src/HOL/Auth/Recur.ML
author paulson
Mon, 27 Jan 1997 15:29:39 +0100
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permissions -rw-r--r--
Tidied unicity theorems
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(*  Title:      HOL/Auth/Recur
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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 "recur" for the Recursive Authentication protocol.
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*)
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open Recur;
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proof_timing:=true;
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HOL_quantifiers := false;
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Pretty.setdepth 30;
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(** Possibility properties: traces that reach the end 
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        ONE theorem would be more elegant and faster!
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        By induction on a list of agents (no repetitions)
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**)
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(*Simplest case: Alice goes directly to the server*)
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goal thy
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 "!!A. A ~= Server   \
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\ ==> EX K NA. EX evs: recur lost.          \
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\     Says Server A {|Crypt (shrK A) {|Key K, Agent Server, Nonce NA|}, \
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\                     Agent Server|}      \
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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 (recur.Nil RS recur.RA1 RS 
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          (respond.One RSN (4,recur.RA3))) 2);
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by possibility_tac;
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result();
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(*Case two: Alice, Bob and the server*)
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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: recur lost.            \
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\       Says B A {|Crypt (shrK A) {|Key K, Agent B, Nonce NA|}, \
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\                  Agent Server|}                               \
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\         : set_of_list evs";
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by (cut_facts_tac [Nonce_supply2, Key_supply2] 1);
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by (REPEAT (eresolve_tac [exE, conjE] 1));
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by (REPEAT (resolve_tac [exI,bexI] 1));
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by (rtac (recur.Nil RS recur.RA1 RS recur.RA2 RS 
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          (respond.One RS respond.Cons RSN (4,recur.RA3)) RS
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          recur.RA4) 2);
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by basic_possibility_tac;
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by (DEPTH_SOLVE (eresolve_tac [asm_rl, less_not_refl2, 
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			       less_not_refl2 RS not_sym] 1));
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result();
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(*Case three: Alice, Bob, Charlie and the server
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  TOO SLOW to run every time!
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goal thy
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 "!!A B. [| A ~= B; B ~= C; A ~= Server; B ~= Server; C ~= Server |]   \
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\ ==> EX K. EX NA. EX evs: recur lost.                          \
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\       Says B A {|Crypt (shrK A) {|Key K, Agent B, Nonce NA|}, \
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\                  Agent Server|}                               \
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\         : set_of_list evs";
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by (cut_facts_tac [Nonce_supply3, Key_supply3] 1);
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by (REPEAT (eresolve_tac [exE, conjE] 1));
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by (REPEAT (resolve_tac [exI,bexI] 1));
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by (rtac (recur.Nil RS recur.RA1 RS recur.RA2 RS recur.RA2 RS 
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          (respond.One RS respond.Cons RS respond.Cons RSN
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           (4,recur.RA3)) RS recur.RA4 RS recur.RA4) 2);
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(*SLOW: 70 seconds*)
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by basic_possibility_tac;
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by (DEPTH_SOLVE (swap_res_tac [refl, conjI, disjCI] 1 
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		 ORELSE
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		 eresolve_tac [asm_rl, less_not_refl2, 
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			       less_not_refl2 RS not_sym] 1));
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result();
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****************)
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(**** Inductive proofs about recur ****)
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(*Monotonicity*)
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goal thy "!!evs. lost' <= lost ==> recur lost' <= recur lost";
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by (rtac subsetI 1);
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by (etac recur.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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                              :: recur.intrs))));
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qed "recur_mono";
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(*Nobody sends themselves messages*)
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goal thy "!!evs. evs : recur lost ==> ALL A X. Says A A X ~: set_of_list evs";
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by (etac recur.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. (PA,RB,KAB) : respond evs ==> Key KAB : parts{RB}";
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by (etac respond.induct 1);
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by (ALLGOALS Simp_tac);
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qed "respond_Key_in_parts";
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goal thy "!!evs. (PA,RB,KAB) : respond evs ==> Key KAB ~: used evs";
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by (etac respond.induct 1);
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by (REPEAT (assume_tac 1));
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qed "respond_imp_not_used";
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goal thy
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 "!!evs. [| Key K : parts {RB};  (PB,RB,K') : respond evs |] \
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\        ==> Key K ~: used evs";
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by (etac rev_mp 1);
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by (etac respond.induct 1);
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by (auto_tac(!claset addDs [Key_not_used, respond_imp_not_used],
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             !simpset));
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qed_spec_mp "Key_in_parts_respond";
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(*Simple inductive reasoning about responses*)
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goal thy "!!evs. (PA,RB,KAB) : respond evs ==> RB : responses evs";
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by (etac respond.induct 1);
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by (REPEAT (ares_tac (respond_imp_not_used::responses.intrs) 1));
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qed "respond_imp_responses";
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(** For reasoning about the encrypted portion of messages **)
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val RA2_analz_sees_Spy = Says_imp_sees_Spy RS analz.Inj |> standard;
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goal thy "!!evs. Says C' B {|Crypt K X, X', RA|} : set_of_list evs \
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\                ==> RA : 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 "RA4_analz_sees_Spy";
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(*RA2_analz... and RA4_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 RA2), and of course Fake
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  messages originate from the Spy. *)
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bind_thm ("RA2_parts_sees_Spy",
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          RA2_analz_sees_Spy RS (impOfSubs analz_subset_parts));
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bind_thm ("RA4_parts_sees_Spy",
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          RA4_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 RA2_parts_sees_Spy 4              THEN
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        etac subst 4 (*RA2: DELETE needless definition of PA!*)  THEN
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        forward_tac [respond_imp_responses] 5 THEN
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        tac RA4_parts_sees_Spy 6
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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 recur.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 long-term key (unless initially lost) **)
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goal thy 
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 "!!evs. evs : recur 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 (ALLGOALS (asm_simp_tac (!simpset addsimps [parts_insert_sees])));
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(*RA3*)
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by (fast_tac (!claset addDs [Key_in_parts_respond]
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                      addss (!simpset addsimps [parts_insert_sees])) 2);
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(*RA2*)
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by (best_tac (!claset addSEs partsEs addSDs [parts_cut]
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                      addss (!simpset)) 1);
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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 : recur 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 : recur 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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(** Nobody can have used non-existent keys! **)
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goal thy
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 "!!evs. [| K : keysFor (parts {RB});  (PB,RB,K') : respond evs |] \
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\        ==> K : range shrK";
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by (etac rev_mp 1);
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by (etac (respond_imp_responses RS responses.induct) 1);
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by (Auto_tac());
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qed_spec_mp "Key_in_keysFor_parts";
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goal thy "!!evs. evs : recur lost ==>          \
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\       Key K ~: used evs --> K ~: keysFor (parts (sees lost Spy evs))";
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by (parts_induct_tac 1);
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(*RA3*)
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by (best_tac (!claset addDs  [Key_in_keysFor_parts]
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                      addss  (!simpset addsimps [parts_insert_sees])) 2);
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(*Fake*)
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by (best_tac
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      (!claset addIs [impOfSubs analz_subset_parts]
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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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               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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(*For proofs involving analz.  We again instantiate the variable to "lost".*)
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val analz_Fake_tac = 
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    etac subst 4 (*RA2: DELETE needless definition of PA!*)  THEN
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    dres_inst_tac [("lost","lost")] RA2_analz_sees_Spy 4 THEN 
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    forward_tac [respond_imp_responses] 5                THEN
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    dres_inst_tac [("lost","lost")] RA4_analz_sees_Spy 6;
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(** Session keys are not used to encrypt other session keys **)
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(*Version for "responses" relation.  Handles case RA3 in the theorem below.  
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  Note that it holds for *any* set H (not just "sees lost Spy evs")
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  satisfying the inductive hypothesis.*)
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goal thy  
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 "!!evs. [| RB : responses evs;                             \
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\           ALL K KK. KK <= Compl (range shrK) -->          \
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\                     (Key K : analz (Key``KK Un H)) =      \
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\                     (K : KK | Key K : analz H) |]         \
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\       ==> ALL K KK. KK <= Compl (range shrK) -->          \
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\                     (Key K : analz (insert RB (Key``KK Un H))) = \
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\                     (K : KK | Key K : analz (insert RB H))";
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by (etac responses.induct 1);
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by (ALLGOALS (asm_simp_tac analz_image_freshK_ss));
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qed "resp_analz_image_freshK_lemma";
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(*Version for the protocol.  Proof is almost trivial, thanks to the lemma.*)
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goal thy  
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 "!!evs. evs : recur lost ==>                                   \
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\  ALL K KK. KK <= Compl (range shrK) -->                       \
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\            (Key K : analz (Key``KK Un (sees lost Spy evs))) = \
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\            (K : KK | Key K : analz (sees lost Spy evs))";
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by (etac recur.induct 1);
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by analz_Fake_tac;
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by (REPEAT_FIRST (resolve_tac [allI, impI]));
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by (REPEAT_FIRST (rtac analz_image_freshK_lemma ));
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by (ALLGOALS 
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    (asm_simp_tac
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     (analz_image_freshK_ss addsimps [resp_analz_image_freshK_lemma])));
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(*Base*)
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by (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1);
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(*RA4, RA2, Fake*) 
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by (REPEAT (spy_analz_tac 1));
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val raw_analz_image_freshK = result();
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qed_spec_mp "analz_image_freshK";
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(*Instance of the lemma with H replaced by (sees lost Spy evs):
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   [| RB : responses evs;  evs : recur lost; |]
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   ==> KK <= Compl (range shrK) --> 
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       Key K : analz (insert RB (Key``KK Un sees lost Spy evs)) =
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       (K : KK | Key K : analz (insert RB (sees lost Spy evs))) 
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*)
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bind_thm ("resp_analz_image_freshK",
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          raw_analz_image_freshK RSN
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            (2, resp_analz_image_freshK_lemma) RS spec RS spec);
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goal thy
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 "!!evs. [| evs : recur lost;  KAB ~: range shrK |] ==>              \
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\        Key K : analz (insert (Key KAB) (sees lost Spy evs)) =      \
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\        (K = KAB | Key K : analz (sees lost Spy evs))";
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by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1);
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qed "analz_insert_freshK";
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(*Everything that's hashed is already in past traffic. *)
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goal thy "!!evs. [| Hash {|Key(shrK A), X|} : parts (sees lost Spy evs);  \
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   304
\                   evs : recur lost;  A ~: lost |]                       \
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   305
\                ==> X : parts (sees lost Spy evs)";
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   306
by (etac rev_mp 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   307
by (etac recur.induct 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   308
by parts_Fake_tac;
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2449
diff changeset
   309
(*RA3 requires a further induction*)
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   310
by (etac responses.induct 5);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   311
by (ALLGOALS Asm_simp_tac);
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   312
(*Fake*)
2485
c4368c967c56 Simplification of some proofs, especially by eliminating
paulson
parents: 2481
diff changeset
   313
by (best_tac (!claset addDs [impOfSubs analz_subset_parts,
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   314
                             impOfSubs Fake_parts_insert]
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   315
                      addss (!simpset addsimps [parts_insert_sees])) 2);
2485
c4368c967c56 Simplification of some proofs, especially by eliminating
paulson
parents: 2481
diff changeset
   316
(*Two others*)
c4368c967c56 Simplification of some proofs, especially by eliminating
paulson
parents: 2481
diff changeset
   317
by (REPEAT (fast_tac (!claset addss (!simpset)) 1));
2550
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   318
qed "Hash_imp_body";
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   319
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   320
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   321
(** The Nonce NA uniquely identifies A's message. 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   322
    This theorem applies to steps RA1 and RA2!
2455
9c4444bfd44e Simplification and generalization of the guarantees.
paulson
parents: 2451
diff changeset
   323
9c4444bfd44e Simplification and generalization of the guarantees.
paulson
parents: 2451
diff changeset
   324
  Unicity is not used in other proofs but is desirable in its own right.
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   325
**)
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   326
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   327
goal thy 
2560
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   328
 "!!evs. [| evs : recur lost; A ~: lost |]                   \
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   329
\ ==> EX B' P'. ALL B P.                                     \
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   330
\        Hash {|Key(shrK A), Agent A, B, NA, P|} : parts (sees lost Spy evs) \
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   331
\          -->  B=B' & P=P'";
2485
c4368c967c56 Simplification of some proofs, especially by eliminating
paulson
parents: 2481
diff changeset
   332
by (parts_induct_tac 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   333
by (etac responses.induct 3);
2485
c4368c967c56 Simplification of some proofs, especially by eliminating
paulson
parents: 2481
diff changeset
   334
by (ALLGOALS (simp_tac (!simpset addsimps [all_conj_distrib]))); 
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   335
by (step_tac (!claset addSEs partsEs) 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   336
(*RA1,2: creation of new Nonce.  Move assertion into global context*)
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   337
by (ALLGOALS (expand_case_tac "NA = ?y"));
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   338
by (REPEAT_FIRST (ares_tac [exI]));
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   339
by (REPEAT (best_tac (!claset addSDs [Hash_imp_body]
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   340
                              addSEs sees_Spy_partsEs) 1));
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   341
val lemma = result();
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   342
2481
ee461c8bc9c3 Now uses HPair
paulson
parents: 2455
diff changeset
   343
goalw thy [HPair_def]
2560
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   344
 "!!evs.[| Hash[Key(shrK A)] {|Agent A,B,NA,P|} : parts (sees lost Spy evs);  \
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   345
\          Hash[Key(shrK A)] {|Agent A,B',NA,P'|} : parts (sees lost Spy evs);\
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   346
\          evs : recur lost;  A ~: lost |]                                    \
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   347
\        ==> B=B' & P=P'";
2481
ee461c8bc9c3 Now uses HPair
paulson
parents: 2455
diff changeset
   348
by (REPEAT (eresolve_tac partsEs 1));
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   349
by (prove_unique_tac lemma 1);
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   350
qed "unique_NA";
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   351
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   352
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   353
(*** Lemmas concerning the Server's response
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   354
      (relations "respond" and "responses") 
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   355
***)
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   356
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   357
goal thy
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   358
 "!!evs. [| RB : responses evs;  evs : recur lost |] \
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   359
\ ==> (Key (shrK B) : analz (insert RB (sees lost Spy evs))) = (B:lost)";
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   360
by (etac responses.induct 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   361
by (ALLGOALS
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   362
    (asm_simp_tac 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   363
     (analz_image_freshK_ss addsimps [Spy_analz_shrK,
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   364
                                      resp_analz_image_freshK])));
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   365
qed "shrK_in_analz_respond";
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   366
Addsimps [shrK_in_analz_respond];
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   367
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   368
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   369
goal thy  
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   370
 "!!evs. [| RB : responses evs;                             \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   371
\           ALL K KK. KK <= Compl (range shrK) -->          \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   372
\                     (Key K : analz (Key``KK Un H)) =      \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   373
\                     (K : KK | Key K : analz H) |]         \
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   374
\       ==> (Key K : analz (insert RB H)) --> \
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   375
\           (Key K : parts{RB} | Key K : analz H)";
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   376
by (etac responses.induct 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   377
by (ALLGOALS
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   378
    (asm_simp_tac 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   379
     (analz_image_freshK_ss addsimps [resp_analz_image_freshK_lemma])));
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   380
(*Simplification using two distinct treatments of "image"*)
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   381
by (simp_tac (!simpset addsimps [parts_insert2]) 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   382
by (fast_tac (!claset delrules [allE]) 1);
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   383
qed "resp_analz_insert_lemma";
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   384
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   385
bind_thm ("resp_analz_insert",
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   386
          raw_analz_image_freshK RSN
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   387
            (2, resp_analz_insert_lemma) RSN(2, rev_mp));
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   388
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   389
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   390
(*The Server does not send such messages.  This theorem lets us avoid
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2449
diff changeset
   391
  assuming B~=Server in RA4.*)
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   392
goal thy 
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   393
 "!!evs. evs : recur lost       \
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   394
\ ==> ALL C X Y P. Says Server C {|X, Agent Server, Agent C, Y, P|} \
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   395
\                  ~: set_of_list evs";
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   396
by (etac recur.induct 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   397
by (etac (respond.induct) 5);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   398
by (Auto_tac());
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   399
qed_spec_mp "Says_Server_not";
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   400
AddSEs [Says_Server_not RSN (2,rev_notE)];
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   401
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   402
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   403
(*The last key returned by respond indeed appears in a certificate*)
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   404
goal thy 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   405
 "!!K. (Hash[Key(shrK A)] {|Agent A, B, NA, P|}, RA, K) : respond evs \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   406
\ ==> Crypt (shrK A) {|Key K, B, NA|} : parts {RA}";
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   407
by (etac respond.elim 1);
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   408
by (ALLGOALS Asm_full_simp_tac);
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   409
qed "respond_certificate";
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   410
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   411
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   412
goal thy 
2560
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   413
 "!!K'. (PB,RB,KXY) : respond evs                          \
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   414
\  ==> EX A' B'. ALL A B N.                                \
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   415
\        Crypt (shrK A) {|Key K, Agent B, N|} : parts {RB} \
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   416
\          -->   (A'=A & B'=B) | (A'=B & B'=A)";
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   417
by (etac respond.induct 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   418
by (ALLGOALS (asm_full_simp_tac (!simpset addsimps [all_conj_distrib]))); 
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   419
(*Base case*)
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   420
by (Fast_tac 1);
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   421
by (Step_tac 1);
2550
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   422
by (expand_case_tac "K = KBC" 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   423
by (dtac respond_Key_in_parts 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   424
by (best_tac (!claset addSIs [exI]
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   425
                      addSEs partsEs
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   426
                      addDs [Key_in_parts_respond]) 1);
2550
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   427
by (expand_case_tac "K = KAB" 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   428
by (REPEAT (ares_tac [exI] 2));
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   429
by (ex_strip_tac 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   430
by (dtac respond_certificate 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   431
by (Fast_tac 1);
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   432
val lemma = result();
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   433
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   434
goal thy 
2560
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   435
 "!!RB. [| Crypt (shrK A) {|Key K, Agent B, N|} : parts {RB};      \
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   436
\          Crypt (shrK A') {|Key K, Agent B', N'|} : parts {RB};   \
2560
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   437
\          (PB,RB,KXY) : respond evs |]                            \
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   438
\ ==>   (A'=A & B'=B) | (A'=B & B'=A)";
2560
c57b585eecd9 Tidied unicity theorems
paulson
parents: 2550
diff changeset
   439
by (prove_unique_tac lemma 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   440
qed "unique_session_keys";
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   441
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   442
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2449
diff changeset
   443
(** Crucial secrecy property: Spy does not see the keys sent in msg RA3
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   444
    Does not in itself guarantee security: an attack could violate 
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   445
    the premises, e.g. by having A=Spy **)
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   446
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   447
goal thy 
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   448
 "!!evs. [| (PB,RB,KAB) : respond evs;  evs : recur lost |]         \
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   449
\        ==> ALL A A' N. A ~: lost & A' ~: lost -->                 \
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   450
\            Crypt (shrK A) {|Key K, Agent A', N|} : parts{RB} -->  \
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   451
\            Key K ~: analz (insert RB (sees lost Spy evs))";
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   452
by (etac respond.induct 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   453
by (forward_tac [respond_imp_responses] 2);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   454
by (forward_tac [respond_imp_not_used] 2);
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   455
by (ALLGOALS (*23 seconds*)
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   456
    (asm_simp_tac 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   457
     (analz_image_freshK_ss addsimps 
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   458
       [shrK_in_analz_respond, resp_analz_image_freshK, parts_insert2])));
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   459
by (ALLGOALS Simp_tac);
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   460
by (fast_tac (!claset addIs [impOfSubs analz_subset_parts]) 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   461
by (step_tac (!claset addSEs [MPair_parts]) 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   462
(** LEVEL 7 **)
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   463
by (fast_tac (!claset addSDs [resp_analz_insert, Key_in_parts_respond]
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   464
                      addDs  [impOfSubs analz_subset_parts]) 4);
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   465
by (fast_tac (!claset addSDs [respond_certificate]) 3);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   466
by (best_tac (!claset addSEs partsEs
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   467
                      addDs [Key_in_parts_respond]
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   468
                      addss (!simpset)) 2);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   469
by (dtac unique_session_keys 1);
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   470
by (etac respond_certificate 1);
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   471
by (assume_tac 1);
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   472
by (Fast_tac 1);
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   473
qed_spec_mp "respond_Spy_not_see_session_key";
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   474
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   475
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   476
goal thy
2550
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   477
 "!!evs. [| Crypt (shrK A) {|Key K, Agent A', N|}          \
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   478
\              : parts (sees lost Spy evs);                \
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   479
\           A ~: lost;  A' ~: lost;  evs : recur lost |]   \
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   480
\        ==> Key K ~: analz (sees lost Spy evs)";
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   481
by (etac rev_mp 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   482
by (etac recur.induct 1);
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   483
by analz_Fake_tac;
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   484
by (ALLGOALS
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   485
    (asm_simp_tac
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   486
     (!simpset addsimps [parts_insert_sees, analz_insert_freshK] 
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   487
               setloop split_tac [expand_if])));
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2449
diff changeset
   488
(*RA4*)
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   489
by (spy_analz_tac 5);
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   490
(*RA2*)
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   491
by (spy_analz_tac 3);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   492
(*Fake*)
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   493
by (spy_analz_tac 2);
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   494
(*Base*)
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   495
by (fast_tac (!claset addss (!simpset)) 1);
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   496
(*RA3 remains*)
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   497
by (step_tac (!claset delrules [impCE]) 1);
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2449
diff changeset
   498
(*RA3, case 2: K is an old key*)
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   499
by (best_tac (!claset addSDs [resp_analz_insert]
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   500
                      addSEs partsEs
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   501
                      addDs [Key_in_parts_respond]
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   502
                      addss (!simpset)) 2);
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2449
diff changeset
   503
(*RA3, case 1: use lemma previously proved by induction*)
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   504
by (fast_tac (!claset addSEs [respond_Spy_not_see_session_key RSN
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   505
                              (2,rev_notE)]) 1);
2550
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   506
qed "Spy_not_see_session_key";
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   507
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   508
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   509
goal thy 
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   510
 "!!evs. [| Crypt (shrK A) {|Key K, Agent A', N|}         \
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   511
\              : parts(sees lost Spy evs);                \
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   512
\           C ~: {A,A',Server};                           \
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   513
\           A ~: lost;  A' ~: lost;  evs : recur lost |]  \
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   514
\        ==> Key K ~: analz (sees lost C evs)";
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   515
by (rtac (subset_insertI RS sees_mono RS analz_mono RS contra_subsetD) 1);
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   516
by (rtac (sees_lost_agent_subset_sees_Spy RS analz_mono RS contra_subsetD) 1);
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   517
by (FIRSTGOAL (rtac Spy_not_see_session_key));
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   518
by (REPEAT_FIRST
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   519
    (deepen_tac
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   520
     (!claset addIs (map impOfSubs [recur_mono, parts_mono, sees_mono])) 0));
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   521
qed "Agent_not_see_session_key";
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   522
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   523
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   524
(**** Authenticity properties for Agents ****)
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   525
2481
ee461c8bc9c3 Now uses HPair
paulson
parents: 2455
diff changeset
   526
(*The response never contains Hashes*)
ee461c8bc9c3 Now uses HPair
paulson
parents: 2455
diff changeset
   527
goal thy
2550
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   528
 "!!evs. [| Hash {|Key (shrK B), M|} : parts (insert RB H); \
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   529
\           (PB,RB,K) : respond evs |]                      \
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   530
\        ==> Hash {|Key (shrK B), M|} : parts H";
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   531
by (etac rev_mp 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   532
by (etac (respond_imp_responses RS responses.induct) 1);
2481
ee461c8bc9c3 Now uses HPair
paulson
parents: 2455
diff changeset
   533
by (Auto_tac());
2550
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   534
qed "Hash_in_parts_respond";
2481
ee461c8bc9c3 Now uses HPair
paulson
parents: 2455
diff changeset
   535
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   536
(*Only RA1 or RA2 can have caused such a part of a message to appear.
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   537
  This result is of no use to B, who cannot verify the Hash.  Moreover,
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   538
  it can say nothing about how recent A's message is.  It might later be
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   539
  used to prove B's presence to A at the run's conclusion.*)
2481
ee461c8bc9c3 Now uses HPair
paulson
parents: 2455
diff changeset
   540
goalw thy [HPair_def]
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   541
 "!!evs. [| Hash {|Key(shrK A), Agent A, Agent B, NA, P|}         \
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   542
\             : parts (sees lost Spy evs);                        \
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   543
\            A ~: lost;  evs : recur lost |]                        \
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   544
\        ==> Says A B (Hash[Key(shrK A)] {|Agent A, Agent B, NA, P|})  \
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   545
\             : set_of_list evs";
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   546
by (etac rev_mp 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   547
by (parts_induct_tac 1);
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2449
diff changeset
   548
(*RA3*)
2485
c4368c967c56 Simplification of some proofs, especially by eliminating
paulson
parents: 2481
diff changeset
   549
by (fast_tac (!claset addSDs [Hash_in_parts_respond]) 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   550
qed_spec_mp "Hash_auth_sender";
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   551
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2485
diff changeset
   552
(** These two results subsume (for all agents) the guarantees proved
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   553
    separately for A and B in the Otway-Rees protocol.
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   554
**)
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   555
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   556
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   557
(*Certificates can only originate with the Server.*)
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   558
goal thy 
2550
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   559
 "!!evs. [| Crypt (shrK A) Y : parts (sees lost Spy evs);    \
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   560
\           A ~: lost;  A ~= Spy;  evs : recur lost |]       \
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   561
\        ==> EX C RC. Says Server C RC : set_of_list evs &   \
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   562
\                     Crypt (shrK A) Y : parts {RC}";
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   563
by (etac rev_mp 1);
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   564
by (parts_induct_tac 1);
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2449
diff changeset
   565
(*RA4*)
2455
9c4444bfd44e Simplification and generalization of the guarantees.
paulson
parents: 2451
diff changeset
   566
by (Fast_tac 4);
9c4444bfd44e Simplification and generalization of the guarantees.
paulson
parents: 2451
diff changeset
   567
(*RA3*)
9c4444bfd44e Simplification and generalization of the guarantees.
paulson
parents: 2451
diff changeset
   568
by (full_simp_tac (!simpset addsimps [parts_insert_sees]) 3
9c4444bfd44e Simplification and generalization of the guarantees.
paulson
parents: 2451
diff changeset
   569
    THEN Fast_tac 3);
9c4444bfd44e Simplification and generalization of the guarantees.
paulson
parents: 2451
diff changeset
   570
(*RA1*)
9c4444bfd44e Simplification and generalization of the guarantees.
paulson
parents: 2451
diff changeset
   571
by (Fast_tac 1);
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2449
diff changeset
   572
(*RA2: it cannot be a new Nonce, contradiction.*)
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   573
by (deepen_tac (!claset delrules [impCE]
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   574
                      addSIs [disjI2]
2455
9c4444bfd44e Simplification and generalization of the guarantees.
paulson
parents: 2451
diff changeset
   575
                      addSEs [MPair_parts]
2533
2d5604a51562 Simplified proofs
paulson
parents: 2516
diff changeset
   576
                      addDs  [parts.Body]
2449
d30ad12b1397 Recursive Authentication Protocol
paulson
parents:
diff changeset
   577
                      addss  (!simpset)) 0 1);
2550
8d8344bcf98a Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents: 2533
diff changeset
   578
qed "Cert_imp_Server_msg";