author | paulson |
Fri, 25 Apr 2003 11:18:14 +0200 | |
changeset 13922 | 75ae4244a596 |
parent 11463 | 96b5b27da55c |
child 13926 | 6e62e5357a10 |
permissions | -rw-r--r-- |
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(* Title: HOL/Auth/Event |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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Theory of events for security protocols |
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Datatype of events; function "spies"; freshness |
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"bad" agents have been broken by the Spy; their private keys and internal |
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stores are visible to him |
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*) |
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theory Event = Message |
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files ("Event_lemmas.ML"): |
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consts (*Initial states of agents -- parameter of the construction*) |
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initState :: "agent => msg set" |
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datatype |
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event = Says agent agent msg |
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| Gets agent msg |
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| Notes agent msg |
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consts |
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bad :: "agent set" (*compromised agents*) |
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knows :: "agent => event list => msg set" |
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(*"spies" is retained for compatibility's sake*) |
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syntax |
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spies :: "event list => msg set" |
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translations |
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"spies" => "knows Spy" |
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axioms |
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(*Spy has access to his own key for spoof messages, but Server is secure*) |
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Spy_in_bad [iff] : "Spy \<in> bad" |
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Server_not_bad [iff] : "Server \<notin> bad" |
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primrec |
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knows_Nil: "knows A [] = initState A" |
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knows_Cons: |
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"knows A (ev # evs) = |
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(if A = Spy then |
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(case ev of |
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Says A' B X => insert X (knows Spy evs) |
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| Gets A' X => knows Spy evs |
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| Notes A' X => |
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if A' \<in> bad then insert X (knows Spy evs) else knows Spy evs) |
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else |
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(case ev of |
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Says A' B X => |
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if A'=A then insert X (knows A evs) else knows A evs |
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| Gets A' X => |
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if A'=A then insert X (knows A evs) else knows A evs |
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| Notes A' X => |
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if A'=A then insert X (knows A evs) else knows A evs))" |
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(* |
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Case A=Spy on the Gets event |
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enforces the fact that if a message is received then it must have been sent, |
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therefore the oops case must use Notes |
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*) |
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consts |
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(*Set of items that might be visible to somebody: |
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complement of the set of fresh items*) |
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used :: "event list => msg set" |
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primrec |
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used_Nil: "used [] = (UN B. parts (initState B))" |
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used_Cons: "used (ev # evs) = |
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(case ev of |
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Says A B X => parts {X} Un (used evs) |
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| Gets A X => used evs |
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| Notes A X => parts {X} Un (used evs))" |
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lemma Notes_imp_used [rule_format]: "Notes A X : set evs --> X : used evs" |
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apply (induct_tac evs); |
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apply (auto split: event.split) |
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done |
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lemma Says_imp_used [rule_format]: "Says A B X : set evs --> X : used evs" |
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apply (induct_tac evs); |
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apply (auto split: event.split) |
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done |
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lemma MPair_used [rule_format]: |
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"MPair X Y : used evs --> X : used evs & Y : used evs" |
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apply (induct_tac evs); |
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apply (auto split: event.split) |
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done |
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use "Event_lemmas.ML" |
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lemma knows_subset_knows_Cons: "knows A evs \<subseteq> knows A (e # evs)" |
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by (induct e, auto simp: knows_Cons) |
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lemma initState_subset_knows: "initState A <= knows A evs" |
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apply (induct_tac evs) |
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apply (simp add: ); |
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apply (blast intro: knows_subset_knows_Cons [THEN subsetD]) |
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done |
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(*For proving new_keys_not_used*) |
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lemma keysFor_parts_insert: |
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"[| K \<in> keysFor (parts (insert X G)); X \<in> synth (analz H) |] \ |
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\ ==> K \<in> keysFor (parts (G Un H)) | Key (invKey K) \<in> parts H"; |
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by (force |
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dest!: parts_insert_subset_Un [THEN keysFor_mono, THEN [2] rev_subsetD] |
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analz_subset_parts [THEN keysFor_mono, THEN [2] rev_subsetD] |
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intro: analz_subset_parts [THEN subsetD] parts_mono [THEN [2] rev_subsetD]) |
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method_setup analz_mono_contra = {* |
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Method.no_args |
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(Method.METHOD (fn facts => REPEAT_FIRST analz_mono_contra_tac)) *} |
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"for proving theorems of the form X \<notin> analz (knows Spy evs) --> P" |
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subsubsection{*Useful for case analysis on whether a hash is a spoof or not*} |
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ML |
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{* |
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val synth_analz_mono = thm "synth_analz_mono"; |
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val synth_analz_mono_contra_tac = |
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let val syan_impI = inst "P" "?Y ~: synth (analz (knows Spy ?evs))" impI |
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in |
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rtac syan_impI THEN' |
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REPEAT1 o |
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(dresolve_tac |
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[knows_Spy_subset_knows_Spy_Says RS synth_analz_mono RS contra_subsetD, |
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knows_Spy_subset_knows_Spy_Notes RS synth_analz_mono RS contra_subsetD, |
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knows_Spy_subset_knows_Spy_Gets RS synth_analz_mono RS contra_subsetD]) |
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THEN' |
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mp_tac |
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end; |
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*} |
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method_setup synth_analz_mono_contra = {* |
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Method.no_args |
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(Method.METHOD (fn facts => REPEAT_FIRST synth_analz_mono_contra_tac)) *} |
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"for proving theorems of the form X \<notin> synth (analz (knows Spy evs)) --> P" |
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end |