New file with general rsa functions.

Rev: src/nettle/rsa.c:1.1

rsa.c

+/* rsa.c
+ *
+ * The RSA publickey algorithm.
+ */
+
+/* nettle, low-level cryptographics library
+ *
+ * Copyright (C) 2001 Niels Mller
+ *  
+ * 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"
+
+/* FIXME: Perhaps we should split this into several functions, so that
+ * one can link in the signature functions without also getting the
+ * verify functions. */
+
+int
+rsa_init_public_key(struct rsa_public_key *key)
+{
+  unsigned size = (mpz_sizeinbase(key->n, 2) + 7) / 8;
+
+  /* For PKCS#1 to make sense, the size of the modulo, in octets, must
+   * be at least 11 + the length of the DER-encoded Digest Info.
+   *
+   * And a DigestInfo is 34 octets for md5, and 35 octets for sha1.
+   * 46 octets is 368 bits. */
+  
+  if (size < 46)
+    {
+      /* Make sure the signing and verification functions doesn't
+       * try to use this key. */
+      key->size = 0;
+
+      return 0;
+    }
+  else
+    {
+      key->size = size;
+      return 1;
+    }
+}
+
+int
+rsa_init_private_key(struct rsa_private_key *key)
+{
+  return rsa_init_public_key(&key->pub);
+}
+
+#ifndef RSA_CRT
+#define RSA_CRT 1
+#endif
+
+/* Internal function for computing an rsa root.
+ *
+ * NOTE: We don't really need n not e, so we could delete the public
+ * key info from struct rsa_private_key. We do need the size,
+ * though. */
+
+void
+rsa_compute_root(struct rsa_private_key *key, mpz_t x, mpz_t m)
+{
+#if RSA_CRT
+  {
+    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);
+  }  
+#else /* !RSA_CRT */
+  mpz_powm(x, m, key->d, key->pub->n);
+#endif /* !RSA_CRT */
+}
+
+#endif /* HAVE_LIBGMP */