+++ /dev/null
-/* -*-c-*-
- *
- * $Id$
- *
- * Miller-Rabin primality test
- *
- * (c) 1999 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "mp.h"
-#include "mpbarrett.h"
-#include "mpmont.h"
-#include "pgen.h"
-#include "rabin.h"
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- @rabin_create@ --- *
- *
- * Arguments: @rabin *r@ = pointer to Rabin-Miller context
- * @mp *m@ = pointer to number to test
- *
- * Returns: Zero on success, nonzero on failure.
- *
- * Use: Precomputes some useful values for performing the
- * Miller-Rabin probabilistic primality test.
- */
-
-int rabin_create(rabin *r, mp *m)
-{
- mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
- if (mpmont_create(&r->mm, m)) {
- MP_DROP(m1);
- return (-1);
- }
- r->r = mp_odd(MP_NEW, m1, &r->s);
- r->m1 = mp_sub(MP_NEW, m, r->mm.r);
- mp_drop(m1);
- return (0);
-}
-
-/* --- @rabin_destroy@ --- *
- *
- * Arguments: @rabin *r@ = pointer to Rabin-Miller context
- *
- * Returns: ---
- *
- * Use: Disposes of a Rabin-Miller context when it's no longer
- * needed.
- */
-
-void rabin_destroy(rabin *r)
-{
- mp_drop(r->r);
- mp_drop(r->m1);
- mpmont_destroy(&r->mm);
-}
-
-/* --- @rabin_test@, @rabin_rtest@ --- *
- *
- * Arguments: @rabin *r@ = pointer to Rabin-Miller context
- * @mp *g@ = base to test the number against
- *
- * Returns: Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
- * if it succeeded.
- *
- * Use: Performs a single iteration of the Rabin-Miller primality
- * test. The @rtest@ variant assumes that %$g$% is either
- * already in Montgomery representation, or you don't care.
- */
-
-int rabin_rtest(rabin *r, mp *g)
-{
- mp *y;
- mp *dd, *spare = MP_NEW;
- size_t j;
- int rc = PGEN_FAIL;
-
- /* --- Calculate %$y R = g^r R \bmod m$% --- *
- *
- * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that
- * @y@ here has an extra factor of %$R$%.
- */
-
- y = mpmont_expr(&r->mm, MP_NEW, g, r->r);
- if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) {
- rc = PGEN_PASS;
- goto done;
- }
-
- /* --- Now for the main loop --- *
- *
- * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
- * composite. Of course, %$j = 0$% has already been tested.
- */
-
- for (j = 1; j < r->s; j++) {
- dd = mp_sqr(spare, y);
- dd = mpmont_reduce(&r->mm, dd, dd);
- spare = y; y = dd;
- if (MP_EQ(y, r->mm.r))
- break;
- if (MP_EQ(y, r->m1)) {
- rc = PGEN_PASS;
- break;
- }
- }
-
- /* --- Done --- */
-
-done:
- if (spare != MP_NEW)
- MP_DROP(spare);
- MP_DROP(y);
- return (rc);
-}
-
-int rabin_test(rabin *r, mp *g)
-{
- int rc;
- g = mpmont_mul(&r->mm, MP_NEW, g, r->mm.r2);
- rc = rabin_rtest(r, g);
- mp_drop(g);
- return (rc);
-}
-
-/* --- @rabin_iters@ --- *
- *
- * Arguments: @unsigned len@ = number of bits in value
- *
- * Returns: Number of iterations recommended.
- *
- * Use: Returns the recommended number of iterations to ensure that a
- * number with @len@ bits is really prime.
- */
-
-int rabin_iters(unsigned len)
-{
- static const struct {
- unsigned b;
- int i;
- } *p, *q, tab[] = {
- { 100, 27 },
- { 150, 18 },
- { 200, 15 },
- { 250, 12 },
- { 300, 9 },
- { 350, 8 },
- { 400, 7 },
- { 450, 6 },
- { 550, 5 },
- { 650, 4 },
- { 850, 3 },
- { 1300, 2 }
- };
-
- unsigned i;
-
- /* --- Binary search through the table --- */
-
- p = tab;
- q = tab + (sizeof(tab)/sizeof(tab[0]));
- for (;;) {
- i = (q - p) / 2;
- if (!i)
- break;
- if (len >= p[i].b && len < p[i + 1].b)
- break;
- if (len > p[i].b)
- p = p + i;
- else
- q = p + i;
- }
- return (p[i].i);
-}
-
-/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff