src/HOL/Auth/Yahalom.ML
author paulson
Thu, 12 Sep 1996 10:40:05 +0200
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child 1995 c80e58e78d9c
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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 Yahalom protocol.
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From page 257 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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(**** Inductive proofs about yahalom ****)
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(*The Enemy can see more than anybody else, except for their initial state*)
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goal thy 
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 "!!evs. evs : yahalom ==> \
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\     sees A evs <= initState A Un sees Enemy evs";
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be yahalom.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_Enemy";
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(*Nobody sends themselves messages*)
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goal thy "!!evs. evs : yahalom ==> ALL A X. Says A A X ~: set_of_list evs";
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be yahalom.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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goal thy "!!evs. evs : yahalom ==> Notes A X ~: set_of_list evs";
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be yahalom.induct 1;
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by (Auto_tac());
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qed "not_Notes";
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Addsimps [not_Notes];
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AddSEs   [not_Notes 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 Enemy evs)";
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by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj]) 1);
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qed "YM2_analz_sees_Enemy";
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goal thy "!!evs. (Says S B {|N, X, X'|}) : set_of_list evs ==> \
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\                X : analz (sees Enemy evs)";
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by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj]) 1);
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qed "YM4_analz_sees_Enemy";
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goal thy "!!evs. (Says B' A {|N, Crypt {|N,K|} K'|}) : set_of_list evs ==> \
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\                K : parts (sees Enemy evs)";
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by (fast_tac (!claset addSEs partsEs
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	              addSDs [Says_imp_sees_Enemy RS parts.Inj]) 1);
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qed "YM5_parts_sees_Enemy";
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(*YM2_analz... and YM4_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 YM2), and of course Fake
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  messages originate from the Enemy. *)
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val YM2_YM4_tac = 
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    dtac (YM2_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 4 THEN
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    dtac (YM4_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 6;
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(*** Shared keys are not betrayed ***)
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(*Enemy never sees another agent's shared key! (unless it is leaked at start)*)
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goal thy 
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 "!!evs. [| evs : yahalom;  A ~: bad |] ==> \
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\        Key (shrK A) ~: parts (sees Enemy evs)";
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be yahalom.induct 1;
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by YM2_YM4_tac;
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by (Auto_tac());
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(*Deals with Fake message*)
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by (best_tac (!claset addDs [impOfSubs analz_subset_parts,
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			     impOfSubs Fake_parts_insert]) 1);
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qed "Enemy_not_see_shrK";
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bind_thm ("Enemy_not_analz_shrK",
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	  [analz_subset_parts, Enemy_not_see_shrK] MRS contra_subsetD);
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Addsimps [Enemy_not_see_shrK, Enemy_not_analz_shrK];
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(*We go to some trouble to preserve R in the 3rd and 4th subgoals
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  As usual fast_tac cannot be used because it uses the equalities too soon*)
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val major::prems = 
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goal thy  "[| Key (shrK A) : parts (sees Enemy evs);       \
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\             evs : yahalom;                                 \
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\             A:bad ==> R                                  \
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\           |] ==> R";
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br ccontr 1;
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br ([major, Enemy_not_see_shrK] MRS rev_notE) 1;
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by (swap_res_tac prems 2);
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by (ALLGOALS (fast_tac (!claset addIs prems)));
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qed "Enemy_see_shrK_E";
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bind_thm ("Enemy_analz_shrK_E", 
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	  analz_subset_parts RS subsetD RS Enemy_see_shrK_E);
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AddSEs [Enemy_see_shrK_E, Enemy_analz_shrK_E];
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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 length comparison, and Union over C, are essential for the 
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  induction! *)
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goal thy "!!evs. evs : yahalom ==> \
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\                length evs <= length evs' --> \
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\                          Key (newK evs') ~: (UN C. parts (sees C evs))";
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be yahalom.induct 1;
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by YM2_YM4_tac;
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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);
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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 : yahalom;  length evs <= length evs' |] ==> \
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\        Key (newK evs') ~: parts (sees 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 : yahalom                 \
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\        |] ==> length evt < length evs";
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br ccontr 1;
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by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Enemy]
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	              addIs [impOfSubs parts_mono, leI]) 1);
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qed "Says_imp_old_keys";
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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 : yahalom ==> \
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\                length evs <= length evs' --> \
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\                newK evs' ~: keysFor (UN C. parts (sees C evs))";
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be yahalom.induct 1;
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by YM2_YM4_tac;
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bd YM5_parts_sees_Enemy 7;
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by (ALLGOALS Asm_simp_tac);
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(*YM1 and YM3*)
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by (EVERY (map (fast_tac (!claset addDs [Suc_leD] addss (!simpset))) [4,2]));
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(*Fake, YM2, YM4: these messages send unknown (X) components*)
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by (EVERY 
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    (map
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     (best_tac
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      (!claset addSDs [newK_invKey]
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	       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)))
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     [3,2,1]));
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(*YM5: dummy message*)
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by (best_tac (!claset addSDs [newK_invKey]
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		        addEs  [new_keys_not_seen RSN(2,rev_notE)]
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			addIs  [less_SucI, impOfSubs keysFor_mono]
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			addss (!simpset addsimps [le_def])) 1);
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val lemma = result();
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goal thy 
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 "!!evs. [| evs : yahalom;  length evs <= length evs' |] ==> \
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\        newK evs' ~: keysFor (parts (sees 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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(** Lemmas concerning the form of items passed in messages **)
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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 Enemy evs)) ==>
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          Key K : analz (sees Enemy evs)
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 A more general formula must be proved inductively.
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****)
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(*NOT useful in this form, but it says that session keys are not used
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  to encrypt messages containing other keys, in the actual protocol.
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  We require that agents should behave like this subsequently also.*)
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goal thy 
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 "!!evs. evs : yahalom ==> \
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\        (Crypt X (newK evt)) : parts (sees Enemy evs) & \
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\        Key K : parts {X} --> Key K : parts (sees Enemy evs)";
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be yahalom.induct 1;
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by YM2_YM4_tac;
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by (ALLGOALS (asm_simp_tac (!simpset addsimps pushes)));
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(*Deals with Faked messages*)
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by (best_tac (!claset addSEs partsEs
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		      addDs [impOfSubs analz_subset_parts,
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                             impOfSubs parts_insert_subset_Un]
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                      addss (!simpset)) 2);
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(*Base case and YM5*)
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by (Auto_tac());
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result();
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(** Specialized rewriting for this proof **)
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Delsimps [image_insert];
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Addsimps [image_insert RS sym];
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Delsimps [image_Un];
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Addsimps [image_Un RS sym];
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goal thy "insert (Key (newK x)) (sees A evs) = \
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\         Key `` (newK``{x}) Un (sees A evs)";
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by (Fast_tac 1);
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val insert_Key_singleton = result();
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goal thy "insert (Key (f x)) (Key``(f``E) Un C) = \
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\         Key `` (f `` (insert x E)) Un C";
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by (Fast_tac 1);
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val insert_Key_image = result();
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(*This lets us avoid analyzing the new message -- unless we have to!*)
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(*NEEDED??*)
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goal thy "synth (analz (sees Enemy evs)) <=   \
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\         synth (analz (sees Enemy (Says A B X # evs)))";
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by (Simp_tac 1);
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br (subset_insertI RS analz_mono RS synth_mono) 1;
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qed "synth_analz_thin";
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AddIs [impOfSubs synth_analz_thin];
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(** Session keys are not used to encrypt other session keys **)
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(*Could generalize this so that the X component doesn't have to be first
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  in the message?*)
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val enemy_analz_tac =
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  SELECT_GOAL 
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   (EVERY [REPEAT (resolve_tac [impI,notI] 1),
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	   dtac (impOfSubs Fake_analz_insert) 1,
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	   eresolve_tac [asm_rl, synth.Inj] 1,
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	   Fast_tac 1,
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	   Asm_full_simp_tac 1,
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	   IF_UNSOLVED (deepen_tac (!claset addIs [impOfSubs analz_mono]) 0 1)
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	   ]);
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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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goal thy  
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 "!!evs. evs : yahalom ==> \
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\  ALL K E. (Key K : analz (Key``(newK``E) Un (sees Enemy evs))) = \
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\           (K : newK``E | Key K : analz (sees Enemy evs))";
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be yahalom.induct 1;
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bd YM2_analz_sees_Enemy 4;
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bd YM4_analz_sees_Enemy 6;
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by (REPEAT_FIRST (resolve_tac [allI, lemma]));
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by (ALLGOALS (*Takes 35 secs*)
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   293
    (asm_simp_tac 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   294
     (!simpset addsimps ([insert_Key_singleton, insert_Key_image, pushKey_newK]
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   295
			 @ pushes)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   296
               setloop split_tac [expand_if])));
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   297
(*YM4*) 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   298
by (enemy_analz_tac 5);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   299
(*YM3*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   300
by (Fast_tac 4);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   301
(*YM2*) (** LEVEL 7 **)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   302
by (res_inst_tac [("x1","X"), ("y1", "{|?XX,?YY|}")] 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   303
    (insert_commute RS ssubst) 3);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   304
by (res_inst_tac [("x1","X"), ("y1", "{|?XX,?YY|}")]
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   305
    (insert_commute RS ssubst) 3);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   306
by (asm_simp_tac (!simpset setloop split_tac [expand_if]) 3);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   307
by (enemy_analz_tac 3);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   308
(*Fake case*) (** LEVEL 11 **)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   309
by (res_inst_tac [("y1","X"), ("A1", "?G Un (?H::msg set)")] 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   310
    (insert_commute RS ssubst) 2);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   311
by (enemy_analz_tac 2);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   312
(*Base case*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   313
by (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   314
qed_spec_mp "analz_image_newK";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   315
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   316
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   317
goal thy
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   318
 "!!evs. evs : yahalom ==>                               \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   319
\        Key K : analz (insert (Key (newK evt)) (sees Enemy evs)) = \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   320
\        (K = newK evt | Key K : analz (sees Enemy evs))";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   321
by (asm_simp_tac (HOL_ss addsimps [pushKey_newK, analz_image_newK, 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   322
				   insert_Key_singleton]) 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   323
by (Fast_tac 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   324
qed "analz_insert_Key_newK";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   325
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   326
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   327
(*Describes the form *and age* of K when the following message is sent*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   328
goal thy 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   329
 "!!evs. [| Says Server B \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   330
\            {|NA, Crypt {|NA, K|} (shrK A),                      \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   331
\                  Crypt {|NB, K|} (shrK B)|} : set_of_list evs;  \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   332
\           evs : yahalom |]                                        \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   333
\        ==> (EX evt:yahalom. K = Key(newK evt) & \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   334
\                           length evt < length evs) &            \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   335
\            (EX i. NA = Nonce i)";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   336
be rev_mp 1;
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   337
be yahalom.induct 1;
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   338
by (ALLGOALS (fast_tac (!claset addIs [less_SucI] addss (!simpset))));
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   339
qed "Says_Server_message_form";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   340
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   341
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   342
(*Crucial secrecy property: Enemy does not see the keys sent in msg YM3*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   343
goal thy 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   344
 "!!evs. [| Says Server A \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   345
\            {|NA, Crypt {|NA, K|} (shrK B),                      \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   346
\                  Crypt {|NB, K|} (shrK A)|} : set_of_list evs;  \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   347
\           A ~: bad;  B ~: bad;  evs : yahalom |] ==>              \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   348
\     K ~: analz (sees Enemy evs)";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   349
be rev_mp 1;
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   350
be yahalom.induct 1;
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   351
bd YM2_analz_sees_Enemy 4;
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   352
bd YM4_analz_sees_Enemy 6;
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   353
by (ALLGOALS Asm_simp_tac);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   354
(*Next 3 steps infer that K has the form "Key (newK evs'" ... *)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   355
by (REPEAT_FIRST (resolve_tac [conjI, impI]));
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   356
by (TRYALL (forward_tac [Says_Server_message_form] THEN' assume_tac));
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   357
by (REPEAT_FIRST (eresolve_tac [bexE, exE, conjE] ORELSE' hyp_subst_tac));
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   358
by (ALLGOALS
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   359
    (asm_full_simp_tac 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   360
     (!simpset addsimps ([analz_subset_parts RS contra_subsetD,
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   361
			  analz_insert_Key_newK] @ pushes)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   362
               setloop split_tac [expand_if])));
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   363
(*YM3*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   364
by (fast_tac (!claset addSEs [less_irrefl]) 3);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   365
(*Fake*) (** LEVEL 10 **)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   366
by (res_inst_tac [("y1","X"), ("x1", "Key ?K")] (insert_commute RS ssubst) 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   367
by (enemy_analz_tac 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   368
(*YM4*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   369
by (mp_tac 2);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   370
by (enemy_analz_tac 2);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   371
(*YM2*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   372
by (mp_tac 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   373
by (res_inst_tac [("x1","X"), ("y1", "{|?XX,?YY|}")]
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   374
    (insert_commute RS ssubst) 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   375
by (asm_simp_tac (!simpset setloop split_tac [expand_if]) 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   376
by (enemy_analz_tac 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   377
qed "Enemy_not_see_encrypted_key";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   378
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   379
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   380
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   381
(*** Session keys are issued at most once, and identify the principals ***)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   382
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   383
(** First, two lemmas for the Fake, YM2 and YM4 cases **)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   384
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   385
goal thy 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   386
 "!!evs. [| X : synth (analz (sees Enemy evs));                \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   387
\           Crypt X' (shrK C) : parts{X};                      \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   388
\           C ~: bad;  evs : yahalom |]  \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   389
\        ==> Crypt X' (shrK C) : parts (sees Enemy evs)";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   390
by (best_tac (!claset addSEs [impOfSubs analz_subset_parts]
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   391
	              addDs [impOfSubs parts_insert_subset_Un]
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   392
                      addss (!simpset)) 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   393
qed "Crypt_Fake_parts";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   394
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   395
goal thy 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   396
 "!!evs. [| Crypt X' K : parts (sees A evs);  evs : yahalom |]  \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   397
\        ==> EX S S' Y. Says S S' Y : set_of_list evs &       \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   398
\            Crypt X' K : parts {Y}";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   399
bd parts_singleton 1;
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   400
by (fast_tac (!claset addSDs [seesD] addss (!simpset)) 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   401
qed "Crypt_parts_singleton";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   402
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   403
fun ex_strip_tac i = REPEAT (ares_tac [exI, conjI] i) THEN assume_tac (i+1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   404
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   405
(*The Key K uniquely identifies a pair of senders in the message encrypted by
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   406
  C, but if C=Enemy then he could send all sorts of nonsense.*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   407
goal thy 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   408
 "!!evs. evs : yahalom ==>                                     \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   409
\      EX A B. ALL C.                                        \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   410
\         C ~: bad -->                                       \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   411
\         (ALL S S' X. Says S S' X : set_of_list evs -->     \
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   412
\           (EX NA. Crypt {|NA, Key K|} (shrK C) : parts{X}) --> C=A | C=B)";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   413
by (Simp_tac 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   414
be yahalom.induct 1;
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   415
bd YM2_analz_sees_Enemy 4;
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   416
bd YM4_analz_sees_Enemy 6;
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   417
by (ALLGOALS 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   418
    (asm_simp_tac (!simpset addsimps [all_conj_distrib, imp_conj_distrib])));
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   419
by (REPEAT_FIRST (etac exE));
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   420
(*YM4*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   421
by (ex_strip_tac 4);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   422
by (fast_tac (!claset addSDs [synth.Inj RS Crypt_Fake_parts, 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   423
			      Crypt_parts_singleton]) 4);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   424
(*YM3: Case split propagates some context to other subgoal...*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   425
	(** LEVEL 8 **)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   426
by (excluded_middle_tac "K = newK evsa" 3);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   427
by (Asm_simp_tac 3);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   428
by (REPEAT (ares_tac [exI] 3));
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   429
(*...we prove this case by contradiction: the key is too new!*)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   430
by (fast_tac (!claset addIs [impOfSubs (subset_insertI RS parts_mono)]
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   431
		      addSEs partsEs
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   432
		      addEs [Says_imp_old_keys RS less_irrefl]
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   433
	              addss (!simpset)) 3);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   434
(*YM2*) (** LEVEL 12 **)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   435
by (ex_strip_tac 2);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   436
by (res_inst_tac [("x1","X"), ("y1", "{|?XX,?YY|}")]
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   437
    (insert_commute RS ssubst) 2);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   438
by (Simp_tac 2);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   439
by (fast_tac (!claset addSDs [synth.Inj RS Crypt_Fake_parts, 
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   440
			      Crypt_parts_singleton]) 2);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   441
(*Fake*) (** LEVEL 16 **)
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   442
by (ex_strip_tac 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   443
by (fast_tac (!claset addSDs [Crypt_Fake_parts, Crypt_parts_singleton]) 1);
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   444
qed "unique_session_keys";
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   445
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   446
(*It seems strange but this theorem is NOT needed to prove the main result!*)