--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: pgen.c,v 1.1 1999/11/19 13:17:57 mdw Exp $
+ *
+ * Finding and testing prime numbers
+ *
+ * (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.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: pgen.c,v $
+ * Revision 1.1 1999/11/19 13:17:57 mdw
+ * Prime number generator and tester.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "mp.h"
+#include "mpmont.h"
+#include "pgen.h"
+#include "ptab.h"
+#include "rabin.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @pgen_create@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ * @mp *m@ = pointer to initial number to test
+ *
+ * Returns: One of the @PGEN@ constants above.
+ *
+ * Use: Tests an initial number for primality by computing its
+ * residue modulo various small prime numbers. This is fairly
+ * quick, but not particularly certain. If a @PGEN_MAYBE@
+ * result is returned, perform Rabin-Miller tests to confirm.
+ */
+
+int pgen_create(pgen *p, mp *m)
+{
+ int rc = PGEN_MAYBE;
+ int i;
+ mp *r = MP_NEW;
+ mpw qw;
+ mp q;
+
+ /* --- Take a copy of the number --- */
+
+ mp_shrink(m);
+ p->m = MP_COPY(m);
+
+ /* --- Fill in the residues --- */
+
+ mp_build(&q, &qw, &qw + 1);
+ for (i = 0; i < NPRIME; i++) {
+ qw = ptab[i];
+ mp_div(0, &r, m, &q);
+ p->r[i] = r->v[0];
+ if (!p->r[i] && rc == PGEN_MAYBE) {
+ if (MP_LEN(m) == 1 && m->v[0] == ptab[i])
+ rc = PGEN_PRIME;
+ else
+ rc = PGEN_COMPOSITE;
+ }
+ }
+
+ /* --- Done --- */
+
+ mp_drop(r);
+ return (rc);
+}
+
+/* --- @pgen_destroy@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ *
+ * Returns: ---
+ *
+ * Use: Discards a context and all the resources it holds.
+ */
+
+void pgen_destroy(pgen *p)
+{
+ mp_drop(p->m);
+}
+
+/* --- @pgen_step@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ * @mpw step@ = how much to step the number
+ *
+ * Returns: One of the @PGEN@ constants above.
+ *
+ * Use: Steps a number by a small amount. Stepping is much faster
+ * than initializing with a new number. The test performed is
+ * the same simple one used by @ptab_create@, so @PGEN_MAYBE@
+ * results should be followed up by a Rabin-Miller test.
+ */
+
+int pgen_step(pgen *p, mpw step)
+{
+ mp s;
+ int rc = PGEN_MAYBE;
+ int i;
+
+ /* --- Add the step on to the number --- */
+
+ mp_build(&s, &step, &step + 1);
+ p->m = mp_add(p->m, p->m, &s);
+
+ /* --- Update the residue table --- */
+
+ for (i = 0; i < NPRIME; i++) {
+ p->r[i] = (p->r[i] + step) % ptab[i];
+ if (!p->r[i] && rc == PGEN_MAYBE) {
+ if (MP_LEN(p->m) == 1 && p->m->v[0] == ptab[i])
+ rc = PGEN_PRIME;
+ else
+ rc = PGEN_COMPOSITE;
+ }
+ }
+
+ /* --- Done --- */
+
+ return (rc);
+}
+
+/* --- @pgen_jump@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ * @pgen *j@ = pointer to another generation context
+ *
+ * Returns: One of the @PGEN@ constants above.
+ *
+ * Use: Steps a number by a large amount. Even so, jumping is much
+ * faster than initializing a new number. The test peformed is
+ * the same simple one used by @ptab_create@, so @PGEN_MAYBE@
+ * results should be followed up by a Rabin-Miller test.
+ *
+ * Note that the number stored in the @j@ context is probably
+ * better off being even than prime. The important thing is
+ * that all of the residues for the number have already been
+ * computed.
+ */
+
+int pgen_jump(pgen *p, pgen *j)
+{
+ int rc = PGEN_MAYBE;
+ int i;
+
+ /* --- Add the step on --- */
+
+ p->m = mp_add(p->m, p->m, j->m);
+
+ /* --- Update the residue table --- */
+
+ for (i = 0; i < NPRIME; i++) {
+ p->r[i] = p->r[i] + j->r[i];
+ if (p->r[i] > ptab[i])
+ p->r[i] -= ptab[i];
+ if (!p->r[i] && rc == PGEN_MAYBE) {
+ if (MP_LEN(p->m) == 1 && p->m->v[0] == ptab[i])
+ rc = PGEN_PRIME;
+ else
+ rc = PGEN_COMPOSITE;
+ }
+ }
+
+ /* --- Done --- */
+
+ return (rc);
+}
+
+/*----- Test code ---------------------------------------------------------*/
+
+#ifdef TEST_RIG
+
+#include <mLib/testrig.h>
+
+static int verify(dstr *v)
+{
+ mp *m = *(mp **)v[0].buf;
+ mp *r = *(mp **)v[1].buf;
+ pgen p;
+ mpw gw;
+ mp g;
+ int rc;
+ static char baton[] = "/-\\|";
+ char *b = baton;
+ int ok = 1;
+
+ mp_build(&g, &gw, &gw + 1);
+ rc = pgen_create(&p, m);
+ for (;;) {
+ if (rc == PGEN_PRIME)
+ break;
+ if (rc == PGEN_MAYBE) {
+ int i;
+ rabin r;
+ rabin_create(&r, p.m);
+ for (i = 0; i < 5; i++) {
+ gw = rand();
+ if (rabin_test(&r, &g) == PGEN_COMPOSITE)
+ break;
+ }
+ rabin_destroy(&r);
+ if (i == 5)
+ break;
+ putc(*b++, stderr);
+ putc('\b', stderr);
+ if (!*b)
+ b = baton;
+ }
+ rc = pgen_step(&p, 2);
+ }
+
+ if (MP_CMP(p.m, !=, r)) {
+ fputs("\n*** failed.", stderr);
+ fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
+ fputs("\np = ", stderr); mp_writefile(p.m, stderr, 10);
+ fputs("\nr = ", stderr); mp_writefile(r, stderr, 10);
+ fputc('\n', stderr);
+ ok = 0;
+ }
+
+ mp_drop(m);
+ mp_drop(r);
+ pgen_destroy(&p);
+ return (ok);
+}
+
+static test_chunk tests[] = {
+ { "pgen", verify, { &type_mp, &type_mp, 0 } },
+ { 0, 0, { 0 } }
+};
+
+int main(int argc, char *argv[])
+{
+ sub_init();
+ test_run(argc, argv, tests, SRCDIR "/tests/pgen");
+ return (0);
+}
+
+#endif
+
+/*----- That's all, folks -------------------------------------------------*/
--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: pgen.h,v 1.1 1999/11/19 13:17:57 mdw Exp $
+ *
+ * Finding and testing prime numbers
+ *
+ * (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.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: pgen.h,v $
+ * Revision 1.1 1999/11/19 13:17:57 mdw
+ * Prime number generator and tester.
+ *
+ */
+
+#ifndef PGEN_H
+#define PGEN_H
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#ifndef MP_H
+# include "mp.h"
+#endif
+
+#ifndef PTAB_H
+# include "ptab.h"
+#endif
+
+/*----- Constants ---------------------------------------------------------*/
+
+#define PGEN_COMPOSITE (-1) /* Number is definitely composite */
+#define PGEN_MAYBE (0) /* Number may be prime */
+#define PGEN_PRIME (1) /* Number is definitely prime */
+
+/*----- Data structures ---------------------------------------------------*/
+
+typedef struct pgen {
+ mp *m;
+ unsigned char r[NPRIME];
+} pgen;
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @pgen_create@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ * @mp *m@ = pointer to initial number to test
+ *
+ * Returns: One of the @PGEN@ constants above.
+ *
+ * Use: Tests an initial number for primality by computing its
+ * residue modulo various small prime numbers. This is fairly
+ * quick, but not particularly certain. If a @PGEN_MAYBE@
+ * result is returned, perform Rabin-Miller tests to confirm.
+ */
+
+extern int pgen_create(pgen */*p*/, mp */*m*/);
+
+/* --- @pgen_destroy@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ *
+ * Returns: ---
+ *
+ * Use: Discards a context and all the resources it holds.
+ */
+
+extern void pgen_destroy(pgen */*p*/);
+
+/* --- @pgen_step@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ * @mpw step@ = how much to step the number
+ *
+ * Returns: One of the @PGEN@ constants above.
+ *
+ * Use: Steps a number by a small amount. Stepping is much faster
+ * than initializing with a new number. The test performed is
+ * the same simple one used by @ptab_create@, so @PGEN_MAYBE@
+ * results should be followed up by a Rabin-Miller test.
+ */
+
+extern int pgen_step(pgen */*p*/, mpw /*step*/);
+
+/* --- @pgen_jump@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ * @pgen *j@ = pointer to another generation context
+ *
+ * Returns: One of the @PGEN@ constants above.
+ *
+ * Use: Steps a number by a large amount. Even so, jumping is much
+ * faster than initializing a new number. The test peformed is
+ * the same simple one used by @ptab_create@, so @PGEN_MAYBE@
+ * results should be followed up by a Rabin-Miller test.
+ *
+ * Note that the number stored in the @j@ context is probably
+ * better off being even than prime. The important thing is
+ * that all of the residues for the number have already been
+ * computed.
+ */
+
+extern int pgen_jump(pgen */*p*/, pgen */*j*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif
--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: rabin.c,v 1.1 1999/11/19 13:17:57 mdw Exp $
+ *
+ * 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.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: rabin.c,v $
+ * Revision 1.1 1999/11/19 13:17:57 mdw
+ * Prime number generator and tester.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "mp.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: ---
+ *
+ * Use: Precomputes some useful values for performing the
+ * Miller-Rabin probabilistic primality test.
+ */
+
+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);
+ mp_drop(m1);
+}
+
+/* --- @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@ --- *
+ *
+ * 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@
+ * if it succeeded.
+ *
+ * Use: Performs a single iteration of the Rabin-Miller primality
+ * test.
+ */
+
+int rabin_test(rabin *r, mp *g)
+{
+ mp *y;
+ mp *dd, *spare = MP_NEW;
+ size_t j;
+ int rc = PGEN_COMPOSITE;
+
+ /* --- 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, g, r->r);
+ if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) {
+ rc = PGEN_MAYBE;
+ 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 = mpmont_mul(&r->mm, spare, y, y); spare = y; y = dd;
+ if (MP_CMP(y, ==, r->mm.r))
+ break;
+ if (MP_CMP(y, ==, r->m1)) {
+ rc = PGEN_MAYBE;
+ break;
+ }
+ }
+
+ /* --- Done --- */
+
+done:
+ if (spare != MP_NEW)
+ MP_DROP(spare);
+ MP_DROP(y);
+ return (rc);
+}
+
+/*----- That's all, folks -------------------------------------------------*/
--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: rabin.h,v 1.1 1999/11/19 13:17:57 mdw Exp $
+ *
+ * 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.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: rabin.h,v $
+ * Revision 1.1 1999/11/19 13:17:57 mdw
+ * Prime number generator and tester.
+ *
+ */
+
+#ifndef RABIN_H
+#define RABIN_H
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#ifndef MP_H
+# include "mp.h"
+#endif
+
+#ifndef MPMONT_H
+# include "mpmont.h"
+#endif
+
+#ifndef PGEN_H
+# include "pgen.h"
+#endif
+
+/*----- Data structures ---------------------------------------------------*/
+
+typedef struct rabin {
+ mpmont mm; /* Montgomery arithmetic context */
+ size_t s; /* %$m = 2^s r + 1$% */
+ mp *r; /* %$m = 2^s r + 1$% */
+ mp *m1; /* %$(m - 1)R \bmod m */
+} rabin;
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @rabin_create@ --- *
+ *
+ * Arguments: @rabin *r@ = pointer to Rabin-Miller context
+ * @mp *m@ = pointer to number to test
+ *
+ * Returns: ---
+ *
+ * Use: Precomputes some useful values for performing the
+ * Miller-Rabin probabilistic primality test.
+ */
+
+extern void rabin_create(rabin */*r*/, mp */*m*/);
+
+/* --- @rabin_destroy@ --- *
+ *
+ * Arguments: @rabin *r@ = pointer to Rabin-Miller context
+ *
+ * Returns: ---
+ *
+ * Use: Disposes of a Rabin-Miller context when it's no longer
+ * needed.
+ */
+
+extern void rabin_destroy(rabin */*r*/);
+
+/* --- @rabin_test@ --- *
+ *
+ * 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@
+ * if it succeeded.
+ *
+ * Use: Performs a single iteration of the Rabin-Miller primality
+ * test.
+ */
+
+extern int rabin_test(rabin */*r*/, mp */*g*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif
projects / u / mdw / catacomb / commitdiff