--- /dev/null
+/* -*-c-*-
+ *
+ * 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 -------------------------------------------------*/