3 * $Id: rabin.c,v 1.3 1999/12/22 15:50:29 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 1.3 1999/12/22 15:50:29 mdw
34 * Reworking for new prime-search system. Add function for working out how
35 * many iterations to use for a particular number.
37 * Revision 1.2 1999/12/10 23:29:48 mdw
38 * Change header file guard names.
40 * Revision 1.1 1999/11/19 13:17:57 mdw
41 * Prime number generator and tester.
45 /*----- Header files ------------------------------------------------------*/
48 #include "mpbarrett.h"
53 /*----- Main code ---------------------------------------------------------*/
55 /* --- @rabin_create@ --- *
57 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
58 * @mp *m@ = pointer to number to test
62 * Use: Precomputes some useful values for performing the
63 * Miller-Rabin probabilistic primality test.
66 void rabin_create(rabin *r, mp *m)
68 mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
72 /* --- Find @r@ and @s@ --- */
74 mpmont_create(&r->mm, m);
77 while (mp_step(&sc)) {
83 r->r = mp_lsr(MP_NEW, m1, s);
85 /* --- Compute %$(m - 1)R \bmod m$% --- */
87 r->m1 = mp_sub(MP_NEW, m, r->mm.r);
91 /* --- @rabin_destroy@ --- *
93 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
97 * Use: Disposes of a Rabin-Miller context when it's no longer
101 void rabin_destroy(rabin *r)
105 mpmont_destroy(&r->mm);
108 /* --- @rabin_test@ --- *
110 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
111 * @mp *g@ = base to test the number against
113 * Returns: Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
116 * Use: Performs a single iteration of the Rabin-Miller primality
120 int rabin_test(rabin *r, mp *g)
123 mp *dd, *spare = MP_NEW;
127 /* --- Calculate %$y R = g^r R \bmod m$% --- *
129 * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that
130 * @y@ here has an extra factor of %$R$%.
133 y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
134 if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) {
139 /* --- Now for the main loop --- *
141 * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
142 * composite. Of course, %$j = 0$% has already been tested.
145 for (j = 1; j < r->s; j++) {
146 dd = mp_sqr(spare, y);
147 dd = mpmont_reduce(&r->mm, dd, dd);
149 if (MP_CMP(y, ==, r->mm.r))
151 if (MP_CMP(y, ==, r->m1)) {
166 /* --- @rabin_iters@ --- *
168 * Arguments: @unsigned len@ = number of bits in value
170 * Returns: Number of iterations recommended.
172 * Use: Returns the recommended number of iterations to ensure that a
173 * number with @len@ bits is really prime.
176 int rabin_iters(unsigned len)
198 /* --- Binary search through the table --- */
201 q = tab + (sizeof(tab)/sizeof(tab[0]));
206 if (len >= p[i].b && len < p[i + 1].b)
216 /*----- That's all, folks -------------------------------------------------*/