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Use libcrypto's bignum support to implement a Pollard Rho factoring 

algorithm so we can factorise numbers larger than a host long.
This commit is contained in:
simonb 2002-06-15 02:12:23 +00:00
parent 1ece0e0c9a
commit a311a7732d
2 changed files with 111 additions and 40 deletions
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4
games/factor/Makefile
View File

@ -1,9 +1,11 @@
# $NetBSD: Makefile,v 1.7 1997/10/22 04:43:26 lukem Exp $
# $NetBSD: Makefile,v 1.8 2002/06/15 02:12:23 simonb Exp $
# @(#)Makefile 8.1 (Berkeley) 5/31/93
PROG= factor
SRCS= factor.c pr_tbl.c
CPPFLAGS+=-I${.CURDIR}/../primes
LDADD+= -lcrypto
DPADD+= ${LIBCRYPTO}
MAN= factor.6
MLINKS+=factor.6 primes.6
.PATH: ${.CURDIR}/../primes

147
games/factor/factor.c
View File

@ -1,4 +1,4 @@
/* $NetBSD: factor.c,v 1.9 1999/09/08 21:17:48 jsm Exp $ */
/* $NetBSD: factor.c,v 1.10 2002/06/15 02:12:23 simonb Exp $ */
/*
* Copyright (c) 1989, 1993
@ -46,7 +46,7 @@ __COPYRIGHT("@(#) Copyright (c) 1989, 1993\n\
#if 0
static char sccsid[] = "@(#)factor.c 8.4 (Berkeley) 5/4/95";
#else
__RCSID("$NetBSD: factor.c,v 1.9 1999/09/08 21:17:48 jsm Exp $");
__RCSID("$NetBSD: factor.c,v 1.10 2002/06/15 02:12:23 simonb Exp $");
#endif
#endif /* not lint */
@ -69,37 +69,45 @@ __RCSID("$NetBSD: factor.c,v 1.9 1999/09/08 21:17:48 jsm Exp $");
* If no args are given, the list of numbers are read from stdin.
*/
#include <err.h>
#include <ctype.h>
#include <err.h>
#include <errno.h>
#include <limits.h>
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <openssl/bn.h>
#include "primes.h"
/*
* prime[i] is the (i-1)th prime.
*
* We are able to sieve 2^32-1 because this byte table yields all primes
* We are able to sieve 2^32-1 because this byte table yields all primes
* up to 65537 and 65537^2 > 2^32-1.
*/
extern const ubig prime[];
extern const ubig *pr_limit; /* largest prime in the prime array */
int main __P((int, char *[]));
void pr_fact __P((ubig)); /* print factors of a value */
void usage __P((void)) __attribute__((__noreturn__));
#define PRIME_CHECKS 5
int main(int, char *[]);
void pr_fact(BIGNUM *); /* print factors of a value */
void BN_print_dec_fp(FILE *, const BIGNUM *);
void pollard_pminus1(BIGNUM *); /* print factors for big numbers */
void usage(void) __attribute__((__noreturn__));
int
main(argc, argv)
int argc;
char *argv[];
main(int argc, char *argv[])
{
ubig val;
BIGNUM *val;
int ch;
char *p, buf[100]; /* > max number of digits. */
char *p, buf[LINE_MAX]; /* > max number of digits. */
val = BN_new();
if (val == NULL)
errx(1, "can't initialise bignum");
while ((ch = getopt(argc, argv, "")) != -1)
switch (ch) {
@ -123,12 +131,8 @@ main(argc, argv)
continue;
if (*p == '-')
errx(1, "negative numbers aren't permitted.");
errno = 0;
val = strtoul(buf, &p, 10);
if (errno)
err(1, "%s", buf);
if (*p != '\n')
errx(1, "%s: illegal numeric format.", buf);
if (BN_dec2bn(&val, buf) == 0)
errx(1, "%s: illegal numeric format.", argv[0]);
pr_fact(val);
}
/* Factor the arguments. */
@ -136,11 +140,7 @@ main(argc, argv)
for (; *argv != NULL; ++argv) {
if (argv[0][0] == '-')
errx(1, "negative numbers aren't permitted.");
errno = 0;
val = strtoul(argv[0], &p, 10);
if (errno)
err(1, "%s", argv[0]);
if (*p != '\0')
if (BN_dec2bn(&val, argv[0]) == 0)
errx(1, "%s: illegal numeric format.", argv[0]);
pr_fact(val);
}
@ -161,49 +161,118 @@ main(argc, argv)
* Factors are printed with leading tabs.
*/
void
pr_fact(val)
ubig val; /* Factor this value. */
pr_fact(BIGNUM *val)
{
const ubig *fact; /* The factor found. */
/* Firewall - catch 0 and 1. */
if (val == 0) /* Historical practice; 0 just exits. */
if (BN_is_zero(val)) /* Historical practice; 0 just exits. */
exit(0);
if (val == 1) {
(void)printf("1: 1\n");
if (BN_is_one(val)) {
printf("1: 1\n");
return;
}
/* Factor value. */
(void)printf("%lu:", val);
for (fact = &prime[0]; val > 1; ++fact) {
BN_print_dec_fp(stdout, val);
putchar(':');
for (fact = &prime[0]; !BN_is_one(val); ++fact) {
/* Look for the smallest factor. */
do {
if (val % (long)*fact == 0)
if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
break;
} while (++fact <= pr_limit);
/* Watch for primes larger than the table. */
if (fact > pr_limit) {
(void)printf(" %lu", val);
pollard_pminus1(val);
break;
}
/* Divide factor out until none are left. */
do {
(void)printf(" %lu", *fact);
val /= (long)*fact;
} while ((val % (long)*fact) == 0);
printf(" %lu", *fact);
BN_div_word(val, (BN_ULONG)*fact);
} while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
/* Let the user know we're doing something. */
(void)fflush(stdout);
fflush(stdout);
}
(void)putchar('\n');
putchar('\n');
}
/*
* Sigh.. No _decimal_ output to file functions in BN.
*/
void
BN_print_dec_fp(FILE *fp, const BIGNUM *num)
{
char *buf;
buf = BN_bn2dec(num);
if (buf == NULL)
return; /* XXX do anything here? */
fprintf(fp, buf);
free(buf);
}
void
usage()
usage(void)
{
(void)fprintf(stderr, "usage: factor [value ...]\n");
fprintf(stderr, "usage: factor [value ...]\n");
exit (0);
}
/* pollard rho, algorithm from Jim Gillogly, May 2000 */
void
pollard_pminus1(BIGNUM *val)
{
BIGNUM *base, *num, *i, *x;
BN_CTX *ctx;
ctx = BN_CTX_new();
base = BN_new();
num = BN_new();
i = BN_new();
x = BN_new();
BN_set_word(i, 2);
BN_set_word(base, 2);
for (;;) {
BN_mod_exp(base, base, i, val, ctx);
BN_copy(x, base);
BN_sub_word(x, 1);
BN_gcd(x, x, val, ctx);
if (!BN_is_one(x)) {
if (BN_is_prime(x, PRIME_CHECKS, NULL, NULL,
NULL) == 1) {
putchar(' ');
BN_print_dec_fp(stdout, x);
} else
pollard_pminus1(x);
fflush(stdout);
BN_div(num, NULL, val, x, ctx);
if (BN_is_one(num))
return;
if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL,
NULL) == 1) {
putchar(' ');
BN_print_dec_fp(stdout, num);
fflush(stdout);
return;
}
BN_copy(val, num);
}
BN_add_word(i, 1);
}
}