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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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