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/* rsa-sign.c
*
* Creating RSA signatures.
*/
/* nettle, low-level cryptographics library
*
* Copyright (C) 2001, 2003 Niels Möller
*
* 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., 51 Franklin Street, Fifth Floor, Boston,
* MA 02111-1301, USA.
*/
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include "rsa.h"
#include "bignum.h"
void
rsa_private_key_init(struct rsa_private_key *key)
{
mpz_init(key->d);
mpz_init(key->p);
mpz_init(key->q);
mpz_init(key->a);
mpz_init(key->b);
mpz_init(key->c);
/* Not really necessary, but it seems cleaner to initialize all the
* storage. */
key->size = 0;
}
void
rsa_private_key_clear(struct rsa_private_key *key)
{
mpz_clear(key->d);
mpz_clear(key->p);
mpz_clear(key->q);
mpz_clear(key->a);
mpz_clear(key->b);
mpz_clear(key->c);
}
int
rsa_private_key_prepare(struct rsa_private_key *key)
{
mpz_t n;
/* The size of the product is the sum of the sizes of the factors,
* or sometimes one less. It's possible but tricky to compute the
* size without computing the full product. */
mpz_init(n);
mpz_mul(n, key->p, key->q);
key->size = _rsa_check_size(n);
mpz_clear(n);
return (key->size > 0);
}
/* Computing an rsa root. */
void
rsa_compute_root(const struct rsa_private_key *key,
mpz_t x, const mpz_t m)
{
mpz_t xp; /* modulo p */
mpz_t xq; /* modulo q */
mpz_init(xp); mpz_init(xq);
/* Compute xq = m^d % q = (m%q)^b % q */
mpz_fdiv_r(xq, m, key->q);
mpz_powm(xq, xq, key->b, key->q);
/* Compute xp = m^d % p = (m%p)^a % p */
mpz_fdiv_r(xp, m, key->p);
mpz_powm(xp, xp, key->a, key->p);
/* Set xp' = (xp - xq) c % p. */
mpz_sub(xp, xp, xq);
mpz_mul(xp, xp, key->c);
mpz_fdiv_r(xp, xp, key->p);
/* Finally, compute x = xq + q xp'
*
* To prove that this works, note that
*
* xp = x + i p,
* xq = x + j q,
* c q = 1 + k p
*
* for some integers i, j and k. Now, for some integer l,
*
* xp' = (xp - xq) c + l p
* = (x + i p - (x + j q)) c + l p
* = (i p - j q) c + l p
* = (i c + l) p - j (c q)
* = (i c + l) p - j (1 + kp)
* = (i c + l - j k) p - j
*
* which shows that xp' = -j (mod p). We get
*
* xq + q xp' = x + j q + (i c + l - j k) p q - j q
* = x + (i c + l - j k) p q
*
* so that
*
* xq + q xp' = x (mod pq)
*
* We also get 0 <= xq + q xp' < p q, because
*
* 0 <= xq < q and 0 <= xp' < p.
*/
mpz_mul(x, key->q, xp);
mpz_add(x, x, xq);
mpz_clear(xp); mpz_clear(xq);
}
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