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 #endif 47 #endif /* not lint */ 48 49 /* 50 * factor - factor a number into primes 51 * 52 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo 53 * 54 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 55 * 56 * usage: 57 * factor [-h] [number] ... 58 * 59 * The form of the output is: 60 * 61 * number: factor1 factor1 factor2 factor3 factor3 factor3 ... 62 * 63 * where factor1 <= factor2 <= factor3 <= ... 64 * 65 * If no args are given, the list of numbers are read from stdin. 66 */ 67 68 #include <ctype.h> 69 #include <err.h> 70 #include <errno.h> 71 #include <inttypes.h> 72 #include <limits.h> 73 #include <stdbool.h> 74 #include <stdio.h> 75 #include <stdlib.h> 76 #include <unistd.h> 77 78 #include "primes.h" 79 80 #ifdef HAVE_OPENSSL 81 82 #include <openssl/bn.h> 83 84 #if OPENSSL_VERSION_NUMBER < 0x30000000L 85 static inline int 86 BN_check_prime(BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb) 87 { 88 const int nchecks = 5; 89 90 return BN_is_prime_ex(p, nchecks, ctx, cb); 91 } 92 #endif 93 94 static void pollard_pminus1(BIGNUM *); /* print factors for big numbers */ 95 96 #else 97 98 typedef ubig BIGNUM; 99 typedef u_long BN_ULONG; 100 101 #define BN_CTX int 102 #define BN_CTX_new() NULL 103 #define BN_new() ((BIGNUM *)calloc(sizeof(BIGNUM), 1)) 104 #define BN_is_zero(v) (*(v) == 0) 105 #define BN_is_one(v) (*(v) == 1) 106 #define BN_mod_word(a, b) (*(a) % (b)) 107 108 static int BN_dec2bn(BIGNUM **, const char *); 109 static int BN_hex2bn(BIGNUM **, const char *); 110 static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG); 111 static void BN_print_fp(FILE *, const BIGNUM *); 112 113 #endif 114 115 static void BN_print_dec_fp(FILE *, const BIGNUM *); 116 static void convert_str2bn(BIGNUM **, char *); 117 static bool is_hex_str(char *); 118 static void pr_fact(BIGNUM *); /* print factors of a value */ 119 static void pr_print(BIGNUM *); /* print a prime */ 120 static void usage(void); 121 122 static BN_CTX *ctx; /* just use a global context */ 123 static int hflag; 124 125 int 126 main(int argc, char *argv[]) 127 { 128 BIGNUM *val; 129 int ch; 130 char *p, buf[LINE_MAX]; /* > max number of digits. */ 131 132 ctx = BN_CTX_new(); 133 val = BN_new(); 134 if (val == NULL) 135 errx(1, "can't initialise bignum"); 136 137 while ((ch = getopt(argc, argv, "h")) != -1) 138 switch (ch) { 139 case 'h': 140 hflag++; 141 break; 142 case '?': 143 default: 144 usage(); 145 } 146 argc -= optind; 147 argv += optind; 148 149 /* No args supplied, read numbers from stdin. */ 150 if (argc == 0) 151 for (;;) { 152 if (fgets(buf, sizeof(buf), stdin) == NULL) { 153 if (ferror(stdin)) 154 err(1, "stdin"); 155 exit (0); 156 } 157 for (p = buf; isblank(*p); ++p); 158 if (*p == '\n' || *p == '\0') 159 continue; 160 convert_str2bn(&val, p); 161 pr_fact(val); 162 } 163 /* Factor the arguments. */ 164 else 165 for (p = *argv; p != NULL; p = *++argv) { 166 convert_str2bn(&val, p); 167 pr_fact(val); 168 } 169 exit(0); 170 } 171 172 /* 173 * pr_fact - print the factors of a number 174 * 175 * Print the factors of the number, from the lowest to the highest. 176 * A factor will be printed multiple times if it divides the value 177 * multiple times. 178 * 179 * Factors are printed with leading tabs. 180 */ 181 static void 182 pr_fact(BIGNUM *val) 183 { 184 const ubig *fact; /* The factor found. */ 185 186 /* Firewall - catch 0 and 1. */ 187 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */ 188 exit(0); 189 if (BN_is_one(val)) { 190 printf("1: 1\n"); 191 return; 192 } 193 194 /* Factor value. */ 195 196 if (hflag) { 197 fputs("0x", stdout); 198 BN_print_fp(stdout, val); 199 } else 200 BN_print_dec_fp(stdout, val); 201 putchar(':'); 202 for (fact = &prime[0]; !BN_is_one(val); ++fact) { 203 /* Look for the smallest factor. */ 204 do { 205 if (BN_mod_word(val, (BN_ULONG)*fact) == 0) 206 break; 207 } while (++fact <= pr_limit); 208 209 /* Watch for primes larger than the table. */ 210 if (fact > pr_limit) { 211 #ifdef HAVE_OPENSSL 212 BIGNUM *bnfact; 213 214 bnfact = BN_new(); 215 BN_set_word(bnfact, *(fact - 1)); 216 if (!BN_sqr(bnfact, bnfact, ctx)) 217 errx(1, "error in BN_sqr()"); 218 if (BN_cmp(bnfact, val) > 0 || 219 BN_check_prime(val, NULL, NULL) == 1) 220 pr_print(val); 221 else 222 pollard_pminus1(val); 223 #else 224 pr_print(val); 225 #endif 226 break; 227 } 228 229 /* Divide factor out until none are left. */ 230 do { 231 printf(hflag ? " 0x%" PRIx64 "" : " %" PRIu64 "", *fact); 232 BN_div_word(val, (BN_ULONG)*fact); 233 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0); 234 235 /* Let the user know we're doing something. */ 236 fflush(stdout); 237 } 238 putchar('\n'); 239 } 240 241 static void 242 pr_print(BIGNUM *val) 243 { 244 if (hflag) { 245 fputs(" 0x", stdout); 246 BN_print_fp(stdout, val); 247 } else { 248 putchar(' '); 249 BN_print_dec_fp(stdout, val); 250 } 251 } 252 253 static void 254 usage(void) 255 { 256 fprintf(stderr, "usage: factor [-h] [value ...]\n"); 257 exit(1); 258 } 259 260 #ifdef HAVE_OPENSSL 261 262 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */ 263 static void 264 pollard_pminus1(BIGNUM *val) 265 { 266 BIGNUM *base, *rbase, *num, *i, *x; 267 268 base = BN_new(); 269 rbase = BN_new(); 270 num = BN_new(); 271 i = BN_new(); 272 x = BN_new(); 273 274 BN_set_word(rbase, 1); 275 newbase: 276 if (!BN_add_word(rbase, 1)) 277 errx(1, "error in BN_add_word()"); 278 BN_set_word(i, 2); 279 BN_copy(base, rbase); 280 281 for (;;) { 282 BN_mod_exp(base, base, i, val, ctx); 283 if (BN_is_one(base)) 284 goto newbase; 285 286 BN_copy(x, base); 287 BN_sub_word(x, 1); 288 if (!BN_gcd(x, x, val, ctx)) 289 errx(1, "error in BN_gcd()"); 290 291 if (!BN_is_one(x)) { 292 if (BN_check_prime(x, NULL, NULL) == 1) 293 pr_print(x); 294 else 295 pollard_pminus1(x); 296 fflush(stdout); 297 298 BN_div(num, NULL, val, x, ctx); 299 if (BN_is_one(num)) 300 return; 301 if (BN_check_prime(num, NULL, NULL) == 1) { 302 pr_print(num); 303 fflush(stdout); 304 return; 305 } 306 BN_copy(val, num); 307 } 308 if (!BN_add_word(i, 1)) 309 errx(1, "error in BN_add_word()"); 310 } 311 } 312 313 /* 314 * Sigh.. No _decimal_ output to file functions in BN. 315 */ 316 static void 317 BN_print_dec_fp(FILE *fp, const BIGNUM *num) 318 { 319 char *buf; 320 321 buf = BN_bn2dec(num); 322 if (buf == NULL) 323 return; /* XXX do anything here? */ 324 fprintf(fp, "%s", buf); 325 free(buf); 326 } 327 328 #else 329 330 static void 331 BN_print_fp(FILE *fp, const BIGNUM *num) 332 { 333 fprintf(fp, "%lx", (unsigned long)*num); 334 } 335 336 static void 337 BN_print_dec_fp(FILE *fp, const BIGNUM *num) 338 { 339 fprintf(fp, "%lu", (unsigned long)*num); 340 } 341 342 static int 343 BN_dec2bn(BIGNUM **a, const char *str) 344 { 345 char *p; 346 347 errno = 0; 348 **a = strtoul(str, &p, 10); 349 return (errno == 0 ? 1 : 0); /* OpenSSL returns 0 on error! */ 350 } 351 352 static int 353 BN_hex2bn(BIGNUM **a, const char *str) 354 { 355 char *p; 356 357 errno = 0; 358 **a = strtoul(str, &p, 16); 359 return (errno == 0 ? 1 : 0); /* OpenSSL returns 0 on error! */ 360 } 361 362 static BN_ULONG 363 BN_div_word(BIGNUM *a, BN_ULONG b) 364 { 365 BN_ULONG mod; 366 367 mod = *a % b; 368 *a /= b; 369 return mod; 370 } 371 372 #endif 373 374 /* 375 * Scan the string from left-to-right to see if the longest substring 376 * is a valid hexadecimal number. 377 */ 378 static bool 379 is_hex_str(char *str) 380 { 381 char c, *p; 382 bool saw_hex = false; 383 384 for (p = str; *p; p++) { 385 if (isdigit(*p)) 386 continue; 387 c = tolower(*p); 388 if (c >= 'a' && c <= 'f') { 389 saw_hex = true; 390 continue; 391 } 392 break; /* Not a hexadecimal digit. */ 393 } 394 return saw_hex; 395 } 396 397 /* Convert string pointed to by *str to a bignum. */ 398 static void 399 convert_str2bn(BIGNUM **val, char *p) 400 { 401 int n = 0; 402 403 if (*p == '+') p++; 404 if (*p == '-') 405 errx(1, "negative numbers aren't permitted."); 406 if (*p == '0') { 407 p++; 408 if (*p == 'x' || *p == 'X') 409 n = BN_hex2bn(val, ++p); 410 } else { 411 n = is_hex_str(p) ? BN_hex2bn(val, p) : BN_dec2bn(val, p); 412 } 413 if (n == 0) 414 errx(1, "%s: illegal numeric format.", p); 415 } 416