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Diffstat (limited to 'crypto/openssh/moduli.c')
| -rw-r--r-- | crypto/openssh/moduli.c | 725 |
1 files changed, 725 insertions, 0 deletions
diff --git a/crypto/openssh/moduli.c b/crypto/openssh/moduli.c new file mode 100644 index 000000000000..5267bb9abece --- /dev/null +++ b/crypto/openssh/moduli.c @@ -0,0 +1,725 @@ +/* $OpenBSD: moduli.c,v 1.26 2012/07/06 00:41:59 dtucker 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 "includes.h" + +#include <sys/param.h> +#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 "xmalloc.h" +#include "dh.h" +#include "log.h" + +#include "openbsd-compat/openssl-compat.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); + + 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 %ld seconds", + ctime(&time_stop), largetries, (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); + + xfree(LargeSieve); + xfree(SmallSieve); + xfree(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[MAXPATHLEN]; + int r; + + r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile); + if (r == -1 || r >= MAXPATHLEN) { + 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)); + 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; +} + +/* + * 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; + BN_CTX *ctx; + 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; + + if (trials < TRIAL_MINIMUM) { + error("Minimum primality trials is %d", TRIAL_MINIMUM); + return (-1); + } + + time(&time_start); + + if ((p = BN_new()) == NULL) + fatal("BN_new failed"); + if ((q = BN_new()) == NULL) + fatal("BN_new failed"); + if ((ctx = BN_CTX_new()) == NULL) + fatal("BN_CTX_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); + if (start_lineno > last_processed) + last_processed = start_lineno; + if (num_lines == 0) + end_lineno = ULONG_MAX; + else + end_lineno = last_processed + num_lines; + debug2("process 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 (checkpoint_file != NULL) { + if (count_in <= last_processed) { + debug3("skipping line %u, before checkpoint", + count_in); + continue; + } + write_checkpoint(checkpoint_file, count_in); + } + 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 if (BN_mod_word(p, 12) == 5) + generator_known = 3; + 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. + */ + if (BN_is_prime_ex(q, 1, ctx, NULL) <= 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. + */ + if (!BN_is_prime_ex(p, trials, ctx, NULL)) { + debug("%10u: p is not prime", count_in); + continue; + } + debug("%10u: p is almost certainly prime", count_in); + + /* recheck q more rigorously */ + if (!BN_is_prime_ex(q, trials - 1, ctx, NULL)) { + 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); + xfree(lp); + BN_free(p); + BN_free(q); + BN_CTX_free(ctx); + + 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); +} |