author | wenzelm |
Tue, 07 Sep 1999 10:40:58 +0200 | |
changeset 7499 | 23e090051cb8 |
parent 7494 | 45905028bb1d |
child 8741 | 61bc5ed22b62 |
permissions | -rw-r--r-- |
6452 | 1 |
(* Title: HOL/Auth/KerberosIV |
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ID: $Id$ |
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Author: Giampaolo Bella, Cambridge University Computer Laboratory |
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Copyright 1998 University of Cambridge |
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The Kerberos protocol, version IV. |
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*) |
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Pretty.setdepth 20; |
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proof_timing:=true; |
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AddIffs [AuthLife_LB, ServLife_LB, AutcLife_LB, RespLife_LB, Tgs_not_bad]; |
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(** Reversed traces **) |
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Goal "spies (evs @ [Says A B X]) = insert X (spies evs)"; |
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by (induct_tac "evs" 1); |
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by (induct_tac "a" 2); |
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by Auto_tac; |
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qed "spies_Says_rev"; |
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Goal "spies (evs @ [Gets A X]) = spies evs"; |
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by (induct_tac "evs" 1); |
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by (induct_tac "a" 2); |
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by Auto_tac; |
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qed "spies_Gets_rev"; |
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Goal "spies (evs @ [Notes A X]) = \ |
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\ (if A:bad then insert X (spies evs) else spies evs)"; |
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by (induct_tac "evs" 1); |
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by (induct_tac "a" 2); |
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by Auto_tac; |
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qed "spies_Notes_rev"; |
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Goal "spies evs = spies (rev evs)"; |
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by (induct_tac "evs" 1); |
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by (induct_tac "a" 2); |
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by (ALLGOALS |
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(asm_simp_tac (simpset() addsimps [spies_Says_rev, spies_Gets_rev, |
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spies_Notes_rev]))); |
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qed "spies_evs_rev"; |
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bind_thm ("parts_spies_evs_revD2", spies_evs_rev RS equalityD2 RS parts_mono); |
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Goal "spies (takeWhile P evs) <= spies evs"; |
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by (induct_tac "evs" 1); |
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by (induct_tac "a" 2); |
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by Auto_tac; |
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(* Resembles "used_subset_append" in Event.ML*) |
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qed "spies_takeWhile"; |
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bind_thm ("parts_spies_takeWhile_mono", spies_takeWhile RS parts_mono); |
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Goal "~P(x) --> takeWhile P (xs @ [x]) = takeWhile P xs"; |
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by (induct_tac "xs" 1); |
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by Auto_tac; |
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qed "takeWhile_tail"; |
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(*****************LEMMAS ABOUT AuthKeys****************) |
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Goalw [AuthKeys_def] "AuthKeys [] = {}"; |
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by (Simp_tac 1); |
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qed "AuthKeys_empty"; |
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||
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Goalw [AuthKeys_def] |
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"(ALL A Tk akey Peer. \ |
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\ ev ~= Says Kas A (Crypt (shrK A) {|akey, Agent Peer, Tk, \ |
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\ (Crypt (shrK Peer) {|Agent A, Agent Peer, akey, Tk|})|}))\ |
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\ ==> AuthKeys (ev # evs) = AuthKeys evs"; |
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by Auto_tac; |
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qed "AuthKeys_not_insert"; |
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Goalw [AuthKeys_def] |
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"AuthKeys \ |
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\ (Says Kas A (Crypt (shrK A) {|Key K, Agent Peer, Number Tk, \ |
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\ (Crypt (shrK Peer) {|Agent A, Agent Peer, Key K, Number Tk|})|}) # evs) \ |
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\ = insert K (AuthKeys evs)"; |
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by Auto_tac; |
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qed "AuthKeys_insert"; |
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Goalw [AuthKeys_def] |
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"K : AuthKeys \ |
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\ (Says Kas A (Crypt (shrK A) {|Key K', Agent Peer, Number Tk, \ |
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\ (Crypt (shrK Peer) {|Agent A, Agent Peer, Key K', Number Tk|})|}) # evs) \ |
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\ ==> K = K' | K : AuthKeys evs"; |
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by Auto_tac; |
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qed "AuthKeys_simp"; |
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Goalw [AuthKeys_def] |
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"Says Kas A (Crypt (shrK A) {|Key K, Agent Tgs, Number Tk, \ |
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\ (Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key K, Number Tk|})|}) : set evs \ |
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\ ==> K : AuthKeys evs"; |
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by Auto_tac; |
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qed "AuthKeysI"; |
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Goalw [AuthKeys_def] "K : AuthKeys evs ==> Key K : used evs"; |
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by (Simp_tac 1); |
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by (blast_tac (claset() addSEs spies_partsEs) 1); |
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qed "AuthKeys_used"; |
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(**** FORWARDING LEMMAS ****) |
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(*--For reasoning about the encrypted portion of message K3--*) |
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Goal "Says Kas' A (Crypt KeyA {|AuthKey, Peer, Tk, AuthTicket|}) \ |
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\ : set evs ==> AuthTicket : parts (spies evs)"; |
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by (blast_tac (claset() addSEs spies_partsEs) 1); |
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qed "K3_msg_in_parts_spies"; |
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Goal "Says Kas A (Crypt KeyA {|AuthKey, Peer, Tk, AuthTicket|}) \ |
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\ : set evs ==> AuthKey : parts (spies evs)"; |
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by (blast_tac (claset() addSEs spies_partsEs) 1); |
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qed "Oops_parts_spies1"; |
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Goal "[| Says Kas A (Crypt KeyA {|Key AuthKey, Peer, Tk, AuthTicket|}) \ |
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\ : set evs ;\ |
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\ evs : kerberos |] ==> AuthKey ~: range shrK"; |
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by (etac rev_mp 1); |
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by (etac kerberos.induct 1); |
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by Auto_tac; |
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qed "Oops_range_spies1"; |
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(*--For reasoning about the encrypted portion of message K5--*) |
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Goal "Says Tgs' A (Crypt AuthKey {|ServKey, Agent B, Tt, ServTicket|})\ |
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\ : set evs ==> ServTicket : parts (spies evs)"; |
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by (blast_tac (claset() addSEs spies_partsEs) 1); |
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qed "K5_msg_in_parts_spies"; |
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Goal "Says Tgs A (Crypt AuthKey {|ServKey, Agent B, Tt, ServTicket|})\ |
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\ : set evs ==> ServKey : parts (spies evs)"; |
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by (blast_tac (claset() addSEs spies_partsEs) 1); |
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qed "Oops_parts_spies2"; |
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Goal "[| Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|}) \ |
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\ : set evs ;\ |
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\ evs : kerberos |] ==> ServKey ~: range shrK"; |
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by (etac rev_mp 1); |
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by (etac kerberos.induct 1); |
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by Auto_tac; |
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qed "Oops_range_spies2"; |
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Goal "Says S A (Crypt K {|SesKey, B, TimeStamp, Ticket|}) : set evs \ |
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\ ==> Ticket : parts (spies evs)"; |
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by (blast_tac (claset() addSEs spies_partsEs) 1); |
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qed "Says_ticket_in_parts_spies"; |
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(*Replaces both K3_msg_in_parts_spies and K5_msg_in_parts_spies*) |
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fun parts_induct_tac i = |
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etac kerberos.induct i THEN |
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REPEAT (FIRSTGOAL analz_mono_contra_tac) THEN |
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ftac K3_msg_in_parts_spies (i+4) THEN |
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ftac K5_msg_in_parts_spies (i+6) THEN |
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ftac Oops_parts_spies1 (i+8) THEN |
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ftac Oops_parts_spies2 (i+9) THEN |
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prove_simple_subgoals_tac 1; |
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(*Spy never sees another agent's shared key! (unless it's lost at start)*) |
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Goal "evs : kerberos ==> (Key (shrK A) : parts (spies evs)) = (A : bad)"; |
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by (parts_induct_tac 1); |
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by (Fake_parts_insert_tac 1); |
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by (ALLGOALS Blast_tac); |
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qed "Spy_see_shrK"; |
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Addsimps [Spy_see_shrK]; |
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Goal "evs : kerberos ==> (Key (shrK A) : analz (spies evs)) = (A : bad)"; |
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by (auto_tac (claset() addDs [impOfSubs analz_subset_parts], simpset())); |
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qed "Spy_analz_shrK"; |
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Addsimps [Spy_analz_shrK]; |
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Goal "[| Key (shrK A) : parts (spies evs); evs : kerberos |] ==> A:bad"; |
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by (blast_tac (claset() addDs [Spy_see_shrK]) 1); |
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qed "Spy_see_shrK_D"; |
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bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D); |
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AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D]; |
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(*Nobody can have used non-existent keys!*) |
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Goal "evs : kerberos ==> \ |
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\ Key K ~: used evs --> K ~: keysFor (parts (spies evs))"; |
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by (parts_induct_tac 1); |
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(*Fake*) |
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by (best_tac |
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(claset() addSDs [impOfSubs (parts_insert_subset_Un RS keysFor_mono)] |
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addIs [impOfSubs analz_subset_parts] |
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addDs [impOfSubs (analz_subset_parts RS keysFor_mono)] |
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addss (simpset())) 1); |
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(*Others*) |
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by (ALLGOALS (blast_tac (claset() addSEs spies_partsEs))); |
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qed_spec_mp "new_keys_not_used"; |
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bind_thm ("new_keys_not_analzd", |
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[analz_subset_parts RS keysFor_mono, |
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new_keys_not_used] MRS contra_subsetD); |
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Addsimps [new_keys_not_used, new_keys_not_analzd]; |
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(*********************** REGULARITY LEMMAS ***********************) |
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(* concerning the form of items passed in messages *) |
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(*****************************************************************) |
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(*Describes the form of AuthKey, AuthTicket, and K sent by Kas*) |
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Goal "[| Says Kas A (Crypt K {|Key AuthKey, Agent Peer, Tk, AuthTicket|}) \ |
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\ : set evs; \ |
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\ evs : kerberos |] \ |
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\ ==> AuthKey ~: range shrK & AuthKey : AuthKeys evs & \ |
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\ AuthTicket = (Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Tk|} ) &\ |
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\ K = shrK A & Peer = Tgs"; |
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by (etac rev_mp 1); |
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by (etac kerberos.induct 1); |
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by (ALLGOALS (simp_tac (simpset() addsimps [AuthKeys_def, AuthKeys_insert]))); |
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by (ALLGOALS Blast_tac); |
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qed "Says_Kas_message_form"; |
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(*This lemma is essential for proving Says_Tgs_message_form: |
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the session key AuthKey |
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supplied by Kas in the authentication ticket |
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cannot be a long-term key! |
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Generalised to any session keys (both AuthKey and ServKey). |
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*) |
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Goal "[| Crypt (shrK Tgs_B) {|Agent A, Agent Tgs_B, Key SesKey, Number T|}\ |
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\ : parts (spies evs); Tgs_B ~: bad;\ |
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\ evs : kerberos |] \ |
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\ ==> SesKey ~: range shrK"; |
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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 "SesKey_is_session_key"; |
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Goal "[| Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Tk|} \ |
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\ : parts (spies evs); \ |
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\ evs : kerberos |] \ |
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\ ==> Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Tk, \ |
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\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Tk|}|}) \ |
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\ : set evs"; |
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by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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(*Fake*) |
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by (Fake_parts_insert_tac 1); |
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(*K4*) |
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by (Blast_tac 1); |
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qed "A_trusts_AuthTicket"; |
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Goal "[| Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}\ |
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\ : parts (spies evs);\ |
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\ evs : kerberos |] \ |
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\ ==> AuthKey : AuthKeys evs"; |
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by (ftac A_trusts_AuthTicket 1); |
6452 | 251 |
by (assume_tac 1); |
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by (simp_tac (simpset() addsimps [AuthKeys_def]) 1); |
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by (Blast_tac 1); |
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qed "AuthTicket_crypt_AuthKey"; |
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(*Describes the form of ServKey, ServTicket and AuthKey sent by Tgs*) |
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Goal "[| Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|})\ |
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\ : set evs; \ |
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\ evs : kerberos |] \ |
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\ ==> B ~= Tgs & ServKey ~: range shrK & ServKey ~: AuthKeys evs &\ |
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\ ServTicket = (Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|} ) & \ |
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\ AuthKey ~: range shrK & AuthKey : AuthKeys evs"; |
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by (etac rev_mp 1); |
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by (etac kerberos.induct 1); |
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by (ALLGOALS |
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(asm_full_simp_tac |
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(simpset() addsimps [AuthKeys_insert, AuthKeys_not_insert, |
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AuthKeys_empty, AuthKeys_simp]))); |
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by (blast_tac (claset() addEs spies_partsEs) 1); |
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by Auto_tac; |
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by (blast_tac (claset() addSDs [AuthKeys_used, Says_Kas_message_form]) 1); |
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by (blast_tac (claset() addSDs [SesKey_is_session_key] |
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addEs spies_partsEs) 1); |
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by (blast_tac (claset() addDs [AuthTicket_crypt_AuthKey] |
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addEs spies_partsEs) 1); |
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qed "Says_Tgs_message_form"; |
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(*If a certain encrypted message appears then it originated with Kas*) |
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Goal "[| Crypt (shrK A) {|Key AuthKey, Peer, Tk, AuthTicket|} \ |
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\ : parts (spies evs); \ |
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\ A ~: bad; evs : kerberos |] \ |
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\ ==> Says Kas A (Crypt (shrK A) {|Key AuthKey, Peer, Tk, AuthTicket|}) \ |
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\ : set evs"; |
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by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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(*Fake*) |
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by (Fake_parts_insert_tac 1); |
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(*K4*) |
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by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj RS parts.Fst, |
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A_trusts_AuthTicket RS Says_Kas_message_form]) |
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1); |
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qed "A_trusts_AuthKey"; |
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293 |
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(*If a certain encrypted message appears then it originated with Tgs*) |
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Goal "[| Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|} \ |
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\ : parts (spies evs); \ |
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\ Key AuthKey ~: analz (spies evs); \ |
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\ AuthKey ~: range shrK; \ |
|
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\ evs : kerberos |] \ |
|
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\==> EX A. Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|})\ |
|
302 |
\ : set evs"; |
|
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by (etac rev_mp 1); |
|
304 |
by (etac rev_mp 1); |
|
305 |
by (parts_induct_tac 1); |
|
306 |
(*Fake*) |
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by (Fake_parts_insert_tac 1); |
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(*K2*) |
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by (Blast_tac 1); |
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(*K4*) |
|
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by Auto_tac; |
|
312 |
qed "A_trusts_K4"; |
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313 |
||
314 |
Goal "[| Crypt (shrK A) {|Key AuthKey, Agent Tgs, Tk, AuthTicket|} \ |
|
315 |
\ : parts (spies evs); \ |
|
316 |
\ A ~: bad; \ |
|
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\ evs : kerberos |] \ |
|
318 |
\ ==> AuthKey ~: range shrK & \ |
|
319 |
\ AuthTicket = Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Tk|}"; |
|
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by (etac rev_mp 1); |
|
321 |
by (parts_induct_tac 1); |
|
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by (Fake_parts_insert_tac 1); |
|
323 |
by (Blast_tac 1); |
|
324 |
qed "AuthTicket_form"; |
|
325 |
||
326 |
(* This form holds also over an AuthTicket, but is not needed below. *) |
|
327 |
Goal "[| Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|} \ |
|
328 |
\ : parts (spies evs); \ |
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329 |
\ Key AuthKey ~: analz (spies evs); \ |
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330 |
\ evs : kerberos |] \ |
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331 |
\ ==> ServKey ~: range shrK & \ |
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332 |
\ (EX A. ServTicket = Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|})"; |
|
333 |
by (etac rev_mp 1); |
|
334 |
by (etac rev_mp 1); |
|
335 |
by (parts_induct_tac 1); |
|
336 |
by (Fake_parts_insert_tac 1); |
|
337 |
qed "ServTicket_form"; |
|
338 |
||
339 |
Goal "[| Says Kas' A (Crypt (shrK A) \ |
|
340 |
\ {|Key AuthKey, Agent Tgs, Tk, AuthTicket|} ) : set evs; \ |
|
341 |
\ evs : kerberos |] \ |
|
342 |
\ ==> AuthKey ~: range shrK & \ |
|
343 |
\ AuthTicket = \ |
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344 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Tk|}\ |
|
345 |
\ | AuthTicket : analz (spies evs)"; |
|
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by (case_tac "A : bad" 1); |
|
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by (force_tac (claset() addSDs [Says_imp_spies RS analz.Inj], simpset()) 1); |
|
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by (forward_tac [Says_imp_spies RS parts.Inj] 1); |
|
349 |
by (blast_tac (claset() addSDs [AuthTicket_form]) 1); |
|
350 |
qed "Says_kas_message_form"; |
|
351 |
(* Essentially the same as AuthTicket_form *) |
|
352 |
||
353 |
Goal "[| Says Tgs' A (Crypt AuthKey \ |
|
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\ {|Key ServKey, Agent B, Tt, ServTicket|} ) : set evs; \ |
|
355 |
\ evs : kerberos |] \ |
|
356 |
\ ==> ServKey ~: range shrK & \ |
|
357 |
\ (EX A. ServTicket = \ |
|
358 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|}) \ |
|
359 |
\ | ServTicket : analz (spies evs)"; |
|
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by (case_tac "Key AuthKey : analz (spies evs)" 1); |
|
361 |
by (force_tac (claset() addSDs [Says_imp_spies RS analz.Inj], simpset()) 1); |
|
362 |
by (forward_tac [Says_imp_spies RS parts.Inj] 1); |
|
363 |
by (blast_tac (claset() addSDs [ServTicket_form]) 1); |
|
364 |
qed "Says_tgs_message_form"; |
|
365 |
(* This form MUST be used in analz_sees_tac below *) |
|
366 |
||
367 |
||
368 |
(*****************UNICITY THEOREMS****************) |
|
369 |
||
370 |
(* The session key, if secure, uniquely identifies the Ticket |
|
371 |
whether AuthTicket or ServTicket. As a matter of fact, one can read |
|
372 |
also Tgs in the place of B. *) |
|
373 |
Goal "evs : kerberos ==> \ |
|
374 |
\ Key SesKey ~: analz (spies evs) --> \ |
|
375 |
\ (EX A B T. ALL A' B' T'. \ |
|
376 |
\ Crypt (shrK B') {|Agent A', Agent B', Key SesKey, T'|} \ |
|
377 |
\ : parts (spies evs) --> A'=A & B'=B & T'=T)"; |
|
378 |
by (parts_induct_tac 1); |
|
379 |
by (REPEAT (etac (exI RSN (2,exE)) 1) (*stripping EXs makes proof faster*) |
|
380 |
THEN Fake_parts_insert_tac 1); |
|
381 |
by (asm_simp_tac (simpset() addsimps [all_conj_distrib]) 1); |
|
382 |
by (expand_case_tac "SesKey = ?y" 1); |
|
383 |
by (blast_tac (claset() addSEs spies_partsEs) 1); |
|
384 |
by (expand_case_tac "SesKey = ?y" 1); |
|
385 |
by (blast_tac (claset() addSEs spies_partsEs) 1); |
|
386 |
val lemma = result(); |
|
387 |
||
388 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key SesKey, T|} \ |
|
389 |
\ : parts (spies evs); \ |
|
390 |
\ Crypt (shrK B') {|Agent A', Agent B', Key SesKey, T'|} \ |
|
391 |
\ : parts (spies evs); \ |
|
392 |
\ evs : kerberos; Key SesKey ~: analz (spies evs) |] \ |
|
393 |
\ ==> A=A' & B=B' & T=T'"; |
|
394 |
by (prove_unique_tac lemma 1); |
|
395 |
qed "unique_CryptKey"; |
|
396 |
||
397 |
Goal "evs : kerberos \ |
|
398 |
\ ==> Key SesKey ~: analz (spies evs) --> \ |
|
399 |
\ (EX K' B' T' Ticket'. ALL K B T Ticket. \ |
|
400 |
\ Crypt K {|Key SesKey, Agent B, T, Ticket|} \ |
|
401 |
\ : parts (spies evs) --> K=K' & B=B' & T=T' & Ticket=Ticket')"; |
|
402 |
by (parts_induct_tac 1); |
|
403 |
by (REPEAT (etac (exI RSN (2,exE)) 1) THEN Fake_parts_insert_tac 1); |
|
404 |
by (asm_simp_tac (simpset() addsimps [all_conj_distrib]) 1); |
|
405 |
by (expand_case_tac "SesKey = ?y" 1); |
|
406 |
by (blast_tac (claset() addSEs spies_partsEs) 1); |
|
407 |
by (expand_case_tac "SesKey = ?y" 1); |
|
408 |
by (blast_tac (claset() addSEs spies_partsEs) 1); |
|
409 |
val lemma = result(); |
|
410 |
||
411 |
(*An AuthKey is encrypted by one and only one Shared key. |
|
412 |
A ServKey is encrypted by one and only one AuthKey. |
|
413 |
*) |
|
414 |
Goal "[| Crypt K {|Key SesKey, Agent B, T, Ticket|} \ |
|
415 |
\ : parts (spies evs); \ |
|
416 |
\ Crypt K' {|Key SesKey, Agent B', T', Ticket'|} \ |
|
417 |
\ : parts (spies evs); \ |
|
418 |
\ evs : kerberos; Key SesKey ~: analz (spies evs) |] \ |
|
419 |
\ ==> K=K' & B=B' & T=T' & Ticket=Ticket'"; |
|
420 |
by (prove_unique_tac lemma 1); |
|
421 |
qed "Key_unique_SesKey"; |
|
422 |
||
423 |
||
424 |
(* |
|
425 |
At reception of any message mentioning A, Kas associates shrK A with |
|
426 |
a new AuthKey. Realistic, as the user gets a new AuthKey at each login. |
|
427 |
Similarly, at reception of any message mentioning an AuthKey |
|
428 |
(a legitimate user could make several requests to Tgs - by K3), Tgs |
|
429 |
associates it with a new ServKey. |
|
430 |
||
431 |
Therefore, a goal like |
|
432 |
||
433 |
"evs : kerberos \ |
|
434 |
\ ==> Key Kc ~: analz (spies evs) --> \ |
|
435 |
\ (EX K' B' T' Ticket'. ALL K B T Ticket. \ |
|
436 |
\ Crypt Kc {|Key K, Agent B, T, Ticket|} \ |
|
437 |
\ : parts (spies evs) --> K=K' & B=B' & T=T' & Ticket=Ticket')"; |
|
438 |
||
439 |
would fail on the K2 and K4 cases. |
|
440 |
*) |
|
441 |
||
442 |
(* AuthKey uniquely identifies the message from Kas *) |
|
443 |
Goal "evs : kerberos ==> \ |
|
444 |
\ EX A' Ka' Tk' X'. ALL A Ka Tk X. \ |
|
445 |
\ Says Kas A (Crypt Ka {|Key AuthKey, Agent Tgs, Tk, X|}) \ |
|
446 |
\ : set evs --> A=A' & Ka=Ka' & Tk=Tk' & X=X'"; |
|
447 |
by (etac kerberos.induct 1); |
|
448 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
|
449 |
by (Step_tac 1); |
|
450 |
(*K2: it can't be a new key*) |
|
451 |
by (expand_case_tac "AuthKey = ?y" 1); |
|
452 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
453 |
by (blast_tac (claset() delrules [conjI] (*prevent split-up into 4 subgoals*) |
|
454 |
addSEs spies_partsEs) 1); |
|
455 |
val lemma = result(); |
|
456 |
||
457 |
Goal "[| Says Kas A \ |
|
458 |
\ (Crypt Ka {|Key AuthKey, Agent Tgs, Tk, X|}) : set evs; \ |
|
459 |
\ Says Kas A' \ |
|
460 |
\ (Crypt Ka' {|Key AuthKey, Agent Tgs, Tk', X'|}) : set evs; \ |
|
461 |
\ evs : kerberos |] ==> A=A' & Ka=Ka' & Tk=Tk' & X=X'"; |
|
462 |
by (prove_unique_tac lemma 1); |
|
463 |
qed "unique_AuthKeys"; |
|
464 |
||
465 |
(* ServKey uniquely identifies the message from Tgs *) |
|
466 |
Goal "evs : kerberos ==> \ |
|
467 |
\ EX A' B' AuthKey' Tk' X'. ALL A B AuthKey Tk X. \ |
|
468 |
\ Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Tk, X|}) \ |
|
469 |
\ : set evs --> A=A' & B=B' & AuthKey=AuthKey' & Tk=Tk' & X=X'"; |
|
470 |
by (etac kerberos.induct 1); |
|
471 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
|
472 |
by (Step_tac 1); |
|
473 |
(*K4: it can't be a new key*) |
|
474 |
by (expand_case_tac "ServKey = ?y" 1); |
|
475 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
476 |
by (blast_tac (claset() delrules [conjI] (*prevent split-up into 4 subgoals*) |
|
477 |
addSEs spies_partsEs) 1); |
|
478 |
val lemma = result(); |
|
479 |
||
480 |
Goal "[| Says Tgs A \ |
|
481 |
\ (Crypt K {|Key ServKey, Agent B, Tt, X|}) : set evs; \ |
|
482 |
\ Says Tgs A' \ |
|
483 |
\ (Crypt K' {|Key ServKey, Agent B', Tt', X'|}) : set evs; \ |
|
484 |
\ evs : kerberos |] ==> A=A' & B=B' & K=K' & Tt=Tt' & X=X'"; |
|
485 |
by (prove_unique_tac lemma 1); |
|
486 |
qed "unique_ServKeys"; |
|
487 |
||
488 |
||
489 |
(*****************LEMMAS ABOUT the predicate KeyCryptKey****************) |
|
490 |
||
491 |
Goalw [KeyCryptKey_def] "~ KeyCryptKey AuthKey ServKey []"; |
|
492 |
by (Simp_tac 1); |
|
493 |
qed "not_KeyCryptKey_Nil"; |
|
494 |
AddIffs [not_KeyCryptKey_Nil]; |
|
495 |
||
496 |
Goalw [KeyCryptKey_def] |
|
497 |
"[| Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, tt, X |}) \ |
|
498 |
\ : set evs; \ |
|
499 |
\ evs : kerberos |] ==> KeyCryptKey AuthKey ServKey evs"; |
|
7499 | 500 |
by (ftac Says_Tgs_message_form 1); |
6452 | 501 |
by (assume_tac 1); |
502 |
by (Blast_tac 1); |
|
503 |
qed "KeyCryptKeyI"; |
|
504 |
||
505 |
Goalw [KeyCryptKey_def] |
|
506 |
"KeyCryptKey AuthKey ServKey (Says S A X # evs) = \ |
|
507 |
\ (Tgs = S & \ |
|
508 |
\ (EX B tt. X = Crypt AuthKey \ |
|
509 |
\ {|Key ServKey, Agent B, tt, \ |
|
510 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, tt|} |}) \ |
|
511 |
\ | KeyCryptKey AuthKey ServKey evs)"; |
|
512 |
by (Simp_tac 1); |
|
513 |
by (Blast_tac 1); |
|
514 |
qed "KeyCryptKey_Says"; |
|
515 |
Addsimps [KeyCryptKey_Says]; |
|
516 |
||
517 |
(*A fresh AuthKey cannot be associated with any other |
|
518 |
(with respect to a given trace). *) |
|
519 |
Goalw [KeyCryptKey_def] |
|
520 |
"[| Key AuthKey ~: used evs; evs : kerberos |] \ |
|
521 |
\ ==> ~ KeyCryptKey AuthKey ServKey evs"; |
|
522 |
by (etac rev_mp 1); |
|
523 |
by (parts_induct_tac 1); |
|
524 |
by (Asm_full_simp_tac 1); |
|
525 |
by (blast_tac (claset() addSEs spies_partsEs) 1); |
|
526 |
qed "Auth_fresh_not_KeyCryptKey"; |
|
527 |
||
528 |
(*A fresh ServKey cannot be associated with any other |
|
529 |
(with respect to a given trace). *) |
|
530 |
Goalw [KeyCryptKey_def] |
|
531 |
"Key ServKey ~: used evs ==> ~ KeyCryptKey AuthKey ServKey evs"; |
|
532 |
by (blast_tac (claset() addSEs spies_partsEs) 1); |
|
533 |
qed "Serv_fresh_not_KeyCryptKey"; |
|
534 |
||
535 |
Goalw [KeyCryptKey_def] |
|
536 |
"[| Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, tk|}\ |
|
537 |
\ : parts (spies evs); evs : kerberos |] \ |
|
538 |
\ ==> ~ KeyCryptKey K AuthKey evs"; |
|
539 |
by (etac rev_mp 1); |
|
540 |
by (parts_induct_tac 1); |
|
541 |
(*K4*) |
|
542 |
by (blast_tac (claset() addEs spies_partsEs) 3); |
|
543 |
(*K2: by freshness*) |
|
544 |
by (blast_tac (claset() addEs spies_partsEs) 2); |
|
545 |
by (Fake_parts_insert_tac 1); |
|
546 |
qed "AuthKey_not_KeyCryptKey"; |
|
547 |
||
548 |
(*A secure serverkey cannot have been used to encrypt others*) |
|
549 |
Goalw [KeyCryptKey_def] |
|
550 |
"[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, tt|} \ |
|
551 |
\ : parts (spies evs); \ |
|
552 |
\ Key ServKey ~: analz (spies evs); \ |
|
553 |
\ B ~= Tgs; evs : kerberos |] \ |
|
554 |
\ ==> ~ KeyCryptKey ServKey K evs"; |
|
555 |
by (etac rev_mp 1); |
|
556 |
by (etac rev_mp 1); |
|
557 |
by (parts_induct_tac 1); |
|
558 |
by (Fake_parts_insert_tac 1); |
|
559 |
(*K4 splits into distinct subcases*) |
|
560 |
by (Step_tac 1); |
|
561 |
by (ALLGOALS Asm_full_simp_tac); |
|
562 |
(*ServKey can't have been enclosed in two certificates*) |
|
563 |
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj] |
|
564 |
addSEs [MPair_parts] |
|
565 |
addDs [unique_CryptKey]) 4); |
|
566 |
(*ServKey is fresh and so could not have been used, by new_keys_not_used*) |
|
567 |
by (force_tac (claset() addSDs [Says_imp_spies RS parts.Inj, |
|
568 |
Crypt_imp_invKey_keysFor], |
|
569 |
simpset()) 2); |
|
570 |
(*Others by freshness*) |
|
571 |
by (REPEAT (blast_tac (claset() addSEs spies_partsEs) 1)); |
|
572 |
qed "ServKey_not_KeyCryptKey"; |
|
573 |
||
574 |
(*Long term keys are not issued as ServKeys*) |
|
575 |
Goalw [KeyCryptKey_def] |
|
576 |
"evs : kerberos ==> ~ KeyCryptKey K (shrK A) evs"; |
|
577 |
by (parts_induct_tac 1); |
|
578 |
qed "shrK_not_KeyCryptKey"; |
|
579 |
||
580 |
(*The Tgs message associates ServKey with AuthKey and therefore not with any |
|
581 |
other key AuthKey.*) |
|
582 |
Goalw [KeyCryptKey_def] |
|
583 |
"[| Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, tt, X |}) \ |
|
584 |
\ : set evs; \ |
|
585 |
\ AuthKey' ~= AuthKey; evs : kerberos |] \ |
|
586 |
\ ==> ~ KeyCryptKey AuthKey' ServKey evs"; |
|
587 |
by (blast_tac (claset() addDs [unique_ServKeys]) 1); |
|
588 |
qed "Says_Tgs_KeyCryptKey"; |
|
589 |
||
590 |
Goal "[| KeyCryptKey AuthKey ServKey evs; evs : kerberos |] \ |
|
591 |
\ ==> ~ KeyCryptKey ServKey K evs"; |
|
592 |
by (etac rev_mp 1); |
|
593 |
by (parts_induct_tac 1); |
|
594 |
by (Step_tac 1); |
|
595 |
by (ALLGOALS Asm_full_simp_tac); |
|
596 |
(*K4 splits into subcases*) |
|
597 |
by (blast_tac (claset() addEs spies_partsEs |
|
598 |
addSDs [AuthKey_not_KeyCryptKey]) 4); |
|
599 |
(*ServKey is fresh and so could not have been used, by new_keys_not_used*) |
|
600 |
by (force_tac (claset() addSDs [Says_imp_spies RS parts.Inj, |
|
601 |
Crypt_imp_invKey_keysFor], |
|
602 |
simpset() addsimps [KeyCryptKey_def]) 2); |
|
603 |
(*Others by freshness*) |
|
604 |
by (REPEAT (blast_tac (claset() addSEs spies_partsEs) 1)); |
|
605 |
qed "KeyCryptKey_not_KeyCryptKey"; |
|
606 |
||
607 |
(*The only session keys that can be found with the help of session keys are |
|
608 |
those sent by Tgs in step K4. *) |
|
609 |
||
610 |
(*We take some pains to express the property |
|
611 |
as a logical equivalence so that the simplifier can apply it.*) |
|
612 |
Goal "P --> (Key K : analz (Key``KK Un H)) --> (K:KK | Key K : analz H) \ |
|
613 |
\ ==> \ |
|
614 |
\ P --> (Key K : analz (Key``KK Un H)) = (K:KK | Key K : analz H)"; |
|
615 |
by (blast_tac (claset() addIs [impOfSubs analz_mono]) 1); |
|
616 |
qed "Key_analz_image_Key_lemma"; |
|
617 |
||
618 |
Goal "[| KeyCryptKey K K' evs; evs : kerberos |] \ |
|
619 |
\ ==> Key K' : analz (insert (Key K) (spies evs))"; |
|
620 |
by (full_simp_tac (simpset() addsimps [KeyCryptKey_def]) 1); |
|
621 |
by (Clarify_tac 1); |
|
622 |
by (dresolve_tac [Says_imp_spies RS analz.Inj RS analz_insertI] 1); |
|
623 |
by Auto_tac; |
|
624 |
qed "KeyCryptKey_analz_insert"; |
|
625 |
||
626 |
Goal "[| K : AuthKeys evs Un range shrK; evs : kerberos |] \ |
|
627 |
\ ==> ALL SK. ~ KeyCryptKey SK K evs"; |
|
628 |
by (asm_full_simp_tac (simpset() addsimps [KeyCryptKey_def]) 1); |
|
629 |
by (blast_tac (claset() addDs [Says_Tgs_message_form]) 1); |
|
630 |
qed "AuthKeys_are_not_KeyCryptKey"; |
|
631 |
||
632 |
Goal "[| K ~: AuthKeys evs; \ |
|
633 |
\ K ~: range shrK; evs : kerberos |] \ |
|
634 |
\ ==> ALL SK. ~ KeyCryptKey K SK evs"; |
|
635 |
by (asm_full_simp_tac (simpset() addsimps [KeyCryptKey_def]) 1); |
|
636 |
by (blast_tac (claset() addDs [Says_Tgs_message_form]) 1); |
|
637 |
qed "not_AuthKeys_not_KeyCryptKey"; |
|
638 |
||
639 |
||
640 |
(*****************SECRECY THEOREMS****************) |
|
641 |
||
642 |
(*For proofs involving analz.*) |
|
643 |
val analz_sees_tac = |
|
644 |
EVERY |
|
645 |
[REPEAT (FIRSTGOAL analz_mono_contra_tac), |
|
7499 | 646 |
ftac Oops_range_spies2 10, |
647 |
ftac Oops_range_spies1 9, |
|
648 |
ftac Says_tgs_message_form 7, |
|
649 |
ftac Says_kas_message_form 5, |
|
6452 | 650 |
REPEAT_FIRST (eresolve_tac [asm_rl, conjE, disjE, exE] |
651 |
ORELSE' hyp_subst_tac)]; |
|
652 |
||
653 |
Goal "[| KK <= -(range shrK); Key K : analz (spies evs); evs: kerberos |] \ |
|
654 |
\ ==> Key K : analz (Key `` KK Un spies evs)"; |
|
655 |
by (blast_tac (claset() addDs [impOfSubs analz_mono]) 1); |
|
656 |
qed "analz_mono_KK"; |
|
657 |
||
658 |
(* Big simplification law for keys SK that are not crypted by keys in KK *) |
|
659 |
(* It helps prove three, otherwise hard, facts about keys. These facts are *) |
|
660 |
(* exploited as simplification laws for analz, and also "limit the damage" *) |
|
661 |
(* in case of loss of a key to the spy. See ESORICS98. *) |
|
662 |
Goal "evs : kerberos ==> \ |
|
663 |
\ (ALL SK KK. KK <= -(range shrK) --> \ |
|
664 |
\ (ALL K: KK. ~ KeyCryptKey K SK evs) --> \ |
|
665 |
\ (Key SK : analz (Key``KK Un (spies evs))) = \ |
|
666 |
\ (SK : KK | Key SK : analz (spies evs)))"; |
|
667 |
by (etac kerberos.induct 1); |
|
668 |
by analz_sees_tac; |
|
669 |
by (REPEAT_FIRST (rtac allI)); |
|
670 |
by (REPEAT_FIRST (rtac (Key_analz_image_Key_lemma RS impI))); |
|
671 |
by (ALLGOALS |
|
672 |
(asm_simp_tac |
|
673 |
(analz_image_freshK_ss addsimps |
|
674 |
[KeyCryptKey_Says, shrK_not_KeyCryptKey, |
|
675 |
Auth_fresh_not_KeyCryptKey, Serv_fresh_not_KeyCryptKey, |
|
676 |
Says_Tgs_KeyCryptKey, Spy_analz_shrK]))); |
|
677 |
(*Fake*) |
|
678 |
by (spy_analz_tac 1); |
|
679 |
(* Base + K2 done by the simplifier! *) |
|
680 |
(*K3*) |
|
681 |
by (Blast_tac 1); |
|
682 |
(*K4*) |
|
683 |
by (blast_tac (claset() addEs spies_partsEs |
|
684 |
addSDs [AuthKey_not_KeyCryptKey]) 1); |
|
685 |
(*K5*) |
|
686 |
by (rtac impI 1); |
|
687 |
by (case_tac "Key ServKey : analz (spies evs5)" 1); |
|
688 |
(*If ServKey is compromised then the result follows directly...*) |
|
689 |
by (asm_simp_tac |
|
690 |
(simpset() addsimps [analz_insert_eq, |
|
691 |
impOfSubs (Un_upper2 RS analz_mono)]) 1); |
|
692 |
(*...therefore ServKey is uncompromised.*) |
|
693 |
by (case_tac "KeyCryptKey ServKey SK evs5" 1); |
|
694 |
by (asm_simp_tac analz_image_freshK_ss 2); |
|
695 |
(*The KeyCryptKey ServKey SK evs5 case leads to a contradiction.*) |
|
696 |
by (blast_tac (claset() addSEs [ServKey_not_KeyCryptKey RSN(2, rev_notE)] |
|
697 |
addEs spies_partsEs delrules [allE, ballE]) 1); |
|
698 |
(** Level 14: Oops1 and Oops2 **) |
|
699 |
by (ALLGOALS Clarify_tac); |
|
700 |
(*Oops 2*) |
|
701 |
by (case_tac "Key ServKey : analz (spies evsO2)" 2); |
|
702 |
by (ALLGOALS Asm_full_simp_tac); |
|
7499 | 703 |
by (ftac analz_mono_KK 2 |
6452 | 704 |
THEN assume_tac 2 |
705 |
THEN assume_tac 2); |
|
7499 | 706 |
by (ftac analz_cut 2 THEN assume_tac 2); |
6452 | 707 |
by (blast_tac (claset() addDs [analz_cut, impOfSubs analz_mono]) 2); |
708 |
by (dres_inst_tac [("x","SK")] spec 2); |
|
709 |
by (dres_inst_tac [("x","insert ServKey KK")] spec 2); |
|
7499 | 710 |
by (ftac Says_Tgs_message_form 2 THEN assume_tac 2); |
6452 | 711 |
by (Clarify_tac 2); |
712 |
by (forward_tac [Says_imp_spies RS parts.Inj RS parts.Body |
|
713 |
RS parts.Snd RS parts.Snd RS parts.Snd] 2); |
|
714 |
by (Asm_full_simp_tac 2); |
|
715 |
by (blast_tac (claset() addSDs [ServKey_not_KeyCryptKey] |
|
7494
45905028bb1d
added theorems le_maxI1 and le_maxI2, also in claset
oheimb
parents:
7239
diff
changeset
|
716 |
delrules [le_maxI1, le_maxI2] |
6452 | 717 |
addDs [impOfSubs analz_mono]) 2); |
7494
45905028bb1d
added theorems le_maxI1 and le_maxI2, also in claset
oheimb
parents:
7239
diff
changeset
|
718 |
(*Level 27: Oops 1*) |
6452 | 719 |
by (dres_inst_tac [("x","SK")] spec 1); |
720 |
by (dres_inst_tac [("x","insert AuthKey KK")] spec 1); |
|
721 |
by (case_tac "KeyCryptKey AuthKey SK evsO1" 1); |
|
722 |
by (ALLGOALS Asm_full_simp_tac); |
|
723 |
by (blast_tac (claset() addSDs [KeyCryptKey_analz_insert]) 1); |
|
7494
45905028bb1d
added theorems le_maxI1 and le_maxI2, also in claset
oheimb
parents:
7239
diff
changeset
|
724 |
by (blast_tac (claset() delrules [le_maxI1, le_maxI2] |
45905028bb1d
added theorems le_maxI1 and le_maxI2, also in claset
oheimb
parents:
7239
diff
changeset
|
725 |
addDs [impOfSubs analz_mono]) 1); |
6452 | 726 |
qed_spec_mp "Key_analz_image_Key"; |
727 |
||
728 |
||
729 |
(* First simplification law for analz: no session keys encrypt *) |
|
730 |
(* authentication keys or shared keys. *) |
|
731 |
Goal "[| evs : kerberos; K : (AuthKeys evs) Un range shrK; \ |
|
732 |
\ SesKey ~: range shrK |] \ |
|
733 |
\ ==> Key K : analz (insert (Key SesKey) (spies evs)) = \ |
|
734 |
\ (K = SesKey | Key K : analz (spies evs))"; |
|
7499 | 735 |
by (ftac AuthKeys_are_not_KeyCryptKey 1 THEN assume_tac 1); |
6452 | 736 |
by (asm_full_simp_tac (analz_image_freshK_ss addsimps [Key_analz_image_Key]) 1); |
737 |
qed "analz_insert_freshK1"; |
|
738 |
||
739 |
||
740 |
(* Second simplification law for analz: no service keys encrypt *) |
|
741 |
(* any other keys. *) |
|
742 |
Goal "[| evs : kerberos; ServKey ~: (AuthKeys evs); ServKey ~: range shrK|]\ |
|
743 |
\ ==> Key K : analz (insert (Key ServKey) (spies evs)) = \ |
|
744 |
\ (K = ServKey | Key K : analz (spies evs))"; |
|
7499 | 745 |
by (ftac not_AuthKeys_not_KeyCryptKey 1 |
6452 | 746 |
THEN assume_tac 1 |
747 |
THEN assume_tac 1); |
|
748 |
by (asm_full_simp_tac (analz_image_freshK_ss addsimps [Key_analz_image_Key]) 1); |
|
749 |
qed "analz_insert_freshK2"; |
|
750 |
||
751 |
||
752 |
(* Third simplification law for analz: only one authentication key *) |
|
753 |
(* encrypts a certain service key. *) |
|
754 |
Goal |
|
755 |
"[| Says Tgs A \ |
|
756 |
\ (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
|
757 |
\ : set evs; \ |
|
758 |
\ AuthKey ~= AuthKey'; AuthKey' ~: range shrK; evs : kerberos |] \ |
|
759 |
\ ==> Key ServKey : analz (insert (Key AuthKey') (spies evs)) = \ |
|
760 |
\ (ServKey = AuthKey' | Key ServKey : analz (spies evs))"; |
|
761 |
by (dres_inst_tac [("AuthKey'","AuthKey'")] Says_Tgs_KeyCryptKey 1); |
|
762 |
by (Blast_tac 1); |
|
763 |
by (assume_tac 1); |
|
764 |
by (asm_full_simp_tac (analz_image_freshK_ss addsimps [Key_analz_image_Key]) 1); |
|
765 |
qed "analz_insert_freshK3"; |
|
766 |
||
767 |
||
768 |
(*a weakness of the protocol*) |
|
769 |
Goal "[| Says Tgs A \ |
|
770 |
\ (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
|
771 |
\ : set evs; \ |
|
772 |
\ Key AuthKey : analz (spies evs); evs : kerberos |] \ |
|
773 |
\ ==> Key ServKey : analz (spies evs)"; |
|
774 |
by (force_tac (claset() addDs [Says_imp_spies RS analz.Inj RS |
|
775 |
analz.Decrypt RS analz.Fst], |
|
776 |
simpset()) 1); |
|
777 |
qed "AuthKey_compromises_ServKey"; |
|
778 |
||
779 |
||
780 |
(********************** Guarantees for Kas *****************************) |
|
781 |
Goal "[| Crypt AuthKey {|Key ServKey, Agent B, Tt, \ |
|
782 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|}|}\ |
|
783 |
\ : parts (spies evs); \ |
|
784 |
\ Key ServKey ~: analz (spies evs); \ |
|
785 |
\ B ~= Tgs; evs : kerberos |] \ |
|
786 |
\ ==> ServKey ~: AuthKeys evs"; |
|
787 |
by (etac rev_mp 1); |
|
788 |
by (etac rev_mp 1); |
|
789 |
by (asm_full_simp_tac (simpset() addsimps [AuthKeys_def]) 1); |
|
790 |
by (parts_induct_tac 1); |
|
791 |
by (Fake_parts_insert_tac 1); |
|
792 |
by (ALLGOALS (blast_tac (claset() addSEs spies_partsEs))); |
|
793 |
bind_thm ("ServKey_notin_AuthKeys", result() RSN (2, rev_notE)); |
|
794 |
bind_thm ("ServKey_notin_AuthKeysD", result()); |
|
795 |
||
796 |
||
797 |
(** If Spy sees the Authentication Key sent in msg K2, then |
|
798 |
the Key has expired **) |
|
799 |
Goal "[| A ~: bad; evs : kerberos |] \ |
|
800 |
\ ==> Says Kas A \ |
|
801 |
\ (Crypt (shrK A) \ |
|
802 |
\ {|Key AuthKey, Agent Tgs, Number Tk, \ |
|
803 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
804 |
\ : set evs --> \ |
|
805 |
\ Key AuthKey : analz (spies evs) --> \ |
|
806 |
\ ExpirAuth Tk evs"; |
|
807 |
by (etac kerberos.induct 1); |
|
808 |
by analz_sees_tac; |
|
809 |
by (ALLGOALS |
|
810 |
(asm_simp_tac |
|
811 |
(simpset() addsimps ([Says_Kas_message_form, |
|
812 |
analz_insert_eq, not_parts_not_analz, |
|
813 |
analz_insert_freshK1] @ pushes)))); |
|
814 |
(*Fake*) |
|
815 |
by (spy_analz_tac 1); |
|
816 |
(*K2*) |
|
817 |
by (blast_tac (claset() addSEs spies_partsEs |
|
818 |
addIs [parts_insertI, impOfSubs analz_subset_parts, less_SucI]) 1); |
|
819 |
(*K4*) |
|
820 |
by (blast_tac (claset() addSEs spies_partsEs) 1); |
|
821 |
(*Level 8: K5*) |
|
822 |
by (blast_tac (claset() addEs [ServKey_notin_AuthKeys] |
|
823 |
addDs [Says_Kas_message_form, |
|
824 |
Says_imp_spies RS parts.Inj] |
|
825 |
addIs [less_SucI]) 1); |
|
826 |
(*Oops1*) |
|
827 |
by (blast_tac (claset() addDs [unique_AuthKeys] addIs [less_SucI]) 1); |
|
828 |
(*Oops2*) |
|
829 |
by (blast_tac (claset() addDs [Says_Tgs_message_form, |
|
830 |
Says_Kas_message_form]) 1); |
|
831 |
val lemma = result() RS mp RS mp RSN(1,rev_notE); |
|
832 |
||
833 |
||
834 |
Goal "[| Says Kas A \ |
|
835 |
\ (Crypt Ka {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}) \ |
|
836 |
\ : set evs; \ |
|
837 |
\ ~ ExpirAuth Tk evs; \ |
|
838 |
\ A ~: bad; evs : kerberos |] \ |
|
839 |
\ ==> Key AuthKey ~: analz (spies evs)"; |
|
7499 | 840 |
by (ftac Says_Kas_message_form 1 THEN assume_tac 1); |
6452 | 841 |
by (blast_tac (claset() addSDs [lemma]) 1); |
842 |
qed "Confidentiality_Kas"; |
|
843 |
||
844 |
||
845 |
||
846 |
||
847 |
||
848 |
||
849 |
(********************** Guarantees for Tgs *****************************) |
|
850 |
||
851 |
(** If Spy sees the Service Key sent in msg K4, then |
|
852 |
the Key has expired **) |
|
853 |
Goal "[| A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
854 |
\ ==> Key AuthKey ~: analz (spies evs) --> \ |
|
855 |
\ Says Tgs A \ |
|
856 |
\ (Crypt AuthKey \ |
|
857 |
\ {|Key ServKey, Agent B, Number Tt, \ |
|
858 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|}|})\ |
|
859 |
\ : set evs --> \ |
|
860 |
\ Key ServKey : analz (spies evs) --> \ |
|
861 |
\ ExpirServ Tt evs"; |
|
862 |
by (etac kerberos.induct 1); |
|
863 |
(*The Oops1 case is unusual: must simplify Authkey ~: analz (spies (ev#evs)) |
|
864 |
rather than weakening it to Authkey ~: analz (spies evs), for we then |
|
865 |
conclude AuthKey ~= AuthKeya.*) |
|
866 |
by (Clarify_tac 9); |
|
867 |
by analz_sees_tac; |
|
868 |
by (rotate_tac ~1 11); |
|
869 |
by (ALLGOALS |
|
870 |
(asm_full_simp_tac |
|
871 |
(simpset() addsimps ([Says_Kas_message_form, Says_Tgs_message_form, |
|
872 |
analz_insert_eq, not_parts_not_analz, |
|
873 |
analz_insert_freshK1, analz_insert_freshK2] @ pushes)))); |
|
874 |
(*Fake*) |
|
875 |
by (spy_analz_tac 1); |
|
876 |
(*K2*) |
|
877 |
by (blast_tac (claset() addSEs spies_partsEs |
|
878 |
addIs [parts_insertI, impOfSubs analz_subset_parts, less_SucI]) 1); |
|
879 |
(*K4*) |
|
880 |
by (case_tac "A ~= Aa" 1); |
|
881 |
by (blast_tac (claset() addSEs spies_partsEs |
|
882 |
addIs [less_SucI]) 1); |
|
883 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj RS parts.Fst, |
|
884 |
A_trusts_AuthTicket, |
|
885 |
Confidentiality_Kas, |
|
886 |
impOfSubs analz_subset_parts]) 1); |
|
887 |
by (ALLGOALS Clarify_tac); |
|
888 |
(*Oops2*) |
|
889 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj, |
|
890 |
Key_unique_SesKey] addIs [less_SucI]) 3); |
|
891 |
(** Level 12 **) |
|
892 |
(*Oops1*) |
|
7499 | 893 |
by (ftac Says_Kas_message_form 2); |
6452 | 894 |
by (assume_tac 2); |
895 |
by (blast_tac (claset() addDs [analz_insert_freshK3, |
|
896 |
Says_Kas_message_form, Says_Tgs_message_form] |
|
897 |
addIs [less_SucI]) 2); |
|
898 |
(** Level 16 **) |
|
899 |
by (thin_tac "Says Aa Tgs ?X : set ?evs" 1); |
|
900 |
by (forward_tac [Says_imp_spies RS parts.Inj RS ServKey_notin_AuthKeysD] 1); |
|
901 |
by (assume_tac 1 THEN Blast_tac 1 THEN assume_tac 1); |
|
902 |
by (rotate_tac ~1 1); |
|
903 |
by (asm_full_simp_tac (simpset() addsimps [analz_insert_freshK2]) 1); |
|
904 |
by (etac disjE 1); |
|
905 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj, |
|
906 |
Key_unique_SesKey]) 1); |
|
907 |
by (blast_tac (claset() addIs [less_SucI]) 1); |
|
908 |
val lemma = result() RS mp RS mp RS mp RSN(1,rev_notE); |
|
909 |
||
910 |
||
911 |
(* In the real world Tgs can't check wheter AuthKey is secure! *) |
|
912 |
Goal |
|
913 |
"[| Says Tgs A \ |
|
914 |
\ (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
|
915 |
\ : set evs; \ |
|
916 |
\ Key AuthKey ~: analz (spies evs); \ |
|
917 |
\ ~ ExpirServ Tt evs; \ |
|
918 |
\ A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
919 |
\ ==> Key ServKey ~: analz (spies evs)"; |
|
7499 | 920 |
by (ftac Says_Tgs_message_form 1 THEN assume_tac 1); |
6452 | 921 |
by (blast_tac (claset() addDs [lemma]) 1); |
922 |
qed "Confidentiality_Tgs1"; |
|
923 |
||
924 |
(* In the real world Tgs CAN check what Kas sends! *) |
|
925 |
Goal |
|
926 |
"[| Says Kas A \ |
|
927 |
\ (Crypt Ka {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}) \ |
|
928 |
\ : set evs; \ |
|
929 |
\ Says Tgs A \ |
|
930 |
\ (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
|
931 |
\ : set evs; \ |
|
932 |
\ ~ ExpirAuth Tk evs; ~ ExpirServ Tt evs; \ |
|
933 |
\ A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
934 |
\ ==> Key ServKey ~: analz (spies evs)"; |
|
935 |
by (blast_tac (claset() addSDs [Confidentiality_Kas, |
|
936 |
Confidentiality_Tgs1]) 1); |
|
937 |
qed "Confidentiality_Tgs2"; |
|
938 |
||
939 |
(*Most general form*) |
|
940 |
val Confidentiality_Tgs3 = A_trusts_AuthTicket RS Confidentiality_Tgs2; |
|
941 |
||
942 |
||
943 |
(********************** Guarantees for Alice *****************************) |
|
944 |
||
945 |
val Confidentiality_Auth_A = A_trusts_AuthKey RS Confidentiality_Kas; |
|
946 |
||
947 |
Goal |
|
948 |
"[| Says Kas A \ |
|
949 |
\ (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Tk, AuthTicket|}) : set evs;\ |
|
950 |
\ Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|} \ |
|
951 |
\ : parts (spies evs); \ |
|
952 |
\ Key AuthKey ~: analz (spies evs); \ |
|
953 |
\ evs : kerberos |] \ |
|
954 |
\==> Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|})\ |
|
955 |
\ : set evs"; |
|
7499 | 956 |
by (ftac Says_Kas_message_form 1 THEN assume_tac 1); |
6452 | 957 |
by (etac rev_mp 1); |
958 |
by (etac rev_mp 1); |
|
959 |
by (etac rev_mp 1); |
|
960 |
by (parts_induct_tac 1); |
|
961 |
by (Fake_parts_insert_tac 1); |
|
962 |
(*K2 and K4 remain*) |
|
963 |
by (blast_tac (claset() addEs spies_partsEs addSEs [MPair_parts] |
|
964 |
addSDs [unique_CryptKey]) 2); |
|
965 |
by (blast_tac (claset() addSDs [A_trusts_K4, Says_Tgs_message_form, |
|
966 |
AuthKeys_used]) 1); |
|
967 |
qed "A_trusts_K4_bis"; |
|
968 |
||
969 |
||
970 |
Goal "[| Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|} \ |
|
971 |
\ : parts (spies evs); \ |
|
972 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
|
973 |
\ : parts (spies evs); \ |
|
974 |
\ ~ ExpirAuth Tk evs; ~ ExpirServ Tt evs; \ |
|
975 |
\ A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
976 |
\ ==> Key ServKey ~: analz (spies evs)"; |
|
977 |
by (dtac A_trusts_AuthKey 1); |
|
978 |
by (assume_tac 1); |
|
979 |
by (assume_tac 1); |
|
980 |
by (blast_tac (claset() addDs [Confidentiality_Kas, |
|
981 |
Says_Kas_message_form, |
|
982 |
A_trusts_K4_bis, Confidentiality_Tgs2]) 1); |
|
983 |
qed "Confidentiality_Serv_A"; |
|
984 |
||
985 |
||
986 |
(********************** Guarantees for Bob *****************************) |
|
987 |
(* Theorems for the refined model have suffix "refined" *) |
|
988 |
||
989 |
Goal |
|
990 |
"[| Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|})\ |
|
991 |
\ : set evs; evs : kerberos|] \ |
|
992 |
\ ==> EX Tk. Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk,\ |
|
993 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
994 |
\ : set evs"; |
|
995 |
by (etac rev_mp 1); |
|
996 |
by (parts_induct_tac 1); |
|
997 |
by Auto_tac; |
|
998 |
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj RS parts.Fst RS |
|
999 |
A_trusts_AuthTicket]) 1); |
|
1000 |
qed "K4_imp_K2"; |
|
1001 |
||
1002 |
Goal |
|
1003 |
"[| Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|})\ |
|
1004 |
\ : set evs; evs : kerberos|] \ |
|
1005 |
\ ==> EX Tk. (Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk,\ |
|
1006 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
1007 |
\ : set evs \ |
|
1008 |
\ & ServLife + Tt <= AuthLife + Tk)"; |
|
1009 |
by (etac rev_mp 1); |
|
1010 |
by (parts_induct_tac 1); |
|
1011 |
by Auto_tac; |
|
1012 |
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj RS parts.Fst RS |
|
1013 |
A_trusts_AuthTicket]) 1); |
|
1014 |
qed "K4_imp_K2_refined"; |
|
1015 |
||
1016 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|} \ |
|
1017 |
\ : parts (spies evs); B ~= Tgs; B ~: bad; \ |
|
1018 |
\ evs : kerberos |] \ |
|
1019 |
\==> EX AuthKey. \ |
|
1020 |
\ Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Tt, \ |
|
1021 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|}|}) \ |
|
1022 |
\ : set evs"; |
|
1023 |
by (etac rev_mp 1); |
|
1024 |
by (parts_induct_tac 1); |
|
1025 |
by (Fake_parts_insert_tac 1); |
|
1026 |
by (Blast_tac 1); |
|
1027 |
qed "B_trusts_ServKey"; |
|
1028 |
||
1029 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
1030 |
\ : parts (spies evs); B ~= Tgs; B ~: bad; \ |
|
1031 |
\ evs : kerberos |] \ |
|
1032 |
\ ==> EX AuthKey Tk. Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk,\ |
|
1033 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
1034 |
\ : set evs"; |
|
1035 |
by (blast_tac (claset() addSDs [B_trusts_ServKey, K4_imp_K2]) 1); |
|
1036 |
qed "B_trusts_ServTicket_Kas"; |
|
1037 |
||
1038 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
1039 |
\ : parts (spies evs); B ~= Tgs; B ~: bad; \ |
|
1040 |
\ evs : kerberos |] \ |
|
1041 |
\ ==> EX AuthKey Tk. (Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk,\ |
|
1042 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
1043 |
\ : set evs \ |
|
1044 |
\ & ServLife + Tt <= AuthLife + Tk)"; |
|
1045 |
by (blast_tac (claset() addSDs [B_trusts_ServKey,K4_imp_K2_refined]) 1); |
|
1046 |
qed "B_trusts_ServTicket_Kas_refined"; |
|
1047 |
||
1048 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
1049 |
\ : parts (spies evs); B ~= Tgs; B ~: bad; \ |
|
1050 |
\ evs : kerberos |] \ |
|
1051 |
\==> EX Tk AuthKey. \ |
|
1052 |
\ Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, \ |
|
1053 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
1054 |
\ : set evs \ |
|
1055 |
\ & Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, \ |
|
1056 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|}|}) \ |
|
1057 |
\ : set evs"; |
|
7499 | 1058 |
by (ftac B_trusts_ServKey 1); |
6452 | 1059 |
by (etac exE 4); |
7499 | 1060 |
by (ftac K4_imp_K2 4); |
6452 | 1061 |
by (Blast_tac 5); |
1062 |
by (ALLGOALS assume_tac); |
|
1063 |
qed "B_trusts_ServTicket"; |
|
1064 |
||
1065 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
1066 |
\ : parts (spies evs); B ~= Tgs; B ~: bad; \ |
|
1067 |
\ evs : kerberos |] \ |
|
1068 |
\==> EX Tk AuthKey. \ |
|
1069 |
\ (Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, \ |
|
1070 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
1071 |
\ : set evs \ |
|
1072 |
\ & Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, \ |
|
1073 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|}|}) \ |
|
1074 |
\ : set evs \ |
|
1075 |
\ & ServLife + Tt <= AuthLife + Tk)"; |
|
7499 | 1076 |
by (ftac B_trusts_ServKey 1); |
6452 | 1077 |
by (etac exE 4); |
7499 | 1078 |
by (ftac K4_imp_K2_refined 4); |
6452 | 1079 |
by (Blast_tac 5); |
1080 |
by (ALLGOALS assume_tac); |
|
1081 |
qed "B_trusts_ServTicket_refined"; |
|
1082 |
||
1083 |
||
1084 |
Goal "[| ~ ExpirServ Tt evs; ServLife + Tt <= AuthLife + Tk |] \ |
|
1085 |
\ ==> ~ ExpirAuth Tk evs"; |
|
1086 |
by (blast_tac (claset() addDs [leI,le_trans] addEs [leE]) 1); |
|
1087 |
qed "NotExpirServ_NotExpirAuth_refined"; |
|
1088 |
||
1089 |
||
1090 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
1091 |
\ : parts (spies evs); \ |
|
1092 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
|
1093 |
\ : parts (spies evs); \ |
|
1094 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}\ |
|
1095 |
\ : parts (spies evs); \ |
|
1096 |
\ ~ ExpirServ Tt evs; ~ ExpirAuth Tk evs; \ |
|
1097 |
\ A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
1098 |
\ ==> Key ServKey ~: analz (spies evs)"; |
|
7499 | 1099 |
by (ftac A_trusts_AuthKey 1); |
1100 |
by (ftac Confidentiality_Kas 3); |
|
1101 |
by (ftac B_trusts_ServTicket 6); |
|
6452 | 1102 |
by (etac exE 9); |
1103 |
by (etac exE 9); |
|
7499 | 1104 |
by (ftac Says_Kas_message_form 9); |
6452 | 1105 |
by (blast_tac (claset() addDs [A_trusts_K4, |
1106 |
unique_ServKeys, unique_AuthKeys, |
|
1107 |
Confidentiality_Tgs2]) 10); |
|
1108 |
by (ALLGOALS assume_tac); |
|
1109 |
(* |
|
1110 |
The proof above executes in 8 secs. It can be done in one command in 50 secs: |
|
1111 |
by (blast_tac (claset() addDs [A_trusts_AuthKey, A_trusts_K4, |
|
1112 |
Says_Kas_message_form, B_trusts_ServTicket, |
|
1113 |
unique_ServKeys, unique_AuthKeys, |
|
1114 |
Confidentiality_Kas, |
|
1115 |
Confidentiality_Tgs2]) 1); |
|
1116 |
*) |
|
1117 |
qed "Confidentiality_B"; |
|
1118 |
||
1119 |
||
1120 |
(*Most general form -- only for refined model! *) |
|
1121 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
1122 |
\ : parts (spies evs); \ |
|
1123 |
\ ~ ExpirServ Tt evs; \ |
|
1124 |
\ A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
1125 |
\ ==> Key ServKey ~: analz (spies evs)"; |
|
1126 |
by (blast_tac (claset() addDs [B_trusts_ServTicket_refined, |
|
1127 |
NotExpirServ_NotExpirAuth_refined, |
|
1128 |
Confidentiality_Tgs2]) 1); |
|
1129 |
qed "Confidentiality_B_refined"; |
|
1130 |
||
1131 |
||
1132 |
(********************** Authenticity theorems *****************************) |
|
1133 |
||
1134 |
(***1. Session Keys authenticity: they originated with servers.***) |
|
1135 |
||
1136 |
(*Authenticity of AuthKey for A: "A_trusts_AuthKey"*) |
|
1137 |
||
1138 |
(*Authenticity of ServKey for A: "A_trusts_ServKey"*) |
|
1139 |
Goal "[| Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|} \ |
|
1140 |
\ : parts (spies evs); \ |
|
1141 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
|
1142 |
\ : parts (spies evs); \ |
|
1143 |
\ ~ ExpirAuth Tk evs; A ~: bad; evs : kerberos |] \ |
|
1144 |
\==>Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|})\ |
|
1145 |
\ : set evs"; |
|
7499 | 1146 |
by (ftac A_trusts_AuthKey 1 THEN assume_tac 1 THEN assume_tac 1); |
6452 | 1147 |
by (blast_tac (claset() addDs [Confidentiality_Auth_A, A_trusts_K4_bis]) 1); |
1148 |
qed "A_trusts_ServKey"; |
|
1149 |
(*Note: requires a temporal check*) |
|
1150 |
||
1151 |
||
1152 |
(*Authenticity of ServKey for B: "B_trusts_ServKey"*) |
|
1153 |
||
1154 |
(***2. Parties authenticity: each party verifies "the identity of |
|
1155 |
another party who generated some data" (quoted from Neuman & Ts'o).***) |
|
1156 |
||
1157 |
(*These guarantees don't assess whether two parties agree on |
|
1158 |
the same session key: sending a message containing a key |
|
1159 |
doesn't a priori state knowledge of the key.***) |
|
1160 |
||
1161 |
(*B checks authenticity of A: theorems "A_Authenticity", |
|
1162 |
"A_authenticity_refined" *) |
|
1163 |
Goal "[| Crypt ServKey {|Agent A, Number Ta|} : parts (spies evs); \ |
|
1164 |
\ Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, \ |
|
1165 |
\ ServTicket|}) : set evs; \ |
|
1166 |
\ Key ServKey ~: analz (spies evs); \ |
|
1167 |
\ A ~: bad; B ~: bad; evs : kerberos |] \ |
|
1168 |
\==> Says A B {|ServTicket, Crypt ServKey {|Agent A, Number Ta|}|} : set evs"; |
|
1169 |
by (etac rev_mp 1); |
|
1170 |
by (etac rev_mp 1); |
|
1171 |
by (etac rev_mp 1); |
|
1172 |
by (etac kerberos.induct 1); |
|
7499 | 1173 |
by (ftac Says_ticket_in_parts_spies 5); |
1174 |
by (ftac Says_ticket_in_parts_spies 7); |
|
6452 | 1175 |
by (REPEAT (FIRSTGOAL analz_mono_contra_tac)); |
1176 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
|
1177 |
by (Fake_parts_insert_tac 1); |
|
1178 |
(*K3*) |
|
1179 |
by (blast_tac (claset() addEs spies_partsEs |
|
1180 |
addDs [A_trusts_AuthKey, |
|
1181 |
Says_Kas_message_form, |
|
1182 |
Says_Tgs_message_form]) 1); |
|
1183 |
(*K4*) |
|
1184 |
by (force_tac (claset() addSDs [Crypt_imp_keysFor], simpset()) 1); |
|
1185 |
(*K5*) |
|
1186 |
by (blast_tac (claset() addDs [Key_unique_SesKey] addEs spies_partsEs) 1); |
|
1187 |
qed "Says_Auth"; |
|
1188 |
||
1189 |
(*The second assumption tells B what kind of key ServKey is.*) |
|
1190 |
Goal "[| Crypt ServKey {|Agent A, Number Ta|} : parts (spies evs); \ |
|
1191 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
1192 |
\ : parts (spies evs); \ |
|
1193 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
|
1194 |
\ : parts (spies evs); \ |
|
1195 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|} \ |
|
1196 |
\ : parts (spies evs); \ |
|
1197 |
\ ~ ExpirServ Tt evs; ~ ExpirAuth Tk evs; \ |
|
1198 |
\ B ~= Tgs; A ~: bad; B ~: bad; evs : kerberos |] \ |
|
1199 |
\ ==> Says A B {|Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|},\ |
|
1200 |
\ Crypt ServKey {|Agent A, Number Ta|} |} : set evs"; |
|
7499 | 1201 |
by (ftac Confidentiality_B 1); |
1202 |
by (ftac B_trusts_ServKey 9); |
|
6452 | 1203 |
by (etac exE 12); |
1204 |
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj, Key_unique_SesKey] |
|
1205 |
addSIs [Says_Auth]) 12); |
|
1206 |
by (ALLGOALS assume_tac); |
|
1207 |
qed "A_Authenticity"; |
|
1208 |
||
1209 |
(*Stronger form in the refined model*) |
|
1210 |
Goal "[| Crypt ServKey {|Agent A, Number Ta2|} : parts (spies evs); \ |
|
1211 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
1212 |
\ : parts (spies evs); \ |
|
1213 |
\ ~ ExpirServ Tt evs; \ |
|
1214 |
\ B ~= Tgs; A ~: bad; B ~: bad; evs : kerberos |] \ |
|
1215 |
\ ==> Says A B {|Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|},\ |
|
1216 |
\ Crypt ServKey {|Agent A, Number Ta2|} |} : set evs"; |
|
7499 | 1217 |
by (ftac Confidentiality_B_refined 1); |
1218 |
by (ftac B_trusts_ServKey 6); |
|
6452 | 1219 |
by (etac exE 9); |
1220 |
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj, Key_unique_SesKey] |
|
1221 |
addSIs [Says_Auth]) 9); |
|
1222 |
by (ALLGOALS assume_tac); |
|
1223 |
qed "A_Authenticity_refined"; |
|
1224 |
||
1225 |
||
1226 |
(*A checks authenticity of B: theorem "B_authenticity"*) |
|
1227 |
||
1228 |
Goal "[| Crypt ServKey (Number Ta) : parts (spies evs); \ |
|
1229 |
\ Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, \ |
|
1230 |
\ ServTicket|}) : set evs; \ |
|
1231 |
\ Key ServKey ~: analz (spies evs); \ |
|
1232 |
\ A ~: bad; B ~: bad; evs : kerberos |] \ |
|
1233 |
\ ==> Says B A (Crypt ServKey (Number Ta)) : set evs"; |
|
1234 |
by (etac rev_mp 1); |
|
1235 |
by (etac rev_mp 1); |
|
1236 |
by (etac rev_mp 1); |
|
1237 |
by (etac kerberos.induct 1); |
|
7499 | 1238 |
by (ftac Says_ticket_in_parts_spies 5); |
1239 |
by (ftac Says_ticket_in_parts_spies 7); |
|
6452 | 1240 |
by (REPEAT (FIRSTGOAL analz_mono_contra_tac)); |
1241 |
by (ALLGOALS Asm_simp_tac); |
|
1242 |
by (Fake_parts_insert_tac 1); |
|
1243 |
by (force_tac (claset() addSDs [Crypt_imp_keysFor], simpset()) 1); |
|
1244 |
by (Clarify_tac 1); |
|
7499 | 1245 |
by (ftac Says_Tgs_message_form 1 THEN assume_tac 1); |
6452 | 1246 |
by (Clarify_tac 1); (*PROOF FAILED if omitted*) |
1247 |
by (blast_tac (claset() addDs [unique_CryptKey] addEs spies_partsEs) 1); |
|
1248 |
qed "Says_K6"; |
|
1249 |
||
1250 |
Goal "[| Crypt AuthKey {|Key ServKey, Agent B, T, ServTicket|} \ |
|
1251 |
\ : parts (spies evs); \ |
|
1252 |
\ Key AuthKey ~: analz (spies evs); AuthKey ~: range shrK; \ |
|
1253 |
\ evs : kerberos |] \ |
|
1254 |
\ ==> EX A. Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, T, ServTicket|})\ |
|
1255 |
\ : set evs"; |
|
1256 |
by (etac rev_mp 1); |
|
1257 |
by (etac rev_mp 1); |
|
1258 |
by (parts_induct_tac 1); |
|
1259 |
by (Fake_parts_insert_tac 1); |
|
1260 |
by (Blast_tac 1); |
|
1261 |
by (Blast_tac 1); |
|
1262 |
qed "K4_trustworthy"; |
|
1263 |
||
1264 |
Goal "[| Crypt ServKey (Number Ta) : parts (spies evs); \ |
|
1265 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
|
1266 |
\ : parts (spies evs); \ |
|
1267 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}\ |
|
1268 |
\ : parts (spies evs); \ |
|
1269 |
\ ~ ExpirAuth Tk evs; ~ ExpirServ Tt evs; \ |
|
1270 |
\ A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
1271 |
\ ==> Says B A (Crypt ServKey (Number Ta)) : set evs"; |
|
7499 | 1272 |
by (ftac A_trusts_AuthKey 1); |
1273 |
by (ftac Says_Kas_message_form 3); |
|
1274 |
by (ftac Confidentiality_Kas 4); |
|
1275 |
by (ftac K4_trustworthy 7); |
|
6452 | 1276 |
by (Blast_tac 8); |
1277 |
by (etac exE 9); |
|
7499 | 1278 |
by (ftac K4_imp_K2 9); |
6452 | 1279 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj, Key_unique_SesKey] |
1280 |
addSIs [Says_K6] |
|
1281 |
addSEs [Confidentiality_Tgs1 RSN (2,rev_notE)]) 10); |
|
1282 |
by (ALLGOALS assume_tac); |
|
1283 |
qed "B_Authenticity"; |
|
1284 |
||
1285 |
||
1286 |
(***3. Parties' knowledge of session keys. A knows a session key if she |
|
1287 |
used it to build a cipher.***) |
|
1288 |
||
1289 |
Goal "[| Says B A (Crypt ServKey (Number Ta)) : set evs; \ |
|
1290 |
\ Key ServKey ~: analz (spies evs); \ |
|
1291 |
\ A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
1292 |
\ ==> B Issues A with (Crypt ServKey (Number Ta)) on evs"; |
|
1293 |
by (simp_tac (simpset() addsimps [Issues_def]) 1); |
|
1294 |
by (rtac exI 1); |
|
1295 |
by (rtac conjI 1); |
|
1296 |
by (assume_tac 1); |
|
1297 |
by (Simp_tac 1); |
|
1298 |
by (etac rev_mp 1); |
|
1299 |
by (etac rev_mp 1); |
|
1300 |
by (etac kerberos.induct 1); |
|
7499 | 1301 |
by (ftac Says_ticket_in_parts_spies 5); |
1302 |
by (ftac Says_ticket_in_parts_spies 7); |
|
6452 | 1303 |
by (REPEAT (FIRSTGOAL analz_mono_contra_tac)); |
1304 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
|
1305 |
by (Fake_parts_insert_tac 1); |
|
1306 |
(*K6 requires numerous lemmas*) |
|
1307 |
by (asm_full_simp_tac (simpset() addsimps [takeWhile_tail]) 1); |
|
1308 |
by (blast_tac (claset() addDs [B_trusts_ServTicket, |
|
1309 |
impOfSubs parts_spies_takeWhile_mono, |
|
1310 |
impOfSubs parts_spies_evs_revD2] |
|
1311 |
addIs [Says_K6] |
|
1312 |
addEs spies_partsEs) 1); |
|
1313 |
qed "B_Knows_B_Knows_ServKey_lemma"; |
|
1314 |
(*Key ServKey ~: analz (spies evs) could be relaxed by Confidentiality_B |
|
1315 |
but this is irrelevant because B knows what he knows! *) |
|
1316 |
||
1317 |
Goal "[| Says B A (Crypt ServKey (Number Ta)) : set evs; \ |
|
1318 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|}\ |
|
1319 |
\ : parts (spies evs);\ |
|
1320 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}\ |
|
1321 |
\ : parts (spies evs);\ |
|
1322 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}\ |
|
1323 |
\ : parts (spies evs); \ |
|
1324 |
\ ~ ExpirServ Tt evs; ~ ExpirAuth Tk evs; \ |
|
1325 |
\ A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
1326 |
\ ==> B Issues A with (Crypt ServKey (Number Ta)) on evs"; |
|
1327 |
by (blast_tac (claset() addSDs [Confidentiality_B, |
|
1328 |
B_Knows_B_Knows_ServKey_lemma]) 1); |
|
1329 |
qed "B_Knows_B_Knows_ServKey"; |
|
1330 |
||
1331 |
Goal "[| Says B A (Crypt ServKey (Number Ta)) : set evs; \ |
|
1332 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|}\ |
|
1333 |
\ : parts (spies evs);\ |
|
1334 |
\ ~ ExpirServ Tt evs; \ |
|
1335 |
\ A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
1336 |
\ ==> B Issues A with (Crypt ServKey (Number Ta)) on evs"; |
|
1337 |
by (blast_tac (claset() addSDs [Confidentiality_B_refined, |
|
1338 |
B_Knows_B_Knows_ServKey_lemma]) 1); |
|
1339 |
qed "B_Knows_B_Knows_ServKey_refined"; |
|
1340 |
||
1341 |
||
1342 |
Goal "[| Crypt ServKey (Number Ta) : parts (spies evs); \ |
|
1343 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
|
1344 |
\ : parts (spies evs); \ |
|
1345 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}\ |
|
1346 |
\ : parts (spies evs); \ |
|
1347 |
\ ~ ExpirAuth Tk evs; ~ ExpirServ Tt evs; \ |
|
1348 |
\ A ~: bad; B ~: bad; B ~= Tgs; evs : kerberos |] \ |
|
1349 |
\ ==> B Issues A with (Crypt ServKey (Number Ta)) on evs"; |
|
1350 |
by (blast_tac (claset() addSDs [B_Authenticity, Confidentiality_Serv_A, |
|
1351 |
B_Knows_B_Knows_ServKey_lemma]) 1); |
|
1352 |
qed "A_Knows_B_Knows_ServKey"; |
|
1353 |
||
1354 |
Goal "[| Says A Tgs \ |
|
1355 |
\ {|AuthTicket, Crypt AuthKey {|Agent A, Number Ta|}, Agent B|}\ |
|
1356 |
\ : set evs; \ |
|
1357 |
\ A ~: bad; evs : kerberos |] \ |
|
1358 |
\ ==> EX Tk. Says Kas A (Crypt (shrK A) \ |
|
1359 |
\ {|Key AuthKey, Agent Tgs, Tk, AuthTicket|}) \ |
|
1360 |
\ : set evs"; |
|
1361 |
by (etac rev_mp 1); |
|
1362 |
by (parts_induct_tac 1); |
|
1363 |
by (Fake_parts_insert_tac 1); |
|
1364 |
by (Blast_tac 1); |
|
1365 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj RS |
|
1366 |
A_trusts_AuthKey]) 1); |
|
1367 |
qed "K3_imp_K2"; |
|
1368 |
||
1369 |
Goal "[| Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
|
1370 |
\ : parts (spies evs); \ |
|
1371 |
\ Says Kas A (Crypt (shrK A) \ |
|
1372 |
\ {|Key AuthKey, Agent Tgs, Tk, AuthTicket|}) \ |
|
1373 |
\ : set evs; \ |
|
1374 |
\ Key AuthKey ~: analz (spies evs); \ |
|
1375 |
\ B ~= Tgs; A ~: bad; B ~: bad; evs : kerberos |] \ |
|
1376 |
\ ==> Says Tgs A (Crypt AuthKey \ |
|
1377 |
\ {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
|
1378 |
\ : set evs"; |
|
1379 |
by (etac rev_mp 1); |
|
1380 |
by (etac rev_mp 1); |
|
1381 |
by (etac rev_mp 1); |
|
1382 |
by (parts_induct_tac 1); |
|
1383 |
by (Fake_parts_insert_tac 1); |
|
1384 |
by (force_tac (claset() addSDs [Crypt_imp_keysFor], simpset()) 1); |
|
1385 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj RS parts.Fst RS |
|
1386 |
A_trusts_AuthTicket, unique_AuthKeys]) 1); |
|
1387 |
qed "K4_trustworthy'"; |
|
1388 |
||
1389 |
Goal "[| Says A B {|ServTicket, Crypt ServKey {|Agent A, Number Ta|}|} \ |
|
1390 |
\ : set evs; \ |
|
1391 |
\ Key ServKey ~: analz (spies evs); \ |
|
1392 |
\ B ~= Tgs; A ~: bad; B ~: bad; evs : kerberos |] \ |
|
1393 |
\ ==> A Issues B with (Crypt ServKey {|Agent A, Number Ta|}) on evs"; |
|
1394 |
by (simp_tac (simpset() addsimps [Issues_def]) 1); |
|
1395 |
by (rtac exI 1); |
|
1396 |
by (rtac conjI 1); |
|
1397 |
by (assume_tac 1); |
|
1398 |
by (Simp_tac 1); |
|
1399 |
by (etac rev_mp 1); |
|
1400 |
by (etac rev_mp 1); |
|
1401 |
by (etac kerberos.induct 1); |
|
7499 | 1402 |
by (ftac Says_ticket_in_parts_spies 5); |
1403 |
by (ftac Says_ticket_in_parts_spies 7); |
|
6452 | 1404 |
by (REPEAT (FIRSTGOAL analz_mono_contra_tac)); |
1405 |
by (ALLGOALS Asm_simp_tac); |
|
1406 |
by (Clarify_tac 1); |
|
1407 |
(*K6*) |
|
1408 |
by Auto_tac; |
|
1409 |
by (asm_full_simp_tac (simpset() addsimps [takeWhile_tail]) 1); |
|
1410 |
(*Level 15: case study necessary because the assumption doesn't state |
|
1411 |
the form of ServTicket. The guarantee becomes stronger.*) |
|
1412 |
by (case_tac "Key AuthKey : analz (spies evs5)" 1); |
|
1413 |
by (force_tac (claset() addDs [Says_imp_spies RS analz.Inj RS |
|
1414 |
analz.Decrypt RS analz.Fst], |
|
1415 |
simpset()) 1); |
|
1416 |
by (blast_tac (claset() addDs [K3_imp_K2, K4_trustworthy', |
|
1417 |
impOfSubs parts_spies_takeWhile_mono, |
|
1418 |
impOfSubs parts_spies_evs_revD2] |
|
1419 |
addIs [Says_Auth] |
|
1420 |
addEs spies_partsEs) 1); |
|
1421 |
by (asm_full_simp_tac (simpset() addsimps [takeWhile_tail]) 1); |
|
1422 |
qed "A_Knows_A_Knows_ServKey_lemma"; |
|
1423 |
||
1424 |
Goal "[| Says A B {|ServTicket, Crypt ServKey {|Agent A, Number Ta|}|} \ |
|
1425 |
\ : set evs; \ |
|
1426 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}\ |
|
1427 |
\ : parts (spies evs);\ |
|
1428 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}\ |
|
1429 |
\ : parts (spies evs); \ |
|
1430 |
\ ~ ExpirAuth Tk evs; ~ ExpirServ Tt evs;\ |
|
1431 |
\ B ~= Tgs; A ~: bad; B ~: bad; evs : kerberos |] \ |
|
1432 |
\ ==> A Issues B with (Crypt ServKey {|Agent A, Number Ta|}) on evs"; |
|
1433 |
by (blast_tac (claset() addSDs [Confidentiality_Serv_A, |
|
1434 |
A_Knows_A_Knows_ServKey_lemma]) 1); |
|
1435 |
qed "A_Knows_A_Knows_ServKey"; |
|
1436 |
||
1437 |
Goal "[| Crypt ServKey {|Agent A, Number Ta|} : parts (spies evs); \ |
|
1438 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
1439 |
\ : parts (spies evs); \ |
|
1440 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
|
1441 |
\ : parts (spies evs); \ |
|
1442 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|} \ |
|
1443 |
\ : parts (spies evs); \ |
|
1444 |
\ ~ ExpirServ Tt evs; ~ ExpirAuth Tk evs; \ |
|
1445 |
\ B ~= Tgs; A ~: bad; B ~: bad; evs : kerberos |] \ |
|
1446 |
\ ==> A Issues B with (Crypt ServKey {|Agent A, Number Ta|}) on evs"; |
|
1447 |
by (blast_tac (claset() addDs [A_Authenticity, Confidentiality_B, |
|
1448 |
A_Knows_A_Knows_ServKey_lemma]) 1); |
|
1449 |
qed "B_Knows_A_Knows_ServKey"; |
|
1450 |
||
1451 |
||
1452 |
Goal "[| Crypt ServKey {|Agent A, Number Ta|} : parts (spies evs); \ |
|
1453 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
1454 |
\ : parts (spies evs); \ |
|
1455 |
\ ~ ExpirServ Tt evs; \ |
|
1456 |
\ B ~= Tgs; A ~: bad; B ~: bad; evs : kerberos |] \ |
|
1457 |
\ ==> A Issues B with (Crypt ServKey {|Agent A, Number Ta|}) on evs"; |
|
1458 |
by (blast_tac (claset() addDs [A_Authenticity_refined, |
|
1459 |
Confidentiality_B_refined, |
|
1460 |
A_Knows_A_Knows_ServKey_lemma]) 1); |
|
1461 |
qed "B_Knows_A_Knows_ServKey_refined"; |