Now uses the Notes constructor to distinguish the Client (who has chosen M)
from the Spy (who may have replayed her messages)
(* Title: HOL/Auth/TLS
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1997 University of Cambridge
Protocol goals:
* M, serverK(NA,NB,M) and clientK(NA,NB,M) will be known only to the two
parties (though A is not necessarily authenticated).
* B upon receiving CERTIFICATE VERIFY knows that A is present (But this
message is optional!)
* A upon receiving SERVER FINISHED knows that B is present
* Each party who has received a FINISHED message can trust that the other
party agrees on all message components, including XA and XB (thus foiling
rollback attacks).
*)
open TLS;
proof_timing:=true;
HOL_quantifiers := false;
AddIffs [Spy_in_lost, Server_not_lost];
Addsimps [certificate_def];
goal thy "!!A. A ~: lost ==> A ~= Spy";
by (Blast_tac 1);
qed "not_lost_not_eq_Spy";
Addsimps [not_lost_not_eq_Spy];
(*Injectiveness of key-generating functions*)
AddIffs [inj_clientK RS inj_eq, inj_serverK RS inj_eq];
(* invKey(clientK x) = clientK x and similarly for serverK*)
Addsimps [isSym_clientK, rewrite_rule [isSymKey_def] isSym_clientK,
isSym_serverK, rewrite_rule [isSymKey_def] isSym_serverK];
(*Replacing the variable by a constant improves search speed by 50%!*)
val Says_imp_sees_Spy' =
read_instantiate_sg (sign_of thy) [("lost","lost")] Says_imp_sees_Spy;
(*** clientK and serverK make symmetric keys; no clashes with pubK or priK ***)
goal thy "pubK A ~= clientK arg";
br notI 1;
by (dres_inst_tac [("f","isSymKey")] arg_cong 1);
by (Full_simp_tac 1);
qed "pubK_neq_clientK";
goal thy "pubK A ~= serverK arg";
br notI 1;
by (dres_inst_tac [("f","isSymKey")] arg_cong 1);
by (Full_simp_tac 1);
qed "pubK_neq_serverK";
goal thy "priK A ~= clientK arg";
br notI 1;
by (dres_inst_tac [("f","isSymKey")] arg_cong 1);
by (Full_simp_tac 1);
qed "priK_neq_clientK";
goal thy "priK A ~= serverK arg";
br notI 1;
by (dres_inst_tac [("f","isSymKey")] arg_cong 1);
by (Full_simp_tac 1);
qed "priK_neq_serverK";
(*clientK and serverK have disjoint ranges*)
goal thy "clientK arg ~= serverK arg'";
by (cut_facts_tac [rangeI RS impOfSubs clientK_range] 1);
by (Blast_tac 1);
qed "clientK_neq_serverK";
val keys_distinct = [pubK_neq_clientK, pubK_neq_serverK,
priK_neq_clientK, priK_neq_serverK, clientK_neq_serverK];
AddIffs (keys_distinct @ (keys_distinct RL [not_sym]));
(**** Protocol Proofs ****)
(*A "possibility property": there are traces that reach the end.
This protocol has three end points and six messages to consider.*)
(*Possibility property ending with ServerFinished.*)
goal thy
"!!A B. A ~= B ==> EX NA XA NB XB M. EX evs: tls. \
\ Says B A (Crypt (serverK(NA,NB,M)) \
\ (Hash{|Hash{|Nonce NA, Nonce NB, Nonce M|}, \
\ Nonce NA, Agent XA, Agent A, \
\ Nonce NB, Agent XB, \
\ certificate B (pubK B)|})) \
\ : set evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
by (rtac (tls.Nil RS tls.ClientHello RS tls.ServerHello RS tls.ClientCertKeyEx
RS tls.ServerFinished) 2);
by possibility_tac;
result();
(*And one for ClientFinished. Either FINISHED message may come first.*)
goal thy
"!!A B. A ~= B ==> EX NA XA NB XB M. EX evs: tls. \
\ Says A B (Crypt (clientK(NA,NB,M)) \
\ (Hash{|Hash{|Nonce NA, Nonce NB, Nonce M|}, \
\ Nonce NA, Agent XA, \
\ certificate A (pubK A), \
\ Nonce NB, Agent XB, Agent B|})) : set evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
by (rtac (tls.Nil RS tls.ClientHello RS tls.ServerHello RS tls.ClientCertKeyEx
RS tls.ClientFinished) 2);
by possibility_tac;
result();
(*Another one, for CertVerify (which is optional)*)
goal thy
"!!A B. A ~= B ==> EX NB M. EX evs: tls. \
\ Says A B (Crypt (priK A) \
\ (Hash{|Nonce NB, certificate B (pubK B), Nonce M|})) : set evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
by (rtac (tls.Nil RS tls.ClientHello RS tls.ServerHello RS tls.ClientCertKeyEx
RS tls.CertVerify) 2);
by possibility_tac;
result();
(**** Inductive proofs about tls ****)
(*Nobody sends themselves messages*)
goal thy "!!evs. evs : tls ==> ALL A X. Says A A X ~: set evs";
by (etac tls.induct 1);
by (Auto_tac());
qed_spec_mp "not_Says_to_self";
Addsimps [not_Says_to_self];
AddSEs [not_Says_to_self RSN (2, rev_notE)];
(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY
sends messages containing X! **)
(*Spy never sees another agent's private key! (unless it's lost at start)*)
goal thy
"!!evs. evs : tls \
\ ==> (Key (priK A) : parts (sees lost Spy evs)) = (A : lost)";
by (etac tls.induct 1);
by (prove_simple_subgoals_tac 1);
by (asm_simp_tac (!simpset setloop split_tac [expand_if]) 2);
by (Fake_parts_insert_tac 1);
qed "Spy_see_priK";
Addsimps [Spy_see_priK];
goal thy
"!!evs. evs : tls \
\ ==> (Key (priK A) : analz (sees lost Spy evs)) = (A : lost)";
by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset));
qed "Spy_analz_priK";
Addsimps [Spy_analz_priK];
goal thy "!!A. [| Key (priK A) : parts (sees lost Spy evs); \
\ evs : tls |] ==> A:lost";
by (blast_tac (!claset addDs [Spy_see_priK]) 1);
qed "Spy_see_priK_D";
bind_thm ("Spy_analz_priK_D", analz_subset_parts RS subsetD RS Spy_see_priK_D);
AddSDs [Spy_see_priK_D, Spy_analz_priK_D];
(*This lemma says that no false certificates exist. One might extend the
model to include bogus certificates for the lost agents, but there seems
little point in doing so: the loss of their private keys is a worse
breach of security.*)
goalw thy [certificate_def]
"!!evs. evs : tls \
\ ==> certificate B KB : parts (sees lost Spy evs) --> KB = pubK B";
by (etac tls.induct 1);
by (ALLGOALS (asm_full_simp_tac (!simpset setloop split_tac [expand_if])));
by (Fake_parts_insert_tac 2);
by (Blast_tac 1);
bind_thm ("Server_cert_pubB", result() RSN (2, rev_mp));
(*Replace key KB in ClientCertKeyEx by (pubK B) *)
val ClientCertKeyEx_tac =
forward_tac [Says_imp_sees_Spy' RS parts.Inj RS
parts.Snd RS parts.Snd RS parts.Snd RS Server_cert_pubB]
THEN' assume_tac
THEN' hyp_subst_tac;
fun analz_induct_tac i =
etac tls.induct i THEN
ClientCertKeyEx_tac (i+7) THEN (*ClientFinished*)
ClientCertKeyEx_tac (i+6) THEN (*CertVerify*)
ClientCertKeyEx_tac (i+5) THEN (*ClientCertKeyEx*)
rewrite_goals_tac [certificate_def] THEN
ALLGOALS (asm_simp_tac
(!simpset addsimps [not_parts_not_analz]
setloop split_tac [expand_if])) THEN
(*Remove instances of pubK B: the Spy already knows all public keys.
Combining the two simplifier calls makes them run extremely slowly.*)
ALLGOALS (asm_simp_tac
(!simpset addsimps [insert_absorb]
setloop split_tac [expand_if]));
(*** Hashing of nonces ***)
(*Every Nonce that's hashed is already in past traffic. *)
goal thy "!!evs. [| Hash {|Nonce N, X|} : parts (sees lost Spy evs); \
\ evs : tls |] \
\ ==> Nonce N : parts (sees lost Spy evs)";
by (etac rev_mp 1);
by (etac tls.induct 1);
by (ALLGOALS (asm_simp_tac (!simpset addsimps [parts_insert_sees]
setloop split_tac [expand_if])));
by (Fake_parts_insert_tac 2);
by (REPEAT (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj]
addSEs partsEs) 1));
qed "Hash_imp_Nonce1";
(*Lemma needed to prove Hash_Hash_imp_Nonce*)
goal thy "!!evs. [| Hash{|Nonce NA, Nonce NB, Nonce M|} \
\ : parts (sees lost Spy evs); \
\ evs : tls |] \
\ ==> Nonce M : parts (sees lost Spy evs)";
by (etac rev_mp 1);
by (etac tls.induct 1);
by (ALLGOALS (asm_simp_tac (!simpset addsimps [parts_insert_sees]
setloop split_tac [expand_if])));
by (Fake_parts_insert_tac 2);
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj]
addSEs partsEs) 1);
qed "Hash_imp_Nonce2";
AddSDs [Hash_imp_Nonce2];
goal thy "!!evs. [| Notes A {|Agent B, X|} : set evs; evs : tls |] \
\ ==> Crypt (pubK B) X : parts (sees lost Spy evs)";
by (etac rev_mp 1);
by (analz_induct_tac 1);
by (blast_tac (!claset addIs [parts_insertI]) 1);
qed "Notes_Crypt_parts_sees";
(*NEEDED??*)
goal thy "!!evs. [| Hash {| Hash{|Nonce NA, Nonce NB, Nonce M|}, X |} \
\ : parts (sees lost Spy evs); \
\ evs : tls |] \
\ ==> Nonce M : parts (sees lost Spy evs)";
by (etac rev_mp 1);
by (etac tls.induct 1);
by (ALLGOALS (asm_simp_tac (!simpset addsimps [parts_insert_sees]
setloop split_tac [expand_if])));
by (Fake_parts_insert_tac 2);
by (step_tac (!claset addSDs [Notes_Crypt_parts_sees,
Says_imp_sees_Spy' RS parts.Inj]
addSEs partsEs) 1);
qed "Hash_Hash_imp_Nonce";
(*NEEDED??
Every Nonce that's hashed is already in past traffic.
This general formulation is tricky to prove and hard to use, since the
2nd premise is typically proved by simplification.*)
goal thy "!!evs. [| Hash X : parts (sees lost Spy evs); \
\ Nonce N : parts {X}; evs : tls |] \
\ ==> Nonce N : parts (sees lost Spy evs)";
by (etac rev_mp 1);
by (etac tls.induct 1);
by (ALLGOALS (asm_simp_tac (!simpset setloop split_tac [expand_if])));
by (step_tac (!claset addSDs [Notes_Crypt_parts_sees,
Says_imp_sees_Spy' RS parts.Inj]
addSEs partsEs) 1);
by (ALLGOALS (asm_full_simp_tac (!simpset addsimps [parts_insert_sees])));
by (Fake_parts_insert_tac 1);
(*CertVerify, ClientFinished, ServerFinished (?)*)
by (REPEAT (Blast_tac 1));
qed "Hash_imp_Nonce_seen";
(*** Protocol goal: if B receives CERTIFICATE VERIFY, then A sent it ***)
(*B can check A's signature if he has received A's certificate.
Perhaps B~=Spy is unnecessary, but there's no obvious proof if the first
message is Fake. We don't need guarantees for the Spy anyway. We must
assume A~:lost; otherwise, the Spy can forge A's signature.*)
goalw thy [certificate_def]
"!!evs. [| X = Crypt (priK A) \
\ (Hash{|Nonce NB, certificate B KB, Nonce M|}); \
\ evs : tls; A ~: lost; B ~= Spy |] \
\ ==> Says B A {|Nonce NA, Nonce NB, Agent XB, certificate B KB|} \
\ : set evs --> \
\ X : parts (sees lost Spy evs) --> Says A B X : set evs";
by (hyp_subst_tac 1);
by (etac tls.induct 1);
by (ALLGOALS (asm_simp_tac (!simpset setloop split_tac [expand_if])));
by (Fake_parts_insert_tac 1);
(*ServerHello: nonce NB cannot be in X because it's fresh!*)
by (blast_tac (!claset addSDs [Hash_imp_Nonce1]
addSEs sees_Spy_partsEs) 1);
qed_spec_mp "TrustCertVerify";
(*If CERTIFICATE VERIFY is present then A has chosen M.*)
goal thy
"!!evs. [| Crypt (priK A) (Hash{|Nonce NB, certificate B KB, Nonce M|}) \
\ : parts (sees lost Spy evs); \
\ evs : tls; A ~: lost |] \
\ ==> Notes A {|Agent B, Nonce M|} : set evs";
be rev_mp 1;
by (etac tls.induct 1);
by (ALLGOALS (asm_full_simp_tac (!simpset setloop split_tac [expand_if])));
by (Fake_parts_insert_tac 2);
by (Blast_tac 1);
qed "UseCertVerify";
(*No collection of keys can help the spy get new private keys*)
goal thy
"!!evs. evs : tls ==> \
\ ALL KK. (Key(priK B) : analz (Key``KK Un (sees lost Spy evs))) = \
\ (priK B : KK | B : lost)";
by (etac tls.induct 1);
by (ALLGOALS
(asm_simp_tac (analz_image_keys_ss
addsimps (certificate_def::keys_distinct))));
(*Fake*)
by (spy_analz_tac 2);
(*Base*)
by (Blast_tac 1);
qed_spec_mp "analz_image_priK";
(*Lemma for the trivial direction of the if-and-only-if*)
goal thy
"!!evs. (X : analz (G Un H)) --> (X : analz H) ==> \
\ (X : analz (G Un H)) = (X : analz H)";
by (blast_tac (!claset addIs [impOfSubs analz_mono]) 1);
val lemma = result();
(*Knowing some clientKs and serverKs is no help in getting new nonces*)
goal thy
"!!evs. evs : tls ==> \
\ ALL KK. KK <= (range clientK Un range serverK) --> \
\ (Nonce N : analz (Key``KK Un (sees lost Spy evs))) = \
\ (Nonce N : analz (sees lost Spy evs))";
by (etac tls.induct 1);
by (ClientCertKeyEx_tac 6);
by (REPEAT_FIRST (resolve_tac [allI, impI]));
by (REPEAT_FIRST (rtac lemma));
writeln"SLOW simplification: 50 secs!??";
by (ALLGOALS
(asm_simp_tac (analz_image_keys_ss
addsimps (analz_image_priK::certificate_def::
keys_distinct))));
by (ALLGOALS (asm_simp_tac (analz_image_keys_ss addsimps [analz_image_priK])));
by (ALLGOALS (asm_simp_tac (!simpset addsimps [insert_absorb])));
(*ClientCertKeyEx: a nonce is sent, but one needs a priK to read it.*)
by (Blast_tac 3);
(*Fake*)
by (spy_analz_tac 2);
(*Base*)
by (Blast_tac 1);
qed_spec_mp "analz_image_keys";
(*If A sends ClientCertKeyEx to an uncompromised B, then M will stay secret.*)
goal thy
"!!evs. [| evs : tls; A ~: lost; B ~: lost |] \
\ ==> Notes A {|Agent B, Nonce M|} : set evs --> \
\ Nonce M ~: analz (sees lost Spy evs)";
by (analz_induct_tac 1);
(*ClientHello*)
by (blast_tac (!claset addSDs [Notes_Crypt_parts_sees]
addSEs sees_Spy_partsEs) 3);
(*SpyKeys*)
by (asm_simp_tac (analz_image_keys_ss addsimps [analz_image_keys]) 2);
(*Fake*)
by (spy_analz_tac 1);
(*ServerHello and ClientCertKeyEx: mostly freshness reasoning*)
by (REPEAT (blast_tac (!claset addSEs partsEs
addDs [Notes_Crypt_parts_sees,
impOfSubs analz_subset_parts,
Says_imp_sees_Spy' RS analz.Inj]) 1));
bind_thm ("Spy_not_see_premaster_secret", result() RSN (2, rev_mp));
(*** Protocol goal: serverK(NA,NB,M) and clientK(NA,NB,M) remain secure ***)
(** First, some lemmas about those write keys. The proofs for serverK are
nearly identical to those for clientK. **)
(*Lemma: those write keys are never sent if M is secure.
Converse doesn't hold; betraying M doesn't force the keys to be sent!*)
goal thy
"!!evs. [| Nonce M ~: analz (sees lost Spy evs); evs : tls |] \
\ ==> Key (clientK(NA,NB,M)) ~: parts (sees lost Spy evs)";
by (etac rev_mp 1);
by (analz_induct_tac 1);
(*SpyKeys*)
by (asm_simp_tac (analz_image_keys_ss addsimps [analz_image_keys]) 3);
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS analz.Inj]) 3);
(*Fake*)
by (spy_analz_tac 2);
(*Base*)
by (Blast_tac 1);
qed "clientK_notin_parts";
Addsimps [clientK_notin_parts];
AddSEs [clientK_notin_parts RSN (2, rev_notE)];
goal thy
"!!evs. [| Nonce M ~: analz (sees lost Spy evs); evs : tls |] \
\ ==> Key (serverK(NA,NB,M)) ~: parts (sees lost Spy evs)";
by (etac rev_mp 1);
by (analz_induct_tac 1);
(*SpyKeys*)
by (asm_simp_tac (analz_image_keys_ss addsimps [analz_image_keys]) 3);
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS analz.Inj]) 3);
(*Fake*)
by (spy_analz_tac 2);
(*Base*)
by (Blast_tac 1);
qed "serverK_notin_parts";
Addsimps [serverK_notin_parts];
AddSEs [serverK_notin_parts RSN (2, rev_notE)];
(*Lemma: those write keys are never used if M is fresh.
Converse doesn't hold; betraying M doesn't force the keys to be sent!
NOT suitable as safe elim rules.*)
goal thy
"!!evs. [| Nonce M ~: used evs; evs : tls |] \
\ ==> Crypt (clientK(NA,NB,M)) Y ~: parts (sees lost Spy evs)";
by (etac rev_mp 1);
by (analz_induct_tac 1);
(*ClientFinished: since M is fresh, a different instance of clientK was used.*)
by (blast_tac (!claset addSDs [Notes_Crypt_parts_sees]
addSEs sees_Spy_partsEs) 3);
by (Fake_parts_insert_tac 2);
(*Base*)
by (Blast_tac 1);
qed "Crypt_clientK_notin_parts";
Addsimps [Crypt_clientK_notin_parts];
AddEs [Crypt_clientK_notin_parts RSN (2, rev_notE)];
goal thy
"!!evs. [| Nonce M ~: used evs; evs : tls |] \
\ ==> Crypt (serverK(NA,NB,M)) Y ~: parts (sees lost Spy evs)";
by (etac rev_mp 1);
by (analz_induct_tac 1);
(*ServerFinished: since M is fresh, a different instance of serverK was used.*)
by (blast_tac (!claset addSDs [Notes_Crypt_parts_sees]
addSEs sees_Spy_partsEs) 3);
by (Fake_parts_insert_tac 2);
(*Base*)
by (Blast_tac 1);
qed "Crypt_serverK_notin_parts";
Addsimps [Crypt_serverK_notin_parts];
AddEs [Crypt_serverK_notin_parts RSN (2, rev_notE)];
(*Weakening A~:lost to A~=Spy would complicate later uses of the rule*)
goal thy
"!!evs. [| Says A B {|certA, Crypt KB (Nonce M)|} : set evs; \
\ A ~: lost; evs : tls |] ==> KB = pubK B";
be rev_mp 1;
by (analz_induct_tac 1);
qed "A_Crypt_pubB";
(*** Unicity results for M, the pre-master-secret ***)
(*Induction for theorems of the form X ~: analz (sees lost Spy evs) --> ...
It simplifies the proof by discarding needless information about
analz (insert X (sees lost Spy evs))
*)
fun analz_mono_parts_induct_tac i =
etac tls.induct i THEN
ClientCertKeyEx_tac (i+5) THEN (*ClientCertKeyEx*)
REPEAT_FIRST analz_mono_contra_tac;
(*M determines B. Proof borrowed from NS_Public/unique_NA and from Yahalom*)
goal thy
"!!evs. [| Nonce M ~: analz (sees lost Spy evs); evs : tls |] \
\ ==> EX B'. ALL B. \
\ Crypt (pubK B) (Nonce M) : parts (sees lost Spy evs) --> B=B'";
by (etac rev_mp 1);
by (analz_mono_parts_induct_tac 1);
by (prove_simple_subgoals_tac 1);
by (asm_simp_tac (!simpset addsimps [all_conj_distrib]
setloop split_tac [expand_if]) 2);
(*ClientCertKeyEx*)
by (expand_case_tac "M = ?y" 2 THEN
REPEAT (blast_tac (!claset addSEs partsEs) 2));
by (Fake_parts_insert_tac 1);
val lemma = result();
goal thy
"!!evs. [| Crypt(pubK B) (Nonce M) : parts (sees lost Spy evs); \
\ Crypt(pubK B') (Nonce M) : parts (sees lost Spy evs); \
\ Nonce M ~: analz (sees lost Spy evs); \
\ evs : tls |] \
\ ==> B=B'";
by (prove_unique_tac lemma 1);
qed "unique_M";
(*In A's note to herself, M determines A and B.*)
goal thy
"!!evs. [| Nonce M ~: analz (sees lost Spy evs); evs : tls |] \
\ ==> EX A' B'. ALL A B. \
\ Notes A {|Agent B, Nonce M|} : set evs --> A=A' & B=B'";
by (etac rev_mp 1);
by (analz_mono_parts_induct_tac 1);
by (prove_simple_subgoals_tac 1);
by (asm_simp_tac (!simpset addsimps [all_conj_distrib]) 1);
(*ClientCertKeyEx: if M is fresh, then it can't appear in Notes A X.*)
by (expand_case_tac "M = ?y" 1 THEN
blast_tac (!claset addSDs [Notes_Crypt_parts_sees] addSEs partsEs) 1);
val lemma = result();
goal thy
"!!evs. [| Notes A {|Agent B, Nonce M|} : set evs; \
\ Notes A' {|Agent B', Nonce M|} : set evs; \
\ Nonce M ~: analz (sees lost Spy evs); \
\ evs : tls |] \
\ ==> A=A' & B=B'";
by (prove_unique_tac lemma 1);
qed "Notes_unique_M";
(*** Protocol goals: if A receives SERVER FINISHED, then B is present
and has used the quoted values XA, XB, etc. Note that it is up to A
to compare XA with what she originally sent.
***)
(*The mention of her name (A) in X assumes A that B knows who she is.*)
goal thy
"!!evs. [| X = Crypt (serverK(NA,NB,M)) \
\ (Hash{|Hash{|Nonce NA, Nonce NB, Nonce M|}, \
\ Nonce NA, Agent XA, Agent A, \
\ Nonce NB, Agent XB, certificate B (pubK B)|}); \
\ evs : tls; A ~: lost; B ~: lost |] \
\ ==> Notes A {|Agent B, Nonce M|} : set evs --> \
\ X : parts (sees lost Spy evs) --> Says B A X : set evs";
by (hyp_subst_tac 1);
by (analz_induct_tac 1);
by (REPEAT_FIRST (rtac impI));
(*Fake: the Spy doesn't have the critical session key!*)
by (REPEAT (rtac impI 1));
by (subgoal_tac "Key (serverK(NA,NB,M)) ~: analz (sees lost Spy evsa)" 1);
by (asm_simp_tac (!simpset addsimps [Spy_not_see_premaster_secret,
not_parts_not_analz]) 2);
by (Fake_parts_insert_tac 1);
qed_spec_mp "TrustServerFinished";
(*This version refers not to SERVER FINISHED but to any message from B.
We don't assume B has received CERTIFICATE VERIFY, and an intruder could
have changed A's identity in all other messages, so we can't be sure
that B sends his message to A.*)
goal thy
"!!evs. [| evs : tls; A ~: lost; B ~: lost |] \
\ ==> Notes A {|Agent B, Nonce M|} : set evs --> \
\ Crypt (serverK(NA,NB,M)) Y : parts (sees lost Spy evs) --> \
\ (EX A'. Says B A' (Crypt (serverK(NA,NB,M)) Y) : set evs)";
by (analz_induct_tac 1);
by (REPEAT_FIRST (rtac impI));
(*Fake: the Spy doesn't have the critical session key!*)
by (subgoal_tac "Key (serverK(NA,NB,M)) ~: analz (sees lost Spy evsa)" 1);
by (asm_simp_tac (!simpset addsimps [Spy_not_see_premaster_secret,
not_parts_not_analz]) 2);
by (Fake_parts_insert_tac 1);
(*ServerFinished. If the message is old then apply induction hypothesis...*)
by (rtac conjI 1 THEN Blast_tac 2);
(*...otherwise delete induction hyp and use unicity of M.*)
by (thin_tac "?PP-->?QQ" 1);
by (Step_tac 1);
by (subgoal_tac "Nonce M ~: analz (sees lost Spy evsa)" 1);
by (asm_simp_tac (!simpset addsimps [Spy_not_see_premaster_secret]) 2);
by (blast_tac (!claset addSEs [MPair_parts]
addDs [Notes_Crypt_parts_sees,
Says_imp_sees_Spy' RS parts.Inj,
unique_M]) 1);
qed_spec_mp "TrustServerMsg";
(*** Protocol goal: if B receives any message encrypted with clientK
then A has sent it, ASSUMING that A chose M. Authentication is
assumed here; B cannot verify it. But if the message is
CLIENT FINISHED, then B can then check the quoted values XA, XB, etc.
***)
goal thy
"!!evs. [| evs : tls; A ~: lost; B ~: lost |] \
\ ==> Notes A {|Agent B, Nonce M|} : set evs --> \
\ Crypt (clientK(NA,NB,M)) Y : parts (sees lost Spy evs) --> \
\ Says A B (Crypt (clientK(NA,NB,M)) Y) : set evs";
by (analz_induct_tac 1);
by (REPEAT_FIRST (rtac impI));
(*Fake: the Spy doesn't have the critical session key!*)
by (subgoal_tac "Key (clientK(NA,NB,M)) ~: analz (sees lost Spy evsa)" 1);
by (asm_simp_tac (!simpset addsimps [Spy_not_see_premaster_secret,
not_parts_not_analz]) 2);
by (Fake_parts_insert_tac 1);
(*ClientFinished. If the message is old then apply induction hypothesis...*)
by (step_tac (!claset delrules [conjI]) 1);
by (subgoal_tac "Nonce M ~: analz (sees lost Spy evsa)" 1);
by (asm_simp_tac (!simpset addsimps [Spy_not_see_premaster_secret]) 2);
by (blast_tac (!claset addSEs [MPair_parts]
addDs [Notes_unique_M]) 1);
qed_spec_mp "TrustClientMsg";
(*** Protocol goal: if B receives CLIENT FINISHED, and if B is able to
check a CERTIFICATE VERIFY from A, then A has used the quoted
values XA, XB, etc. Even this one requires A to be uncompromised.
***)
goal thy
"!!evs. [| Says A' B (Crypt (clientK(NA,NB,M)) Y) : set evs; \
\ Says B A {|Nonce NA, Nonce NB, Agent XB, certificate B KB|} \
\ : set evs; \
\ Says A'' B (Crypt (priK A) \
\ (Hash{|Nonce NB, certificate B KB, Nonce M|})) \
\ : set evs; \
\ evs : tls; A ~: lost; B ~: lost |] \
\ ==> Says A B (Crypt (clientK(NA,NB,M)) Y) : set evs";
by (blast_tac (!claset addSIs [TrustClientMsg, UseCertVerify]
addDs [Says_imp_sees_Spy RS parts.Inj]) 1);
qed "AuthClientFinished";