From e89a1126494e764fee659879e4fc1165c05d661f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Niels=20M=C3=B6ller?= <nisse@lysator.liu.se>
Date: Wed, 16 Jan 2002 21:07:25 +0100
Subject: [PATCH] New file.
Rev: src/nettle/rsa-keygen.c:1.1
---
rsa-keygen.c | 346 +++++++++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 346 insertions(+)
create mode 100644 rsa-keygen.c
diff --git a/rsa-keygen.c b/rsa-keygen.c
new file mode 100644
index 00000000..2d2cc922
--- /dev/null
+++ b/rsa-keygen.c
@@ -0,0 +1,346 @@
+/* rsa-keygen.c
+ *
+ * Generation of RSA keypairs
+ */
+
+/* nettle, low-level cryptographics library
+ *
+ * Copyright (C) 2002 Niels M�ller
+ *
+ * The nettle library is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Lesser General Public License as published by
+ * the Free Software Foundation; either version 2.1 of the License, or (at your
+ * option) any later version.
+ *
+ * The nettle library is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
+ * License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with the nettle library; see the file COPYING.LIB. If not, write to
+ * the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+#if HAVE_CONFIG_H
+#include "config.h"
+#endif
+
+#if HAVE_LIBGMP
+
+#include "rsa.h"
+#include "bignum.h"
+
+#include <assert.h>
+#include <limits.h>
+#include <stdlib.h>
+
+#ifndef DEBUG
+# define DEBUG 0
+#endif
+
+#if DEBUG
+# include <stdio.h>
+#endif
+
+/* Returns a random number, 0 <= x < 2^bits. */
+static void
+bignum_random_size(mpz_t x, unsigned bits,
+ void *random_ctx, nettle_random_func random)
+{
+ unsigned length = (bits + 7) / 8;
+ uint8_t *data = alloca(length);
+
+ random(random_ctx, length, data);
+
+ nettle_mpz_set_str_256(x, length, data);
+
+ if (bits % 8)
+ mpz_fdiv_r_2exp(x, x, bits);
+}
+
+#define NUMBER_OF_PRIMES 167
+
+static const unsigned long primes[NUMBER_OF_PRIMES] = {
+ 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
+ 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139,
+ 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211,
+ 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
+ 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367,
+ 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
+ 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523,
+ 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613,
+ 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691,
+ 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787,
+ 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877,
+ 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971,
+ 977, 983, 991, 997
+};
+
+/* NOTE: The mpz_nextprime in current GMP is unoptimized. */
+static void
+bignum_next_prime(mpz_t p, mpz_t n, int count,
+ void *progress_ctx, nettle_progress_func progress)
+{
+ mpz_t tmp;
+ unsigned long *moduli = NULL;
+ unsigned long difference;
+ int prime_limit = NUMBER_OF_PRIMES;
+
+ /* First handle tiny numbers */
+ if (mpz_cmp_ui(n, 2) <= 0)
+ {
+ mpz_set_ui(p, 2);
+ return;
+ }
+ mpz_set(p, n);
+ mpz_setbit(p, 0);
+
+ if (mpz_cmp_ui(p, 8) < 0)
+ return;
+
+ mpz_init(tmp);
+
+ if (prime_limit && (mpz_cmp_ui(p, primes[prime_limit]) <= 0) )
+ /* Use unly 3, 5 and 7 */
+ prime_limit = 3;
+
+ if (prime_limit)
+ {
+ /* Compute residues modulo small odd primes */
+ int i;
+
+ moduli = alloca(prime_limit * sizeof(*moduli));
+ for (i = 0; i < prime_limit; i++)
+ moduli[i] = mpz_fdiv_ui(p, primes[i]);
+ }
+
+ for (difference = 0; ; difference += 2)
+ {
+ if (difference >= ULONG_MAX - 10)
+ { /* Should not happen, at least not very often... */
+ mpz_add_ui(p, p, difference);
+ difference = 0;
+ }
+
+ /* First check residues */
+ if (prime_limit)
+ {
+ int composite = 0;
+ int i;
+
+ for (i = 0; i < prime_limit; i++)
+ {
+ if (moduli[i] == 0)
+ composite = 1;
+ moduli[i] = (moduli[i] + 2) % primes[i];
+ }
+ if (composite)
+ continue;
+ }
+
+ mpz_add_ui(p, p, difference);
+ difference = 0;
+
+ if (progress)
+ progress(progress_ctx, '.');
+
+ /* Fermat test, with respect to 2 */
+ mpz_set_ui(tmp, 2);
+ mpz_powm(tmp, tmp, p, p);
+ if (mpz_cmp_ui(tmp, 2) != 0)
+ continue;
+
+ if (progress)
+ progress(progress_ctx, '+');
+
+ /* Miller-Rabin test */
+ if (mpz_probab_prime_p(p, count))
+ break;
+ }
+ mpz_clear(tmp);
+}
+
+/* Returns a random prime of size BITS */
+static void
+bignum_random_prime(mpz_t x, unsigned bits,
+ void *random_ctx, nettle_random_func random,
+ void *progress_ctx, nettle_progress_func progress)
+{
+ assert(bits);
+
+ for (;;)
+ {
+ bignum_random_size(x, bits, random_ctx, random);
+ mpz_setbit(x, bits - 1);
+
+ /* Miller-rabin count of 25 is probably much overkill. */
+ bignum_next_prime(x, x, 25, progress_ctx, progress);
+
+ if (mpz_sizeinbase(x, 2) == bits)
+ break;
+ }
+}
+
+int
+rsa_generate_keypair(struct rsa_public_key *pub,
+ struct rsa_private_key *key,
+ void *random_ctx, nettle_random_func random,
+ void *progress_ctx, nettle_progress_func progress,
+ unsigned n_size,
+ unsigned e_size)
+{
+ mpz_t p1;
+ mpz_t q1;
+ mpz_t phi;
+ mpz_t tmp;
+
+ if (e_size)
+ {
+ /* We should choose e randomly. Is the size reasonable? */
+ if ((e_size < 16) || (e_size > n_size) )
+ return 0;
+ }
+ else
+ {
+ /* We have a fixed e. Check that it makes sense */
+
+ /* It must be odd */
+ if (!mpz_tstbit(pub->e, 0))
+ return 0;
+
+ /* And 3 or larger */
+ if (mpz_cmp_ui(pub->e, 3) < 0)
+ return 0;
+ }
+
+ if (n_size < RSA_MINIMUM_N_BITS)
+ return 0;
+
+ mpz_init(p1); mpz_init(q1); mpz_init(phi); mpz_init(tmp);
+
+ /* Generate primes */
+ for (;;)
+ {
+ /* Generate p, such that gcd(p-1, e) = 1 */
+ for (;;)
+ {
+ bignum_random_prime(key->p, (n_size+1)/2,
+ random_ctx, random,
+ progress_ctx, progress);
+ mpz_sub_ui(p1, key->p, 1);
+
+ /* If e was given, we must chose p such that p-1 has no factors in
+ * common with e. */
+ if (e_size)
+ break;
+
+ mpz_gcd(tmp, pub->e, p1);
+
+ if (mpz_cmp_ui(tmp, 1) == 0)
+ break;
+ else if (progress) progress(progress_ctx, 'c');
+ }
+
+ if (progress)
+ progress(progress_ctx, '\n');
+
+ /* Generate q, such that gcd(q-1, e) = 1 */
+ for (;;)
+ {
+ bignum_random_prime(key->q, n_size/2,
+ random_ctx, random,
+ progress_ctx, progress);
+ mpz_sub_ui(q1, key->q, 1);
+
+ /* If e was given, we must chose q such that q-1 has no factors in
+ * common with e. */
+ if (e_size)
+ break;
+
+ mpz_gcd(tmp, pub->e, q1);
+
+ if (mpz_cmp_ui(tmp, 1) == 0)
+ break;
+ else if (progress) progress(progress_ctx, 'c');
+ }
+
+ /* Now we have the primes. Is the product of the right size? */
+ mpz_mul(pub->n, key->p, key->q);
+
+ if (mpz_sizeinbase(pub->n, 2) != n_size)
+ /* We might get an n of size n_size-1. Then just try again. */
+ {
+#if DEBUG
+ fprintf(stderr,
+ "\nWanted size: %d, p-size: %d, q-size: %d, n-size: %d\n",
+ n_size,
+ mpz_sizeinbase(key->p,2),
+ mpz_sizeinbase(key->q,2),
+ mpz_sizeinbase(pub->n,2));
+#endif
+ if (progress)
+ {
+ progress(progress_ctx, 'b');
+ progress(progress_ctx, '\n');
+ }
+ continue;
+ }
+
+ if (progress)
+ progress(progress_ctx, '\n');
+
+ /* c = q^{-1} (mod p) */
+ if (mpz_invert(key->c, key->q, key->p))
+ /* This should succeed everytime. But if it doesn't,
+ * we try again. */
+ break;
+ else if (progress) progress(progress_ctx, '?');
+ }
+
+ mpz_mul(phi, p1, q1);
+
+ /* If we didn't have a given e, generate one now. */
+ if (e_size)
+ for (;;)
+ {
+ bignum_random_size(pub->e, e_size,
+ random_ctx, random);
+
+ /* Make sure it's odd and that the most significant bit is
+ * set */
+ mpz_setbit(pub->e, 0);
+ mpz_setbit(pub->e, e_size - 1);
+
+ /* Needs gmp-3, or inverse might be negative. */
+ if (mpz_invert(key->d, pub->e, phi))
+ break;
+ else if (progress) progress(progress_ctx, 'e');
+ }
+ else
+ {
+ /* Must always succeed, as we already that e
+ * doesn't have any common factor with p-1 or q-1. */
+ int res = mpz_invert(key->d, pub->e, phi);
+ assert(res);
+ }
+
+ /* Done! Almost, we must compute the auxillary private values. */
+ /* a = d % (p-1) */
+ mpz_fdiv_r(key->a, key->d, p1);
+
+ /* b = d % (q-1) */
+ mpz_fdiv_r(key->b, key->d, q1);
+
+ /* c was computed earlier */
+
+ pub->size = key->size = (mpz_sizeinbase(pub->n, 2) + 7) / 8;
+ assert(pub->size >= RSA_MINIMUM_N_OCTETS);
+
+ mpz_clear(p1); mpz_clear(q1); mpz_clear(phi); mpz_clear(tmp);
+
+ return 1;
+}
+
+#endif /* HAVE_LIBGMP */
--
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