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RSA.java

package gnu.crypto.sig.rsa;

// ----------------------------------------------------------------------------
// $Id: RSA.java,v 1.8 2003/11/09 12:01:26 raif Exp $
//
// Copyright (C) 2001, 2002, 2003 Free Software Foundation, Inc.
//
// This file is part of GNU Crypto.
//
// GNU Crypto is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2, or (at your option)
// any later version.
//
// GNU Crypto 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
// General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; see the file COPYING.  If not, write to the
//
//    Free Software Foundation Inc.,
//    59 Temple Place - Suite 330,
//    Boston, MA 02111-1307
//    USA
//
// Linking this library statically or dynamically with other modules is
// making a combined work based on this library.  Thus, the terms and
// conditions of the GNU General Public License cover the whole
// combination.
//
// As a special exception, the copyright holders of this library give
// you permission to link this library with independent modules to
// produce an executable, regardless of the license terms of these
// independent modules, and to copy and distribute the resulting
// executable under terms of your choice, provided that you also meet,
// for each linked independent module, the terms and conditions of the
// license of that module.  An independent module is a module which is
// not derived from or based on this library.  If you modify this
// library, you may extend this exception to your version of the
// library, but you are not obligated to do so.  If you do not wish to
// do so, delete this exception statement from your version.
// ----------------------------------------------------------------------------

import gnu.crypto.Properties;
import gnu.crypto.util.PRNG;
import gnu.crypto.key.rsa.GnuRSAKey;

import java.math.BigInteger;
import java.security.PrivateKey;
import java.security.PublicKey;
import java.security.interfaces.RSAPrivateCrtKey;
import java.security.interfaces.RSAPrivateKey;
import java.security.interfaces.RSAPublicKey;

/**
 * <p>Utility methods related to the RSA algorithm.</p>
 *
 * <p>References:</p>
 * <ol>
 *    <li><a href="http://www.cosic.esat.kuleuven.ac.be/nessie/workshop/submissions/rsa-pss.zip">
 *    RSA-PSS Signature Scheme with Appendix, part B.</a><br>
 *    Primitive specification and supporting documentation.<br>
 *    Jakob Jonsson and Burt Kaliski.</li>
 *
 *    <li><a href="http://www.ietf.org/rfc/rfc3447.txt">Public-Key Cryptography
 *    Standards (PKCS) #1:</a><br>
 *    RSA Cryptography Specifications Version 2.1.<br>
 *    Jakob Jonsson and Burt Kaliski.</li>
 *
 *    <li><a href="http://crypto.stanford.edu/~dabo/abstracts/ssl-timing.html">
 *    Remote timing attacks are practical</a><br>
 *    D. Boneh and D. Brumley.</li>
 * </ol>
 *
 * @version $Revision: 1.8 $
 */
00079 public class RSA {

   // Constants and variables
   // -------------------------------------------------------------------------

   private static final BigInteger ZERO = BigInteger.ZERO;
   private static final BigInteger ONE = BigInteger.ONE;

   // Constructor(s)
   // -------------------------------------------------------------------------

   /** Trivial private constructor to enforce Singleton pattern. */
00091    private RSA() {
      super();
   }

   // Class methods
   // -------------------------------------------------------------------------

   // Signature and verification methods --------------------------------------

   /**
    * <p>An implementation of the <b>RSASP</b> method: Assuming that the
    * designated RSA private key is a valid one, this method computes a
    * <i>signature representative</i> for a designated <i>message
    * representative</i> signed by the holder of the designated RSA private
    * key.<p>
    *
    * @param K the RSA private key.
    * @param m the <i>message representative</i>: an integer between
    * <code>0</code> and <code>n - 1</code>, where <code>n</code> is the RSA
    * <i>modulus</i>.
    * @return the <i>signature representative</i>, an integer between
    * <code>0</code> and <code>n - 1</code>, where <code>n</code> is the RSA
    * <i>modulus</i>.
    * @throws ClassCastException if <code>K</code> is not an RSA one.
    * @throws IllegalArgumentException if <code>m</code> (the <i>message
    * representative</i>) is out of range.
    */
00118    public static final BigInteger sign(final PrivateKey K, final BigInteger m) {
      try {
         return RSADP((RSAPrivateKey) K, m);
      } catch (IllegalArgumentException x) {
         throw new IllegalArgumentException("message representative out of range");
      }
   }

   /**
    * <p>An implementation of the <b>RSAVP</b> method: Assuming that the
    * designated RSA public key is a valid one, this method computes a
    * <i>message representative</i> for the designated <i>signature
    * representative</i> generated by an RSA private key, for a message
    * intended for the holder of the designated RSA public key.</p>
    *
    * @param K the RSA public key.
    * @param s the <i>signature representative</i>, an integer between
    * <code>0</code> and <code>n - 1</code>, where <code>n</code> is the RSA
    * <i>modulus</i>.
    * @return a <i>message representative</i>: an integer between <code>0</code>
    * and <code>n - 1</code>, where <code>n</code> is the RSA <i>modulus</i>.
    * @throws ClassCastException if <code>K</code> is not an RSA one.
    * @throws IllegalArgumentException if <code>s</code> (the <i>signature
    * representative</i>) is out of range.
    */
00143    public static final BigInteger verify(final PublicKey K, final BigInteger s) {
      try {
         return RSAEP((RSAPublicKey) K, s);
      } catch (IllegalArgumentException x) {
         throw new IllegalArgumentException("signature representative out of range");
      }
   }

   // Encryption and decryption methods ---------------------------------------

   /**
    * <p>An implementation of the <code>RSAEP</code> algorithm.</p>
    *
    * @param K the recipient's RSA public key.
    * @param m the message representative as an MPI.
    * @return the resulting MPI --an MPI between <code>0</code> and
    * <code>n - 1</code> (<code>n</code> being the public shared modulus)-- that
    * will eventually be padded with an appropriate framing/padding scheme.
    * @throws ClassCastException if <code>K</code> is not an RSA one.
    * @throws IllegalArgumentException if <code>m</code>, the message
    * representative is not between <code>0</code> and <code>n - 1</code>
    * (<code>n</code> being the public shared modulus).
    */
00166    public static final BigInteger encrypt(final PublicKey K, final BigInteger m) {
      try {
         return RSAEP((RSAPublicKey) K, m);
      } catch (IllegalArgumentException x) {
         throw new IllegalArgumentException("message representative out of range");
      }
   }

   /**
    * <p>An implementation of the <code>RSADP</code> algorithm.</p>
    *
    * @param K the recipient's RSA private key.
    * @param c the ciphertext representative as an MPI.
    * @return the message representative, an MPI between <code>0</code> and
    * <code>n - 1</code> (<code>n</code> being the shared public modulus).
    * @throws ClassCastException if <code>K</code> is not an RSA one.
    * @throws IllegalArgumentException if <code>c</code>, the ciphertext
    * representative is not between <code>0</code> and <code>n - 1</code>
    * (<code>n</code> being the shared public modulus).
    */
00186    public static final BigInteger decrypt(final PrivateKey K, final BigInteger c) {
      try {
         return RSADP((RSAPrivateKey) K, c);
      } catch (IllegalArgumentException x) {
         throw new IllegalArgumentException("ciphertext representative out of range");
      }
   }

   // Conversion methods ------------------------------------------------------

   /**
    * <p>Converts a <i>multi-precision integer</i> (MPI) <code>s</code> into an
    * octet sequence of length <code>k</code>.</p>
    *
    * @param s the multi-precision integer to convert.
    * @param k the length of the output.
    * @return the result of the transform.
    * @exception IllegalArgumentException if the length in octets of meaningful
    * bytes of <code>s</code> is greater than <code>k</code>.
    */
00206    public static final byte[] I2OSP(final BigInteger s, final int k) {
      byte[] result = s.toByteArray();
      if (result.length < k) {
         final byte[] newResult = new byte[k];
         System.arraycopy(result, 0, newResult, k-result.length, result.length);
         result = newResult;
      } else if (result.length > k) { // leftmost extra bytes should all be 0
         final int limit = result.length - k;
         for (int i = 0; i < limit; i++) {
            if (result[i] != 0x00) {
               throw new IllegalArgumentException("integer too large");
            }
         }
         final byte[] newResult = new byte[k];
         System.arraycopy(result, limit, newResult, 0, k);
         result = newResult;
      }
      return result;
   }

   // helper methods ----------------------------------------------------------

   private static final BigInteger RSAEP(final RSAPublicKey K, final BigInteger m) {
      // 1. If the representative m is not between 0 and n - 1, output
      //    "representative out of range" and stop.
      final BigInteger n = K.getModulus();
      if (m.compareTo(ZERO) < 0 || m.compareTo(n.subtract(ONE)) > 0) {
         throw new IllegalArgumentException();
      }
      // 2. Let c = m^e mod n.
      final BigInteger e = K.getPublicExponent();
      final BigInteger result = m.modPow(e, n);
      // 3. Output c.
      return result;
   }

   private static final BigInteger RSADP(final RSAPrivateKey K, BigInteger c) {
      // 1. If the representative c is not between 0 and n - 1, output
      //    "representative out of range" and stop.
      final BigInteger n = K.getModulus();
      if (c.compareTo(ZERO) < 0 || c.compareTo(n.subtract(ONE)) > 0) {
         throw new IllegalArgumentException();
      }

      // 2. The representative m is computed as follows.
      BigInteger result;
      if (!(K instanceof RSAPrivateCrtKey)) {
         // a. If the first form (n, d) of K is used, let m = c^d mod n.
         final BigInteger d = K.getPrivateExponent();
         result = c.modPow(d, n);
      } else {
         // from [3] p.13 --see class docs:
         // The RSA blinding operation calculates x = (r^e) * g mod n before
         // decryption, where r is random, e is the RSA encryption exponent, and
         // g is the ciphertext to be decrypted. x is then decrypted as normal,
         // followed by division by r, i.e. (x^e) / r mod n. Since r is random,
         // x is random and timing the decryption should not reveal information
         // about the key. Note that r should be a new random number for every
         // decryption.
         final boolean rsaBlinding = Properties.doRSABlinding();
         BigInteger r = null;
         BigInteger e = null;
         if (rsaBlinding) { // pre-decryption
            r = newR(n);
            e = ((RSAPrivateCrtKey) K).getPublicExponent();
            final BigInteger x = r.modPow(e, n).multiply(c).mod(n);
            c = x;
         }

         // b. If the second form (p, q, dP, dQ, qInv) and (r_i, d_i, t_i)
         //    of K is used, proceed as follows:
         final BigInteger p =    ((RSAPrivateCrtKey) K).getPrimeP();
         final BigInteger q =    ((RSAPrivateCrtKey) K).getPrimeQ();
         final BigInteger dP =   ((RSAPrivateCrtKey) K).getPrimeExponentP();
         final BigInteger dQ =   ((RSAPrivateCrtKey) K).getPrimeExponentQ();
         final BigInteger qInv = ((RSAPrivateCrtKey) K).getCrtCoefficient();

         // i.    Let m_1 = c^dP mod p and m_2 = c^dQ mod q.
         final BigInteger m_1 = c.modPow(dP, p);
         final BigInteger m_2 = c.modPow(dQ, q);
         // ii.   If u > 2, let m_i = c^(d_i) mod r_i, i = 3, ..., u.
         // iii.  Let h = (m_1 - m_2) * qInv mod p.
         final BigInteger h = m_1.subtract(m_2).multiply(qInv).mod(p);
         // iv.   Let m = m_2 + q * h.
         result = m_2.add(q.multiply(h));

         if (rsaBlinding) { // post-decryption
            result = result.multiply(r.modInverse(n)).mod(n);
         }
      }

      // 3. Output m
      return result;
   }

   /**
    * <p>Returns a random MPI with a random bit-length of the form <code>8b</code>,
    * where <code>b</code> is in the range <code>[32..64]</code>.</p>
    *
    * @return a random MPI whose length in bytes is between 32 and 64 inclusive.
    */
00307    private static final BigInteger newR(final BigInteger N) {
      final int upper = (N.bitLength() + 7) / 8;
      final int lower = upper / 2;
      final byte[] bl = new byte[1];
      int b;
      do {
         PRNG.nextBytes(bl);
         b = bl[0] & 0xFF;
      } while (b < lower || b > upper);
      final byte[] buffer = new byte[b]; // 256-bit MPI
      PRNG.nextBytes(buffer);
      return new BigInteger(1, buffer);
   }
}

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