3 * $Id: rabin.c,v 1.2 1999/12/10 23:29:48 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 1.2 1999/12/10 23:29:48 mdw
34 * Change header file guard names.
36 * Revision 1.1 1999/11/19 13:17:57 mdw
37 * Prime number generator and tester.
41 /*----- Header files ------------------------------------------------------*/
48 /*----- Main code ---------------------------------------------------------*/
50 /* --- @rabin_create@ --- *
52 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
53 * @mp *m@ = pointer to number to test
57 * Use: Precomputes some useful values for performing the
58 * Miller-Rabin probabilistic primality test.
61 void rabin_create(rabin *r, mp *m)
63 mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
67 /* --- Find @r@ and @s@ --- */
69 mpmont_create(&r->mm, m);
72 while (mp_step(&sc)) {
78 r->r = mp_lsr(MP_NEW, m1, s);
80 /* --- Compute %$(m - 1)R \bmod m$% --- */
82 r->m1 = mpmont_mul(&r->mm, MP_NEW, m1, r->mm.r2);
86 /* --- @rabin_destroy@ --- *
88 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
92 * Use: Disposes of a Rabin-Miller context when it's no longer
96 void rabin_destroy(rabin *r)
100 mpmont_destroy(&r->mm);
103 /* --- @rabin_test@ --- *
105 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
106 * @mp *g@ = base to test the number against
108 * Returns: Either @PGEN_COMPOSITE@ if the test failed, or @PGEN_MAYBE@
111 * Use: Performs a single iteration of the Rabin-Miller primality
115 int rabin_test(rabin *r, mp *g)
118 mp *dd, *spare = MP_NEW;
120 int rc = PGEN_COMPOSITE;
122 /* --- Calculate %$y R = g^r R \bmod m$% --- *
124 * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that
125 * @y@ here has an extra factor of %$R$%.
128 y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
129 if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) {
134 /* --- Now for the main loop --- *
136 * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
137 * composite. Of course, %$j = 0$% has already been tested.
140 for (j = 1; j < r->s; j++) {
141 dd = mpmont_mul(&r->mm, spare, y, y); spare = y; y = dd;
142 if (MP_CMP(y, ==, r->mm.r))
144 if (MP_CMP(y, ==, r->m1)) {
159 /*----- That's all, folks -------------------------------------------------*/