3 * $Id: rabin.c,v 1.4 2000/06/22 19:03:02 mdw Exp $
5 * Miller-Rabin primality test
7 * (c) 1999 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Revision history --------------------------------------------------*
33 * Revision 1.4 2000/06/22 19:03:02 mdw
34 * Use the new @mp_odd@ function.
36 * Revision 1.3 1999/12/22 15:50:29 mdw
37 * Reworking for new prime-search system. Add function for working out how
38 * many iterations to use for a particular number.
40 * Revision 1.2 1999/12/10 23:29:48 mdw
41 * Change header file guard names.
43 * Revision 1.1 1999/11/19 13:17:57 mdw
44 * Prime number generator and tester.
48 /*----- Header files ------------------------------------------------------*/
51 #include "mpbarrett.h"
56 /*----- Main code ---------------------------------------------------------*/
58 /* --- @rabin_create@ --- *
60 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
61 * @mp *m@ = pointer to number to test
65 * Use: Precomputes some useful values for performing the
66 * Miller-Rabin probabilistic primality test.
69 void rabin_create(rabin *r, mp *m)
71 mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
72 mpmont_create(&r->mm, m);
73 r->r = mp_odd(MP_NEW, m1, &r->s);
74 r->m1 = mp_sub(MP_NEW, m, r->mm.r);
78 /* --- @rabin_destroy@ --- *
80 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
84 * Use: Disposes of a Rabin-Miller context when it's no longer
88 void rabin_destroy(rabin *r)
92 mpmont_destroy(&r->mm);
95 /* --- @rabin_test@ --- *
97 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
98 * @mp *g@ = base to test the number against
100 * Returns: Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
103 * Use: Performs a single iteration of the Rabin-Miller primality
107 int rabin_test(rabin *r, mp *g)
110 mp *dd, *spare = MP_NEW;
114 /* --- Calculate %$y R = g^r R \bmod m$% --- *
116 * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that
117 * @y@ here has an extra factor of %$R$%.
120 y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
121 if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) {
126 /* --- Now for the main loop --- *
128 * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
129 * composite. Of course, %$j = 0$% has already been tested.
132 for (j = 1; j < r->s; j++) {
133 dd = mp_sqr(spare, y);
134 dd = mpmont_reduce(&r->mm, dd, dd);
136 if (MP_CMP(y, ==, r->mm.r))
138 if (MP_CMP(y, ==, r->m1)) {
153 /* --- @rabin_iters@ --- *
155 * Arguments: @unsigned len@ = number of bits in value
157 * Returns: Number of iterations recommended.
159 * Use: Returns the recommended number of iterations to ensure that a
160 * number with @len@ bits is really prime.
163 int rabin_iters(unsigned len)
185 /* --- Binary search through the table --- */
188 q = tab + (sizeof(tab)/sizeof(tab[0]));
193 if (len >= p[i].b && len < p[i + 1].b)
203 /*----- That's all, folks -------------------------------------------------*/