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by Marek Habersack
Import upstream version 1.10 |
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/* rsa-keygen.c
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*
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* Generation of RSA keypairs
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*/
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/* nettle, low-level cryptographics library
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*
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* Copyright (C) 2002 Niels Möller
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*
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* The nettle library is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or (at your
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* option) any later version.
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*
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* The nettle library is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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* License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with the nettle library; see the file COPYING.LIB. If not, write to
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* the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
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* MA 02111-1307, USA.
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*/
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#if HAVE_CONFIG_H
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# include "config.h"
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#endif
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#if WITH_PUBLIC_KEY
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#include <assert.h> |
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#include <limits.h> |
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#include <stdlib.h> |
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#include "rsa.h" |
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#include "bignum.h" |
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#include "nettle-internal.h" |
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#ifndef DEBUG
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# define DEBUG 0
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#endif
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#if DEBUG
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# include <stdio.h>
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#endif
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#define NUMBER_OF_PRIMES 167
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static const unsigned long primes[NUMBER_OF_PRIMES] = { |
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3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, |
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71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, |
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149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, |
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223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, |
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283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, |
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373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, |
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449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, |
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541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, |
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617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, |
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701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, |
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797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, |
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881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, |
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977, 983, 991, 997 |
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};
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/* NOTE: The mpz_nextprime in current GMP is unoptimized. */
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static void |
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bignum_next_prime(mpz_t p, mpz_t n, int count, |
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void *progress_ctx, nettle_progress_func progress) |
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{
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mpz_t tmp; |
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TMP_DECL(moduli, unsigned long, NUMBER_OF_PRIMES); |
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unsigned long difference; |
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unsigned prime_limit = NUMBER_OF_PRIMES; |
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/* First handle tiny numbers */
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if (mpz_cmp_ui(n, 2) <= 0) |
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{
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mpz_set_ui(p, 2); |
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return; |
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}
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mpz_set(p, n); |
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mpz_setbit(p, 0); |
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if (mpz_cmp_ui(p, 8) < 0) |
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return; |
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mpz_init(tmp); |
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if (mpz_cmp_ui(p, primes[prime_limit-1]) <= 0) |
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/* Use only 3, 5 and 7 */
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prime_limit = 3; |
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/* Compute residues modulo small odd primes */
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TMP_ALLOC(moduli, prime_limit); |
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{
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unsigned i; |
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for (i = 0; i < prime_limit; i++) |
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moduli[i] = mpz_fdiv_ui(p, primes[i]); |
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}
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for (difference = 0; ; difference += 2) |
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{
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int composite = 0; |
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unsigned i; |
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if (difference >= ULONG_MAX - 10) |
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{ /* Should not happen, at least not very often... */ |
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mpz_add_ui(p, p, difference); |
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difference = 0; |
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}
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/* First check residues */
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for (i = 0; i < prime_limit; i++) |
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{
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if (moduli[i] == 0) |
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composite = 1; |
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moduli[i] = (moduli[i] + 2) % primes[i]; |
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}
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if (composite) |
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continue; |
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mpz_add_ui(p, p, difference); |
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difference = 0; |
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if (progress) |
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progress(progress_ctx, '.'); |
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/* Fermat test, with respect to 2 */
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mpz_set_ui(tmp, 2); |
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mpz_powm(tmp, tmp, p, p); |
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if (mpz_cmp_ui(tmp, 2) != 0) |
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continue; |
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if (progress) |
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progress(progress_ctx, '+'); |
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/* Miller-Rabin test */
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if (mpz_probab_prime_p(p, count)) |
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break; |
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}
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mpz_clear(tmp); |
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}
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/* Returns a random prime of size BITS */
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static void |
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bignum_random_prime(mpz_t x, unsigned bits, |
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void *random_ctx, nettle_random_func random, |
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void *progress_ctx, nettle_progress_func progress) |
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{
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assert(bits); |
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for (;;) |
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{
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nettle_mpz_random_size(x, random_ctx, random, bits); |
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mpz_setbit(x, bits - 1); |
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/* Miller-rabin count of 25 is probably much overkill. */
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bignum_next_prime(x, x, 25, progress_ctx, progress); |
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if (mpz_sizeinbase(x, 2) == bits) |
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break; |
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}
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}
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int
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rsa_generate_keypair(struct rsa_public_key *pub, |
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struct rsa_private_key *key, |
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void *random_ctx, nettle_random_func random, |
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void *progress_ctx, nettle_progress_func progress, |
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unsigned n_size, |
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unsigned e_size) |
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{
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mpz_t p1; |
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mpz_t q1; |
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mpz_t phi; |
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mpz_t tmp; |
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if (e_size) |
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{
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/* We should choose e randomly. Is the size reasonable? */
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if ((e_size < 16) || (e_size > n_size) ) |
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return 0; |
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}
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else
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{
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/* We have a fixed e. Check that it makes sense */
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/* It must be odd */
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if (!mpz_tstbit(pub->e, 0)) |
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return 0; |
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/* And 3 or larger */
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if (mpz_cmp_ui(pub->e, 3) < 0) |
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return 0; |
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}
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if (n_size < RSA_MINIMUM_N_BITS) |
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return 0; |
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mpz_init(p1); mpz_init(q1); mpz_init(phi); mpz_init(tmp); |
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/* Generate primes */
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for (;;) |
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{
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/* Generate p, such that gcd(p-1, e) = 1 */
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for (;;) |
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{
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bignum_random_prime(key->p, (n_size+1)/2, |
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random_ctx, random, |
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progress_ctx, progress); |
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mpz_sub_ui(p1, key->p, 1); |
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/* If e was given, we must chose p such that p-1 has no factors in
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* common with e. */
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if (e_size) |
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break; |
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mpz_gcd(tmp, pub->e, p1); |
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if (mpz_cmp_ui(tmp, 1) == 0) |
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break; |
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else if (progress) progress(progress_ctx, 'c'); |
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}
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if (progress) |
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progress(progress_ctx, '\n'); |
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/* Generate q, such that gcd(q-1, e) = 1 */
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for (;;) |
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{
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bignum_random_prime(key->q, n_size/2, |
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random_ctx, random, |
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progress_ctx, progress); |
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mpz_sub_ui(q1, key->q, 1); |
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/* If e was given, we must chose q such that q-1 has no factors in
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* common with e. */
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if (e_size) |
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break; |
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mpz_gcd(tmp, pub->e, q1); |
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if (mpz_cmp_ui(tmp, 1) == 0) |
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break; |
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else if (progress) progress(progress_ctx, 'c'); |
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}
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/* Now we have the primes. Is the product of the right size? */
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mpz_mul(pub->n, key->p, key->q); |
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if (mpz_sizeinbase(pub->n, 2) != n_size) |
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/* We might get an n of size n_size-1. Then just try again. */
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{
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#if DEBUG
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fprintf(stderr, |
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"\nWanted size: %d, p-size: %d, q-size: %d, n-size: %d\n", |
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n_size, |
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mpz_sizeinbase(key->p,2), |
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mpz_sizeinbase(key->q,2), |
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mpz_sizeinbase(pub->n,2)); |
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#endif
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if (progress) |
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{
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progress(progress_ctx, 'b'); |
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progress(progress_ctx, '\n'); |
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}
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continue; |
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}
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if (progress) |
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progress(progress_ctx, '\n'); |
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/* c = q^{-1} (mod p) */
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if (mpz_invert(key->c, key->q, key->p)) |
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/* This should succeed everytime. But if it doesn't,
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* we try again. */
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break; |
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else if (progress) progress(progress_ctx, '?'); |
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}
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mpz_mul(phi, p1, q1); |
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/* If we didn't have a given e, generate one now. */
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if (e_size) |
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{
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int retried = 0; |
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for (;;) |
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{
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nettle_mpz_random_size(pub->e, |
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random_ctx, random, |
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e_size); |
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/* Make sure it's odd and that the most significant bit is
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* set */
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mpz_setbit(pub->e, 0); |
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mpz_setbit(pub->e, e_size - 1); |
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/* Needs gmp-3, or inverse might be negative. */
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if (mpz_invert(key->d, pub->e, phi)) |
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break; |
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if (progress) progress(progress_ctx, 'e'); |
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retried = 1; |
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}
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if (retried && progress) |
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progress(progress_ctx, '\n'); |
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}
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else
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{
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/* Must always succeed, as we already that e
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* doesn't have any common factor with p-1 or q-1. */
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int res = mpz_invert(key->d, pub->e, phi); |
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assert(res); |
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}
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/* Done! Almost, we must compute the auxillary private values. */
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/* a = d % (p-1) */
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mpz_fdiv_r(key->a, key->d, p1); |
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/* b = d % (q-1) */
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mpz_fdiv_r(key->b, key->d, q1); |
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/* c was computed earlier */
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pub->size = key->size = (mpz_sizeinbase(pub->n, 2) + 7) / 8; |
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assert(pub->size >= RSA_MINIMUM_N_OCTETS); |
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mpz_clear(p1); mpz_clear(q1); mpz_clear(phi); mpz_clear(tmp); |
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return 1; |
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}
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#endif /* WITH_PUBLIC_KEY */ |