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 chongo@toad.com, ...!{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 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 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 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 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 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 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 325 BN_print_fp(FILE *fp, const BIGNUM *num) 326 { 327 fprintf(fp, "%lx", (unsigned long)*num); 328 } 329 330 static void 331 BN_print_dec_fp(FILE *fp, const BIGNUM *num) 332 { 333 fprintf(fp, "%lu", (unsigned long)*num); 334 } 335 336 static int 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 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 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 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 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