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IABSD.fr/src/usr.bin/ssh/moduli.c
djm
- usr.bin/ssh/moduli.c
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/* $OpenBSD: moduli.c,v 1.37 2019/11/15 06:00:20 djm Exp $ */ /* * Copyright 1994 Phil Karn <karn@qualcomm.com> * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com> * Copyright 2000 Niels Provos <provos@citi.umich.edu> * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* * Two-step process to generate safe primes for DHGEX * * Sieve candidates for "safe" primes, * suitable for use as Diffie-Hellman moduli; * that is, where q = (p-1)/2 is also prime. * * First step: generate candidate primes (memory intensive) * Second step: test primes' safety (processor intensive) */ #include <sys/types.h> #include <openssl/bn.h> #include <openssl/dh.h> #include <errno.h> #include <stdio.h> #include <stdlib.h> #include <string.h> #include <stdarg.h> #include <time.h> #include <unistd.h> #include <limits.h> #include "xmalloc.h" #include "dh.h" #include "log.h" #include "misc.h" /* * File output defines */ /* need line long enough for largest moduli plus headers */ #define QLINESIZE (100+8192) /* * Size: decimal. * Specifies the number of the most significant bit (0 to M). * WARNING: internally, usually 1 to N. */ #define QSIZE_MINIMUM (511) /* * Prime sieving defines */ /* Constant: assuming 8 bit bytes and 32 bit words */ #define SHIFT_BIT (3) #define SHIFT_BYTE (2) #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) #define SHIFT_MEGABYTE (20) #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) /* * Using virtual memory can cause thrashing. This should be the largest * number that is supported without a large amount of disk activity -- * that would increase the run time from hours to days or weeks! */ #define LARGE_MINIMUM (8UL) /* megabytes */ /* * Do not increase this number beyond the unsigned integer bit size. * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). */ #define LARGE_MAXIMUM (127UL) /* megabytes */ /* * Constant: when used with 32-bit integers, the largest sieve prime * has to be less than 2**32. */ #define SMALL_MAXIMUM (0xffffffffUL) /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ #define TINY_NUMBER (1UL<<16) /* Ensure enough bit space for testing 2*q. */ #define TEST_MAXIMUM (1UL<<16) #define TEST_MINIMUM (QSIZE_MINIMUM + 1) /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ /* bit operations on 32-bit words */ #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) /* * Prime testing defines */ /* Minimum number of primality tests to perform */ #define TRIAL_MINIMUM (4) /* * Sieving data (XXX - move to struct) */ /* sieve 2**16 */ static u_int32_t *TinySieve, tinybits; /* sieve 2**30 in 2**16 parts */ static u_int32_t *SmallSieve, smallbits, smallbase; /* sieve relative to the initial value */ static u_int32_t *LargeSieve, largewords, largetries, largenumbers; static u_int32_t largebits, largememory; /* megabytes */ static BIGNUM *largebase; int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long, unsigned long); /* * print moduli out in consistent form, */ static int qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) { struct tm *gtm; time_t time_now; int res; time(&time_now); gtm = gmtime(&time_now); if (gtm == NULL) return -1; res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, gtm->tm_hour, gtm->tm_min, gtm->tm_sec, otype, otests, otries, osize, ogenerator); if (res < 0) return (-1); if (BN_print_fp(ofile, omodulus) < 1) return (-1); res = fprintf(ofile, "\n"); fflush(ofile); return (res > 0 ? 0 : -1); } /* ** Sieve p's and q's with small factors */ static void sieve_large(u_int32_t s) { u_int32_t r, u; debug3("sieve_large %u", s); largetries++; /* r = largebase mod s */ r = BN_mod_word(largebase, s); if (r == 0) u = 0; /* s divides into largebase exactly */ else u = s - r; /* largebase+u is first entry divisible by s */ if (u < largebits * 2) { /* * The sieve omits p's and q's divisible by 2, so ensure that * largebase+u is odd. Then, step through the sieve in * increments of 2*s */ if (u & 0x1) u += s; /* Make largebase+u odd, and u even */ /* Mark all multiples of 2*s */ for (u /= 2; u < largebits; u += s) BIT_SET(LargeSieve, u); } /* r = p mod s */ r = (2 * r + 1) % s; if (r == 0) u = 0; /* s divides p exactly */ else u = s - r; /* p+u is first entry divisible by s */ if (u < largebits * 4) { /* * The sieve omits p's divisible by 4, so ensure that * largebase+u is not. Then, step through the sieve in * increments of 4*s */ while (u & 0x3) { if (SMALL_MAXIMUM - u < s) return; u += s; } /* Mark all multiples of 4*s */ for (u /= 4; u < largebits; u += s) BIT_SET(LargeSieve, u); } } /* * list candidates for Sophie-Germain primes (where q = (p-1)/2) * to standard output. * The list is checked against small known primes (less than 2**30). */ int gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) { BIGNUM *q; u_int32_t j, r, s, t; u_int32_t smallwords = TINY_NUMBER >> 6; u_int32_t tinywords = TINY_NUMBER >> 6; time_t time_start, time_stop; u_int32_t i; int ret = 0; largememory = memory; if (memory != 0 && (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { error("Invalid memory amount (min %ld, max %ld)", LARGE_MINIMUM, LARGE_MAXIMUM); return (-1); } /* * Set power to the length in bits of the prime to be generated. * This is changed to 1 less than the desired safe prime moduli p. */ if (power > TEST_MAXIMUM) { error("Too many bits: %u > %lu", power, TEST_MAXIMUM); return (-1); } else if (power < TEST_MINIMUM) { error("Too few bits: %u < %u", power, TEST_MINIMUM); return (-1); } power--; /* decrement before squaring */ /* * The density of ordinary primes is on the order of 1/bits, so the * density of safe primes should be about (1/bits)**2. Set test range * to something well above bits**2 to be reasonably sure (but not * guaranteed) of catching at least one safe prime. */ largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); /* * Need idea of how much memory is available. We don't have to use all * of it. */ if (largememory > LARGE_MAXIMUM) { logit("Limited memory: %u MB; limit %lu MB", largememory, LARGE_MAXIMUM); largememory = LARGE_MAXIMUM; } if (largewords <= (largememory << SHIFT_MEGAWORD)) { logit("Increased memory: %u MB; need %u bytes", largememory, (largewords << SHIFT_BYTE)); largewords = (largememory << SHIFT_MEGAWORD); } else if (largememory > 0) { logit("Decreased memory: %u MB; want %u bytes", largememory, (largewords << SHIFT_BYTE)); largewords = (largememory << SHIFT_MEGAWORD); } TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); tinybits = tinywords << SHIFT_WORD; SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); smallbits = smallwords << SHIFT_WORD; /* * dynamically determine available memory */ while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ largebits = largewords << SHIFT_WORD; largenumbers = largebits * 2; /* even numbers excluded */ /* validation check: count the number of primes tried */ largetries = 0; if ((q = BN_new()) == NULL) fatal("BN_new failed"); /* * Generate random starting point for subprime search, or use * specified parameter. */ if ((largebase = BN_new()) == NULL) fatal("BN_new failed"); if (start == NULL) { if (BN_rand(largebase, power, 1, 1) == 0) fatal("BN_rand failed"); } else { if (BN_copy(largebase, start) == NULL) fatal("BN_copy: failed"); } /* ensure odd */ if (BN_set_bit(largebase, 0) == 0) fatal("BN_set_bit: failed"); time(&time_start); logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), largenumbers, power); debug2("start point: 0x%s", BN_bn2hex(largebase)); /* * TinySieve */ for (i = 0; i < tinybits; i++) { if (BIT_TEST(TinySieve, i)) continue; /* 2*i+3 is composite */ /* The next tiny prime */ t = 2 * i + 3; /* Mark all multiples of t */ for (j = i + t; j < tinybits; j += t) BIT_SET(TinySieve, j); sieve_large(t); } /* * Start the small block search at the next possible prime. To avoid * fencepost errors, the last pass is skipped. */ for (smallbase = TINY_NUMBER + 3; smallbase < (SMALL_MAXIMUM - TINY_NUMBER); smallbase += TINY_NUMBER) { for (i = 0; i < tinybits; i++) { if (BIT_TEST(TinySieve, i)) continue; /* 2*i+3 is composite */ /* The next tiny prime */ t = 2 * i + 3; r = smallbase % t; if (r == 0) { s = 0; /* t divides into smallbase exactly */ } else { /* smallbase+s is first entry divisible by t */ s = t - r; } /* * The sieve omits even numbers, so ensure that * smallbase+s is odd. Then, step through the sieve * in increments of 2*t */ if (s & 1) s += t; /* Make smallbase+s odd, and s even */ /* Mark all multiples of 2*t */ for (s /= 2; s < smallbits; s += t) BIT_SET(SmallSieve, s); } /* * SmallSieve */ for (i = 0; i < smallbits; i++) { if (BIT_TEST(SmallSieve, i)) continue; /* 2*i+smallbase is composite */ /* The next small prime */ sieve_large((2 * i) + smallbase); } memset(SmallSieve, 0, smallwords << SHIFT_BYTE); } time(&time_stop); logit("%.24s Sieved with %u small primes in %lld seconds", ctime(&time_stop), largetries, (long long)(time_stop - time_start)); for (j = r = 0; j < largebits; j++) { if (BIT_TEST(LargeSieve, j)) continue; /* Definitely composite, skip */ debug2("test q = largebase+%u", 2 * j); if (BN_set_word(q, 2 * j) == 0) fatal("BN_set_word failed"); if (BN_add(q, q, largebase) == 0) fatal("BN_add failed"); if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN, MODULI_TESTS_SIEVE, largetries, (power - 1) /* MSB */, (0), q) == -1) { ret = -1; break; } r++; /* count q */ } time(&time_stop); free(LargeSieve); free(SmallSieve); free(TinySieve); logit("%.24s Found %u candidates", ctime(&time_stop), r); return (ret); } static void write_checkpoint(char *cpfile, u_int32_t lineno) { FILE *fp; char tmp[PATH_MAX]; int r; r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile); if (r < 0 || r >= PATH_MAX) { logit("write_checkpoint: temp pathname too long"); return; } if ((r = mkstemp(tmp)) == -1) { logit("mkstemp(%s): %s", tmp, strerror(errno)); return; } if ((fp = fdopen(r, "w")) == NULL) { logit("write_checkpoint: fdopen: %s", strerror(errno)); unlink(tmp); close(r); return; } if (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0 && fclose(fp) == 0 && rename(tmp, cpfile) == 0) debug3("wrote checkpoint line %lu to '%s'", (unsigned long)lineno, cpfile); else logit("failed to write to checkpoint file '%s': %s", cpfile, strerror(errno)); } static unsigned long read_checkpoint(char *cpfile) { FILE *fp; unsigned long lineno = 0; if ((fp = fopen(cpfile, "r")) == NULL) return 0; if (fscanf(fp, "%lu\n", &lineno) < 1) logit("Failed to load checkpoint from '%s'", cpfile); else logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno); fclose(fp); return lineno; } static unsigned long count_lines(FILE *f) { unsigned long count = 0; char lp[QLINESIZE + 1]; if (fseek(f, 0, SEEK_SET) != 0) { debug("input file is not seekable"); return ULONG_MAX; } while (fgets(lp, QLINESIZE + 1, f) != NULL) count++; rewind(f); debug("input file has %lu lines", count); return count; } static char * fmt_time(time_t seconds) { int day, hr, min; static char buf[128]; min = (seconds / 60) % 60; hr = (seconds / 60 / 60) % 24; day = seconds / 60 / 60 / 24; if (day > 0) snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min); else snprintf(buf, sizeof buf, "%d:%02d", hr, min); return buf; } static void print_progress(unsigned long start_lineno, unsigned long current_lineno, unsigned long end_lineno) { static time_t time_start, time_prev; time_t time_now, elapsed; unsigned long num_to_process, processed, remaining, percent, eta; double time_per_line; char *eta_str; time_now = monotime(); if (time_start == 0) { time_start = time_prev = time_now; return; } /* print progress after 1m then once per 5m */ if (time_now - time_prev < 5 * 60) return; time_prev = time_now; elapsed = time_now - time_start; processed = current_lineno - start_lineno; remaining = end_lineno - current_lineno; num_to_process = end_lineno - start_lineno; time_per_line = (double)elapsed / processed; /* if we don't know how many we're processing just report count+time */ time(&time_now); if (end_lineno == ULONG_MAX) { logit("%.24s processed %lu in %s", ctime(&time_now), processed, fmt_time(elapsed)); return; } percent = 100 * processed / num_to_process; eta = time_per_line * remaining; eta_str = xstrdup(fmt_time(eta)); logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s", ctime(&time_now), processed, num_to_process, percent, fmt_time(elapsed), eta_str); free(eta_str); } /* * perform a Miller-Rabin primality test * on the list of candidates * (checking both q and p) * The result is a list of so-call "safe" primes */ int prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted, char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines) { BIGNUM *q, *p, *a; char *cp, *lp; u_int32_t count_in = 0, count_out = 0, count_possible = 0; u_int32_t generator_known, in_tests, in_tries, in_type, in_size; unsigned long last_processed = 0, end_lineno; time_t time_start, time_stop; int res, is_prime; if (trials < TRIAL_MINIMUM) { error("Minimum primality trials is %d", TRIAL_MINIMUM); return (-1); } if (num_lines == 0) end_lineno = count_lines(in); else end_lineno = start_lineno + num_lines; time(&time_start); if ((p = BN_new()) == NULL) fatal("BN_new failed"); if ((q = BN_new()) == NULL) fatal("BN_new failed"); debug2("%.24s Final %u Miller-Rabin trials (%x generator)", ctime(&time_start), trials, generator_wanted); if (checkpoint_file != NULL) last_processed = read_checkpoint(checkpoint_file); last_processed = start_lineno = MAXIMUM(last_processed, start_lineno); if (end_lineno == ULONG_MAX) debug("process from line %lu from pipe", last_processed); else debug("process from line %lu to line %lu", last_processed, end_lineno); res = 0; lp = xmalloc(QLINESIZE + 1); while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) { count_in++; if (count_in <= last_processed) { debug3("skipping line %u, before checkpoint or " "specified start line", count_in); continue; } if (checkpoint_file != NULL) write_checkpoint(checkpoint_file, count_in); print_progress(start_lineno, count_in, end_lineno); if (strlen(lp) < 14 || *lp == '!' || *lp == '#') { debug2("%10u: comment or short line", count_in); continue; } /* XXX - fragile parser */ /* time */ cp = &lp[14]; /* (skip) */ /* type */ in_type = strtoul(cp, &cp, 10); /* tests */ in_tests = strtoul(cp, &cp, 10); if (in_tests & MODULI_TESTS_COMPOSITE) { debug2("%10u: known composite", count_in); continue; } /* tries */ in_tries = strtoul(cp, &cp, 10); /* size (most significant bit) */ in_size = strtoul(cp, &cp, 10); /* generator (hex) */ generator_known = strtoul(cp, &cp, 16); /* Skip white space */ cp += strspn(cp, " "); /* modulus (hex) */ switch (in_type) { case MODULI_TYPE_SOPHIE_GERMAIN: debug2("%10u: (%u) Sophie-Germain", count_in, in_type); a = q; if (BN_hex2bn(&a, cp) == 0) fatal("BN_hex2bn failed"); /* p = 2*q + 1 */ if (BN_lshift(p, q, 1) == 0) fatal("BN_lshift failed"); if (BN_add_word(p, 1) == 0) fatal("BN_add_word failed"); in_size += 1; generator_known = 0; break; case MODULI_TYPE_UNSTRUCTURED: case MODULI_TYPE_SAFE: case MODULI_TYPE_SCHNORR: case MODULI_TYPE_STRONG: case MODULI_TYPE_UNKNOWN: debug2("%10u: (%u)", count_in, in_type); a = p; if (BN_hex2bn(&a, cp) == 0) fatal("BN_hex2bn failed"); /* q = (p-1) / 2 */ if (BN_rshift(q, p, 1) == 0) fatal("BN_rshift failed"); break; default: debug2("Unknown prime type"); break; } /* * due to earlier inconsistencies in interpretation, check * the proposed bit size. */ if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { debug2("%10u: bit size %u mismatch", count_in, in_size); continue; } if (in_size < QSIZE_MINIMUM) { debug2("%10u: bit size %u too short", count_in, in_size); continue; } if (in_tests & MODULI_TESTS_MILLER_RABIN) in_tries += trials; else in_tries = trials; /* * guess unknown generator */ if (generator_known == 0) { if (BN_mod_word(p, 24) == 11) generator_known = 2; else { u_int32_t r = BN_mod_word(p, 10); if (r == 3 || r == 7) generator_known = 5; } } /* * skip tests when desired generator doesn't match */ if (generator_wanted > 0 && generator_wanted != generator_known) { debug2("%10u: generator %d != %d", count_in, generator_known, generator_wanted); continue; } /* * Primes with no known generator are useless for DH, so * skip those. */ if (generator_known == 0) { debug2("%10u: no known generator", count_in); continue; } count_possible++; /* * The (1/4)^N performance bound on Miller-Rabin is * extremely pessimistic, so don't spend a lot of time * really verifying that q is prime until after we know * that p is also prime. A single pass will weed out the * vast majority of composite q's. */ is_prime = BN_is_prime_ex(q, 1, NULL, NULL); if (is_prime < 0) fatal("BN_is_prime_ex failed"); if (is_prime == 0) { debug("%10u: q failed first possible prime test", count_in); continue; } /* * q is possibly prime, so go ahead and really make sure * that p is prime. If it is, then we can go back and do * the same for q. If p is composite, chances are that * will show up on the first Rabin-Miller iteration so it * doesn't hurt to specify a high iteration count. */ is_prime = BN_is_prime_ex(p, trials, NULL, NULL); if (is_prime < 0) fatal("BN_is_prime_ex failed"); if (is_prime == 0) { debug("%10u: p is not prime", count_in); continue; } debug("%10u: p is almost certainly prime", count_in); /* recheck q more rigorously */ is_prime = BN_is_prime_ex(q, trials - 1, NULL, NULL); if (is_prime < 0) fatal("BN_is_prime_ex failed"); if (is_prime == 0) { debug("%10u: q is not prime", count_in); continue; } debug("%10u: q is almost certainly prime", count_in); if (qfileout(out, MODULI_TYPE_SAFE, in_tests | MODULI_TESTS_MILLER_RABIN, in_tries, in_size, generator_known, p)) { res = -1; break; } count_out++; } time(&time_stop); free(lp); BN_free(p); BN_free(q); if (checkpoint_file != NULL) unlink(checkpoint_file); logit("%.24s Found %u safe primes of %u candidates in %ld seconds", ctime(&time_stop), count_out, count_possible, (long) (time_stop - time_start)); return (res); }