1 /*
2 * Copyright (c) 1989, 1993
3 * The Regents of the University of California. All rights reserved.
4 *
5 * This code is derived from software contributed to Berkeley by
6 * Landon Curt Noll.
7 *
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
10 * are met:
11 * 1. Redistributions of source code must retain the above copyright
12 * notice, this list of conditions and the following disclaimer.
13 * 2. Redistributions in binary form must reproduce the above copyright
14 * notice, this list of conditions and the following disclaimer in the
15 * documentation and/or other materials provided with the distribution.
16 * 3. Neither the name of the University nor the names of its contributors
17 * may be used to endorse or promote products derived from this software
18 * without specific prior written permission.
19 *
20 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
21 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
22 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
23 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
24 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
25 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
26 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
27 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
28 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
29 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
30 * SUCH DAMAGE.
31 */
32
33 #ifndef lint
34 #include <sys/cdefs.h>
35 #ifdef __COPYRIGHT
36 __COPYRIGHT("@(#) Copyright (c) 1989, 1993\
37 The Regents of the University of California. All rights reserved.");
38 #endif
39 #ifdef __SCCSID
40 __SCCSID("@(#)factor.c 8.4 (Berkeley) 5/4/95");
41 #endif
42 #ifdef __RCSID
43 __RCSID("$NetBSD: factor.c,v 1.19 2009/08/12 05:54:31 dholland Exp $");
44 #endif
45 #ifdef __FBSDID
46 __FBSDID("$FreeBSD$");
47 #endif
48 #endif /* not lint */
49
50 /*
51 * factor - factor a number into primes
52 *
53 * By: Landon Curt Noll [email protected], ...!{sun,tolsoft}!hoptoad!chongo
54 *
55 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
56 *
57 * usage:
58 * factor [-h] [number] ...
59 *
60 * The form of the output is:
61 *
62 * number: factor1 factor1 factor2 factor3 factor3 factor3 ...
63 *
64 * where factor1 <= factor2 <= factor3 <= ...
65 *
66 * If no args are given, the list of numbers are read from stdin.
67 */
68
69 #include <ctype.h>
70 #include <err.h>
71 #include <errno.h>
72 #include <inttypes.h>
73 #include <limits.h>
74 #include <stdbool.h>
75 #include <stdio.h>
76 #include <stdlib.h>
77 #include <unistd.h>
78
79 #include "primes.h"
80
81 #ifdef HAVE_OPENSSL
82
83 #include <openssl/bn.h>
84
85 #define PRIME_CHECKS 5
86
87 static void pollard_pminus1(BIGNUM *); /* print factors for big numbers */
88
89 #else
90
91 typedef ubig BIGNUM;
92 typedef u_long BN_ULONG;
93
94 #define BN_CTX int
95 #define BN_CTX_new() NULL
96 #define BN_new() ((BIGNUM *)calloc(sizeof(BIGNUM), 1))
97 #define BN_is_zero(v) (*(v) == 0)
98 #define BN_is_one(v) (*(v) == 1)
99 #define BN_mod_word(a, b) (*(a) % (b))
100
101 static int BN_dec2bn(BIGNUM **, const char *);
102 static int BN_hex2bn(BIGNUM **, const char *);
103 static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG);
104 static void BN_print_fp(FILE *, const BIGNUM *);
105
106 #endif
107
108 static void BN_print_dec_fp(FILE *, const BIGNUM *);
109 static void convert_str2bn(BIGNUM **, char *);
110 static bool is_hex_str(char *);
111 static void pr_fact(BIGNUM *); /* print factors of a value */
112 static void pr_print(BIGNUM *); /* print a prime */
113 static void usage(void);
114
115 static BN_CTX *ctx; /* just use a global context */
116 static int hflag;
117
118 int
main(int argc,char * argv[])119 main(int argc, char *argv[])
120 {
121 BIGNUM *val;
122 int ch;
123 char *p, buf[LINE_MAX]; /* > max number of digits. */
124
125 ctx = BN_CTX_new();
126 val = BN_new();
127 if (val == NULL)
128 errx(1, "can't initialise bignum");
129
130 while ((ch = getopt(argc, argv, "h")) != -1)
131 switch (ch) {
132 case 'h':
133 hflag++;
134 break;
135 case '?':
136 default:
137 usage();
138 }
139 argc -= optind;
140 argv += optind;
141
142 /* No args supplied, read numbers from stdin. */
143 if (argc == 0)
144 for (;;) {
145 if (fgets(buf, sizeof(buf), stdin) == NULL) {
146 if (ferror(stdin))
147 err(1, "stdin");
148 exit (0);
149 }
150 for (p = buf; isblank(*p); ++p);
151 if (*p == '\n' || *p == '\0')
152 continue;
153 convert_str2bn(&val, p);
154 pr_fact(val);
155 }
156 /* Factor the arguments. */
157 else
158 for (p = *argv; p != NULL; p = *++argv) {
159 convert_str2bn(&val, p);
160 pr_fact(val);
161 }
162 exit(0);
163 }
164
165 /*
166 * pr_fact - print the factors of a number
167 *
168 * Print the factors of the number, from the lowest to the highest.
169 * A factor will be printed multiple times if it divides the value
170 * multiple times.
171 *
172 * Factors are printed with leading tabs.
173 */
174 static void
pr_fact(BIGNUM * val)175 pr_fact(BIGNUM *val)
176 {
177 const ubig *fact; /* The factor found. */
178
179 /* Firewall - catch 0 and 1. */
180 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */
181 exit(0);
182 if (BN_is_one(val)) {
183 printf("1: 1\n");
184 return;
185 }
186
187 /* Factor value. */
188
189 if (hflag) {
190 fputs("0x", stdout);
191 BN_print_fp(stdout, val);
192 } else
193 BN_print_dec_fp(stdout, val);
194 putchar(':');
195 for (fact = &prime[0]; !BN_is_one(val); ++fact) {
196 /* Look for the smallest factor. */
197 do {
198 if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
199 break;
200 } while (++fact <= pr_limit);
201
202 /* Watch for primes larger than the table. */
203 if (fact > pr_limit) {
204 #ifdef HAVE_OPENSSL
205 BIGNUM *bnfact;
206
207 bnfact = BN_new();
208 BN_set_word(bnfact, *(fact - 1));
209 if (!BN_sqr(bnfact, bnfact, ctx))
210 errx(1, "error in BN_sqr()");
211 if (BN_cmp(bnfact, val) > 0 ||
212 BN_is_prime_ex(val, PRIME_CHECKS, NULL, NULL) == 1)
213 pr_print(val);
214 else
215 pollard_pminus1(val);
216 #else
217 pr_print(val);
218 #endif
219 break;
220 }
221
222 /* Divide factor out until none are left. */
223 do {
224 printf(hflag ? " 0x%" PRIx64 "" : " %" PRIu64 "", *fact);
225 BN_div_word(val, (BN_ULONG)*fact);
226 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
227
228 /* Let the user know we're doing something. */
229 fflush(stdout);
230 }
231 putchar('\n');
232 }
233
234 static void
pr_print(BIGNUM * val)235 pr_print(BIGNUM *val)
236 {
237 if (hflag) {
238 fputs(" 0x", stdout);
239 BN_print_fp(stdout, val);
240 } else {
241 putchar(' ');
242 BN_print_dec_fp(stdout, val);
243 }
244 }
245
246 static void
usage(void)247 usage(void)
248 {
249 fprintf(stderr, "usage: factor [-h] [value ...]\n");
250 exit(1);
251 }
252
253 #ifdef HAVE_OPENSSL
254
255 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */
256 static void
pollard_pminus1(BIGNUM * val)257 pollard_pminus1(BIGNUM *val)
258 {
259 BIGNUM *base, *rbase, *num, *i, *x;
260
261 base = BN_new();
262 rbase = BN_new();
263 num = BN_new();
264 i = BN_new();
265 x = BN_new();
266
267 BN_set_word(rbase, 1);
268 newbase:
269 if (!BN_add_word(rbase, 1))
270 errx(1, "error in BN_add_word()");
271 BN_set_word(i, 2);
272 BN_copy(base, rbase);
273
274 for (;;) {
275 BN_mod_exp(base, base, i, val, ctx);
276 if (BN_is_one(base))
277 goto newbase;
278
279 BN_copy(x, base);
280 BN_sub_word(x, 1);
281 if (!BN_gcd(x, x, val, ctx))
282 errx(1, "error in BN_gcd()");
283
284 if (!BN_is_one(x)) {
285 if (BN_is_prime_ex(x, PRIME_CHECKS, NULL, NULL) == 1)
286 pr_print(x);
287 else
288 pollard_pminus1(x);
289 fflush(stdout);
290
291 BN_div(num, NULL, val, x, ctx);
292 if (BN_is_one(num))
293 return;
294 if (BN_is_prime_ex(num, PRIME_CHECKS, NULL,
295 NULL) == 1) {
296 pr_print(num);
297 fflush(stdout);
298 return;
299 }
300 BN_copy(val, num);
301 }
302 if (!BN_add_word(i, 1))
303 errx(1, "error in BN_add_word()");
304 }
305 }
306
307 /*
308 * Sigh.. No _decimal_ output to file functions in BN.
309 */
310 static void
BN_print_dec_fp(FILE * fp,const BIGNUM * num)311 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
312 {
313 char *buf;
314
315 buf = BN_bn2dec(num);
316 if (buf == NULL)
317 return; /* XXX do anything here? */
318 fprintf(fp, "%s", buf);
319 free(buf);
320 }
321
322 #else
323
324 static void
BN_print_fp(FILE * fp,const BIGNUM * num)325 BN_print_fp(FILE *fp, const BIGNUM *num)
326 {
327 fprintf(fp, "%lx", (unsigned long)*num);
328 }
329
330 static void
BN_print_dec_fp(FILE * fp,const BIGNUM * num)331 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
332 {
333 fprintf(fp, "%lu", (unsigned long)*num);
334 }
335
336 static int
BN_dec2bn(BIGNUM ** a,const char * str)337 BN_dec2bn(BIGNUM **a, const char *str)
338 {
339 char *p;
340
341 errno = 0;
342 **a = strtoul(str, &p, 10);
343 return (errno == 0 ? 1 : 0); /* OpenSSL returns 0 on error! */
344 }
345
346 static int
BN_hex2bn(BIGNUM ** a,const char * str)347 BN_hex2bn(BIGNUM **a, const char *str)
348 {
349 char *p;
350
351 errno = 0;
352 **a = strtoul(str, &p, 16);
353 return (errno == 0 ? 1 : 0); /* OpenSSL returns 0 on error! */
354 }
355
356 static BN_ULONG
BN_div_word(BIGNUM * a,BN_ULONG b)357 BN_div_word(BIGNUM *a, BN_ULONG b)
358 {
359 BN_ULONG mod;
360
361 mod = *a % b;
362 *a /= b;
363 return mod;
364 }
365
366 #endif
367
368 /*
369 * Scan the string from left-to-right to see if the longest substring
370 * is a valid hexadecimal number.
371 */
372 static bool
is_hex_str(char * str)373 is_hex_str(char *str)
374 {
375 char c, *p;
376 bool saw_hex = false;
377
378 for (p = str; *p; p++) {
379 if (isdigit(*p))
380 continue;
381 c = tolower(*p);
382 if (c >= 'a' && c <= 'f') {
383 saw_hex = true;
384 continue;
385 }
386 break; /* Not a hexadecimal digit. */
387 }
388 return saw_hex;
389 }
390
391 /* Convert string pointed to by *str to a bignum. */
392 static void
convert_str2bn(BIGNUM ** val,char * p)393 convert_str2bn(BIGNUM **val, char *p)
394 {
395 int n = 0;
396
397 if (*p == '+') p++;
398 if (*p == '-')
399 errx(1, "negative numbers aren't permitted.");
400 if (*p == '0') {
401 p++;
402 if (*p == 'x' || *p == 'X')
403 n = BN_hex2bn(val, ++p);
404 } else {
405 n = is_hex_str(p) ? BN_hex2bn(val, p) : BN_dec2bn(val, p);
406 }
407 if (n == 0)
408 errx(1, "%s: illegal numeric format.", p);
409 }
410