Mercurial > dropbear
annotate libtommath/bn_mp_prime_strong_lucas_selfridge.c @ 1857:6022df862942
Use DSCP for IP QoS traffic classes
The previous TOS values are deprecated and not used by modern traffic
classifiers. This sets AF21 for "interactive" traffic (with a tty).
Non-tty traffic sets AF11 - that indicates high throughput but is not
lowest priority (which would be CS1 or LE).
This differs from the CS1 used by OpenSSH, it lets interactive git over SSH
have higher priority than background least effort traffic. Dropbear's settings
here should be suitable with the diffservs used by CAKE qdisc.
| author | Matt Johnston <matt@ucc.asn.au> |
|---|---|
| date | Tue, 25 Jan 2022 17:32:20 +0800 |
| parents | 1051e4eea25a |
| children |
| rev | line source |
|---|---|
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1 #include "tommath_private.h" |
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2 #ifdef BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C |
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3 |
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4 /* LibTomMath, multiple-precision integer library -- Tom St Denis */ |
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5 /* SPDX-License-Identifier: Unlicense */ |
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6 |
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7 /* |
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8 * See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details |
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9 */ |
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10 #ifndef LTM_USE_ONLY_MR |
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11 |
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12 /* |
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13 * 8-bit is just too small. You can try the Frobenius test |
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14 * but that frobenius test can fail, too, for the same reason. |
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15 */ |
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16 #ifndef MP_8BIT |
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17 |
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18 /* |
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19 * multiply bigint a with int d and put the result in c |
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20 * Like mp_mul_d() but with a signed long as the small input |
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21 */ |
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22 static mp_err s_mp_mul_si(const mp_int *a, int32_t d, mp_int *c) |
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23 { |
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24 mp_int t; |
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25 mp_err err; |
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26 |
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27 if ((err = mp_init(&t)) != MP_OKAY) { |
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28 return err; |
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29 } |
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30 |
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31 /* |
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32 * mp_digit might be smaller than a long, which excludes |
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33 * the use of mp_mul_d() here. |
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34 */ |
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35 mp_set_i32(&t, d); |
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36 err = mp_mul(a, &t, c); |
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37 mp_clear(&t); |
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38 return err; |
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39 } |
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40 /* |
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41 Strong Lucas-Selfridge test. |
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42 returns MP_YES if it is a strong L-S prime, MP_NO if it is composite |
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43 |
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44 Code ported from Thomas Ray Nicely's implementation of the BPSW test |
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45 at http://www.trnicely.net/misc/bpsw.html |
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46 |
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47 Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>. |
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48 Released into the public domain by the author, who disclaims any legal |
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49 liability arising from its use |
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50 |
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51 The multi-line comments are made by Thomas R. Nicely and are copied verbatim. |
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52 Additional comments marked "CZ" (without the quotes) are by the code-portist. |
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53 |
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54 (If that name sounds familiar, he is the guy who found the fdiv bug in the |
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55 Pentium (P5x, I think) Intel processor) |
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56 */ |
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57 mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, mp_bool *result) |
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58 { |
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59 /* CZ TODO: choose better variable names! */ |
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60 mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz; |
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61 /* CZ TODO: Some of them need the full 32 bit, hence the (temporary) exclusion of MP_8BIT */ |
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62 int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits; |
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63 mp_err err; |
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64 mp_bool oddness; |
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65 |
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66 *result = MP_NO; |
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67 /* |
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68 Find the first element D in the sequence {5, -7, 9, -11, 13, ...} |
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69 such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory |
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70 indicates that, if N is not a perfect square, D will "nearly |
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71 always" be "small." Just in case, an overflow trap for D is |
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72 included. |
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73 */ |
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74 |
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75 if ((err = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz, |
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76 NULL)) != MP_OKAY) { |
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77 return err; |
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78 } |
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79 |
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80 D = 5; |
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81 sign = 1; |
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82 |
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83 for (;;) { |
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84 Ds = sign * D; |
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85 sign = -sign; |
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86 mp_set_u32(&Dz, (uint32_t)D); |
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87 if ((err = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) goto LBL_LS_ERR; |
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88 |
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89 /* if 1 < GCD < N then N is composite with factor "D", and |
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90 Jacobi(D,N) is technically undefined (but often returned |
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91 as zero). */ |
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92 if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) { |
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93 goto LBL_LS_ERR; |
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94 } |
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95 if (Ds < 0) { |
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96 Dz.sign = MP_NEG; |
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97 } |
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98 if ((err = mp_kronecker(&Dz, a, &J)) != MP_OKAY) goto LBL_LS_ERR; |
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99 |
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100 if (J == -1) { |
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101 break; |
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102 } |
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103 D += 2; |
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104 |
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105 if (D > (INT_MAX - 2)) { |
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106 err = MP_VAL; |
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107 goto LBL_LS_ERR; |
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108 } |
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109 } |
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110 |
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111 |
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112 |
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113 P = 1; /* Selfridge's choice */ |
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114 Q = (1 - Ds) / 4; /* Required so D = P*P - 4*Q */ |
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115 |
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116 /* NOTE: The conditions (a) N does not divide Q, and |
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117 (b) D is square-free or not a perfect square, are included by |
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118 some authors; e.g., "Prime numbers and computer methods for |
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119 factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston), |
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120 p. 130. For this particular application of Lucas sequences, |
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121 these conditions were found to be immaterial. */ |
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122 |
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123 /* Now calculate N - Jacobi(D,N) = N + 1 (even), and calculate the |
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124 odd positive integer d and positive integer s for which |
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125 N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test). |
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126 The strong Lucas-Selfridge test then returns N as a strong |
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127 Lucas probable prime (slprp) if any of the following |
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128 conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0, |
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129 V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0 |
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130 (all equalities mod N). Thus d is the highest index of U that |
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131 must be computed (since V_2m is independent of U), compared |
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132 to U_{N+1} for the standard Lucas-Selfridge test; and no |
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133 index of V beyond (N+1)/2 is required, just as in the |
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134 standard Lucas-Selfridge test. However, the quantity Q^d must |
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135 be computed for use (if necessary) in the latter stages of |
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136 the test. The result is that the strong Lucas-Selfridge test |
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137 has a running time only slightly greater (order of 10 %) than |
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138 that of the standard Lucas-Selfridge test, while producing |
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139 only (roughly) 30 % as many pseudoprimes (and every strong |
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140 Lucas pseudoprime is also a standard Lucas pseudoprime). Thus |
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141 the evidence indicates that the strong Lucas-Selfridge test is |
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142 more effective than the standard Lucas-Selfridge test, and a |
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143 Baillie-PSW test based on the strong Lucas-Selfridge test |
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144 should be more reliable. */ |
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145 |
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146 if ((err = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) goto LBL_LS_ERR; |
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147 s = mp_cnt_lsb(&Np1); |
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148 |
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149 /* CZ |
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150 * This should round towards zero because |
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151 * Thomas R. Nicely used GMP's mpz_tdiv_q_2exp() |
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152 * and mp_div_2d() is equivalent. Additionally: |
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153 * dividing an even number by two does not produce |
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154 * any leftovers. |
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155 */ |
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156 if ((err = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) goto LBL_LS_ERR; |
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157 /* We must now compute U_d and V_d. Since d is odd, the accumulated |
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158 values U and V are initialized to U_1 and V_1 (if the target |
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159 index were even, U and V would be initialized instead to U_0=0 |
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160 and V_0=2). The values of U_2m and V_2m are also initialized to |
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161 U_1 and V_1; the FOR loop calculates in succession U_2 and V_2, |
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162 U_4 and V_4, U_8 and V_8, etc. If the corresponding bits |
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163 (1, 2, 3, ...) of t are on (the zero bit having been accounted |
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164 for in the initialization of U and V), these values are then |
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165 combined with the previous totals for U and V, using the |
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166 composition formulas for addition of indices. */ |
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167 |
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168 mp_set(&Uz, 1uL); /* U=U_1 */ |
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169 mp_set(&Vz, (mp_digit)P); /* V=V_1 */ |
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170 mp_set(&U2mz, 1uL); /* U_1 */ |
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171 mp_set(&V2mz, (mp_digit)P); /* V_1 */ |
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172 |
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173 mp_set_i32(&Qmz, Q); |
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174 if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR; |
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175 /* Initializes calculation of Q^d */ |
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176 mp_set_i32(&Qkdz, Q); |
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177 |
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178 Nbits = mp_count_bits(&Dz); |
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179 |
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180 for (u = 1; u < Nbits; u++) { /* zero bit off, already accounted for */ |
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181 /* Formulas for doubling of indices (carried out mod N). Note that |
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182 * the indices denoted as "2m" are actually powers of 2, specifically |
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183 * 2^(ul-1) beginning each loop and 2^ul ending each loop. |
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184 * |
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185 * U_2m = U_m*V_m |
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186 * V_2m = V_m*V_m - 2*Q^m |
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187 */ |
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188 |
|
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189 if ((err = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) goto LBL_LS_ERR; |
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Update LibTomMath to 1.2.0 (#84)
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190 if ((err = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) goto LBL_LS_ERR; |
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Update LibTomMath to 1.2.0 (#84)
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191 if ((err = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; |
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192 if ((err = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; |
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193 if ((err = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; |
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194 |
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195 /* Must calculate powers of Q for use in V_2m, also for Q^d later */ |
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196 if ((err = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) goto LBL_LS_ERR; |
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197 |
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198 /* prevents overflow */ /* CZ still necessary without a fixed prealloc'd mem.? */ |
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199 if ((err = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) goto LBL_LS_ERR; |
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200 if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR; |
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201 |
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202 if (s_mp_get_bit(&Dz, (unsigned int)u) == MP_YES) { |
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203 /* Formulas for addition of indices (carried out mod N); |
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204 * |
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205 * U_(m+n) = (U_m*V_n + U_n*V_m)/2 |
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206 * V_(m+n) = (V_m*V_n + D*U_m*U_n)/2 |
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207 * |
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208 * Be careful with division by 2 (mod N)! |
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209 */ |
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210 if ((err = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) goto LBL_LS_ERR; |
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211 if ((err = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) goto LBL_LS_ERR; |
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212 if ((err = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) goto LBL_LS_ERR; |
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213 if ((err = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) goto LBL_LS_ERR; |
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Update LibTomMath to 1.2.0 (#84)
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214 if ((err = s_mp_mul_si(&T4z, Ds, &T4z)) != MP_OKAY) goto LBL_LS_ERR; |
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215 if ((err = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) goto LBL_LS_ERR; |
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216 if (MP_IS_ODD(&Uz)) { |
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217 if ((err = mp_add(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR; |
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218 } |
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219 /* CZ |
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220 * This should round towards negative infinity because |
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221 * Thomas R. Nicely used GMP's mpz_fdiv_q_2exp(). |
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222 * But mp_div_2() does not do so, it is truncating instead. |
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223 */ |
|
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224 oddness = MP_IS_ODD(&Uz) ? MP_YES : MP_NO; |
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225 if ((err = mp_div_2(&Uz, &Uz)) != MP_OKAY) goto LBL_LS_ERR; |
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226 if ((Uz.sign == MP_NEG) && (oddness != MP_NO)) { |
|
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227 if ((err = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) goto LBL_LS_ERR; |
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228 } |
|
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229 if ((err = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) goto LBL_LS_ERR; |
|
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Update LibTomMath to 1.2.0 (#84)
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230 if (MP_IS_ODD(&Vz)) { |
|
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231 if ((err = mp_add(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; |
|
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232 } |
|
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233 oddness = MP_IS_ODD(&Vz) ? MP_YES : MP_NO; |
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234 if ((err = mp_div_2(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; |
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235 if ((Vz.sign == MP_NEG) && (oddness != MP_NO)) { |
|
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236 if ((err = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) goto LBL_LS_ERR; |
|
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237 } |
|
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Update LibTomMath to 1.2.0 (#84)
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238 if ((err = mp_mod(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR; |
|
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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239 if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; |
|
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Update LibTomMath to 1.2.0 (#84)
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240 |
|
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241 /* Calculating Q^d for later use */ |
|
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242 if ((err = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; |
|
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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|
243 if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; |
|
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|
244 } |
|
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|
245 } |
|
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|
246 |
|
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247 /* If U_d or V_d is congruent to 0 mod N, then N is a prime or a |
|
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|
248 strong Lucas pseudoprime. */ |
|
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249 if (MP_IS_ZERO(&Uz) || MP_IS_ZERO(&Vz)) { |
|
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250 *result = MP_YES; |
|
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251 goto LBL_LS_ERR; |
|
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|
252 } |
|
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253 |
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254 /* NOTE: Ribenboim ("The new book of prime number records," 3rd ed., |
|
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|
255 1995/6) omits the condition V0 on p.142, but includes it on |
|
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|
256 p. 130. The condition is NECESSARY; otherwise the test will |
|
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|
257 return false negatives---e.g., the primes 29 and 2000029 will be |
|
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|
258 returned as composite. */ |
|
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259 |
|
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260 /* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d} |
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|
261 by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of |
|
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262 these are congruent to 0 mod N, then N is a prime or a strong |
|
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|
263 Lucas pseudoprime. */ |
|
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|
264 |
|
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|
265 /* Initialize 2*Q^(d*2^r) for V_2m */ |
|
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|
266 if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR; |
|
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|
267 |
|
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|
268 for (r = 1; r < s; r++) { |
|
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Update LibTomMath to 1.2.0 (#84)
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|
269 if ((err = mp_sqr(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; |
|
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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|
270 if ((err = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; |
|
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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changeset
|
271 if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; |
|
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
1655
diff
changeset
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272 if (MP_IS_ZERO(&Vz)) { |
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1655
f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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273 *result = MP_YES; |
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f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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274 goto LBL_LS_ERR; |
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f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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275 } |
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f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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276 /* Calculate Q^{d*2^r} for next r (final iteration irrelevant). */ |
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f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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277 if (r < (s - 1)) { |
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1692
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
1655
diff
changeset
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278 if ((err = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; |
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1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
1655
diff
changeset
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279 if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; |
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1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
1655
diff
changeset
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280 if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR; |
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1655
f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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281 } |
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f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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282 } |
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f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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283 LBL_LS_ERR: |
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f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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284 mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL); |
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1692
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
1655
diff
changeset
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285 return err; |
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1655
f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
|
286 } |
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f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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287 #endif |
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f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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288 #endif |
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f52919ffd3b1
update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents:
diff
changeset
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289 #endif |