src/HOL/Auth/OtwayRees.ML
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(*  Title:      HOL/Auth/OtwayRees
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1996  University of Cambridge
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Inductive relation "otway" for the Otway-Rees protocol.
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Version that encrypts Nonce NB
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From page 244 of
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  Burrows, Abadi and Needham.  A Logic of Authentication.
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  Proc. Royal Soc. 426 (1989)
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*)
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AddEs knows_Spy_partsEs;
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AddDs [impOfSubs analz_subset_parts];
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AddDs [impOfSubs Fake_parts_insert];
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1996
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(*A "possibility property": there are traces that reach the end*)
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Goal "[| B ~= Server |]   \
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\     ==> EX NA K. EX evs: otway.          \
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\            Says B A {|Nonce NA, Crypt (shrK A) {|Nonce NA, Key K|}|} \
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\              : set evs";
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by (REPEAT (resolve_tac [exI,bexI] 1));
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by (rtac (otway.Nil RS 
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          otway.OR1 RS otway.Reception RS
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          otway.OR2 RS otway.Reception RS 
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          otway.OR3 RS otway.Reception RS otway.OR4) 2);
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by possibility_tac;
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result();
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Goal "[| Gets B X : set evs; evs : otway |] ==> EX A. Says A B X : set evs";
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by (etac rev_mp 1);
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by (etac otway.induct 1);
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by Auto_tac;
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qed"Gets_imp_Says";
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(*Must be proved separately for each protocol*)
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Goal "[| Gets B X : set evs; evs : otway |]  ==> X : knows Spy evs";
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by (blast_tac (claset() addSDs [Gets_imp_Says, Says_imp_knows_Spy]) 1);
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qed"Gets_imp_knows_Spy";
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AddDs [Gets_imp_knows_Spy RS parts.Inj];
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(**** Inductive proofs about otway ****)
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(** For reasoning about the encrypted portion of messages **)
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Goal "[| Gets B {|N, Agent A, Agent B, X|} : set evs;  evs : otway |]  \
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\     ==> X : analz (knows Spy evs)";
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by (blast_tac (claset() addSDs [Gets_imp_knows_Spy RS analz.Inj]) 1);
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qed "OR2_analz_knows_Spy";
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Goal "[| Gets B {|N, X, Crypt (shrK B) X'|} : set evs;  evs : otway |] \
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\     ==> X : analz (knows Spy evs)";
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by (blast_tac (claset() addSDs [Gets_imp_knows_Spy RS analz.Inj]) 1);
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qed "OR4_analz_knows_Spy";
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Goal "Says Server B {|NA, X, Crypt K' {|NB,K|}|} : set evs \
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\     ==> K : parts (knows Spy evs)";
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by (Blast_tac 1);
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qed "Oops_parts_knows_Spy";
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bind_thm ("OR2_parts_knows_Spy",
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          OR2_analz_knows_Spy RS (impOfSubs analz_subset_parts));
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bind_thm ("OR4_parts_knows_Spy",
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          OR4_analz_knows_Spy RS (impOfSubs analz_subset_parts));
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(*For proving the easier theorems about X ~: parts (knows Spy evs).*)
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fun parts_induct_tac i = 
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    etac otway.induct i			THEN 
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    ftac Oops_parts_knows_Spy (i+7) THEN
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    ftac OR4_parts_knows_Spy (i+6) THEN
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    ftac OR2_parts_knows_Spy (i+4) THEN 
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    prove_simple_subgoals_tac  i;
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(** Theorems of the form X ~: parts (knows Spy evs) imply that NOBODY
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    sends messages containing X! **)
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(*Spy never sees a good agent's shared key!*)
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Goal "evs : otway ==> (Key (shrK A) : parts (knows Spy evs)) = (A : bad)";
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by (parts_induct_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 "evs : otway ==> (Key (shrK A) : analz (knows Spy 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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AddSDs [Spy_see_shrK RSN (2, rev_iffD1), 
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	Spy_analz_shrK RSN (2, rev_iffD1)];
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(*Nobody can have used non-existent keys!*)
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Goal "evs: otway ==> Key K ~: used evs --> K ~: keysFor(parts(knows Spy evs))";
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by (parts_induct_tac 1);
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(*Fake*)
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by (blast_tac (claset() addSDs [keysFor_parts_insert]) 1);
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(*OR2, OR3*)
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by (ALLGOALS Blast_tac);
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qed_spec_mp "new_keys_not_used";
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bind_thm ("new_keys_not_analzd",
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          [analz_subset_parts RS keysFor_mono,
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           new_keys_not_used] MRS contra_subsetD);
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Addsimps [new_keys_not_used, new_keys_not_analzd];
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(*** Proofs involving analz ***)
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(*Describes the form of K and NA when the Server sends this message.  Also
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  for Oops case.*)
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Goal "[| Says Server B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs; \
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\        evs : otway |]                                           \
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\     ==> K ~: range shrK & (EX i. NA = Nonce i) & (EX j. NB = Nonce j)";
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by (etac rev_mp 1);
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by (etac otway.induct 1);
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by (ALLGOALS Simp_tac);
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by (ALLGOALS Blast_tac);
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qed "Says_Server_message_form";
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(*For proofs involving analz.*)
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val analz_knows_Spy_tac = 
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    dtac OR2_analz_knows_Spy 5 THEN assume_tac 5 THEN 
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    dtac OR4_analz_knows_Spy 7 THEN assume_tac 7 THEN
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    ftac Says_Server_message_form 8 THEN assume_tac 8 THEN
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    REPEAT ((eresolve_tac [exE, conjE] ORELSE' hyp_subst_tac) 8);
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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) (knows Spy evs)) ==>
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  Key K : analz (knows Spy evs)
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 A more general formula must be proved inductively.
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****)
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(** Session keys are not used to encrypt other session keys **)
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(*The equality makes the induction hypothesis easier to apply*)
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Goal "evs : otway ==> ALL K KK. KK <= - (range shrK) -->           \
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\                      (Key K : analz (Key``KK Un (knows Spy evs))) =  \
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\                      (K : KK | Key K : analz (knows Spy evs))";
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by (etac otway.induct 1);
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by analz_knows_Spy_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 "[| evs : otway;  KAB ~: range shrK |]               \
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\     ==> Key K : analz (insert (Key KAB) (knows Spy evs)) =  \
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\         (K = KAB | Key K : analz (knows 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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(*** The Key K uniquely identifies the Server's  message. **)
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Goal "evs : otway ==>                                                  \
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\     EX B' NA' NB' X'. ALL B NA NB X.                                 \
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\     Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set evs -->  \
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\     B=B' & NA=NA' & NB=NB' & X=X'";
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by (etac otway.induct 1);
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by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib])));
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by (ALLGOALS Clarify_tac);
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(*Remaining cases: OR3 and OR4*)
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by (ex_strip_tac 2);
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by (Best_tac 2);	(*Blast_tac's too slow (in reconstruction)*)
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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 knows_Spy_partsEs) 1);
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val lemma = result();
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Goal "[| Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|}   : set evs; \ 
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\        Says Server B' {|NA',X',Crypt (shrK B') {|NB',K|}|} : set evs; \
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\        evs : otway |] ==> X=X' & 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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(**** Authenticity properties relating to NA ****)
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(*Only OR1 can have caused such a part of a message to appear.*)
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Goal "[| A ~: bad;  evs : otway |]                             \
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\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (knows Spy evs) --> \
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\     Says A B {|NA, Agent A, Agent B,                      \
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\                Crypt (shrK A) {|NA, Agent A, Agent B|}|}  \
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\       : set evs";
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by (parts_induct_tac 1);
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by (Blast_tac 1);
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qed_spec_mp "Crypt_imp_OR1";
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Goal "[| Gets B {|NA, Agent A, Agent B,                      \
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\                 Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \
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\        A ~: bad; evs : otway |]                             \
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\      ==> Says A B {|NA, Agent A, Agent B,                      \
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\                     Crypt (shrK A) {|NA, Agent A, Agent B|}|}  \
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\            : set evs";
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by (blast_tac (claset() addDs [Crypt_imp_OR1]) 1);
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qed"Crypt_imp_OR1_Gets";
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(** The Nonce NA uniquely identifies A's message. **)
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Goal "[| evs : otway; A ~: bad |]               \
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\ ==> EX B'. ALL B.                                 \
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\        Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (knows Spy evs) \
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\        --> B = B'";
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by (parts_induct_tac 1);
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by (Blast_tac 1);
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by (simp_tac (simpset() addsimps [all_conj_distrib]) 1); 
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(*OR1: creation of new Nonce.  Move assertion into global context*)
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by (expand_case_tac "NA = ?y" 1);
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by (Blast_tac 1);
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val lemma = result();
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Goal "[| Crypt (shrK A) {|NA, Agent A, Agent B|}: parts (knows Spy evs); \
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\        Crypt (shrK A) {|NA, Agent A, Agent C|}: parts (knows Spy evs); \
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\        evs : otway;  A ~: bad |]                                   \
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\     ==> B = C";
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by (prove_unique_tac lemma 1);
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qed "unique_NA";
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(*It is impossible to re-use a nonce in both OR1 and OR2.  This holds because
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  OR2 encrypts Nonce NB.  It prevents the attack that can occur in the
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  over-simplified version of this protocol: see OtwayRees_Bad.*)
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Goal "[| A ~: bad;  evs : otway |]                      \
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\     ==> Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (knows Spy evs) --> \
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\         Crypt (shrK A) {|NA', NA, Agent A', Agent A|}  \
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\           ~: parts (knows Spy evs)";
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by (parts_induct_tac 1);
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by Auto_tac;
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qed_spec_mp "no_nonce_OR1_OR2";
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val nonce_OR1_OR2_E = no_nonce_OR1_OR2 RSN (2, rev_notE);
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(*Crucial property: If the encrypted message appears, and A has used NA
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  to start a run, then it originated with the Server!*)
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Goal "[| A ~: bad;  evs : otway |]                                  \
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\     ==> Crypt (shrK A) {|NA, Key K|} : parts (knows Spy evs)          \
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\         --> Says A B {|NA, Agent A, Agent B,                          \
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\                        Crypt (shrK A) {|NA, Agent A, Agent B|}|}      \
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\               : set evs -->                                           \
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\             (EX NB. Says Server B                                     \
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\                  {|NA,                                                \
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\                    Crypt (shrK A) {|NA, Key K|},                      \
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\                    Crypt (shrK B) {|NB, Key K|}|}                     \
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\                    : set evs)";
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by (parts_induct_tac 1);
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by (Blast_tac 1);
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(*OR1: it cannot be a new Nonce, contradiction.*)
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by (Blast_tac 1);
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(*OR3 and OR4*)
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by (asm_simp_tac (simpset() addsimps [ex_disj_distrib]) 1);
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   270
by (rtac conjI 1);
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by (ALLGOALS Clarify_tac);
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   272
(*OR4*)
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   273
by (blast_tac (claset() addSIs [Crypt_imp_OR1]) 3);
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   274
(*OR3, two cases*)  (** LEVEL 7 **)
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   275
by (blast_tac (claset() addSEs  [nonce_OR1_OR2_E]
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   276
                        delrules [conjI] (*stop split-up into 4 subgoals*)) 2);
6308
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by (blast_tac (claset() addIs [unique_NA]) 1);
2048
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   278
qed_spec_mp "NA_Crypt_imp_Server_msg";
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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diff changeset
   279
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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   280
2053
6c0594bfa726 Greatly simplified the proof of A_can_trust
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   281
(*Corollary: if A receives B's OR4 message and the nonce NA agrees
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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diff changeset
   282
  then the key really did come from the Server!  CANNOT prove this of the
2048
bb54fbba0071 Added new guarantees for A and B
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diff changeset
   283
  bad form of this protocol, even though we can prove
2032
1bbf1bdcaf56 Introduction of "lost" argument
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diff changeset
   284
  Spy_not_see_encrypted_key*)
5278
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   285
Goal "[| Says A  B {|NA, Agent A, Agent B,                       \
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\                Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \
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   287
\        Gets A {|NA, Crypt (shrK A) {|NA, Key K|}|} : set evs; \
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\    A ~: bad;  evs : otway |]                              \
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   289
\ ==> EX NB. Says Server B                                  \
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   290
\              {|NA,                                        \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
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   291
\                Crypt (shrK A) {|NA, Key K|},              \
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   292
\                Crypt (shrK B) {|NB, Key K|}|}             \
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   293
\                : set evs";
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   294
by (blast_tac (claset() addSIs [NA_Crypt_imp_Server_msg]) 1);
2328
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diff changeset
   295
qed "A_trusts_OR4";
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   296
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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   297
2048
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   298
(** Crucial secrecy property: Spy does not see the keys sent in msg OR3
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   299
    Does not in itself guarantee security: an attack could violate 
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   300
    the premises, e.g. by having A=Spy **)
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   301
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
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   302
Goal "[| A ~: bad;  B ~: bad;  evs : otway |]                  \
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   303
\ ==> Says Server B                                            \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
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   304
\       {|NA, Crypt (shrK A) {|NA, Key K|},                    \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
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   305
\         Crypt (shrK B) {|NB, Key K|}|} : set evs -->         \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
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   306
\     Notes Spy {|NA, NB, Key K|} ~: set evs -->               \
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
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   307
\     Key K ~: analz (knows Spy evs)";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
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diff changeset
   308
by (etac otway.induct 1);
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   309
by analz_knows_Spy_tac;
1964
d551e68b7a36 Stronger proofs; work for Otway-Rees
paulson
parents: 1945
diff changeset
   310
by (ALLGOALS
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parents: 3961
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   311
    (asm_simp_tac (simpset() addcongs [conj_cong] 
4509
828148415197 Making proofs faster, especially using keysFor_parts_insert
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   312
                             addsimps [analz_insert_eq, analz_insert_freshK]
5535
678999604ee9 deleted needless parentheses
paulson
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diff changeset
   313
                                      @ pushes @ split_ifs)));
3451
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paulson
parents: 3207
diff changeset
   314
(*Oops*)
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   315
by (blast_tac (claset() addSDs [unique_session_keys]) 4);
3451
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paulson
parents: 3207
diff changeset
   316
(*OR4*) 
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   317
by (Blast_tac 3);
1941
f97a6e5b6375 Initial working proof of Otway-Rees protocol
paulson
parents:
diff changeset
   318
(*OR3*)
4470
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paulson
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diff changeset
   319
by (Blast_tac 2);
3451
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paulson
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diff changeset
   320
(*Fake*) 
d10f100676d8 Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents: 3207
diff changeset
   321
by (spy_analz_tac 1);
2014
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
paulson
parents: 1999
diff changeset
   322
val lemma = result() RS mp RS mp RSN(2,rev_notE);
5be4c8ca7b25 Correction of protocol; addition of Reveal message; proofs of
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parents: 1999
diff changeset
   323
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   324
Goal "[| Says Server B                                           \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
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diff changeset
   325
\         {|NA, Crypt (shrK A) {|NA, Key K|},                    \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
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parents: 5076
diff changeset
   326
\               Crypt (shrK B) {|NB, Key K|}|} : set evs;        \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
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parents: 5076
diff changeset
   327
\        Notes Spy {|NA, NB, Key K|} ~: set evs;                 \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
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parents: 5076
diff changeset
   328
\        A ~: bad;  B ~: bad;  evs : otway |]                    \
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   329
\     ==> Key K ~: analz (knows Spy evs)";
7499
23e090051cb8 isatool expandshort;
wenzelm
parents: 6308
diff changeset
   330
by (ftac Says_Server_message_form 1 THEN assume_tac 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   331
by (blast_tac (claset() addSEs [lemma]) 1);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   332
qed "Spy_not_see_encrypted_key";
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   333
1945
20ca9cf90e69 A further tidying
paulson
parents: 1941
diff changeset
   334
4598
649bf14debe7 Added some more explicit guarantees of key secrecy for agents
paulson
parents: 4537
diff changeset
   335
(*A's guarantee.  The Oops premise quantifies over NB because A cannot know
649bf14debe7 Added some more explicit guarantees of key secrecy for agents
paulson
parents: 4537
diff changeset
   336
  what it is.*)
5114
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parents: 5076
diff changeset
   337
Goal "[| Says A  B {|NA, Agent A, Agent B,                       \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   338
\                    Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   339
\        Gets A {|NA, Crypt (shrK A) {|NA, Key K|}|} : set evs; \
5114
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paulson
parents: 5076
diff changeset
   340
\        ALL NB. Notes Spy {|NA, NB, Key K|} ~: set evs;         \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
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   341
\        A ~: bad;  B ~: bad;  evs : otway |]                    \
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   342
\     ==> Key K ~: analz (knows Spy evs)";
4598
649bf14debe7 Added some more explicit guarantees of key secrecy for agents
paulson
parents: 4537
diff changeset
   343
by (blast_tac (claset() addSDs [A_trusts_OR4, Spy_not_see_encrypted_key]) 1);
649bf14debe7 Added some more explicit guarantees of key secrecy for agents
paulson
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   344
qed "A_gets_good_key";
649bf14debe7 Added some more explicit guarantees of key secrecy for agents
paulson
parents: 4537
diff changeset
   345
649bf14debe7 Added some more explicit guarantees of key secrecy for agents
paulson
parents: 4537
diff changeset
   346
2048
bb54fbba0071 Added new guarantees for A and B
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   347
(**** Authenticity properties relating to NB ****)
bb54fbba0071 Added new guarantees for A and B
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diff changeset
   348
bb54fbba0071 Added new guarantees for A and B
paulson
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diff changeset
   349
(*Only OR2 can have caused such a part of a message to appear.  We do not
2194
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   350
  know anything about X: it does NOT have to have the right form.*)
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   351
Goal "[| Crypt (shrK B) {|NA, NB, Agent A, Agent B|}       \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   352
\          : parts (knows Spy evs);  \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   353
\        B ~: bad;  evs : otway |]                         \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   354
\     ==> EX X. Says B Server                              \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   355
\                {|NA, Agent A, Agent B, X,                       \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   356
\                  Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|}  \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   357
\                : set evs";
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   358
by (etac rev_mp 1);
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   359
by (parts_induct_tac 1);
3102
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   360
by (ALLGOALS Blast_tac);
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   361
qed "Crypt_imp_OR2";
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   362
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   363
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   364
(** The Nonce NB uniquely identifies B's  message. **)
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   365
5114
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paulson
parents: 5076
diff changeset
   366
Goal "[| evs : otway; B ~: bad |]  \
4598
649bf14debe7 Added some more explicit guarantees of key secrecy for agents
paulson
parents: 4537
diff changeset
   367
\ ==> EX NA' A'. ALL NA A.            \
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   368
\      Crypt (shrK B) {|NA, NB, Agent A, Agent B|} : parts(knows Spy evs) \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   369
\      --> NA = NA' & A = A'";
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   370
by (parts_induct_tac 1);
4470
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   371
by (Blast_tac 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   372
by (simp_tac (simpset() addsimps [all_conj_distrib]) 1); 
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   373
(*OR2: creation of new Nonce.  Move assertion into global context*)
2064
5a5e508e2a2b Simple tidying
paulson
parents: 2053
diff changeset
   374
by (expand_case_tac "NB = ?y" 1);
4470
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   375
by (Blast_tac 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   376
val lemma = result();
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   377
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   378
Goal "[| Crypt (shrK B) {|NA, NB, Agent A, Agent B|} : parts(knows Spy evs); \
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   379
\        Crypt (shrK B) {|NC, NB, Agent C, Agent B|} : parts(knows Spy evs); \
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3674
diff changeset
   380
\          evs : otway;  B ~: bad |]             \
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   381
\        ==> NC = NA & C = A";
2417
95f275c8476e New tactic: prove_unique_tac
paulson
parents: 2375
diff changeset
   382
by (prove_unique_tac lemma 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   383
qed "unique_NB";
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   384
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   385
(*If the encrypted message appears, and B has used Nonce NB,
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   386
  then it originated with the Server!*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   387
Goal "[| B ~: bad;  evs : otway |]                                    \
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   388
\ ==> Crypt (shrK B) {|NB, Key K|} : parts (knows Spy evs)            \
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   389
\     --> (ALL X'. Says B Server                                      \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   390
\                    {|NA, Agent A, Agent B, X',                      \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   391
\                      Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|}  \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   392
\          : set evs                                                  \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   393
\          --> Says Server B                                          \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   394
\               {|NA, Crypt (shrK A) {|NA, Key K|},                   \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   395
\                     Crypt (shrK B) {|NB, Key K|}|}                  \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3451
diff changeset
   396
\                   : set evs)";
3519
ab0a9fbed4c0 Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents: 3516
diff changeset
   397
by (parts_induct_tac 1);
4470
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   398
by (Blast_tac 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   399
(*OR1: it cannot be a new Nonce, contradiction.*)
4470
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   400
by (Blast_tac 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   401
(*OR4*)
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   402
by (blast_tac (claset() addSDs [Crypt_imp_OR2]) 2);
2194
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   403
(*OR3*)
4470
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   404
(*Provable in 38s by the single command
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   405
    by (blast_tac (claset() addDs  [unique_NB] addEs[nonce_OR1_OR2_E]) 1);
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   406
*)
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3961
diff changeset
   407
by (safe_tac (claset() delrules [disjCI, impCE]));
4470
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   408
by (Blast_tac 3); 
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   409
by (blast_tac (claset() addSDs  [unique_NB]
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   410
                        delrules [impCE] (*stop split-up*)) 2);
4470
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   411
by (blast_tac (claset() addSEs [nonce_OR1_OR2_E]
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   412
                        delrules [conjI] (*stop split-up*)) 1);
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   413
qed_spec_mp "NB_Crypt_imp_Server_msg";
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   414
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   415
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   416
(*Guarantee for B: if it gets a message with matching NB then the Server
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   417
  has sent the correct message.*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   418
Goal "[| Says B Server {|NA, Agent A, Agent B, X',              \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   419
\                        Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   420
\          : set evs;                                           \
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   421
\        Gets B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs;   \
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   422
\        B ~: bad;  evs : otway |]                              \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   423
\     ==> Says Server B                                         \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   424
\              {|NA,                                            \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   425
\                Crypt (shrK A) {|NA, Key K|},                  \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   426
\                Crypt (shrK B) {|NB, Key K|}|}                 \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   427
\                : set evs";
4470
af3239def3d4 Tidied using more default rules
paulson
parents: 4449
diff changeset
   428
by (blast_tac (claset() addSIs [NB_Crypt_imp_Server_msg]) 1);
2328
e984c12ce5b4 Minor renamings
paulson
parents: 2284
diff changeset
   429
qed "B_trusts_OR3";
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   430
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   431
4598
649bf14debe7 Added some more explicit guarantees of key secrecy for agents
paulson
parents: 4537
diff changeset
   432
(*The obvious combination of B_trusts_OR3 with Spy_not_see_encrypted_key*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   433
Goal "[| Says B Server {|NA, Agent A, Agent B, X',              \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   434
\                        Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   435
\          : set evs;                                           \
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   436
\        Gets B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs;   \
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   437
\        Notes Spy {|NA, NB, Key K|} ~: set evs;                \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   438
\        A ~: bad;  B ~: bad;  evs : otway |]                   \
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   439
\     ==> Key K ~: analz (knows Spy evs)";
4598
649bf14debe7 Added some more explicit guarantees of key secrecy for agents
paulson
parents: 4537
diff changeset
   440
by (blast_tac (claset() addSDs [B_trusts_OR3, Spy_not_see_encrypted_key]) 1);
649bf14debe7 Added some more explicit guarantees of key secrecy for agents
paulson
parents: 4537
diff changeset
   441
qed "B_gets_good_key";
2048
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   442
bb54fbba0071 Added new guarantees for A and B
paulson
parents: 2045
diff changeset
   443
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   444
Goal "[| Says Server B                                       \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   445
\           {|NA, Crypt (shrK A) {|NA, Key K|},              \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   446
\             Crypt (shrK B) {|NB, Key K|}|} : set evs;      \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   447
\        B ~: bad;  evs : otway |]                           \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   448
\ ==> EX X. Says B Server {|NA, Agent A, Agent B, X,         \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   449
\                           Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   450
\             : set evs";
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   451
by (etac rev_mp 1);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2026
diff changeset
   452
by (etac otway.induct 1);
3102
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   453
by (ALLGOALS Asm_simp_tac);
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   454
by (blast_tac (claset() addSDs [Crypt_imp_OR2]) 3);
3102
4d01cdc119d2 Some blast_tac calls; more needed
paulson
parents: 2837
diff changeset
   455
by (ALLGOALS Blast_tac);
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   456
qed "OR3_imp_OR2";
2194
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   457
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   458
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   459
(*After getting and checking OR4, agent A can trust that B has been active.
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   460
  We could probably prove that X has the expected form, but that is not
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   461
  strictly necessary for authentication.*)
6308
76f3865a2b1d Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
paulson
parents: 5535
diff changeset
   462
Goal "[| Gets A {|NA, Crypt (shrK A) {|NA, Key K|}|} : set evs;        \
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   463
\        Says A  B {|NA, Agent A, Agent B,                                \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   464
\                    Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5076
diff changeset
   465
\        A ~: bad;  B ~: bad;  evs : otway |]                             \
8215
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   466
\ ==> EX NB X. Says B Server {|NA, Agent A, Agent B, X,               \
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   467
\                              Crypt (shrK B)  {|NA, NB, Agent A, Agent B|} |}\
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   468
\                : set evs";
d3eba67a9e67 tidying: mostly spacing, but also simpler forms for Crypt_imp_OR2 & OR3_imp_OR2
paulson
parents: 7499
diff changeset
   469
by (blast_tac (claset() addSDs [A_trusts_OR4, OR3_imp_OR2]) 1);
2194
63a68a3a8a76 Removal of an obsolete result, and authentication of
paulson
parents: 2171
diff changeset
   470
qed "A_auths_B";