src/HOL/Auth/TLS.ML
author paulson
Fri Oct 03 10:32:50 1997 +0200 (1997-10-03)
changeset 3772 6ee707a73248
parent 3760 77f71f650433
child 3919 c036caebfc75
permissions -rw-r--r--
Routine tidying up
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(*  Title:      HOL/Auth/TLS
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1997  University of Cambridge
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Protocol goals: 
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* M, serverK(NA,NB,M) and clientK(NA,NB,M) will be known only to the two
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     parties (though A is not necessarily authenticated).
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* B upon receiving CertVerify knows that A is present (But this
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    message is optional!)
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* A upon receiving ServerFinished knows that B is present
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* Each party who has received a FINISHED message can trust that the other
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  party agrees on all message components, including PA and PB (thus foiling
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  rollback attacks).
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*)
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open TLS;
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proof_timing:=true;
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HOL_quantifiers := false;
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(*Automatically unfold the definition of "certificate"*)
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Addsimps [certificate_def];
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(*Injectiveness of key-generating functions*)
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AddIffs [inj_PRF RS inj_eq, inj_sessionK RS inj_eq];
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(* invKey(sessionK x) = sessionK x*)
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Addsimps [isSym_sessionK, rewrite_rule [isSymKey_def] isSym_sessionK];
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(*** clientK and serverK make symmetric keys; no clashes with pubK or priK ***)
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goal thy "pubK A ~= sessionK arg";
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br notI 1;
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by (dres_inst_tac [("f","isSymKey")] arg_cong 1);
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by (Full_simp_tac 1);
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qed "pubK_neq_sessionK";
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goal thy "priK A ~= sessionK arg";
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br notI 1;
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by (dres_inst_tac [("f","isSymKey")] arg_cong 1);
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by (Full_simp_tac 1);
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qed "priK_neq_sessionK";
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val keys_distinct = [pubK_neq_sessionK, priK_neq_sessionK];
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AddIffs (keys_distinct @ (keys_distinct RL [not_sym]));
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(**** Protocol Proofs ****)
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(*Possibility properties state that some traces run the protocol to the end.
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  Four paths and 12 rules are considered.*)
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(** These proofs assume that the Nonce_supply nonces 
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	(which have the form  @ N. Nonce N ~: used evs)
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    lie outside the range of PRF.  It seems reasonable, but as it is needed
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    only for the possibility theorems, it is not taken as an axiom.
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**)
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(*Possibility property ending with ClientAccepts.*)
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goal thy 
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 "!!A B. [| ALL evs. (@ N. Nonce N ~: used evs) ~: range PRF;  \
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\           A ~= B |]            \
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\  ==> EX SID M. EX evs: tls.    \
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\        Notes A {|Number SID, Agent A, Agent B, Nonce M|} : set evs";
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by (REPEAT (resolve_tac [exI,bexI] 1));
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by (rtac (tls.Nil RS tls.ClientHello RS tls.ServerHello RS tls.Certificate RS
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	  tls.ClientKeyExch RS tls.ClientFinished RS tls.ServerFinished RS
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	  tls.ClientAccepts) 2);
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by possibility_tac;
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by (REPEAT (Blast_tac 1));
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result();
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(*And one for ServerAccepts.  Either FINISHED message may come first.*)
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goal thy 
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 "!!A B. [| ALL evs. (@ N. Nonce N ~: used evs) ~: range PRF;  \
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\           A ~= B |]                        \
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\  ==> EX SID NA PA NB PB M. EX evs: tls.    \
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\        Notes B {|Number SID, Agent A, Agent B, Nonce M|} : set evs";
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by (REPEAT (resolve_tac [exI,bexI] 1));
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by (rtac (tls.Nil RS tls.ClientHello RS tls.ServerHello RS tls.Certificate RS
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	  tls.ClientKeyExch RS tls.ServerFinished RS tls.ClientFinished RS
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	  tls.ServerAccepts) 2);
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by possibility_tac;
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by (REPEAT (Blast_tac 1));
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result();
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(*Another one, for CertVerify (which is optional)*)
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goal thy 
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 "!!A B. [| ALL evs. (@ N. Nonce N ~: used evs) ~: range PRF;  \
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\           A ~= B |]                       \
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\  ==> EX NB PMS. EX evs: tls.   \
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\  Says A B (Crypt (priK A) (Hash{|Nonce NB, Agent B, Nonce PMS|})) : set evs";
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by (REPEAT (resolve_tac [exI,bexI] 1));
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by (rtac (tls.Nil RS tls.ClientHello RS tls.ServerHello RS tls.Certificate RS
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	  tls.ClientKeyExch RS tls.CertVerify) 2);
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by possibility_tac;
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by (REPEAT (Blast_tac 1));
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result();
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(*Another one, for session resumption (both ServerResume and ClientResume) *)
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goal thy 
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 "!!A B. [| evs0 : tls;     \
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\           Notes A {|Number SID, Agent A, Agent B, Nonce M|} : set evs0; \
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\           Notes B {|Number SID, Agent A, Agent B, Nonce M|} : set evs0; \
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\           ALL evs. (@ N. Nonce N ~: used evs) ~: range PRF;  \
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\           A ~= B |] ==> EX NA PA NB PB X. EX evs: tls.    \
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\      X = Hash{|Number SID, Nonce M,             \
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\                       Nonce NA, Number PA, Agent A,      \
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\                       Nonce NB, Number PB, Agent B|}  &  \
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\      Says A B (Crypt (clientK(NA,NB,M)) X) : set evs  &  \
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\      Says B A (Crypt (serverK(NA,NB,M)) X) : set evs";
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by (REPEAT (resolve_tac [exI,bexI] 1));
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by (etac (tls.ClientHello RS tls.ServerHello RS tls.ServerResume RS 
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	  tls.ClientResume) 2);
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by possibility_tac;
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by (REPEAT (Blast_tac 1));
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result();
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(**** Inductive proofs about tls ****)
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(*Nobody sends themselves messages*)
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goal thy "!!evs. evs : tls ==> ALL A X. Says A A X ~: set evs";
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by (etac tls.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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(*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 tls.induct i
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    THEN 
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    REPEAT (FIRSTGOAL analz_mono_contra_tac)
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    THEN 
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    fast_tac (!claset addss (!simpset)) i THEN
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    ALLGOALS (asm_simp_tac (!simpset setloop split_tac [expand_if]));
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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 private key! (unless it's bad at start)*)
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goal thy 
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 "!!evs. evs : tls ==> (Key (priK 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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qed "Spy_see_priK";
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Addsimps [Spy_see_priK];
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goal thy 
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 "!!evs. evs : tls ==> (Key (priK 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_priK";
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Addsimps [Spy_analz_priK];
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goal thy  "!!A. [| Key (priK A) : parts (spies evs);  evs : tls |] ==> A:bad";
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by (blast_tac (!claset addDs [Spy_see_priK]) 1);
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qed "Spy_see_priK_D";
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bind_thm ("Spy_analz_priK_D", analz_subset_parts RS subsetD RS Spy_see_priK_D);
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AddSDs [Spy_see_priK_D, Spy_analz_priK_D];
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(*This lemma says that no false certificates exist.  One might extend the
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  model to include bogus certificates for the agents, but there seems
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  little point in doing so: the loss of their private keys is a worse
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  breach of security.*)
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goalw thy [certificate_def]
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 "!!evs. [| certificate B KB : parts (spies evs);  evs : tls |]  \
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\        ==> pubK B = KB";
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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 "certificate_valid";
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(*Replace key KB in ClientKeyExch by (pubK B) *)
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val ClientKeyExch_tac = 
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    forward_tac [Says_imp_spies RS parts.Inj RS certificate_valid]
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    THEN' assume_tac
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    THEN' hyp_subst_tac;
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fun analz_induct_tac i = 
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    etac tls.induct i   THEN
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    ClientKeyExch_tac  (i+6)  THEN	(*ClientKeyExch*)
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    ALLGOALS (asm_simp_tac 
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              (!simpset addcongs [if_weak_cong]
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                        setloop split_tac [expand_if]))  THEN
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    (*Remove instances of pubK B:  the Spy already knows all public keys.
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      Combining the two simplifier calls makes them run extremely slowly.*)
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    ALLGOALS (asm_simp_tac 
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              (!simpset addcongs [if_weak_cong]
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			addsimps [insert_absorb]
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                        setloop split_tac [expand_if]));
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(*** Properties of items found in Notes ***)
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goal thy "!!evs. [| Notes A {|Agent B, X|} : set evs;  evs : tls |]  \
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\                ==> Crypt (pubK B) X : parts (spies evs)";
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by (etac rev_mp 1);
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by (analz_induct_tac 1);
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by (blast_tac (!claset addIs [parts_insertI]) 1);
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qed "Notes_Crypt_parts_spies";
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(*C may be either A or B*)
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goal thy
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 "!!evs. [| Notes C {|s, Agent A, Agent B, Nonce(PRF(PMS,NA,NB))|} : set evs; \
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\           evs : tls     \
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\        |] ==> Crypt (pubK B) (Nonce PMS) : parts (spies evs)";
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by (etac rev_mp 1);
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by (parts_induct_tac 1);
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by (ALLGOALS Clarify_tac);
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(*Fake*)
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by (blast_tac (!claset addIs [parts_insertI]) 1);
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(*Client, Server Accept*)
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by (REPEAT (blast_tac (!claset addSEs spies_partsEs
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                               addSDs [Notes_Crypt_parts_spies]) 1));
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qed "Notes_master_imp_Crypt_PMS";
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(*Compared with the theorem above, both premise and conclusion are stronger*)
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goal thy
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 "!!evs. [| Notes A {|s, Agent A, Agent B, Nonce(PRF(PMS,NA,NB))|} : set evs;\
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\           evs : tls     \
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\        |] ==> Notes A {|Agent B, Nonce PMS|} : set evs";
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by (etac rev_mp 1);
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by (parts_induct_tac 1);
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(*ServerAccepts*)
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by (Fast_tac 1);	(*Blast_tac's very slow here*)
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qed "Notes_master_imp_Notes_PMS";
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(*** Protocol goal: if B receives CertVerify, then A sent it ***)
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(*B can check A's signature if he has received A's certificate.*)
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goal thy
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 "!!evs. [| X : parts (spies evs);                          \
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\           X = Crypt (priK A) (Hash{|nb, Agent B, pms|});  \
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\           evs : tls;  A ~: bad |]                         \
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\    ==> Says A B X : set evs";
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by (etac rev_mp 1);
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by (hyp_subst_tac 1);
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by (parts_induct_tac 1);
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by (Fake_parts_insert_tac 1);
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val lemma = result();
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(*Final version: B checks X using the distributed KA instead of priK A*)
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goal thy
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 "!!evs. [| X : parts (spies evs);                            \
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\           X = Crypt (invKey KA) (Hash{|nb, Agent B, pms|}); \
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\           certificate A KA : parts (spies evs);             \
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\           evs : tls;  A ~: bad |]                           \
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\    ==> Says A B X : set evs";
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by (blast_tac (!claset addSDs [certificate_valid] addSIs [lemma]) 1);
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qed "TrustCertVerify";
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(*If CertVerify is present then A has chosen PMS.*)
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goal thy
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 "!!evs. [| Crypt (priK A) (Hash{|nb, Agent B, Nonce PMS|}) \
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\             : parts (spies evs);                          \
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\           evs : tls;  A ~: bad |]                         \
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\        ==> Notes A {|Agent B, Nonce PMS|} : set evs";
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be 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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val lemma = result();
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(*Final version using the distributed KA instead of priK A*)
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goal thy
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 "!!evs. [| Crypt (invKey KA) (Hash{|nb, Agent B, Nonce PMS|}) \
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\             : parts (spies evs);                             \
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\           certificate A KA : parts (spies evs);              \
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\           evs : tls;  A ~: bad |]                            \
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\        ==> Notes A {|Agent B, Nonce PMS|} : set evs";
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by (blast_tac (!claset addSDs [certificate_valid] addSIs [lemma]) 1);
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qed "UseCertVerify";
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goal thy "!!evs. evs : tls ==> Notes A {|Agent B, Nonce (PRF x)|} ~: set evs";
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by (parts_induct_tac 1);
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(*ClientKeyExch: PMS is assumed to differ from any PRF.*)
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by (Blast_tac 1);
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qed "no_Notes_A_PRF";
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Addsimps [no_Notes_A_PRF];
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goal thy "!!evs. [| Nonce (PRF (PMS,NA,NB)) : parts (spies evs);  \
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\                   evs : tls |]  \
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\                ==> Nonce PMS : parts (spies evs)";
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by (etac rev_mp 1);
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by (parts_induct_tac 1);
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by (ALLGOALS (asm_simp_tac (!simpset addsimps [parts_insert_spies])));
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by (Fake_parts_insert_tac 1);
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(*Six others, all trivial or by freshness*)
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by (REPEAT (blast_tac (!claset addSDs [Notes_Crypt_parts_spies]
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                               addSEs spies_partsEs) 1));
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qed "MS_imp_PMS";
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AddSDs [MS_imp_PMS];
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   316
(*** Unicity results for PMS, the pre-master-secret ***)
paulson@3515
   317
paulson@3672
   318
(*PMS determines B.  Proof borrowed from NS_Public/unique_NA and from Yahalom*)
paulson@3515
   319
goal thy 
paulson@3683
   320
 "!!evs. [| Nonce PMS ~: analz (spies evs);  evs : tls |]   \
paulson@3515
   321
\        ==> EX B'. ALL B.   \
paulson@3683
   322
\              Crypt (pubK B) (Nonce PMS) : parts (spies evs) --> B=B'";
paulson@3515
   323
by (etac rev_mp 1);
paulson@3519
   324
by (parts_induct_tac 1);
paulson@3519
   325
by (Fake_parts_insert_tac 1);
paulson@3745
   326
(*ClientKeyExch*)
paulson@3745
   327
by (ClientKeyExch_tac 1);
paulson@3519
   328
by (asm_simp_tac (!simpset addsimps [all_conj_distrib]) 1);
paulson@3672
   329
by (expand_case_tac "PMS = ?y" 1 THEN
paulson@3519
   330
    blast_tac (!claset addSEs partsEs) 1);
paulson@3515
   331
val lemma = result();
paulson@3515
   332
paulson@3515
   333
goal thy 
paulson@3683
   334
 "!!evs. [| Crypt(pubK B)  (Nonce PMS) : parts (spies evs); \
paulson@3683
   335
\           Crypt(pubK B') (Nonce PMS) : parts (spies evs); \
paulson@3683
   336
\           Nonce PMS ~: analz (spies evs);                 \
paulson@3515
   337
\           evs : tls |]                                          \
paulson@3515
   338
\        ==> B=B'";
paulson@3515
   339
by (prove_unique_tac lemma 1);
paulson@3704
   340
qed "Crypt_unique_PMS";
paulson@3704
   341
paulson@3515
   342
paulson@3685
   343
(** It is frustrating that we need two versions of the unicity results.
paulson@3704
   344
    But Notes A {|Agent B, Nonce PMS|} determines both A and B.  Sometimes
paulson@3704
   345
    we have only the weaker assertion Crypt(pubK B) (Nonce PMS), which 
paulson@3704
   346
    determines B alone, and only if PMS is secret.
paulson@3685
   347
**)
paulson@3515
   348
paulson@3677
   349
(*In A's internal Note, PMS determines A and B.*)
paulson@3704
   350
goal thy "!!evs. evs : tls               \
paulson@3704
   351
\                ==> EX A' B'. ALL A B.  \
paulson@3704
   352
\                    Notes A {|Agent B, Nonce PMS|} : set evs --> A=A' & B=B'";
paulson@3519
   353
by (parts_induct_tac 1);
paulson@3515
   354
by (asm_simp_tac (!simpset addsimps [all_conj_distrib]) 1);
paulson@3745
   355
(*ClientKeyExch: if PMS is fresh, then it can't appear in Notes A X.*)
paulson@3672
   356
by (expand_case_tac "PMS = ?y" 1 THEN
paulson@3683
   357
    blast_tac (!claset addSDs [Notes_Crypt_parts_spies] addSEs partsEs) 1);
paulson@3515
   358
val lemma = result();
paulson@3515
   359
paulson@3515
   360
goal thy 
paulson@3672
   361
 "!!evs. [| Notes A  {|Agent B,  Nonce PMS|} : set evs;  \
paulson@3672
   362
\           Notes A' {|Agent B', Nonce PMS|} : set evs;  \
paulson@3515
   363
\           evs : tls |]                               \
paulson@3515
   364
\        ==> A=A' & B=B'";
paulson@3515
   365
by (prove_unique_tac lemma 1);
paulson@3672
   366
qed "Notes_unique_PMS";
paulson@3515
   367
paulson@3515
   368
paulson@3474
   369
paulson@3772
   370
(**** Secrecy Theorems ****)
paulson@3772
   371
paulson@3772
   372
(*Key compromise lemma needed to prove analz_image_keys.
paulson@3772
   373
  No collection of keys can help the spy get new private keys.*)
paulson@3772
   374
goal thy  
paulson@3772
   375
 "!!evs. evs : tls ==>                                      \
paulson@3772
   376
\  ALL KK. (Key(priK B) : analz (Key``KK Un (spies evs))) = \
paulson@3772
   377
\          (priK B : KK | B : bad)";
paulson@3772
   378
by (etac tls.induct 1);
paulson@3772
   379
by (ALLGOALS
paulson@3772
   380
    (asm_simp_tac (analz_image_keys_ss
paulson@3772
   381
		   addsimps (certificate_def::keys_distinct))));
paulson@3772
   382
(*Fake*) 
paulson@3772
   383
by (spy_analz_tac 2);
paulson@3772
   384
(*Base*)
paulson@3772
   385
by (Blast_tac 1);
paulson@3772
   386
qed_spec_mp "analz_image_priK";
paulson@3772
   387
paulson@3772
   388
paulson@3772
   389
(*slightly speeds up the big simplification below*)
paulson@3772
   390
goal thy "!!evs. KK <= range sessionK ==> priK B ~: KK";
paulson@3772
   391
by (Blast_tac 1);
paulson@3772
   392
val range_sessionkeys_not_priK = result();
paulson@3772
   393
paulson@3772
   394
(*Lemma for the trivial direction of the if-and-only-if*)
paulson@3772
   395
goal thy  
paulson@3772
   396
 "!!evs. (X : analz (G Un H)) --> (X : analz H)  ==> \
paulson@3772
   397
\        (X : analz (G Un H))  =  (X : analz H)";
paulson@3772
   398
by (blast_tac (!claset addIs [impOfSubs analz_mono]) 1);
paulson@3772
   399
val lemma = result();
paulson@3772
   400
paulson@3772
   401
(** Strangely, the following version doesn't work:
paulson@3772
   402
\    ALL Z. (Nonce N : analz (Key``(sessionK``Z) Un (spies evs))) = \
paulson@3772
   403
\           (Nonce N : analz (spies evs))";
paulson@3772
   404
**)
paulson@3772
   405
paulson@3772
   406
goal thy  
paulson@3772
   407
 "!!evs. evs : tls ==>                                    \
paulson@3772
   408
\    ALL KK. KK <= range sessionK -->                     \
paulson@3772
   409
\            (Nonce N : analz (Key``KK Un (spies evs))) = \
paulson@3772
   410
\            (Nonce N : analz (spies evs))";
paulson@3772
   411
by (etac tls.induct 1);
paulson@3772
   412
by (ClientKeyExch_tac 7);
paulson@3772
   413
by (REPEAT_FIRST (resolve_tac [allI, impI]));
paulson@3772
   414
by (REPEAT_FIRST (rtac lemma));
paulson@3772
   415
by (ALLGOALS    (*24 seconds*)
paulson@3772
   416
    (asm_simp_tac (analz_image_keys_ss 
paulson@3772
   417
		   addsimps [range_sessionkeys_not_priK, 
paulson@3772
   418
                             analz_image_priK, certificate_def])));
paulson@3772
   419
by (ALLGOALS (asm_simp_tac (!simpset addsimps [insert_absorb])));
paulson@3772
   420
(*Fake*) 
paulson@3772
   421
by (spy_analz_tac 2);
paulson@3772
   422
(*Base*)
paulson@3772
   423
by (Blast_tac 1);
paulson@3772
   424
qed_spec_mp "analz_image_keys";
paulson@3772
   425
paulson@3772
   426
(*Knowing some session keys is no help in getting new nonces*)
paulson@3772
   427
goal thy
paulson@3772
   428
 "!!evs. evs : tls ==>          \
paulson@3772
   429
\        Nonce N : analz (insert (Key (sessionK z)) (spies evs)) =  \
paulson@3772
   430
\        (Nonce N : analz (spies evs))";
paulson@3772
   431
by (asm_simp_tac (analz_image_keys_ss addsimps [analz_image_keys]) 1);
paulson@3772
   432
qed "analz_insert_key";
paulson@3772
   433
Addsimps [analz_insert_key];
paulson@3772
   434
paulson@3772
   435
paulson@3772
   436
(*** Protocol goal: serverK(Na,Nb,M) and clientK(Na,Nb,M) remain secure ***)
paulson@3772
   437
paulson@3772
   438
(** Some lemmas about session keys, comprising clientK and serverK **)
paulson@3772
   439
paulson@3772
   440
paulson@3772
   441
(*Lemma: session keys are never used if PMS is fresh.  
paulson@3772
   442
  Nonces don't have to agree, allowing session resumption.
paulson@3772
   443
  Converse doesn't hold; revealing PMS doesn't force the keys to be sent.
paulson@3772
   444
  THEY ARE NOT SUITABLE AS SAFE ELIM RULES.*)
paulson@3772
   445
goal thy 
paulson@3772
   446
 "!!evs. [| Nonce PMS ~: parts (spies evs);  \
paulson@3772
   447
\           K = sessionK((Na, Nb, PRF(PMS,NA,NB)), b);  \
paulson@3772
   448
\           evs : tls |]             \
paulson@3772
   449
\  ==> Key K ~: parts (spies evs) & (ALL Y. Crypt K Y ~: parts (spies evs))";
paulson@3772
   450
by (etac rev_mp 1);
paulson@3772
   451
by (hyp_subst_tac 1);
paulson@3772
   452
by (analz_induct_tac 1);
paulson@3772
   453
(*SpyKeys*)
paulson@3772
   454
by (blast_tac (!claset addSEs spies_partsEs) 3);
paulson@3772
   455
(*Fake*)
paulson@3772
   456
by (simp_tac (!simpset addsimps [parts_insert_spies]) 2);
paulson@3772
   457
by (Fake_parts_insert_tac 2);
paulson@3772
   458
(** LEVEL 6 **)
paulson@3772
   459
(*Oops*)
paulson@3772
   460
by (fast_tac (!claset addSEs [MPair_parts]
paulson@3772
   461
		       addDs  [Says_imp_spies RS parts.Inj]
paulson@3772
   462
		       addss (!simpset)) 6);
paulson@3772
   463
by (REPEAT 
paulson@3772
   464
    (blast_tac (!claset addSDs [Notes_Crypt_parts_spies, 
paulson@3772
   465
				Notes_master_imp_Crypt_PMS]
paulson@3772
   466
                        addSEs spies_partsEs) 1));
paulson@3772
   467
val lemma = result();
paulson@3772
   468
paulson@3772
   469
goal thy 
paulson@3772
   470
 "!!evs. [| Nonce PMS ~: parts (spies evs);  evs : tls |]             \
paulson@3772
   471
\  ==> Key (sessionK((Na, Nb, PRF(PMS,NA,NB)), b)) ~: parts (spies evs)";
paulson@3772
   472
by (blast_tac (!claset addDs [lemma]) 1);
paulson@3772
   473
qed "PMS_sessionK_not_spied";
paulson@3772
   474
bind_thm ("PMS_sessionK_spiedE", 
paulson@3772
   475
	  PMS_sessionK_not_spied RSN (2,rev_notE));
paulson@3772
   476
paulson@3772
   477
goal thy 
paulson@3772
   478
 "!!evs. [| Nonce PMS ~: parts (spies evs);  evs : tls |]             \
paulson@3772
   479
\  ==> Crypt (sessionK((Na, Nb, PRF(PMS,NA,NB)), b)) Y ~: parts (spies evs)";
paulson@3772
   480
by (blast_tac (!claset addDs [lemma]) 1);
paulson@3772
   481
qed "PMS_Crypt_sessionK_not_spied";
paulson@3772
   482
bind_thm ("PMS_Crypt_sessionK_spiedE", 
paulson@3772
   483
	  PMS_Crypt_sessionK_not_spied RSN (2,rev_notE));
paulson@3772
   484
paulson@3772
   485
(*Lemma: write keys are never sent if M (MASTER SECRET) is secure.  
paulson@3772
   486
  Converse doesn't hold; betraying M doesn't force the keys to be sent!
paulson@3772
   487
  The strong Oops condition can be weakened later by unicity reasoning, 
paulson@3772
   488
	with some effort.*)
paulson@3772
   489
goal thy 
paulson@3772
   490
 "!!evs. [| ALL A. Says A Spy (Key (sessionK((NA,NB,M),b))) ~: set evs; \
paulson@3772
   491
\           Nonce M ~: analz (spies evs);  evs : tls |]   \
paulson@3772
   492
\        ==> Key (sessionK((NA,NB,M),b)) ~: parts (spies evs)";
paulson@3772
   493
by (etac rev_mp 1);
paulson@3772
   494
by (etac rev_mp 1);
paulson@3772
   495
by (analz_induct_tac 1);        (*17 seconds*)
paulson@3772
   496
(*Oops*)
paulson@3772
   497
by (Blast_tac 4);
paulson@3772
   498
(*SpyKeys*)
paulson@3772
   499
by (blast_tac (!claset addDs [Says_imp_spies RS analz.Inj]) 3);
paulson@3772
   500
(*Fake*) 
paulson@3772
   501
by (spy_analz_tac 2);
paulson@3772
   502
(*Base*)
paulson@3772
   503
by (Blast_tac 1);
paulson@3772
   504
qed "sessionK_not_spied";
paulson@3772
   505
Addsimps [sessionK_not_spied];
paulson@3772
   506
paulson@3772
   507
paulson@3745
   508
(*If A sends ClientKeyExch to an honest B, then the PMS will stay secret.*)
paulson@3677
   509
goal thy
paulson@3683
   510
 "!!evs. [| evs : tls;  A ~: bad;  B ~: bad |]           \
paulson@3677
   511
\        ==> Notes A {|Agent B, Nonce PMS|} : set evs  -->   \
paulson@3683
   512
\            Nonce PMS ~: analz (spies evs)";
paulson@3745
   513
by (analz_induct_tac 1);   (*11 seconds*)
paulson@3677
   514
(*ClientAccepts and ServerAccepts: because PMS ~: range PRF*)
paulson@3745
   515
by (REPEAT (fast_tac (!claset addss (!simpset)) 6));
paulson@3745
   516
(*ClientHello, ServerHello, ClientKeyExch, ServerResume: 
paulson@3687
   517
  mostly freshness reasoning*)
paulson@3677
   518
by (REPEAT (blast_tac (!claset addSEs partsEs
paulson@3683
   519
			       addDs  [Notes_Crypt_parts_spies,
paulson@3677
   520
				       impOfSubs analz_subset_parts,
paulson@3687
   521
				       Says_imp_spies RS analz.Inj]) 3));
paulson@3677
   522
(*SpyKeys*)
paulson@3677
   523
by (fast_tac (!claset addss (!simpset)) 2);
paulson@3677
   524
(*Fake*)
paulson@3677
   525
by (spy_analz_tac 1);
paulson@3677
   526
bind_thm ("Spy_not_see_PMS", result() RSN (2, rev_mp));
paulson@3677
   527
paulson@3677
   528
paulson@3745
   529
(*If A sends ClientKeyExch to an honest B, then the MASTER SECRET
paulson@3677
   530
  will stay secret.*)
paulson@3677
   531
goal thy
paulson@3683
   532
 "!!evs. [| evs : tls;  A ~: bad;  B ~: bad |]           \
paulson@3677
   533
\        ==> Notes A {|Agent B, Nonce PMS|} : set evs  -->   \
paulson@3683
   534
\            Nonce (PRF(PMS,NA,NB)) ~: analz (spies evs)";
paulson@3745
   535
by (analz_induct_tac 1);   (*13 seconds*)
paulson@3677
   536
(*ClientAccepts and ServerAccepts: because PMS was already visible*)
paulson@3677
   537
by (REPEAT (blast_tac (!claset addDs [Spy_not_see_PMS, 
paulson@3683
   538
				      Says_imp_spies RS analz.Inj,
paulson@3683
   539
				      Notes_imp_spies RS analz.Inj]) 6));
paulson@3677
   540
(*ClientHello*)
paulson@3677
   541
by (Blast_tac 3);
paulson@3677
   542
(*SpyKeys: by secrecy of the PMS, Spy cannot make the MS*)
paulson@3677
   543
by (blast_tac (!claset addSDs [Spy_not_see_PMS, 
paulson@3683
   544
			       Says_imp_spies RS analz.Inj]) 2);
paulson@3677
   545
(*Fake*)
paulson@3677
   546
by (spy_analz_tac 1);
paulson@3745
   547
(*ServerHello and ClientKeyExch: mostly freshness reasoning*)
paulson@3677
   548
by (REPEAT (blast_tac (!claset addSEs partsEs
paulson@3683
   549
			       addDs  [Notes_Crypt_parts_spies,
paulson@3677
   550
				       impOfSubs analz_subset_parts,
paulson@3683
   551
				       Says_imp_spies RS analz.Inj]) 1));
paulson@3677
   552
bind_thm ("Spy_not_see_MS", result() RSN (2, rev_mp));
paulson@3677
   553
paulson@3677
   554
paulson@3704
   555
(*** Weakening the Oops conditions for leakage of clientK ***)
paulson@3704
   556
paulson@3704
   557
(*If A created PMS then nobody other than the Spy would send a message
paulson@3704
   558
  using a clientK generated from that PMS.*)
paulson@3704
   559
goal thy
paulson@3704
   560
 "!!evs. [| evs : tls;  A' ~= Spy |]                \
paulson@3704
   561
\  ==> Notes A {|Agent B, Nonce PMS|} : set evs -->                  \
paulson@3704
   562
\      Says A' B' (Crypt (clientK(Na,Nb,PRF(PMS,NA,NB))) Y) : set evs -->  \
paulson@3704
   563
\      A = A'";
paulson@3745
   564
by (analz_induct_tac 1);	(*8 seconds*)
paulson@3711
   565
by (ALLGOALS Clarify_tac);
paulson@3704
   566
(*ClientFinished, ClientResume: by unicity of PMS*)
paulson@3704
   567
by (REPEAT 
paulson@3704
   568
    (blast_tac (!claset addSDs [Notes_master_imp_Notes_PMS]
paulson@3704
   569
     	 	        addIs  [Notes_unique_PMS RS conjunct1]) 2));
paulson@3745
   570
(*ClientKeyExch*)
paulson@3772
   571
by (blast_tac (!claset addSEs [PMS_Crypt_sessionK_spiedE]
paulson@3704
   572
	               addSDs [Says_imp_spies RS parts.Inj]) 1);
paulson@3704
   573
bind_thm ("Says_clientK_unique",
paulson@3704
   574
	  result() RSN(2,rev_mp) RSN(2,rev_mp));
paulson@3704
   575
paulson@3704
   576
paulson@3704
   577
(*If A created PMS and has not leaked her clientK to the Spy, 
paulson@3704
   578
  then nobody has.*)
paulson@3704
   579
goal thy
paulson@3704
   580
 "!!evs. evs : tls                         \
paulson@3704
   581
\  ==> Says A Spy (Key(clientK(Na,Nb,PRF(PMS,NA,NB)))) ~: set evs --> \
paulson@3704
   582
\      Notes A {|Agent B, Nonce PMS|} : set evs -->                   \
paulson@3704
   583
\      (ALL A. Says A Spy (Key(clientK(Na,Nb,PRF(PMS,NA,NB)))) ~: set evs) ";
paulson@3704
   584
by (etac tls.induct 1);
paulson@3704
   585
(*This roundabout proof sequence avoids looping in simplification*)
paulson@3704
   586
by (ALLGOALS Simp_tac);
paulson@3711
   587
by (ALLGOALS Clarify_tac);
paulson@3704
   588
by (Fake_parts_insert_tac 1);
paulson@3704
   589
by (ALLGOALS Asm_simp_tac);
paulson@3704
   590
(*Oops*)
paulson@3704
   591
by (blast_tac (!claset addIs [Says_clientK_unique]) 2);
paulson@3745
   592
(*ClientKeyExch*)
paulson@3772
   593
by (blast_tac (!claset addSEs (PMS_sessionK_spiedE::spies_partsEs)) 1);
paulson@3704
   594
qed_spec_mp "clientK_Oops_ALL";
paulson@3704
   595
paulson@3704
   596
paulson@3704
   597
paulson@3704
   598
(*** Weakening the Oops conditions for leakage of serverK ***)
paulson@3704
   599
paulson@3704
   600
(*If A created PMS for B, then nobody other than B or the Spy would
paulson@3704
   601
  send a message using a serverK generated from that PMS.*)
paulson@3704
   602
goal thy
paulson@3704
   603
 "!!evs. [| evs : tls;  A ~: bad;  B ~: bad;  B' ~= Spy |]                \
paulson@3704
   604
\  ==> Notes A {|Agent B, Nonce PMS|} : set evs -->                  \
paulson@3704
   605
\      Says B' A' (Crypt (serverK(Na,Nb,PRF(PMS,NA,NB))) Y) : set evs -->  \
paulson@3704
   606
\      B = B'";
paulson@3745
   607
by (analz_induct_tac 1);	(*9 seconds*)
paulson@3711
   608
by (ALLGOALS Clarify_tac);
paulson@3704
   609
(*ServerResume, ServerFinished: by unicity of PMS*)
paulson@3704
   610
by (REPEAT
paulson@3704
   611
    (blast_tac (!claset addSEs [MPair_parts]
paulson@3704
   612
		        addSDs [Notes_master_imp_Crypt_PMS, 
paulson@3704
   613
				Says_imp_spies RS parts.Inj]
paulson@3704
   614
                        addDs  [Spy_not_see_PMS, 
paulson@3704
   615
				Notes_Crypt_parts_spies,
paulson@3704
   616
				Crypt_unique_PMS]) 2));
paulson@3745
   617
(*ClientKeyExch*)
paulson@3772
   618
by (blast_tac (!claset addSEs [PMS_Crypt_sessionK_spiedE]
paulson@3704
   619
	               addSDs [Says_imp_spies RS parts.Inj]) 1);
paulson@3704
   620
bind_thm ("Says_serverK_unique",
paulson@3704
   621
	  result() RSN(2,rev_mp) RSN(2,rev_mp));
paulson@3704
   622
paulson@3704
   623
(*If A created PMS for B, and B has not leaked his serverK to the Spy, 
paulson@3704
   624
  then nobody has.*)
paulson@3704
   625
goal thy
paulson@3704
   626
 "!!evs. [| evs : tls;  A ~: bad;  B ~: bad |]                        \
paulson@3704
   627
\  ==> Says B Spy (Key(serverK(Na,Nb,PRF(PMS,NA,NB)))) ~: set evs --> \
paulson@3704
   628
\      Notes A {|Agent B, Nonce PMS|} : set evs -->                   \
paulson@3704
   629
\      (ALL A. Says A Spy (Key(serverK(Na,Nb,PRF(PMS,NA,NB)))) ~: set evs) ";
paulson@3704
   630
by (etac tls.induct 1);
paulson@3704
   631
(*This roundabout proof sequence avoids looping in simplification*)
paulson@3704
   632
by (ALLGOALS Simp_tac);
paulson@3711
   633
by (ALLGOALS Clarify_tac);
paulson@3704
   634
by (Fake_parts_insert_tac 1);
paulson@3704
   635
by (ALLGOALS Asm_simp_tac);
paulson@3704
   636
(*Oops*)
paulson@3704
   637
by (blast_tac (!claset addIs [Says_serverK_unique]) 2);
paulson@3745
   638
(*ClientKeyExch*)
paulson@3772
   639
by (blast_tac (!claset addSEs (PMS_sessionK_spiedE::spies_partsEs)) 1);
paulson@3704
   640
qed_spec_mp "serverK_Oops_ALL";
paulson@3704
   641
paulson@3704
   642
paulson@3704
   643
paulson@3685
   644
(*** Protocol goals: if A receives ServerFinished, then B is present 
paulson@3729
   645
     and has used the quoted values PA, PB, etc.  Note that it is up to A
paulson@3729
   646
     to compare PA with what she originally sent.
paulson@3474
   647
***)
paulson@3474
   648
paulson@3685
   649
(*The mention of her name (A) in X assures A that B knows who she is.*)
paulson@3515
   650
goal thy
paulson@3772
   651
 "!!evs. [| X = Crypt (serverK(Na,Nb,M))                  \
paulson@3758
   652
\                 (Hash{|Number SID, Nonce M,             \
paulson@3745
   653
\                        Nonce Na, Number PA, Agent A,    \
paulson@3745
   654
\                        Nonce Nb, Number PB, Agent B|}); \
paulson@3676
   655
\           M = PRF(PMS,NA,NB);                           \
paulson@3772
   656
\           evs : tls;  A ~: bad;  B ~: bad |]            \
paulson@3772
   657
\        ==> (ALL A. Says A Spy (Key(serverK(Na,Nb,M))) ~: set evs) --> \
paulson@3772
   658
\            Notes A {|Agent B, Nonce PMS|} : set evs --> \
paulson@3772
   659
\            X : parts (spies evs) --> Says B A X : set evs";
paulson@3480
   660
by (hyp_subst_tac 1);
paulson@3745
   661
by (analz_induct_tac 1);        (*22 seconds*)
paulson@3704
   662
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib])));
paulson@3711
   663
(*proves ServerResume*)
paulson@3711
   664
by (ALLGOALS Clarify_tac);
paulson@3745
   665
(*ClientKeyExch*)
paulson@3704
   666
by (fast_tac  (*blast_tac gives PROOF FAILED*)
paulson@3772
   667
    (!claset addSEs [PMS_Crypt_sessionK_spiedE]) 2);
paulson@3480
   668
(*Fake: the Spy doesn't have the critical session key!*)
paulson@3683
   669
by (subgoal_tac "Key (serverK(Na,Nb,PRF(PMS,NA,NB))) ~: analz(spies evsa)" 1);
paulson@3672
   670
by (asm_simp_tac (!simpset addsimps [Spy_not_see_MS, 
paulson@3480
   671
				     not_parts_not_analz]) 2);
paulson@3474
   672
by (Fake_parts_insert_tac 1);
paulson@3772
   673
val lemma = normalize_thm [RSmp] (result());
paulson@3704
   674
paulson@3704
   675
(*Final version*)
paulson@3704
   676
goal thy
paulson@3704
   677
 "!!evs. [| X = Crypt (serverK(Na,Nb,M))                  \
paulson@3758
   678
\                 (Hash{|Number SID, Nonce M,             \
paulson@3745
   679
\                        Nonce Na, Number PA, Agent A,    \
paulson@3745
   680
\                        Nonce Nb, Number PB, Agent B|}); \
paulson@3704
   681
\           M = PRF(PMS,NA,NB);                           \
paulson@3704
   682
\           X : parts (spies evs);                        \
paulson@3704
   683
\           Notes A {|Agent B, Nonce PMS|} : set evs;     \
paulson@3704
   684
\           Says B Spy (Key (serverK(Na,Nb,M))) ~: set evs; \
paulson@3704
   685
\           evs : tls;  A ~: bad;  B ~: bad |]          \
paulson@3704
   686
\        ==> Says B A X : set evs";
paulson@3704
   687
by (blast_tac (!claset addIs [lemma]
paulson@3704
   688
                       addEs [serverK_Oops_ALL RSN(2, rev_notE)]) 1);
paulson@3474
   689
qed_spec_mp "TrustServerFinished";
paulson@3474
   690
paulson@3474
   691
paulson@3704
   692
paulson@3685
   693
(*This version refers not to ServerFinished but to any message from B.
paulson@3685
   694
  We don't assume B has received CertVerify, and an intruder could
paulson@3515
   695
  have changed A's identity in all other messages, so we can't be sure
paulson@3519
   696
  that B sends his message to A.  If CLIENT KEY EXCHANGE were augmented
paulson@3704
   697
  to bind A's identity with PMS, then we could replace A' by A below.*)
paulson@3515
   698
goal thy
paulson@3772
   699
 "!!evs. [| M = PRF(PMS,NA,NB);  evs : tls;  A ~: bad;  B ~: bad |]     \
paulson@3772
   700
\        ==> (ALL A. Says A Spy (Key(serverK(Na,Nb,M))) ~: set evs) --> \
paulson@3772
   701
\            Notes A {|Agent B, Nonce PMS|} : set evs -->              \
paulson@3683
   702
\            Crypt (serverK(Na,Nb,M)) Y : parts (spies evs)  -->  \
paulson@3672
   703
\            (EX A'. Says B A' (Crypt (serverK(Na,Nb,M)) Y) : set evs)";
paulson@3672
   704
by (hyp_subst_tac 1);
paulson@3686
   705
by (analz_induct_tac 1);	(*20 seconds*)
paulson@3704
   706
by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib])));
paulson@3711
   707
by (ALLGOALS Clarify_tac);
paulson@3704
   708
(*ServerResume, ServerFinished: by unicity of PMS*)
paulson@3704
   709
by (REPEAT
paulson@3704
   710
    (blast_tac (!claset addSEs [MPair_parts]
paulson@3704
   711
		        addSDs [Notes_master_imp_Crypt_PMS, 
paulson@3704
   712
				Says_imp_spies RS parts.Inj]
paulson@3704
   713
                        addDs  [Spy_not_see_PMS, 
paulson@3704
   714
				Notes_Crypt_parts_spies,
paulson@3704
   715
				Crypt_unique_PMS]) 3));
paulson@3745
   716
(*ClientKeyExch*)
paulson@3704
   717
by (blast_tac
paulson@3772
   718
    (!claset addSEs [PMS_Crypt_sessionK_spiedE]) 2);
paulson@3515
   719
(*Fake: the Spy doesn't have the critical session key!*)
paulson@3683
   720
by (subgoal_tac "Key (serverK(Na,Nb,PRF(PMS,NA,NB))) ~: analz(spies evsa)" 1);
paulson@3672
   721
by (asm_simp_tac (!simpset addsimps [Spy_not_see_MS, 
paulson@3515
   722
				     not_parts_not_analz]) 2);
paulson@3515
   723
by (Fake_parts_insert_tac 1);
paulson@3772
   724
val lemma = normalize_thm [RSmp] (result());
paulson@3704
   725
paulson@3704
   726
(*Final version*)
paulson@3704
   727
goal thy
paulson@3704
   728
 "!!evs. [| M = PRF(PMS,NA,NB);                           \
paulson@3704
   729
\           Crypt (serverK(Na,Nb,M)) Y : parts (spies evs); \
paulson@3704
   730
\           Notes A {|Agent B, Nonce PMS|} : set evs;     \
paulson@3704
   731
\           Says B Spy (Key (serverK(Na,Nb,M))) ~: set evs; \
paulson@3704
   732
\           evs : tls;  A ~: bad;  B ~: bad |]          \
paulson@3704
   733
\        ==> EX A'. Says B A' (Crypt (serverK(Na,Nb,M)) Y) : set evs";
paulson@3704
   734
by (blast_tac (!claset addIs [lemma]
paulson@3704
   735
                       addEs [serverK_Oops_ALL RSN(2, rev_notE)]) 1);
paulson@3515
   736
qed_spec_mp "TrustServerMsg";
paulson@3515
   737
paulson@3515
   738
paulson@3704
   739
paulson@3515
   740
(*** Protocol goal: if B receives any message encrypted with clientK
paulson@3672
   741
     then A has sent it, ASSUMING that A chose PMS.  Authentication is
paulson@3515
   742
     assumed here; B cannot verify it.  But if the message is
paulson@3729
   743
     ClientFinished, then B can then check the quoted values PA, PB, etc.
paulson@3506
   744
***)
paulson@3704
   745
paulson@3515
   746
goal thy
paulson@3772
   747
 "!!evs. [| M = PRF(PMS,NA,NB);  evs : tls;  A ~: bad;  B ~: bad |] \
paulson@3772
   748
\    ==> (ALL A. Says A Spy (Key(clientK(Na,Nb,M))) ~: set evs) --> \
paulson@3772
   749
\        Notes A {|Agent B, Nonce PMS|} : set evs -->               \
paulson@3772
   750
\        Crypt (clientK(Na,Nb,M)) Y : parts (spies evs) -->         \
paulson@3772
   751
\        Says A B (Crypt (clientK(Na,Nb,M)) Y) : set evs";
paulson@3772
   752
by (hyp_subst_tac 1);
paulson@3745
   753
by (analz_induct_tac 1);	(*15 seconds*)
paulson@3711
   754
by (ALLGOALS Clarify_tac);
paulson@3704
   755
(*ClientFinished, ClientResume: by unicity of PMS*)
paulson@3704
   756
by (REPEAT (blast_tac (!claset delrules [conjI]
paulson@3704
   757
		               addSDs [Notes_master_imp_Notes_PMS]
paulson@3704
   758
	 	               addDs  [Notes_unique_PMS]) 3));
paulson@3745
   759
(*ClientKeyExch*)
paulson@3704
   760
by (fast_tac  (*blast_tac gives PROOF FAILED*)
paulson@3772
   761
    (!claset addSEs [PMS_Crypt_sessionK_spiedE]) 2);
paulson@3480
   762
(*Fake: the Spy doesn't have the critical session key!*)
paulson@3683
   763
by (subgoal_tac "Key (clientK(Na,Nb,PRF(PMS,NA,NB))) ~: analz(spies evsa)" 1);
paulson@3672
   764
by (asm_simp_tac (!simpset addsimps [Spy_not_see_MS, 
paulson@3480
   765
				     not_parts_not_analz]) 2);
paulson@3474
   766
by (Fake_parts_insert_tac 1);
paulson@3772
   767
val lemma = normalize_thm [RSmp] (result());
paulson@3704
   768
paulson@3704
   769
(*Final version*)
paulson@3704
   770
goal thy
paulson@3772
   771
 "!!evs. [| M = PRF(PMS,NA,NB);                           \
paulson@3772
   772
\           Crypt (clientK(Na,Nb,M)) Y : parts (spies evs);  \
paulson@3704
   773
\           Notes A {|Agent B, Nonce PMS|} : set evs;        \
paulson@3772
   774
\           Says A Spy (Key(clientK(Na,Nb,M))) ~: set evs;  \
paulson@3704
   775
\           evs : tls;  A ~: bad;  B ~: bad |]                         \
paulson@3772
   776
\  ==> Says A B (Crypt (clientK(Na,Nb,M)) Y) : set evs";
paulson@3704
   777
by (blast_tac (!claset addIs [lemma]
paulson@3704
   778
                       addEs [clientK_Oops_ALL RSN(2, rev_notE)]) 1);
paulson@3772
   779
qed "TrustClientMsg";
paulson@3506
   780
paulson@3506
   781
paulson@3685
   782
paulson@3685
   783
(*** Protocol goal: if B receives ClientFinished, and if B is able to
paulson@3685
   784
     check a CertVerify from A, then A has used the quoted
paulson@3729
   785
     values PA, PB, etc.  Even this one requires A to be uncompromised.
paulson@3506
   786
 ***)
paulson@3506
   787
goal thy
paulson@3772
   788
 "!!evs. [| M = PRF(PMS,NA,NB);                           \
paulson@3772
   789
\           Says A Spy (Key(clientK(Na,Nb,M))) ~: set evs;\
paulson@3772
   790
\           Says A' B (Crypt (clientK(Na,Nb,M)) Y) : set evs; \
paulson@3745
   791
\           certificate A KA : parts (spies evs);       \
paulson@3745
   792
\           Says A'' B (Crypt (invKey KA) (Hash{|nb, Agent B, Nonce PMS|}))\
paulson@3515
   793
\             : set evs;                                                  \
paulson@3683
   794
\        evs : tls;  A ~: bad;  B ~: bad |]                             \
paulson@3772
   795
\     ==> Says A B (Crypt (clientK(Na,Nb,M)) Y) : set evs";
paulson@3515
   796
by (blast_tac (!claset addSIs [TrustClientMsg, UseCertVerify]
paulson@3683
   797
                       addDs  [Says_imp_spies RS parts.Inj]) 1);
paulson@3515
   798
qed "AuthClientFinished";
paulson@3687
   799
paulson@3687
   800
(*22/9/97: loads in 622s, which is 10 minutes 22 seconds*)
paulson@3711
   801
(*24/9/97: loads in 672s, which is 11 minutes 12 seconds [stronger theorems]*)
paulson@3745
   802
(*29/9/97: loads in 481s, after removing Certificate from ClientKeyExch*)
paulson@3758
   803
(*30/9/97: loads in 476s, after removing unused theorems*)
paulson@3760
   804
(*30/9/97: loads in 448s, after fixing ServerResume*)