author  paulson 
Mon, 29 Sep 1997 11:47:01 +0200  
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child 3919  c036caebfc75 
permissions  rwrr 
1839  1 
(* Title: HOL/Auth/Message 
2 
ID: $Id$ 

3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 

4 
Copyright 1996 University of Cambridge 

5 

6 
Datatypes of agents and messages; 

1913  7 
Inductive relations "parts", "analz" and "synth" 
1839  8 
*) 
9 

3702  10 

11 
(*Eliminates a commonlyoccurring expression*) 

12 
goal HOL.thy "~ (ALL x. x~=y)"; 

13 
by (Blast_tac 1); 

14 
Addsimps [result()]; 

15 

1839  16 
open Message; 
17 

3668  18 
AddIffs atomic.inject; 
19 
AddIffs msg.inject; 

1839  20 

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(*Holds because Friend is injective: thus cannot prove for all f*) 
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goal thy "(Friend x : Friend``A) = (x:A)"; 
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by (Auto_tac()); 
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qed "Friend_image_eq"; 
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Addsimps [Friend_image_eq]; 
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1839  28 
(** Inverse of keys **) 
29 

30 
goal thy "!!K K'. (invKey K = invKey K') = (K=K')"; 

3730  31 
by Safe_tac; 
2032  32 
by (rtac box_equals 1); 
1839  33 
by (REPEAT (rtac invKey 2)); 
34 
by (Asm_simp_tac 1); 

35 
qed "invKey_eq"; 

36 

37 
Addsimps [invKey, invKey_eq]; 

38 

39 

40 
(**** keysFor operator ****) 

41 

42 
goalw thy [keysFor_def] "keysFor {} = {}"; 

2891  43 
by (Blast_tac 1); 
1839  44 
qed "keysFor_empty"; 
45 

46 
goalw thy [keysFor_def] "keysFor (H Un H') = keysFor H Un keysFor H'"; 

2891  47 
by (Blast_tac 1); 
1839  48 
qed "keysFor_Un"; 
49 

50 
goalw thy [keysFor_def] "keysFor (UN i. H i) = (UN i. keysFor (H i))"; 

2891  51 
by (Blast_tac 1); 
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qed "keysFor_UN1"; 
1839  53 

54 
(*Monotonicity*) 

55 
goalw thy [keysFor_def] "!!G H. G<=H ==> keysFor(G) <= keysFor(H)"; 

2891  56 
by (Blast_tac 1); 
1839  57 
qed "keysFor_mono"; 
58 

59 
goalw thy [keysFor_def] "keysFor (insert (Agent A) H) = keysFor H"; 

3102  60 
by (Blast_tac 1); 
1839  61 
qed "keysFor_insert_Agent"; 
62 

63 
goalw thy [keysFor_def] "keysFor (insert (Nonce N) H) = keysFor H"; 

3102  64 
by (Blast_tac 1); 
1839  65 
qed "keysFor_insert_Nonce"; 
66 

3668  67 
goalw thy [keysFor_def] "keysFor (insert (Number N) H) = keysFor H"; 
68 
by (Blast_tac 1); 

69 
qed "keysFor_insert_Number"; 

70 

1839  71 
goalw thy [keysFor_def] "keysFor (insert (Key K) H) = keysFor H"; 
3102  72 
by (Blast_tac 1); 
1839  73 
qed "keysFor_insert_Key"; 
74 

2373  75 
goalw thy [keysFor_def] "keysFor (insert (Hash X) H) = keysFor H"; 
3102  76 
by (Blast_tac 1); 
2373  77 
qed "keysFor_insert_Hash"; 
78 

1839  79 
goalw thy [keysFor_def] "keysFor (insert {X,Y} H) = keysFor H"; 
3102  80 
by (Blast_tac 1); 
1839  81 
qed "keysFor_insert_MPair"; 
82 

83 
goalw thy [keysFor_def] 

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"keysFor (insert (Crypt K X) H) = insert (invKey K) (keysFor H)"; 
1839  85 
by (Auto_tac()); 
86 
qed "keysFor_insert_Crypt"; 

87 

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Addsimps [keysFor_empty, keysFor_Un, keysFor_UN1, 
3668  89 
keysFor_insert_Agent, keysFor_insert_Nonce, 
90 
keysFor_insert_Number, keysFor_insert_Key, 

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keysFor_insert_Hash, keysFor_insert_MPair, keysFor_insert_Crypt]; 
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AddSEs [keysFor_Un RS equalityD1 RS subsetD RS UnE, 
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keysFor_UN1 RS equalityD1 RS subsetD RS UN1_E]; 
1839  94 

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goalw thy [keysFor_def] "keysFor (Key``E) = {}"; 
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by (Auto_tac ()); 
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qed "keysFor_image_Key"; 
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Addsimps [keysFor_image_Key]; 
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goalw thy [keysFor_def] "!!H. Crypt K X : H ==> invKey K : keysFor H"; 
2891  101 
by (Blast_tac 1); 
2068  102 
qed "Crypt_imp_invKey_keysFor"; 
103 

1839  104 

105 
(**** Inductive relation "parts" ****) 

106 

107 
val major::prems = 

108 
goal thy "[ {X,Y} : parts H; \ 

109 
\ [ X : parts H; Y : parts H ] ==> P \ 

110 
\ ] ==> P"; 

111 
by (cut_facts_tac [major] 1); 

2032  112 
by (resolve_tac prems 1); 
1839  113 
by (REPEAT (eresolve_tac [asm_rl, parts.Fst, parts.Snd] 1)); 
114 
qed "MPair_parts"; 

115 

116 
AddIs [parts.Inj]; 

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val partsEs = [MPair_parts, make_elim parts.Body]; 
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AddSEs partsEs; 
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(*NB These two rules are UNSAFE in the formal sense, as they discard the 
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compound message. They work well on THIS FILE, perhaps because its 
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proofs concern only atomic messages.*) 
1839  124 

125 
goal thy "H <= parts(H)"; 

2891  126 
by (Blast_tac 1); 
1839  127 
qed "parts_increasing"; 
128 

129 
(*Monotonicity*) 

130 
goalw thy parts.defs "!!G H. G<=H ==> parts(G) <= parts(H)"; 

131 
by (rtac lfp_mono 1); 

132 
by (REPEAT (ares_tac basic_monos 1)); 

133 
qed "parts_mono"; 

134 

2373  135 
val parts_insertI = impOfSubs (subset_insertI RS parts_mono); 
136 

1839  137 
goal thy "parts{} = {}"; 
3730  138 
by Safe_tac; 
2032  139 
by (etac parts.induct 1); 
2891  140 
by (ALLGOALS Blast_tac); 
1839  141 
qed "parts_empty"; 
142 
Addsimps [parts_empty]; 

143 

144 
goal thy "!!X. X: parts{} ==> P"; 

145 
by (Asm_full_simp_tac 1); 

146 
qed "parts_emptyE"; 

147 
AddSEs [parts_emptyE]; 

148 

1893  149 
(*WARNING: loops if H = {Y}, therefore must not be repeated!*) 
150 
goal thy "!!H. X: parts H ==> EX Y:H. X: parts {Y}"; 

2032  151 
by (etac parts.induct 1); 
2891  152 
by (ALLGOALS Blast_tac); 
1893  153 
qed "parts_singleton"; 
154 

1839  155 

156 
(** Unions **) 

157 

158 
goal thy "parts(G) Un parts(H) <= parts(G Un H)"; 

159 
by (REPEAT (ares_tac [Un_least, parts_mono, Un_upper1, Un_upper2] 1)); 

160 
val parts_Un_subset1 = result(); 

161 

162 
goal thy "parts(G Un H) <= parts(G) Un parts(H)"; 

2032  163 
by (rtac subsetI 1); 
164 
by (etac parts.induct 1); 

2891  165 
by (ALLGOALS Blast_tac); 
1839  166 
val parts_Un_subset2 = result(); 
167 

168 
goal thy "parts(G Un H) = parts(G) Un parts(H)"; 

169 
by (REPEAT (ares_tac [equalityI, parts_Un_subset1, parts_Un_subset2] 1)); 

170 
qed "parts_Un"; 

171 

2011  172 
goal thy "parts (insert X H) = parts {X} Un parts H"; 
1852  173 
by (stac (read_instantiate [("A","H")] insert_is_Un) 1); 
2011  174 
by (simp_tac (HOL_ss addsimps [parts_Un]) 1); 
175 
qed "parts_insert"; 

176 

177 
(*TWO inserts to avoid looping. This rewrite is better than nothing. 

178 
Not suitable for Addsimps: its behaviour can be strange.*) 

179 
goal thy "parts (insert X (insert Y H)) = parts {X} Un parts {Y} Un parts H"; 

180 
by (simp_tac (!simpset addsimps [Un_assoc]) 1); 

181 
by (simp_tac (!simpset addsimps [parts_insert RS sym]) 1); 

1852  182 
qed "parts_insert2"; 
183 

1839  184 
goal thy "(UN x:A. parts(H x)) <= parts(UN x:A. H x)"; 
185 
by (REPEAT (ares_tac [UN_least, parts_mono, UN_upper] 1)); 

186 
val parts_UN_subset1 = result(); 

187 

188 
goal thy "parts(UN x:A. H x) <= (UN x:A. parts(H x))"; 

2032  189 
by (rtac subsetI 1); 
190 
by (etac parts.induct 1); 

2891  191 
by (ALLGOALS Blast_tac); 
1839  192 
val parts_UN_subset2 = result(); 
193 

194 
goal thy "parts(UN x:A. H x) = (UN x:A. parts(H x))"; 

195 
by (REPEAT (ares_tac [equalityI, parts_UN_subset1, parts_UN_subset2] 1)); 

196 
qed "parts_UN"; 

197 

198 
goal thy "parts(UN x. H x) = (UN x. parts(H x))"; 

199 
by (simp_tac (!simpset addsimps [UNION1_def, parts_UN]) 1); 

200 
qed "parts_UN1"; 

201 

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(*Added to simplify arguments to parts, analz and synth. 
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NOTE: the UN versions are no longer used!*) 
1839  204 
Addsimps [parts_Un, parts_UN, parts_UN1]; 
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AddSEs [parts_Un RS equalityD1 RS subsetD RS UnE, 
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parts_UN RS equalityD1 RS subsetD RS UN_E, 
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parts_UN1 RS equalityD1 RS subsetD RS UN1_E]; 
1839  208 

209 
goal thy "insert X (parts H) <= parts(insert X H)"; 

2922  210 
by (blast_tac (!claset addIs [impOfSubs parts_mono]) 1); 
1839  211 
qed "parts_insert_subset"; 
212 

213 
(** Idempotence and transitivity **) 

214 

215 
goal thy "!!H. X: parts (parts H) ==> X: parts H"; 

2032  216 
by (etac parts.induct 1); 
2891  217 
by (ALLGOALS Blast_tac); 
2922  218 
qed "parts_partsD"; 
219 
AddSDs [parts_partsD]; 

1839  220 

221 
goal thy "parts (parts H) = parts H"; 

2891  222 
by (Blast_tac 1); 
1839  223 
qed "parts_idem"; 
224 
Addsimps [parts_idem]; 

225 

226 
goal thy "!!H. [ X: parts G; G <= parts H ] ==> X: parts H"; 

227 
by (dtac parts_mono 1); 

2891  228 
by (Blast_tac 1); 
1839  229 
qed "parts_trans"; 
230 

231 
(*Cut*) 

2373  232 
goal thy "!!H. [ Y: parts (insert X G); X: parts H ] \ 
233 
\ ==> Y: parts (G Un H)"; 

2032  234 
by (etac parts_trans 1); 
2373  235 
by (Auto_tac()); 
1839  236 
qed "parts_cut"; 
237 

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goal thy "!!H. X: parts H ==> parts (insert X H) = parts H"; 
2373  239 
by (fast_tac (!claset addSDs [parts_cut] 
240 
addIs [parts_insertI] 

241 
addss (!simpset)) 1); 

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qed "parts_cut_eq"; 
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Addsimps [parts_cut_eq]; 
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1839  246 

247 
(** Rewrite rules for pulling out atomic messages **) 

248 

2373  249 
fun parts_tac i = 
250 
EVERY [rtac ([subsetI, parts_insert_subset] MRS equalityI) i, 

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etac parts.induct i, 
3102  252 
REPEAT (Blast_tac i)]; 
2373  253 

1839  254 
goal thy "parts (insert (Agent agt) H) = insert (Agent agt) (parts H)"; 
2373  255 
by (parts_tac 1); 
1839  256 
qed "parts_insert_Agent"; 
257 

258 
goal thy "parts (insert (Nonce N) H) = insert (Nonce N) (parts H)"; 

2373  259 
by (parts_tac 1); 
1839  260 
qed "parts_insert_Nonce"; 
261 

3668  262 
goal thy "parts (insert (Number N) H) = insert (Number N) (parts H)"; 
263 
by (parts_tac 1); 

264 
qed "parts_insert_Number"; 

265 

1839  266 
goal thy "parts (insert (Key K) H) = insert (Key K) (parts H)"; 
2373  267 
by (parts_tac 1); 
1839  268 
qed "parts_insert_Key"; 
269 

2373  270 
goal thy "parts (insert (Hash X) H) = insert (Hash X) (parts H)"; 
271 
by (parts_tac 1); 

272 
qed "parts_insert_Hash"; 

273 

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goal thy "parts (insert (Crypt K X) H) = \ 
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\ insert (Crypt K X) (parts (insert X H))"; 
2032  276 
by (rtac equalityI 1); 
277 
by (rtac subsetI 1); 

278 
by (etac parts.induct 1); 

1839  279 
by (Auto_tac()); 
2032  280 
by (etac parts.induct 1); 
2922  281 
by (ALLGOALS (blast_tac (!claset addIs [parts.Body]))); 
1839  282 
qed "parts_insert_Crypt"; 
283 

284 
goal thy "parts (insert {X,Y} H) = \ 

285 
\ insert {X,Y} (parts (insert X (insert Y H)))"; 

2032  286 
by (rtac equalityI 1); 
287 
by (rtac subsetI 1); 

288 
by (etac parts.induct 1); 

1839  289 
by (Auto_tac()); 
2032  290 
by (etac parts.induct 1); 
2922  291 
by (ALLGOALS (blast_tac (!claset addIs [parts.Fst, parts.Snd]))); 
1839  292 
qed "parts_insert_MPair"; 
293 

3668  294 
Addsimps [parts_insert_Agent, parts_insert_Nonce, 
295 
parts_insert_Number, parts_insert_Key, 

2373  296 
parts_insert_Hash, parts_insert_Crypt, parts_insert_MPair]; 
1839  297 

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goal thy "parts (Key``N) = Key``N"; 
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by (Auto_tac()); 
2032  301 
by (etac parts.induct 1); 
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by (Auto_tac()); 
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qed "parts_image_Key"; 
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Addsimps [parts_image_Key]; 
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(*In any message, there is an upper bound N on its greatest nonce.*) 
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goal thy "EX N. ALL n. N<=n > Nonce n ~: parts {msg}"; 
3668  309 
by (induct_tac "msg" 1); 
310 
by (induct_tac "atomic" 1); 

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by (ALLGOALS (asm_simp_tac (!simpset addsimps [exI, parts_insert2]))); 
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(*MPair case: blast_tac works out the necessary sum itself!*) 
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by (blast_tac (!claset addSEs [add_leE]) 2); 
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(*Nonce case*) 
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by (res_inst_tac [("x","N + Suc nat")] exI 1); 
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by (fast_tac (!claset addSEs [add_leE] addaltern trans_tac) 1); 
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qed "msg_Nonce_supply"; 
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1913  320 
(**** Inductive relation "analz" ****) 
1839  321 

322 
val major::prems = 

1913  323 
goal thy "[ {X,Y} : analz H; \ 
324 
\ [ X : analz H; Y : analz H ] ==> P \ 

1839  325 
\ ] ==> P"; 
326 
by (cut_facts_tac [major] 1); 

2032  327 
by (resolve_tac prems 1); 
1913  328 
by (REPEAT (eresolve_tac [asm_rl, analz.Fst, analz.Snd] 1)); 
329 
qed "MPair_analz"; 

1839  330 

1913  331 
AddIs [analz.Inj]; 
2011  332 
AddSEs [MPair_analz]; (*Perhaps it should NOT be deemed safe!*) 
1913  333 
AddDs [analz.Decrypt]; 
1839  334 

1913  335 
Addsimps [analz.Inj]; 
1885  336 

1913  337 
goal thy "H <= analz(H)"; 
2891  338 
by (Blast_tac 1); 
1913  339 
qed "analz_increasing"; 
1839  340 

1913  341 
goal thy "analz H <= parts H"; 
1839  342 
by (rtac subsetI 1); 
2032  343 
by (etac analz.induct 1); 
2891  344 
by (ALLGOALS Blast_tac); 
1913  345 
qed "analz_subset_parts"; 
1839  346 

1913  347 
bind_thm ("not_parts_not_analz", analz_subset_parts RS contra_subsetD); 
1839  348 

349 

1913  350 
goal thy "parts (analz H) = parts H"; 
2032  351 
by (rtac equalityI 1); 
352 
by (rtac (analz_subset_parts RS parts_mono RS subset_trans) 1); 

1839  353 
by (Simp_tac 1); 
2891  354 
by (blast_tac (!claset addIs [analz_increasing RS parts_mono RS subsetD]) 1); 
1913  355 
qed "parts_analz"; 
356 
Addsimps [parts_analz]; 

1839  357 

1913  358 
goal thy "analz (parts H) = parts H"; 
1885  359 
by (Auto_tac()); 
2032  360 
by (etac analz.induct 1); 
1885  361 
by (Auto_tac()); 
1913  362 
qed "analz_parts"; 
363 
Addsimps [analz_parts]; 

1885  364 

1839  365 
(*Monotonicity; Lemma 1 of Lowe*) 
1913  366 
goalw thy analz.defs "!!G H. G<=H ==> analz(G) <= analz(H)"; 
1839  367 
by (rtac lfp_mono 1); 
368 
by (REPEAT (ares_tac basic_monos 1)); 

1913  369 
qed "analz_mono"; 
1839  370 

2373  371 
val analz_insertI = impOfSubs (subset_insertI RS analz_mono); 
372 

1839  373 
(** General equational properties **) 
374 

1913  375 
goal thy "analz{} = {}"; 
3730  376 
by Safe_tac; 
2032  377 
by (etac analz.induct 1); 
2891  378 
by (ALLGOALS Blast_tac); 
1913  379 
qed "analz_empty"; 
380 
Addsimps [analz_empty]; 

1839  381 

1913  382 
(*Converse fails: we can analz more from the union than from the 
1839  383 
separate parts, as a key in one might decrypt a message in the other*) 
1913  384 
goal thy "analz(G) Un analz(H) <= analz(G Un H)"; 
385 
by (REPEAT (ares_tac [Un_least, analz_mono, Un_upper1, Un_upper2] 1)); 

386 
qed "analz_Un"; 

1839  387 

1913  388 
goal thy "insert X (analz H) <= analz(insert X H)"; 
2922  389 
by (blast_tac (!claset addIs [impOfSubs analz_mono]) 1); 
1913  390 
qed "analz_insert"; 
1839  391 

392 
(** Rewrite rules for pulling out atomic messages **) 

393 

2373  394 
fun analz_tac i = 
395 
EVERY [rtac ([subsetI, analz_insert] MRS equalityI) i, 

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396 
etac analz.induct i, 
3102  397 
REPEAT (Blast_tac i)]; 
2373  398 

1913  399 
goal thy "analz (insert (Agent agt) H) = insert (Agent agt) (analz H)"; 
2373  400 
by (analz_tac 1); 
1913  401 
qed "analz_insert_Agent"; 
1839  402 

1913  403 
goal thy "analz (insert (Nonce N) H) = insert (Nonce N) (analz H)"; 
2373  404 
by (analz_tac 1); 
1913  405 
qed "analz_insert_Nonce"; 
1839  406 

3668  407 
goal thy "analz (insert (Number N) H) = insert (Number N) (analz H)"; 
408 
by (analz_tac 1); 

409 
qed "analz_insert_Number"; 

410 

2373  411 
goal thy "analz (insert (Hash X) H) = insert (Hash X) (analz H)"; 
412 
by (analz_tac 1); 

413 
qed "analz_insert_Hash"; 

414 

1839  415 
(*Can only pull out Keys if they are not needed to decrypt the rest*) 
416 
goalw thy [keysFor_def] 

1913  417 
"!!K. K ~: keysFor (analz H) ==> \ 
418 
\ analz (insert (Key K) H) = insert (Key K) (analz H)"; 

2373  419 
by (analz_tac 1); 
1913  420 
qed "analz_insert_Key"; 
1839  421 

1913  422 
goal thy "analz (insert {X,Y} H) = \ 
423 
\ insert {X,Y} (analz (insert X (insert Y H)))"; 

2032  424 
by (rtac equalityI 1); 
425 
by (rtac subsetI 1); 

426 
by (etac analz.induct 1); 

1885  427 
by (Auto_tac()); 
2032  428 
by (etac analz.induct 1); 
2922  429 
by (ALLGOALS (blast_tac (!claset addIs [analz.Fst, analz.Snd]))); 
1913  430 
qed "analz_insert_MPair"; 
1885  431 

432 
(*Can pull out enCrypted message if the Key is not known*) 

1913  433 
goal thy "!!H. Key (invKey K) ~: analz H ==> \ 
2284
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434 
\ analz (insert (Crypt K X) H) = \ 
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435 
\ insert (Crypt K X) (analz H)"; 
2373  436 
by (analz_tac 1); 
1913  437 
qed "analz_insert_Crypt"; 
1839  438 

1913  439 
goal thy "!!H. Key (invKey K) : analz H ==> \ 
2284
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440 
\ analz (insert (Crypt K X) H) <= \ 
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441 
\ insert (Crypt K X) (analz (insert X H))"; 
2032  442 
by (rtac subsetI 1); 
1913  443 
by (eres_inst_tac [("za","x")] analz.induct 1); 
3102  444 
by (ALLGOALS (Blast_tac)); 
1839  445 
val lemma1 = result(); 
446 

1913  447 
goal thy "!!H. Key (invKey K) : analz H ==> \ 
2284
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changeset

448 
\ insert (Crypt K X) (analz (insert X H)) <= \ 
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449 
\ analz (insert (Crypt K X) H)"; 
1839  450 
by (Auto_tac()); 
1913  451 
by (eres_inst_tac [("za","x")] analz.induct 1); 
1839  452 
by (Auto_tac()); 
3449  453 
by (blast_tac (!claset addIs [analz_insertI, analz.Decrypt]) 1); 
1839  454 
val lemma2 = result(); 
455 

1913  456 
goal thy "!!H. Key (invKey K) : analz H ==> \ 
2284
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diff
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457 
\ analz (insert (Crypt K X) H) = \ 
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diff
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458 
\ insert (Crypt K X) (analz (insert X H))"; 
1839  459 
by (REPEAT (ares_tac [equalityI, lemma1, lemma2] 1)); 
1913  460 
qed "analz_insert_Decrypt"; 
1839  461 

1885  462 
(*Case analysis: either the message is secure, or it is not! 
1946  463 
Effective, but can cause subgoals to blow up! 
1885  464 
Use with expand_if; apparently split_tac does not cope with patterns 
2284
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diff
changeset

465 
such as "analz (insert (Crypt K X) H)" *) 
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changeset

466 
goal thy "analz (insert (Crypt K X) H) = \ 
2154  467 
\ (if (Key (invKey K) : analz H) \ 
2284
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diff
changeset

468 
\ then insert (Crypt K X) (analz (insert X H)) \ 
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diff
changeset

469 
\ else insert (Crypt K X) (analz H))"; 
2102  470 
by (case_tac "Key (invKey K) : analz H " 1); 
1913  471 
by (ALLGOALS (asm_simp_tac (!simpset addsimps [analz_insert_Crypt, 
2032  472 
analz_insert_Decrypt]))); 
1913  473 
qed "analz_Crypt_if"; 
1885  474 

3668  475 
Addsimps [analz_insert_Agent, analz_insert_Nonce, 
476 
analz_insert_Number, analz_insert_Key, 

2516
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2484
diff
changeset

477 
analz_insert_Hash, analz_insert_MPair, analz_Crypt_if]; 
1839  478 

479 
(*This rule supposes "for the sake of argument" that we have the key.*) 

2284
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2170
diff
changeset

480 
goal thy "analz (insert (Crypt K X) H) <= \ 
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parents:
2170
diff
changeset

481 
\ insert (Crypt K X) (analz (insert X H))"; 
2032  482 
by (rtac subsetI 1); 
483 
by (etac analz.induct 1); 

1839  484 
by (Auto_tac()); 
1913  485 
qed "analz_insert_Crypt_subset"; 
1839  486 

487 

2026
0df5a96bf77e
Last working version prior to introduction of "lost"
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parents:
2011
diff
changeset

488 
goal thy "analz (Key``N) = Key``N"; 
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Last working version prior to introduction of "lost"
paulson
parents:
2011
diff
changeset

489 
by (Auto_tac()); 
2032  490 
by (etac analz.induct 1); 
2026
0df5a96bf77e
Last working version prior to introduction of "lost"
paulson
parents:
2011
diff
changeset

491 
by (Auto_tac()); 
0df5a96bf77e
Last working version prior to introduction of "lost"
paulson
parents:
2011
diff
changeset

492 
qed "analz_image_Key"; 
0df5a96bf77e
Last working version prior to introduction of "lost"
paulson
parents:
2011
diff
changeset

493 

0df5a96bf77e
Last working version prior to introduction of "lost"
paulson
parents:
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diff
changeset

494 
Addsimps [analz_image_Key]; 
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Last working version prior to introduction of "lost"
paulson
parents:
2011
diff
changeset

495 

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Last working version prior to introduction of "lost"
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parents:
2011
diff
changeset

496 

1839  497 
(** Idempotence and transitivity **) 
498 

1913  499 
goal thy "!!H. X: analz (analz H) ==> X: analz H"; 
2032  500 
by (etac analz.induct 1); 
2891  501 
by (ALLGOALS Blast_tac); 
2922  502 
qed "analz_analzD"; 
503 
AddSDs [analz_analzD]; 

1839  504 

1913  505 
goal thy "analz (analz H) = analz H"; 
2891  506 
by (Blast_tac 1); 
1913  507 
qed "analz_idem"; 
508 
Addsimps [analz_idem]; 

1839  509 

1913  510 
goal thy "!!H. [ X: analz G; G <= analz H ] ==> X: analz H"; 
511 
by (dtac analz_mono 1); 

2891  512 
by (Blast_tac 1); 
1913  513 
qed "analz_trans"; 
1839  514 

515 
(*Cut; Lemma 2 of Lowe*) 

1998
f8230821f1e8
Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents:
1994
diff
changeset

516 
goal thy "!!H. [ Y: analz (insert X H); X: analz H ] ==> Y: analz H"; 
2032  517 
by (etac analz_trans 1); 
2891  518 
by (Blast_tac 1); 
1913  519 
qed "analz_cut"; 
1839  520 

521 
(*Cut can be proved easily by induction on 

1913  522 
"!!H. Y: analz (insert X H) ==> X: analz H > Y: analz H" 
1839  523 
*) 
524 

3449  525 
(*This rewrite rule helps in the simplification of messages that involve 
526 
the forwarding of unknown components (X). Without it, removing occurrences 

527 
of X can be very complicated. *) 

3431  528 
goal thy "!!H. X: analz H ==> analz (insert X H) = analz H"; 
529 
by (blast_tac (!claset addIs [analz_cut, analz_insertI]) 1); 

530 
qed "analz_insert_eq"; 

531 

1885  532 

1913  533 
(** A congruence rule for "analz" **) 
1885  534 

1913  535 
goal thy "!!H. [ analz G <= analz G'; analz H <= analz H' \ 
536 
\ ] ==> analz (G Un H) <= analz (G' Un H')"; 

3714  537 
by (Clarify_tac 1); 
2032  538 
by (etac analz.induct 1); 
1913  539 
by (ALLGOALS (best_tac (!claset addIs [analz_mono RS subsetD]))); 
540 
qed "analz_subset_cong"; 

1885  541 

1913  542 
goal thy "!!H. [ analz G = analz G'; analz H = analz H' \ 
543 
\ ] ==> analz (G Un H) = analz (G' Un H')"; 

544 
by (REPEAT_FIRST (ares_tac [equalityI, analz_subset_cong] 

2032  545 
ORELSE' etac equalityE)); 
1913  546 
qed "analz_cong"; 
1885  547 

548 

1913  549 
goal thy "!!H. analz H = analz H' ==> analz(insert X H) = analz(insert X H')"; 
3583
5a47b869d16a
Had to remove {x.x=a} = a from !simpset in one proof.
nipkow
parents:
3519
diff
changeset

550 
by (asm_simp_tac (!simpset addsimps [insert_def] delsimps [singleton_conv] 
2032  551 
setloop (rtac analz_cong)) 1); 
1913  552 
qed "analz_insert_cong"; 
1885  553 

1913  554 
(*If there are no pairs or encryptions then analz does nothing*) 
2284
80ebd1a213fd
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paulson
parents:
2170
diff
changeset

555 
goal thy "!!H. [ ALL X Y. {X,Y} ~: H; ALL X K. Crypt K X ~: H ] ==> \ 
1913  556 
\ analz H = H"; 
3730  557 
by Safe_tac; 
2032  558 
by (etac analz.induct 1); 
2891  559 
by (ALLGOALS Blast_tac); 
1913  560 
qed "analz_trivial"; 
1839  561 

562 
(*Helps to prove Fake cases*) 

1913  563 
goal thy "!!X. X: analz (UN i. analz (H i)) ==> X: analz (UN i. H i)"; 
2032  564 
by (etac analz.induct 1); 
2922  565 
by (ALLGOALS (blast_tac (!claset addIs [impOfSubs analz_mono]))); 
1839  566 
val lemma = result(); 
567 

1913  568 
goal thy "analz (UN i. analz (H i)) = analz (UN i. H i)"; 
2922  569 
by (blast_tac (!claset addIs [lemma, impOfSubs analz_mono]) 1); 
1913  570 
qed "analz_UN_analz"; 
571 
Addsimps [analz_UN_analz]; 

1839  572 

573 

1913  574 
(**** Inductive relation "synth" ****) 
1839  575 

1913  576 
AddIs synth.intrs; 
1839  577 

2011  578 
(*Can only produce a nonce or key if it is already known, 
579 
but can synth a pair or encryption from its components...*) 

3668  580 
val mk_cases = synth.mk_cases (atomic.simps @ msg.simps); 
2011  581 

3668  582 
(*NO Agent_synth, as any Agent name can be synthesized. Ditto for Number*) 
2011  583 
val Nonce_synth = mk_cases "Nonce n : synth H"; 
584 
val Key_synth = mk_cases "Key K : synth H"; 

2373  585 
val Hash_synth = mk_cases "Hash X : synth H"; 
2011  586 
val MPair_synth = mk_cases "{X,Y} : synth H"; 
2284
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parents:
2170
diff
changeset

587 
val Crypt_synth = mk_cases "Crypt K X : synth H"; 
2011  588 

2373  589 
AddSEs [Nonce_synth, Key_synth, Hash_synth, MPair_synth, Crypt_synth]; 
2011  590 

1913  591 
goal thy "H <= synth(H)"; 
2891  592 
by (Blast_tac 1); 
1913  593 
qed "synth_increasing"; 
1839  594 

595 
(*Monotonicity*) 

1913  596 
goalw thy synth.defs "!!G H. G<=H ==> synth(G) <= synth(H)"; 
1839  597 
by (rtac lfp_mono 1); 
598 
by (REPEAT (ares_tac basic_monos 1)); 

1913  599 
qed "synth_mono"; 
1839  600 

601 
(** Unions **) 

602 

1913  603 
(*Converse fails: we can synth more from the union than from the 
1839  604 
separate parts, building a compound message using elements of each.*) 
1913  605 
goal thy "synth(G) Un synth(H) <= synth(G Un H)"; 
606 
by (REPEAT (ares_tac [Un_least, synth_mono, Un_upper1, Un_upper2] 1)); 

607 
qed "synth_Un"; 

1839  608 

1913  609 
goal thy "insert X (synth H) <= synth(insert X H)"; 
2922  610 
by (blast_tac (!claset addIs [impOfSubs synth_mono]) 1); 
1913  611 
qed "synth_insert"; 
1885  612 

1839  613 
(** Idempotence and transitivity **) 
614 

1913  615 
goal thy "!!H. X: synth (synth H) ==> X: synth H"; 
2032  616 
by (etac synth.induct 1); 
2891  617 
by (ALLGOALS Blast_tac); 
2922  618 
qed "synth_synthD"; 
619 
AddSDs [synth_synthD]; 

1839  620 

1913  621 
goal thy "synth (synth H) = synth H"; 
2891  622 
by (Blast_tac 1); 
1913  623 
qed "synth_idem"; 
1839  624 

1913  625 
goal thy "!!H. [ X: synth G; G <= synth H ] ==> X: synth H"; 
626 
by (dtac synth_mono 1); 

2891  627 
by (Blast_tac 1); 
1913  628 
qed "synth_trans"; 
1839  629 

630 
(*Cut; Lemma 2 of Lowe*) 

1998
f8230821f1e8
Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents:
1994
diff
changeset

631 
goal thy "!!H. [ Y: synth (insert X H); X: synth H ] ==> Y: synth H"; 
2032  632 
by (etac synth_trans 1); 
2891  633 
by (Blast_tac 1); 
1913  634 
qed "synth_cut"; 
1839  635 

1946  636 
goal thy "Agent A : synth H"; 
2891  637 
by (Blast_tac 1); 
1946  638 
qed "Agent_synth"; 
639 

3668  640 
goal thy "Number n : synth H"; 
641 
by (Blast_tac 1); 

642 
qed "Number_synth"; 

643 

1913  644 
goal thy "(Nonce N : synth H) = (Nonce N : H)"; 
2891  645 
by (Blast_tac 1); 
1913  646 
qed "Nonce_synth_eq"; 
1839  647 

1913  648 
goal thy "(Key K : synth H) = (Key K : H)"; 
2891  649 
by (Blast_tac 1); 
1913  650 
qed "Key_synth_eq"; 
1839  651 

2373  652 
goal thy "!!K. Key K ~: H ==> (Crypt K X : synth H) = (Crypt K X : H)"; 
2891  653 
by (Blast_tac 1); 
2011  654 
qed "Crypt_synth_eq"; 
655 

3668  656 
Addsimps [Agent_synth, Number_synth, 
657 
Nonce_synth_eq, Key_synth_eq, Crypt_synth_eq]; 

1839  658 

659 

660 
goalw thy [keysFor_def] 

1913  661 
"keysFor (synth H) = keysFor H Un invKey``{K. Key K : H}"; 
2891  662 
by (Blast_tac 1); 
1913  663 
qed "keysFor_synth"; 
664 
Addsimps [keysFor_synth]; 

1839  665 

666 

1913  667 
(*** Combinations of parts, analz and synth ***) 
1839  668 

1913  669 
goal thy "parts (synth H) = parts H Un synth H"; 
2032  670 
by (rtac equalityI 1); 
671 
by (rtac subsetI 1); 

672 
by (etac parts.induct 1); 

1839  673 
by (ALLGOALS 
2922  674 
(blast_tac (!claset addIs ((synth_increasing RS parts_mono RS subsetD) 
2032  675 
::parts.intrs)))); 
1913  676 
qed "parts_synth"; 
677 
Addsimps [parts_synth]; 

1839  678 

2373  679 
goal thy "analz (analz G Un H) = analz (G Un H)"; 
680 
by (REPEAT_FIRST (resolve_tac [equalityI, analz_subset_cong])); 

681 
by (ALLGOALS Simp_tac); 

682 
qed "analz_analz_Un"; 

683 

684 
goal thy "analz (synth G Un H) = analz (G Un H) Un synth G"; 

2032  685 
by (rtac equalityI 1); 
686 
by (rtac subsetI 1); 

687 
by (etac analz.induct 1); 

2922  688 
by (blast_tac (!claset addIs [impOfSubs analz_mono]) 5); 
689 
by (ALLGOALS (blast_tac (!claset addIs analz.intrs))); 

2373  690 
qed "analz_synth_Un"; 
691 

692 
goal thy "analz (synth H) = analz H Un synth H"; 

693 
by (cut_inst_tac [("H","{}")] analz_synth_Un 1); 

694 
by (Full_simp_tac 1); 

1913  695 
qed "analz_synth"; 
2373  696 
Addsimps [analz_analz_Un, analz_synth_Un, analz_synth]; 
1839  697 

1946  698 

699 
(** For reasoning about the Fake rule in traces **) 

700 

1929
f0839bab4b00
Working version of NS, messages 13, WITH INTERLEAVING
paulson
parents:
1913
diff
changeset

701 
goal thy "!!Y. X: G ==> parts(insert X H) <= parts G Un parts H"; 
2032  702 
by (rtac ([parts_mono, parts_Un_subset2] MRS subset_trans) 1); 
2891  703 
by (Blast_tac 1); 
1929
f0839bab4b00
Working version of NS, messages 13, WITH INTERLEAVING
paulson
parents:
1913
diff
changeset

704 
qed "parts_insert_subset_Un"; 
f0839bab4b00
Working version of NS, messages 13, WITH INTERLEAVING
paulson
parents:
1913
diff
changeset

705 

1946  706 
(*More specifically for Fake*) 
707 
goal thy "!!H. X: synth (analz G) ==> \ 

708 
\ parts (insert X H) <= synth (analz G) Un parts G Un parts H"; 

2032  709 
by (dtac parts_insert_subset_Un 1); 
1946  710 
by (Full_simp_tac 1); 
2891  711 
by (Blast_tac 1); 
1946  712 
qed "Fake_parts_insert"; 
713 

2061  714 
goal thy 
2284
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paulson
parents:
2170
diff
changeset

715 
"!!H. [ Crypt K Y : parts (insert X H); X: synth (analz G); \ 
2061  716 
\ Key K ~: analz G ] \ 
2284
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parents:
2170
diff
changeset

717 
\ ==> Crypt K Y : parts G Un parts H"; 
2061  718 
by (dtac (impOfSubs Fake_parts_insert) 1); 
2170  719 
by (assume_tac 1); 
3102  720 
by (blast_tac (!claset addDs [impOfSubs analz_subset_parts]) 1); 
2061  721 
qed "Crypt_Fake_parts_insert"; 
722 

2373  723 
goal thy "!!H. X: synth (analz G) ==> \ 
724 
\ analz (insert X H) <= synth (analz G) Un analz (G Un H)"; 

725 
by (rtac subsetI 1); 

726 
by (subgoal_tac "x : analz (synth (analz G) Un H)" 1); 

2922  727 
by (blast_tac (!claset addIs [impOfSubs analz_mono, 
728 
impOfSubs (analz_mono RS synth_mono)]) 2); 

2373  729 
by (Full_simp_tac 1); 
2891  730 
by (Blast_tac 1); 
2373  731 
qed "Fake_analz_insert"; 
732 

2011  733 
goal thy "(X: analz H & X: parts H) = (X: analz H)"; 
2891  734 
by (blast_tac (!claset addIs [impOfSubs analz_subset_parts]) 1); 
2011  735 
val analz_conj_parts = result(); 
736 

737 
goal thy "(X: analz H  X: parts H) = (X: parts H)"; 

2891  738 
by (blast_tac (!claset addIs [impOfSubs analz_subset_parts]) 1); 
2011  739 
val analz_disj_parts = result(); 
740 

741 
AddIffs [analz_conj_parts, analz_disj_parts]; 

742 

1998
f8230821f1e8
Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents:
1994
diff
changeset

743 
(*Without this equation, other rules for synth and analz would yield 
f8230821f1e8
Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents:
1994
diff
changeset

744 
redundant cases*) 
f8230821f1e8
Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents:
1994
diff
changeset

745 
goal thy "({X,Y} : synth (analz H)) = \ 
f8230821f1e8
Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents:
1994
diff
changeset

746 
\ (X : synth (analz H) & Y : synth (analz H))"; 
2891  747 
by (Blast_tac 1); 
1998
f8230821f1e8
Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents:
1994
diff
changeset

748 
qed "MPair_synth_analz"; 
f8230821f1e8
Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents:
1994
diff
changeset

749 

f8230821f1e8
Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents:
1994
diff
changeset

750 
AddIffs [MPair_synth_analz]; 
1929
f0839bab4b00
Working version of NS, messages 13, WITH INTERLEAVING
paulson
parents:
1913
diff
changeset

751 

2154  752 
goal thy "!!K. [ Key K : analz H; Key (invKey K) : analz H ] \ 
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2170
diff
changeset

753 
\ ==> (Crypt K X : synth (analz H)) = (X : synth (analz H))"; 
2891  754 
by (Blast_tac 1); 
2154  755 
qed "Crypt_synth_analz"; 
756 

1929
f0839bab4b00
Working version of NS, messages 13, WITH INTERLEAVING
paulson
parents:
1913
diff
changeset

757 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

758 
goal thy "!!K. X ~: synth (analz H) \ 
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

759 
\ ==> (Hash{X,Y} : synth (analz H)) = (Hash{X,Y} : analz H)"; 
2891  760 
by (Blast_tac 1); 
2373  761 
qed "Hash_synth_analz"; 
762 
Addsimps [Hash_synth_analz]; 

763 

764 

2484  765 
(**** HPair: a combination of Hash and MPair ****) 
766 

767 
(*** Freeness ***) 

768 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

769 
goalw thy [HPair_def] "Agent A ~= Hash[X] Y"; 
2484  770 
by (Simp_tac 1); 
771 
qed "Agent_neq_HPair"; 

772 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

773 
goalw thy [HPair_def] "Nonce N ~= Hash[X] Y"; 
2484  774 
by (Simp_tac 1); 
775 
qed "Nonce_neq_HPair"; 

776 

3668  777 
goalw thy [HPair_def] "Number N ~= Hash[X] Y"; 
778 
by (Simp_tac 1); 

779 
qed "Number_neq_HPair"; 

780 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

781 
goalw thy [HPair_def] "Key K ~= Hash[X] Y"; 
2484  782 
by (Simp_tac 1); 
783 
qed "Key_neq_HPair"; 

784 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

785 
goalw thy [HPair_def] "Hash Z ~= Hash[X] Y"; 
2484  786 
by (Simp_tac 1); 
787 
qed "Hash_neq_HPair"; 

788 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

789 
goalw thy [HPair_def] "Crypt K X' ~= Hash[X] Y"; 
2484  790 
by (Simp_tac 1); 
791 
qed "Crypt_neq_HPair"; 

792 

3668  793 
val HPair_neqs = [Agent_neq_HPair, Nonce_neq_HPair, Number_neq_HPair, 
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

794 
Key_neq_HPair, Hash_neq_HPair, Crypt_neq_HPair]; 
2484  795 

796 
AddIffs HPair_neqs; 

797 
AddIffs (HPair_neqs RL [not_sym]); 

798 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

799 
goalw thy [HPair_def] "(Hash[X'] Y' = Hash[X] Y) = (X' = X & Y'=Y)"; 
2484  800 
by (Simp_tac 1); 
801 
qed "HPair_eq"; 

802 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

803 
goalw thy [HPair_def] "({X',Y'} = Hash[X] Y) = (X' = Hash{X,Y} & Y'=Y)"; 
2484  804 
by (Simp_tac 1); 
805 
qed "MPair_eq_HPair"; 

806 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

807 
goalw thy [HPair_def] "(Hash[X] Y = {X',Y'}) = (X' = Hash{X,Y} & Y'=Y)"; 
2484  808 
by (Auto_tac()); 
809 
qed "HPair_eq_MPair"; 

810 

811 
AddIffs [HPair_eq, MPair_eq_HPair, HPair_eq_MPair]; 

812 

813 

814 
(*** Specialized laws, proved in terms of those for Hash and MPair ***) 

815 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

816 
goalw thy [HPair_def] "keysFor (insert (Hash[X] Y) H) = keysFor H"; 
2484  817 
by (Simp_tac 1); 
818 
qed "keysFor_insert_HPair"; 

819 

820 
goalw thy [HPair_def] 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

821 
"parts (insert (Hash[X] Y) H) = \ 
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

822 
\ insert (Hash[X] Y) (insert (Hash{X,Y}) (parts (insert Y H)))"; 
2484  823 
by (Simp_tac 1); 
824 
qed "parts_insert_HPair"; 

825 

826 
goalw thy [HPair_def] 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

827 
"analz (insert (Hash[X] Y) H) = \ 
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

828 
\ insert (Hash[X] Y) (insert (Hash{X,Y}) (analz (insert Y H)))"; 
2484  829 
by (Simp_tac 1); 
830 
qed "analz_insert_HPair"; 

831 

832 
goalw thy [HPair_def] "!!H. X ~: synth (analz H) \ 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

833 
\ ==> (Hash[X] Y : synth (analz H)) = \ 
2484  834 
\ (Hash {X, Y} : analz H & Y : synth (analz H))"; 
835 
by (Simp_tac 1); 

2891  836 
by (Blast_tac 1); 
2484  837 
qed "HPair_synth_analz"; 
838 

839 
Addsimps [keysFor_insert_HPair, parts_insert_HPair, analz_insert_HPair, 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

840 
HPair_synth_analz, HPair_synth_analz]; 
2484  841 

842 

1929
f0839bab4b00
Working version of NS, messages 13, WITH INTERLEAVING
paulson
parents:
1913
diff
changeset

843 
(*We do NOT want Crypt... messages broken up in protocols!!*) 
f0839bab4b00
Working version of NS, messages 13, WITH INTERLEAVING
paulson
parents:
1913
diff
changeset

844 
Delrules partsEs; 
f0839bab4b00
Working version of NS, messages 13, WITH INTERLEAVING
paulson
parents:
1913
diff
changeset

845 

2327  846 

847 
(** Rewrites to push in Key and Crypt messages, so that other messages can 

848 
be pulled out using the analz_insert rules **) 

849 

850 
fun insComm thy x y = read_instantiate_sg (sign_of thy) [("x",x), ("y",y)] 

851 
insert_commute; 

852 

853 
val pushKeys = map (insComm thy "Key ?K") 

3668  854 
["Agent ?C", "Nonce ?N", "Number ?N", 
855 
"Hash ?X", "MPair ?X ?Y", "Crypt ?X ?K'"]; 

2327  856 

857 
val pushCrypts = map (insComm thy "Crypt ?X ?K") 

3668  858 
["Agent ?C", "Nonce ?N", "Number ?N", 
859 
"Hash ?X'", "MPair ?X' ?Y"]; 

2327  860 

861 
(*Cannot be added with Addsimps  we don't always want to reorder messages*) 

862 
val pushes = pushKeys@pushCrypts; 

863 

3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

864 

cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

865 
(*** Tactics useful for many protocol proofs ***) 
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

866 

3470  867 
(*Prove base case (subgoal i) and simplify others. A typical base case 
3683  868 
concerns Crypt K X ~: Key``shrK``bad and cannot be proved by rewriting 
3470  869 
alone.*) 
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

870 
fun prove_simple_subgoals_tac i = 
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

871 
fast_tac (!claset addss (!simpset)) i THEN 
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

872 
ALLGOALS Asm_simp_tac; 
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

873 

cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

874 
fun Fake_parts_insert_tac i = 
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

875 
blast_tac (!claset addDs [impOfSubs analz_subset_parts, 
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

876 
impOfSubs Fake_parts_insert]) i; 
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

877 

cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

878 
(*Apply rules to break down assumptions of the form 
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

879 
Y : parts(insert X H) and Y : analz(insert X H) 
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset

880 
*) 
2373  881 
val Fake_insert_tac = 
882 
dresolve_tac [impOfSubs Fake_analz_insert, 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

883 
impOfSubs Fake_parts_insert] THEN' 
2373  884 
eresolve_tac [asm_rl, synth.Inj]; 
885 

3702  886 
fun Fake_insert_simp_tac i = 
887 
REPEAT (Fake_insert_tac i) THEN Asm_full_simp_tac i; 

888 

889 

3449  890 
(*Analysis of Fake cases. Also works for messages that forward unknown parts, 
891 
but this application is no longer necessary if analz_insert_eq is used. 

2327  892 
Abstraction over i is ESSENTIAL: it delays the dereferencing of claset 
893 
DEPENDS UPON "X" REFERRING TO THE FRADULENT MESSAGE *) 

894 
fun spy_analz_tac i = 

2373  895 
DETERM 
896 
(SELECT_GOAL 

897 
(EVERY 

898 
[ (*push in occurrences of X...*) 

899 
(REPEAT o CHANGED) 

900 
(res_inst_tac [("x1","X")] (insert_commute RS ssubst) 1), 

901 
(*...allowing further simplifications*) 

902 
simp_tac (!simpset setloop split_tac [expand_if]) 1, 

3476
1be4fee7606b
spy_analz_tac: Restored iffI to the list of rules used to break down
paulson
parents:
3470
diff
changeset

903 
REPEAT (FIRSTGOAL (resolve_tac [allI,impI,notI,conjI,iffI])), 
2373  904 
DEPTH_SOLVE 
3702  905 
(Fake_insert_simp_tac 1 
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

906 
THEN 
3102  907 
IF_UNSOLVED (Blast.depth_tac 
3650
282ffdc91884
Replacing impOfSubs analz_mono by analz_insertI should improve convergence
paulson
parents:
3583
diff
changeset

908 
(!claset addIs [analz_insertI, 
3668  909 
impOfSubs analz_subset_parts]) 4 1)) 
2373  910 
]) i); 
2327  911 

2415  912 
(** Useful in many uniqueness proofs **) 
2327  913 
fun ex_strip_tac i = REPEAT (swap_res_tac [exI, conjI] i) THEN 
914 
assume_tac (i+1); 

915 

2415  916 
(*Apply the EXALL quantifification to prove uniqueness theorems in 
917 
their standard form*) 

918 
fun prove_unique_tac lemma = 

919 
EVERY' [dtac lemma, 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

920 
REPEAT o (mp_tac ORELSE' eresolve_tac [asm_rl,exE]), 
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

921 
(*Duplicate the assumption*) 
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2484
diff
changeset

922 
forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl, 
3102  923 
Blast.depth_tac (!claset addSDs [spec]) 0]; 
2415  924 

2373  925 

926 
(*Needed occasionally with spy_analz_tac, e.g. in analz_insert_Key_newK*) 

927 
goal Set.thy "A Un (B Un A) = B Un A"; 

2891  928 
by (Blast_tac 1); 
2373  929 
val Un_absorb3 = result(); 
930 
Addsimps [Un_absorb3]; 

3514
eb16b8e8d872
Moved some declarations to Message from Public and Shared
paulson
parents:
3476
diff
changeset

931 

eb16b8e8d872
Moved some declarations to Message from Public and Shared
paulson
parents:
3476
diff
changeset

932 
(*By default only o_apply is builtin. But in the presence of etaexpansion 
eb16b8e8d872
Moved some declarations to Message from Public and Shared
paulson
parents:
3476
diff
changeset

933 
this means that some terms displayed as (f o g) will be rewritten, and others 
eb16b8e8d872
Moved some declarations to Message from Public and Shared
paulson
parents:
3476
diff
changeset

934 
will not!*) 
eb16b8e8d872
Moved some declarations to Message from Public and Shared
paulson
parents:
3476
diff
changeset

935 
Addsimps [o_def]; 