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 #if OPENSSL_VERSION_NUMBER < 0x30000000L 86 static inline int 87 BN_check_prime(BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb) 88 { 89 const int nchecks = 5; 90 91 return BN_is_prime_ex(p, nchecks, ctx, cb); 92 } 93 #endif 94 95 static void pollard_pminus1(BIGNUM *); /* print factors for big numbers */ 96 97 #else 98 99 typedef ubig BIGNUM; 100 typedef u_long BN_ULONG; 101 102 #define BN_CTX int 103 #define BN_CTX_new() NULL 104 #define BN_new() ((BIGNUM *)calloc(sizeof(BIGNUM), 1)) 105 #define BN_is_zero(v) (*(v) == 0) 106 #define BN_is_one(v) (*(v) == 1) 107 #define BN_mod_word(a, b) (*(a) % (b)) 108 109 static int BN_dec2bn(BIGNUM **, const char *); 110 static int BN_hex2bn(BIGNUM **, const char *); 111 static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG); 112 static void BN_print_fp(FILE *, const BIGNUM *); 113 114 #endif 115 116 static void BN_print_dec_fp(FILE *, const BIGNUM *); 117 static void convert_str2bn(BIGNUM **, char *); 118 static bool is_hex_str(char *); 119 static void pr_fact(BIGNUM *); /* print factors of a value */ 120 static void pr_print(BIGNUM *); /* print a prime */ 121 static void usage(void); 122 123 static BN_CTX *ctx; /* just use a global context */ 124 static int hflag; 125 126 int 127 main(int argc, char *argv[]) 128 { 129 BIGNUM *val; 130 int ch; 131 char *p, buf[LINE_MAX]; /* > max number of digits. */ 132 133 ctx = BN_CTX_new(); 134 val = BN_new(); 135 if (val == NULL) 136 errx(1, "can't initialise bignum"); 137 138 while ((ch = getopt(argc, argv, "h")) != -1) 139 switch (ch) { 140 case 'h': 141 hflag++; 142 break; 143 case '?': 144 default: 145 usage(); 146 } 147 argc -= optind; 148 argv += optind; 149 150 /* No args supplied, read numbers from stdin. */ 151 if (argc == 0) 152 for (;;) { 153 if (fgets(buf, sizeof(buf), stdin) == NULL) { 154 if (ferror(stdin)) 155 err(1, "stdin"); 156 exit (0); 157 } 158 for (p = buf; isblank(*p); ++p); 159 if (*p == '\n' || *p == '\0') 160 continue; 161 convert_str2bn(&val, p); 162 pr_fact(val); 163 } 164 /* Factor the arguments. */ 165 else 166 for (p = *argv; p != NULL; p = *++argv) { 167 convert_str2bn(&val, p); 168 pr_fact(val); 169 } 170 exit(0); 171 } 172 173 /* 174 * pr_fact - print the factors of a number 175 * 176 * Print the factors of the number, from the lowest to the highest. 177 * A factor will be printed multiple times if it divides the value 178 * multiple times. 179 * 180 * Factors are printed with leading tabs. 181 */ 182 static void 183 pr_fact(BIGNUM *val) 184 { 185 const ubig *fact; /* The factor found. */ 186 187 /* Firewall - catch 0 and 1. */ 188 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */ 189 exit(0); 190 if (BN_is_one(val)) { 191 printf("1: 1\n"); 192 return; 193 } 194 195 /* Factor value. */ 196 197 if (hflag) { 198 fputs("0x", stdout); 199 BN_print_fp(stdout, val); 200 } else 201 BN_print_dec_fp(stdout, val); 202 putchar(':'); 203 for (fact = &prime[0]; !BN_is_one(val); ++fact) { 204 /* Look for the smallest factor. */ 205 do { 206 if (BN_mod_word(val, (BN_ULONG)*fact) == 0) 207 break; 208 } while (++fact <= pr_limit); 209 210 /* Watch for primes larger than the table. */ 211 if (fact > pr_limit) { 212 #ifdef HAVE_OPENSSL 213 BIGNUM *bnfact; 214 215 bnfact = BN_new(); 216 BN_set_word(bnfact, *(fact - 1)); 217 if (!BN_sqr(bnfact, bnfact, ctx)) 218 errx(1, "error in BN_sqr()"); 219 if (BN_cmp(bnfact, val) > 0 || 220 BN_check_prime(val, NULL, NULL) == 1) 221 pr_print(val); 222 else 223 pollard_pminus1(val); 224 #else 225 pr_print(val); 226 #endif 227 break; 228 } 229 230 /* Divide factor out until none are left. */ 231 do { 232 printf(hflag ? " 0x%" PRIx64 "" : " %" PRIu64 "", *fact); 233 BN_div_word(val, (BN_ULONG)*fact); 234 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0); 235 236 /* Let the user know we're doing something. */ 237 fflush(stdout); 238 } 239 putchar('\n'); 240 } 241 242 static void 243 pr_print(BIGNUM *val) 244 { 245 if (hflag) { 246 fputs(" 0x", stdout); 247 BN_print_fp(stdout, val); 248 } else { 249 putchar(' '); 250 BN_print_dec_fp(stdout, val); 251 } 252 } 253 254 static void 255 usage(void) 256 { 257 fprintf(stderr, "usage: factor [-h] [value ...]\n"); 258 exit(1); 259 } 260 261 #ifdef HAVE_OPENSSL 262 263 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */ 264 static void 265 pollard_pminus1(BIGNUM *val) 266 { 267 BIGNUM *base, *rbase, *num, *i, *x; 268 269 base = BN_new(); 270 rbase = BN_new(); 271 num = BN_new(); 272 i = BN_new(); 273 x = BN_new(); 274 275 BN_set_word(rbase, 1); 276 newbase: 277 if (!BN_add_word(rbase, 1)) 278 errx(1, "error in BN_add_word()"); 279 BN_set_word(i, 2); 280 BN_copy(base, rbase); 281 282 for (;;) { 283 BN_mod_exp(base, base, i, val, ctx); 284 if (BN_is_one(base)) 285 goto newbase; 286 287 BN_copy(x, base); 288 BN_sub_word(x, 1); 289 if (!BN_gcd(x, x, val, ctx)) 290 errx(1, "error in BN_gcd()"); 291 292 if (!BN_is_one(x)) { 293 if (BN_check_prime(x, NULL, NULL) == 1) 294 pr_print(x); 295 else 296 pollard_pminus1(x); 297 fflush(stdout); 298 299 BN_div(num, NULL, val, x, ctx); 300 if (BN_is_one(num)) 301 return; 302 if (BN_check_prime(num, NULL, NULL) == 1) { 303 pr_print(num); 304 fflush(stdout); 305 return; 306 } 307 BN_copy(val, num); 308 } 309 if (!BN_add_word(i, 1)) 310 errx(1, "error in BN_add_word()"); 311 } 312 } 313 314 /* 315 * Sigh.. No _decimal_ output to file functions in BN. 316 */ 317 static void 318 BN_print_dec_fp(FILE *fp, const BIGNUM *num) 319 { 320 char *buf; 321 322 buf = BN_bn2dec(num); 323 if (buf == NULL) 324 return; /* XXX do anything here? */ 325 fprintf(fp, "%s", buf); 326 free(buf); 327 } 328 329 #else 330 331 static void 332 BN_print_fp(FILE *fp, const BIGNUM *num) 333 { 334 fprintf(fp, "%lx", (unsigned long)*num); 335 } 336 337 static void 338 BN_print_dec_fp(FILE *fp, const BIGNUM *num) 339 { 340 fprintf(fp, "%lu", (unsigned long)*num); 341 } 342 343 static int 344 BN_dec2bn(BIGNUM **a, const char *str) 345 { 346 char *p; 347 348 errno = 0; 349 **a = strtoul(str, &p, 10); 350 return (errno == 0 ? 1 : 0); /* OpenSSL returns 0 on error! */ 351 } 352 353 static int 354 BN_hex2bn(BIGNUM **a, const char *str) 355 { 356 char *p; 357 358 errno = 0; 359 **a = strtoul(str, &p, 16); 360 return (errno == 0 ? 1 : 0); /* OpenSSL returns 0 on error! */ 361 } 362 363 static BN_ULONG 364 BN_div_word(BIGNUM *a, BN_ULONG b) 365 { 366 BN_ULONG mod; 367 368 mod = *a % b; 369 *a /= b; 370 return mod; 371 } 372 373 #endif 374 375 /* 376 * Scan the string from left-to-right to see if the longest substring 377 * is a valid hexadecimal number. 378 */ 379 static bool 380 is_hex_str(char *str) 381 { 382 char c, *p; 383 bool saw_hex = false; 384 385 for (p = str; *p; p++) { 386 if (isdigit(*p)) 387 continue; 388 c = tolower(*p); 389 if (c >= 'a' && c <= 'f') { 390 saw_hex = true; 391 continue; 392 } 393 break; /* Not a hexadecimal digit. */ 394 } 395 return saw_hex; 396 } 397 398 /* Convert string pointed to by *str to a bignum. */ 399 static void 400 convert_str2bn(BIGNUM **val, char *p) 401 { 402 int n = 0; 403 404 if (*p == '+') p++; 405 if (*p == '-') 406 errx(1, "negative numbers aren't permitted."); 407 if (*p == '0') { 408 p++; 409 if (*p == 'x' || *p == 'X') 410 n = BN_hex2bn(val, ++p); 411 } else { 412 n = is_hex_str(p) ? BN_hex2bn(val, p) : BN_dec2bn(val, p); 413 } 414 if (n == 0) 415 errx(1, "%s: illegal numeric format.", p); 416 } 417