src/HOL/Auth/OtwayRees_Bad.ML
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(*  Title:      HOL/Auth/OtwayRees_Bad
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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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The FAULTY version omitting encryption of Nonce NB, as suggested on page 247 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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This file illustrates the consequences of such errors.  We can still prove
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impressive-looking properties such as Spy_not_see_encrypted_key, yet the
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protocol is open to a middleperson attack.  Attempting to prove some key lemmas
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indicates the possibility of this attack.
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*)
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open OtwayRees_Bad;
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proof_timing:=true;
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HOL_quantifiers := false;
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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.          \
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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 (ALLGOALS (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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(*The Spy can see more than anybody else, except for their initial state*)
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goal thy 
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 "!!evs. evs : otway ==> \
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\     sees lost A evs <= initState lost A Un sees lost Spy evs";
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by (etac otway.induct 1);
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by (ALLGOALS (fast_tac (!claset addDs [sees_Says_subset_insert RS subsetD] 
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                                addss (!simpset))));
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qed "sees_agent_subset_sees_Spy";
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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_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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val parts_Fake_tac = 
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    forward_tac [OR2_parts_sees_Spy] 4 THEN 
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    forward_tac [OR4_parts_sees_Spy] 6 THEN
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    forward_tac [Oops_parts_sees_Spy] 7;
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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 \
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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 \
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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 |] ==> 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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  This has to be proved anew for each protocol description,
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  but should go by similar reasoning every time.  Hardest case is the
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  standard Fake rule.  
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      The Union over C is essential for the induction! *)
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goal thy "!!evs. evs : otway ==> \
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\                length evs <= length evs' --> \
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\                          Key (newK evs') ~: (UN C. parts (sees lost C 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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val lemma = result();
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(*Variant needed for the main theorem below*)
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goal thy 
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 "!!evs. [| evs : otway;  length evs <= length evs' |]    \
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\        ==> Key (newK evs') ~: parts (sees lost C evs)";
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by (fast_tac (!claset addDs [lemma]) 1);
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qed "new_keys_not_seen";
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Addsimps [new_keys_not_seen];
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(*Another 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                 \
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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! [proofs resemble those above] ***)
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goal thy "!!evs. evs : otway ==> \
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\                length evs <= length evs' --> \
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\                      Nonce (newN evs') ~: (UN C. parts (sees lost C evs))";
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by (etac otway.induct 1);
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(*auto_tac does not work here, as it performs safe_tac first*)
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by (ALLGOALS (asm_simp_tac (!simpset addsimps [parts_insert2]
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                                     addcongs [disj_cong])));
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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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val lemma = result();
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(*Variant needed for the main theorem below*)
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goal thy 
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 "!!evs. [| evs : otway;  length evs <= length evs' |]    \
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\        ==> Nonce (newN evs') ~: parts (sees lost C evs)";
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by (fast_tac (!claset addDs [lemma]) 1);
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qed "new_nonces_not_seen";
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Addsimps [new_nonces_not_seen];
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(*Another variant: old messages must contain old nonces!*)
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goal thy 
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 "!!evs. [| Says A B X : set_of_list evs;  \
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\           Nonce (newN evt) : parts {X};    \
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\           evs : otway                 \
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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 ==> \
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\                length evs <= length evs' --> \
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\                newK evs' ~: keysFor (UN C. parts (sees lost C 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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val lemma = result();
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goal thy 
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 "!!evs. [| evs : otway;  length evs <= length evs' |]    \
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\        ==> newK evs' ~: keysFor (parts (sees lost C evs))";
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by (fast_tac (!claset addSDs [lemma] addss (!simpset)) 1);
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qed "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 |]                                   \
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\        ==> (EX evt: otway. 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.*)
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val analz_Fake_tac = 
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    dtac OR2_analz_sees_Spy 4 THEN 
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    dtac OR4_analz_sees_Spy 6 THEN
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    forward_tac [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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(*Lemma for the trivial direction of the if-and-only-if*)
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goal thy  
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 "!!evs. (Key K : analz (Key``nE Un sEe)) --> \
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\         (K : nE | Key K : analz sEe)  ==>     \
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\        (Key K : analz (Key``nE Un sEe)) = (K : nE | Key K : analz sEe)";
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by (fast_tac (!claset addSEs [impOfSubs analz_mono]) 1);
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val lemma = result();
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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 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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diff changeset
   294
by analz_Fake_tac;
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   295
by (REPEAT_FIRST (ares_tac [allI, lemma]));
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   296
by (ALLGOALS
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   297
    (asm_simp_tac 
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   298
     (!simpset addsimps ([insert_Key_singleton, insert_Key_image, pushKey_newK]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2002
diff changeset
   299
                         @ pushes)
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   300
               setloop split_tac [expand_if])));
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   301
(** LEVEL 7 **)
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   302
(*OR4, OR2, Fake*) 
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   303
by (EVERY (map spy_analz_tac [5,3,2]));
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   304
(*Oops, OR3, Base*)
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   305
by (REPEAT (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1));
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   306
qed_spec_mp "analz_image_newK";
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   307
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   308
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   309
goal thy
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   310
 "!!evs. evs : otway ==>                               \
2052
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   311
\        Key K : analz (insert (Key (newK evt)) (sees lost Spy evs)) = \
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   312
\        (K = newK evt | Key K : analz (sees lost Spy evs))";
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   313
by (asm_simp_tac (HOL_ss addsimps [pushKey_newK, analz_image_newK, 
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2002
diff changeset
   314
                                   insert_Key_singleton]) 1);
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   315
by (Fast_tac 1);
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   316
qed "analz_insert_Key_newK";
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   317
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   318
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   319
(*** The Key K uniquely identifies the Server's  message. **)
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   320
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   321
goal thy 
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   322
 "!!evs. evs : otway ==>                                                 \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   323
\   EX B' NA' NB' X'. ALL B NA NB X.                                          \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   324
\     Says Server B {|NA, X, Crypt {|NB, K|} (shrK B)|} : set_of_list evs --> \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   325
\     B=B' & NA=NA' & NB=NB' & X=X'";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2002
diff changeset
   326
by (etac otway.induct 1);
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   327
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib])));
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   328
by (Step_tac 1);
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   329
(*Remaining cases: OR3 and OR4*)
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   330
by (ex_strip_tac 2);
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   331
by (Fast_tac 2);
2107
23e8f15ec95f The new proof of the lemma for new_nonces_not_seen is faster
paulson
parents: 2052
diff changeset
   332
by (expand_case_tac "K = ?y" 1);
23e8f15ec95f The new proof of the lemma for new_nonces_not_seen is faster
paulson
parents: 2052
diff changeset
   333
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2));
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   334
(*...we assume X is a very new message, and handle this case by contradiction*)
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   335
by (fast_tac (!claset addEs [Says_imp_old_keys RS less_irrefl]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2002
diff changeset
   336
                      delrules [conjI]    (*prevent split-up into 4 subgoals*)
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2002
diff changeset
   337
                      addss (!simpset addsimps [parts_insertI])) 1);
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   338
val lemma = result();
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   339
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   340
goal thy 
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   341
 "!!evs. [| Says Server B {|NA, X, Crypt {|NB, K|} (shrK B)|}      \
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   342
\            : set_of_list evs;                                    \ 
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   343
\           Says Server B' {|NA',X',Crypt {|NB',K|} (shrK B')|}    \
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   344
\            : set_of_list evs;                                    \
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   345
\           evs : otway |] ==> X=X' & B=B' & NA=NA' & NB=NB'";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2002
diff changeset
   346
by (dtac lemma 1);
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   347
by (REPEAT (etac exE 1));
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   348
(*Duplicate the assumption*)
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   349
by (forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl 1);
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   350
by (fast_tac (!claset addSDs [spec]) 1);
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   351
qed "unique_session_keys";
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   352
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   353
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   354
(*Crucial security property, but not itself enough to guarantee correctness!*)
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   355
goal thy 
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   356
 "!!evs. [| A ~: lost;  B ~: lost;  evs : otway;  evt : otway |]        \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   357
\    ==> Says Server B \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   358
\          {|NA, Crypt {|NA, Key K|} (shrK A), \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   359
\            Crypt {|NB, Key K|} (shrK B)|} : set_of_list evs --> \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   360
\            Says B Spy {|NA, NB, Key K|} ~: set_of_list evs -->           \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   361
\        Key K ~: analz (sees lost Spy evs)";
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   362
by (etac otway.induct 1);
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   363
by analz_Fake_tac;
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   364
by (ALLGOALS
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   365
    (asm_full_simp_tac 
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   366
     (!simpset addsimps ([analz_subset_parts RS contra_subsetD,
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   367
                          analz_insert_Key_newK] @ pushes)
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   368
               setloop split_tac [expand_if])));
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   369
(*OR3*)
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   370
by (fast_tac (!claset addSIs [parts_insertI]
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   371
                      addEs [Says_imp_old_keys RS less_irrefl]
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   372
                      addss (!simpset addsimps [parts_insert2])) 3);
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   373
(*OR4, OR2, Fake*) 
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   374
by (REPEAT_FIRST (resolve_tac [conjI, impI] ORELSE' spy_analz_tac));
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   375
(*Oops*) (** LEVEL 5 **)
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   376
by (fast_tac (!claset delrules [disjE]
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   377
		      addDs [unique_session_keys] addss (!simpset)) 1);
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   378
val lemma = result() RS mp RS mp RSN(2,rev_notE);
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   379
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   380
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   381
goal thy 
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   382
 "!!evs. [| Says Server B                                         \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   383
\            {|NA, Crypt {|NA, K|} (shrK A),                      \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   384
\                  Crypt {|NB, K|} (shrK B)|} : set_of_list evs;  \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   385
\            Says B Spy {|NA, NB, K|} ~: set_of_list evs;         \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   386
\           A ~: lost;  B ~: lost;  evs : otway |]                \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   387
\        ==> K ~: analz (sees lost Spy evs)";
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   388
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1);
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   389
by (fast_tac (!claset addSEs [lemma]) 1);
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   390
qed "Spy_not_see_encrypted_key";
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   391
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   392
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   393
(*** Attempting to prove stronger properties ***)
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   394
2052
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   395
(*Only OR1 can have caused such a part of a message to appear.
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   396
  I'm not sure why A ~= B premise is needed: OtwayRees.ML doesn't need it.
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   397
  Perhaps it's because OR2 has two similar-looking encrypted messages in
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   398
	this version.*)
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   399
goal thy 
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   400
 "!!evs. [| A ~: lost;  A ~= B; evs : otway |]                 \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   401
\        ==> Crypt {|NA, Agent A, Agent B|} (shrK A)           \
2052
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   402
\             : parts (sees lost Spy evs) -->                  \
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   403
\            Says A B {|NA, Agent A, Agent B,                  \
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   404
\                       Crypt {|NA, Agent A, Agent B|} (shrK A)|}  \
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   405
\             : set_of_list evs";
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   406
by (parts_induct_tac 1);
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   407
by (Fast_tac 1);
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   408
qed_spec_mp "Crypt_imp_OR1";
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   409
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   410
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   411
(*Crucial property: If the encrypted message appears, and A has used NA
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   412
  to start a run, then it originated with the Server!*)
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   413
(*Only it is FALSE.  Somebody could make a fake message to Server
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   414
          substituting some other nonce NA' for NB.*)
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   415
goal thy 
2052
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   416
 "!!evs. [| A ~: lost;  A ~= Spy;  evs : otway |]                        \
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   417
\        ==> Crypt {|NA, Key K|} (shrK A) : parts (sees lost Spy evs) --> \
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   418
\            Says A B {|NA, Agent A, Agent B,                  \
2052
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   419
\                       Crypt {|NA, Agent A, Agent B|} (shrK A)|}  \
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   420
\             : set_of_list evs -->                            \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   421
\            (EX B NB. Says Server B                           \
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   422
\                 {|NA,                                        \
2052
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   423
\                   Crypt {|NA, Key K|} (shrK A),              \
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   424
\                   Crypt {|NB, Key K|} (shrK B)|}             \
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   425
\                   : set_of_list evs)";
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   426
by (parts_induct_tac 1);
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   427
(*OR1: it cannot be a new Nonce, contradiction.*)
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   428
by (fast_tac (!claset addSIs [parts_insertI]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2002
diff changeset
   429
                      addSEs partsEs
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2002
diff changeset
   430
                      addEs [Says_imp_old_nonces RS less_irrefl]
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2002
diff changeset
   431
                      addss (!simpset)) 1);
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   432
(*OR4*)
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   433
by (REPEAT (Safe_step_tac 2));
2052
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   434
by (REPEAT (best_tac (!claset addSDs [parts_cut]) 3));
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   435
by (fast_tac (!claset addSIs [Crypt_imp_OR1]
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   436
                      addEs  partsEs
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   437
                      addDs [Says_imp_sees_Spy RS parts.Inj]) 2);
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   438
(*OR3*)  (** LEVEL 5 **)
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   439
by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib])));
2052
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   440
by (step_tac (!claset delrules [disjCI, impCE]) 1);
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   441
(*The hypotheses at this point suggest an attack in which nonce NA is used
2052
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   442
  in two different roles:
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   443
          Says B' Server
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   444
           {|Nonce NAa, Agent Aa, Agent A,
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   445
             Crypt {|Nonce NAa, Agent Aa, Agent A|} (shrK Aa), Nonce NA,
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   446
             Crypt {|Nonce NAa, Agent Aa, Agent A|} (shrK A)|}
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   447
          : set_of_list evsa;
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   448
          Says A B
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   449
           {|Nonce NA, Agent A, Agent B,
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   450
             Crypt {|Nonce NA, Agent A, Agent B|} (shrK A)|}
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   451
          : set_of_list evsa 
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   452
*)
2131
3106a99d30a5 Changing from the Reveal to the Oops rule
paulson
parents: 2107
diff changeset
   453
writeln "GIVE UP! on NA_Crypt_imp_Server_msg";
2002
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   454
ed423882c6a9 Bad version of Otway-Rees and the new attack on it
paulson
parents:
diff changeset
   455
2052
d9f7f4b2613e Working again with new theory Shared
paulson
parents: 2032
diff changeset
   456
(*Thus the key property A_can_trust probably fails too.*)