X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ba6e6b64033b1f9de49feccb5c9cd438354481f7..0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a:/math/rabin.c

diff --git a/math/rabin.c b/math/rabin.c
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+/* -*-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 -------------------------------------------------*/