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+/* RSA.java --
+ Copyright (C) 2001, 2002, 2003, 2006 Free Software Foundation, Inc.
+
+This file is a part of GNU Classpath.
+
+GNU Classpath 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 of the License, or (at
+your option) any later version.
+
+GNU Classpath 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 GNU Classpath; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, 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 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. */
+
+
+package gnu.java.security.sig.rsa;
+
+import gnu.java.security.Properties;
+import gnu.java.security.util.PRNG;
+
+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;
+
+/**
+ * Utility methods related to the RSA algorithm.
+ * <p>
+ * References:
+ * <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>
+ */
+public class RSA
+{
+ private static final BigInteger ZERO = BigInteger.ZERO;
+
+ private static final BigInteger ONE = BigInteger.ONE;
+
+ /** Our default source of randomness. */
+ private static final PRNG prng = PRNG.getInstance();
+
+ /** Trivial private constructor to enforce Singleton pattern. */
+ private RSA()
+ {
+ super();
+ }
+
+ /**
+ * 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.
+ *
+ * @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");
+ }
+ }
+
+ /**
+ * 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.
+ *
+ * @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");
+ }
+ }
+
+ /**
+ * An implementation of the <code>RSAEP</code> algorithm.
+ *
+ * @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");
+ }
+ }
+
+ /**
+ * An implementation of the <code>RSADP</code> algorithm.
+ *
+ * @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");
+ }
+ }
+
+ /**
+ * Converts a <i>multi-precision integer</i> (MPI) <code>s</code> into an
+ * octet sequence of length <code>k</code>.
+ *
+ * @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;
+ }
+
+ 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;
+ }
+
+ /**
+ * 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>.
+ *
+ * @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);
+ }
+}