1 /* RSA.java -- 2 Copyright (C) 2001, 2002, 2003, 2006 Free Software Foundation, Inc. 3 4 This file is a part of GNU Classpath. 5 6 GNU Classpath is free software; you can redistribute it and/or modify 7 it under the terms of the GNU General Public License as published by 8 the Free Software Foundation; either version 2 of the License, or (at 9 your option) any later version. 10 11 GNU Classpath is distributed in the hope that it will be useful, but 12 WITHOUT ANY WARRANTY; without even the implied warranty of 13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 14 General Public License for more details. 15 16 You should have received a copy of the GNU General Public License 17 along with GNU Classpath; if not, write to the Free Software 18 Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 19 USA 20 21 Linking this library statically or dynamically with other modules is 22 making a combined work based on this library. Thus, the terms and 23 conditions of the GNU General Public License cover the whole 24 combination. 25 26 As a special exception, the copyright holders of this library give you 27 permission to link this library with independent modules to produce an 28 executable, regardless of the license terms of these independent 29 modules, and to copy and distribute the resulting executable under 30 terms of your choice, provided that you also meet, for each linked 31 independent module, the terms and conditions of the license of that 32 module. An independent module is a module which is not derived from 33 or based on this library. If you modify this library, you may extend 34 this exception to your version of the library, but you are not 35 obligated to do so. If you do not wish to do so, delete this 36 exception statement from your version. */ 37 38 39 package gnu.java.security.sig.rsa; 40 41 import gnu.java.security.Properties; 42 import gnu.java.security.util.PRNG; 43 44 import java.math.BigInteger; 45 import java.security.PrivateKey; 46 import java.security.PublicKey; 47 import java.security.interfaces.RSAPrivateCrtKey; 48 import java.security.interfaces.RSAPrivateKey; 49 import java.security.interfaces.RSAPublicKey; 50 51 /** 52 * Utility methods related to the RSA algorithm. 53 * <p> 54 * References: 55 * <ol> 56 * <li><a 57 * href="http://www.cosic.esat.kuleuven.ac.be/nessie/workshop/submissions/rsa-pss.zip"> 58 * RSA-PSS Signature Scheme with Appendix, part B.</a><br> 59 * Primitive specification and supporting documentation.<br> 60 * Jakob Jonsson and Burt Kaliski.</li> 61 * <li><a href="http://www.ietf.org/rfc/rfc3447.txt">Public-Key Cryptography 62 * Standards (PKCS) #1:</a><br> 63 * RSA Cryptography Specifications Version 2.1.<br> 64 * Jakob Jonsson and Burt Kaliski.</li> 65 * <li><a href="http://crypto.stanford.edu/~dabo/abstracts/ssl-timing.html"> 66 * Remote timing attacks are practical</a><br> 67 * D. Boneh and D. Brumley.</li> 68 * </ol> 69 */ 70 public class RSA 71 { 72 private static final BigInteger ZERO = BigInteger.ZERO; 73 74 private static final BigInteger ONE = BigInteger.ONE; 75 76 /** Our default source of randomness. */ 77 private static final PRNG prng = PRNG.getInstance(); 78 79 /** Trivial private constructor to enforce Singleton pattern. */ RSA()80 private RSA() 81 { 82 super(); 83 } 84 85 /** 86 * An implementation of the <b>RSASP</b> method: Assuming that the designated 87 * RSA private key is a valid one, this method computes a <i>signature 88 * representative</i> for a designated <i>message representative</i> signed 89 * by the holder of the designated RSA private key. 90 * 91 * @param K the RSA private key. 92 * @param m the <i>message representative</i>: an integer between 93 * <code>0</code> and <code>n - 1</code>, where <code>n</code> 94 * is the RSA <i>modulus</i>. 95 * @return the <i>signature representative</i>, an integer between 96 * <code>0</code> and <code>n - 1</code>, where <code>n</code> 97 * is the RSA <i>modulus</i>. 98 * @throws ClassCastException if <code>K</code> is not an RSA one. 99 * @throws IllegalArgumentException if <code>m</code> (the <i>message 100 * representative</i>) is out of range. 101 */ sign(final PrivateKey K, final BigInteger m)102 public static final BigInteger sign(final PrivateKey K, final BigInteger m) 103 { 104 try 105 { 106 return RSADP((RSAPrivateKey) K, m); 107 } 108 catch (IllegalArgumentException x) 109 { 110 throw new IllegalArgumentException("message representative out of range"); 111 } 112 } 113 114 /** 115 * An implementation of the <b>RSAVP</b> method: Assuming that the designated 116 * RSA public key is a valid one, this method computes a <i>message 117 * representative</i> for the designated <i>signature representative</i> 118 * generated by an RSA private key, for a message intended for the holder of 119 * the designated RSA public key. 120 * 121 * @param K the RSA public key. 122 * @param s the <i>signature representative</i>, an integer between 123 * <code>0</code> and <code>n - 1</code>, where <code>n</code> 124 * is the RSA <i>modulus</i>. 125 * @return a <i>message representative</i>: an integer between <code>0</code> 126 * and <code>n - 1</code>, where <code>n</code> is the RSA 127 * <i>modulus</i>. 128 * @throws ClassCastException if <code>K</code> is not an RSA one. 129 * @throws IllegalArgumentException if <code>s</code> (the <i>signature 130 * representative</i>) is out of range. 131 */ verify(final PublicKey K, final BigInteger s)132 public static final BigInteger verify(final PublicKey K, final BigInteger s) 133 { 134 try 135 { 136 return RSAEP((RSAPublicKey) K, s); 137 } 138 catch (IllegalArgumentException x) 139 { 140 throw new IllegalArgumentException("signature representative out of range"); 141 } 142 } 143 144 /** 145 * An implementation of the <code>RSAEP</code> algorithm. 146 * 147 * @param K the recipient's RSA public key. 148 * @param m the message representative as an MPI. 149 * @return the resulting MPI --an MPI between <code>0</code> and 150 * <code>n - 1</code> (<code>n</code> being the public shared 151 * modulus)-- that will eventually be padded with an appropriate 152 * framing/padding scheme. 153 * @throws ClassCastException if <code>K</code> is not an RSA one. 154 * @throws IllegalArgumentException if <code>m</code>, the message 155 * representative is not between <code>0</code> and 156 * <code>n - 1</code> (<code>n</code> being the public shared 157 * modulus). 158 */ encrypt(final PublicKey K, final BigInteger m)159 public static final BigInteger encrypt(final PublicKey K, final BigInteger m) 160 { 161 try 162 { 163 return RSAEP((RSAPublicKey) K, m); 164 } 165 catch (IllegalArgumentException x) 166 { 167 throw new IllegalArgumentException("message representative out of range"); 168 } 169 } 170 171 /** 172 * An implementation of the <code>RSADP</code> algorithm. 173 * 174 * @param K the recipient's RSA private key. 175 * @param c the ciphertext representative as an MPI. 176 * @return the message representative, an MPI between <code>0</code> and 177 * <code>n - 1</code> (<code>n</code> being the shared public 178 * modulus). 179 * @throws ClassCastException if <code>K</code> is not an RSA one. 180 * @throws IllegalArgumentException if <code>c</code>, the ciphertext 181 * representative is not between <code>0</code> and 182 * <code>n - 1</code> (<code>n</code> being the shared public 183 * modulus). 184 */ decrypt(final PrivateKey K, final BigInteger c)185 public static final BigInteger decrypt(final PrivateKey K, final BigInteger c) 186 { 187 try 188 { 189 return RSADP((RSAPrivateKey) K, c); 190 } 191 catch (IllegalArgumentException x) 192 { 193 throw new IllegalArgumentException("ciphertext representative out of range"); 194 } 195 } 196 197 /** 198 * Converts a <i>multi-precision integer</i> (MPI) <code>s</code> into an 199 * octet sequence of length <code>k</code>. 200 * 201 * @param s the multi-precision integer to convert. 202 * @param k the length of the output. 203 * @return the result of the transform. 204 * @exception IllegalArgumentException if the length in octets of meaningful 205 * bytes of <code>s</code> is greater than <code>k</code>. 206 */ I2OSP(final BigInteger s, final int k)207 public static final byte[] I2OSP(final BigInteger s, final int k) 208 { 209 byte[] result = s.toByteArray(); 210 if (result.length < k) 211 { 212 final byte[] newResult = new byte[k]; 213 System.arraycopy(result, 0, newResult, k - result.length, result.length); 214 result = newResult; 215 } 216 else if (result.length > k) 217 { // leftmost extra bytes should all be 0 218 final int limit = result.length - k; 219 for (int i = 0; i < limit; i++) 220 { 221 if (result[i] != 0x00) 222 throw new IllegalArgumentException("integer too large"); 223 } 224 final byte[] newResult = new byte[k]; 225 System.arraycopy(result, limit, newResult, 0, k); 226 result = newResult; 227 } 228 return result; 229 } 230 RSAEP(final RSAPublicKey K, final BigInteger m)231 private static final BigInteger RSAEP(final RSAPublicKey K, final BigInteger m) 232 { 233 // 1. If the representative m is not between 0 and n - 1, output 234 // "representative out of range" and stop. 235 final BigInteger n = K.getModulus(); 236 if (m.compareTo(ZERO) < 0 || m.compareTo(n.subtract(ONE)) > 0) 237 throw new IllegalArgumentException(); 238 // 2. Let c = m^e mod n. 239 final BigInteger e = K.getPublicExponent(); 240 final BigInteger result = m.modPow(e, n); 241 // 3. Output c. 242 return result; 243 } 244 RSADP(final RSAPrivateKey K, BigInteger c)245 private static final BigInteger RSADP(final RSAPrivateKey K, BigInteger c) 246 { 247 // 1. If the representative c is not between 0 and n - 1, output 248 // "representative out of range" and stop. 249 final BigInteger n = K.getModulus(); 250 if (c.compareTo(ZERO) < 0 || c.compareTo(n.subtract(ONE)) > 0) 251 throw new IllegalArgumentException(); 252 // 2. The representative m is computed as follows. 253 BigInteger result; 254 if (! (K instanceof RSAPrivateCrtKey)) 255 { 256 // a. If the first form (n, d) of K is used, let m = c^d mod n. 257 final BigInteger d = K.getPrivateExponent(); 258 result = c.modPow(d, n); 259 } 260 else 261 { 262 // from [3] p.13 --see class docs: 263 // The RSA blinding operation calculates x = (r^e) * g mod n before 264 // decryption, where r is random, e is the RSA encryption exponent, and 265 // g is the ciphertext to be decrypted. x is then decrypted as normal, 266 // followed by division by r, i.e. (x^e) / r mod n. Since r is random, 267 // x is random and timing the decryption should not reveal information 268 // about the key. Note that r should be a new random number for every 269 // decryption. 270 final boolean rsaBlinding = Properties.doRSABlinding(); 271 BigInteger r = null; 272 BigInteger e = null; 273 if (rsaBlinding) 274 { // pre-decryption 275 r = newR(n); 276 e = ((RSAPrivateCrtKey) K).getPublicExponent(); 277 final BigInteger x = r.modPow(e, n).multiply(c).mod(n); 278 c = x; 279 } 280 // b. If the second form (p, q, dP, dQ, qInv) and (r_i, d_i, t_i) 281 // of K is used, proceed as follows: 282 final BigInteger p = ((RSAPrivateCrtKey) K).getPrimeP(); 283 final BigInteger q = ((RSAPrivateCrtKey) K).getPrimeQ(); 284 final BigInteger dP = ((RSAPrivateCrtKey) K).getPrimeExponentP(); 285 final BigInteger dQ = ((RSAPrivateCrtKey) K).getPrimeExponentQ(); 286 final BigInteger qInv = ((RSAPrivateCrtKey) K).getCrtCoefficient(); 287 // i. Let m_1 = c^dP mod p and m_2 = c^dQ mod q. 288 final BigInteger m_1 = c.modPow(dP, p); 289 final BigInteger m_2 = c.modPow(dQ, q); 290 // ii. If u > 2, let m_i = c^(d_i) mod r_i, i = 3, ..., u. 291 // iii. Let h = (m_1 - m_2) * qInv mod p. 292 final BigInteger h = m_1.subtract(m_2).multiply(qInv).mod(p); 293 // iv. Let m = m_2 + q * h. 294 result = m_2.add(q.multiply(h)); 295 if (rsaBlinding) // post-decryption 296 result = result.multiply(r.modInverse(n)).mod(n); 297 } 298 // 3. Output m 299 return result; 300 } 301 302 /** 303 * Returns a random MPI with a random bit-length of the form <code>8b</code>, 304 * where <code>b</code> is in the range <code>[32..64]</code>. 305 * 306 * @return a random MPI whose length in bytes is between 32 and 64 inclusive. 307 */ newR(final BigInteger N)308 private static final BigInteger newR(final BigInteger N) 309 { 310 final int upper = (N.bitLength() + 7) / 8; 311 final int lower = upper / 2; 312 final byte[] bl = new byte[1]; 313 int b; 314 do 315 { 316 prng.nextBytes(bl); 317 b = bl[0] & 0xFF; 318 } 319 while (b < lower || b > upper); 320 final byte[] buffer = new byte[b]; // 256-bit MPI 321 prng.nextBytes(buffer); 322 return new BigInteger(1, buffer); 323 } 324 } 325