package gnu.crypto.sig.rsa;
// ----------------------------------------------------------------------------
// $Id: RSA.java,v 1.9 2005/10/06 04:24:18 rsdio 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.,
// 51 Franklin Street, Fifth Floor,
// Boston, MA 02110-1301
// 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
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// for each linked independent module, the terms and conditions of the
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// library, you may extend this exception to your version of the
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// 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: 1.9 $
*/
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. */
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.
*/
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.
*/
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).
*/
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).
*/
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>.
*/
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.
*/
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);
}
}