src/HOL/Auth/Event.thy
author haftmann
Fri Apr 20 11:21:42 2007 +0200 (2007-04-20)
changeset 22744 5cbe966d67a2
parent 21588 cd0dc678a205
child 24122 fc7f857d33c8
permissions -rw-r--r--
Isar definitions are now added explicitly to code theorem table
paulson@3512
     1
(*  Title:      HOL/Auth/Event
paulson@3512
     2
    ID:         $Id$
paulson@3512
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
paulson@3512
     4
    Copyright   1996  University of Cambridge
paulson@3512
     5
paulson@3683
     6
Datatype of events; function "spies"; freshness
paulson@3678
     7
paulson@3683
     8
"bad" agents have been broken by the Spy; their private keys and internal
paulson@3678
     9
    stores are visible to him
paulson@3512
    10
*)
paulson@3512
    11
paulson@13956
    12
header{*Theory of Events for Security Protocols*}
paulson@13956
    13
haftmann@16417
    14
theory Event imports Message begin
paulson@11104
    15
paulson@3512
    16
consts  (*Initial states of agents -- parameter of the construction*)
paulson@11104
    17
  initState :: "agent => msg set"
paulson@3512
    18
paulson@6399
    19
datatype
paulson@3512
    20
  event = Says  agent agent msg
paulson@6399
    21
        | Gets  agent       msg
paulson@3512
    22
        | Notes agent       msg
paulson@6308
    23
       
paulson@6308
    24
consts 
paulson@11104
    25
  bad    :: "agent set"				(*compromised agents*)
paulson@11104
    26
  knows  :: "agent => event list => msg set"
paulson@3512
    27
paulson@6308
    28
paulson@14126
    29
text{*The constant "spies" is retained for compatibility's sake*}
wenzelm@20768
    30
wenzelm@20768
    31
abbreviation (input)
wenzelm@21404
    32
  spies  :: "event list => msg set" where
wenzelm@20768
    33
  "spies == knows Spy"
paulson@6308
    34
paulson@14126
    35
text{*Spy has access to his own key for spoof messages, but Server is secure*}
paulson@14126
    36
specification (bad)
paulson@14200
    37
  Spy_in_bad     [iff]: "Spy \<in> bad"
paulson@14200
    38
  Server_not_bad [iff]: "Server \<notin> bad"
paulson@14126
    39
    by (rule exI [of _ "{Spy}"], simp)
paulson@6308
    40
berghofe@5183
    41
primrec
paulson@11104
    42
  knows_Nil:   "knows A [] = initState A"
paulson@11104
    43
  knows_Cons:
paulson@6399
    44
    "knows A (ev # evs) =
paulson@6399
    45
       (if A = Spy then 
paulson@6399
    46
	(case ev of
paulson@6399
    47
	   Says A' B X => insert X (knows Spy evs)
paulson@6399
    48
	 | Gets A' X => knows Spy evs
paulson@6399
    49
	 | Notes A' X  => 
paulson@13922
    50
	     if A' \<in> bad then insert X (knows Spy evs) else knows Spy evs)
paulson@6399
    51
	else
paulson@6399
    52
	(case ev of
paulson@6399
    53
	   Says A' B X => 
paulson@6399
    54
	     if A'=A then insert X (knows A evs) else knows A evs
paulson@6399
    55
	 | Gets A' X    => 
paulson@6399
    56
	     if A'=A then insert X (knows A evs) else knows A evs
paulson@6399
    57
	 | Notes A' X    => 
paulson@6399
    58
	     if A'=A then insert X (knows A evs) else knows A evs))"
paulson@6308
    59
paulson@6308
    60
(*
paulson@6308
    61
  Case A=Spy on the Gets event
paulson@6308
    62
  enforces the fact that if a message is received then it must have been sent,
paulson@6308
    63
  therefore the oops case must use Notes
paulson@6308
    64
*)
paulson@3678
    65
paulson@3683
    66
consts
paulson@3683
    67
  (*Set of items that might be visible to somebody:
paulson@3683
    68
    complement of the set of fresh items*)
paulson@11104
    69
  used :: "event list => msg set"
paulson@3512
    70
berghofe@5183
    71
primrec
paulson@11104
    72
  used_Nil:   "used []         = (UN B. parts (initState B))"
paulson@11104
    73
  used_Cons:  "used (ev # evs) =
paulson@11104
    74
		     (case ev of
paulson@13935
    75
			Says A B X => parts {X} \<union> used evs
paulson@11104
    76
		      | Gets A X   => used evs
paulson@13935
    77
		      | Notes A X  => parts {X} \<union> used evs)"
paulson@13935
    78
    --{*The case for @{term Gets} seems anomalous, but @{term Gets} always
paulson@13935
    79
        follows @{term Says} in real protocols.  Seems difficult to change.
paulson@13935
    80
        See @{text Gets_correct} in theory @{text "Guard/Extensions.thy"}. *}
paulson@6308
    81
paulson@13926
    82
lemma Notes_imp_used [rule_format]: "Notes A X \<in> set evs --> X \<in> used evs"
paulson@13926
    83
apply (induct_tac evs)
paulson@11463
    84
apply (auto split: event.split) 
paulson@11463
    85
done
paulson@11463
    86
paulson@13926
    87
lemma Says_imp_used [rule_format]: "Says A B X \<in> set evs --> X \<in> used evs"
paulson@13926
    88
apply (induct_tac evs)
paulson@11463
    89
apply (auto split: event.split) 
paulson@11463
    90
done
paulson@11463
    91
paulson@13926
    92
paulson@13926
    93
subsection{*Function @{term knows}*}
paulson@13926
    94
paulson@13956
    95
(*Simplifying   
paulson@13956
    96
 parts(insert X (knows Spy evs)) = parts{X} \<union> parts(knows Spy evs).
paulson@13956
    97
  This version won't loop with the simplifier.*)
paulson@13935
    98
lemmas parts_insert_knows_A = parts_insert [of _ "knows A evs", standard]
paulson@13926
    99
paulson@13926
   100
lemma knows_Spy_Says [simp]:
paulson@13926
   101
     "knows Spy (Says A B X # evs) = insert X (knows Spy evs)"
paulson@13926
   102
by simp
paulson@13926
   103
paulson@14200
   104
text{*Letting the Spy see "bad" agents' notes avoids redundant case-splits
paulson@14200
   105
      on whether @{term "A=Spy"} and whether @{term "A\<in>bad"}*}
paulson@13926
   106
lemma knows_Spy_Notes [simp]:
paulson@13926
   107
     "knows Spy (Notes A X # evs) =  
paulson@13926
   108
          (if A:bad then insert X (knows Spy evs) else knows Spy evs)"
paulson@13926
   109
by simp
paulson@13926
   110
paulson@13926
   111
lemma knows_Spy_Gets [simp]: "knows Spy (Gets A X # evs) = knows Spy evs"
paulson@13926
   112
by simp
paulson@13926
   113
paulson@13926
   114
lemma knows_Spy_subset_knows_Spy_Says:
paulson@13935
   115
     "knows Spy evs \<subseteq> knows Spy (Says A B X # evs)"
paulson@13926
   116
by (simp add: subset_insertI)
paulson@13926
   117
paulson@13926
   118
lemma knows_Spy_subset_knows_Spy_Notes:
paulson@13935
   119
     "knows Spy evs \<subseteq> knows Spy (Notes A X # evs)"
paulson@13926
   120
by force
paulson@13926
   121
paulson@13926
   122
lemma knows_Spy_subset_knows_Spy_Gets:
paulson@13935
   123
     "knows Spy evs \<subseteq> knows Spy (Gets A X # evs)"
paulson@13926
   124
by (simp add: subset_insertI)
paulson@13926
   125
paulson@13926
   126
text{*Spy sees what is sent on the traffic*}
paulson@13926
   127
lemma Says_imp_knows_Spy [rule_format]:
paulson@13926
   128
     "Says A B X \<in> set evs --> X \<in> knows Spy evs"
paulson@13926
   129
apply (induct_tac "evs")
paulson@13926
   130
apply (simp_all (no_asm_simp) split add: event.split)
paulson@13926
   131
done
paulson@13926
   132
paulson@13926
   133
lemma Notes_imp_knows_Spy [rule_format]:
paulson@13926
   134
     "Notes A X \<in> set evs --> A: bad --> X \<in> knows Spy evs"
paulson@13926
   135
apply (induct_tac "evs")
paulson@13926
   136
apply (simp_all (no_asm_simp) split add: event.split)
paulson@13926
   137
done
paulson@13926
   138
paulson@13926
   139
paulson@13926
   140
text{*Elimination rules: derive contradictions from old Says events containing
paulson@13926
   141
  items known to be fresh*}
paulson@13926
   142
lemmas knows_Spy_partsEs =
paulson@13926
   143
     Says_imp_knows_Spy [THEN parts.Inj, THEN revcut_rl, standard] 
paulson@13926
   144
     parts.Body [THEN revcut_rl, standard]
paulson@13926
   145
paulson@18570
   146
lemmas Says_imp_analz_Spy = Says_imp_knows_Spy [THEN analz.Inj]
paulson@18570
   147
paulson@13926
   148
text{*Compatibility for the old "spies" function*}
paulson@13926
   149
lemmas spies_partsEs = knows_Spy_partsEs
paulson@13926
   150
lemmas Says_imp_spies = Says_imp_knows_Spy
paulson@13935
   151
lemmas parts_insert_spies = parts_insert_knows_A [of _ Spy]
paulson@13926
   152
paulson@13926
   153
paulson@13926
   154
subsection{*Knowledge of Agents*}
paulson@13926
   155
paulson@13926
   156
lemma knows_Says: "knows A (Says A B X # evs) = insert X (knows A evs)"
paulson@13926
   157
by simp
paulson@13926
   158
paulson@13926
   159
lemma knows_Notes: "knows A (Notes A X # evs) = insert X (knows A evs)"
paulson@13926
   160
by simp
paulson@13926
   161
paulson@13926
   162
lemma knows_Gets:
paulson@13926
   163
     "A \<noteq> Spy --> knows A (Gets A X # evs) = insert X (knows A evs)"
paulson@13926
   164
by simp
paulson@13926
   165
paulson@13926
   166
paulson@13935
   167
lemma knows_subset_knows_Says: "knows A evs \<subseteq> knows A (Says A' B X # evs)"
paulson@13935
   168
by (simp add: subset_insertI)
paulson@13926
   169
paulson@13935
   170
lemma knows_subset_knows_Notes: "knows A evs \<subseteq> knows A (Notes A' X # evs)"
paulson@13935
   171
by (simp add: subset_insertI)
paulson@13926
   172
paulson@13935
   173
lemma knows_subset_knows_Gets: "knows A evs \<subseteq> knows A (Gets A' X # evs)"
paulson@13935
   174
by (simp add: subset_insertI)
paulson@13926
   175
paulson@13926
   176
text{*Agents know what they say*}
paulson@13926
   177
lemma Says_imp_knows [rule_format]: "Says A B X \<in> set evs --> X \<in> knows A evs"
paulson@13926
   178
apply (induct_tac "evs")
paulson@13926
   179
apply (simp_all (no_asm_simp) split add: event.split)
paulson@13926
   180
apply blast
paulson@13926
   181
done
paulson@13926
   182
paulson@13926
   183
text{*Agents know what they note*}
paulson@13926
   184
lemma Notes_imp_knows [rule_format]: "Notes A X \<in> set evs --> X \<in> knows A evs"
paulson@13926
   185
apply (induct_tac "evs")
paulson@13926
   186
apply (simp_all (no_asm_simp) split add: event.split)
paulson@13926
   187
apply blast
paulson@13926
   188
done
paulson@13926
   189
paulson@13926
   190
text{*Agents know what they receive*}
paulson@13926
   191
lemma Gets_imp_knows_agents [rule_format]:
paulson@13926
   192
     "A \<noteq> Spy --> Gets A X \<in> set evs --> X \<in> knows A evs"
paulson@13926
   193
apply (induct_tac "evs")
paulson@13926
   194
apply (simp_all (no_asm_simp) split add: event.split)
paulson@13926
   195
done
paulson@13926
   196
paulson@13926
   197
paulson@13926
   198
text{*What agents DIFFERENT FROM Spy know 
paulson@13926
   199
  was either said, or noted, or got, or known initially*}
paulson@13926
   200
lemma knows_imp_Says_Gets_Notes_initState [rule_format]:
paulson@13926
   201
     "[| X \<in> knows A evs; A \<noteq> Spy |] ==> EX B.  
paulson@13926
   202
  Says A B X \<in> set evs | Gets A X \<in> set evs | Notes A X \<in> set evs | X \<in> initState A"
paulson@13926
   203
apply (erule rev_mp)
paulson@13926
   204
apply (induct_tac "evs")
paulson@13926
   205
apply (simp_all (no_asm_simp) split add: event.split)
paulson@13926
   206
apply blast
paulson@13926
   207
done
paulson@13926
   208
paulson@13926
   209
text{*What the Spy knows -- for the time being --
paulson@13926
   210
  was either said or noted, or known initially*}
paulson@13926
   211
lemma knows_Spy_imp_Says_Notes_initState [rule_format]:
paulson@13926
   212
     "[| X \<in> knows Spy evs |] ==> EX A B.  
paulson@13926
   213
  Says A B X \<in> set evs | Notes A X \<in> set evs | X \<in> initState Spy"
paulson@13926
   214
apply (erule rev_mp)
paulson@13926
   215
apply (induct_tac "evs")
paulson@13926
   216
apply (simp_all (no_asm_simp) split add: event.split)
paulson@13926
   217
apply blast
paulson@13926
   218
done
paulson@13926
   219
paulson@13935
   220
lemma parts_knows_Spy_subset_used: "parts (knows Spy evs) \<subseteq> used evs"
paulson@13935
   221
apply (induct_tac "evs", force)  
paulson@13935
   222
apply (simp add: parts_insert_knows_A knows_Cons add: event.split, blast) 
paulson@13926
   223
done
paulson@13926
   224
paulson@13926
   225
lemmas usedI = parts_knows_Spy_subset_used [THEN subsetD, intro]
paulson@13926
   226
paulson@13926
   227
lemma initState_into_used: "X \<in> parts (initState B) ==> X \<in> used evs"
paulson@13926
   228
apply (induct_tac "evs")
paulson@13935
   229
apply (simp_all add: parts_insert_knows_A split add: event.split, blast)
paulson@13926
   230
done
paulson@13926
   231
paulson@13926
   232
lemma used_Says [simp]: "used (Says A B X # evs) = parts{X} \<union> used evs"
paulson@13926
   233
by simp
paulson@13926
   234
paulson@13926
   235
lemma used_Notes [simp]: "used (Notes A X # evs) = parts{X} \<union> used evs"
paulson@13926
   236
by simp
paulson@13926
   237
paulson@13926
   238
lemma used_Gets [simp]: "used (Gets A X # evs) = used evs"
paulson@13926
   239
by simp
paulson@13926
   240
paulson@13935
   241
lemma used_nil_subset: "used [] \<subseteq> used evs"
paulson@13935
   242
apply simp
paulson@13926
   243
apply (blast intro: initState_into_used)
paulson@13926
   244
done
paulson@13926
   245
paulson@13926
   246
text{*NOTE REMOVAL--laws above are cleaner, as they don't involve "case"*}
paulson@13935
   247
declare knows_Cons [simp del]
paulson@13935
   248
        used_Nil [simp del] used_Cons [simp del]
paulson@13926
   249
paulson@13926
   250
paulson@13926
   251
text{*For proving theorems of the form @{term "X \<notin> analz (knows Spy evs) --> P"}
paulson@13926
   252
  New events added by induction to "evs" are discarded.  Provided 
paulson@13926
   253
  this information isn't needed, the proof will be much shorter, since
paulson@13926
   254
  it will omit complicated reasoning about @{term analz}.*}
paulson@13926
   255
paulson@13926
   256
lemmas analz_mono_contra =
paulson@13926
   257
       knows_Spy_subset_knows_Spy_Says [THEN analz_mono, THEN contra_subsetD]
paulson@13926
   258
       knows_Spy_subset_knows_Spy_Notes [THEN analz_mono, THEN contra_subsetD]
paulson@13926
   259
       knows_Spy_subset_knows_Spy_Gets [THEN analz_mono, THEN contra_subsetD]
paulson@13926
   260
paulson@13926
   261
ML
paulson@13926
   262
{*
paulson@13926
   263
val analz_mono_contra_tac = 
paulson@13926
   264
  let val analz_impI = inst "P" "?Y \<notin> analz (knows Spy ?evs)" impI
paulson@13926
   265
  in
paulson@13926
   266
    rtac analz_impI THEN' 
paulson@13926
   267
    REPEAT1 o 
paulson@13926
   268
      (dresolve_tac (thms"analz_mono_contra"))
paulson@13926
   269
    THEN' mp_tac
paulson@13926
   270
  end
paulson@13926
   271
*}
paulson@13926
   272
paulson@11104
   273
paulson@13922
   274
lemma knows_subset_knows_Cons: "knows A evs \<subseteq> knows A (e # evs)"
paulson@13922
   275
by (induct e, auto simp: knows_Cons)
paulson@13922
   276
paulson@13935
   277
lemma initState_subset_knows: "initState A \<subseteq> knows A evs"
paulson@13926
   278
apply (induct_tac evs, simp) 
paulson@13922
   279
apply (blast intro: knows_subset_knows_Cons [THEN subsetD])
paulson@13922
   280
done
paulson@13922
   281
paulson@13922
   282
paulson@13926
   283
text{*For proving @{text new_keys_not_used}*}
paulson@13922
   284
lemma keysFor_parts_insert:
paulson@13926
   285
     "[| K \<in> keysFor (parts (insert X G));  X \<in> synth (analz H) |] 
paulson@13926
   286
      ==> K \<in> keysFor (parts (G \<union> H)) | Key (invKey K) \<in> parts H"; 
paulson@13922
   287
by (force 
paulson@13922
   288
    dest!: parts_insert_subset_Un [THEN keysFor_mono, THEN [2] rev_subsetD]
paulson@13922
   289
           analz_subset_parts [THEN keysFor_mono, THEN [2] rev_subsetD]
paulson@13922
   290
    intro: analz_subset_parts [THEN subsetD] parts_mono [THEN [2] rev_subsetD])
paulson@13922
   291
paulson@11104
   292
method_setup analz_mono_contra = {*
wenzelm@21588
   293
    Method.no_args (Method.SIMPLE_METHOD (REPEAT_FIRST analz_mono_contra_tac)) *}
paulson@13922
   294
    "for proving theorems of the form X \<notin> analz (knows Spy evs) --> P"
paulson@13922
   295
paulson@13922
   296
subsubsection{*Useful for case analysis on whether a hash is a spoof or not*}
paulson@13922
   297
paulson@13922
   298
ML
paulson@13922
   299
{*
paulson@13926
   300
val knows_Cons     = thm "knows_Cons"
paulson@13926
   301
val used_Nil       = thm "used_Nil"
paulson@13926
   302
val used_Cons      = thm "used_Cons"
paulson@13926
   303
paulson@13926
   304
val Notes_imp_used = thm "Notes_imp_used";
paulson@13926
   305
val Says_imp_used = thm "Says_imp_used";
paulson@13926
   306
val Says_imp_knows_Spy = thm "Says_imp_knows_Spy";
paulson@13926
   307
val Notes_imp_knows_Spy = thm "Notes_imp_knows_Spy";
paulson@13926
   308
val knows_Spy_partsEs = thms "knows_Spy_partsEs";
paulson@13926
   309
val spies_partsEs = thms "spies_partsEs";
paulson@13926
   310
val Says_imp_spies = thm "Says_imp_spies";
paulson@13926
   311
val parts_insert_spies = thm "parts_insert_spies";
paulson@13926
   312
val Says_imp_knows = thm "Says_imp_knows";
paulson@13926
   313
val Notes_imp_knows = thm "Notes_imp_knows";
paulson@13926
   314
val Gets_imp_knows_agents = thm "Gets_imp_knows_agents";
paulson@13926
   315
val knows_imp_Says_Gets_Notes_initState = thm "knows_imp_Says_Gets_Notes_initState";
paulson@13926
   316
val knows_Spy_imp_Says_Notes_initState = thm "knows_Spy_imp_Says_Notes_initState";
paulson@13926
   317
val usedI = thm "usedI";
paulson@13926
   318
val initState_into_used = thm "initState_into_used";
paulson@13926
   319
val used_Says = thm "used_Says";
paulson@13926
   320
val used_Notes = thm "used_Notes";
paulson@13926
   321
val used_Gets = thm "used_Gets";
paulson@13926
   322
val used_nil_subset = thm "used_nil_subset";
paulson@13926
   323
val analz_mono_contra = thms "analz_mono_contra";
paulson@13926
   324
val knows_subset_knows_Cons = thm "knows_subset_knows_Cons";
paulson@13926
   325
val initState_subset_knows = thm "initState_subset_knows";
paulson@13926
   326
val keysFor_parts_insert = thm "keysFor_parts_insert";
paulson@13926
   327
paulson@13926
   328
paulson@13922
   329
val synth_analz_mono = thm "synth_analz_mono";
paulson@13922
   330
paulson@13935
   331
val knows_Spy_subset_knows_Spy_Says = thm "knows_Spy_subset_knows_Spy_Says";
paulson@13935
   332
val knows_Spy_subset_knows_Spy_Notes = thm "knows_Spy_subset_knows_Spy_Notes";
paulson@13935
   333
val knows_Spy_subset_knows_Spy_Gets = thm "knows_Spy_subset_knows_Spy_Gets";
paulson@13935
   334
paulson@13935
   335
paulson@13922
   336
val synth_analz_mono_contra_tac = 
paulson@13926
   337
  let val syan_impI = inst "P" "?Y \<notin> synth (analz (knows Spy ?evs))" impI
paulson@13922
   338
  in
paulson@13922
   339
    rtac syan_impI THEN' 
paulson@13922
   340
    REPEAT1 o 
paulson@13922
   341
      (dresolve_tac 
paulson@13922
   342
       [knows_Spy_subset_knows_Spy_Says RS synth_analz_mono RS contra_subsetD,
paulson@13922
   343
        knows_Spy_subset_knows_Spy_Notes RS synth_analz_mono RS contra_subsetD,
paulson@13922
   344
	knows_Spy_subset_knows_Spy_Gets RS synth_analz_mono RS contra_subsetD])
paulson@13922
   345
    THEN'
paulson@13922
   346
    mp_tac
paulson@13922
   347
  end;
paulson@13922
   348
*}
paulson@13922
   349
paulson@13922
   350
method_setup synth_analz_mono_contra = {*
wenzelm@21588
   351
    Method.no_args (Method.SIMPLE_METHOD (REPEAT_FIRST synth_analz_mono_contra_tac)) *}
paulson@13922
   352
    "for proving theorems of the form X \<notin> synth (analz (knows Spy evs)) --> P"
paulson@3512
   353
paulson@3512
   354
end