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-rw-r--r--moduli/qsieve/qsieve.c473
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diff --git a/moduli/qsieve/qsieve.c b/moduli/qsieve/qsieve.c
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-/* $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);
-}
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