src/HOL/Auth/Yahalom.ML
author paulson
Tue, 16 Dec 1997 15:17:26 +0100
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parent 4238 679a233fb206
child 4449 df30e75f670f
permissions -rw-r--r--
Simplified proofs using rewrites for f``A where f is injective
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(*  Title:      HOL/Auth/Yahalom
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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 "yahalom" 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 Yahalom;
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proof_timing:=true;
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HOL_quantifiers := false;
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Pretty.setdepth 25;
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(*A "possibility property": there are traces that reach the end*)
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goal thy 
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 "!!A B. [| A ~= B; A ~= Server; B ~= Server |]   \
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\        ==> EX X NB K. EX evs: yahalom.     \
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\               Says A B {|X, Crypt K (Nonce NB)|} : set evs";
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by (REPEAT (resolve_tac [exI,bexI] 1));
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by (rtac (yahalom.Nil RS yahalom.YM1 RS yahalom.YM2 RS yahalom.YM3 RS 
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          yahalom.YM4) 2);
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by possibility_tac;
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result();
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(**** Inductive proofs about yahalom ****)
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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 evs";
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by (etac 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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(** For reasoning about the encrypted portion of messages **)
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(*Lets us treat YM4 using a similar argument as for the Fake case.*)
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goal thy "!!evs. Says S A {|Crypt (shrK A) Y, X|} : set evs ==> \
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\                X : analz (spies evs)";
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by (blast_tac (claset() addSDs [Says_imp_spies RS analz.Inj]) 1);
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qed "YM4_analz_spies";
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bind_thm ("YM4_parts_spies",
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          YM4_analz_spies RS (impOfSubs analz_subset_parts));
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(*Relates to both YM4 and Oops*)
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goal thy "!!evs. Says S A {|Crypt (shrK A) {|B,K,NA,NB|}, X|} : set evs ==> \
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\                K : parts (spies evs)";
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by (blast_tac (claset() addSEs partsEs
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                        addSDs [Says_imp_spies RS parts.Inj]) 1);
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qed "YM4_Key_parts_spies";
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(*For proving the easier theorems about X ~: parts (spies evs).*)
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fun parts_spies_tac i = 
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    forward_tac [YM4_Key_parts_spies] (i+6) THEN
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    forward_tac [YM4_parts_spies] (i+5)     THEN
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    prove_simple_subgoals_tac  i;
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(*Induction for regularity theorems.  If induction formula has the form
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   X ~: analz (spies evs) --> ... then it shortens the proof by discarding
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   needless information about analz (insert X (spies evs))  *)
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fun parts_induct_tac i = 
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    etac yahalom.induct i
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    THEN 
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    REPEAT (FIRSTGOAL analz_mono_contra_tac)
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    THEN  parts_spies_tac i;
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(** Theorems of the form X ~: parts (spies evs) imply that NOBODY
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    sends messages containing X! **)
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(*Spy never sees another agent's shared key! (unless it's bad at start)*)
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goal thy 
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 "!!evs. evs : yahalom ==> (Key (shrK A) : parts (spies evs)) = (A : bad)";
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by (parts_induct_tac 1);
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by (Fake_parts_insert_tac 1);
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by (ALLGOALS Blast_tac);
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qed "Spy_see_shrK";
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Addsimps [Spy_see_shrK];
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goal thy 
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 "!!evs. evs : yahalom ==> (Key (shrK A) : analz (spies evs)) = (A : bad)";
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by (auto_tac(claset() addDs [impOfSubs analz_subset_parts], simpset()));
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qed "Spy_analz_shrK";
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Addsimps [Spy_analz_shrK];
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goal thy  "!!A. [| Key (shrK A) : parts (spies evs);       \
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\                  evs : yahalom |] ==> A:bad";
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by (blast_tac (claset() addDs [Spy_see_shrK]) 1);
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qed "Spy_see_shrK_D";
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bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D);
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AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D];
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(*Nobody can have used non-existent keys!  Needed to apply analz_insert_Key*)
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goal thy "!!evs. evs : yahalom ==>          \
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\         Key K ~: used evs --> K ~: keysFor (parts (spies evs))";
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by (parts_induct_tac 1);
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(*Fake*)
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by (best_tac
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      (claset() addSDs [impOfSubs (parts_insert_subset_Un RS keysFor_mono)]
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                addIs  [impOfSubs analz_subset_parts]
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                addDs  [impOfSubs (analz_subset_parts RS keysFor_mono)]
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                addss  (simpset())) 1);
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(*YM2-4: Because Key K is not fresh, etc.*)
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by (REPEAT (blast_tac (claset() addSEs spies_partsEs) 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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(*Describes the form of K when the Server sends this message.  Useful for
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  Oops as well as main secrecy property.*)
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goal thy 
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 "!!evs. [| Says Server A {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, X|} \
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\             : set evs;                                                   \
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\           evs : yahalom |]                                          \
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\        ==> K ~: range shrK";
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by (etac rev_mp 1);
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by (etac yahalom.induct 1);
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by (ALLGOALS Asm_simp_tac);
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by (Blast_tac 1);
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qed "Says_Server_message_form";
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(*For proofs involving analz.*)
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val analz_spies_tac = 
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    forward_tac [YM4_analz_spies] 6 THEN
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    forward_tac [Says_Server_message_form] 7 THEN
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    assume_tac 7 THEN REPEAT ((etac exE ORELSE' hyp_subst_tac) 7);
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(****
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 The following is to prove theorems of the form
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  Key K : analz (insert (Key KAB) (spies evs)) ==>
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  Key K : analz (spies evs)
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 A more general formula must be proved inductively.
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****)
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(** Session keys are not used to encrypt other session keys **)
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goal thy  
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 "!!evs. evs : yahalom ==>                                 \
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\  ALL K KK. KK <= Compl (range shrK) -->                       \
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\            (Key K : analz (Key``KK Un (spies evs))) = \
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\            (K : KK | Key K : analz (spies evs))";
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by (etac yahalom.induct 1);
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by analz_spies_tac;
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by (REPEAT_FIRST (resolve_tac [allI, impI]));
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by (REPEAT_FIRST (rtac analz_image_freshK_lemma));
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by (ALLGOALS (asm_simp_tac analz_image_freshK_ss));
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(*Fake*) 
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by (spy_analz_tac 1);
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qed_spec_mp "analz_image_freshK";
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goal thy
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 "!!evs. [| evs : yahalom;  KAB ~: range shrK |] ==>             \
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\        Key K : analz (insert (Key KAB) (spies evs)) =       \
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\        (K = KAB | Key K : analz (spies evs))";
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by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1);
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qed "analz_insert_freshK";
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(*** The Key K uniquely identifies the Server's  message. **)
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goal thy 
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 "!!evs. evs : yahalom ==>                                     \
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\      EX A' B' na' nb' X'. ALL A B na nb X.                        \
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\          Says Server A                                            \
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\           {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, X|}        \
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\          : set evs --> A=A' & B=B' & na=na' & nb=nb' & X=X'";
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by (etac yahalom.induct 1);
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by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib])));
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by (ALLGOALS Clarify_tac);
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by (ex_strip_tac 2);
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by (Blast_tac 2);
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(*Remaining case: YM3*)
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by (expand_case_tac "K = ?y" 1);
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by (REPEAT (ares_tac [refl,exI,impI,conjI] 2));
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(*...we assume X is a recent message and handle this case by contradiction*)
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by (blast_tac (claset() addSEs spies_partsEs
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                        delrules [conjI]    (*no split-up to 4 subgoals*)) 1);
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val lemma = result();
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goal thy 
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"!!evs. [| Says Server A                                                 \
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\            {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, X|} : set evs; \
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\          Says Server A'                                                \
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\            {|Crypt (shrK A') {|Agent B', Key K, na', nb'|}, X'|} : set evs; \
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\          evs : yahalom |]                                    \
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\       ==> A=A' & B=B' & na=na' & nb=nb'";
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by (prove_unique_tac lemma 1);
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qed "unique_session_keys";
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(** Crucial secrecy property: Spy does not see the keys sent in msg YM3 **)
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goal thy 
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 "!!evs. [| A ~: bad;  B ~: bad;  evs : yahalom |]         \
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\        ==> Says Server A                                        \
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\              {|Crypt (shrK A) {|Agent B, Key K, na, nb|},       \
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\                Crypt (shrK B) {|Agent A, Key K|}|}              \
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\             : set evs -->                                       \
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\            Says A Spy {|na, nb, Key K|} ~: set evs -->          \
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\            Key K ~: analz (spies evs)";
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by (etac yahalom.induct 1);
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by analz_spies_tac;
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by (ALLGOALS
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    (asm_simp_tac 
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     (simpset() addsimps (expand_ifs@pushes)
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	        addsimps [analz_insert_eq, analz_insert_freshK])));
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(*Oops*)
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by (blast_tac (claset() addDs [unique_session_keys]) 3);
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(*YM3*)
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by (blast_tac (claset() delrules [impCE]
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                        addSEs spies_partsEs
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                        addIs [impOfSubs analz_subset_parts]) 2);
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(*Fake*) 
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by (spy_analz_tac 1);
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val lemma = result() RS mp RS mp RSN(2,rev_notE);
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4b7a432fb3ed Proof of Says_imp_old_keys is now more robust
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(*Final version*)
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goal thy 
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 "!!evs. [| Says Server A                                         \
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\              {|Crypt (shrK A) {|Agent B, Key K, na, nb|},       \
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\                Crypt (shrK B) {|Agent A, Key K|}|}              \
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\             : set evs;                                          \
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\           Says A Spy {|na, nb, Key K|} ~: set evs;              \
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\           A ~: bad;  B ~: bad;  evs : yahalom |]         \
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\        ==> Key K ~: analz (spies evs)";
2013
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by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1);
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by (blast_tac (claset() addSEs [lemma]) 1);
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qed "Spy_not_see_encrypted_key";
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974167c1d2c4 Reformatting; proved B_gets_secure_key
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(** Security Guarantee for A upon receiving YM3 **)
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(*If the encrypted message appears then it originated with the Server*)
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goal thy
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 "!!evs. [| Crypt (shrK A) {|Agent B, Key K, na, nb|} : parts (spies evs); \
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\           A ~: bad;  evs : yahalom |]                          \
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\         ==> Says Server A                                            \
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\              {|Crypt (shrK A) {|Agent B, Key K, na, nb|},            \
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\                Crypt (shrK B) {|Agent A, Key K|}|}                   \
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\             : set evs";
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by (etac rev_mp 1);
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by (parts_induct_tac 1);
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by (Fake_parts_insert_tac 1);
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qed "A_trusts_YM3";
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(** Security Guarantees for B upon receiving YM4 **)
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(*B knows, by the first part of A's message, that the Server distributed 
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  the key for A and B.  But this part says nothing about nonces.*)
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goal thy 
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 "!!evs. [| Crypt (shrK B) {|Agent A, Key K|} : parts (spies evs);   \
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\           B ~: bad;  evs : yahalom |]                                \
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\        ==> EX NA NB. Says Server A                                    \
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\                        {|Crypt (shrK A) {|Agent B, Key K,             \
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\                                           Nonce NA, Nonce NB|},       \
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\                          Crypt (shrK B) {|Agent A, Key K|}|}          \
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\                       : set evs";
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by (etac rev_mp 1);
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by (parts_induct_tac 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
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   282
by (Fake_parts_insert_tac 1);
2110
d01151e66cd4 Addition of Reveal message
paulson
parents: 2060
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   283
(*YM3*)
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
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   284
by (Blast_tac 1);
2110
d01151e66cd4 Addition of Reveal message
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parents: 2060
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   285
qed "B_trusts_YM4_shrK";
d01151e66cd4 Addition of Reveal message
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parents: 2060
diff changeset
   286
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
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   287
(*B knows, by the second part of A's message, that the Server distributed 
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
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   288
  the key quoting nonce NB.  This part says nothing about agent names. 
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
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parents: 3432
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   289
  Secrecy of NB is crucial.*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
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   290
goal thy 
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
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   291
 "!!evs. evs : yahalom                                             \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
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parents: 3679
diff changeset
   292
\        ==> Nonce NB ~: analz (spies evs) -->                  \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   293
\            Crypt K (Nonce NB) : parts (spies evs) -->         \
3543
82f33248d89d Cosmetic changes: margins, indentation, ...
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parents: 3519
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   294
\            (EX A B NA. Says Server A                             \
82f33248d89d Cosmetic changes: margins, indentation, ...
paulson
parents: 3519
diff changeset
   295
\                        {|Crypt (shrK A) {|Agent B, Key K,        \
82f33248d89d Cosmetic changes: margins, indentation, ...
paulson
parents: 3519
diff changeset
   296
\                                  Nonce NA, Nonce NB|},           \
82f33248d89d Cosmetic changes: margins, indentation, ...
paulson
parents: 3519
diff changeset
   297
\                          Crypt (shrK B) {|Agent A, Key K|}|}     \
3465
e85c24717cad set_of_list -> set
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parents: 3464
diff changeset
   298
\                       : set evs)";
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   299
by (parts_induct_tac 1);
3708
56facaebf3e3 Changed some proofs to use Clarify_tac
paulson
parents: 3683
diff changeset
   300
by (ALLGOALS Clarify_tac);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   301
(*YM3 & Fake*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
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parents: 3432
diff changeset
   302
by (Blast_tac 2);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   303
by (Fake_parts_insert_tac 1);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   304
(*YM4*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
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parents: 3432
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   305
(*A is uncompromised because NB is secure*)
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   306
by (not_bad_tac "A" 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   307
(*A's certificate guarantees the existence of the Server message*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   308
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj RS parts.Fst RS
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   309
			       A_trusts_YM3]) 1);
3464
315694e22856 Trivial changes in connection with the Yahalom paper.
paulson
parents: 3450
diff changeset
   310
bind_thm ("B_trusts_YM4_newK", result() RS mp RSN (2, rev_mp));
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   311
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
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parents: 3432
diff changeset
   312
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   313
(**** Towards proving secrecy of Nonce NB ****)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
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parents: 3432
diff changeset
   314
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   315
(** Lemmas about the predicate KeyWithNonce **)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
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parents: 3432
diff changeset
   316
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   317
goalw thy [KeyWithNonce_def]
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   318
 "!!evs. Says Server A                                              \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   319
\            {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB|}, X|} \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3464
diff changeset
   320
\          : set evs ==> KeyWithNonce K NB evs";
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   321
by (Blast_tac 1);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   322
qed "KeyWithNonceI";
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   323
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   324
goalw thy [KeyWithNonce_def]
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   325
   "KeyWithNonce K NB (Says S A X # evs) =                                    \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   326
\    (Server = S &                                                            \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   327
\     (EX B n X'. X = {|Crypt (shrK A) {|Agent B, Key K, n, Nonce NB|}, X'|}) \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   328
\    | KeyWithNonce K NB evs)";
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   329
by (Simp_tac 1);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   330
by (Blast_tac 1);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   331
qed "KeyWithNonce_Says";
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   332
Addsimps [KeyWithNonce_Says];
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   333
3464
315694e22856 Trivial changes in connection with the Yahalom paper.
paulson
parents: 3450
diff changeset
   334
(*A fresh key cannot be associated with any nonce 
315694e22856 Trivial changes in connection with the Yahalom paper.
paulson
parents: 3450
diff changeset
   335
  (with respect to a given trace). *)
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   336
goalw thy [KeyWithNonce_def]
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   337
 "!!evs. Key K ~: used evs ==> ~ KeyWithNonce K NB evs";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   338
by (blast_tac (claset() addSEs spies_partsEs) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   339
qed "fresh_not_KeyWithNonce";
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   340
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   341
(*The Server message associates K with NB' and therefore not with any 
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   342
  other nonce NB.*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   343
goalw thy [KeyWithNonce_def]
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   344
 "!!evs. [| Says Server A                                                \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   345
\                {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB'|}, X|} \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   346
\             : set evs;                                                 \
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   347
\           NB ~= NB';  evs : yahalom |]                            \
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   348
\        ==> ~ KeyWithNonce K NB evs";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   349
by (blast_tac (claset() addDs [unique_session_keys]) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   350
qed "Says_Server_KeyWithNonce";
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   351
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   352
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   353
(*The only nonces that can be found with the help of session keys are
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   354
  those distributed as nonce NB by the Server.  The form of the theorem
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   355
  recalls analz_image_freshK, but it is much more complicated.*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   356
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   357
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   358
(*As with analz_image_freshK, we take some pains to express the property
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   359
  as a logical equivalence so that the simplifier can apply it.*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   360
goal thy  
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   361
 "!!evs. P --> (X : analz (G Un H)) --> (X : analz H)  ==> \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   362
\        P --> (X : analz (G Un H)) = (X : analz H)";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   363
by (blast_tac (claset() addIs [impOfSubs analz_mono]) 1);
3961
6a8996fb7d99 Many minor speedups:
paulson
parents: 3919
diff changeset
   364
val Nonce_secrecy_lemma = result();
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   365
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   366
goal thy 
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   367
 "!!evs. evs : yahalom ==>                                         \
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   368
\        (ALL KK. KK <= Compl (range shrK) -->                          \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   369
\             (ALL K: KK. ~ KeyWithNonce K NB evs)   -->                \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   370
\             (Nonce NB : analz (Key``KK Un (spies evs))) =     \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   371
\             (Nonce NB : analz (spies evs)))";
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   372
by (etac yahalom.induct 1);
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   373
by analz_spies_tac;
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   374
by (REPEAT_FIRST (resolve_tac [impI RS allI]));
3961
6a8996fb7d99 Many minor speedups:
paulson
parents: 3919
diff changeset
   375
by (REPEAT_FIRST (rtac Nonce_secrecy_lemma));
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   376
(*For Oops, simplification proves NBa~=NB.  By Says_Server_KeyWithNonce,
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   377
  we get (~ KeyWithNonce K NB evsa); then simplification can apply the
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   378
  induction hypothesis with KK = {K}.*)
3961
6a8996fb7d99 Many minor speedups:
paulson
parents: 3919
diff changeset
   379
by (ALLGOALS  (*12 seconds*)
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   380
    (asm_simp_tac 
3961
6a8996fb7d99 Many minor speedups:
paulson
parents: 3919
diff changeset
   381
     (analz_image_freshK_ss 
6a8996fb7d99 Many minor speedups:
paulson
parents: 3919
diff changeset
   382
       addsimps expand_ifs
6a8996fb7d99 Many minor speedups:
paulson
parents: 3919
diff changeset
   383
       addsimps [all_conj_distrib, analz_image_freshK,
6a8996fb7d99 Many minor speedups:
paulson
parents: 3919
diff changeset
   384
		 KeyWithNonce_Says, fresh_not_KeyWithNonce, 
6a8996fb7d99 Many minor speedups:
paulson
parents: 3919
diff changeset
   385
		 imp_disj_not1,		     (*Moves NBa~=NB to the front*)
6a8996fb7d99 Many minor speedups:
paulson
parents: 3919
diff changeset
   386
		 Says_Server_KeyWithNonce])));
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   387
(*Fake*) 
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   388
by (spy_analz_tac 1);
4422
21238c9d363e Simplified proofs using rewrites for f``A where f is injective
paulson
parents: 4238
diff changeset
   389
(*YM4*)  (** LEVEL 6 **)
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   390
by (not_bad_tac "A" 1);
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   391
by (dtac (Says_imp_spies RS parts.Inj RS parts.Fst RS A_trusts_YM3) 1
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   392
    THEN REPEAT (assume_tac 1));
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   393
by (blast_tac (claset() addIs [KeyWithNonceI]) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   394
qed_spec_mp "Nonce_secrecy";
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   395
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   396
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   397
(*Version required below: if NB can be decrypted using a session key then it
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   398
  was distributed with that key.  The more general form above is required
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   399
  for the induction to carry through.*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   400
goal thy 
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   401
 "!!evs. [| Says Server A                                                 \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   402
\            {|Crypt (shrK A) {|Agent B, Key KAB, na, Nonce NB'|}, X|}    \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   403
\           : set evs;                                                    \
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   404
\           NB ~= NB';  KAB ~: range shrK;  evs : yahalom |]         \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   405
\        ==> (Nonce NB : analz (insert (Key KAB) (spies evs))) =  \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   406
\            (Nonce NB : analz (spies evs))";
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   407
by (asm_simp_tac (analz_image_freshK_ss addsimps 
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   408
		  [Nonce_secrecy, Says_Server_KeyWithNonce]) 1);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   409
qed "single_Nonce_secrecy";
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   410
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   411
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   412
(*** The Nonce NB uniquely identifies B's message. ***)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   413
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   414
goal thy 
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   415
 "!!evs. evs : yahalom ==>                                            \
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   416
\   EX NA' A' B'. ALL NA A B.                                              \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   417
\      Crypt (shrK B) {|Agent A, Nonce NA, nb|} : parts(spies evs) \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   418
\      --> B ~: bad --> NA = NA' & A = A' & B = B'";
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   419
by (parts_induct_tac 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   420
(*Fake*)
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   421
by (REPEAT (etac (exI RSN (2,exE)) 1)   (*stripping EXs makes proof faster*)
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   422
    THEN Fake_parts_insert_tac 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   423
by (asm_simp_tac (simpset() addsimps [all_conj_distrib]) 1); 
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   424
(*YM2: creation of new Nonce.  Move assertion into global context*)
3501
4ab477ffb4c6 Changed some variables of type msg to lower case (e.g. from NB to nb
paulson
parents: 3466
diff changeset
   425
by (expand_case_tac "nb = ?y" 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2454
diff changeset
   426
by (REPEAT (resolve_tac [exI, conjI, impI, refl] 1));
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   427
by (blast_tac (claset() addSEs spies_partsEs) 1);
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   428
val lemma = result();
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   429
2110
d01151e66cd4 Addition of Reveal message
paulson
parents: 2060
diff changeset
   430
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   431
 "!!evs.[| Crypt (shrK B) {|Agent A, Nonce NA, nb|} : parts (spies evs); \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   432
\          Crypt (shrK B') {|Agent A', Nonce NA', nb|} : parts (spies evs); \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   433
\          evs : yahalom;  B ~: bad;  B' ~: bad |]  \
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   434
\        ==> NA' = NA & A' = A & B' = B";
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2377
diff changeset
   435
by (prove_unique_tac lemma 1);
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   436
qed "unique_NB";
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   437
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   438
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   439
(*Variant useful for proving secrecy of NB: the Says... form allows 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   440
  not_bad_tac to remove the assumption B' ~: bad.*)
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   441
goal thy 
3501
4ab477ffb4c6 Changed some variables of type msg to lower case (e.g. from NB to nb
paulson
parents: 3466
diff changeset
   442
 "!!evs.[| Says C D   {|X,  Crypt (shrK B) {|Agent A, Nonce NA, nb|}|}    \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   443
\            : set evs;          B ~: bad;                               \
3501
4ab477ffb4c6 Changed some variables of type msg to lower case (e.g. from NB to nb
paulson
parents: 3466
diff changeset
   444
\          Says C' D' {|X', Crypt (shrK B') {|Agent A', Nonce NA', nb|}|} \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   445
\            : set evs;                                                   \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   446
\          nb ~: analz (spies evs);  evs : yahalom |]        \
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   447
\        ==> NA' = NA & A' = A & B' = B";
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   448
by (not_bad_tac "B'" 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   449
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj]
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   450
                        addSEs [MPair_parts]
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   451
                        addDs  [unique_NB]) 1);
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   452
qed "Says_unique_NB";
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   453
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   454
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   455
(** A nonce value is never used both as NA and as NB **)
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   456
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   457
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   458
 "!!evs. [| B ~: bad;  evs : yahalom  |]            \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   459
\ ==> Nonce NB ~: analz (spies evs) -->           \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   460
\     Crypt (shrK B') {|Agent A', Nonce NB, nb'|} : parts(spies evs) --> \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   461
\     Crypt (shrK B)  {|Agent A, Nonce NA, Nonce NB|} ~: parts(spies evs)";
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   462
by (parts_induct_tac 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   463
by (Fake_parts_insert_tac 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   464
by (blast_tac (claset() addDs [Says_imp_spies RS analz.Inj]
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   465
                        addSIs [parts_insertI]
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   466
                        addSEs partsEs) 1);
3464
315694e22856 Trivial changes in connection with the Yahalom paper.
paulson
parents: 3450
diff changeset
   467
bind_thm ("no_nonce_YM1_YM2", result() RS mp RSN (2,rev_mp) RSN (2,rev_notE));
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   468
3464
315694e22856 Trivial changes in connection with the Yahalom paper.
paulson
parents: 3450
diff changeset
   469
(*The Server sends YM3 only in response to YM2.*)
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   470
goal thy 
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   471
 "!!evs. [| Says Server A                                                \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   472
\            {|Crypt (shrK A) {|Agent B, k, na, nb|}, X|} : set evs;     \
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   473
\           evs : yahalom |]                                             \
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   474
\        ==> EX B'. Says B' Server                                       \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2269
diff changeset
   475
\                      {| Agent B, Crypt (shrK B) {|Agent A, na, nb|} |} \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3464
diff changeset
   476
\                   : set evs";
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   477
by (etac rev_mp 1);
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   478
by (etac yahalom.induct 1);
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   479
by (ALLGOALS Asm_simp_tac);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   480
by (ALLGOALS Blast_tac);
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   481
qed "Says_Server_imp_YM2";
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   482
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   483
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   484
(*A vital theorem for B, that nonce NB remains secure from the Spy.*)
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   485
goal thy 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   486
 "!!evs. [| A ~: bad;  B ~: bad;  evs : yahalom |]  \
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   487
\ ==> Says B Server                                                    \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2269
diff changeset
   488
\          {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|} \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   489
\     : set evs -->                                                    \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   490
\     (ALL k. Says A Spy {|Nonce NA, Nonce NB, k|} ~: set evs) -->     \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   491
\     Nonce NB ~: analz (spies evs)";
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   492
by (etac yahalom.induct 1);
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   493
by analz_spies_tac;
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   494
by (ALLGOALS
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   495
    (asm_simp_tac 
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   496
     (simpset() addsimps (expand_ifs@pushes)
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   497
	        addsimps [analz_insert_eq, analz_insert_freshK])));
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3444
diff changeset
   498
(*Prove YM3 by showing that no NB can also be an NA*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   499
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj]
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   500
	                addSEs [MPair_parts]
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   501
		        addDs  [no_nonce_YM1_YM2, Says_unique_NB]) 4
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3444
diff changeset
   502
    THEN flexflex_tac);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   503
(*YM2: similar freshness reasoning*) 
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   504
by (blast_tac (claset() addSEs partsEs
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   505
		        addDs  [Says_imp_spies RS analz.Inj,
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   506
				impOfSubs analz_subset_parts]) 3);
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3444
diff changeset
   507
(*YM1: NB=NA is impossible anyway, but NA is secret because it is fresh!*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   508
by (blast_tac (claset() addSIs [parts_insertI]
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   509
                        addSEs spies_partsEs) 2);
2377
ad9d2dedaeaa Streamlined many proofs
paulson
parents: 2322
diff changeset
   510
(*Fake*)
ad9d2dedaeaa Streamlined many proofs
paulson
parents: 2322
diff changeset
   511
by (spy_analz_tac 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   512
(** LEVEL 7: YM4 and Oops remain **)
3708
56facaebf3e3 Changed some proofs to use Clarify_tac
paulson
parents: 3683
diff changeset
   513
by (ALLGOALS Clarify_tac);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   514
(*YM4: key K is visible to Spy, contradicting session key secrecy theorem*) 
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   515
by (not_bad_tac "Aa" 1);
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   516
by (dtac (Says_imp_spies RS parts.Inj RS parts.Fst RS A_trusts_YM3) 1);
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   517
by (forward_tac [Says_Server_message_form] 3);
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   518
by (forward_tac [Says_Server_imp_YM2] 4);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   519
by (REPEAT_FIRST (eresolve_tac [asm_rl, bexE, exE, disjE]));
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   520
(*  use Says_unique_NB to identify message components: Aa=A, Ba=B, NAa=NA *)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   521
by (blast_tac (claset() addDs [Says_unique_NB, Spy_not_see_encrypted_key,
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   522
			       impOfSubs Fake_analz_insert]) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   523
(** LEVEL 14 **)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   524
(*Oops case: if the nonce is betrayed now, show that the Oops event is 
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   525
  covered by the quantified Oops assumption.*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   526
by (full_simp_tac (simpset() addsimps [all_conj_distrib]) 1);
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   527
by (forward_tac [Says_Server_imp_YM2] 1 THEN assume_tac 1 THEN etac exE 1);
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   528
by (expand_case_tac "NB = NBa" 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   529
(*If NB=NBa then all other components of the Oops message agree*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   530
by (blast_tac (claset() addDs [Says_unique_NB]) 1 THEN flexflex_tac);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   531
(*case NB ~= NBa*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   532
by (asm_simp_tac (simpset() addsimps [single_Nonce_secrecy]) 1);
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   533
by (blast_tac (claset() addSEs [MPair_parts]
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   534
		        addDs  [Says_imp_spies RS parts.Inj, 
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   535
			        no_nonce_YM1_YM2 (*to prove NB~=NAa*) ]) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   536
bind_thm ("Spy_not_see_NB", result() RSN(2,rev_mp) RSN(2,rev_mp));
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   537
2001
974167c1d2c4 Reformatting; proved B_gets_secure_key
paulson
parents: 1995
diff changeset
   538
3464
315694e22856 Trivial changes in connection with the Yahalom paper.
paulson
parents: 3450
diff changeset
   539
(*B's session key guarantee from YM4.  The two certificates contribute to a
315694e22856 Trivial changes in connection with the Yahalom paper.
paulson
parents: 3450
diff changeset
   540
  single conclusion about the Server's message.  Note that the "Says A Spy"
315694e22856 Trivial changes in connection with the Yahalom paper.
paulson
parents: 3450
diff changeset
   541
  assumption must quantify over ALL POSSIBLE keys instead of our particular K.
315694e22856 Trivial changes in connection with the Yahalom paper.
paulson
parents: 3450
diff changeset
   542
  If this run is broken and the spy substitutes a certificate containing an
315694e22856 Trivial changes in connection with the Yahalom paper.
paulson
parents: 3450
diff changeset
   543
  old key, B has no means of telling.*)
2001
974167c1d2c4 Reformatting; proved B_gets_secure_key
paulson
parents: 1995
diff changeset
   544
goal thy 
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   545
 "!!evs. [| Says B Server                                                   \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   546
\             {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}   \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   547
\             : set evs;                                                    \
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   548
\           Says A' B {|Crypt (shrK B) {|Agent A, Key K|},                  \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   549
\                       Crypt K (Nonce NB)|} : set evs;                     \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   550
\           ALL k. Says A Spy {|Nonce NA, Nonce NB, k|} ~: set evs;         \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   551
\           A ~: bad;  B ~: bad;  evs : yahalom |]       \
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   552
\         ==> Says Server A                                                 \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   553
\                     {|Crypt (shrK A) {|Agent B, Key K,                    \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   554
\                               Nonce NA, Nonce NB|},                       \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   555
\                       Crypt (shrK B) {|Agent A, Key K|}|}                 \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3464
diff changeset
   556
\               : set evs";
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   557
by (forward_tac [Spy_not_see_NB] 1 THEN REPEAT (assume_tac 1));
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   558
by (etac (Says_imp_spies RS parts.Inj RS MPair_parts) 1 THEN
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   559
    dtac B_trusts_YM4_shrK 1);
2170
c5e460f1ebb4 Ran expandshort
paulson
parents: 2160
diff changeset
   560
by (dtac B_trusts_YM4_newK 3);
2110
d01151e66cd4 Addition of Reveal message
paulson
parents: 2060
diff changeset
   561
by (REPEAT_FIRST (eresolve_tac [asm_rl, exE]));
2133
f00a688760b9 Simplified proofs
paulson
parents: 2110
diff changeset
   562
by (forward_tac [Says_Server_imp_YM2] 1 THEN assume_tac 1);
2170
c5e460f1ebb4 Ran expandshort
paulson
parents: 2160
diff changeset
   563
by (dtac unique_session_keys 1 THEN REPEAT (assume_tac 1));
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   564
by (blast_tac (claset() addDs [Says_unique_NB]) 1);
2322
fbe6dd4abddc Trivial renamings
paulson
parents: 2284
diff changeset
   565
qed "B_trusts_YM4";
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   566
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   567
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   568
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   569
(*** Authenticating B to A ***)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   570
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   571
(*The encryption in message YM2 tells us it cannot be faked.*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   572
goal thy 
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   573
 "!!evs. evs : yahalom                                            \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   574
\  ==> Crypt (shrK B) {|Agent A, Nonce NA, nb|} : parts (spies evs) --> \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   575
\      B ~: bad -->                                              \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   576
\      Says B Server {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, nb|}|}  \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3464
diff changeset
   577
\         : set evs";
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   578
by (parts_induct_tac 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   579
by (Fake_parts_insert_tac 1);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   580
bind_thm ("B_Said_YM2", result() RSN (2, rev_mp) RS mp);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   581
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   582
(*If the server sends YM3 then B sent YM2*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   583
goal thy 
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   584
 "!!evs. evs : yahalom                                                      \
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   585
\  ==> Says Server A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, nb|}, X|} \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   586
\         : set evs -->                                                     \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   587
\      B ~: bad -->                                                        \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   588
\      Says B Server {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, nb|}|}  \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3464
diff changeset
   589
\                 : set evs";
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   590
by (etac yahalom.induct 1);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   591
by (ALLGOALS Asm_simp_tac);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   592
(*YM4*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   593
by (Blast_tac 2);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   594
(*YM3*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   595
by (best_tac (claset() addSDs [B_Said_YM2, Says_imp_spies RS parts.Inj]
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   596
		       addSEs [MPair_parts]) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   597
val lemma = result() RSN (2, rev_mp) RS mp |> standard;
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   598
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   599
(*If A receives YM3 then B has used nonce NA (and therefore is alive)*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   600
goal thy
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   601
 "!!evs. [| Says S A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, nb|}, X|} \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   602
\             : set evs;                                                    \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   603
\           A ~: bad;  B ~: bad;  evs : yahalom |]                        \
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   604
\   ==> Says B Server {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, nb|}|} \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3464
diff changeset
   605
\         : set evs";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   606
by (blast_tac (claset() addSDs [A_trusts_YM3, lemma]
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   607
		        addEs spies_partsEs) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   608
qed "YM3_auth_B_to_A";
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   609
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   610
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   611
(*** Authenticating A to B using the certificate Crypt K (Nonce NB) ***)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   612
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   613
(*Assuming the session key is secure, if both certificates are present then
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   614
  A has said NB.  We can't be sure about the rest of A's message, but only
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   615
  NB matters for freshness.*)  
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   616
goal thy 
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   617
 "!!evs. evs : yahalom                                             \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   618
\        ==> Key K ~: analz (spies evs) -->                     \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   619
\            Crypt K (Nonce NB) : parts (spies evs) -->         \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   620
\            Crypt (shrK B) {|Agent A, Key K|} : parts (spies evs) --> \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   621
\            B ~: bad -->                                         \
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   622
\            (EX X. Says A B {|X, Crypt K (Nonce NB)|} : set evs)";
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   623
by (parts_induct_tac 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   624
(*Fake*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   625
by (Fake_parts_insert_tac 1);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   626
(*YM3: by new_keys_not_used we note that Crypt K (Nonce NB) could not exist*)
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   627
by (fast_tac (claset() addSDs [Crypt_imp_keysFor] addss (simpset())) 1); 
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   628
(*YM4: was Crypt K (Nonce NB) the very last message?  If not, use ind. hyp.*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   629
by (asm_simp_tac (simpset() addsimps [ex_disj_distrib]) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   630
(*yes: apply unicity of session keys*)
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   631
by (not_bad_tac "Aa" 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   632
by (blast_tac (claset() addSEs [MPair_parts]
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   633
                        addSDs [A_trusts_YM3, B_trusts_YM4_shrK]
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   634
		        addDs  [Says_imp_spies RS parts.Inj,
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   635
				unique_session_keys]) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   636
val lemma = normalize_thm [RSspec, RSmp] (result()) |> standard;
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   637
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   638
(*If B receives YM4 then A has used nonce NB (and therefore is alive).
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   639
  Moreover, A associates K with NB (thus is talking about the same run).
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   640
  Other premises guarantee secrecy of K.*)
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   641
goal thy 
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   642
 "!!evs. [| Says B Server                                                   \
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   643
\             {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}   \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   644
\             : set evs;                                                    \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   645
\           Says A' B {|Crypt (shrK B) {|Agent A, Key K|},                  \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   646
\                       Crypt K (Nonce NB)|} : set evs;                     \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   647
\           (ALL NA k. Says A Spy {|Nonce NA, Nonce NB, k|} ~: set evs);    \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   648
\           A ~: bad;  B ~: bad;  evs : yahalom |]       \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3464
diff changeset
   649
\        ==> EX X. Says A B {|X, Crypt K (Nonce NB)|} : set evs";
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   650
by (dtac B_trusts_YM4 1);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   651
by (REPEAT_FIRST (eresolve_tac [asm_rl, spec]));
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3679
diff changeset
   652
by (etac (Says_imp_spies RS parts.Inj RS MPair_parts) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   653
by (rtac lemma 1);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   654
by (rtac Spy_not_see_encrypted_key 2);
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   655
by (REPEAT_FIRST assume_tac);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   656
by (blast_tac (claset() addSEs [MPair_parts]
4238
679a233fb206 Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents: 4091
diff changeset
   657
	       	        addDs [Says_imp_spies RS parts.Inj]) 1);
3444
919de2cb3487 Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents: 3432
diff changeset
   658
qed_spec_mp "YM4_imp_A_Said_YM3";