diff options
| -rw-r--r-- | moduli/Makefile | 5 | ||||
| -rw-r--r-- | moduli/Makefile.inc | 7 | ||||
| -rw-r--r-- | moduli/qsafe/Makefile | 10 | ||||
| -rw-r--r-- | moduli/qsafe/qsafe.c | 334 | ||||
| -rw-r--r-- | moduli/qsieve/Makefile | 8 | ||||
| -rw-r--r-- | moduli/qsieve/qfile.c | 80 | ||||
| -rw-r--r-- | moduli/qsieve/qfile.h | 71 | ||||
| -rw-r--r-- | moduli/qsieve/qsieve.6 | 117 | ||||
| -rw-r--r-- | moduli/qsieve/qsieve.c | 473 |
9 files changed, 1105 insertions, 0 deletions
diff --git a/moduli/Makefile b/moduli/Makefile new file mode 100644 index 00000000..4e8099bd --- /dev/null +++ b/moduli/Makefile @@ -0,0 +1,5 @@ +# $NetBSD: Makefile,v 1.1 2006/01/19 23:23:58 elad Exp $ + +SUBDIR= qsieve qsafe + +.include <bsd.subdir.mk> diff --git a/moduli/Makefile.inc b/moduli/Makefile.inc new file mode 100644 index 00000000..a5346c37 --- /dev/null +++ b/moduli/Makefile.inc @@ -0,0 +1,7 @@ +# $NetBSD: Makefile.inc,v 1.1 2006/01/19 23:23:58 elad Exp $ + +.include <bsd.own.mk> + +WARNS=4 +DPADD+= ${LIBCRYPTO} +LDADD+= -lcrypto diff --git a/moduli/qsafe/Makefile b/moduli/qsafe/Makefile new file mode 100644 index 00000000..ab8484ae --- /dev/null +++ b/moduli/qsafe/Makefile @@ -0,0 +1,10 @@ +# $NetBSD: Makefile,v 1.1 2006/01/19 23:23:58 elad Exp $ + +NOMAN=yes +PROG= qsafe +SRCS= qsafe.c qfile.c +QSIEVE=${.CURDIR}/../qsieve +.PATH: ${QSIEVE} +CPPFLAGS+=-I${QSIEVE} + +.include <bsd.prog.mk> diff --git a/moduli/qsafe/qsafe.c b/moduli/qsafe/qsafe.c new file mode 100644 index 00000000..99c1e8c1 --- /dev/null +++ b/moduli/qsafe/qsafe.c @@ -0,0 +1,334 @@ +/* $NetBSD: qsafe.c,v 1.1 2006/01/19 23:23:58 elad Exp $ */ + +/*- + * Copyright 1994 Phil Karn <karn@qualcomm.com> + * Copyright 1996-1998, 2003 William Allen206 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. + */ + +/* + * Test probable "safe" primes, + * + * suitable for use as Diffie-Hellman moduli; + * that is, where q = (p-1)/2 is also prime. + * + * This is the second of two steps. + * This step is processor intensive. + * + * 1996 May William Allen Simpson + * extracted from earlier code by Phil Karn, April 1994. + * read large prime candidates list (q), + * and check prime probability of (p). + * 1998 May William Allen Simpson + * parameterized. + * optionally limit to a single generator. + * 2000 Dec Niels Provos + * convert from GMP to openssl BN. + * 2003 Jun William Allen Simpson + * change outfile definition slightly to match openssh mistake. + * move common file i/o to own file for better documentation. + * redo debugprint again. + */ + +#include <stdlib.h> +#include <stdio.h> +#include <string.h> +#include <time.h> +#include <openssl/bn.h> +#include "qfile.h" + +/* define DEBUGPRINT 1 */ +#define TRIAL_MINIMUM (4) + +static void usage(void); + +/* + * perform a Miller-Rabin primality test + * on the list of candidates + * (checking both q and p) + * from standard input. + * The result is a list of so-call "safe" primes + * to standard output, + */ +int +main(int argc, char *argv[]) +{ + BIGNUM *q, *p, *a; + BN_CTX *ctx; + char *cp; + char *lp; + uint32_t count_in = 0; + uint32_t count_out = 0; + uint32_t count_possible = 0; + uint32_t generator_known; + uint32_t generator_wanted = 0; + uint32_t in_tests; + uint32_t in_tries; + uint32_t in_type; + uint32_t in_size; + int trials; + time_t time_start; + time_t time_stop; + + setprogname(argv[0]); + + if (argc < 2) { + usage(); + } + + if ((trials = strtoul(argv[1], NULL, 10)) < TRIAL_MINIMUM) { + trials = TRIAL_MINIMUM; + } + + if (argc > 2) { + generator_wanted = strtoul(argv[2], NULL, 16); + } + + time(&time_start); + + p = BN_new(); + q = BN_new(); + ctx = BN_CTX_new(); + + (void)fprintf(stderr, + "%.24s Final %d Miller-Rabin trials (%x generator)\n", + ctime(&time_start), trials, generator_wanted); + + lp = (char *) malloc((unsigned long) QLINESIZE + 1); + + while (fgets(lp, QLINESIZE, stdin) != NULL) { + size_t ll = strlen(lp); + + count_in++; + + if (ll < 14 || *lp == '!' || *lp == '#') { +#ifdef DEBUGPRINT + (void)fprintf(stderr, "%10lu: comment or short" + " line\n", count_in); +#endif + continue; + } + + /* time */ + cp = &lp[14]; /* (skip) */ + + /* type */ + in_type = strtoul(cp, &cp, 10); + + /* tests */ + in_tests = strtoul(cp, &cp, 10); + if (in_tests & QTEST_COMPOSITE) { +#ifdef DEBUGPRINT + (void)fprintf(stderr, "%10lu: known composite\n", + count_in); +#endif + continue; + } + + /* tries */ + in_tries = (uint32_t) strtoul(cp, &cp, 10); + + /* size (most significant bit) */ + in_size = (uint32_t) strtoul(cp, &cp, 10); + + /* generator (hex) */ + generator_known = (uint32_t) strtoul(cp, &cp, 16); + + /* Skip white space */ + cp += strspn(cp, " "); + + /* modulus (hex) */ + switch (in_type) { + case QTYPE_SOPHIE_GERMAINE: +#ifdef DEBUGPRINT + (void)fprintf(stderr, "%10lu: (%lu) " + "Sophie-Germaine\n", count_in, + in_type); +#endif + + a = q; + BN_hex2bn(&a, cp); + /* p = 2*q + 1 */ + BN_lshift(p, q, 1); + BN_add_word(p, 1UL); + in_size += 1; + generator_known = 0; + + break; + + default: +#ifdef DEBUGPRINT + (void)fprintf(stderr, "%10lu: (%lu)\n", + count_in, in_type); +#endif + a = p; + BN_hex2bn(&a, cp); + /* q = (p-1) / 2 */ + BN_rshift(q, p, 1); + + break; + } + + /* + * due to earlier inconsistencies in interpretation, check the + * proposed bit size. + */ + if (BN_num_bits(p) != (in_size + 1)) { +#ifdef DEBUGPRINT + (void)fprintf(stderr, "%10lu: bit size %ul " + "mismatch\n", count_in, in_size); +#endif + continue; + } + + if (in_size < QSIZE_MINIMUM) { +#ifdef DEBUGPRINT + (void)fprintf(stderr, "%10lu: bit size %ul " + "too short\n", count_in, in_size); +#endif + continue; + } + + if (in_tests & QTEST_MILLER_RABIN) + in_tries += trials; + else + in_tries = trials; + + /* + * guess unknown generator + */ + if (generator_known == 0) { + if (BN_mod_word(p, 24UL) == 11) + generator_known = 2; + else if (BN_mod_word(p, 12UL) == 5) + generator_known = 3; + else { + BN_ULONG r = BN_mod_word(p, 10UL); + + if (r == 3 || r == 7) { + generator_known = 5; + } + } + } + + /* + * skip tests when desired generator doesn't match + */ + if (generator_wanted > 0 && + generator_wanted != generator_known) { +#ifdef DEBUGPRINT + (void)fprintf(stderr, + "%10lu: generator %ld != %ld\n", + count_in, generator_known, generator_wanted); +#endif + 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(q, 1, NULL, ctx, NULL) <= 0) { +#ifdef DEBUGPRINT + (void)fprintf(stderr, "%10lu: q failed first " + "possible prime test\n", count_in); +#endif + 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(p, trials, NULL, ctx, NULL)) { +#ifdef DEBUGPRINT + (void)fprintf(stderr, "%10lu: p is not prime\n", + count_in); +#endif + continue; + } + +#ifdef DEBUGPRINT + (void)fprintf(stderr, "%10lu: p is almost certainly " + "prime\n", count_in); +#endif + + /* recheck q more rigorously */ + if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) { +#ifdef DEBUGPRINT + (void)fprintf(stderr, "%10lu: q is not prime\n", + count_in); +#endif + continue; + } +#ifdef DEBUGPRINT + fprintf(stderr, "%10lu: q is almost certainly prime\n", + count_in); +#endif + if (0 > qfileout(stdout, + QTYPE_SAFE, + (in_tests | QTEST_MILLER_RABIN), + in_tries, + in_size, + generator_known, + p)) { + break; + } + count_out++; +#ifdef DEBUGPRINT + fflush(stderr); + fflush(stdout); +#endif + } + + time(&time_stop); + free(lp); + BN_free(p); + BN_free(q); + BN_CTX_free(ctx); + fflush(stdout); /* fclose(stdout); */ + /* fclose(stdin); */ + (void)fprintf(stderr, + "%.24s Found %u safe primes of %u candidates in %lu seconds\n", + ctime(&time_stop), count_out, count_possible, + (long) (time_stop - time_start)); + + return (0); +} + +static void +usage(void) +{ + (void)fprintf(stderr, "Usage: %s <trials> [generator]\n", + getprogname()); + exit(1); +} diff --git a/moduli/qsieve/Makefile b/moduli/qsieve/Makefile new file mode 100644 index 00000000..e6efe9da --- /dev/null +++ b/moduli/qsieve/Makefile @@ -0,0 +1,8 @@ +# $NetBSD: Makefile,v 1.1 2006/01/19 23:23:58 elad Exp $ + +PROG= qsieve +SRCS= qsieve.c qfile.c +MAN= qsieve.6 +MLINKS = qsieve.6 qsafe.6 + +.include <bsd.prog.mk> diff --git a/moduli/qsieve/qfile.c b/moduli/qsieve/qfile.c new file mode 100644 index 00000000..b6038794 --- /dev/null +++ b/moduli/qsieve/qfile.c @@ -0,0 +1,80 @@ +/* $NetBSD: qfile.c,v 1.1 2006/01/19 23:23:58 elad Exp $ */ + +/*- + * Copyright 1994 Phil Karn <karn@qualcomm.com> + * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com> + * 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. + */ + +/* + * File I/O for qsafe and qsieve. + * + * 1996 May William Allen Simpson extracted from earlier code by Phil Karn, + * April 1994. save large primes list for later processing. 1998 May + * William Allen Simpson parameterized. 2003 Jun William Allen Simpson + * move common file i/o to own file for better documentation. + */ + +#include <stdio.h> +#include <stdlib.h> +#include <time.h> +#include <openssl/bn.h> +#include "qfile.h" + +/* + * print moduli out in consistent form, + * normalizing error returns to printf-like expectations. + */ +int +qfileout(FILE * ofile, uint32_t otype, uint32_t otests, uint32_t otries, + uint32_t osize, uint32_t ogenerator, BIGNUM * omodulus) +{ + struct tm *gtm; + time_t time_now; + + time(&time_now); + gtm = gmtime(&time_now); + + if (0 > 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)) { + + return (-1); + } + + if (1 > BN_print_fp(ofile, omodulus)) { + return (-1); + } + + return (fprintf(ofile, "\n")); +} diff --git a/moduli/qsieve/qfile.h b/moduli/qsieve/qfile.h new file mode 100644 index 00000000..d24f6856 --- /dev/null +++ b/moduli/qsieve/qfile.h @@ -0,0 +1,71 @@ +/* $NetBSD: qfile.h,v 1.1 2006/01/19 23:23:58 elad Exp $ */ + +/*- + * Copyright 1994 Phil Karn <karn@qualcomm.com> + * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com> + * 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. + */ + +#ifndef _QFILE_H_ +#define _QFILE_H_ + +#include <stdio.h> +#include <stdlib.h> +#include <openssl/bn.h> + +/* need line long enough for largest moduli plus headers */ +#define QLINESIZE (100+8192) + +/* + * Type: decimal. Specifies the internal structure of the prime modulus. + */ +#define QTYPE_UNKNOWN (0) +#define QTYPE_UNSTRUCTURED (1) +#define QTYPE_SAFE (2) +#define QTYPE_SCHNOOR (3) +#define QTYPE_SOPHIE_GERMAINE (4) +#define QTYPE_STRONG (5) + +/* + * Tests: decimal (bit field). Specifies the methods used in checking for + * primality. Usually, more than one test is used. + */ +#define QTEST_UNTESTED (0x00) +#define QTEST_COMPOSITE (0x01) +#define QTEST_SIEVE (0x02) +#define QTEST_MILLER_RABIN (0x04) +#define QTEST_JACOBI (0x08) +#define QTEST_ELLIPTIC (0x10) + +/* + * Size: decimal. Specifies the number of the most significant bit (0 to M). * + * WARNING: internally, usually 1 to N. + */ +#define QSIZE_MINIMUM (511) + + +int +qfileout(FILE *, uint32_t, uint32_t, uint32_t, uint32_t, uint32_t, + BIGNUM *); + +#endif /* !_QFILE_H_ */ diff --git a/moduli/qsieve/qsieve.6 b/moduli/qsieve/qsieve.6 new file mode 100644 index 00000000..4279236d --- /dev/null +++ b/moduli/qsieve/qsieve.6 @@ -0,0 +1,117 @@ +.\" $NetBSD: qsieve.6,v 1.1 2006/01/19 23:23:58 elad Exp $ +.\" +.\" Copyright 1997, 2003 William Allen Simpson <wsimpson@greendragon.com> +.\" 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. +.\" 3. All advertising materials mentioning features or use of this software +.\" must display the following acknowledgement: +.\" This product includes software designed by William Allen Simpson. +.\" 4. The name of the author may not be used to endorse or promote products +.\" derived from this software without specific prior written permission. +.\" +.\" 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. +.\" +.\" Manual page, using -mandoc macros +.\" +.Dd July 28, 1997 +.Dt QSIEVE 1 +.Os +.Sh NAME +.Nm qsieve , +.Nm qsafe +.Nd generate system moduli file +.Sh SYNOPSIS +.Nm +.Op Ar megabytes Ar bits Op Ar initial +.br +.Nm qsafe +.Op Ar trials Op Ar generator +.Sh DESCRIPTION +The +.Nm +utility will list candidates for Sophie-Germaine primes +(where q = (p-1)/2) +to standard output. +The list is checked against small known primes +(less than 2**30). +This step is both processor and memory intensive. +.Pp +The +.Ar megabytes +value +sets a limit for the internal sieve buffer. +This should be small enough to remain entirely in memory. +Swap thrashing can increase the run time +from hours to days or weeks! +When the +.Ar megabytes +value is zero (0), +.Nm +will select a default suitable for the +.Ar bits . +.Pp +The +.Ar bits +value +sets the length of the generated possible primes +(typically 768, 1024, 1536, 2048, 3072, or 4096, +although others can be used for variety). +.Pp +The optional +.Ar initial +value (hex) +specifies the beginning of the search. +Otherwise, +.Nm +generates a randomly selected number. +.Pp +The +.Nm qsafe +utility will perform a Miller-Rabin primality test +on the list of candidates +(checking both q and p) +from standard input. +The result is a list of so-call "safe" primes +to standard output, +suitable for use as Diffie-Hellman moduli. +This step is merely processor intensive. +.Pp +The +.Ar trials +value +sets the number of Miller-Rabin interations +(typically 16 to 128). +.Pp +The optional +.Ar generator +value (hex) +limits testing to candidates with a specific generator +(usually 2). +Otherwise, +.Nm qsafe +will test each candidate +and suggest a generator. +.Sh SEE ALSO +.Xr moduli 5 +.Sh HISTORY +These programs were originally developed for +the Photuris project, +and later +the OpenSSH project. diff --git a/moduli/qsieve/qsieve.c b/moduli/qsieve/qsieve.c new file mode 100644 index 00000000..34e5a339 --- /dev/null +++ b/moduli/qsieve/qsieve.c @@ -0,0 +1,473 @@ +/* $NetBSD: qsieve.c,v 1.1 2006/01/19 23:23:58 elad 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. + */ + +/* + * Sieve candidates for "safe" primes, + * suitable for use as Diffie-Hellman moduli; + * that is, where q = (p-1)/2 is also prime. + * + * This is the first of two steps. + * This step is memory intensive. + * + * 1996 May William Allen Simpson + * extracted from earlier code by Phil Karn, April 1994. + * save large primes list for later processing. + * 1998 May William Allen Simpson + * parameterized. + * 2000 Dec Niels Provos + * convert from GMP to openssl BN. + * 2003 Jun William Allen Simpson + * change outfile definition slightly to match openssh mistake. + * move common file i/o to own file for better documentation. + * redo memory again. + */ + +#include <stdio.h> +#include <stdlib.h> +#include <time.h> +#include <openssl/bn.h> +#include <string.h> +#include <err.h> +#include "qfile.h" + +/* define DEBUG_LARGE 1 */ +/* define DEBUG_SMALL 1 */ + +/* + * 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: 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) + +/* + * 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] &= ~(1U << ((n) & 31))) +#define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1U << ((n) & 31))) +#define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1U << ((n) & 31))) + +/* + * sieve relative to the initial value + */ +uint32_t *LargeSieve; +uint32_t largewords; +uint32_t largetries; +uint32_t largenumbers; +uint32_t largememory; /* megabytes */ +uint32_t largebits; +BIGNUM *largebase; + +/* + * sieve 2**30 in 2**16 parts + */ +uint32_t *SmallSieve; +uint32_t smallbits; +uint32_t smallbase; + +/* + * sieve 2**16 + */ +uint32_t *TinySieve; +uint32_t tinybits; + +static void usage(void); +void sieve_large(uint32_t); + +/* + * Sieve p's and q's with small factors + */ +void +sieve_large(uint32_t s) +{ + BN_ULONG r; + BN_ULONG u; + +#ifdef DEBUG_SMALL + (void)fprintf(stderr, "%lu\n", s); +#endif + largetries++; + /* r = largebase mod s */ + r = BN_mod_word(largebase, (BN_ULONG) s); + if (r == 0) { + /* s divides into largebase exactly */ + u = 0; + } else { + /* largebase+u is first entry divisible by s */ + u = s - r; + } + + 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) { + /* Make largebase+u odd, and u even */ + u += s; + } + + /* Mark all multiples of 2*s */ + for (u /= 2; u < largebits; u += s) { + BIT_SET(LargeSieve, (uint32_t)u); + } + } + + /* r = p mod s */ + r = (2 * r + 1) % s; + + if (r == 0) { + /* s divides p exactly */ + u = 0; + } else { + /* p+u is first entry divisible by s */ + u = s - r; + } + + 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, (uint32_t)u); + } + } +} + +/* + * list candidates for Sophie-Germaine primes + * (where q = (p-1)/2) + * to standard output. + * The list is checked against small known primes + * (less than 2**30). + */ +int +main(int argc, char *argv[]) +{ + BIGNUM *q; + uint32_t j; + int power; + uint32_t r; + uint32_t s; + uint32_t smallwords = TINY_NUMBER >> 6; + uint32_t t; + time_t time_start; + time_t time_stop; + uint32_t tinywords = TINY_NUMBER >> 6; + unsigned int i; + + setprogname(argv[0]); + + if (argc < 3) { + usage(); + } + + /* + * 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. + */ + power = (int) strtoul(argv[2], NULL, 10); + if (power > TEST_MAXIMUM) { + errx(1, "Too many bits: %d > %lu.", power, + (unsigned long)TEST_MAXIMUM); + } else if (power < TEST_MINIMUM) { + errx(1, "Too few bits: %d < %lu.", power, + (unsigned long)TEST_MINIMUM); + } + + 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 = (uint32_t)((unsigned long) + (power * power) >> (SHIFT_WORD - TEST_POWER)); + + /* + * Need idea of how much memory is available. We don't have to use all + * of it. + */ + largememory = (uint32_t)strtoul(argv[1], NULL, 10); + if (largememory > LARGE_MAXIMUM) { + warnx("Limited memory: %u MB; limit %lu MB.", largememory, + LARGE_MAXIMUM); + largememory = LARGE_MAXIMUM; + } + + if (largewords <= (largememory << SHIFT_MEGAWORD)) { + warnx("Increased memory: %u MB; need %u bytes.", + largememory, (largewords << SHIFT_BYTE)); + largewords = (largememory << SHIFT_MEGAWORD); + } else if (largememory > 0) { + warnx("Decreased memory: %u MB; want %u bytes.", + largememory, (largewords << SHIFT_BYTE)); + largewords = (largememory << SHIFT_MEGAWORD); + } + + if ((TinySieve = (uint32_t *) calloc((size_t) tinywords, sizeof(uint32_t))) == NULL) { + errx(1, "Insufficient memory for tiny sieve: need %u byts.", + tinywords << SHIFT_BYTE); + } + tinybits = tinywords << SHIFT_WORD; + + if ((SmallSieve = (uint32_t *) calloc((size_t) smallwords, sizeof(uint32_t))) == NULL) { + errx(1, "Insufficient memory for small sieve: need %u bytes.", + smallwords << SHIFT_BYTE); + } + smallbits = smallwords << SHIFT_WORD; + + /* + * dynamically determine available memory + */ + while ((LargeSieve = (uint32_t *)calloc((size_t)largewords, + sizeof(uint32_t))) == NULL) { + /* 1/4 MB chunks */ + largewords -= (1L << (SHIFT_MEGAWORD - 2)); + } + largebits = largewords << SHIFT_WORD; + largenumbers = largebits * 2; /* even numbers excluded */ + + /* validation check: count the number of primes tried */ + largetries = 0; + + q = BN_new(); + largebase = BN_new(); + + /* + * Generate random starting point for subprime search, or use + * specified parameter. + */ + if (argc < 4) { + BN_rand(largebase, power, 1, 1); + } else { + BIGNUM *a; + + a = largebase; + BN_hex2bn(&a, argv[2]); + } + + /* ensure odd */ + if (!BN_is_odd(largebase)) { + BN_set_bit(largebase, 0); + } + + time(&time_start); + (void)fprintf(stderr, + "%.24s Sieve next %u plus %d-bit start point:\n# ", + ctime(&time_start), largenumbers, power); + BN_print_fp(stderr, largebase); + (void)fprintf(stderr, "\n"); + + /* + * TinySieve + */ + for (i = 0; i < tinybits; i++) { + if (BIT_TEST(TinySieve, i)) { + /* 2*i+3 is composite */ + continue; + } + + /* 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)) { + /* 2*i+3 is composite */ + continue; + } + + /* The next tiny prime */ + t = 2 * i + 3; + r = smallbase % t; + + if (r == 0) { + /* t divides into smallbase exactly */ + s = 0; + } 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) { + /* Make smallbase+s odd, and s even */ + s += t; + } + + /* 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)) { + /* 2*i+smallbase is composite */ + continue; + } + + /* The next small prime */ + sieve_large((2 * i) + smallbase); + } + + memset(SmallSieve, 0, (size_t)(smallwords << SHIFT_BYTE)); + } + + time(&time_stop); + (void)fprintf(stderr, + "%.24s Sieved with %u small primes in %lu seconds\n", + ctime(&time_stop), largetries, + (long) (time_stop - time_start)); + + for (j = r = 0; j < largebits; j++) { + if (BIT_TEST(LargeSieve, j)) { + /* Definitely composite, skip */ + continue; + } + +#ifdef DEBUG_LARGE + (void)fprintf(stderr, "test q = largebase+%lu\n", 2 * j); +#endif + + BN_set_word(q, (unsigned long)(2 * j)); + BN_add(q, q, largebase); + + if (0 > qfileout(stdout, + (uint32_t) QTYPE_SOPHIE_GERMAINE, + (uint32_t) QTEST_SIEVE, + largetries, + (uint32_t) (power - 1), /* MSB */ + (uint32_t) (0), /* generator unknown */ + q)) { + break; + } + + r++; /* count q */ + } + + time(&time_stop); + + free(LargeSieve); + free(SmallSieve); + free(TinySieve); + + fflush(stdout); + /* fclose(stdout); */ + + (void) fprintf(stderr, "%.24s Found %u candidates\n", + ctime(&time_stop), r); + + return (0); +} + +static void +usage(void) +{ + (void)fprintf(stderr, "Usage: %s <megabytes> <bits> [initial]\n" + "Possible values for <megabytes>: 0, %lu to %lu\n" + "Possible values for <bits>: %lu to %lu\n", + getprogname(), + LARGE_MINIMUM, + LARGE_MAXIMUM, + (unsigned long) TEST_MINIMUM, + (unsigned long) TEST_MAXIMUM); + + exit(1); +} |