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NetBSD/usr.bin/moduli/qsieve/qsieve.c

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/* $NetBSD: qsieve.c,v 1.3 2011/09/04 20:55:43 joerg 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
*/
static uint32_t *LargeSieve;
static uint32_t largewords;
static uint32_t largetries;
static uint32_t largenumbers;
static uint32_t largememory; /* megabytes */
static uint32_t largebits;
static BIGNUM *largebase;
/*
* sieve 2**30 in 2**16 parts
*/
static uint32_t *SmallSieve;
static uint32_t smallbits;
static uint32_t smallbase;
/*
* sieve 2**16
*/
static uint32_t *TinySieve;
static uint32_t tinybits;
__dead static void usage(void);
static void sieve_large(uint32_t);
/*
* Sieve p's and q's with small factors
*/
static 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 ((unsigned)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);
}
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