1 /* $OpenBSD: moduli.c,v 1.34 2019/01/23 09:49:00 dtucker Exp $ */ 2 /* 3 * Copyright 1994 Phil Karn <karn@qualcomm.com> 4 * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com> 5 * Copyright 2000 Niels Provos <provos@citi.umich.edu> 6 * All rights reserved. 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 * 17 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 18 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 20 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 22 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 23 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 24 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 25 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 26 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 27 */ 28 29 /* 30 * Two-step process to generate safe primes for DHGEX 31 * 32 * Sieve candidates for "safe" primes, 33 * suitable for use as Diffie-Hellman moduli; 34 * that is, where q = (p-1)/2 is also prime. 35 * 36 * First step: generate candidate primes (memory intensive) 37 * Second step: test primes' safety (processor intensive) 38 */ 39 40 #include "includes.h" 41 42 #ifdef WITH_OPENSSL 43 44 #include <sys/types.h> 45 46 #include <openssl/bn.h> 47 #include <openssl/dh.h> 48 49 #include <errno.h> 50 #include <stdio.h> 51 #include <stdlib.h> 52 #include <string.h> 53 #include <stdarg.h> 54 #include <time.h> 55 #include <unistd.h> 56 #include <limits.h> 57 58 #include "xmalloc.h" 59 #include "dh.h" 60 #include "log.h" 61 #include "misc.h" 62 63 #include "openbsd-compat/openssl-compat.h" 64 65 /* 66 * File output defines 67 */ 68 69 /* need line long enough for largest moduli plus headers */ 70 #define QLINESIZE (100+8192) 71 72 /* 73 * Size: decimal. 74 * Specifies the number of the most significant bit (0 to M). 75 * WARNING: internally, usually 1 to N. 76 */ 77 #define QSIZE_MINIMUM (511) 78 79 /* 80 * Prime sieving defines 81 */ 82 83 /* Constant: assuming 8 bit bytes and 32 bit words */ 84 #define SHIFT_BIT (3) 85 #define SHIFT_BYTE (2) 86 #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) 87 #define SHIFT_MEGABYTE (20) 88 #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) 89 90 /* 91 * Using virtual memory can cause thrashing. This should be the largest 92 * number that is supported without a large amount of disk activity -- 93 * that would increase the run time from hours to days or weeks! 94 */ 95 #define LARGE_MINIMUM (8UL) /* megabytes */ 96 97 /* 98 * Do not increase this number beyond the unsigned integer bit size. 99 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). 100 */ 101 #define LARGE_MAXIMUM (127UL) /* megabytes */ 102 103 /* 104 * Constant: when used with 32-bit integers, the largest sieve prime 105 * has to be less than 2**32. 106 */ 107 #define SMALL_MAXIMUM (0xffffffffUL) 108 109 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ 110 #define TINY_NUMBER (1UL<<16) 111 112 /* Ensure enough bit space for testing 2*q. */ 113 #define TEST_MAXIMUM (1UL<<16) 114 #define TEST_MINIMUM (QSIZE_MINIMUM + 1) 115 /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ 116 #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ 117 118 /* bit operations on 32-bit words */ 119 #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) 120 #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) 121 #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) 122 123 /* 124 * Prime testing defines 125 */ 126 127 /* Minimum number of primality tests to perform */ 128 #define TRIAL_MINIMUM (4) 129 130 /* 131 * Sieving data (XXX - move to struct) 132 */ 133 134 /* sieve 2**16 */ 135 static u_int32_t *TinySieve, tinybits; 136 137 /* sieve 2**30 in 2**16 parts */ 138 static u_int32_t *SmallSieve, smallbits, smallbase; 139 140 /* sieve relative to the initial value */ 141 static u_int32_t *LargeSieve, largewords, largetries, largenumbers; 142 static u_int32_t largebits, largememory; /* megabytes */ 143 static BIGNUM *largebase; 144 145 int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); 146 int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long, 147 unsigned long); 148 149 /* 150 * print moduli out in consistent form, 151 */ 152 static int 153 qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, 154 u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) 155 { 156 struct tm *gtm; 157 time_t time_now; 158 int res; 159 160 time(&time_now); 161 gtm = gmtime(&time_now); 162 163 res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", 164 gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, 165 gtm->tm_hour, gtm->tm_min, gtm->tm_sec, 166 otype, otests, otries, osize, ogenerator); 167 168 if (res < 0) 169 return (-1); 170 171 if (BN_print_fp(ofile, omodulus) < 1) 172 return (-1); 173 174 res = fprintf(ofile, "\n"); 175 fflush(ofile); 176 177 return (res > 0 ? 0 : -1); 178 } 179 180 181 /* 182 ** Sieve p's and q's with small factors 183 */ 184 static void 185 sieve_large(u_int32_t s) 186 { 187 u_int32_t r, u; 188 189 debug3("sieve_large %u", s); 190 largetries++; 191 /* r = largebase mod s */ 192 r = BN_mod_word(largebase, s); 193 if (r == 0) 194 u = 0; /* s divides into largebase exactly */ 195 else 196 u = s - r; /* largebase+u is first entry divisible by s */ 197 198 if (u < largebits * 2) { 199 /* 200 * The sieve omits p's and q's divisible by 2, so ensure that 201 * largebase+u is odd. Then, step through the sieve in 202 * increments of 2*s 203 */ 204 if (u & 0x1) 205 u += s; /* Make largebase+u odd, and u even */ 206 207 /* Mark all multiples of 2*s */ 208 for (u /= 2; u < largebits; u += s) 209 BIT_SET(LargeSieve, u); 210 } 211 212 /* r = p mod s */ 213 r = (2 * r + 1) % s; 214 if (r == 0) 215 u = 0; /* s divides p exactly */ 216 else 217 u = s - r; /* p+u is first entry divisible by s */ 218 219 if (u < largebits * 4) { 220 /* 221 * The sieve omits p's divisible by 4, so ensure that 222 * largebase+u is not. Then, step through the sieve in 223 * increments of 4*s 224 */ 225 while (u & 0x3) { 226 if (SMALL_MAXIMUM - u < s) 227 return; 228 u += s; 229 } 230 231 /* Mark all multiples of 4*s */ 232 for (u /= 4; u < largebits; u += s) 233 BIT_SET(LargeSieve, u); 234 } 235 } 236 237 /* 238 * list candidates for Sophie-Germain primes (where q = (p-1)/2) 239 * to standard output. 240 * The list is checked against small known primes (less than 2**30). 241 */ 242 int 243 gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) 244 { 245 BIGNUM *q; 246 u_int32_t j, r, s, t; 247 u_int32_t smallwords = TINY_NUMBER >> 6; 248 u_int32_t tinywords = TINY_NUMBER >> 6; 249 time_t time_start, time_stop; 250 u_int32_t i; 251 int ret = 0; 252 253 largememory = memory; 254 255 if (memory != 0 && 256 (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { 257 error("Invalid memory amount (min %ld, max %ld)", 258 LARGE_MINIMUM, LARGE_MAXIMUM); 259 return (-1); 260 } 261 262 /* 263 * Set power to the length in bits of the prime to be generated. 264 * This is changed to 1 less than the desired safe prime moduli p. 265 */ 266 if (power > TEST_MAXIMUM) { 267 error("Too many bits: %u > %lu", power, TEST_MAXIMUM); 268 return (-1); 269 } else if (power < TEST_MINIMUM) { 270 error("Too few bits: %u < %u", power, TEST_MINIMUM); 271 return (-1); 272 } 273 power--; /* decrement before squaring */ 274 275 /* 276 * The density of ordinary primes is on the order of 1/bits, so the 277 * density of safe primes should be about (1/bits)**2. Set test range 278 * to something well above bits**2 to be reasonably sure (but not 279 * guaranteed) of catching at least one safe prime. 280 */ 281 largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); 282 283 /* 284 * Need idea of how much memory is available. We don't have to use all 285 * of it. 286 */ 287 if (largememory > LARGE_MAXIMUM) { 288 logit("Limited memory: %u MB; limit %lu MB", 289 largememory, LARGE_MAXIMUM); 290 largememory = LARGE_MAXIMUM; 291 } 292 293 if (largewords <= (largememory << SHIFT_MEGAWORD)) { 294 logit("Increased memory: %u MB; need %u bytes", 295 largememory, (largewords << SHIFT_BYTE)); 296 largewords = (largememory << SHIFT_MEGAWORD); 297 } else if (largememory > 0) { 298 logit("Decreased memory: %u MB; want %u bytes", 299 largememory, (largewords << SHIFT_BYTE)); 300 largewords = (largememory << SHIFT_MEGAWORD); 301 } 302 303 TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); 304 tinybits = tinywords << SHIFT_WORD; 305 306 SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); 307 smallbits = smallwords << SHIFT_WORD; 308 309 /* 310 * dynamically determine available memory 311 */ 312 while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) 313 largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ 314 315 largebits = largewords << SHIFT_WORD; 316 largenumbers = largebits * 2; /* even numbers excluded */ 317 318 /* validation check: count the number of primes tried */ 319 largetries = 0; 320 if ((q = BN_new()) == NULL) 321 fatal("BN_new failed"); 322 323 /* 324 * Generate random starting point for subprime search, or use 325 * specified parameter. 326 */ 327 if ((largebase = BN_new()) == NULL) 328 fatal("BN_new failed"); 329 if (start == NULL) { 330 if (BN_rand(largebase, power, 1, 1) == 0) 331 fatal("BN_rand failed"); 332 } else { 333 if (BN_copy(largebase, start) == NULL) 334 fatal("BN_copy: failed"); 335 } 336 337 /* ensure odd */ 338 if (BN_set_bit(largebase, 0) == 0) 339 fatal("BN_set_bit: failed"); 340 341 time(&time_start); 342 343 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), 344 largenumbers, power); 345 debug2("start point: 0x%s", BN_bn2hex(largebase)); 346 347 /* 348 * TinySieve 349 */ 350 for (i = 0; i < tinybits; i++) { 351 if (BIT_TEST(TinySieve, i)) 352 continue; /* 2*i+3 is composite */ 353 354 /* The next tiny prime */ 355 t = 2 * i + 3; 356 357 /* Mark all multiples of t */ 358 for (j = i + t; j < tinybits; j += t) 359 BIT_SET(TinySieve, j); 360 361 sieve_large(t); 362 } 363 364 /* 365 * Start the small block search at the next possible prime. To avoid 366 * fencepost errors, the last pass is skipped. 367 */ 368 for (smallbase = TINY_NUMBER + 3; 369 smallbase < (SMALL_MAXIMUM - TINY_NUMBER); 370 smallbase += TINY_NUMBER) { 371 for (i = 0; i < tinybits; i++) { 372 if (BIT_TEST(TinySieve, i)) 373 continue; /* 2*i+3 is composite */ 374 375 /* The next tiny prime */ 376 t = 2 * i + 3; 377 r = smallbase % t; 378 379 if (r == 0) { 380 s = 0; /* t divides into smallbase exactly */ 381 } else { 382 /* smallbase+s is first entry divisible by t */ 383 s = t - r; 384 } 385 386 /* 387 * The sieve omits even numbers, so ensure that 388 * smallbase+s is odd. Then, step through the sieve 389 * in increments of 2*t 390 */ 391 if (s & 1) 392 s += t; /* Make smallbase+s odd, and s even */ 393 394 /* Mark all multiples of 2*t */ 395 for (s /= 2; s < smallbits; s += t) 396 BIT_SET(SmallSieve, s); 397 } 398 399 /* 400 * SmallSieve 401 */ 402 for (i = 0; i < smallbits; i++) { 403 if (BIT_TEST(SmallSieve, i)) 404 continue; /* 2*i+smallbase is composite */ 405 406 /* The next small prime */ 407 sieve_large((2 * i) + smallbase); 408 } 409 410 memset(SmallSieve, 0, smallwords << SHIFT_BYTE); 411 } 412 413 time(&time_stop); 414 415 logit("%.24s Sieved with %u small primes in %lld seconds", 416 ctime(&time_stop), largetries, (long long)(time_stop - time_start)); 417 418 for (j = r = 0; j < largebits; j++) { 419 if (BIT_TEST(LargeSieve, j)) 420 continue; /* Definitely composite, skip */ 421 422 debug2("test q = largebase+%u", 2 * j); 423 if (BN_set_word(q, 2 * j) == 0) 424 fatal("BN_set_word failed"); 425 if (BN_add(q, q, largebase) == 0) 426 fatal("BN_add failed"); 427 if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN, 428 MODULI_TESTS_SIEVE, largetries, 429 (power - 1) /* MSB */, (0), q) == -1) { 430 ret = -1; 431 break; 432 } 433 434 r++; /* count q */ 435 } 436 437 time(&time_stop); 438 439 free(LargeSieve); 440 free(SmallSieve); 441 free(TinySieve); 442 443 logit("%.24s Found %u candidates", ctime(&time_stop), r); 444 445 return (ret); 446 } 447 448 static void 449 write_checkpoint(char *cpfile, u_int32_t lineno) 450 { 451 FILE *fp; 452 char tmp[PATH_MAX]; 453 int r; 454 455 r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile); 456 if (r == -1 || r >= PATH_MAX) { 457 logit("write_checkpoint: temp pathname too long"); 458 return; 459 } 460 if ((r = mkstemp(tmp)) == -1) { 461 logit("mkstemp(%s): %s", tmp, strerror(errno)); 462 return; 463 } 464 if ((fp = fdopen(r, "w")) == NULL) { 465 logit("write_checkpoint: fdopen: %s", strerror(errno)); 466 unlink(tmp); 467 close(r); 468 return; 469 } 470 if (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0 && fclose(fp) == 0 471 && rename(tmp, cpfile) == 0) 472 debug3("wrote checkpoint line %lu to '%s'", 473 (unsigned long)lineno, cpfile); 474 else 475 logit("failed to write to checkpoint file '%s': %s", cpfile, 476 strerror(errno)); 477 } 478 479 static unsigned long 480 read_checkpoint(char *cpfile) 481 { 482 FILE *fp; 483 unsigned long lineno = 0; 484 485 if ((fp = fopen(cpfile, "r")) == NULL) 486 return 0; 487 if (fscanf(fp, "%lu\n", &lineno) < 1) 488 logit("Failed to load checkpoint from '%s'", cpfile); 489 else 490 logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno); 491 fclose(fp); 492 return lineno; 493 } 494 495 static unsigned long 496 count_lines(FILE *f) 497 { 498 unsigned long count = 0; 499 char lp[QLINESIZE + 1]; 500 501 if (fseek(f, 0, SEEK_SET) != 0) { 502 debug("input file is not seekable"); 503 return ULONG_MAX; 504 } 505 while (fgets(lp, QLINESIZE + 1, f) != NULL) 506 count++; 507 rewind(f); 508 debug("input file has %lu lines", count); 509 return count; 510 } 511 512 static char * 513 fmt_time(time_t seconds) 514 { 515 int day, hr, min; 516 static char buf[128]; 517 518 min = (seconds / 60) % 60; 519 hr = (seconds / 60 / 60) % 24; 520 day = seconds / 60 / 60 / 24; 521 if (day > 0) 522 snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min); 523 else 524 snprintf(buf, sizeof buf, "%d:%02d", hr, min); 525 return buf; 526 } 527 528 static void 529 print_progress(unsigned long start_lineno, unsigned long current_lineno, 530 unsigned long end_lineno) 531 { 532 static time_t time_start, time_prev; 533 time_t time_now, elapsed; 534 unsigned long num_to_process, processed, remaining, percent, eta; 535 double time_per_line; 536 char *eta_str; 537 538 time_now = monotime(); 539 if (time_start == 0) { 540 time_start = time_prev = time_now; 541 return; 542 } 543 /* print progress after 1m then once per 5m */ 544 if (time_now - time_prev < 5 * 60) 545 return; 546 time_prev = time_now; 547 elapsed = time_now - time_start; 548 processed = current_lineno - start_lineno; 549 remaining = end_lineno - current_lineno; 550 num_to_process = end_lineno - start_lineno; 551 time_per_line = (double)elapsed / processed; 552 /* if we don't know how many we're processing just report count+time */ 553 time(&time_now); 554 if (end_lineno == ULONG_MAX) { 555 logit("%.24s processed %lu in %s", ctime(&time_now), 556 processed, fmt_time(elapsed)); 557 return; 558 } 559 percent = 100 * processed / num_to_process; 560 eta = time_per_line * remaining; 561 eta_str = xstrdup(fmt_time(eta)); 562 logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s", 563 ctime(&time_now), processed, num_to_process, percent, 564 fmt_time(elapsed), eta_str); 565 free(eta_str); 566 } 567 568 /* 569 * perform a Miller-Rabin primality test 570 * on the list of candidates 571 * (checking both q and p) 572 * The result is a list of so-call "safe" primes 573 */ 574 int 575 prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted, 576 char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines) 577 { 578 BIGNUM *q, *p, *a; 579 BN_CTX *ctx; 580 char *cp, *lp; 581 u_int32_t count_in = 0, count_out = 0, count_possible = 0; 582 u_int32_t generator_known, in_tests, in_tries, in_type, in_size; 583 unsigned long last_processed = 0, end_lineno; 584 time_t time_start, time_stop; 585 int res, is_prime; 586 587 if (trials < TRIAL_MINIMUM) { 588 error("Minimum primality trials is %d", TRIAL_MINIMUM); 589 return (-1); 590 } 591 592 if (num_lines == 0) 593 end_lineno = count_lines(in); 594 else 595 end_lineno = start_lineno + num_lines; 596 597 time(&time_start); 598 599 if ((p = BN_new()) == NULL) 600 fatal("BN_new failed"); 601 if ((q = BN_new()) == NULL) 602 fatal("BN_new failed"); 603 if ((ctx = BN_CTX_new()) == NULL) 604 fatal("BN_CTX_new failed"); 605 606 debug2("%.24s Final %u Miller-Rabin trials (%x generator)", 607 ctime(&time_start), trials, generator_wanted); 608 609 if (checkpoint_file != NULL) 610 last_processed = read_checkpoint(checkpoint_file); 611 last_processed = start_lineno = MAXIMUM(last_processed, start_lineno); 612 if (end_lineno == ULONG_MAX) 613 debug("process from line %lu from pipe", last_processed); 614 else 615 debug("process from line %lu to line %lu", last_processed, 616 end_lineno); 617 618 res = 0; 619 lp = xmalloc(QLINESIZE + 1); 620 while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) { 621 count_in++; 622 if (count_in <= last_processed) { 623 debug3("skipping line %u, before checkpoint or " 624 "specified start line", count_in); 625 continue; 626 } 627 if (checkpoint_file != NULL) 628 write_checkpoint(checkpoint_file, count_in); 629 print_progress(start_lineno, count_in, end_lineno); 630 if (strlen(lp) < 14 || *lp == '!' || *lp == '#') { 631 debug2("%10u: comment or short line", count_in); 632 continue; 633 } 634 635 /* XXX - fragile parser */ 636 /* time */ 637 cp = &lp[14]; /* (skip) */ 638 639 /* type */ 640 in_type = strtoul(cp, &cp, 10); 641 642 /* tests */ 643 in_tests = strtoul(cp, &cp, 10); 644 645 if (in_tests & MODULI_TESTS_COMPOSITE) { 646 debug2("%10u: known composite", count_in); 647 continue; 648 } 649 650 /* tries */ 651 in_tries = strtoul(cp, &cp, 10); 652 653 /* size (most significant bit) */ 654 in_size = strtoul(cp, &cp, 10); 655 656 /* generator (hex) */ 657 generator_known = strtoul(cp, &cp, 16); 658 659 /* Skip white space */ 660 cp += strspn(cp, " "); 661 662 /* modulus (hex) */ 663 switch (in_type) { 664 case MODULI_TYPE_SOPHIE_GERMAIN: 665 debug2("%10u: (%u) Sophie-Germain", count_in, in_type); 666 a = q; 667 if (BN_hex2bn(&a, cp) == 0) 668 fatal("BN_hex2bn failed"); 669 /* p = 2*q + 1 */ 670 if (BN_lshift(p, q, 1) == 0) 671 fatal("BN_lshift failed"); 672 if (BN_add_word(p, 1) == 0) 673 fatal("BN_add_word failed"); 674 in_size += 1; 675 generator_known = 0; 676 break; 677 case MODULI_TYPE_UNSTRUCTURED: 678 case MODULI_TYPE_SAFE: 679 case MODULI_TYPE_SCHNORR: 680 case MODULI_TYPE_STRONG: 681 case MODULI_TYPE_UNKNOWN: 682 debug2("%10u: (%u)", count_in, in_type); 683 a = p; 684 if (BN_hex2bn(&a, cp) == 0) 685 fatal("BN_hex2bn failed"); 686 /* q = (p-1) / 2 */ 687 if (BN_rshift(q, p, 1) == 0) 688 fatal("BN_rshift failed"); 689 break; 690 default: 691 debug2("Unknown prime type"); 692 break; 693 } 694 695 /* 696 * due to earlier inconsistencies in interpretation, check 697 * the proposed bit size. 698 */ 699 if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { 700 debug2("%10u: bit size %u mismatch", count_in, in_size); 701 continue; 702 } 703 if (in_size < QSIZE_MINIMUM) { 704 debug2("%10u: bit size %u too short", count_in, in_size); 705 continue; 706 } 707 708 if (in_tests & MODULI_TESTS_MILLER_RABIN) 709 in_tries += trials; 710 else 711 in_tries = trials; 712 713 /* 714 * guess unknown generator 715 */ 716 if (generator_known == 0) { 717 if (BN_mod_word(p, 24) == 11) 718 generator_known = 2; 719 else { 720 u_int32_t r = BN_mod_word(p, 10); 721 722 if (r == 3 || r == 7) 723 generator_known = 5; 724 } 725 } 726 /* 727 * skip tests when desired generator doesn't match 728 */ 729 if (generator_wanted > 0 && 730 generator_wanted != generator_known) { 731 debug2("%10u: generator %d != %d", 732 count_in, generator_known, generator_wanted); 733 continue; 734 } 735 736 /* 737 * Primes with no known generator are useless for DH, so 738 * skip those. 739 */ 740 if (generator_known == 0) { 741 debug2("%10u: no known generator", count_in); 742 continue; 743 } 744 745 count_possible++; 746 747 /* 748 * The (1/4)^N performance bound on Miller-Rabin is 749 * extremely pessimistic, so don't spend a lot of time 750 * really verifying that q is prime until after we know 751 * that p is also prime. A single pass will weed out the 752 * vast majority of composite q's. 753 */ 754 is_prime = BN_is_prime_ex(q, 1, ctx, NULL); 755 if (is_prime < 0) 756 fatal("BN_is_prime_ex failed"); 757 if (is_prime == 0) { 758 debug("%10u: q failed first possible prime test", 759 count_in); 760 continue; 761 } 762 763 /* 764 * q is possibly prime, so go ahead and really make sure 765 * that p is prime. If it is, then we can go back and do 766 * the same for q. If p is composite, chances are that 767 * will show up on the first Rabin-Miller iteration so it 768 * doesn't hurt to specify a high iteration count. 769 */ 770 is_prime = BN_is_prime_ex(p, trials, ctx, NULL); 771 if (is_prime < 0) 772 fatal("BN_is_prime_ex failed"); 773 if (is_prime == 0) { 774 debug("%10u: p is not prime", count_in); 775 continue; 776 } 777 debug("%10u: p is almost certainly prime", count_in); 778 779 /* recheck q more rigorously */ 780 is_prime = BN_is_prime_ex(q, trials - 1, ctx, NULL); 781 if (is_prime < 0) 782 fatal("BN_is_prime_ex failed"); 783 if (is_prime == 0) { 784 debug("%10u: q is not prime", count_in); 785 continue; 786 } 787 debug("%10u: q is almost certainly prime", count_in); 788 789 if (qfileout(out, MODULI_TYPE_SAFE, 790 in_tests | MODULI_TESTS_MILLER_RABIN, 791 in_tries, in_size, generator_known, p)) { 792 res = -1; 793 break; 794 } 795 796 count_out++; 797 } 798 799 time(&time_stop); 800 free(lp); 801 BN_free(p); 802 BN_free(q); 803 BN_CTX_free(ctx); 804 805 if (checkpoint_file != NULL) 806 unlink(checkpoint_file); 807 808 logit("%.24s Found %u safe primes of %u candidates in %ld seconds", 809 ctime(&time_stop), count_out, count_possible, 810 (long) (time_stop - time_start)); 811 812 return (res); 813 } 814 815 #endif /* WITH_OPENSSL */ 816