/* -*-c-*-
*
- * $Id: rabin.c,v 1.1 1999/11/19 13:17:57 mdw Exp $
+ * $Id: rabin.c,v 1.7 2002/01/13 13:42:53 mdw Exp $
*
* Miller-Rabin primality test
*
/*----- Revision history --------------------------------------------------*
*
* $Log: rabin.c,v $
+ * Revision 1.7 2002/01/13 13:42:53 mdw
+ * More efficient Rabin-Miller test: with random witnesses, skip redundant
+ * Montgomerization. (Being bijective, it can't affect the distribution.)
+ *
+ * Revision 1.6 2001/06/16 12:56:38 mdw
+ * Fixes for interface change to @mpmont_expr@ and @mpmont_mexpr@.
+ *
+ * Revision 1.5 2000/10/08 12:11:22 mdw
+ * Use @MP_EQ@ instead of @MP_CMP@.
+ *
+ * Revision 1.4 2000/06/22 19:03:02 mdw
+ * Use the new @mp_odd@ function.
+ *
+ * Revision 1.3 1999/12/22 15:50:29 mdw
+ * Reworking for new prime-search system. Add function for working out how
+ * many iterations to use for a particular number.
+ *
+ * Revision 1.2 1999/12/10 23:29:48 mdw
+ * Change header file guard names.
+ *
* Revision 1.1 1999/11/19 13:17:57 mdw
* Prime number generator and tester.
*
/*----- Header files ------------------------------------------------------*/
#include "mp.h"
+#include "mpbarrett.h"
#include "mpmont.h"
#include "pgen.h"
#include "rabin.h"
void rabin_create(rabin *r, mp *m)
{
mp *m1 = mp_sub(MP_NEW, m, MP_ONE);
- mpscan sc;
- size_t s;
-
- /* --- Find @r@ and @s@ --- */
-
mpmont_create(&r->mm, m);
- mp_scan(&sc, m1);
- s = 0;
- while (mp_step(&sc)) {
- if (mp_bit(&sc))
- break;
- s++;
- }
- r->s = s;
- r->r = mp_lsr(MP_NEW, m1, s);
-
- /* --- Compute %$(m - 1)R \bmod m$% --- */
-
- r->m1 = mpmont_mul(&r->mm, MP_NEW, m1, r->mm.r2);
+ r->r = mp_odd(MP_NEW, m1, &r->s);
+ r->m1 = mp_sub(MP_NEW, m, r->mm.r);
mp_drop(m1);
}
mpmont_destroy(&r->mm);
}
-/* --- @rabin_test@ --- *
+/* --- @rabin_test@, @rabin_rtest@ --- *
*
* Arguments: @rabin *r@ = pointer to Rabin-Miller context
* @mp *g@ = base to test the number against
*
- * Returns: Either @PGEN_COMPOSITE@ if the test failed, or @PGEN_MAYBE@
+ * 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.
+ * test. The @rtest@ variant assumes that %$g$% is either
+ * already in Montgomery representation, or you don't care.
*/
-int rabin_test(rabin *r, mp *g)
+int rabin_rtest(rabin *r, mp *g)
{
mp *y;
mp *dd, *spare = MP_NEW;
size_t j;
- int rc = PGEN_COMPOSITE;
+ int rc = PGEN_FAIL;
/* --- Calculate %$y R = g^r R \bmod m$% --- *
*
* @y@ here has an extra factor of %$R$%.
*/
- y = mpmont_expr(&r->mm, g, r->r);
- if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) {
- rc = PGEN_MAYBE;
+ 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;
}
*/
for (j = 1; j < r->s; j++) {
- dd = mpmont_mul(&r->mm, spare, y, y); spare = y; y = dd;
- if (MP_CMP(y, ==, r->mm.r))
+ 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_CMP(y, ==, r->m1)) {
- rc = PGEN_MAYBE;
+ if (MP_EQ(y, r->m1)) {
+ rc = PGEN_PASS;
break;
}
}
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 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 -------------------------------------------------*/