src/HOL/Auth/OtwayRees.ML
author paulson
Tue, 16 Dec 1997 15:17:26 +0100
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permissions -rw-r--r--
Simplified proofs using rewrites for f``A where f is injective
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(*  Title:      HOL/Auth/OtwayRees
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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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Inductive relation "otway" for the Otway-Rees protocol.
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Version that encrypts Nonce NB
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From page 244 of
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  Burrows, Abadi and Needham.  A Logic of Authentication.
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  Proc. Royal Soc. 426 (1989)
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*)
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open OtwayRees;
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proof_timing:=true;
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HOL_quantifiers := false;
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1996
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(*A "possibility property": there are traces that reach the end*)
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goal thy 
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 "!!A B. [| A ~= B; A ~= Server; B ~= Server |]   \
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\        ==> EX K. EX NA. EX evs: otway.          \
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\               Says B A {|Nonce NA, Crypt (shrK A) {|Nonce NA, Key K|}|} \
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\                 : set evs";
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by (REPEAT (resolve_tac [exI,bexI] 1));
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by (rtac (otway.Nil RS otway.OR1 RS otway.OR2 RS otway.OR3 RS otway.OR4) 2);
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by possibility_tac;
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result();
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(**** Inductive proofs about otway ****)
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(*Nobody sends themselves messages*)
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goal thy "!!evs. evs : otway ==> ALL A X. Says A A X ~: set evs";
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by (etac otway.induct 1);
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by (Auto_tac());
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qed_spec_mp "not_Says_to_self";
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Addsimps [not_Says_to_self];
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AddSEs   [not_Says_to_self RSN (2, rev_notE)];
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(** For reasoning about the encrypted portion of messages **)
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goal thy "!!evs. Says A' B {|N, Agent A, Agent B, X|} : set evs \
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\                ==> X : analz (spies evs)";
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by (blast_tac (claset() addSDs [Says_imp_spies RS analz.Inj]) 1);
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qed "OR2_analz_spies";
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goal thy "!!evs. Says S' B {|N, X, Crypt (shrK B) X'|} : set evs \
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\                ==> X : analz (spies evs)";
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by (blast_tac (claset() addSDs [Says_imp_spies RS analz.Inj]) 1);
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qed "OR4_analz_spies";
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goal thy "!!evs. Says Server B {|NA, X, Crypt K' {|NB,K|}|} : set evs \
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\                 ==> K : parts (spies evs)";
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by (blast_tac (claset() addSEs spies_partsEs) 1);
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qed "Oops_parts_spies";
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(*OR2_analz... and OR4_analz... let us treat those cases using the same 
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  argument as for the Fake case.  This is possible for most, but not all,
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  proofs: Fake does not invent new nonces (as in OR2), and of course Fake
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  messages originate from the Spy. *)
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bind_thm ("OR2_parts_spies",
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          OR2_analz_spies RS (impOfSubs analz_subset_parts));
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bind_thm ("OR4_parts_spies",
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          OR4_analz_spies RS (impOfSubs analz_subset_parts));
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(*For proving the easier theorems about X ~: parts (spies evs).*)
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fun parts_induct_tac i = 
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    etac otway.induct i			THEN 
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    forward_tac [Oops_parts_spies] (i+6) THEN
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    forward_tac [OR4_parts_spies]  (i+5) THEN
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    forward_tac [OR2_parts_spies]  (i+3) THEN 
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    prove_simple_subgoals_tac  i;
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(** Theorems of the form X ~: parts (spies evs) imply that NOBODY
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    sends messages containing X! **)
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(*Spy never sees another agent's shared key! (unless it's bad at start)*)
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goal thy 
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 "!!evs. evs : otway ==> (Key (shrK A) : parts (spies evs)) = (A : bad)";
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by (parts_induct_tac 1);
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by (Fake_parts_insert_tac 1);
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by (ALLGOALS Blast_tac);
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qed "Spy_see_shrK";
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Addsimps [Spy_see_shrK];
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goal thy 
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 "!!evs. evs : otway ==> (Key (shrK A) : analz (spies evs)) = (A : bad)";
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by (auto_tac(claset() addDs [impOfSubs analz_subset_parts], simpset()));
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qed "Spy_analz_shrK";
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Addsimps [Spy_analz_shrK];
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goal thy  "!!A. [| Key (shrK A) : parts (spies evs); evs : otway |] ==> A:bad";
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by (blast_tac (claset() addDs [Spy_see_shrK]) 1);
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qed "Spy_see_shrK_D";
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bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D);
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AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D];
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(*Nobody can have used non-existent keys!*)
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goal thy "!!evs. evs : otway ==>          \
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\         Key K ~: used evs --> K ~: keysFor (parts (spies evs))";
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by (parts_induct_tac 1);
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(*Fake*)
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by (best_tac
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      (claset() addSDs [impOfSubs (parts_insert_subset_Un RS keysFor_mono)]
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               addIs  [impOfSubs analz_subset_parts]
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               addDs  [impOfSubs (analz_subset_parts RS keysFor_mono)]
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               addss  (simpset())) 1);
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by (ALLGOALS Blast_tac);
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qed_spec_mp "new_keys_not_used";
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bind_thm ("new_keys_not_analzd",
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          [analz_subset_parts RS keysFor_mono,
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           new_keys_not_used] MRS contra_subsetD);
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Addsimps [new_keys_not_used, new_keys_not_analzd];
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(*** Proofs involving analz ***)
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(*Describes the form of K and NA when the Server sends this message.  Also
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  for Oops case.*)
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goal thy 
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 "!!evs. [| Says Server B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs; \
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\           evs : otway |]                                           \
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\     ==> K ~: range shrK & (EX i. NA = Nonce i) & (EX j. NB = Nonce j)";
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by (etac rev_mp 1);
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by (etac otway.induct 1);
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by (ALLGOALS Simp_tac);
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by (ALLGOALS Blast_tac);
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qed "Says_Server_message_form";
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(*For proofs involving analz.*)
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val analz_spies_tac = 
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    dtac OR2_analz_spies 4 THEN 
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    dtac OR4_analz_spies 6 THEN
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    forward_tac [Says_Server_message_form] 7 THEN
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    assume_tac 7 THEN
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    REPEAT ((eresolve_tac [exE, conjE] ORELSE' hyp_subst_tac) 7);
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(****
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 The following is to prove theorems of the form
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  Key K : analz (insert (Key KAB) (spies evs)) ==>
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  Key K : analz (spies evs)
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 A more general formula must be proved inductively.
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****)
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(** Session keys are not used to encrypt other session keys **)
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(*The equality makes the induction hypothesis easier to apply*)
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goal thy  
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 "!!evs. evs : otway ==>                                    \
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\  ALL K KK. KK <= Compl (range shrK) -->                   \
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\            (Key K : analz (Key``KK Un (spies evs))) =  \
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\            (K : KK | Key K : analz (spies evs))";
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by (etac otway.induct 1);
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by analz_spies_tac;
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by (REPEAT_FIRST (resolve_tac [allI, impI]));
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by (REPEAT_FIRST (rtac analz_image_freshK_lemma ));
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by (ALLGOALS (asm_simp_tac analz_image_freshK_ss));
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(*Fake*) 
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by (spy_analz_tac 1);
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qed_spec_mp "analz_image_freshK";
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goal thy
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 "!!evs. [| evs : otway;  KAB ~: range shrK |] ==>          \
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\        Key K : analz (insert (Key KAB) (spies evs)) =  \
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\        (K = KAB | Key K : analz (spies evs))";
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by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1);
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qed "analz_insert_freshK";
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(*** The Key K uniquely identifies the Server's  message. **)
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goal thy 
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 "!!evs. evs : otway ==>                                                  \
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\   EX B' NA' NB' X'. ALL B NA NB X.                                      \
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\     Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set evs -->     \
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\     B=B' & NA=NA' & NB=NB' & X=X'";
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by (etac otway.induct 1);
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by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib])));
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by (ALLGOALS Clarify_tac);
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(*Remaining cases: OR3 and OR4*)
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by (ex_strip_tac 2);
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by (Best_tac 2);
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by (expand_case_tac "K = ?y" 1);
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by (REPEAT (ares_tac [refl,exI,impI,conjI] 2));
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(*...we assume X is a recent message, and handle this case by contradiction*)
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by (blast_tac (claset() addSEs spies_partsEs
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                       delrules [conjI] (*no split-up into 4 subgoals*)) 1);
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val lemma = result();
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goal thy 
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 "!!evs. [| Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|}   : set evs; \ 
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\           Says Server B' {|NA',X',Crypt (shrK B') {|NB',K|}|} : set evs; \
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\           evs : otway |] ==> X=X' & B=B' & NA=NA' & NB=NB'";
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by (prove_unique_tac lemma 1);
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qed "unique_session_keys";
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(**** Authenticity properties relating to NA ****)
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(*Only OR1 can have caused such a part of a message to appear.*)
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goal thy 
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 "!!evs. [| A ~: bad;  evs : otway |]                             \
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\        ==> Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (spies evs) --> \
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\            Says A B {|NA, Agent A, Agent B,                      \
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\                       Crypt (shrK A) {|NA, Agent A, Agent B|}|}  \
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\             : set evs";
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by (parts_induct_tac 1);
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by (Fake_parts_insert_tac 1);
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qed_spec_mp "Crypt_imp_OR1";
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(** The Nonce NA uniquely identifies A's message. **)
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goal thy 
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 "!!evs. [| evs : otway; A ~: bad |]               \
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\ ==> EX B'. ALL B.                                 \
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\        Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (spies evs) \
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\        --> B = B'";
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by (parts_induct_tac 1);
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by (Fake_parts_insert_tac 1);
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by (simp_tac (simpset() addsimps [all_conj_distrib]) 1); 
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(*OR1: creation of new Nonce.  Move assertion into global context*)
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by (expand_case_tac "NA = ?y" 1);
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by (blast_tac (claset() addSEs spies_partsEs) 1);
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val lemma = result();
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goal thy 
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 "!!evs.[| Crypt (shrK A) {|NA, Agent A, Agent B|}: parts (spies evs); \
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\          Crypt (shrK A) {|NA, Agent A, Agent C|}: parts (spies evs); \
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\          evs : otway;  A ~: bad |]                                   \
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\        ==> B = C";
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by (prove_unique_tac lemma 1);
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qed "unique_NA";
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(*It is impossible to re-use a nonce in both OR1 and OR2.  This holds because
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  OR2 encrypts Nonce NB.  It prevents the attack that can occur in the
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  over-simplified version of this protocol: see OtwayRees_Bad.*)
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goal thy 
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 "!!evs. [| A ~: bad;  evs : otway |]                      \
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\        ==> Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (spies evs) --> \
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\            Crypt (shrK A) {|NA', NA, Agent A', Agent A|}  \
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\             ~: parts (spies evs)";
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by (parts_induct_tac 1);
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by (Fake_parts_insert_tac 1);
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by (REPEAT (blast_tac (claset() addSEs spies_partsEs
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                               addSDs  [impOfSubs parts_insert_subset_Un]) 1));
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qed_spec_mp"no_nonce_OR1_OR2";
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(*Crucial property: If the encrypted message appears, and A has used NA
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  to start a run, then it originated with the Server!*)
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goal thy 
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 "!!evs. [| A ~: bad;  A ~= Spy;  evs : otway |]                      \
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\    ==> Crypt (shrK A) {|NA, Key K|} : parts (spies evs)              \
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\        --> Says A B {|NA, Agent A, Agent B,                          \
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\                       Crypt (shrK A) {|NA, Agent A, Agent B|}|}      \
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\             : set evs -->                                            \
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\            (EX NB. Says Server B                                     \
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\                 {|NA,                                                \
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\                   Crypt (shrK A) {|NA, Key K|},                      \
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\                   Crypt (shrK B) {|NB, Key K|}|}                     \
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\                   : set evs)";
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by (parts_induct_tac 1);
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by (Fake_parts_insert_tac 1);
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(*OR1: it cannot be a new Nonce, contradiction.*)
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by (blast_tac (claset() addSIs [parts_insertI] addSEs spies_partsEs) 1);
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(*OR3 and OR4*)
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   288
by (asm_simp_tac (simpset() addsimps [ex_disj_distrib]) 1);
3730
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3683
diff changeset
   289
by (rtac conjI 1);
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3683
diff changeset
   290
by (ALLGOALS Clarify_tac);
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3683
diff changeset
   291
(*OR4*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
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   292
by (blast_tac (claset() addSIs [Crypt_imp_OR1]
3730
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3683
diff changeset
   293
                       addEs  spies_partsEs) 3);
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3683
diff changeset
   294
(*OR3, two cases*)  (** LEVEL 5 **)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   295
by (blast_tac (claset() addSEs [MPair_parts]
3730
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3683
diff changeset
   296
                       addSDs [Says_imp_spies RS parts.Inj]
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3683
diff changeset
   297
                       addEs  [no_nonce_OR1_OR2 RSN (2, rev_notE)]
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3683
diff changeset
   298
                       delrules [conjI] (*stop split-up into 4 subgoals*)) 2);
4091
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wenzelm
parents: 3961
diff changeset
   299
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj]
3730
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3683
diff changeset
   300
                       addSEs [MPair_parts]
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3683
diff changeset
   301
                       addIs  [unique_NA]) 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
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diff changeset
   302
qed_spec_mp "NA_Crypt_imp_Server_msg";
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   303
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   304
2053
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   305
(*Corollary: if A receives B's OR4 message and the nonce NA agrees
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   306
  then the key really did come from the Server!  CANNOT prove this of the
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   307
  bad form of this protocol, even though we can prove
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   308
  Spy_not_see_encrypted_key*)
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   309
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   310
 "!!evs. [| Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} : set evs; \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   311
\           Says A  B {|NA, Agent A, Agent B,                       \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   312
\                       Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   313
\           A ~: bad;  A ~= Spy;  evs : otway |]                  \
2053
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   314
\        ==> EX NB. Says Server B                                  \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   315
\                     {|NA,                                        \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   316
\                       Crypt (shrK A) {|NA, Key K|},              \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   317
\                       Crypt (shrK B) {|NB, Key K|}|}             \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3451
diff changeset
   318
\                       : set evs";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   319
by (blast_tac (claset() addSIs [NA_Crypt_imp_Server_msg]
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   320
                       addEs  spies_partsEs) 1);
2328
e984c12ce5b4 Minor renamings
paulson
parents: 2284
diff changeset
   321
qed "A_trusts_OR4";
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   322
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   323
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   324
(** Crucial secrecy property: Spy does not see the keys sent in msg OR3
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   325
    Does not in itself guarantee security: an attack could violate 
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   326
    the premises, e.g. by having A=Spy **)
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   327
1941
f97a6e5b6375 Initial working proof of Otway-Rees protocol
paulson
parents:
diff changeset
   328
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   329
 "!!evs. [| A ~: bad;  B ~: bad;  evs : otway |]                    \
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   330
\        ==> Says Server B                                            \
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   331
\              {|NA, Crypt (shrK A) {|NA, Key K|},                    \
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   332
\                Crypt (shrK B) {|NB, Key K|}|} : set evs -->         \
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   333
\            Says B Spy {|NA, NB, Key K|} ~: set evs -->              \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   334
\            Key K ~: analz (spies evs)";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   335
by (etac otway.induct 1);
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   336
by analz_spies_tac;
1964
d551e68b7a36 Stronger proofs; work for Otway-Rees
paulson
parents: 1945
diff changeset
   337
by (ALLGOALS
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   338
    (asm_simp_tac (simpset() addcongs [conj_cong] 
3674
65ec38fbb265 Deleted the redundant simprule not_parts_not_analz
paulson
parents: 3543
diff changeset
   339
                            addsimps [analz_insert_eq, analz_insert_freshK]
3961
6a8996fb7d99 Many minor speedups:
paulson
parents: 3919
diff changeset
   340
                            addsimps (pushes@expand_ifs))));
3451
d10f100676d8 Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents: 3207
diff changeset
   341
(*Oops*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   342
by (blast_tac (claset() addSDs [unique_session_keys]) 4);
3451
d10f100676d8 Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents: 3207
diff changeset
   343
(*OR4*) 
d10f100676d8 Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents: 3207
diff changeset
   344
by (Blast_tac 3);
1941
f97a6e5b6375 Initial working proof of Otway-Rees protocol
paulson
parents:
diff changeset
   345
(*OR3*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   346
by (blast_tac (claset() addSEs spies_partsEs
3451
d10f100676d8 Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents: 3207
diff changeset
   347
                       addIs [impOfSubs analz_subset_parts]) 2);
d10f100676d8 Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents: 3207
diff changeset
   348
(*Fake*) 
d10f100676d8 Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents: 3207
diff changeset
   349
by (spy_analz_tac 1);
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   350
val lemma = result() RS mp RS mp RSN(2,rev_notE);
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   351
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   352
goal thy 
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   353
 "!!evs. [| Says Server B                                           \
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   354
\            {|NA, Crypt (shrK A) {|NA, Key K|},                    \
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   355
\                  Crypt (shrK B) {|NB, Key K|}|} : set evs;        \
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   356
\           Says B Spy {|NA, NB, Key K|} ~: set evs;                \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   357
\           A ~: bad;  B ~: bad;  evs : otway |]                  \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   358
\        ==> Key K ~: analz (spies evs)";
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   359
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   360
by (blast_tac (claset() addSEs [lemma]) 1);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   361
qed "Spy_not_see_encrypted_key";
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   362
1945
20ca9cf90e69 A further tidying
paulson
parents: 1941
diff changeset
   363
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   364
(**** Authenticity properties relating to NB ****)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   365
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   366
(*Only OR2 can have caused such a part of a message to appear.  We do not
2194
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   367
  know anything about X: it does NOT have to have the right form.*)
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   368
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   369
 "!!evs. [| B ~: bad;  evs : otway |]                         \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   370
\        ==> Crypt (shrK B) {|NA, NB, Agent A, Agent B|}       \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   371
\             : parts (spies evs) -->                       \
2194
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   372
\            (EX X. Says B Server                              \
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   373
\             {|NA, Agent A, Agent B, X,                       \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   374
\               Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|}  \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3451
diff changeset
   375
\             : set evs)";
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   376
by (parts_induct_tac 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   377
by (Fake_parts_insert_tac 1);
3102
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   378
by (ALLGOALS Blast_tac);
2194
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   379
bind_thm ("Crypt_imp_OR2", result() RSN (2,rev_mp) RS exE);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   380
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   381
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   382
(** The Nonce NB uniquely identifies B's  message. **)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   383
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   384
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   385
 "!!evs. [| evs : otway; B ~: bad |]                    \
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   386
\ ==> EX NA' A'. ALL NA A.                               \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   387
\      Crypt (shrK B) {|NA, NB, Agent A, Agent B|} : parts(spies evs) \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   388
\      --> NA = NA' & A = A'";
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   389
by (parts_induct_tac 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   390
by (Fake_parts_insert_tac 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   391
by (simp_tac (simpset() addsimps [all_conj_distrib]) 1); 
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   392
(*OR2: creation of new Nonce.  Move assertion into global context*)
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   393
by (expand_case_tac "NB = ?y" 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   394
by (blast_tac (claset() addSEs spies_partsEs) 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   395
val lemma = result();
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   396
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   397
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   398
 "!!evs.[| Crypt (shrK B) {|NA, NB, Agent A, Agent B|} : parts(spies evs); \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   399
\          Crypt (shrK B) {|NC, NB, Agent C, Agent B|} : parts(spies evs); \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   400
\          evs : otway;  B ~: bad |]             \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   401
\        ==> NC = NA & C = A";
2417
95f275c8476e New tactic: prove_unique_tac
paulson
parents: 2375
diff changeset
   402
by (prove_unique_tac lemma 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   403
qed "unique_NB";
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   404
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   405
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   406
(*If the encrypted message appears, and B has used Nonce NB,
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   407
  then it originated with the Server!*)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   408
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   409
 "!!evs. [| B ~: bad;  B ~= Spy;  evs : otway |]                        \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   410
\    ==> Crypt (shrK B) {|NB, Key K|} : parts (spies evs)             \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   411
\        --> (ALL X'. Says B Server                                      \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   412
\                       {|NA, Agent A, Agent B, X',                      \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   413
\                         Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|}  \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   414
\             : set evs                                                  \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   415
\             --> Says Server B                                          \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   416
\                  {|NA, Crypt (shrK A) {|NA, Key K|},                   \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   417
\                        Crypt (shrK B) {|NB, Key K|}|}                  \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3451
diff changeset
   418
\                   : set evs)";
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   419
by (parts_induct_tac 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   420
by (Fake_parts_insert_tac 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   421
(*OR1: it cannot be a new Nonce, contradiction.*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   422
by (blast_tac (claset() addSIs [parts_insertI] addSEs spies_partsEs) 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   423
(*OR4*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   424
by (blast_tac (claset() addSEs [MPair_parts, Crypt_imp_OR2]) 2);
2194
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   425
(*OR3*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   426
by (safe_tac (claset() delrules [disjCI, impCE]));
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   427
by (blast_tac (claset() delrules [conjI] (*stop split-up*)) 3); 
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   428
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj]
3102
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   429
                       addSEs [MPair_parts]
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   430
                       addDs  [unique_NB]) 2);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   431
by (blast_tac (claset() addSEs [MPair_parts, no_nonce_OR1_OR2 RSN (2, rev_notE)]
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   432
                       addSDs [Says_imp_spies RS parts.Inj]
3102
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   433
                       delrules [conjI, impCE] (*stop split-up*)) 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   434
qed_spec_mp "NB_Crypt_imp_Server_msg";
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   435
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   436
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   437
(*Guarantee for B: if it gets a message with matching NB then the Server
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   438
  has sent the correct message.*)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   439
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   440
 "!!evs. [| B ~: bad;  B ~= Spy;  evs : otway;                    \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   441
\           Says S' B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs; \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   442
\           Says B Server {|NA, Agent A, Agent B, X',              \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   443
\                           Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   444
\            : set evs |]                                          \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   445
\        ==> Says Server B                                         \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   446
\                 {|NA,                                            \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   447
\                   Crypt (shrK A) {|NA, Key K|},                  \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   448
\                   Crypt (shrK B) {|NB, Key K|}|}                 \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3451
diff changeset
   449
\                   : set evs";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   450
by (blast_tac (claset() addSIs [NB_Crypt_imp_Server_msg]
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   451
                       addSEs spies_partsEs) 1);
2328
e984c12ce5b4 Minor renamings
paulson
parents: 2284
diff changeset
   452
qed "B_trusts_OR3";
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   453
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   454
2328
e984c12ce5b4 Minor renamings
paulson
parents: 2284
diff changeset
   455
B_trusts_OR3 RS Spy_not_see_encrypted_key;
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   456
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   457
1945
20ca9cf90e69 A further tidying
paulson
parents: 1941
diff changeset
   458
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   459
 "!!evs. [| B ~: bad;  evs : otway |]                           \
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   460
\        ==> Says Server B                                       \
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   461
\              {|NA, Crypt (shrK A) {|NA, Key K|},               \
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   462
\                Crypt (shrK B) {|NB, Key K|}|} : set evs -->    \
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   463
\            (EX X. Says B Server {|NA, Agent A, Agent B, X,     \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   464
\                            Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3451
diff changeset
   465
\            : set evs)";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   466
by (etac otway.induct 1);
3102
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   467
by (ALLGOALS Asm_simp_tac);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   468
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj]
3102
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   469
		       addSEs [MPair_parts, Crypt_imp_OR2]) 3);
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   470
by (ALLGOALS Blast_tac);
2194
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   471
bind_thm ("OR3_imp_OR2", result() RSN (2,rev_mp) RS exE);
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   472
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   473
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   474
(*After getting and checking OR4, agent A can trust that B has been active.
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   475
  We could probably prove that X has the expected form, but that is not
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   476
  strictly necessary for authentication.*)
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   477
goal thy 
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   478
 "!!evs. [| Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} : set evs;       \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   479
\           Says A B {|NA, Agent A, Agent B,                                \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   480
\                      Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   481
\           A ~: bad;  A ~= Spy;  B ~: bad;  evs : otway |]               \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   482
\        ==> EX NB X. Says B Server {|NA, Agent A, Agent B, X,              \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   483
\                              Crypt (shrK B)  {|NA, NB, Agent A, Agent B|} |}\
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3451
diff changeset
   484
\            : set evs";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   485
by (blast_tac (claset() addSDs  [A_trusts_OR4]
3102
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   486
                       addSEs [OR3_imp_OR2]) 1);
2194
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   487
qed "A_auths_B";