Update contrib.
1 /* crypto/des/set_key.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
59 © Portions copyright (c) 2006 Nokia Corporation. All rights reserved.
64 /* set_key.c v 1.4 eay 24/9/91
65 * 1.4 Speed up by 400% :-)
66 * 1.3 added register declarations.
67 * 1.2 unrolled make_key_sched a bit more
68 * 1.1 added norm_expand_bits
69 * 1.0 First working version
72 #if (defined(SYMBIAN) && (defined(__WINSCW__) || defined(__WINS__)))
73 #include "libcrypto_wsd_macros.h"
74 #include "libcrypto_wsd.h"
78 OPENSSL_IMPLEMENT_GLOBAL(int,DES_check_key); /* defaults to false */
80 #define DES_check_key libcrypto_ImpurePtr()->_shadow_DES_check_key
82 static const unsigned char odd_parity[256]={
83 1, 1, 2, 2, 4, 4, 7, 7, 8, 8, 11, 11, 13, 13, 14, 14,
84 16, 16, 19, 19, 21, 21, 22, 22, 25, 25, 26, 26, 28, 28, 31, 31,
85 32, 32, 35, 35, 37, 37, 38, 38, 41, 41, 42, 42, 44, 44, 47, 47,
86 49, 49, 50, 50, 52, 52, 55, 55, 56, 56, 59, 59, 61, 61, 62, 62,
87 64, 64, 67, 67, 69, 69, 70, 70, 73, 73, 74, 74, 76, 76, 79, 79,
88 81, 81, 82, 82, 84, 84, 87, 87, 88, 88, 91, 91, 93, 93, 94, 94,
89 97, 97, 98, 98,100,100,103,103,104,104,107,107,109,109,110,110,
90 112,112,115,115,117,117,118,118,121,121,122,122,124,124,127,127,
91 128,128,131,131,133,133,134,134,137,137,138,138,140,140,143,143,
92 145,145,146,146,148,148,151,151,152,152,155,155,157,157,158,158,
93 161,161,162,162,164,164,167,167,168,168,171,171,173,173,174,174,
94 176,176,179,179,181,181,182,182,185,185,186,186,188,188,191,191,
95 193,193,194,194,196,196,199,199,200,200,203,203,205,205,206,206,
96 208,208,211,211,213,213,214,214,217,217,218,218,220,220,223,223,
97 224,224,227,227,229,229,230,230,233,233,234,234,236,236,239,239,
98 241,241,242,242,244,244,247,247,248,248,251,251,253,253,254,254};
100 EXPORT_C void DES_set_odd_parity(DES_cblock *key)
104 for (i=0; i<DES_KEY_SZ; i++)
105 (*key)[i]=odd_parity[(*key)[i]];
108 EXPORT_C int DES_check_key_parity(const_DES_cblock *key)
112 for (i=0; i<DES_KEY_SZ; i++)
114 if ((*key)[i] != odd_parity[(*key)[i]])
120 /* Weak and semi week keys as take from
123 * %T Security for Computer Networks
124 * %I John Wiley & Sons
126 * Many thanks to smb@ulysses.att.com (Steven Bellovin) for the reference
127 * (and actual cblock values).
129 #define NUM_WEAK_KEY 16
131 static DES_cblock weak_keys[NUM_WEAK_KEY]={
133 {0x01,0x01,0x01,0x01,0x01,0x01,0x01,0x01},
134 {0xFE,0xFE,0xFE,0xFE,0xFE,0xFE,0xFE,0xFE},
135 {0x1F,0x1F,0x1F,0x1F,0x0E,0x0E,0x0E,0x0E},
136 {0xE0,0xE0,0xE0,0xE0,0xF1,0xF1,0xF1,0xF1},
138 {0x01,0xFE,0x01,0xFE,0x01,0xFE,0x01,0xFE},
139 {0xFE,0x01,0xFE,0x01,0xFE,0x01,0xFE,0x01},
140 {0x1F,0xE0,0x1F,0xE0,0x0E,0xF1,0x0E,0xF1},
141 {0xE0,0x1F,0xE0,0x1F,0xF1,0x0E,0xF1,0x0E},
142 {0x01,0xE0,0x01,0xE0,0x01,0xF1,0x01,0xF1},
143 {0xE0,0x01,0xE0,0x01,0xF1,0x01,0xF1,0x01},
144 {0x1F,0xFE,0x1F,0xFE,0x0E,0xFE,0x0E,0xFE},
145 {0xFE,0x1F,0xFE,0x1F,0xFE,0x0E,0xFE,0x0E},
146 {0x01,0x1F,0x01,0x1F,0x01,0x0E,0x01,0x0E},
147 {0x1F,0x01,0x1F,0x01,0x0E,0x01,0x0E,0x01},
148 {0xE0,0xFE,0xE0,0xFE,0xF1,0xFE,0xF1,0xFE},
149 {0xFE,0xE0,0xFE,0xE0,0xFE,0xF1,0xFE,0xF1}};
151 const DES_cblock temp_weak_keys[NUM_WEAK_KEY]={
153 {0x01,0x01,0x01,0x01,0x01,0x01,0x01,0x01},
154 {0xFE,0xFE,0xFE,0xFE,0xFE,0xFE,0xFE,0xFE},
155 {0x1F,0x1F,0x1F,0x1F,0x0E,0x0E,0x0E,0x0E},
156 {0xE0,0xE0,0xE0,0xE0,0xF1,0xF1,0xF1,0xF1},
158 {0x01,0xFE,0x01,0xFE,0x01,0xFE,0x01,0xFE},
159 {0xFE,0x01,0xFE,0x01,0xFE,0x01,0xFE,0x01},
160 {0x1F,0xE0,0x1F,0xE0,0x0E,0xF1,0x0E,0xF1},
161 {0xE0,0x1F,0xE0,0x1F,0xF1,0x0E,0xF1,0x0E},
162 {0x01,0xE0,0x01,0xE0,0x01,0xF1,0x01,0xF1},
163 {0xE0,0x01,0xE0,0x01,0xF1,0x01,0xF1,0x01},
164 {0x1F,0xFE,0x1F,0xFE,0x0E,0xFE,0x0E,0xFE},
165 {0xFE,0x1F,0xFE,0x1F,0xFE,0x0E,0xFE,0x0E},
166 {0x01,0x1F,0x01,0x1F,0x01,0x0E,0x01,0x0E},
167 {0x1F,0x01,0x1F,0x01,0x0E,0x01,0x0E,0x01},
168 {0xE0,0xFE,0xE0,0xFE,0xF1,0xFE,0xF1,0xFE},
169 {0xFE,0xE0,0xFE,0xE0,0xFE,0xF1,0xFE,0xF1}};
171 GET_STATIC_ARRAY_FROM_TLS(weak_keys,set_key_c,DES_cblock)
172 #define weak_keys (GET_WSD_VAR_NAME(weak_keys,set_key_c, s)())
175 EXPORT_C int DES_is_weak_key(const_DES_cblock *key)
179 for (i=0; i<NUM_WEAK_KEY; i++)
180 /* Added == 0 to comparison, I obviously don't run
181 * this section very often :-(, thanks to
182 * engineering@MorningStar.Com for the fix
184 * Another problem, I was comparing only the first 4
186 if (memcmp(weak_keys[i],key,sizeof(DES_cblock)) == 0) return(1);
190 /* NOW DEFINED IN des_local.h
191 * See ecb_encrypt.c for a pseudo description of these macros.
192 * #define PERM_OP(a,b,t,n,m) ((t)=((((a)>>(n))^(b))&(m)),\
194 * (a)=((a)^((t)<<(n))))
197 #define HPERM_OP(a,t,n,m) ((t)=((((a)<<(16-(n)))^(a))&(m)),\
198 (a)=(a)^(t)^(t>>(16-(n))))
200 static const DES_LONG des_skb[8][64]={
202 /* for C bits (numbered as per FIPS 46) 1 2 3 4 5 6 */
203 0x00000000L,0x00000010L,0x20000000L,0x20000010L,
204 0x00010000L,0x00010010L,0x20010000L,0x20010010L,
205 0x00000800L,0x00000810L,0x20000800L,0x20000810L,
206 0x00010800L,0x00010810L,0x20010800L,0x20010810L,
207 0x00000020L,0x00000030L,0x20000020L,0x20000030L,
208 0x00010020L,0x00010030L,0x20010020L,0x20010030L,
209 0x00000820L,0x00000830L,0x20000820L,0x20000830L,
210 0x00010820L,0x00010830L,0x20010820L,0x20010830L,
211 0x00080000L,0x00080010L,0x20080000L,0x20080010L,
212 0x00090000L,0x00090010L,0x20090000L,0x20090010L,
213 0x00080800L,0x00080810L,0x20080800L,0x20080810L,
214 0x00090800L,0x00090810L,0x20090800L,0x20090810L,
215 0x00080020L,0x00080030L,0x20080020L,0x20080030L,
216 0x00090020L,0x00090030L,0x20090020L,0x20090030L,
217 0x00080820L,0x00080830L,0x20080820L,0x20080830L,
218 0x00090820L,0x00090830L,0x20090820L,0x20090830L,
220 /* for C bits (numbered as per FIPS 46) 7 8 10 11 12 13 */
221 0x00000000L,0x02000000L,0x00002000L,0x02002000L,
222 0x00200000L,0x02200000L,0x00202000L,0x02202000L,
223 0x00000004L,0x02000004L,0x00002004L,0x02002004L,
224 0x00200004L,0x02200004L,0x00202004L,0x02202004L,
225 0x00000400L,0x02000400L,0x00002400L,0x02002400L,
226 0x00200400L,0x02200400L,0x00202400L,0x02202400L,
227 0x00000404L,0x02000404L,0x00002404L,0x02002404L,
228 0x00200404L,0x02200404L,0x00202404L,0x02202404L,
229 0x10000000L,0x12000000L,0x10002000L,0x12002000L,
230 0x10200000L,0x12200000L,0x10202000L,0x12202000L,
231 0x10000004L,0x12000004L,0x10002004L,0x12002004L,
232 0x10200004L,0x12200004L,0x10202004L,0x12202004L,
233 0x10000400L,0x12000400L,0x10002400L,0x12002400L,
234 0x10200400L,0x12200400L,0x10202400L,0x12202400L,
235 0x10000404L,0x12000404L,0x10002404L,0x12002404L,
236 0x10200404L,0x12200404L,0x10202404L,0x12202404L,
238 /* for C bits (numbered as per FIPS 46) 14 15 16 17 19 20 */
239 0x00000000L,0x00000001L,0x00040000L,0x00040001L,
240 0x01000000L,0x01000001L,0x01040000L,0x01040001L,
241 0x00000002L,0x00000003L,0x00040002L,0x00040003L,
242 0x01000002L,0x01000003L,0x01040002L,0x01040003L,
243 0x00000200L,0x00000201L,0x00040200L,0x00040201L,
244 0x01000200L,0x01000201L,0x01040200L,0x01040201L,
245 0x00000202L,0x00000203L,0x00040202L,0x00040203L,
246 0x01000202L,0x01000203L,0x01040202L,0x01040203L,
247 0x08000000L,0x08000001L,0x08040000L,0x08040001L,
248 0x09000000L,0x09000001L,0x09040000L,0x09040001L,
249 0x08000002L,0x08000003L,0x08040002L,0x08040003L,
250 0x09000002L,0x09000003L,0x09040002L,0x09040003L,
251 0x08000200L,0x08000201L,0x08040200L,0x08040201L,
252 0x09000200L,0x09000201L,0x09040200L,0x09040201L,
253 0x08000202L,0x08000203L,0x08040202L,0x08040203L,
254 0x09000202L,0x09000203L,0x09040202L,0x09040203L,
256 /* for C bits (numbered as per FIPS 46) 21 23 24 26 27 28 */
257 0x00000000L,0x00100000L,0x00000100L,0x00100100L,
258 0x00000008L,0x00100008L,0x00000108L,0x00100108L,
259 0x00001000L,0x00101000L,0x00001100L,0x00101100L,
260 0x00001008L,0x00101008L,0x00001108L,0x00101108L,
261 0x04000000L,0x04100000L,0x04000100L,0x04100100L,
262 0x04000008L,0x04100008L,0x04000108L,0x04100108L,
263 0x04001000L,0x04101000L,0x04001100L,0x04101100L,
264 0x04001008L,0x04101008L,0x04001108L,0x04101108L,
265 0x00020000L,0x00120000L,0x00020100L,0x00120100L,
266 0x00020008L,0x00120008L,0x00020108L,0x00120108L,
267 0x00021000L,0x00121000L,0x00021100L,0x00121100L,
268 0x00021008L,0x00121008L,0x00021108L,0x00121108L,
269 0x04020000L,0x04120000L,0x04020100L,0x04120100L,
270 0x04020008L,0x04120008L,0x04020108L,0x04120108L,
271 0x04021000L,0x04121000L,0x04021100L,0x04121100L,
272 0x04021008L,0x04121008L,0x04021108L,0x04121108L,
274 /* for D bits (numbered as per FIPS 46) 1 2 3 4 5 6 */
275 0x00000000L,0x10000000L,0x00010000L,0x10010000L,
276 0x00000004L,0x10000004L,0x00010004L,0x10010004L,
277 0x20000000L,0x30000000L,0x20010000L,0x30010000L,
278 0x20000004L,0x30000004L,0x20010004L,0x30010004L,
279 0x00100000L,0x10100000L,0x00110000L,0x10110000L,
280 0x00100004L,0x10100004L,0x00110004L,0x10110004L,
281 0x20100000L,0x30100000L,0x20110000L,0x30110000L,
282 0x20100004L,0x30100004L,0x20110004L,0x30110004L,
283 0x00001000L,0x10001000L,0x00011000L,0x10011000L,
284 0x00001004L,0x10001004L,0x00011004L,0x10011004L,
285 0x20001000L,0x30001000L,0x20011000L,0x30011000L,
286 0x20001004L,0x30001004L,0x20011004L,0x30011004L,
287 0x00101000L,0x10101000L,0x00111000L,0x10111000L,
288 0x00101004L,0x10101004L,0x00111004L,0x10111004L,
289 0x20101000L,0x30101000L,0x20111000L,0x30111000L,
290 0x20101004L,0x30101004L,0x20111004L,0x30111004L,
292 /* for D bits (numbered as per FIPS 46) 8 9 11 12 13 14 */
293 0x00000000L,0x08000000L,0x00000008L,0x08000008L,
294 0x00000400L,0x08000400L,0x00000408L,0x08000408L,
295 0x00020000L,0x08020000L,0x00020008L,0x08020008L,
296 0x00020400L,0x08020400L,0x00020408L,0x08020408L,
297 0x00000001L,0x08000001L,0x00000009L,0x08000009L,
298 0x00000401L,0x08000401L,0x00000409L,0x08000409L,
299 0x00020001L,0x08020001L,0x00020009L,0x08020009L,
300 0x00020401L,0x08020401L,0x00020409L,0x08020409L,
301 0x02000000L,0x0A000000L,0x02000008L,0x0A000008L,
302 0x02000400L,0x0A000400L,0x02000408L,0x0A000408L,
303 0x02020000L,0x0A020000L,0x02020008L,0x0A020008L,
304 0x02020400L,0x0A020400L,0x02020408L,0x0A020408L,
305 0x02000001L,0x0A000001L,0x02000009L,0x0A000009L,
306 0x02000401L,0x0A000401L,0x02000409L,0x0A000409L,
307 0x02020001L,0x0A020001L,0x02020009L,0x0A020009L,
308 0x02020401L,0x0A020401L,0x02020409L,0x0A020409L,
310 /* for D bits (numbered as per FIPS 46) 16 17 18 19 20 21 */
311 0x00000000L,0x00000100L,0x00080000L,0x00080100L,
312 0x01000000L,0x01000100L,0x01080000L,0x01080100L,
313 0x00000010L,0x00000110L,0x00080010L,0x00080110L,
314 0x01000010L,0x01000110L,0x01080010L,0x01080110L,
315 0x00200000L,0x00200100L,0x00280000L,0x00280100L,
316 0x01200000L,0x01200100L,0x01280000L,0x01280100L,
317 0x00200010L,0x00200110L,0x00280010L,0x00280110L,
318 0x01200010L,0x01200110L,0x01280010L,0x01280110L,
319 0x00000200L,0x00000300L,0x00080200L,0x00080300L,
320 0x01000200L,0x01000300L,0x01080200L,0x01080300L,
321 0x00000210L,0x00000310L,0x00080210L,0x00080310L,
322 0x01000210L,0x01000310L,0x01080210L,0x01080310L,
323 0x00200200L,0x00200300L,0x00280200L,0x00280300L,
324 0x01200200L,0x01200300L,0x01280200L,0x01280300L,
325 0x00200210L,0x00200310L,0x00280210L,0x00280310L,
326 0x01200210L,0x01200310L,0x01280210L,0x01280310L,
328 /* for D bits (numbered as per FIPS 46) 22 23 24 25 27 28 */
329 0x00000000L,0x04000000L,0x00040000L,0x04040000L,
330 0x00000002L,0x04000002L,0x00040002L,0x04040002L,
331 0x00002000L,0x04002000L,0x00042000L,0x04042000L,
332 0x00002002L,0x04002002L,0x00042002L,0x04042002L,
333 0x00000020L,0x04000020L,0x00040020L,0x04040020L,
334 0x00000022L,0x04000022L,0x00040022L,0x04040022L,
335 0x00002020L,0x04002020L,0x00042020L,0x04042020L,
336 0x00002022L,0x04002022L,0x00042022L,0x04042022L,
337 0x00000800L,0x04000800L,0x00040800L,0x04040800L,
338 0x00000802L,0x04000802L,0x00040802L,0x04040802L,
339 0x00002800L,0x04002800L,0x00042800L,0x04042800L,
340 0x00002802L,0x04002802L,0x00042802L,0x04042802L,
341 0x00000820L,0x04000820L,0x00040820L,0x04040820L,
342 0x00000822L,0x04000822L,0x00040822L,0x04040822L,
343 0x00002820L,0x04002820L,0x00042820L,0x04042820L,
344 0x00002822L,0x04002822L,0x00042822L,0x04042822L,
347 EXPORT_C int DES_set_key(const_DES_cblock *key, DES_key_schedule *schedule)
351 return DES_set_key_checked(key, schedule);
355 DES_set_key_unchecked(key, schedule);
360 /* return 0 if key parity is odd (correct),
361 * return -1 if key parity error,
362 * return -2 if illegal weak key.
364 EXPORT_C int DES_set_key_checked(const_DES_cblock *key, DES_key_schedule *schedule)
366 if (!DES_check_key_parity(key))
368 if (DES_is_weak_key(key))
370 DES_set_key_unchecked(key, schedule);
374 EXPORT_C void DES_set_key_unchecked(const_DES_cblock *key, DES_key_schedule *schedule)
377 static int shifts2[16]={0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,0};
379 static const int shifts2[16]={0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,0};
381 register DES_LONG c,d,t,s,t2;
382 register const unsigned char *in;
383 register DES_LONG *k;
386 #ifdef OPENBSD_DEV_CRYPTO
387 memcpy(schedule->key,key,sizeof schedule->key);
388 schedule->session=NULL;
390 k = &schedule->ks->deslong[0];
396 /* do PC1 in 47 simple operations :-)
397 * Thanks to John Fletcher (john_fletcher@lccmail.ocf.llnl.gov)
398 * for the inspiration. :-) */
399 PERM_OP (d,c,t,4,0x0f0f0f0fL);
400 HPERM_OP(c,t,-2,0xcccc0000L);
401 HPERM_OP(d,t,-2,0xcccc0000L);
402 PERM_OP (d,c,t,1,0x55555555L);
403 PERM_OP (c,d,t,8,0x00ff00ffL);
404 PERM_OP (d,c,t,1,0x55555555L);
405 d= (((d&0x000000ffL)<<16L)| (d&0x0000ff00L) |
406 ((d&0x00ff0000L)>>16L)|((c&0xf0000000L)>>4L));
409 for (i=0; i<ITERATIONS; i++)
412 { c=((c>>2L)|(c<<26L)); d=((d>>2L)|(d<<26L)); }
414 { c=((c>>1L)|(c<<27L)); d=((d>>1L)|(d<<27L)); }
417 /* could be a few less shifts but I am to lazy at this
418 * point in time to investigate */
419 s= des_skb[0][ (c )&0x3f ]|
420 des_skb[1][((c>> 6L)&0x03)|((c>> 7L)&0x3c)]|
421 des_skb[2][((c>>13L)&0x0f)|((c>>14L)&0x30)]|
422 des_skb[3][((c>>20L)&0x01)|((c>>21L)&0x06) |
424 t= des_skb[4][ (d )&0x3f ]|
425 des_skb[5][((d>> 7L)&0x03)|((d>> 8L)&0x3c)]|
426 des_skb[6][ (d>>15L)&0x3f ]|
427 des_skb[7][((d>>21L)&0x0f)|((d>>22L)&0x30)];
429 /* table contained 0213 4657 */
430 t2=((t<<16L)|(s&0x0000ffffL))&0xffffffffL;
431 *(k++)=ROTATE(t2,30)&0xffffffffL;
433 t2=((s>>16L)|(t&0xffff0000L));
434 *(k++)=ROTATE(t2,26)&0xffffffffL;
438 EXPORT_C int DES_key_sched(const_DES_cblock *key, DES_key_schedule *schedule)
440 return(DES_set_key(key,schedule));
443 #undef des_fixup_key_parity
444 void des_fixup_key_parity(des_cblock *key)
446 des_set_odd_parity(key);