| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: strongprime.c,v 1.1 1999/12/22 15:51:22 mdw Exp $ |
| 4 | * |
| 5 | * Generate `strong' prime numbers |
| 6 | * |
| 7 | * (c) 1999 Straylight/Edgeware |
| 8 | */ |
| 9 | |
| 10 | /*----- Licensing notice --------------------------------------------------* |
| 11 | * |
| 12 | * This file is part of Catacomb. |
| 13 | * |
| 14 | * Catacomb is free software; you can redistribute it and/or modify |
| 15 | * it under the terms of the GNU Library General Public License as |
| 16 | * published by the Free Software Foundation; either version 2 of the |
| 17 | * License, or (at your option) any later version. |
| 18 | * |
| 19 | * Catacomb is distributed in the hope that it will be useful, |
| 20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 22 | * GNU Library General Public License for more details. |
| 23 | * |
| 24 | * You should have received a copy of the GNU Library General Public |
| 25 | * License along with Catacomb; if not, write to the Free |
| 26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 27 | * MA 02111-1307, USA. |
| 28 | */ |
| 29 | |
| 30 | /*----- Revision history --------------------------------------------------* |
| 31 | * |
| 32 | * $Log: strongprime.c,v $ |
| 33 | * Revision 1.1 1999/12/22 15:51:22 mdw |
| 34 | * Find `strong' RSA primes using Gordon's algorithm. |
| 35 | * |
| 36 | */ |
| 37 | |
| 38 | /*----- Header files ------------------------------------------------------*/ |
| 39 | |
| 40 | #include <mLib/dstr.h> |
| 41 | |
| 42 | #include "grand.h" |
| 43 | #include "rand.h" |
| 44 | #include "mp.h" |
| 45 | #include "mpmont.h" |
| 46 | #include "mprand.h" |
| 47 | #include "pgen.h" |
| 48 | #include "pfilt.h" |
| 49 | #include "rabin.h" |
| 50 | |
| 51 | /*----- Main code ---------------------------------------------------------*/ |
| 52 | |
| 53 | /* --- @strongprime@ --- * |
| 54 | * |
| 55 | * Arguments: @const char *name@ = pointer to name root |
| 56 | * @mp *d@ = destination integer |
| 57 | * @unsigned nbits@ = number of bits wanted |
| 58 | * @grand *r@ = random number source |
| 59 | * @unsigned n@ = number of attempts to make |
| 60 | * @pgen_proc *event@ = event handler function |
| 61 | * @void *ectx@ = argument for the event handler |
| 62 | * |
| 63 | * Returns: A `strong' prime, or zero. |
| 64 | * |
| 65 | * Use: Finds `strong' primes. A strong prime %$p$% is such that |
| 66 | * |
| 67 | * * %$p - 1$% has a large prime factor %$r$%, |
| 68 | * * %$p + 1$% has a large prime factor %$s$%, and |
| 69 | * * %$r - 1$% has a large prime factor %$t$%. |
| 70 | * |
| 71 | * The numbers produced may be slightly larger than requested, |
| 72 | * by a few bits. |
| 73 | */ |
| 74 | |
| 75 | mp *strongprime(const char *name, mp *d, unsigned nbits, grand *r, |
| 76 | unsigned n, pgen_proc *event, void *ectx) |
| 77 | { |
| 78 | mp *s, *t, *q, *p = 0; |
| 79 | dstr dn = DSTR_INIT; |
| 80 | |
| 81 | mp *rr = MP_NEW; |
| 82 | pgen_filterctx c; |
| 83 | pgen_jumpctx cj; |
| 84 | rabin rb; |
| 85 | |
| 86 | /* --- The bitslop parameter --- * |
| 87 | * |
| 88 | * There's quite a lot of prime searching to be done. The constant |
| 89 | * @BITSLOP@ is a (low) approximation to the base-2 log of the expected |
| 90 | * number of steps to find a prime number. Experimentation shows that |
| 91 | * numbers around 10 seem to be good. |
| 92 | */ |
| 93 | |
| 94 | #define BITSLOP 10 |
| 95 | |
| 96 | /* --- Choose two primes %$s$% and %$t$% of half the required size --- */ |
| 97 | |
| 98 | nbits = nbits/2 - BITSLOP; |
| 99 | c.step = 1; |
| 100 | |
| 101 | rr = mprand(rr, nbits, r, 1); |
| 102 | DRESET(&dn); dstr_putf(&dn, "%s [s]", name); |
| 103 | if ((s = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_filter, &c, |
| 104 | rabin_iters(nbits), pgen_test, &rb)) == 0) |
| 105 | goto fail_s; |
| 106 | mp_burn(s); |
| 107 | |
| 108 | rr = mprand(rr, nbits, r, 1); |
| 109 | DRESET(&dn); dstr_putf(&dn, "%s [t]", name); |
| 110 | if ((t = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_filter, &c, |
| 111 | rabin_iters(nbits), pgen_test, &rb)) == 0) |
| 112 | goto fail_t; |
| 113 | mp_burn(t); |
| 114 | |
| 115 | /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- */ |
| 116 | |
| 117 | rr = mp_lsl(rr, t, 1); |
| 118 | pfilt_create(&c.f, rr); |
| 119 | rr = mp_lsl(rr, rr, BITSLOP - 1); |
| 120 | rr = mp_add(rr, rr, MP_ONE); |
| 121 | DRESET(&dn); dstr_putf(&dn, "%s [r]", name); |
| 122 | cj.j = &c.f; |
| 123 | nbits += BITSLOP; |
| 124 | if ((q = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_jump, &cj, |
| 125 | rabin_iters(nbits), pgen_test, &rb)) == 0) |
| 126 | goto fail_r; |
| 127 | pfilt_destroy(&c.f); |
| 128 | |
| 129 | /* --- Select a suitable starting-point for finding %$p$% --- * |
| 130 | * |
| 131 | * This computes %$p_0 = 2(s^{r - 2} \bmod r)s - 1$%. |
| 132 | */ |
| 133 | |
| 134 | { |
| 135 | mpmont mm; |
| 136 | |
| 137 | mpmont_create(&mm, q); |
| 138 | rr = mp_sub(rr, q, MP_TWO); |
| 139 | rr = mpmont_exp(&mm, rr, s, rr); |
| 140 | mpmont_destroy(&mm); |
| 141 | rr = mp_mul(rr, rr, s); |
| 142 | rr = mp_lsl(rr, rr, 1); |
| 143 | rr = mp_sub(rr, rr, MP_ONE); |
| 144 | } |
| 145 | |
| 146 | /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */ |
| 147 | |
| 148 | { |
| 149 | mp *x; |
| 150 | x = mp_mul(MP_NEW, q, s); |
| 151 | x = mp_lsl(x, x, 1); |
| 152 | pfilt_create(&c.f, x); |
| 153 | x = mp_lsl(x, x, BITSLOP - 1); |
| 154 | rr = mp_add(rr, rr, x); |
| 155 | mp_drop(x); |
| 156 | } |
| 157 | |
| 158 | if ((p = pgen(name, d, rr, event, ectx, n, pgen_jump, &cj, |
| 159 | rabin_iters(nbits * 2), pgen_test, &rb)) == 0) |
| 160 | goto fail_p; |
| 161 | |
| 162 | /* --- Tidy up because we've finished --- */ |
| 163 | |
| 164 | fail_p: |
| 165 | mp_drop(q); |
| 166 | fail_r: |
| 167 | pfilt_destroy(&c.f); |
| 168 | mp_drop(t); |
| 169 | fail_t: |
| 170 | mp_drop(s); |
| 171 | fail_s: |
| 172 | mp_drop(rr); |
| 173 | dstr_destroy(&dn); |
| 174 | |
| 175 | return (p); |
| 176 | |
| 177 | #undef BITSLOP |
| 178 | } |
| 179 | |
| 180 | /*----- That's all, folks -------------------------------------------------*/ |