| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Miller-Rabin primality test |
| 4 | * |
| 5 | * (c) 1999 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 9 | * |
| 10 | * This file is part of Catacomb. |
| 11 | * |
| 12 | * Catacomb is free software; you can redistribute it and/or modify |
| 13 | * it under the terms of the GNU Library General Public License as |
| 14 | * published by the Free Software Foundation; either version 2 of the |
| 15 | * License, or (at your option) any later version. |
| 16 | * |
| 17 | * Catacomb is distributed in the hope that it will be useful, |
| 18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 20 | * GNU Library General Public License for more details. |
| 21 | * |
| 22 | * You should have received a copy of the GNU Library General Public |
| 23 | * License along with Catacomb; if not, write to the Free |
| 24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 25 | * MA 02111-1307, USA. |
| 26 | */ |
| 27 | |
| 28 | /*----- Header files ------------------------------------------------------*/ |
| 29 | |
| 30 | #include "mp.h" |
| 31 | #include "mpbarrett.h" |
| 32 | #include "mpmont.h" |
| 33 | #include "pgen.h" |
| 34 | #include "rabin.h" |
| 35 | |
| 36 | /*----- Main code ---------------------------------------------------------*/ |
| 37 | |
| 38 | /* --- @rabin_create@ --- * |
| 39 | * |
| 40 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
| 41 | * @mp *m@ = pointer to number to test |
| 42 | * |
| 43 | * Returns: Zero on success, nonzero on failure. |
| 44 | * |
| 45 | * Use: Precomputes some useful values for performing the |
| 46 | * Miller-Rabin probabilistic primality test. |
| 47 | */ |
| 48 | |
| 49 | int rabin_create(rabin *r, mp *m) |
| 50 | { |
| 51 | mp *m1 = mp_sub(MP_NEW, m, MP_ONE); |
| 52 | if (mpmont_create(&r->mm, m)) { |
| 53 | MP_DROP(m1); |
| 54 | return (-1); |
| 55 | } |
| 56 | r->r = mp_odd(MP_NEW, m1, &r->s); |
| 57 | r->m1 = mp_sub(MP_NEW, m, r->mm.r); |
| 58 | mp_drop(m1); |
| 59 | return (0); |
| 60 | } |
| 61 | |
| 62 | /* --- @rabin_destroy@ --- * |
| 63 | * |
| 64 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
| 65 | * |
| 66 | * Returns: --- |
| 67 | * |
| 68 | * Use: Disposes of a Rabin-Miller context when it's no longer |
| 69 | * needed. |
| 70 | */ |
| 71 | |
| 72 | void rabin_destroy(rabin *r) |
| 73 | { |
| 74 | mp_drop(r->r); |
| 75 | mp_drop(r->m1); |
| 76 | mpmont_destroy(&r->mm); |
| 77 | } |
| 78 | |
| 79 | /* --- @rabin_test@, @rabin_rtest@ --- * |
| 80 | * |
| 81 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
| 82 | * @mp *g@ = base to test the number against |
| 83 | * |
| 84 | * Returns: Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@ |
| 85 | * if it succeeded. |
| 86 | * |
| 87 | * Use: Performs a single iteration of the Rabin-Miller primality |
| 88 | * test. The @rtest@ variant assumes that %$g$% is either |
| 89 | * already in Montgomery representation, or you don't care. |
| 90 | */ |
| 91 | |
| 92 | int rabin_rtest(rabin *r, mp *g) |
| 93 | { |
| 94 | mp *y; |
| 95 | mp *dd, *spare = MP_NEW; |
| 96 | size_t j; |
| 97 | int rc = PGEN_FAIL; |
| 98 | |
| 99 | /* --- Calculate %$y R = g^r R \bmod m$% --- * |
| 100 | * |
| 101 | * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that |
| 102 | * @y@ here has an extra factor of %$R$%. |
| 103 | */ |
| 104 | |
| 105 | y = mpmont_expr(&r->mm, MP_NEW, g, r->r); |
| 106 | if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) { |
| 107 | rc = PGEN_PASS; |
| 108 | goto done; |
| 109 | } |
| 110 | |
| 111 | /* --- Now for the main loop --- * |
| 112 | * |
| 113 | * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is |
| 114 | * composite. Of course, %$j = 0$% has already been tested. |
| 115 | */ |
| 116 | |
| 117 | for (j = 1; j < r->s; j++) { |
| 118 | dd = mp_sqr(spare, y); |
| 119 | dd = mpmont_reduce(&r->mm, dd, dd); |
| 120 | spare = y; y = dd; |
| 121 | if (MP_EQ(y, r->mm.r)) |
| 122 | break; |
| 123 | if (MP_EQ(y, r->m1)) { |
| 124 | rc = PGEN_PASS; |
| 125 | break; |
| 126 | } |
| 127 | } |
| 128 | |
| 129 | /* --- Done --- */ |
| 130 | |
| 131 | done: |
| 132 | if (spare != MP_NEW) |
| 133 | MP_DROP(spare); |
| 134 | MP_DROP(y); |
| 135 | return (rc); |
| 136 | } |
| 137 | |
| 138 | int rabin_test(rabin *r, mp *g) |
| 139 | { |
| 140 | int rc; |
| 141 | g = mpmont_mul(&r->mm, MP_NEW, g, r->mm.r2); |
| 142 | rc = rabin_rtest(r, g); |
| 143 | mp_drop(g); |
| 144 | return (rc); |
| 145 | } |
| 146 | |
| 147 | /* --- @rabin_iters@ --- * |
| 148 | * |
| 149 | * Arguments: @unsigned len@ = number of bits in value |
| 150 | * |
| 151 | * Returns: Number of iterations recommended. |
| 152 | * |
| 153 | * Use: Returns the recommended number of iterations to ensure that a |
| 154 | * number with @len@ bits is really prime. |
| 155 | */ |
| 156 | |
| 157 | int rabin_iters(unsigned len) |
| 158 | { |
| 159 | static const struct { |
| 160 | unsigned b; |
| 161 | int i; |
| 162 | } *p, *q, tab[] = { |
| 163 | { 100, 27 }, |
| 164 | { 150, 18 }, |
| 165 | { 200, 15 }, |
| 166 | { 250, 12 }, |
| 167 | { 300, 9 }, |
| 168 | { 350, 8 }, |
| 169 | { 400, 7 }, |
| 170 | { 450, 6 }, |
| 171 | { 550, 5 }, |
| 172 | { 650, 4 }, |
| 173 | { 850, 3 }, |
| 174 | { 1300, 2 } |
| 175 | }; |
| 176 | |
| 177 | unsigned i; |
| 178 | |
| 179 | /* --- Binary search through the table --- */ |
| 180 | |
| 181 | p = tab; |
| 182 | q = tab + (sizeof(tab)/sizeof(tab[0])); |
| 183 | for (;;) { |
| 184 | i = (q - p) / 2; |
| 185 | if (!i) |
| 186 | break; |
| 187 | if (len >= p[i].b && len < p[i + 1].b) |
| 188 | break; |
| 189 | if (len > p[i].b) |
| 190 | p = p + i; |
| 191 | else |
| 192 | q = p + i; |
| 193 | } |
| 194 | return (p[i].i); |
| 195 | } |
| 196 | |
| 197 | /*----- That's all, folks -------------------------------------------------*/ |