author | paulson |
Mon, 07 Jul 1997 10:49:14 +0200 | |
changeset 3506 | a36e0a49d2cd |
parent 3500 | 0d8ad2f192d8 |
child 3515 | d8a71f6eaf40 |
permissions | -rw-r--r-- |
3474 | 1 |
(* 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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The public-key model has a weakness, especially concerning anonymous sessions. |
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The Spy's state is recorded as the trace of message. But if he himself is the |
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Client and invents M, then he encrypts M with B's public key before sending |
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it. This message gives no evidence that the spy knows M, and yet the spy |
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actually chose M! So, in any property concerning the secrecy of some item, |
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one must establish that the spy didn't choose the item. Guarantees normally |
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assume that the other party is uncompromised (otherwise, one can prove |
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little). |
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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 CERTIFICATE VERIFY knows that A is present (But this |
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message is optional!) |
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* A upon receiving SERVER FINISHED 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 XA and XB (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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AddIffs [Spy_in_lost, Server_not_lost]; |
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Addsimps [certificate_def]; |
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goal thy "!!A. A ~: lost ==> A ~= Spy"; |
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by (Blast_tac 1); |
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qed "not_lost_not_eq_Spy"; |
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Addsimps [not_lost_not_eq_Spy]; |
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(*Injectiveness of key-generating functions*) |
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AddIffs [inj_clientK RS inj_eq, inj_serverK RS inj_eq]; |
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(* invKey(clientK x) = clientK x and similarly for serverK*) |
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Addsimps [isSym_clientK, rewrite_rule [isSymKey_def] isSym_clientK, |
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isSym_serverK, rewrite_rule [isSymKey_def] isSym_serverK]; |
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(*Replacing the variable by a constant improves search speed by 50%!*) |
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val Says_imp_sees_Spy' = |
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read_instantiate_sg (sign_of thy) [("lost","lost")] Says_imp_sees_Spy; |
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(*** clientK and serverK make symmetric keys; no clashes with pubK or priK ***) |
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goal thy "pubK A ~= clientK 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_clientK"; |
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goal thy "pubK A ~= serverK 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_serverK"; |
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goal thy "priK A ~= clientK 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_clientK"; |
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goal thy "priK A ~= serverK 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_serverK"; |
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(*clientK and serverK have disjoint ranges*) |
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goal thy "clientK arg ~= serverK arg'"; |
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by (cut_facts_tac [rangeI RS impOfSubs clientK_range] 1); |
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by (Blast_tac 1); |
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qed "clientK_neq_serverK"; |
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val ths = [pubK_neq_clientK, pubK_neq_serverK, |
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priK_neq_clientK, priK_neq_serverK, clientK_neq_serverK]; |
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AddIffs (ths @ (ths RL [not_sym])); |
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(**** Protocol Proofs ****) |
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(*A "possibility property": there are traces that reach the end. |
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This protocol has three end points and six messages to consider.*) |
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(*Possibility property ending with ServerFinished.*) |
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goal thy |
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"!!A B. A ~= B ==> EX NA XA NB XB M. EX evs: tls. \ |
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\ Says B A (Crypt (serverK(NA,NB,M)) \ |
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\ (Hash{|Hash{|Nonce NA, Nonce NB, Nonce M|}, \ |
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\ Nonce NA, Agent XA, Agent A, \ |
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\ Nonce NB, Agent XB, \ |
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\ certificate B (pubK B)|})) \ |
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\ : 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.ClientCertKeyEx |
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RS tls.ServerFinished) 2); |
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by possibility_tac; |
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result(); |
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(*And one for ClientFinished. Either FINISHED message may come first.*) |
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goal thy |
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"!!A B. A ~= B ==> EX NA XA NB XB M. EX evs: tls. \ |
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\ Says A B (Crypt (clientK(NA,NB,M)) \ |
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\ (Hash{|Hash{|Nonce NA, Nonce NB, Nonce M|}, \ |
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\ Nonce NA, Agent XA, \ |
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\ certificate A (pubK A), \ |
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\ Nonce NB, Agent XB, Agent B|})) : 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.ClientCertKeyEx |
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RS tls.ClientFinished) 2); |
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by possibility_tac; |
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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. A ~= B ==> EX NB M. EX evs: tls. \ |
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\ Says A B (Crypt (priK A) \ |
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\ (Hash{|Nonce NB, certificate B (pubK 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.ClientCertKeyEx |
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RS tls.CertVerify) 2); |
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by possibility_tac; |
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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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(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY |
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sends messages containing X! **) |
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(*Spy never sees another agent's private key! (unless it's lost at start)*) |
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goal thy |
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"!!evs. evs : tls \ |
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\ ==> (Key (priK A) : parts (sees lost Spy evs)) = (A : lost)"; |
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by (etac tls.induct 1); |
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by (prove_simple_subgoals_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 \ |
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\ ==> (Key (priK A) : analz (sees lost Spy evs)) = (A : lost)"; |
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by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset)); |
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qed "Spy_analz_priK"; |
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Addsimps [Spy_analz_priK]; |
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goal thy "!!A. [| Key (priK A) : parts (sees lost Spy evs); \ |
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\ evs : tls |] ==> A:lost"; |
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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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(*Every Nonce that's hashed is already in past traffic. *) |
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goal thy "!!evs. [| Hash {|Nonce N, X|} : parts (sees lost Spy evs); \ |
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\ evs : tls |] \ |
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\ ==> Nonce N : parts (sees lost Spy evs)"; |
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by (etac rev_mp 1); |
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by (etac tls.induct 1); |
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by (ALLGOALS (asm_simp_tac (!simpset addsimps [parts_insert_sees]))); |
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by (step_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj] |
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addSEs partsEs) 1); |
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by (Fake_parts_insert_tac 1); |
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qed "Hash_imp_Nonce1"; |
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(*Lemma needed to prove Hash_Hash_imp_Nonce*) |
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goal thy "!!evs. [| Hash{|Nonce NA, Nonce NB, Nonce M|} \ |
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\ : parts (sees lost Spy evs); \ |
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\ evs : tls |] \ |
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\ ==> Nonce M : parts (sees lost Spy evs)"; |
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by (etac rev_mp 1); |
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by (etac tls.induct 1); |
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by (ALLGOALS (asm_simp_tac (!simpset addsimps [parts_insert_sees]))); |
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by (step_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj] |
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addSEs partsEs) 1); |
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by (Fake_parts_insert_tac 1); |
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qed "Hash_imp_Nonce2"; |
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AddSDs [Hash_imp_Nonce2]; |
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goal thy "!!evs. [| Hash {| Hash{|Nonce NA, Nonce NB, Nonce M|}, X |} \ |
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\ : parts (sees lost Spy evs); \ |
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\ evs : tls |] \ |
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\ ==> Nonce M : parts (sees lost Spy evs)"; |
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by (etac rev_mp 1); |
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by (etac tls.induct 1); |
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by (ALLGOALS (asm_simp_tac (!simpset addsimps [parts_insert_sees]))); |
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by (step_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj] |
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addSEs partsEs) 1); |
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by (Fake_parts_insert_tac 1); |
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qed "Hash_Hash_imp_Nonce"; |
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(*NEEDED?? |
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Every Nonce that's hashed is already in past traffic. |
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This general formulation is tricky to prove and hard to use, since the |
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2nd premise is typically proved by simplification.*) |
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goal thy "!!evs. [| Hash X : parts (sees lost Spy evs); \ |
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\ Nonce N : parts {X}; evs : tls |] \ |
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\ ==> Nonce N : parts (sees lost Spy evs)"; |
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by (etac rev_mp 1); |
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by (etac tls.induct 1); |
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by (ALLGOALS Asm_simp_tac); |
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by (step_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj] |
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addSEs partsEs) 1); |
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by (ALLGOALS (asm_full_simp_tac (!simpset addsimps [parts_insert_sees]))); |
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by (Fake_parts_insert_tac 1); |
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(*CertVerify, ClientFinished, ServerFinished (?)*) |
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by (REPEAT (Blast_tac 1)); |
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qed "Hash_imp_Nonce_seen"; |
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(*** Protocol goal: if B receives CERTIFICATE VERIFY, 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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Perhaps B~=Spy is unnecessary, but there's no obvious proof if the first |
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message is Fake. We don't need guarantees for the Spy anyway. We must |
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assume A~:lost; otherwise, the Spy can forge A's signature.*) |
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goalw thy [certificate_def] |
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"!!evs. [| X = Crypt (priK A) \ |
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\ (Hash{|Nonce NB, certificate B KB, Nonce M|}); \ |
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\ evs : tls; A ~: lost; B ~= Spy |] \ |
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\ ==> Says B A {|Nonce NA, Nonce NB, Agent XB, certificate B KB|} \ |
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\ : set evs --> \ |
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\ X : parts (sees lost Spy evs) --> Says A B X : set evs"; |
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by (hyp_subst_tac 1); |
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by (etac tls.induct 1); |
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by (ALLGOALS Asm_simp_tac); |
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by (Fake_parts_insert_tac 1); |
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(*ServerHello: nonce NB cannot be in X because it's fresh!*) |
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by (blast_tac (!claset addSDs [Hash_imp_Nonce1] |
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addSEs sees_Spy_partsEs) 1); |
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qed_spec_mp "TrustCertVerify"; |
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goal thy |
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"!!evs. [| evs : tls; A ~= Spy |] \ |
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\ ==> Says A B (Crypt (priK A) \ |
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\ (Hash{|Nonce NB, certificate B KB, Nonce M|})) : set evs \ |
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\ --> Says A B {|certificate A (pubK A), Crypt KB (Nonce M)|} : set evs"; |
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by (etac tls.induct 1); |
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by (ALLGOALS Asm_full_simp_tac); |
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bind_thm ("UseCertVerify", result() RSN (2, rev_mp)); |
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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 lost 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. evs : tls \ |
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\ ==> certificate B KB : parts (sees lost Spy evs) --> KB = pubK B"; |
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by (etac tls.induct 1); |
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by (ALLGOALS Asm_simp_tac); |
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by (Fake_parts_insert_tac 2); |
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by (Blast_tac 1); |
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bind_thm ("Server_cert_pubB", result() RSN (2, rev_mp)); |
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(*Replace key KB in ClientCertKeyEx by (pubK B) *) |
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val ClientCertKeyEx_tac = |
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forward_tac [Says_imp_sees_Spy' RS parts.Inj RS |
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parts.Snd RS parts.Snd RS parts.Snd RS Server_cert_pubB] |
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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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ClientCertKeyEx_tac (i+5) THEN |
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ALLGOALS (asm_simp_tac |
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(!simpset addsimps [not_parts_not_analz] |
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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 addsimps [insert_absorb] |
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setloop split_tac [expand_if])); |
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(*** Specialized rewriting for the analz_image_... theorems ***) |
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goal thy "insert (Key K) H = Key `` {K} Un H"; |
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|
305 |
by (Blast_tac 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
306 |
qed "insert_Key_singleton"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
307 |
|
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More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
308 |
goal thy "insert (Key K) (Key``KK Un C) = Key `` (insert K KK) Un C"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
309 |
by (Blast_tac 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
310 |
qed "insert_Key_image"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
311 |
|
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More realistic model: the Spy can compute clientK and serverK
paulson
parents:
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diff
changeset
|
312 |
(*Reverse the normal simplification of "image" to build up (not break down) |
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More realistic model: the Spy can compute clientK and serverK
paulson
parents:
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diff
changeset
|
313 |
the set of keys. Based on analz_image_freshK_ss, but simpler.*) |
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More realistic model: the Spy can compute clientK and serverK
paulson
parents:
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diff
changeset
|
314 |
val analz_image_keys_ss = |
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More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
315 |
!simpset delsimps [image_insert, image_Un] |
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More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
316 |
addsimps [image_insert RS sym, image_Un RS sym, |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
317 |
rangeI, |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
318 |
insert_Key_singleton, |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
319 |
insert_Key_image, Un_assoc RS sym] |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
320 |
setloop split_tac [expand_if]; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
321 |
|
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
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diff
changeset
|
322 |
(*No collection of keys can help the spy get new private keys*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
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diff
changeset
|
323 |
goal thy |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
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diff
changeset
|
324 |
"!!evs. evs : tls ==> \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
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diff
changeset
|
325 |
\ ALL KK. (Key(priK B) : analz (Key``KK Un (sees lost Spy evs))) = \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
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diff
changeset
|
326 |
\ (priK B : KK | B : lost)"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
327 |
by (etac tls.induct 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
328 |
by (ALLGOALS (asm_simp_tac analz_image_keys_ss)); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
329 |
(*Fake*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
330 |
by (spy_analz_tac 2); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
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diff
changeset
|
331 |
(*Base*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
332 |
by (Blast_tac 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
333 |
qed_spec_mp "analz_image_priK"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
334 |
|
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
335 |
|
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
336 |
(*Lemma for the trivial direction of the if-and-only-if*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
337 |
goal thy |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
338 |
"!!evs. (X : analz (G Un H)) --> (X : analz H) ==> \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
339 |
\ (X : analz (G Un H)) = (X : analz H)"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
340 |
by (blast_tac (!claset addIs [impOfSubs analz_mono]) 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
341 |
val lemma = result(); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
342 |
|
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
343 |
(*Knowing some clientKs and serverKs is no help in getting new nonces*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
344 |
goal thy |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
345 |
"!!evs. evs : tls ==> \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
346 |
\ ALL KK. KK <= (range clientK Un range serverK) --> \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
347 |
\ (Nonce N : analz (Key``KK Un (sees lost Spy evs))) = \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
348 |
\ (Nonce N : analz (sees lost Spy evs))"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
349 |
by (etac tls.induct 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
350 |
by (ClientCertKeyEx_tac 6); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
351 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
352 |
by (REPEAT_FIRST (rtac lemma )); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
353 |
(*SLOW: 30s!*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
354 |
by (ALLGOALS (asm_simp_tac analz_image_keys_ss)); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
355 |
by (ALLGOALS (asm_simp_tac |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
356 |
(!simpset addsimps [analz_image_priK, insert_absorb]))); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
357 |
(*ClientCertKeyEx: a nonce is sent, but one needs a priK to read it.*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
358 |
by (Blast_tac 3); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
359 |
(*Fake*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
360 |
by (spy_analz_tac 2); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
361 |
(*Base*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
362 |
by (Blast_tac 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
363 |
qed_spec_mp "analz_image_keys"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
364 |
|
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
365 |
|
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
366 |
(*If A sends ClientCertKeyEx to an uncompromised B, then M will stay secret. |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
367 |
The assumption is A~=Spy, not A~:lost, since A doesn't use her private key |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
368 |
here.*) |
3500 | 369 |
goalw thy [certificate_def] |
3506 | 370 |
"!!evs. [| evs : tls; A~=Spy; B ~: lost |] \ |
371 |
\ ==> Says A B {|certificate A (pubK A), Crypt KB (Nonce M)|} \ |
|
372 |
\ : set evs --> Nonce M ~: analz (sees lost Spy evs)"; |
|
3474 | 373 |
by (analz_induct_tac 1); |
374 |
(*ClientHello*) |
|
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
375 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 3); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
376 |
(*SpyKeys*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
377 |
by (asm_simp_tac (analz_image_keys_ss addsimps [analz_image_keys]) 2); |
3474 | 378 |
(*Fake*) |
379 |
by (spy_analz_tac 1); |
|
380 |
(*ServerHello and ClientCertKeyEx: mostly freshness reasoning*) |
|
381 |
by (REPEAT (blast_tac (!claset addSEs partsEs |
|
382 |
addDs [impOfSubs analz_subset_parts, |
|
383 |
Says_imp_sees_Spy' RS analz.Inj]) 1)); |
|
384 |
bind_thm ("Spy_not_see_premaster_secret", result() RSN (2, rev_mp)); |
|
385 |
||
386 |
||
387 |
(*** Protocol goal: serverK(NA,NB,M) and clientK(NA,NB,M) remain secure ***) |
|
388 |
||
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
389 |
(*The two proofs are identical*) |
3474 | 390 |
goal thy |
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
391 |
"!!evs. [| Nonce M ~: analz (sees lost Spy evs); \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
392 |
\ evs : tls |] \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
393 |
\ ==> Key (clientK(NA,NB,M)) ~: parts (sees lost Spy evs)"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
394 |
by (etac rev_mp 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
395 |
by (analz_induct_tac 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
396 |
(*SpyKeys*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
397 |
by (asm_simp_tac (analz_image_keys_ss addsimps [analz_image_keys]) 3); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
398 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS analz.Inj]) 3); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
399 |
(*Fake*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
400 |
by (spy_analz_tac 2); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
401 |
(*Base*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
402 |
by (Blast_tac 1); |
3474 | 403 |
qed "clientK_notin_parts"; |
404 |
||
405 |
goal thy |
|
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
406 |
"!!evs. [| Nonce M ~: analz (sees lost Spy evs); \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
407 |
\ evs : tls |] \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
408 |
\ ==> Key (serverK(NA,NB,M)) ~: parts (sees lost Spy evs)"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
409 |
by (etac rev_mp 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
410 |
by (analz_induct_tac 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
411 |
(*SpyKeys*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
412 |
by (asm_simp_tac (analz_image_keys_ss addsimps [analz_image_keys]) 3); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
413 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS analz.Inj]) 3); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
414 |
(*Fake*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
415 |
by (spy_analz_tac 2); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
416 |
(*Base*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
417 |
by (Blast_tac 1); |
3474 | 418 |
qed "serverK_notin_parts"; |
419 |
||
420 |
||
421 |
(*** Protocol goals: if A receives SERVER FINISHED, then B is present |
|
422 |
and has used the quoted values XA, XB, etc. Note that it is up to A |
|
423 |
to compare XA with what she originally sent. |
|
424 |
***) |
|
425 |
||
3500 | 426 |
goalw thy [certificate_def] |
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
427 |
"!!evs. [| X = Crypt (serverK(NA,NB,M)) \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
428 |
\ (Hash{|Hash{|Nonce NA, Nonce NB, Nonce M|}, \ |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
429 |
\ Nonce NA, Agent XA, Agent A, \ |
3506 | 430 |
\ Nonce NB, Agent XB, certificate B (pubK B)|}); \ |
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
431 |
\ evs : tls; A~=Spy; B ~: lost |] \ |
3506 | 432 |
\ ==> Says A B {|certificate A (pubK A), Crypt KB (Nonce M)|} \ |
433 |
\ : set evs --> \ |
|
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
434 |
\ X : parts (sees lost Spy evs) --> Says B A X : set evs"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
435 |
by (hyp_subst_tac 1); |
3474 | 436 |
by (etac tls.induct 1); |
437 |
by (ALLGOALS Asm_simp_tac); |
|
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
438 |
(*ClientCertKeyEx: M isn't in the Hash because it's fresh!*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
439 |
by (blast_tac (!claset addSDs [Hash_Hash_imp_Nonce] |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
440 |
addSEs sees_Spy_partsEs) 2); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
441 |
(*Fake: the Spy doesn't have the critical session key!*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
442 |
by (REPEAT (rtac impI 1)); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
443 |
by (subgoal_tac "Key (serverK(NA,NB,M)) ~: analz (sees lost Spy evsa)" 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
444 |
by (asm_simp_tac (!simpset addsimps [Spy_not_see_premaster_secret, |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
445 |
serverK_notin_parts, |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
446 |
not_parts_not_analz]) 2); |
3474 | 447 |
by (Fake_parts_insert_tac 1); |
448 |
qed_spec_mp "TrustServerFinished"; |
|
449 |
||
450 |
||
3500 | 451 |
(*** Protocol goal: if B receives CLIENT FINISHED, then A has used the |
452 |
quoted values XA, XB, etc., which B can then check. BUT NOTE: |
|
3506 | 453 |
B has no way of knowing that A is the sender of CLIENT CERTIFICATE! |
454 |
***) |
|
3500 | 455 |
goalw thy [certificate_def] |
3474 | 456 |
"!!evs. [| X = Crypt (clientK(NA,NB,M)) \ |
457 |
\ (Hash{|Hash{|Nonce NA, Nonce NB, Nonce M|}, \ |
|
458 |
\ Nonce NA, Agent XA, \ |
|
3500 | 459 |
\ certificate A (pubK A), \ |
3474 | 460 |
\ Nonce NB, Agent XB, Agent B|}); \ |
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
461 |
\ evs : tls; A~=Spy; B ~: lost |] \ |
3500 | 462 |
\ ==> Says A B {|certificate A (pubK A), \ |
3506 | 463 |
\ Crypt KB (Nonce M)|} : set evs --> \ |
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
464 |
\ X : parts (sees lost Spy evs) --> Says A B X : set evs"; |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
465 |
by (hyp_subst_tac 1); |
3474 | 466 |
by (etac tls.induct 1); |
467 |
by (ALLGOALS Asm_simp_tac); |
|
3480
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
468 |
(*ClientCertKeyEx: M isn't in the Hash because it's fresh!*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
469 |
by (blast_tac (!claset addSDs [Hash_Hash_imp_Nonce] |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
470 |
addSEs sees_Spy_partsEs) 2); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
471 |
(*Fake: the Spy doesn't have the critical session key!*) |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
472 |
by (REPEAT (rtac impI 1)); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
473 |
by (subgoal_tac "Key (clientK(NA,NB,M)) ~: analz (sees lost Spy evsa)" 1); |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
474 |
by (asm_simp_tac (!simpset addsimps [Spy_not_see_premaster_secret, |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
475 |
clientK_notin_parts, |
d59bbf053258
More realistic model: the Spy can compute clientK and serverK
paulson
parents:
3474
diff
changeset
|
476 |
not_parts_not_analz]) 2); |
3474 | 477 |
by (Fake_parts_insert_tac 1); |
478 |
qed_spec_mp "TrustClientFinished"; |
|
3506 | 479 |
|
480 |
||
481 |
(*** Protocol goal: if B receives CLIENT FINISHED, and if B is able to |
|
482 |
check a CERTIFICATE VERIFY from A, then A has used the quoted |
|
483 |
values XA, XB, etc. Even this one requires A to be uncompromised. |
|
484 |
***) |
|
485 |
goal thy |
|
486 |
"!!evs. [| X = Crypt (clientK(NA,NB,M)) \ |
|
487 |
\ (Hash{|Hash{|Nonce NA, Nonce NB, Nonce M|}, \ |
|
488 |
\ Nonce NA, Agent XA, \ |
|
489 |
\ certificate A (pubK A), \ |
|
490 |
\ Nonce NB, Agent XB, Agent B|}); \ |
|
491 |
\ Says A' B X : set evs; \ |
|
492 |
\ Says B A {|Nonce NA, Nonce NB, Agent XB, certificate B KB|} \ |
|
493 |
\ : set evs; \ |
|
494 |
\ Says A'' B (Crypt (priK A) \ |
|
495 |
\ (Hash{|Nonce NB, certificate B KB, Nonce M|})) \ |
|
496 |
\ : set evs; \ |
|
497 |
\ evs : tls; A ~: lost; B ~: lost |] \ |
|
498 |
\ ==> Says A B X : set evs"; |
|
499 |
br TrustClientFinished 1; |
|
500 |
br (TrustCertVerify RS UseCertVerify) 5; |
|
501 |
by (REPEAT_FIRST (ares_tac [refl])); |
|
502 |
by (ALLGOALS |
|
503 |
(asm_full_simp_tac (!simpset addsimps [Says_imp_sees_Spy RS parts.Inj]))); |
|
504 |
qed_spec_mp "AuthClientFinished"; |