src/HOL/Auth/OtwayRees.ML
author paulson
Tue, 05 Nov 1996 11:20:52 +0100
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permissions -rw-r--r--
Simplified new_keys_not_seen, etc.: replaced the union over all agents by the Spy alone. Proofs run faster and they do not have to be set up in terms of a previous lemma.
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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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Pretty.setdepth 15;
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(*Weak liveness: 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 lost.          \
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\               Says B A {|Nonce NA, Crypt {|Nonce NA, Key K|} (shrK A)|} \
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\                 : set_of_list 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 (ALLGOALS (simp_tac (!simpset setsolver safe_solver)));
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by (REPEAT_FIRST (resolve_tac [refl, conjI]));
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by (REPEAT_FIRST (fast_tac (!claset addss (!simpset setsolver safe_solver))));
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result();
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(**** Inductive proofs about otway ****)
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(*Monotonicity*)
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goal thy "!!evs. lost' <= lost ==> otway lost' <= otway lost";
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by (rtac subsetI 1);
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by (etac otway.induct 1);
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by (REPEAT_FIRST
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    (best_tac (!claset addIs (impOfSubs (sees_mono RS analz_mono RS synth_mono)
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                              :: otway.intrs))));
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qed "otway_mono";
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(*Nobody sends themselves messages*)
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goal thy "!!evs. evs : otway lost ==> ALL A X. Says A A X ~: set_of_list 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_of_list evs \
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\                ==> X : analz (sees lost Spy evs)";
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by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1);
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qed "OR2_analz_sees_Spy";
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goal thy "!!evs. Says S B {|N, X, X'|} : set_of_list evs \
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\                ==> X : analz (sees lost Spy evs)";
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by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1);
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qed "OR4_analz_sees_Spy";
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goal thy "!!evs. Says Server B {|NA, X, Crypt {|NB,K|} K'|} : set_of_list evs \
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\                 ==> K : parts (sees lost Spy evs)";
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by (fast_tac (!claset addSEs partsEs
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                      addSDs [Says_imp_sees_Spy RS parts.Inj]) 1);
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qed "Oops_parts_sees_Spy";
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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_sees_Spy",
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          OR2_analz_sees_Spy RS (impOfSubs analz_subset_parts));
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bind_thm ("OR4_parts_sees_Spy",
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          OR4_analz_sees_Spy RS (impOfSubs analz_subset_parts));
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(*We instantiate the variable to "lost".  Leaving it as a Var makes proofs
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  harder to complete, since simplification does less for us.*)
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val parts_Fake_tac = 
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    let val tac = forw_inst_tac [("lost","lost")] 
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    in  tac OR2_parts_sees_Spy 4 THEN 
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        tac OR4_parts_sees_Spy 6 THEN
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        tac Oops_parts_sees_Spy 7
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    end;
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(*For proving the easier theorems about X ~: parts (sees lost Spy evs) *)
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fun parts_induct_tac i = SELECT_GOAL
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    (DETERM (etac otway.induct 1 THEN parts_Fake_tac THEN
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	     (*Fake message*)
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	     TRY (best_tac (!claset addDs [impOfSubs analz_subset_parts,
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					   impOfSubs Fake_parts_insert]
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                                    addss (!simpset)) 2)) THEN
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     (*Base case*)
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     fast_tac (!claset addss (!simpset)) 1 THEN
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     ALLGOALS Asm_simp_tac) i;
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(** Theorems of the form X ~: parts (sees lost Spy 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 lost at start)*)
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goal thy 
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 "!!evs. evs : otway lost \
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\        ==> (Key (shrK A) : parts (sees lost Spy evs)) = (A : lost)";
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by (parts_induct_tac 1);
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by (Auto_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 lost \
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\        ==> (Key (shrK A) : analz (sees lost Spy evs)) = (A : lost)";
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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 (sees lost Spy evs);       \
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\                  evs : otway lost |] ==> A:lost";
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by (fast_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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(*** Future keys can't be seen or used! ***)
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(*Nobody can have SEEN keys that will be generated in the future. *)
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goal thy "!!evs. evs : otway lost ==> \
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\                length evs <= length evs' --> \
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\                Key (newK evs') ~: parts (sees lost Spy evs)";
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by (parts_induct_tac 1);
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by (REPEAT_FIRST (best_tac (!claset addDs [impOfSubs analz_subset_parts,
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                                           impOfSubs parts_insert_subset_Un,
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                                           Suc_leD]
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                                    addss (!simpset))));
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qed_spec_mp "new_keys_not_seen";
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Addsimps [new_keys_not_seen];
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(*Variant: old messages must contain old keys!*)
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goal thy 
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 "!!evs. [| Says A B X : set_of_list evs;  \
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\           Key (newK evt) : parts {X};    \
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\           evs : otway lost                 \
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\        |] ==> length evt < length evs";
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by (rtac ccontr 1);
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by (dtac leI 1);
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by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Spy]
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                      addIs  [impOfSubs parts_mono]) 1);
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qed "Says_imp_old_keys";
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(*** Future nonces can't be seen or used! ***)
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goal thy "!!evs. evs : otway lost ==> \
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\                length evs <= length evt --> \
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\                Nonce (newN evt) ~: parts (sees lost Spy evs)";
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by (parts_induct_tac 1);
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by (REPEAT_FIRST (fast_tac (!claset 
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                              addSEs partsEs
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                              addSDs  [Says_imp_sees_Spy RS parts.Inj]
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                              addDs  [impOfSubs analz_subset_parts,
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                                      impOfSubs parts_insert_subset_Un,
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                                      Suc_leD]
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                              addss (!simpset))));
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qed_spec_mp "new_nonces_not_seen";
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Addsimps [new_nonces_not_seen];
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(*Variant: old messages must contain old nonces!*)
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goal thy "!!evs. [| Says A B X : set_of_list evs;    \
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\                   Nonce (newN evt) : parts {X};    \
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\                   evs : otway lost                 \
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\                |] ==> length evt < length evs";
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by (rtac ccontr 1);
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by (dtac leI 1);
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by (fast_tac (!claset addSDs [new_nonces_not_seen, Says_imp_sees_Spy]
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                      addIs  [impOfSubs parts_mono]) 1);
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qed "Says_imp_old_nonces";
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(*Nobody can have USED keys that will be generated in the future.
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  ...very like new_keys_not_seen*)
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goal thy "!!evs. evs : otway lost ==>          \
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\                length evs <= length evs' --> \
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\                newK evs' ~: keysFor (parts (sees lost Spy evs))";
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by (parts_induct_tac 1);
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(*OR1 and OR3*)
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by (EVERY (map (fast_tac (!claset addDs [Suc_leD] addss (!simpset))) [4,2]));
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(*Fake, OR2, OR4: these messages send unknown (X) components*)
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by (REPEAT
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    (best_tac
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      (!claset addDs [impOfSubs (analz_subset_parts RS keysFor_mono),
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                      impOfSubs (parts_insert_subset_Un RS keysFor_mono),
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                      Suc_leD]
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               addEs [new_keys_not_seen RS not_parts_not_analz RSN(2,rev_notE)]
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               addss (!simpset)) 1));
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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 \
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\            {|NA, X, Crypt {|NB, K|} (shrK B)|} : set_of_list evs;  \
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\           evs : otway lost |]                                   \
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\        ==> (EX evt: otway lost. K = Key(newK evt)) &            \
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\            (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 (fast_tac (!claset addss (!simpset))));
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qed "Says_Server_message_form";
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(*For proofs involving analz.  We again instantiate the variable to "lost".*)
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val analz_Fake_tac = 
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    dres_inst_tac [("lost","lost")] OR2_analz_sees_Spy 4 THEN 
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    dres_inst_tac [("lost","lost")] OR4_analz_sees_Spy 6 THEN
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    forw_inst_tac [("lost","lost")] Says_Server_message_form 7 THEN
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    assume_tac 7 THEN Full_simp_tac 7 THEN
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    REPEAT ((eresolve_tac [bexE, 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 (newK evt)) (sees lost Spy evs)) ==>
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          Key K : analz (sees lost Spy 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 lost ==> \
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\  ALL K E. (Key K : analz (Key``(newK``E) Un (sees lost Spy evs))) = \
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\           (K : newK``E | Key K : analz (sees lost Spy evs))";
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by (etac otway.induct 1);
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by analz_Fake_tac;
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by (REPEAT_FIRST (ares_tac [allI, analz_image_newK_lemma]));
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by (ALLGOALS (*Takes 14 secs*)
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    (asm_simp_tac 
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     (!simpset addsimps ([insert_Key_singleton, insert_Key_image, pushKey_newK]
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                         @ pushes)
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               setloop split_tac [expand_if])));
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(*OR4, OR2, Fake*) 
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by (EVERY (map spy_analz_tac [5,3,2]));
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(*Oops, OR3, Base*)
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by (REPEAT (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1));
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qed_spec_mp "analz_image_newK";
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goal thy
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 "!!evs. evs : otway lost ==>                               \
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\        Key K : analz (insert (Key (newK evt)) (sees lost Spy evs)) = \
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\        (K = newK evt | Key K : analz (sees lost Spy evs))";
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by (asm_simp_tac (HOL_ss addsimps [pushKey_newK, analz_image_newK, 
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                                   insert_Key_singleton]) 1);
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by (Fast_tac 1);
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qed "analz_insert_Key_newK";
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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 lost ==>                                                 \
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\   EX B' NA' NB' X'. ALL B NA NB X.                                          \
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\     Says Server B {|NA, X, Crypt {|NB, K|} (shrK B)|} : set_of_list 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 (Step_tac 1);
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(*Remaining cases: OR3 and OR4*)
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by (ex_strip_tac 2);
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by (Fast_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 very new message, and handle this case by contradiction*)
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by (fast_tac (!claset addEs [Says_imp_old_keys RS less_irrefl]
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                      delrules [conjI]    (*prevent split-up into 4 subgoals*)
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                      addss (!simpset addsimps [parts_insertI])) 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 {|NB, K|} (shrK B)|}      \
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\            : set_of_list evs;                                    \ 
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   304
\           Says Server B' {|NA',X',Crypt {|NB',K|} (shrK B')|}    \
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   305
\            : set_of_list evs;                                    \
2135
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parents: 2134
diff changeset
   306
\           evs : otway lost |] ==> X=X' & B=B' & NA=NA' & NB=NB'";
2032
1bbf1bdcaf56 Introduction of "lost" argument
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parents: 2026
diff changeset
   307
by (dtac lemma 1);
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   308
by (REPEAT (etac exE 1));
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   309
(*Duplicate the assumption*)
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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diff changeset
   310
by (forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl 1);
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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diff changeset
   311
by (fast_tac (!claset addSDs [spec]) 1);
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   312
qed "unique_session_keys";
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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diff changeset
   313
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   314
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   315
2048
bb54fbba0071 Added new guarantees for A and B
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parents: 2045
diff changeset
   316
(**** Authenticity properties relating to NA ****)
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   317
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   318
(*Only OR1 can have caused such a part of a message to appear.*)
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   319
goal thy 
2064
5a5e508e2a2b Simple tidying
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parents: 2053
diff changeset
   320
 "!!evs. [| A ~: lost;  evs : otway lost |]                        \
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   321
\        ==> Crypt {|NA, Agent A, Agent B|} (shrK A)               \
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   322
\             : parts (sees lost Spy evs) -->                      \
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   323
\            Says A B {|NA, Agent A, Agent B,                      \
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   324
\                       Crypt {|NA, Agent A, Agent B|} (shrK A)|}  \
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   325
\             : set_of_list evs";
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   326
by (parts_induct_tac 1);
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   327
qed_spec_mp "Crypt_imp_OR1";
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   328
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   329
2064
5a5e508e2a2b Simple tidying
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parents: 2053
diff changeset
   330
(** The Nonce NA uniquely identifies A's message. **)
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   331
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   332
goal thy 
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   333
 "!!evs. [| evs : otway lost; A ~: lost |]               \
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   334
\ ==> EX B'. ALL B.    \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   335
\        Crypt {|NA, Agent A, Agent B|} (shrK A) : parts (sees lost Spy evs) \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   336
\        --> B = B'";
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   337
by (parts_induct_tac 1);
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   338
by (simp_tac (!simpset addsimps [all_conj_distrib]) 1); 
2026
0df5a96bf77e Last working version prior to introduction of "lost"
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parents: 2014
diff changeset
   339
(*OR1: creation of new Nonce.  Move assertion into global context*)
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   340
by (expand_case_tac "NA = ?y" 1);
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   341
by (best_tac (!claset addSEs partsEs
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   342
                      addEs  [new_nonces_not_seen RSN(2,rev_notE)]) 1);
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   343
val lemma = result();
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   344
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   345
goal thy 
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   346
 "!!evs.[| Crypt {|NA, Agent A, Agent B|} (shrK A): parts(sees lost Spy evs); \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   347
\          Crypt {|NA, Agent A, Agent C|} (shrK A): parts(sees lost Spy evs); \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   348
\          evs : otway lost;  A ~: lost |]                                    \
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   349
\        ==> B = C";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   350
by (dtac lemma 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   351
by (assume_tac 1);
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   352
by (etac exE 1);
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   353
(*Duplicate the assumption*)
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   354
by (forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl 1);
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   355
by (fast_tac (!claset addSDs [spec]) 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   356
qed "unique_NA";
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   357
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   358
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   359
val nonce_not_seen_now = le_refl RSN (2, new_nonces_not_seen) RSN (2,rev_notE);
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   360
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   361
(*It is impossible to re-use a nonce in both OR1 and OR2.  This holds because
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   362
  OR2 encrypts Nonce NB.  It prevents the attack that can occur in the
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   363
  over-simplified version of this protocol: see OtwayRees_Bad.*)
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   364
goal thy 
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   365
 "!!evs. [| A ~: lost;  evs : otway lost |]                            \
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   366
\        ==> Crypt {|NA, Agent A, Agent B|} (shrK A)             \
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   367
\             : parts (sees lost Spy evs) -->                       \
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   368
\            Crypt {|NA', NA, Agent A', Agent A|} (shrK A)       \
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   369
\             ~: parts (sees lost Spy evs)";
2071
0debdc018d26 Put in a simpler and *much* faster proof of no_nonce_OR1_OR2
paulson
parents: 2064
diff changeset
   370
by (parts_induct_tac 1);
0debdc018d26 Put in a simpler and *much* faster proof of no_nonce_OR1_OR2
paulson
parents: 2064
diff changeset
   371
by (REPEAT (fast_tac (!claset addSEs (partsEs@[nonce_not_seen_now])
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2014
diff changeset
   372
                              addSDs  [impOfSubs parts_insert_subset_Un]
2071
0debdc018d26 Put in a simpler and *much* faster proof of no_nonce_OR1_OR2
paulson
parents: 2064
diff changeset
   373
                              addss (!simpset)) 1));
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   374
qed_spec_mp"no_nonce_OR1_OR2";
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   375
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   376
2053
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   377
(*Crucial property: If the encrypted message appears, and A has used NA
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   378
  to start a run, then it originated with the Server!*)
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   379
goal thy 
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   380
 "!!evs. [| A ~: lost;  A ~= Spy;  evs : otway lost |]                 \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   381
\    ==> Crypt {|NA, Key K|} (shrK A) : parts (sees lost Spy evs)      \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   382
\        --> Says A B {|NA, Agent A, Agent B,                          \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   383
\                       Crypt {|NA, Agent A, Agent B|} (shrK A)|}      \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   384
\             : set_of_list evs -->                                    \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   385
\            (EX NB. Says Server B                                     \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   386
\                 {|NA,                                                \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   387
\                   Crypt {|NA, Key K|} (shrK A),                      \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   388
\                   Crypt {|NB, Key K|} (shrK B)|}                     \
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   389
\                   : set_of_list evs)";
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   390
by (parts_induct_tac 1);
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   391
(*OR1: it cannot be a new Nonce, contradiction.*)
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   392
by (fast_tac (!claset addSIs [parts_insertI]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   393
                      addSEs partsEs
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   394
                      addEs [Says_imp_old_nonces RS less_irrefl]
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   395
                      addss (!simpset)) 1);
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   396
(*OR3 and OR4*) 
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   397
(*OR4*)
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   398
by (REPEAT (Safe_step_tac 2));
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   399
by (REPEAT (best_tac (!claset addSDs [parts_cut]) 3));
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   400
by (fast_tac (!claset addSIs [Crypt_imp_OR1]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   401
                      addEs  partsEs
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   402
                      addDs [Says_imp_sees_Spy RS parts.Inj]) 2);
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   403
(*OR3*)  (** LEVEL 5 **)
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   404
by (asm_simp_tac (!simpset addsimps [ex_disj_distrib]) 1);
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   405
by (step_tac (!claset delrules [disjCI, impCE]) 1);
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   406
by (fast_tac (!claset addSEs [MPair_parts]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   407
                      addSDs [Says_imp_sees_Spy RS parts.Inj]
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   408
                      addEs  [no_nonce_OR1_OR2 RSN (2, rev_notE)]
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   409
                      delrules [conjI] (*stop split-up into 4 subgoals*)) 2);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   410
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS parts.Inj]
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   411
                      addSEs [MPair_parts]
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   412
                      addEs  [unique_NA]) 1);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   413
qed_spec_mp "NA_Crypt_imp_Server_msg";
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   414
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   415
2053
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   416
(*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
   417
  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
   418
  bad form of this protocol, even though we can prove
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   419
  Spy_not_see_encrypted_key*)
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   420
goal thy 
2053
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   421
 "!!evs. [| Says B' A {|NA, Crypt {|NA, Key K|} (shrK A)|}         \
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   422
\            : set_of_list evs;                                    \
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   423
\           Says A B {|NA, Agent A, Agent B,                       \
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   424
\                      Crypt {|NA, Agent A, Agent B|} (shrK A)|}   \
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   425
\            : set_of_list evs;                                    \
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   426
\           A ~: lost;  A ~= Spy;  evs : otway lost |]             \
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   427
\        ==> EX NB. Says Server B                                  \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   428
\                     {|NA,                                        \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   429
\                       Crypt {|NA, Key K|} (shrK A),              \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   430
\                       Crypt {|NB, Key K|} (shrK B)|}             \
2053
6c0594bfa726 Greatly simplified the proof of A_can_trust
paulson
parents: 2048
diff changeset
   431
\                       : set_of_list evs";
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   432
by (fast_tac (!claset addSIs [NA_Crypt_imp_Server_msg]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   433
                      addEs  partsEs
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   434
                      addDs  [Says_imp_sees_Spy RS parts.Inj]) 1);
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   435
qed "A_trust_OR4";
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   436
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   437
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   438
(** 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
   439
    Does not in itself guarantee security: an attack could violate 
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   440
    the premises, e.g. by having A=Spy **)
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   441
1941
f97a6e5b6375 Initial working proof of Otway-Rees protocol
paulson
parents:
diff changeset
   442
goal thy 
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   443
 "!!evs. [| A ~: lost;  B ~: lost;  evs : otway lost;  evt : otway lost |] \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   444
\        ==> Says Server B                                                 \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   445
\              {|NA, Crypt {|NA, Key K|} (shrK A),                         \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   446
\                Crypt {|NB, Key K|} (shrK B)|} : set_of_list evs -->      \
2135
80477862ab33 Minor corrections
paulson
parents: 2134
diff changeset
   447
\            Says B Spy {|NA, NB, Key K|} ~: set_of_list evs -->           \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   448
\            Key K ~: analz (sees lost Spy evs)";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   449
by (etac otway.induct 1);
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   450
by analz_Fake_tac;
1964
d551e68b7a36 Stronger proofs; work for Otway-Rees
paulson
parents: 1945
diff changeset
   451
by (ALLGOALS
1941
f97a6e5b6375 Initial working proof of Otway-Rees protocol
paulson
parents:
diff changeset
   452
    (asm_full_simp_tac 
f97a6e5b6375 Initial working proof of Otway-Rees protocol
paulson
parents:
diff changeset
   453
     (!simpset addsimps ([analz_subset_parts RS contra_subsetD,
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   454
                          analz_insert_Key_newK] @ pushes)
1941
f97a6e5b6375 Initial working proof of Otway-Rees protocol
paulson
parents:
diff changeset
   455
               setloop split_tac [expand_if])));
f97a6e5b6375 Initial working proof of Otway-Rees protocol
paulson
parents:
diff changeset
   456
(*OR3*)
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   457
by (fast_tac (!claset addSIs [parts_insertI]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   458
                      addEs [Says_imp_old_keys RS less_irrefl]
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   459
                      addss (!simpset addsimps [parts_insert2])) 3);
2135
80477862ab33 Minor corrections
paulson
parents: 2134
diff changeset
   460
(*OR4, OR2, Fake*) 
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   461
by (REPEAT_FIRST (resolve_tac [conjI, impI] ORELSE' spy_analz_tac));
2135
80477862ab33 Minor corrections
paulson
parents: 2134
diff changeset
   462
(*Oops*) (** LEVEL 5 **)
80477862ab33 Minor corrections
paulson
parents: 2134
diff changeset
   463
by (fast_tac (!claset delrules [disjE]
80477862ab33 Minor corrections
paulson
parents: 2134
diff changeset
   464
		      addDs [unique_session_keys] addss (!simpset)) 1);
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   465
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
   466
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   467
goal thy 
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   468
 "!!evs. [| Says Server B \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   469
\            {|NA, Crypt {|NA, K|} (shrK A),                             \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   470
\                  Crypt {|NB, K|} (shrK B)|} : set_of_list evs;         \
2135
80477862ab33 Minor corrections
paulson
parents: 2134
diff changeset
   471
\           Says B Spy {|NA, NB, K|} ~: set_of_list evs;                 \
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   472
\           A ~: lost;  B ~: lost;  evs : otway lost |]                  \
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   473
\        ==> K ~: analz (sees lost Spy evs)";
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   474
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1);
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   475
by (fast_tac (!claset addSEs [lemma]) 1);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   476
qed "Spy_not_see_encrypted_key";
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   477
1945
20ca9cf90e69 A further tidying
paulson
parents: 1941
diff changeset
   478
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   479
goal thy 
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   480
 "!!evs. [| C ~: {A,B,Server};                                           \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   481
\           Says Server B                                                \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   482
\            {|NA, Crypt {|NA, K|} (shrK A),                             \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   483
\                  Crypt {|NB, K|} (shrK B)|} : set_of_list evs;         \
2135
80477862ab33 Minor corrections
paulson
parents: 2134
diff changeset
   484
\           Says B Spy {|NA, NB, K|} ~: set_of_list evs;                 \
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   485
\           A ~: lost;  B ~: lost;  evs : otway lost |]                  \
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   486
\        ==> K ~: analz (sees lost C evs)";
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   487
by (rtac (subset_insertI RS sees_mono RS analz_mono RS contra_subsetD) 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   488
by (rtac (sees_lost_agent_subset_sees_Spy RS analz_mono RS contra_subsetD) 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   489
by (FIRSTGOAL (rtac Spy_not_see_encrypted_key));
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   490
by (REPEAT_FIRST (fast_tac (!claset addIs [otway_mono RS subsetD])));
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   491
qed "Agent_not_see_encrypted_key";
1945
20ca9cf90e69 A further tidying
paulson
parents: 1941
diff changeset
   492
20ca9cf90e69 A further tidying
paulson
parents: 1941
diff changeset
   493
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   494
(**** Authenticity properties relating to NB ****)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   495
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   496
(*Only OR2 can have caused such a part of a message to appear.  We do not
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   497
  know anything about X'.*)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   498
goal thy 
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   499
 "!!evs. [| B ~: lost;  evs : otway lost |]                    \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   500
\        ==> Crypt {|NA, NB, Agent A, Agent B|} (shrK B)       \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   501
\             : parts (sees lost Spy evs) -->                  \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   502
\            (EX X'. Says B Server                             \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   503
\             {|NA, Agent A, Agent B, X',                      \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   504
\               Crypt {|NA, NB, Agent A, Agent B|} (shrK B)|}  \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   505
\             : set_of_list evs)";
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   506
by (parts_induct_tac 1);
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   507
by (auto_tac (!claset, !simpset addcongs [conj_cong]));
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   508
qed_spec_mp "Crypt_imp_OR2";
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   509
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   510
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   511
(** The Nonce NB uniquely identifies B's  message. **)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   512
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   513
goal thy 
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   514
 "!!evs. [| evs : otway lost; B ~: lost |]               \
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   515
\ ==> EX NA' A'. ALL NA A.                               \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   516
\      Crypt {|NA, NB, Agent A, Agent B|} (shrK B) : parts(sees lost Spy evs) \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   517
\      --> NA = NA' & A = A'";
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   518
by (parts_induct_tac 1);
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   519
by (simp_tac (!simpset addsimps [all_conj_distrib]) 1); 
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   520
(*OR2: creation of new Nonce.  Move assertion into global context*)
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   521
by (expand_case_tac "NB = ?y" 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   522
by (fast_tac (!claset addSEs (nonce_not_seen_now::partsEs)) 1);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   523
val lemma = result();
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   524
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   525
goal thy 
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   526
 "!!evs.[| Crypt {|NA, NB, Agent A, Agent B|} (shrK B) \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   527
\                  : parts(sees lost Spy evs);         \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   528
\          Crypt {|NC, NB, Agent C, Agent B|} (shrK B) \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   529
\                  : parts(sees lost Spy evs);         \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   530
\          evs : otway lost;  B ~: lost |]             \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   531
\        ==> NC = NA & C = A";
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   532
by (dtac lemma 1);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   533
by (assume_tac 1);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   534
by (REPEAT (etac exE 1));
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   535
(*Duplicate the assumption*)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   536
by (forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl 1);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   537
by (fast_tac (!claset addSDs [spec]) 1);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   538
qed "unique_NB";
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   539
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   540
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   541
(*If the encrypted message appears, and B has used Nonce NB,
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   542
  then it originated with the Server!*)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   543
goal thy 
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   544
 "!!evs. [| B ~: lost;  B ~= Spy;  evs : otway lost |]                   \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   545
\    ==> Crypt {|NB, Key K|} (shrK B) : parts (sees lost Spy evs)        \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   546
\        --> (ALL X'. Says B Server                                      \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   547
\                       {|NA, Agent A, Agent B, X',                      \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   548
\                         Crypt {|NA, NB, Agent A, Agent B|} (shrK B)|}  \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   549
\             : set_of_list evs                                          \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   550
\             --> Says Server B                                          \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   551
\                  {|NA, Crypt {|NA, Key K|} (shrK A),                   \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   552
\                        Crypt {|NB, Key K|} (shrK B)|}                  \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   553
\                   : set_of_list evs)";
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   554
by (parts_induct_tac 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   555
(*OR1: it cannot be a new Nonce, contradiction.*)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   556
by (fast_tac (!claset addSIs [parts_insertI]
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   557
                      addSEs partsEs
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   558
                      addEs [Says_imp_old_nonces RS less_irrefl]
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   559
                      addss (!simpset)) 1);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   560
(*OR3 and OR4*)  (** LEVEL 5 **)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   561
(*OR4*)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   562
by (REPEAT (Safe_step_tac 2));
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   563
br (Crypt_imp_OR2 RS exE) 2;
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   564
by (REPEAT (fast_tac (!claset addEs partsEs) 2));
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   565
(*OR3*)  (** LEVEL 8 **)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   566
by (step_tac (!claset delrules [disjCI, impCE]) 1);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   567
by (fast_tac (!claset delrules [conjI] (*stop split-up*)) 3); 
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   568
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS parts.Inj]
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   569
                      addSEs [MPair_parts]
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   570
                      addDs  [unique_NB]) 2);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   571
by (fast_tac (!claset addSEs [MPair_parts]
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   572
                      addSDs [Says_imp_sees_Spy RS parts.Inj]
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   573
                      addSEs  [no_nonce_OR1_OR2 RSN (2, rev_notE)]
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   574
                      delrules [conjI, impCE] (*stop split-up*)) 1);
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   575
qed_spec_mp "NB_Crypt_imp_Server_msg";
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   576
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   577
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   578
(*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
   579
  has sent the correct message.*)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   580
goal thy 
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   581
 "!!evs. [| B ~: lost;  B ~= Spy;  evs : otway lost;               \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   582
\           Says S B {|NA, X, Crypt {|NB, Key K|} (shrK B)|}       \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   583
\            : set_of_list evs;                                    \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   584
\           Says B Server {|NA, Agent A, Agent B, X',              \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   585
\                           Crypt {|NA, NB, Agent A, Agent B|}     \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   586
\                                 (shrK B)|}                       \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   587
\            : set_of_list evs |]                                  \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   588
\        ==> Says Server B                                         \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   589
\                 {|NA,                                            \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   590
\                   Crypt {|NA, Key K|} (shrK A),                  \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   591
\                   Crypt {|NB, Key K|} (shrK B)|}                 \
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   592
\                   : set_of_list evs";
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   593
by (fast_tac (!claset addSIs [NB_Crypt_imp_Server_msg]
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   594
                      addEs  partsEs
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   595
                      addDs  [Says_imp_sees_Spy RS parts.Inj]) 1);
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   596
qed "B_trust_OR3";
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   597
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   598
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   599
B_trust_OR3 RS Spy_not_see_encrypted_key;
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   600
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   601
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2014
diff changeset
   602
(** A session key uniquely identifies a pair of senders in the message
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   603
    encrypted by a good agent C.  NEEDED?  INTERESTING?**)
1945
20ca9cf90e69 A further tidying
paulson
parents: 1941
diff changeset
   604
goal thy 
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   605
 "!!evs. evs : otway lost ==>                                           \
2135
80477862ab33 Minor corrections
paulson
parents: 2134
diff changeset
   606
\      EX A B. ALL C N.                                                 \
80477862ab33 Minor corrections
paulson
parents: 2134
diff changeset
   607
\         C ~: lost -->                                                 \
80477862ab33 Minor corrections
paulson
parents: 2134
diff changeset
   608
\         Crypt {|N, Key K|} (shrK C) : parts (sees lost Spy evs) -->   \
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2014
diff changeset
   609
\         C=A | C=B";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   610
by (Simp_tac 1);        (*Miniscoping*)
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   611
by (etac otway.induct 1);
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   612
by analz_Fake_tac;
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   613
(*spy_analz_tac just does not work here: it is an entirely different proof!*)
1945
20ca9cf90e69 A further tidying
paulson
parents: 1941
diff changeset
   614
by (ALLGOALS 
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2014
diff changeset
   615
    (asm_simp_tac (!simpset addsimps [all_conj_distrib, ex_disj_distrib,
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2104
diff changeset
   616
                                      imp_conjR, parts_insert_sees,
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   617
                                      parts_insert2])));
1945
20ca9cf90e69 A further tidying
paulson
parents: 1941
diff changeset
   618
by (REPEAT_FIRST (etac exE));
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2014
diff changeset
   619
(*OR3: extraction of K = newK evsa to global context...*) (** LEVEL 6 **)
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   620
by (expand_case_tac "K = ?y" 4);
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   621
by (REPEAT (ares_tac [exI] 5));
1945
20ca9cf90e69 A further tidying
paulson
parents: 1941
diff changeset
   622
(*...we prove this case by contradiction: the key is too new!*)
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2014
diff changeset
   623
by (fast_tac (!claset addSEs partsEs
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   624
                      addEs [Says_imp_old_keys RS less_irrefl]
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   625
                      addss (!simpset)) 4);
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2014
diff changeset
   626
(*Base, Fake, OR2, OR4*)
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2014
diff changeset
   627
by (REPEAT_FIRST ex_strip_tac);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   628
by (dtac synth.Inj 4);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   629
by (dtac synth.Inj 3);
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2014
diff changeset
   630
(*Now in effect there are three Fake cases*)
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2014
diff changeset
   631
by (REPEAT_FIRST (best_tac (!claset addDs [impOfSubs Fake_parts_insert]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   632
                                    delrules [disjCI, disjE]
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   633
                                    addss (!simpset))));
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   634
qed "key_identifies_senders";