/* -*-c-*-
*
- * $Id: pgen.c,v 1.2 1999/11/20 22:23:05 mdw Exp $
+ * $Id$
*
- * Finding and testing prime numbers
+ * Prime generation glue
*
* (c) 1999 Straylight/Edgeware
*/
-/*----- Licensing notice --------------------------------------------------*
+/*----- Licensing notice --------------------------------------------------*
*
* This file is part of Catacomb.
*
* 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 1.2 1999/11/20 22:23:05 mdw
- * Add multiply-and-add function for Diffie-Hellman safe prime generation.
- *
- * Revision 1.1 1999/11/19 13:17:57 mdw
- * Prime number generator and tester.
- *
- */
-
/*----- Header files ------------------------------------------------------*/
+#include <assert.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "fibrand.h"
+#include "grand.h"
#include "mp.h"
-#include "mpmont.h"
+#include "mprand.h"
#include "pgen.h"
-#include "ptab.h"
+#include "pfilt.h"
#include "rabin.h"
-/*----- Main code ---------------------------------------------------------*/
+/*----- Standard prime filter ---------------------------------------------*/
-/* --- @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.
- */
+/* --- @pgen_filter@ --- */
-int pgen_create(pgen *p, mp *m)
+int pgen_filter(int rq, pgen_event *ev, void *p)
{
- 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;
- }
- }
+ pgen_filterctx *f = p;
+ int rc = PGEN_FAIL;
- /* --- Done --- */
+ switch (rq) {
+ case PGEN_BEGIN:
+ rc = pfilt_create(&f->f, ev->m);
+ mp_drop(ev->m);
+ break;
+ case PGEN_TRY:
+ mp_drop(ev->m);
+ break;
+ case PGEN_DONE:
+ pfilt_destroy(&f->f);
+ return (PGEN_DONE);
+ default:
+ rc = PGEN_ABORT;
+ break;
+ }
- mp_drop(r);
+ if (rc == PGEN_FAIL && !((f->step | f->f.m->v[0]) & 1))
+ rc = pfilt_step(&f->f, 1);
+ while (rc == PGEN_FAIL)
+ rc = pfilt_step(&f->f, f->step);
+ ev->m = MP_COPY(f->f.m);
return (rc);
}
-/* --- @pgen_destroy@ --- *
- *
- * Arguments: @pgen *p@ = pointer to prime generation context
- *
- * Returns: ---
+/* --- @pgen_jump@ --- *
*
- * Use: Discards a context and all the resources it holds.
+ * Similar to the standard @pgen_filter@, but jumps in large steps rather
+ * than small ones.
*/
-void pgen_destroy(pgen *p)
+int pgen_jump(int rq, pgen_event *ev, void *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.
- */
+ pgen_jumpctx *f = p;
+ int rc = PGEN_ABORT;
+
+ switch (rq) {
+ case PGEN_BEGIN: {
+ mp *g = MP_NEW;
+ mp_gcd(&g, 0, 0, ev->m, f->j->m);
+ if (MP_CMP(g, >, MP_ONE)) {
+ mp_drop(g);
+ return (PGEN_ABORT);
+ }
+ mp_drop(g);
+ rc = pfilt_create(&f->f, ev->m);
+ mp_drop(ev->m);
+ } break;
+ case PGEN_TRY:
+ mp_drop(ev->m);
+ rc = pfilt_jump(&f->f, f->j);
+ break;
+ case PGEN_DONE:
+ pfilt_destroy(&f->f);
+ return (PGEN_DONE);
+ }
-int pgen_step(pgen *p, mpw step)
-{
- int rc = PGEN_MAYBE;
- int i;
+ while (rc == PGEN_FAIL)
+ rc = pfilt_jump(&f->f, f->j);
+ ev->m = MP_COPY(f->f.m);
+ return (rc);
+}
- /* --- Add the step on to the number --- */
+/*----- Standard prime test -----------------------------------------------*/
- p->m = mp_modify(p->m, MP_LEN(p->m) + 1);
- mpx_uaddn(p->m->v, p->m->vl, step);
- mp_shrink(p->m);
+/* --- @pgen_test@ --- */
- /* --- Update the residue table --- */
+int pgen_test(int rq, pgen_event *ev, void *p)
+{
+ rabin *r = p;
+ int rc = PGEN_ABORT;
- 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;
- }
+ switch (rq) {
+ case PGEN_BEGIN:
+ rabin_create(r, ev->m);
+ rc = PGEN_TRY;
+ break;
+ case PGEN_TRY:
+ if (!ev->tests)
+ rc = rabin_rtest(r, MP_TWO);
+ else {
+ mp *a = mprand_range(MP_NEW, ev->m, ev->r, 0);
+ rc = rabin_rtest(r, a);
+ mp_drop(a);
+ }
+ break;
+ case PGEN_DONE:
+ rabin_destroy(r);
+ rc = PGEN_DONE;
+ break;
}
- /* --- Small numbers must be prime --- */
-
- if (rc == PGEN_MAYBE && MP_LEN(p->m) == 1 &&
- p->m->v[0] < MAXPRIME * MAXPRIME)
- rc = PGEN_PRIME;
-
- /* --- Done --- */
-
return (rc);
}
-/* --- @pgen_muladd@ --- *
- *
- * Arguments: @pgen *p@ = destination prime generation context
- * @const pgen *q@ = source prime generation context
- * @mpw m@ = number to multiply by
- * @mpw a@ = number to add
+/*----- The main driver ---------------------------------------------------*/
+
+/* --- @pgen@ --- *
*
- * Returns: One of the @PGEN@ constants above.
+ * Arguments: @const char *name@ = name of the value being searched for
+ * @mp *d@ = destination for the result integer
+ * @mp *m@ = start value to pass to stepper
+ * @pgen_proc *event@ = event handler function
+ * @void *ectx@ = context argument for event andler
+ * @unsigned steps@ = number of steps to take in search
+ * @pgen_proc *step@ = stepper function to use
+ * @void *sctx@ = context argument for stepper
+ * @unsigned tests@ = number of tests to make
+ * @pgen_proc *test@ = tester function to use
+ * @void *tctx@ = context argument for tester
*
- * Use: Multiplies the number in a prime generation context by a
- * small value and then adds a small value. The destination
- * should either be uninitialized or the same as the source.
+ * Returns: Pointer to final result, or null.
*
- * Common things to do include multiplying by 2 and adding 0 to
- * turn a prime into a jump for finding other primes with @q@ as
- * a factor of @p - 1@, or multiplying by 2 and adding 1.
+ * Use: A generalized prime-number search skeleton. Yes, that's a
+ * scary number of arguments.
*/
-int pgen_muladd(pgen *p, const pgen *q, mpw m, mpw a)
+mp *pgen(const char *name, mp *d, mp *m, pgen_proc *event, void *ectx,
+ unsigned steps, pgen_proc *step, void *sctx,
+ unsigned tests, pgen_proc *test, void *tctx)
{
- int rc = PGEN_MAYBE;
- int i;
-
- /* --- Multiply the big number --- */
-
- {
- mp *d = mp_create(MP_LEN(q->m) + 2);
- mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m);
- mpx_uaddn(d->v, d->vl, a);
- d->f = q->m->f;
- if (p == q)
- mp_drop(p->m);
- mp_shrink(d);
- p->m = d;
+ pgen_event ev;
+ int rq, rc;
+ pgen_proc *proc;
+ void *ctx;
+ int p;
+
+ enum { P_STEP, P_TEST };
+
+ /* --- Set up the initial event block --- */
+
+ ev.name = name;
+ if (m)
+ ev.m = MP_COPY(m);
+ else
+ ev.m = 0;
+ ev.steps = 0;
+ ev.tests = 0;
+ ev.r = fibrand_create(0);
+
+ /* --- Tell the event handler we're under way --- */
+
+ if (event && event(PGEN_BEGIN, &ev, ectx) == PGEN_ABORT) {
+ ev.r->ops->destroy(ev.r);
+ return (0);
}
- /* --- Gallivant through the residue table --- */
-
- for (i = 0; i < NPRIME; i++) {
- p->r[i] = (q->r[i] * m + a) % 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;
+ /* --- Set up for the initial call --- */
+
+ proc = step; ctx = sctx; p = P_STEP; rq = PGEN_BEGIN;
+
+ /* --- Enter the great maelstrom of state transitions --- */
+
+ for (;;) {
+ unsigned act = 0;
+
+#define A_STEP 1u
+#define A_TEST 2u
+#define A_EVENT 4u
+#define A_ENDTEST 8u
+#define A_ENDSTEP 16u
+#define A_DONE 32u
+
+ /* --- Call the procedure and decide what to do next --- */
+
+ rc = proc(rq, &ev, ctx);
+ switch (rc) {
+ case PGEN_TRY:
+ if (p == P_TEST)
+ rq = PGEN_TRY;
+ else {
+ act |= A_EVENT;
+ proc = test; ctx = tctx; p = P_TEST;
+ rq = PGEN_BEGIN;
+ }
+ break;
+ case PGEN_PASS:
+ act |= A_TEST | A_EVENT;
+ if (p == P_TEST)
+ rq = PGEN_TRY;
+ else {
+ proc = test; ctx = tctx; p = P_TEST;
+ rq = PGEN_BEGIN;
+ }
+ break;
+ case PGEN_FAIL:
+ act |= A_STEP;
+ if (p == P_TEST) {
+ act |= A_ENDTEST | A_EVENT;
+ proc = step; ctx = sctx; p = P_STEP;
+ }
+ rq = PGEN_TRY;
+ break;
+ case PGEN_DONE:
+ act |= A_EVENT | A_DONE | A_ENDSTEP;
+ if (p == P_TEST)
+ act |= A_ENDTEST;
+ break;
+ case PGEN_ABORT:
+ act |= A_EVENT | A_DONE;
+ if (p == P_TEST || rq == PGEN_TRY)
+ act |= A_ENDSTEP;
+ if (p == P_TEST && rq != PGEN_BEGIN)
+ act |= A_ENDTEST;
+ break;
+ default:
+ assert(((void)"Invalid response from function", 0));
+ break;
}
- }
- /* --- Small numbers must be prime --- */
+ /* --- If decrementing counters is requested, do that --- */
- if (rc == PGEN_MAYBE && MP_LEN(p->m) == 1 &&
- p->m->v[0] < MAXPRIME * MAXPRIME)
- rc = PGEN_PRIME;
+ if ((act & A_STEP) && steps) {
+ ev.steps++;
+ if (ev.steps == steps) {
+ act |= A_EVENT | A_ENDSTEP | A_DONE;
+ rc = PGEN_ABORT;
+ }
+ ev.tests = 0;
+ }
- /* --- Finished --- */
+ if ((act & A_TEST) && tests) {
+ ev.tests++;
+ if (ev.tests == tests) {
+ act |= A_ENDTEST | A_ENDSTEP | A_DONE;
+ rc = PGEN_DONE;
+ }
+ }
- return (rc);
-}
+ /* --- Report an event if so directed --- */
+ if ((act & A_EVENT) && event && event(rc, &ev, ectx) == PGEN_ABORT) {
+ rc = PGEN_ABORT;
+ if (!(act & A_DONE)) {
+ act |= A_ENDSTEP | A_DONE;
+ if (p == P_TEST)
+ act |= A_ENDTEST;
+ }
+ }
-/* --- @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.
- */
+ /* --- Close down tester and stepper functions --- */
-int pgen_jump(pgen *p, pgen *j)
-{
- int rc = PGEN_MAYBE;
- int i;
+ if (act & A_ENDTEST)
+ test(PGEN_DONE, &ev, tctx);
+ if (act & A_ENDSTEP)
+ step(PGEN_DONE, &ev, sctx);
- /* --- Add the step on --- */
+ /* --- Stop the entire test if necessary --- */
- p->m = mp_add(p->m, p->m, j->m);
+ if (act & A_DONE)
+ break;
+ }
- /* --- Update the residue table --- */
+ /* --- Tidy up and return --- */
- 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;
- }
+ if (rc == PGEN_ABORT) {
+ mp_drop(ev.m);
+ ev.m = 0;
}
+ ev.r->ops->destroy(ev.r);
+ mp_drop(d);
- /* --- Small numbers must be prime --- */
+ return (ev.m);
+}
- if (rc == PGEN_MAYBE && MP_LEN(p->m) == 1 &&
- p->m->v[0] < MAXPRIME * MAXPRIME)
- rc = PGEN_PRIME;
+/* --- @pgen_primep@ --- *
+ *
+ * Arguments: @mp *p@ = a number to check
+ * @grand *gr@ = a random number source
+ *
+ * Returns: Nonzero if @p@ is really prime.
+ */
- /* --- Done --- */
+int pgen_primep(mp *p, grand *gr)
+{
+ int i;
+ rabin r;
+ mp *x = MP_NEW;
- return (rc);
+ if (MP_NEGP(p)) return (0);
+ switch (pfilt_smallfactor(p)) {
+ case PGEN_DONE: return (1);
+ case PGEN_FAIL: return (0);
+ }
+ rabin_create(&r, p);
+ for (i = 32; i; i--) {
+ x = mprand_range(x, p, gr, 0);
+ if (rabin_rtest(&r, x) == PGEN_FAIL)
+ break;
+ }
+ MP_DROP(x);
+ rabin_destroy(&r);
+ return (!i);
}
-/*----- Test code ---------------------------------------------------------*/
+/*----- Test rig ----------------------------------------------------------*/
#ifdef TEST_RIG
#include <mLib/testrig.h>
-static int verify(dstr *v)
+static int t_primep(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 e = *(int *)v[1].buf;
+ int r;
+ grand *rng;
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);
+ rng = fibrand_create(0);
+ r = pgen_primep(m, rng);
+ GR_DESTROY(rng);
+ if (e != r) {
+ fputs("\n*** primep failed", stderr);
+ fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
+ fprintf(stderr, "\nexpected %d", e);
+ fprintf(stderr, "\nreported %d", r);
+ fputc('\n', stderr);
+ ok = 0;
}
- if (MP_CMP(p.m, !=, r)) {
- fputs("\n*** failed.", stderr);
+ mp_drop(m);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
+ return (ok);
+}
+
+static int verify(dstr *v)
+{
+ mp *m = *(mp **)v[0].buf;
+ mp *q = *(mp **)v[1].buf;
+ mp *p;
+ int ok = 1;
+
+ pgen_filterctx pf;
+ rabin r;
+
+ pf.step = 2;
+ p = pgen("p", MP_NEW, m, pgen_evspin, 0, 0, pgen_filter, &pf,
+ rabin_iters(mp_bits(m)), pgen_test, &r);
+ if (!p || !MP_EQ(p, q)) {
+ fputs("\n*** pgen 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);
+ fputs("\np = ", stderr); mp_writefile(p, stderr, 10);
+ fputs("\nq = ", stderr); mp_writefile(q, stderr, 10);
fputc('\n', stderr);
ok = 0;
}
mp_drop(m);
- mp_drop(r);
- pgen_destroy(&p);
+ mp_drop(q);
+ mp_drop(p);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
return (ok);
}
static test_chunk tests[] = {
{ "pgen", verify, { &type_mp, &type_mp, 0 } },
+ { "primep", t_primep, { &type_mp, &type_int, 0 } },
{ 0, 0, { 0 } }
};
test_run(argc, argv, tests, SRCDIR "/tests/pgen");
return (0);
}
-
#endif
/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff