NativeCrypto.java revision 12cd1f00c2fa1a7f37bf644cecdf7588bdc0b0a9
1/*
2 * Copyright (C) 2008 The Android Open Source Project
3 *
4 * Licensed under the Apache License, Version 2.0 (the "License");
5 * you may not use this file except in compliance with the License.
6 * You may obtain a copy of the License at
7 *
8 *      http://www.apache.org/licenses/LICENSE-2.0
9 *
10 * Unless required by applicable law or agreed to in writing, software
11 * distributed under the License is distributed on an "AS IS" BASIS,
12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13 * See the License for the specific language governing permissions and
14 * limitations under the License.
15 */
16
17package org.apache.harmony.xnet.provider.jsse;
18
19import java.io.IOException;
20import java.net.Socket;
21import java.security.PrivateKey;
22import java.security.cert.CertificateException;
23import java.security.interfaces.RSAPublicKey;
24import java.util.ArrayList;
25import java.util.HashMap;
26import java.util.LinkedHashMap;
27import java.util.List;
28import java.util.Map;
29
30/**
31 * Provides the Java side of our JNI glue for OpenSSL.
32 */
33public final class NativeCrypto {
34
35    // --- OpenSSL library initialization --------------------------------------
36    static {
37        clinit();
38    }
39
40    private native static void clinit();
41
42    // --- DSA/RSA public/private key handling functions -----------------------
43
44    public static native int EVP_PKEY_new_DSA(byte[] p, byte[] q, byte[] g,
45                                              byte[] priv_key, byte[] pub_key);
46
47    public static native int EVP_PKEY_new_RSA(byte[] n, byte[] e, byte[] d, byte[] p, byte[] q);
48
49    public static native void EVP_PKEY_free(int pkey);
50
51    // --- General context handling functions (despite the names) --------------
52
53    public static native int EVP_new();
54
55    public static native void EVP_free(int ctx);
56
57    // --- Digest handling functions -------------------------------------------
58
59    public static native void EVP_DigestInit(int ctx, String algorithm);
60
61    public static native void EVP_DigestUpdate(int ctx, byte[] buffer, int offset, int length);
62
63    public static native int EVP_DigestFinal(int ctx, byte[] hash, int offset);
64
65    public static native int EVP_DigestSize(int ctx);
66
67    public static native int EVP_DigestBlockSize(int ctx);
68
69    // --- Signature handling functions ----------------------------------------
70
71    public static native void EVP_VerifyInit(int ctx, String algorithm);
72
73    public static native void EVP_VerifyUpdate(int ctx, byte[] buffer,
74                                               int offset, int length);
75
76    public static native int EVP_VerifyFinal(int ctx, byte[] signature,
77                                             int offset, int length, int key);
78
79    // --- Legacy Signature handling -------------------------------------------
80    // TODO rewrite/replace with EVP_Verify*
81    /**
82     * Verifies an RSA signature. Conceptually, this method doesn't really
83     * belong here, but due to its native code being closely tied to OpenSSL
84     * (just like the rest of this class), we put it here for the time being.
85     * This also solves potential problems with native library initialization.
86     *
87     * @param message The message to verify
88     * @param signature The signature to verify
89     * @param algorithm The hash/sign algorithm to use, i.e. "RSA-SHA1"
90     * @param key The RSA public key to use
91     * @return true if the verification succeeds, false otherwise
92     */
93    public static boolean verifySignature(
94            byte[] message, byte[] signature, String algorithm, RSAPublicKey key) {
95        byte[] modulus = key.getModulus().toByteArray();
96        byte[] exponent = key.getPublicExponent().toByteArray();
97
98        return verifySignature(message, signature, algorithm, modulus, exponent) == 1;
99    }
100
101    private static native int verifySignature(byte[] message, byte[] signature,
102            String algorithm, byte[] modulus, byte[] exponent);
103
104    // --- RAND seeding --------------------------------------------------------
105
106    public static final int RAND_SEED_LENGTH_IN_BYTES = 1024;
107
108    public static native void RAND_seed(byte[] seed);
109
110    public static native int RAND_load_file(String filename, long max_bytes);
111
112    // --- SSL handling --------------------------------------------------------
113
114    private static final String SUPPORTED_PROTOCOL_SSLV3 = "SSLv3";
115    private static final String SUPPORTED_PROTOCOL_TLSV1 = "TLSv1";
116
117    public static final Map<String, String> OPENSSL_TO_STANDARD
118        = new HashMap<String, String>();
119    public static final Map<String, String> STANDARD_TO_OPENSSL
120        = new LinkedHashMap<String, String>();
121
122    private static void add(String standard, String openssl) {
123        OPENSSL_TO_STANDARD.put(openssl, standard);
124        STANDARD_TO_OPENSSL.put(standard, openssl);
125    }
126
127    static {
128        // Note these are added in priority order
129        // Android doesn't currently support Elliptic Curve
130        add("SSL_RSA_WITH_RC4_128_MD5",              "RC4-MD5");
131        add("SSL_RSA_WITH_RC4_128_SHA",              "RC4-SHA");
132        add("TLS_RSA_WITH_AES_128_CBC_SHA",          "AES128-SHA");
133        add("TLS_RSA_WITH_AES_256_CBC_SHA",          "AES256-SHA");
134        // add("TLS_ECDH_ECDSA_WITH_RC4_128_SHA",       "ECDH-ECDSA-RC4-SHA");
135        // add("TLS_ECDH_ECDSA_WITH_AES_128_CBC_SHA",   "ECDH-ECDSA-AES128-SHA");
136        // add("TLS_ECDH_ECDSA_WITH_AES_256_CBC_SHA",   "ECDH-ECDSA-AES256-SHA");
137        // add("TLS_ECDH_RSA_WITH_RC4_128_SHA",         "ECDH-RSA-RC4-SHA");
138        // add("TLS_ECDH_RSA_WITH_AES_128_CBC_SHA",     "ECDH-RSA-AES128-SHA");
139        // add("TLS_ECDH_RSA_WITH_AES_256_CBC_SHA",     "ECDH-RSA-AES256-SHA");
140        // add("TLS_ECDHE_ECDSA_WITH_RC4_128_SHA",      "ECDHE-ECDSA-RC4-SHA");
141        // add("TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA",  "ECDHE-ECDSA-AES128-SHA");
142        // add("TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA",  "ECDHE-ECDSA-AES256-SHA");
143        // add("TLS_ECDHE_RSA_WITH_RC4_128_SHA",        "ECDHE-RSA-RC4-SHA");
144        // add("TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA",    "ECDHE-RSA-AES128-SHA");
145        // add("TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA",    "ECDHE-RSA-AES256-SHA");
146        add("TLS_DHE_RSA_WITH_AES_128_CBC_SHA",      "DHE-RSA-AES128-SHA");
147        add("TLS_DHE_RSA_WITH_AES_256_CBC_SHA",      "DHE-RSA-AES256-SHA");
148        add("TLS_DHE_DSS_WITH_AES_128_CBC_SHA",      "DHE-DSS-AES128-SHA");
149        add("TLS_DHE_DSS_WITH_AES_256_CBC_SHA",      "DHE-DSS-AES256-SHA");
150        add("SSL_RSA_WITH_3DES_EDE_CBC_SHA",         "DES-CBC3-SHA");
151        // add("TLS_ECDH_ECDSA_WITH_3DES_EDE_CBC_SHA",  "ECDH-ECDSA-DES-CBC3-SHA");
152        // add("TLS_ECDH_RSA_WITH_3DES_EDE_CBC_SHA",    "ECDH-RSA-DES-CBC3-SHA");
153        // add("TLS_ECDHE_ECDSA_WITH_3DES_EDE_CBC_SHA", "ECDHE-ECDSA-DES-CBC3-SHA");
154        // add("TLS_ECDHE_RSA_WITH_3DES_EDE_CBC_SHA",   "ECDHE-RSA-DES-CBC3-SHA");
155        add("SSL_DHE_RSA_WITH_3DES_EDE_CBC_SHA",     "EDH-RSA-DES-CBC3-SHA");
156        add("SSL_DHE_DSS_WITH_3DES_EDE_CBC_SHA",     "EDH-DSS-DES-CBC3-SHA");
157        add("SSL_RSA_WITH_DES_CBC_SHA",              "DES-CBC-SHA");
158        add("SSL_DHE_RSA_WITH_DES_CBC_SHA",          "EDH-RSA-DES-CBC-SHA");
159        add("SSL_DHE_DSS_WITH_DES_CBC_SHA",          "EDH-DSS-DES-CBC-SHA");
160        add("SSL_RSA_EXPORT_WITH_RC4_40_MD5",        "EXP-RC4-MD5");
161        add("SSL_RSA_EXPORT_WITH_DES40_CBC_SHA",     "EXP-DES-CBC-SHA");
162        add("SSL_DHE_RSA_EXPORT_WITH_DES40_CBC_SHA", "EXP-EDH-RSA-DES-CBC-SHA");
163        add("SSL_DHE_DSS_EXPORT_WITH_DES40_CBC_SHA", "EXP-EDH-DSS-DES-CBC-SHA");
164        add("SSL_RSA_WITH_NULL_MD5",                 "NULL-MD5");
165        add("SSL_RSA_WITH_NULL_SHA",                 "NULL-SHA");
166        // add("TLS_ECDH_ECDSA_WITH_NULL_SHA",          "ECDH-ECDSA-NULL-SHA");
167        // add("TLS_ECDH_RSA_WITH_NULL_SHA",            "ECDH-RSA-NULL-SHA");
168        // add("TLS_ECDHE_ECDSA_WITH_NULL_SHA",         "ECDHE-ECDSA-NULL-SHA");
169        // add("TLS_ECDHE_RSA_WITH_NULL_SHA",           "ECDHE-RSA-NULL-SHA");
170        add("SSL_DH_anon_WITH_RC4_128_MD5",          "ADH-RC4-MD5");
171        add("TLS_DH_anon_WITH_AES_128_CBC_SHA",      "ADH-AES128-SHA");
172        add("TLS_DH_anon_WITH_AES_256_CBC_SHA",      "ADH-AES256-SHA");
173        add("SSL_DH_anon_WITH_3DES_EDE_CBC_SHA",     "ADH-DES-CBC3-SHA");
174        add("SSL_DH_anon_WITH_DES_CBC_SHA",          "ADH-DES-CBC-SHA");
175        // add("TLS_ECDH_anon_WITH_RC4_128_SHA",        "AECDH-RC4-SHA");
176        // add("TLS_ECDH_anon_WITH_AES_128_CBC_SHA",    "AECDH-AES128-SHA");
177        // add("TLS_ECDH_anon_WITH_AES_256_CBC_SHA",    "AECDH-AES256-SHA");
178        // add("TLS_ECDH_anon_WITH_3DES_EDE_CBC_SHA",   "AECDH-DES-CBC3-SHA");
179        add("SSL_DH_anon_EXPORT_WITH_RC4_40_MD5",    "EXP-ADH-RC4-MD5");
180        add("SSL_DH_anon_EXPORT_WITH_DES40_CBC_SHA", "EXP-ADH-DES-CBC-SHA");
181        // add("TLS_ECDH_anon_WITH_NULL_SHA",           "AECDH-NULL-SHA");
182
183        // No Kerberos in Android
184        // add("TLS_KRB5_WITH_RC4_128_SHA",           "KRB5-RC4-SHA");
185        // add("TLS_KRB5_WITH_RC4_128_MD5",           "KRB5-RC4-MD5");
186        // add("TLS_KRB5_WITH_3DES_EDE_CBC_SHA",      "KRB5-DES-CBC3-SHA");
187        // add("TLS_KRB5_WITH_3DES_EDE_CBC_MD5",      "KRB5-DES-CBC3-MD5");
188        // add("TLS_KRB5_WITH_DES_CBC_SHA",           "KRB5-DES-CBC-SHA");
189        // add("TLS_KRB5_WITH_DES_CBC_MD5",           "KRB5-DES-CBC-MD5");
190        // add("TLS_KRB5_EXPORT_WITH_RC4_40_SHA",     "EXP-KRB5-RC4-SHA");
191        // add("TLS_KRB5_EXPORT_WITH_RC4_40_MD5",     "EXP-KRB5-RC4-MD5");
192        // add("TLS_KRB5_EXPORT_WITH_DES_CBC_40_SHA", "EXP-KRB5-DES-CBC-SHA");
193        // add("TLS_KRB5_EXPORT_WITH_DES_CBC_40_MD5", "EXP-KRB5-DES-CBC-MD5");
194
195        // not implemented by either RI or OpenSSL
196        // add("SSL_DH_DSS_EXPORT_WITH_DES40_CBC_SHA", null);
197        // add("SSL_DH_RSA_EXPORT_WITH_DES40_CBC_SHA", null);
198
199        // EXPORT1024 suites were never standardized but were widely implemented.
200        // OpenSSL 0.9.8c and later have disabled TLS1_ALLOW_EXPERIMENTAL_CIPHERSUITES
201        // add("SSL_RSA_EXPORT1024_WITH_DES_CBC_SHA", "EXP1024-DES-CBC-SHA");
202        // add("SSL_RSA_EXPORT1024_WITH_RC4_56_SHA",  "EXP1024-RC4-SHA");
203
204        // No RC2
205        // add("SSL_RSA_EXPORT_WITH_RC2_CBC_40_MD5",  "EXP-RC2-CBC-MD5");
206        // add("TLS_KRB5_EXPORT_WITH_RC2_CBC_40_SHA", "EXP-KRB5-RC2-CBC-SHA");
207        // add("TLS_KRB5_EXPORT_WITH_RC2_CBC_40_MD5", "EXP-KRB5-RC2-CBC-MD5");
208
209        // PSK is Private Shared Key - didn't exist in Froyo's openssl - no JSSE equivalent
210        // add(null, "PSK-3DES-EDE-CBC-SHA");
211        // add(null, "PSK-AES128-CBC-SHA");
212        // add(null, "PSK-AES256-CBC-SHA");
213        // add(null, "PSK-RC4-SHA");
214
215    }
216
217    private static final String[] SUPPORTED_CIPHER_SUITES
218        = STANDARD_TO_OPENSSL.keySet().toArray(new String[0]);
219
220    // SSL mode
221    public static long SSL_MODE_HANDSHAKE_CUTTHROUGH = 0x00000040L;
222
223    // SSL options
224    public static long SSL_OP_NO_SSLv3 = 0x02000000L;
225    public static long SSL_OP_NO_TLSv1 = 0x04000000L;
226
227    public static native int SSL_CTX_new();
228
229    public static String[] getDefaultCipherSuites() {
230        return new String[] {
231            "SSL_RSA_WITH_RC4_128_MD5",
232            "SSL_RSA_WITH_RC4_128_SHA",
233            "TLS_RSA_WITH_AES_128_CBC_SHA",
234            "TLS_DHE_RSA_WITH_AES_128_CBC_SHA",
235            "TLS_DHE_DSS_WITH_AES_128_CBC_SHA",
236            "SSL_RSA_WITH_3DES_EDE_CBC_SHA",
237            "SSL_DHE_RSA_WITH_3DES_EDE_CBC_SHA",
238            "SSL_DHE_DSS_WITH_3DES_EDE_CBC_SHA",
239            "SSL_RSA_WITH_DES_CBC_SHA",
240            "SSL_DHE_RSA_WITH_DES_CBC_SHA",
241            "SSL_DHE_DSS_WITH_DES_CBC_SHA",
242            "SSL_RSA_EXPORT_WITH_RC4_40_MD5",
243            "SSL_RSA_EXPORT_WITH_DES40_CBC_SHA",
244            "SSL_DHE_RSA_EXPORT_WITH_DES40_CBC_SHA",
245            "SSL_DHE_DSS_EXPORT_WITH_DES40_CBC_SHA"
246        };
247    }
248
249    public static String[] getSupportedCipherSuites() {
250        return SUPPORTED_CIPHER_SUITES.clone();
251    }
252
253    public static native void SSL_CTX_free(int ssl_ctx);
254
255    public static native int SSL_new(int ssl_ctx) throws IOException;
256
257    public static final String[] KEY_TYPES = new String[] { "RSA", "DSA", "DH_RSA" , "DH_DSA" };
258
259    public static native void SSL_use_certificate(int ssl, byte[][] asn1DerEncodedCertificate);
260
261    public static native void SSL_use_PrivateKey(int ssl, byte[] pkcs8EncodedPrivateKey);
262
263    public static native void SSL_check_private_key(int ssl);
264
265    public static native long SSL_get_mode(int ssl);
266
267    public static native long SSL_set_mode(int ssl, long mode);
268
269    public static native long SSL_clear_mode(int ssl, long mode);
270
271    public static native long SSL_get_options(int ssl);
272
273    public static native long SSL_set_options(int ssl, long options);
274
275    public static native long SSL_clear_options(int ssl, long options);
276
277    public static String[] getSupportedProtocols() {
278        return new String[] { SUPPORTED_PROTOCOL_SSLV3, SUPPORTED_PROTOCOL_TLSV1 };
279    }
280
281    public static void setEnabledProtocols(int ssl, String[] protocols) {
282        if (protocols == null) {
283            throw new IllegalArgumentException("protocols == null");
284        }
285
286        // openssl uses negative logic letting you disable protocols.
287        // so first, assume we need to set all (disable all) and clear none (enable none).
288        // in the loop, selectively move bits from set to clear (from disable to enable)
289        long optionsToSet = (SSL_OP_NO_SSLv3 | SSL_OP_NO_TLSv1);
290        long optionsToClear = 0;
291        for (int i = 0; i < protocols.length; i++) {
292            String protocol = protocols[i];
293            if (protocol == null) {
294                throw new IllegalArgumentException("protocols[" + i + "] == null");
295            }
296            if (protocol.equals(SUPPORTED_PROTOCOL_SSLV3)) {
297                optionsToSet &= ~SSL_OP_NO_SSLv3;
298                optionsToClear |= SSL_OP_NO_SSLv3;
299            } else if (protocol.equals(SUPPORTED_PROTOCOL_TLSV1)) {
300                optionsToSet &= ~SSL_OP_NO_TLSv1;
301                optionsToClear |= SSL_OP_NO_TLSv1;
302            } else {
303                throw new IllegalArgumentException("protocol " + protocol
304                                                   + " is not supported");
305            }
306        }
307
308        SSL_set_options(ssl, optionsToSet);
309        SSL_clear_options(ssl, optionsToClear);
310    }
311
312    public static String[] checkEnabledProtocols(String[] protocols) {
313        if (protocols == null) {
314            throw new IllegalArgumentException("protocols == null");
315        }
316        for (int i = 0; i < protocols.length; i++) {
317            String protocol = protocols[i];
318            if (protocol == null) {
319                throw new IllegalArgumentException("protocols[" + i + "] == null");
320            }
321            if ((!protocol.equals(SUPPORTED_PROTOCOL_SSLV3))
322                    && (!protocol.equals(SUPPORTED_PROTOCOL_TLSV1))) {
323                throw new IllegalArgumentException("protocol " + protocol
324                                                   + " is not supported");
325            }
326        }
327        return protocols;
328    }
329
330    public static native void SSL_set_cipher_lists(int ssl, String[] ciphers);
331
332    public static void setEnabledCipherSuites(int ssl, String[] cipherSuites) {
333        checkEnabledCipherSuites(cipherSuites);
334        List<String> opensslSuites = new ArrayList<String>();
335        for (int i = 0; i < cipherSuites.length; i++) {
336            String cipherSuite = cipherSuites[i];
337            String openssl = STANDARD_TO_OPENSSL.get(cipherSuite);
338            String cs = (openssl == null) ? cipherSuite : openssl;
339            opensslSuites.add(cs);
340        }
341        SSL_set_cipher_lists(ssl, opensslSuites.toArray(new String[opensslSuites.size()]));
342    }
343
344    public static String[] checkEnabledCipherSuites(String[] cipherSuites) {
345        if (cipherSuites == null) {
346            throw new IllegalArgumentException("cipherSuites == null");
347        }
348        // makes sure all suites are valid, throwing on error
349        for (int i = 0; i < cipherSuites.length; i++) {
350            String cipherSuite = cipherSuites[i];
351            if (cipherSuite == null) {
352                throw new IllegalArgumentException("cipherSuites[" + i + "] == null");
353            }
354            if (STANDARD_TO_OPENSSL.containsKey(cipherSuite)) {
355                continue;
356            }
357            if (OPENSSL_TO_STANDARD.containsKey(cipherSuite)) {
358                // TODO log warning about using backward compatability
359                continue;
360            }
361            throw new IllegalArgumentException("cipherSuite " + cipherSuite + " is not supported.");
362        }
363        return cipherSuites;
364    }
365
366    /*
367     * See the OpenSSL ssl.h header file for more information.
368     */
369    public static final int SSL_VERIFY_NONE =                 0x00;
370    public static final int SSL_VERIFY_PEER =                 0x01;
371    public static final int SSL_VERIFY_FAIL_IF_NO_PEER_CERT = 0x02;
372    public static final int SSL_VERIFY_CLIENT_ONCE =          0x04;
373
374    public static native void SSL_set_verify(int sslNativePointer, int mode) throws IOException;
375
376    public static native void SSL_set_session(int sslNativePointer, int sslSessionNativePointer)
377        throws IOException;
378
379    public static native void SSL_set_session_creation_enabled(
380            int sslNativePointer, boolean creationEnabled) throws IOException;
381
382    /**
383     * Returns the sslSessionNativePointer of the negotiated session
384     */
385    public static native int SSL_do_handshake(int sslNativePointer,
386                                              Socket sock,
387                                              SSLHandshakeCallbacks shc,
388                                              int timeout,
389                                              boolean client_mode)
390        throws IOException, CertificateException;
391
392    public static native byte[][] SSL_get_certificate(int sslNativePointer);
393
394    /**
395     * Reads with the native SSL_read function from the encrypted data stream
396     * @return -1 if error or the end of the stream is reached.
397     */
398    public static native int SSL_read_byte(int sslNativePointer, int timeout) throws IOException;
399    public static native int SSL_read(int sslNativePointer, byte[] b, int off, int len, int timeout)
400        throws IOException;
401
402    /**
403     * Writes with the native SSL_write function to the encrypted data stream.
404     */
405    public static native void SSL_write_byte(int sslNativePointer, int b) throws IOException;
406    public static native void SSL_write(int sslNativePointer, byte[] b, int off, int len)
407        throws IOException;
408
409    public static native void SSL_interrupt(int sslNativePointer) throws IOException;
410    public static native void SSL_shutdown(int sslNativePointer) throws IOException;
411
412    public static native void SSL_free(int sslNativePointer);
413
414    public static native byte[] SSL_SESSION_session_id(int sslSessionNativePointer);
415
416    /**
417     * Returns the X509 certificates of the peer in the PEM format.
418     */
419    public static native byte[][] SSL_SESSION_get_peer_cert_chain(int sslCtxNativePointer,
420                                                                  int sslSessionNativePointer);
421
422    public static native long SSL_SESSION_get_time(int sslSessionNativePointer);
423
424    public static native String SSL_SESSION_get_version(int sslSessionNativePointer);
425
426    public static native String SSL_SESSION_cipher(int sslSessionNativePointer);
427
428    public static native void SSL_SESSION_free(int sslSessionNativePointer);
429
430    public static native byte[] i2d_SSL_SESSION(int sslSessionNativePointer);
431
432    public static native int d2i_SSL_SESSION(byte[] data, int size);
433
434    /**
435     * A collection of callbacks from the native OpenSSL code that are
436     * related to the SSL handshake initiated by SSL_do_handshake.
437     */
438    public interface SSLHandshakeCallbacks {
439        /**
440         * Verify that we trust the certificate chain is trusted.
441         *
442         * @param bytes An array of certficates in PEM encode bytes
443         * @param authMethod auth algorithm name
444         *
445         * @throws CertificateException if the certificate is untrusted
446         */
447        public void verifyCertificateChain(byte[][] bytes, String authMethod)
448            throws CertificateException;
449
450        /**
451         * Called on an SSL client when the server requests (or
452         * requires a certificate). The client can respond by using
453         * SSL_use_certificate and SSL_use_PrivateKey to set a
454         * certificate if has an appropriate one available, similar to
455         * how the server provides its certificate.
456         *
457         * @param keyType One of KEY_TYPES such as RSA or DSA
458         */
459        public void clientCertificateRequested(String keyType)
460            throws IOException;
461
462        /**
463         * Called when SSL handshake is completed. Note that this can
464         * be after SSL_do_handshake returns when handshake cutthrough
465         * is enabled.
466         */
467        public void handshakeCompleted();
468    }
469}
470