| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Generate `strong' prime numbers |
| 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 <mLib/dstr.h> |
| 31 | |
| 32 | #include "grand.h" |
| 33 | #include "mp.h" |
| 34 | #include "mpmont.h" |
| 35 | #include "mprand.h" |
| 36 | #include "pgen.h" |
| 37 | #include "pfilt.h" |
| 38 | #include "rabin.h" |
| 39 | |
| 40 | /*----- Main code ---------------------------------------------------------*/ |
| 41 | |
| 42 | /* --- @strongprime_setup@ --- * |
| 43 | * |
| 44 | * Arguments: @const char *name@ = pointer to name root |
| 45 | * @mp *d@ = destination for search start point |
| 46 | * @pfilt *f@ = where to store filter jump context |
| 47 | * @unsigned nbits@ = number of bits wanted |
| 48 | * @grand *r@ = random number source |
| 49 | * @unsigned n@ = number of attempts to make |
| 50 | * @pgen_proc *event@ = event handler function |
| 51 | * @void *ectx@ = argument for the event handler |
| 52 | * |
| 53 | * Returns: A starting point for a `strong' prime search, or zero. |
| 54 | * |
| 55 | * Use: Sets up for a strong prime search, so that primes with |
| 56 | * particular properties can be found. It's probably important |
| 57 | * to note that the number left in the filter context @f@ is |
| 58 | * congruent to 2 (mod 4). |
| 59 | */ |
| 60 | |
| 61 | mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits, |
| 62 | grand *r, unsigned n, pgen_proc *event, void *ectx) |
| 63 | { |
| 64 | mp *s, *t, *q; |
| 65 | dstr dn = DSTR_INIT; |
| 66 | unsigned slop, nb, u, i; |
| 67 | |
| 68 | mp *rr = d; |
| 69 | pgen_filterctx c; |
| 70 | pgen_jumpctx j; |
| 71 | rabin rb; |
| 72 | |
| 73 | /* --- Figure out how large the smaller primes should be --- * |
| 74 | * |
| 75 | * We want them to be `as large as possible', subject to the constraint |
| 76 | * that we produce a number of the requested size at the end. This is |
| 77 | * tricky, because the final prime search is going to involve quite large |
| 78 | * jumps from its starting point; the size of the jumps are basically |
| 79 | * determined by our choice here, and if they're too big then we won't find |
| 80 | * a prime in time. |
| 81 | * |
| 82 | * Let's suppose we're trying to make an %$N$%-bit prime. The expected |
| 83 | * number of steps tends to increase linearly with size, i.e., we need to |
| 84 | * take about %2^k N$% steps for some %$k$%. If we're jumping by a |
| 85 | * %$J$%-bit quantity each time, from an %$N$%-bit starting point, then we |
| 86 | * will only be able to find a match if %$2^k N 2^{J-1} \le 2^{N-1}$%, |
| 87 | * i.e., if %$J \le N - (k + \log_2 N)$%. |
| 88 | * |
| 89 | * Experimentation shows that taking %$k + \log_2 N = 12$% works well for |
| 90 | * %$N = 1024$%, so %$k = 2$%. |
| 91 | */ |
| 92 | |
| 93 | for (i = 1; i && nbits >> i; i <<= 1); assert(i); |
| 94 | for (slop = 2, nb = nbits; nb > 1; i >>= 1) { |
| 95 | u = nb >> i; |
| 96 | if (u) { slop += i; nb = u; } |
| 97 | } |
| 98 | if (nbits/2 <= slop) return (0); |
| 99 | |
| 100 | /* --- Choose two primes %$s$% and %$t$% of half the required size --- */ |
| 101 | |
| 102 | nb = nbits/2 - slop; |
| 103 | c.step = 1; |
| 104 | |
| 105 | rr = mprand(rr, nb, r, 1); |
| 106 | DRESET(&dn); dstr_putf(&dn, "%s [s]", name); |
| 107 | if ((s = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c, |
| 108 | rabin_iters(nb), pgen_test, &rb)) == 0) |
| 109 | goto fail_s; |
| 110 | |
| 111 | rr = mprand(rr, nb, r, 1); |
| 112 | DRESET(&dn); dstr_putf(&dn, "%s [t]", name); |
| 113 | if ((t = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c, |
| 114 | rabin_iters(nb), pgen_test, &rb)) == 0) |
| 115 | goto fail_t; |
| 116 | |
| 117 | /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- */ |
| 118 | |
| 119 | rr = mp_lsl(rr, t, 1); |
| 120 | pfilt_create(&c.f, rr); |
| 121 | rr = mp_lsl(rr, rr, slop - 1); |
| 122 | rr = mp_add(rr, rr, MP_ONE); |
| 123 | DRESET(&dn); dstr_putf(&dn, "%s [r]", name); |
| 124 | j.j = &c.f; |
| 125 | q = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_jump, &j, |
| 126 | rabin_iters(nb + slop), pgen_test, &rb); |
| 127 | pfilt_destroy(&c.f); |
| 128 | if (!q) |
| 129 | goto fail_r; |
| 130 | |
| 131 | /* --- Select a suitable starting-point for finding %$p$% --- * |
| 132 | * |
| 133 | * This computes %$p_0 = 2 s (s^{r - 2} \bmod r) - 1$%. |
| 134 | */ |
| 135 | |
| 136 | { |
| 137 | mpmont mm; |
| 138 | |
| 139 | mpmont_create(&mm, q); |
| 140 | rr = mp_sub(rr, q, MP_TWO); |
| 141 | rr = mpmont_exp(&mm, rr, s, rr); |
| 142 | mpmont_destroy(&mm); |
| 143 | rr = mp_mul(rr, rr, s); |
| 144 | rr = mp_lsl(rr, rr, 1); |
| 145 | rr = mp_sub(rr, rr, MP_ONE); |
| 146 | } |
| 147 | |
| 148 | /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */ |
| 149 | |
| 150 | { |
| 151 | mp *x, *y; |
| 152 | x = mp_mul(MP_NEW, q, s); |
| 153 | x = mp_lsl(x, x, 1); |
| 154 | pfilt_create(f, x); |
| 155 | y = mp_lsl(MP_NEW, MP_ONE, nbits - 1); |
| 156 | rr = mp_leastcongruent(rr, y, rr, x); |
| 157 | mp_drop(x); mp_drop(y); |
| 158 | } |
| 159 | |
| 160 | /* --- Return the result --- */ |
| 161 | |
| 162 | mp_drop(q); |
| 163 | mp_drop(t); |
| 164 | mp_drop(s); |
| 165 | dstr_destroy(&dn); |
| 166 | return (rr); |
| 167 | |
| 168 | /* --- Tidy up if something failed --- */ |
| 169 | |
| 170 | fail_r: |
| 171 | mp_drop(t); |
| 172 | fail_t: |
| 173 | mp_drop(s); |
| 174 | fail_s: |
| 175 | mp_drop(rr); |
| 176 | dstr_destroy(&dn); |
| 177 | return (0); |
| 178 | } |
| 179 | |
| 180 | /* --- @strongprime@ --- * |
| 181 | * |
| 182 | * Arguments: @const char *name@ = pointer to name root |
| 183 | * @mp *d@ = destination integer |
| 184 | * @unsigned nbits@ = number of bits wanted |
| 185 | * @grand *r@ = random number source |
| 186 | * @unsigned n@ = number of attempts to make |
| 187 | * @pgen_proc *event@ = event handler function |
| 188 | * @void *ectx@ = argument for the event handler |
| 189 | * |
| 190 | * Returns: A `strong' prime, or zero. |
| 191 | * |
| 192 | * Use: Finds `strong' primes. A strong prime %$p$% is such that |
| 193 | * |
| 194 | * * %$p - 1$% has a large prime factor %$r$%, |
| 195 | * * %$p + 1$% has a large prime factor %$s$%, and |
| 196 | * * %$r - 1$% has a large prime factor %$t$%. |
| 197 | */ |
| 198 | |
| 199 | mp *strongprime(const char *name, mp *d, unsigned nbits, grand *r, |
| 200 | unsigned n, pgen_proc *event, void *ectx) |
| 201 | { |
| 202 | mp *p; |
| 203 | pfilt f; |
| 204 | pgen_jumpctx j; |
| 205 | rabin rb; |
| 206 | |
| 207 | if (d) mp_copy(d); |
| 208 | p = strongprime_setup(name, d, &f, nbits, r, n, event, ectx); |
| 209 | if (!p) { mp_drop(d); return (0); } |
| 210 | j.j = &f; |
| 211 | p = pgen(name, p, p, event, ectx, n, pgen_jump, &j, |
| 212 | rabin_iters(nbits), pgen_test, &rb); |
| 213 | if (mp_bits(p) != nbits) { mp_drop(p); return (0); } |
| 214 | pfilt_destroy(&f); |
| 215 | mp_drop(d); |
| 216 | return (p); |
| 217 | } |
| 218 | |
| 219 | /*----- That's all, folks -------------------------------------------------*/ |