix]); |
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227 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { |
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228 goto LBL_B; |
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229 } |
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230 if (res == MP_NO) { |
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231 goto LBL_B; |
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232 } |
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233 } |
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234 } |
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235 /* |
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236 Do "t" M-R tests with random bases between 3 and "a". |
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237 See Fips 186.4 p. 126ff |
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238 */ |
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239 else if (t > 0) { |
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240 /* |
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241 * The mp_digit's have a defined bit-size but the size of the |
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242 * array a.dp is a simple 'int' and this library can not assume full |
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243 * compliance to the current C-standard (ISO/IEC 9899:2011) because |
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244 * it gets used for small embeded processors, too. Some of those MCUs |
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245 * have compilers that one cannot call standard compliant by any means. |
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246 * Hence the ugly type-fiddling in the following code. |
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247 */ |
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248 size_a = mp_count_bits(a); |
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249 mask = (1u << s_floor_ilog2(size_a)) - 1u; |
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250 /* |
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251 Assuming the General Rieman hypothesis (never thought to write that in a |
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252 comment) the upper bound can be lowered to 2*(log a)^2. |
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253 E. Bach, "Explicit bounds for primality testing and related problems," |
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254 Math. Comp. 55 (1990), 355-380. |
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255 |
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256 size_a = (size_a/10) * 7; |
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257 len = 2 * (size_a * size_a); |
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258 |
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259 E.g.: a number of size 2^2048 would be reduced to the upper limit |
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260 |
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261 floor(2048/10)*7 = 1428 |
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262 2 * 1428^2 = 4078368 |
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263 |
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264 (would have been ~4030331.9962 with floats and natural log instead) |
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265 That number is smaller than 2^28, the default bit-size of mp_digit. |
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266 */ |
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267 |
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268 /* |
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269 How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame |
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270 does exactly 1. In words: one. Look at the end of _GMP_is_prime() in |
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271 Math-Prime-Util-GMP-0.50/primality.c if you do not believe it. |
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272 |
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273 The function mp_rand() goes to some length to use a cryptographically |
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274 good PRNG. That also means that the chance to always get the same base |
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275 in the loop is non-zero, although very low. |
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276 If the BPSW test and/or the addtional Frobenious test have been |
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277 performed instead of just the Miller-Rabin test with the bases 2 and 3, |
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278 a single extra test should suffice, so such a very unlikely event |
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279 will not do much harm. |
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280 |
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281 To preemptivly answer the dangling question: no, a witness does not |
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282 need to be prime. |
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283 */ |
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284 for (ix = 0; ix < t; ix++) { |
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285 /* mp_rand() guarantees the first digit to be non-zero */ |
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286 if ((err = mp_rand(&b, 1)) != MP_OKAY) { |
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287 goto LBL_B; |
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288 } |
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289 /* |
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290 * Reduce digit before casting because mp_digit might be bigger than |
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291 * an unsigned int and "mask" on the other side is most probably not. |
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292 */ |
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293 fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask); |
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294 #ifdef MP_8BIT |
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295 /* |
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296 * One 8-bit digit is too small, so concatenate two if the size of |
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297 * unsigned int allows for it. |
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298 */ |
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299 if (((sizeof(unsigned int) * CHAR_BIT)/2) >= (sizeof(mp_digit) * CHAR_BIT)) { |
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300 if ((err = mp_rand(&b, 1)) != MP_OKAY) { |
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301 goto LBL_B; |
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302 } |
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303 fips_rand <<= sizeof(mp_digit) * CHAR_BIT; |
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304 fips_rand |= (unsigned int) b.dp[0]; |
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305 fips_rand &= mask; |
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306 } |
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307 #endif |
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308 if (fips_rand > (unsigned int)(INT_MAX - DIGIT_BIT)) { |
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309 len = INT_MAX / DIGIT_BIT; |
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310 } else { |
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311 len = (((int)fips_rand + DIGIT_BIT) / DIGIT_BIT); |
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312 } |
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313 /* Unlikely. */ |
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314 if (len < 0) { |
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315 ix--; |
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316 continue; |
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317 } |
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318 /* |
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319 * As mentioned above, one 8-bit digit is too small and |
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320 * although it can only happen in the unlikely case that |
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321 * an "unsigned int" is smaller than 16 bit a simple test |
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322 * is cheap and the correction even cheaper. |
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323 */ |
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324 #ifdef MP_8BIT |
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325 /* All "a" < 2^8 have been caught before */ |
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326 if (len == 1) { |
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327 len++; |
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328 } |
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329 #endif |
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330 if ((err = mp_rand(&b, len)) != MP_OKAY) { |
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331 goto LBL_B; |
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332 } |
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333 /* |
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334 * That number might got too big and the witness has to be |
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335 * smaller than "a" |
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336 */ |
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337 len = mp_count_bits(&b); |
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338 if (len >= size_a) { |
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339 len = (len - size_a) + 1; |
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340 if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) { |
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341 goto LBL_B; |
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342 } |
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343 } |
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344 /* Although the chance for b <= 3 is miniscule, try again. */ |
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345 if (mp_cmp_d(&b, 3uL) != MP_GT) { |
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346 ix--; |
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347 continue; |
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348 } |
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349 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { |
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350 goto LBL_B; |
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351 } |
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352 if (res == MP_NO) { |
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353 goto LBL_B; |
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354 } |
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355 } |
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356 } |
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357 |
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358 /* passed the test */ |
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359 *result = MP_YES; |
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360 LBL_B: |
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361 mp_clear(&b); |
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362 return err; |
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363 } |
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364 |
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365 #endif |
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366 |
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367 /* ref: HEAD -> master, tag: v1.1.0 */ |
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368 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */ |
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369 /* commit time: 2019-01-28 20:32:32 +0100 */ |