author | wenzelm |
Wed, 03 Oct 2001 20:54:16 +0200 | |
changeset 11655 | 923e4d0d36d5 |
parent 11288 | 7fe6593133d4 |
child 13630 | a013a9dd370f |
permissions | -rw-r--r-- |
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(* 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. Proofs streamlined by lcp. |
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*) |
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AddDs [Says_imp_knows_Spy RS parts.Inj, parts.Body]; |
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AddDs [impOfSubs analz_subset_parts, impOfSubs Fake_parts_insert]; |
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Pretty.setdepth 20; |
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set timing; |
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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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(*****************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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Goalw [AuthKeys_def] |
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"(\\<forall>A Tk akey Peer. \ |
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\ ev \\<noteq> 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 \\<in> 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 \\<in> 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|})|}) \\<in> set evs \ |
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\ ==> K \\<in> AuthKeys evs"; |
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by Auto_tac; |
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qed "AuthKeysI"; |
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Goalw [AuthKeys_def] "K \\<in> AuthKeys evs ==> Key K \\<in> used evs"; |
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by (Simp_tac 1); |
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by (Blast_tac 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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\ \\<in> set evs ==> AuthTicket \\<in> parts (spies evs)"; |
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by (Blast_tac 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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\ \\<in> set evs ==> AuthKey \\<in> parts (spies evs)"; |
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by (Blast_tac 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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\ \\<in> set evs ;\ |
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\ evs \\<in> kerberos |] ==> AuthKey \\<notin> 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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\ \\<in> set evs ==> ServTicket \\<in> parts (spies evs)"; |
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by (Blast_tac 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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\ \\<in> set evs ==> ServKey \\<in> parts (spies evs)"; |
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by (Blast_tac 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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\ \\<in> set evs ;\ |
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\ evs \\<in> kerberos |] ==> ServKey \\<notin> 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|}) \\<in> set evs \ |
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\ ==> Ticket \\<in> parts (spies evs)"; |
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by (Blast_tac 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 \\<in> kerberos ==> (Key (shrK A) \\<in> parts (spies evs)) = (A \\<in> bad)"; |
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by (parts_induct_tac 1); |
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by (ALLGOALS Blast_tac); |
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qed "Spy_see_shrK"; |
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Addsimps [Spy_see_shrK]; |
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Goal "evs \\<in> kerberos ==> (Key (shrK A) \\<in> analz (spies evs)) = (A \\<in> bad)"; |
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by Auto_tac; |
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qed "Spy_analz_shrK"; |
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Addsimps [Spy_analz_shrK]; |
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Goal "[| Key (shrK A) \\<in> parts (spies evs); evs \\<in> 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 \\<in> kerberos ==> \ |
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\ Key K \\<notin> used evs --> K \\<notin> keysFor (parts (spies evs))"; |
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by (parts_induct_tac 1); |
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(*Fake*) |
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by (blast_tac (claset() addSDs [keysFor_parts_insert]) 1); |
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(*Others*) |
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by (ALLGOALS Blast_tac); |
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qed_spec_mp "new_keys_not_used"; |
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Addsimps [new_keys_not_used]; |
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(*Earlier, all protocol proofs declared this theorem. |
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But few of them actually need it! (Another is Yahalom) *) |
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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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(*********************** 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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\ \\<in> set evs; \ |
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\ evs \\<in> kerberos |] \ |
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\ ==> AuthKey \\<notin> range shrK & AuthKey \\<in> 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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\ \\<in> parts (spies evs); Tgs_B \\<notin> bad;\ |
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\ evs \\<in> kerberos |] \ |
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\ ==> SesKey \\<notin> 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 (Blast_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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\ \\<in> parts (spies evs); \ |
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\ evs \\<in> 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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\ \\<in> set evs"; |
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by (etac rev_mp 1); |
234 |
by (parts_induct_tac 1); |
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(*Fake, K4*) |
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by (ALLGOALS Blast_tac); |
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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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\ \\<in> parts (spies evs);\ |
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\ evs \\<in> kerberos |] \ |
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\ ==> AuthKey \\<in> AuthKeys evs"; |
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by (ftac A_trusts_AuthTicket 1); |
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by (assume_tac 1); |
245 |
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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\ \\<in> set evs; \ |
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\ evs \\<in> kerberos |] \ |
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\ ==> B \\<noteq> Tgs & ServKey \\<notin> range shrK & ServKey \\<notin> AuthKeys evs &\ |
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\ ServTicket = (Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|} ) & \ |
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\ AuthKey \\<notin> range shrK & AuthKey \\<in> AuthKeys evs"; |
6452 | 256 |
by (etac rev_mp 1); |
257 |
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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261 |
AuthKeys_empty, AuthKeys_simp]))); |
|
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by (Blast_tac 1); |
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by Auto_tac; |
11288 | 264 |
(*Three subcases of Message 4*) |
6452 | 265 |
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]) 1); |
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by (blast_tac (claset() addDs [AuthTicket_crypt_AuthKey]) 1); |
|
6452 | 268 |
qed "Says_Tgs_message_form"; |
269 |
||
270 |
(*If a certain encrypted message appears then it originated with Kas*) |
|
271 |
Goal "[| Crypt (shrK A) {|Key AuthKey, Peer, Tk, AuthTicket|} \ |
|
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\ \\<in> parts (spies evs); \ |
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273 |
\ A \\<notin> bad; evs \\<in> kerberos |] \ |
6452 | 274 |
\ ==> Says Kas A (Crypt (shrK A) {|Key AuthKey, Peer, Tk, AuthTicket|}) \ |
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275 |
\ \\<in> set evs"; |
6452 | 276 |
by (etac rev_mp 1); |
277 |
by (parts_induct_tac 1); |
|
278 |
(*Fake*) |
|
11222 | 279 |
by (Blast_tac 1); |
6452 | 280 |
(*K4*) |
11222 | 281 |
by (blast_tac (claset() addSDs [A_trusts_AuthTicket RS Says_Kas_message_form]) |
6452 | 282 |
1); |
283 |
qed "A_trusts_AuthKey"; |
|
284 |
||
285 |
||
286 |
(*If a certain encrypted message appears then it originated with Tgs*) |
|
287 |
Goal "[| Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|} \ |
|
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288 |
\ \\<in> parts (spies evs); \ |
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289 |
\ Key AuthKey \\<notin> analz (spies evs); \ |
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290 |
\ AuthKey \\<notin> range shrK; \ |
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291 |
\ evs \\<in> kerberos |] \ |
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292 |
\==> \\<exists>A. Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|})\ |
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293 |
\ \\<in> set evs"; |
6452 | 294 |
by (etac rev_mp 1); |
295 |
by (etac rev_mp 1); |
|
296 |
by (parts_induct_tac 1); |
|
297 |
(*Fake*) |
|
11222 | 298 |
by (Blast_tac 1); |
6452 | 299 |
(*K2*) |
300 |
by (Blast_tac 1); |
|
301 |
(*K4*) |
|
302 |
by Auto_tac; |
|
303 |
qed "A_trusts_K4"; |
|
304 |
||
305 |
Goal "[| Crypt (shrK A) {|Key AuthKey, Agent Tgs, Tk, AuthTicket|} \ |
|
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306 |
\ \\<in> parts (spies evs); \ |
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307 |
\ A \\<notin> bad; \ |
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308 |
\ evs \\<in> kerberos |] \ |
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309 |
\ ==> AuthKey \\<notin> range shrK & \ |
6452 | 310 |
\ AuthTicket = Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Tk|}"; |
311 |
by (etac rev_mp 1); |
|
312 |
by (parts_induct_tac 1); |
|
11222 | 313 |
by (ALLGOALS Blast_tac); |
6452 | 314 |
qed "AuthTicket_form"; |
315 |
||
316 |
(* This form holds also over an AuthTicket, but is not needed below. *) |
|
317 |
Goal "[| Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|} \ |
|
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318 |
\ \\<in> parts (spies evs); \ |
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319 |
\ Key AuthKey \\<notin> analz (spies evs); \ |
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320 |
\ evs \\<in> kerberos |] \ |
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321 |
\ ==> ServKey \\<notin> range shrK & \ |
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322 |
\ (\\<exists>A. ServTicket = Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|})"; |
6452 | 323 |
by (etac rev_mp 1); |
324 |
by (etac rev_mp 1); |
|
325 |
by (parts_induct_tac 1); |
|
11222 | 326 |
by (Blast_tac 1); |
6452 | 327 |
qed "ServTicket_form"; |
328 |
||
329 |
Goal "[| Says Kas' A (Crypt (shrK A) \ |
|
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330 |
\ {|Key AuthKey, Agent Tgs, Tk, AuthTicket|} ) \\<in> set evs; \ |
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331 |
\ evs \\<in> kerberos |] \ |
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332 |
\ ==> AuthKey \\<notin> range shrK & \ |
6452 | 333 |
\ AuthTicket = \ |
334 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Tk|}\ |
|
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335 |
\ | AuthTicket \\<in> analz (spies evs)"; |
11222 | 336 |
by (blast_tac (claset() addDs [Says_imp_spies RS analz.Inj, |
337 |
AuthTicket_form]) 1); |
|
6452 | 338 |
qed "Says_kas_message_form"; |
339 |
(* Essentially the same as AuthTicket_form *) |
|
340 |
||
341 |
Goal "[| Says Tgs' A (Crypt AuthKey \ |
|
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342 |
\ {|Key ServKey, Agent B, Tt, ServTicket|} ) \\<in> set evs; \ |
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343 |
\ evs \\<in> kerberos |] \ |
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344 |
\ ==> ServKey \\<notin> range shrK & \ |
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345 |
\ (\\<exists>A. ServTicket = \ |
6452 | 346 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|}) \ |
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347 |
\ | ServTicket \\<in> analz (spies evs)"; |
11222 | 348 |
by (blast_tac (claset() addDs [Says_imp_spies RS analz.Inj, |
349 |
ServTicket_form]) 1); |
|
6452 | 350 |
qed "Says_tgs_message_form"; |
351 |
(* This form MUST be used in analz_sees_tac below *) |
|
352 |
||
353 |
||
354 |
(*****************UNICITY THEOREMS****************) |
|
355 |
||
356 |
(* The session key, if secure, uniquely identifies the Ticket |
|
357 |
whether AuthTicket or ServTicket. As a matter of fact, one can read |
|
358 |
also Tgs in the place of B. *) |
|
359 |
||
360 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key SesKey, T|} \ |
|
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361 |
\ \\<in> parts (spies evs); \ |
6452 | 362 |
\ Crypt (shrK B') {|Agent A', Agent B', Key SesKey, T'|} \ |
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363 |
\ \\<in> parts (spies evs); Key SesKey \\<notin> analz (spies evs); \ |
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364 |
\ evs \\<in> kerberos |] \ |
6452 | 365 |
\ ==> A=A' & B=B' & T=T'"; |
11104 | 366 |
by (etac rev_mp 1); |
367 |
by (etac rev_mp 1); |
|
368 |
by (etac rev_mp 1); |
|
369 |
by (parts_induct_tac 1); |
|
370 |
(*Fake, K2, K4*) |
|
11222 | 371 |
by (ALLGOALS Blast_tac); |
6452 | 372 |
qed "unique_CryptKey"; |
373 |
||
374 |
(*An AuthKey is encrypted by one and only one Shared key. |
|
375 |
A ServKey is encrypted by one and only one AuthKey. |
|
376 |
*) |
|
377 |
Goal "[| Crypt K {|Key SesKey, Agent B, T, Ticket|} \ |
|
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378 |
\ \\<in> parts (spies evs); \ |
6452 | 379 |
\ Crypt K' {|Key SesKey, Agent B', T', Ticket'|} \ |
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380 |
\ \\<in> parts (spies evs); Key SesKey \\<notin> analz (spies evs); \ |
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|
381 |
\ evs \\<in> kerberos |] \ |
6452 | 382 |
\ ==> K=K' & B=B' & T=T' & Ticket=Ticket'"; |
11104 | 383 |
by (etac rev_mp 1); |
384 |
by (etac rev_mp 1); |
|
385 |
by (etac rev_mp 1); |
|
386 |
by (parts_induct_tac 1); |
|
387 |
(*Fake, K2, K4*) |
|
11222 | 388 |
by (ALLGOALS Blast_tac); |
6452 | 389 |
qed "Key_unique_SesKey"; |
390 |
||
391 |
||
392 |
(* |
|
393 |
At reception of any message mentioning A, Kas associates shrK A with |
|
394 |
a new AuthKey. Realistic, as the user gets a new AuthKey at each login. |
|
395 |
Similarly, at reception of any message mentioning an AuthKey |
|
396 |
(a legitimate user could make several requests to Tgs - by K3), Tgs |
|
397 |
associates it with a new ServKey. |
|
398 |
||
399 |
Therefore, a goal like |
|
400 |
||
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|
401 |
"evs \\<in> kerberos \ |
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|
402 |
\ ==> Key Kc \\<notin> analz (spies evs) --> \ |
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|
403 |
\ (\\<exists>K' B' T' Ticket'. \\<forall>K B T Ticket. \ |
6452 | 404 |
\ Crypt Kc {|Key K, Agent B, T, Ticket|} \ |
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|
405 |
\ \\<in> parts (spies evs) --> K=K' & B=B' & T=T' & Ticket=Ticket')"; |
6452 | 406 |
|
407 |
would fail on the K2 and K4 cases. |
|
408 |
*) |
|
409 |
||
410 |
Goal "[| Says Kas A \ |
|
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|
411 |
\ (Crypt Ka {|Key AuthKey, Agent Tgs, Tk, X|}) \\<in> set evs; \ |
6452 | 412 |
\ Says Kas A' \ |
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|
413 |
\ (Crypt Ka' {|Key AuthKey, Agent Tgs, Tk', X'|}) \\<in> set evs; \ |
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|
414 |
\ evs \\<in> kerberos |] ==> A=A' & Ka=Ka' & Tk=Tk' & X=X'"; |
11104 | 415 |
by (etac rev_mp 1); |
416 |
by (etac rev_mp 1); |
|
417 |
by (parts_induct_tac 1); |
|
418 |
(*K2*) |
|
11222 | 419 |
by (Blast_tac 1); |
6452 | 420 |
qed "unique_AuthKeys"; |
421 |
||
422 |
(* ServKey uniquely identifies the message from Tgs *) |
|
423 |
Goal "[| Says Tgs A \ |
|
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424 |
\ (Crypt K {|Key ServKey, Agent B, Tt, X|}) \\<in> set evs; \ |
6452 | 425 |
\ Says Tgs A' \ |
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|
426 |
\ (Crypt K' {|Key ServKey, Agent B', Tt', X'|}) \\<in> set evs; \ |
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|
427 |
\ evs \\<in> kerberos |] ==> A=A' & B=B' & K=K' & Tt=Tt' & X=X'"; |
11104 | 428 |
by (etac rev_mp 1); |
429 |
by (etac rev_mp 1); |
|
430 |
by (parts_induct_tac 1); |
|
431 |
(*K4*) |
|
11222 | 432 |
by (Blast_tac 1); |
6452 | 433 |
qed "unique_ServKeys"; |
434 |
||
435 |
||
436 |
(*****************LEMMAS ABOUT the predicate KeyCryptKey****************) |
|
437 |
||
438 |
Goalw [KeyCryptKey_def] "~ KeyCryptKey AuthKey ServKey []"; |
|
439 |
by (Simp_tac 1); |
|
440 |
qed "not_KeyCryptKey_Nil"; |
|
441 |
AddIffs [not_KeyCryptKey_Nil]; |
|
442 |
||
443 |
Goalw [KeyCryptKey_def] |
|
11288 | 444 |
"[| Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, tt, X |}) \\<in> set evs; \ |
445 |
\ evs \\<in> kerberos |] ==> KeyCryptKey AuthKey ServKey evs"; |
|
11222 | 446 |
by (blast_tac (claset() addDs [Says_Tgs_message_form]) 1); |
6452 | 447 |
qed "KeyCryptKeyI"; |
448 |
||
449 |
Goalw [KeyCryptKey_def] |
|
450 |
"KeyCryptKey AuthKey ServKey (Says S A X # evs) = \ |
|
451 |
\ (Tgs = S & \ |
|
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|
452 |
\ (\\<exists>B tt. X = Crypt AuthKey \ |
6452 | 453 |
\ {|Key ServKey, Agent B, tt, \ |
454 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, tt|} |}) \ |
|
455 |
\ | KeyCryptKey AuthKey ServKey evs)"; |
|
456 |
by (Simp_tac 1); |
|
457 |
by (Blast_tac 1); |
|
458 |
qed "KeyCryptKey_Says"; |
|
459 |
Addsimps [KeyCryptKey_Says]; |
|
460 |
||
461 |
(*A fresh AuthKey cannot be associated with any other |
|
462 |
(with respect to a given trace). *) |
|
463 |
Goalw [KeyCryptKey_def] |
|
11288 | 464 |
"[| Key AuthKey \\<notin> used evs; evs \\<in> kerberos |] \ |
465 |
\ ==> ~ KeyCryptKey AuthKey ServKey evs"; |
|
6452 | 466 |
by (etac rev_mp 1); |
467 |
by (parts_induct_tac 1); |
|
468 |
by (Asm_full_simp_tac 1); |
|
11222 | 469 |
by (Blast_tac 1); |
6452 | 470 |
qed "Auth_fresh_not_KeyCryptKey"; |
471 |
||
472 |
(*A fresh ServKey cannot be associated with any other |
|
473 |
(with respect to a given trace). *) |
|
474 |
Goalw [KeyCryptKey_def] |
|
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|
475 |
"Key ServKey \\<notin> used evs ==> ~ KeyCryptKey AuthKey ServKey evs"; |
11222 | 476 |
by (Blast_tac 1); |
6452 | 477 |
qed "Serv_fresh_not_KeyCryptKey"; |
478 |
||
11288 | 479 |
Goal "[| Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, tk|}\ |
480 |
\ \\<in> parts (spies evs); evs \\<in> kerberos |] \ |
|
481 |
\ ==> ~ KeyCryptKey K AuthKey evs"; |
|
6452 | 482 |
by (etac rev_mp 1); |
483 |
by (parts_induct_tac 1); |
|
484 |
(*K4*) |
|
11222 | 485 |
by (Blast_tac 3); |
6452 | 486 |
(*K2: by freshness*) |
11204 | 487 |
by (asm_full_simp_tac (simpset() addsimps [KeyCryptKey_def]) 2); |
11222 | 488 |
by (ALLGOALS Blast_tac); |
6452 | 489 |
qed "AuthKey_not_KeyCryptKey"; |
490 |
||
491 |
(*A secure serverkey cannot have been used to encrypt others*) |
|
11204 | 492 |
Goal |
493 |
"[| Crypt (shrK B) {|Agent A, Agent B, Key SK, tt|} \\<in> parts (spies evs); \ |
|
494 |
\ Key SK \\<notin> analz (spies evs); \ |
|
495 |
\ B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
|
496 |
\ ==> ~ KeyCryptKey SK K evs"; |
|
6452 | 497 |
by (etac rev_mp 1); |
498 |
by (etac rev_mp 1); |
|
499 |
by (parts_induct_tac 1); |
|
11222 | 500 |
by (Blast_tac 1); |
6452 | 501 |
(*K4 splits into distinct subcases*) |
11204 | 502 |
by Auto_tac; |
6452 | 503 |
(*ServKey can't have been enclosed in two certificates*) |
11222 | 504 |
by (blast_tac (claset() addDs [unique_CryptKey]) 2); |
6452 | 505 |
(*ServKey is fresh and so could not have been used, by new_keys_not_used*) |
11222 | 506 |
by (force_tac (claset() addSDs [Crypt_imp_invKey_keysFor], |
507 |
simpset() addsimps [KeyCryptKey_def]) 1); |
|
6452 | 508 |
qed "ServKey_not_KeyCryptKey"; |
509 |
||
510 |
(*Long term keys are not issued as ServKeys*) |
|
511 |
Goalw [KeyCryptKey_def] |
|
11288 | 512 |
"evs \\<in> kerberos ==> ~ KeyCryptKey K (shrK A) evs"; |
6452 | 513 |
by (parts_induct_tac 1); |
514 |
qed "shrK_not_KeyCryptKey"; |
|
515 |
||
516 |
(*The Tgs message associates ServKey with AuthKey and therefore not with any |
|
517 |
other key AuthKey.*) |
|
518 |
Goalw [KeyCryptKey_def] |
|
11288 | 519 |
"[| Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, tt, X |}) \ |
520 |
\ \\<in> set evs; \ |
|
521 |
\ AuthKey' \\<noteq> AuthKey; evs \\<in> kerberos |] \ |
|
522 |
\ ==> ~ KeyCryptKey AuthKey' ServKey evs"; |
|
6452 | 523 |
by (blast_tac (claset() addDs [unique_ServKeys]) 1); |
524 |
qed "Says_Tgs_KeyCryptKey"; |
|
525 |
||
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|
526 |
Goal "[| KeyCryptKey AuthKey ServKey evs; evs \\<in> kerberos |] \ |
6452 | 527 |
\ ==> ~ KeyCryptKey ServKey K evs"; |
528 |
by (etac rev_mp 1); |
|
529 |
by (parts_induct_tac 1); |
|
11288 | 530 |
by Safe_tac; |
531 |
(*K4 splits into subcases*) |
|
6452 | 532 |
by (ALLGOALS Asm_full_simp_tac); |
11222 | 533 |
by (blast_tac (claset() addSDs [AuthKey_not_KeyCryptKey]) 4); |
6452 | 534 |
(*ServKey is fresh and so could not have been used, by new_keys_not_used*) |
535 |
by (force_tac (claset() addSDs [Says_imp_spies RS parts.Inj, |
|
536 |
Crypt_imp_invKey_keysFor], |
|
11222 | 537 |
simpset() addsimps [KeyCryptKey_def]) 2); |
6452 | 538 |
(*Others by freshness*) |
11222 | 539 |
by (ALLGOALS Blast_tac); |
6452 | 540 |
qed "KeyCryptKey_not_KeyCryptKey"; |
541 |
||
542 |
(*The only session keys that can be found with the help of session keys are |
|
543 |
those sent by Tgs in step K4. *) |
|
544 |
||
545 |
(*We take some pains to express the property |
|
546 |
as a logical equivalence so that the simplifier can apply it.*) |
|
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|
547 |
Goal "P --> (Key K \\<in> analz (Key`KK Un H)) --> (K:KK | Key K \\<in> analz H) \ |
6452 | 548 |
\ ==> \ |
11185
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|
549 |
\ P --> (Key K \\<in> analz (Key`KK Un H)) = (K:KK | Key K \\<in> analz H)"; |
6452 | 550 |
by (blast_tac (claset() addIs [impOfSubs analz_mono]) 1); |
551 |
qed "Key_analz_image_Key_lemma"; |
|
552 |
||
11185
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|
553 |
Goal "[| KeyCryptKey K K' evs; evs \\<in> kerberos |] \ |
1b737b4c2108
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|
554 |
\ ==> Key K' \\<in> analz (insert (Key K) (spies evs))"; |
6452 | 555 |
by (full_simp_tac (simpset() addsimps [KeyCryptKey_def]) 1); |
556 |
by (Clarify_tac 1); |
|
557 |
by (dresolve_tac [Says_imp_spies RS analz.Inj RS analz_insertI] 1); |
|
558 |
by Auto_tac; |
|
559 |
qed "KeyCryptKey_analz_insert"; |
|
560 |
||
11185
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|
561 |
Goal "[| K \\<in> AuthKeys evs Un range shrK; evs \\<in> kerberos |] \ |
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|
562 |
\ ==> \\<forall>SK. ~ KeyCryptKey SK K evs"; |
6452 | 563 |
by (asm_full_simp_tac (simpset() addsimps [KeyCryptKey_def]) 1); |
564 |
by (blast_tac (claset() addDs [Says_Tgs_message_form]) 1); |
|
565 |
qed "AuthKeys_are_not_KeyCryptKey"; |
|
566 |
||
11185
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|
567 |
Goal "[| K \\<notin> AuthKeys evs; \ |
1b737b4c2108
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|
568 |
\ K \\<notin> range shrK; evs \\<in> kerberos |] \ |
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|
569 |
\ ==> \\<forall>SK. ~ KeyCryptKey K SK evs"; |
6452 | 570 |
by (asm_full_simp_tac (simpset() addsimps [KeyCryptKey_def]) 1); |
571 |
by (blast_tac (claset() addDs [Says_Tgs_message_form]) 1); |
|
572 |
qed "not_AuthKeys_not_KeyCryptKey"; |
|
573 |
||
574 |
||
575 |
(*****************SECRECY THEOREMS****************) |
|
576 |
||
577 |
(*For proofs involving analz.*) |
|
578 |
val analz_sees_tac = |
|
579 |
EVERY |
|
580 |
[REPEAT (FIRSTGOAL analz_mono_contra_tac), |
|
7499 | 581 |
ftac Oops_range_spies2 10, |
582 |
ftac Oops_range_spies1 9, |
|
583 |
ftac Says_tgs_message_form 7, |
|
584 |
ftac Says_kas_message_form 5, |
|
6452 | 585 |
REPEAT_FIRST (eresolve_tac [asm_rl, conjE, disjE, exE] |
586 |
ORELSE' hyp_subst_tac)]; |
|
587 |
||
8954
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rewrote a very long proof (Key_analz_image_Key) because it had stopped working
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|
588 |
(*For the Oops2 case of the next theorem*) |
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|
589 |
Goal "[| evs \\<in> kerberos; \ |
8954
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
parents:
8741
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|
590 |
\ Says Tgs A (Crypt AuthKey \ |
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
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|
591 |
\ {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
11185
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Some X-symbols for <notin>, <noteq>, <forall>, <exists>
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|
592 |
\ \\<in> set evs |] \ |
8954
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
parents:
8741
diff
changeset
|
593 |
\ ==> ~ KeyCryptKey ServKey SK evs"; |
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
parents:
8741
diff
changeset
|
594 |
by (blast_tac (claset() addDs [KeyCryptKeyI, KeyCryptKey_not_KeyCryptKey]) 1); |
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
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diff
changeset
|
595 |
qed "Oops2_not_KeyCryptKey"; |
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
parents:
8741
diff
changeset
|
596 |
|
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
parents:
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diff
changeset
|
597 |
|
6452 | 598 |
(* Big simplification law for keys SK that are not crypted by keys in KK *) |
599 |
(* It helps prove three, otherwise hard, facts about keys. These facts are *) |
|
600 |
(* exploited as simplification laws for analz, and also "limit the damage" *) |
|
601 |
(* in case of loss of a key to the spy. See ESORICS98. *) |
|
8954
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
parents:
8741
diff
changeset
|
602 |
(* [simplified by LCP] *) |
11185
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changeset
|
603 |
Goal "evs \\<in> kerberos ==> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
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11104
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changeset
|
604 |
\ (\\<forall>SK KK. KK <= -(range shrK) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
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parents:
11104
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changeset
|
605 |
\ (\\<forall>K \\<in> KK. ~ KeyCryptKey K SK evs) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
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11104
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changeset
|
606 |
\ (Key SK \\<in> analz (Key`KK Un (spies evs))) = \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
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parents:
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changeset
|
607 |
\ (SK \\<in> KK | Key SK \\<in> analz (spies evs)))"; |
6452 | 608 |
by (etac kerberos.induct 1); |
609 |
by analz_sees_tac; |
|
610 |
by (REPEAT_FIRST (rtac allI)); |
|
611 |
by (REPEAT_FIRST (rtac (Key_analz_image_Key_lemma RS impI))); |
|
8954
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
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diff
changeset
|
612 |
(*Case-splits for Oops1 & 5: the negated case simplifies using the ind hyp*) |
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
parents:
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changeset
|
613 |
by (case_tac "KeyCryptKey AuthKey SK evsO1" 11); |
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
parents:
8741
diff
changeset
|
614 |
by (case_tac "KeyCryptKey ServKey SK evs5" 8); |
6452 | 615 |
by (ALLGOALS |
616 |
(asm_simp_tac |
|
617 |
(analz_image_freshK_ss addsimps |
|
8954
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rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
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8741
diff
changeset
|
618 |
[KeyCryptKey_Says, shrK_not_KeyCryptKey, Oops2_not_KeyCryptKey, |
6452 | 619 |
Auth_fresh_not_KeyCryptKey, Serv_fresh_not_KeyCryptKey, |
620 |
Says_Tgs_KeyCryptKey, Spy_analz_shrK]))); |
|
621 |
(*Fake*) |
|
622 |
by (spy_analz_tac 1); |
|
623 |
(* Base + K2 done by the simplifier! *) |
|
624 |
(*K3*) |
|
625 |
by (Blast_tac 1); |
|
626 |
(*K4*) |
|
11222 | 627 |
by (blast_tac (claset() addSDs [AuthKey_not_KeyCryptKey]) 1); |
6452 | 628 |
(*K5*) |
11185
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|
629 |
by (case_tac "Key ServKey \\<in> analz (spies evs5)" 1); |
6452 | 630 |
(*If ServKey is compromised then the result follows directly...*) |
631 |
by (asm_simp_tac |
|
632 |
(simpset() addsimps [analz_insert_eq, |
|
633 |
impOfSubs (Un_upper2 RS analz_mono)]) 1); |
|
634 |
(*...therefore ServKey is uncompromised.*) |
|
635 |
(*The KeyCryptKey ServKey SK evs5 case leads to a contradiction.*) |
|
636 |
by (blast_tac (claset() addSEs [ServKey_not_KeyCryptKey RSN(2, rev_notE)] |
|
11222 | 637 |
delrules [allE, ballE]) 1); |
8954
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
parents:
8741
diff
changeset
|
638 |
(** Level 13: Oops1 **) |
4fbdda40bb5f
rewrote a very long proof (Key_analz_image_Key) because it had stopped working
paulson
parents:
8741
diff
changeset
|
639 |
by (Asm_full_simp_tac 1); |
6452 | 640 |
by (blast_tac (claset() addSDs [KeyCryptKey_analz_insert]) 1); |
641 |
qed_spec_mp "Key_analz_image_Key"; |
|
642 |
||
643 |
||
644 |
(* First simplification law for analz: no session keys encrypt *) |
|
645 |
(* authentication keys or shared keys. *) |
|
11185
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Some X-symbols for <notin>, <noteq>, <forall>, <exists>
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diff
changeset
|
646 |
Goal "[| evs \\<in> kerberos; K \\<in> (AuthKeys evs) Un range shrK; \ |
1b737b4c2108
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11104
diff
changeset
|
647 |
\ SesKey \\<notin> range shrK |] \ |
11655 | 648 |
\ ==> (Key K \\<in> analz (insert (Key SesKey) (spies evs))) = \ |
11185
1b737b4c2108
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parents:
11104
diff
changeset
|
649 |
\ (K = SesKey | Key K \\<in> analz (spies evs))"; |
7499 | 650 |
by (ftac AuthKeys_are_not_KeyCryptKey 1 THEN assume_tac 1); |
11288 | 651 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [Key_analz_image_Key]) 1); |
6452 | 652 |
qed "analz_insert_freshK1"; |
653 |
||
654 |
||
655 |
(* Second simplification law for analz: no service keys encrypt *) |
|
656 |
(* any other keys. *) |
|
11185
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Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
657 |
Goal "[| evs \\<in> kerberos; ServKey \\<notin> (AuthKeys evs); ServKey \\<notin> range shrK|]\ |
11655 | 658 |
\ ==> (Key K \\<in> analz (insert (Key ServKey) (spies evs))) = \ |
11185
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paulson
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11104
diff
changeset
|
659 |
\ (K = ServKey | Key K \\<in> analz (spies evs))"; |
7499 | 660 |
by (ftac not_AuthKeys_not_KeyCryptKey 1 |
6452 | 661 |
THEN assume_tac 1 |
662 |
THEN assume_tac 1); |
|
11288 | 663 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [Key_analz_image_Key]) 1); |
6452 | 664 |
qed "analz_insert_freshK2"; |
665 |
||
666 |
||
667 |
(* Third simplification law for analz: only one authentication key *) |
|
668 |
(* encrypts a certain service key. *) |
|
669 |
Goal |
|
670 |
"[| Says Tgs A \ |
|
671 |
\ (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
|
11185
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Some X-symbols for <notin>, <noteq>, <forall>, <exists>
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parents:
11104
diff
changeset
|
672 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
673 |
\ AuthKey \\<noteq> AuthKey'; AuthKey' \\<notin> range shrK; evs \\<in> kerberos |] \ |
11655 | 674 |
\ ==> (Key ServKey \\<in> analz (insert (Key AuthKey') (spies evs))) = \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
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11104
diff
changeset
|
675 |
\ (ServKey = AuthKey' | Key ServKey \\<in> analz (spies evs))"; |
6452 | 676 |
by (dres_inst_tac [("AuthKey'","AuthKey'")] Says_Tgs_KeyCryptKey 1); |
677 |
by (Blast_tac 1); |
|
678 |
by (assume_tac 1); |
|
11288 | 679 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [Key_analz_image_Key]) 1); |
6452 | 680 |
qed "analz_insert_freshK3"; |
681 |
||
682 |
||
683 |
(*a weakness of the protocol*) |
|
684 |
Goal "[| Says Tgs A \ |
|
685 |
\ (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
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parents:
11104
diff
changeset
|
686 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
687 |
\ Key AuthKey \\<in> analz (spies evs); evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
688 |
\ ==> Key ServKey \\<in> analz (spies evs)"; |
6452 | 689 |
by (force_tac (claset() addDs [Says_imp_spies RS analz.Inj RS |
690 |
analz.Decrypt RS analz.Fst], |
|
691 |
simpset()) 1); |
|
692 |
qed "AuthKey_compromises_ServKey"; |
|
693 |
||
694 |
||
695 |
(********************** Guarantees for Kas *****************************) |
|
696 |
Goal "[| Crypt AuthKey {|Key ServKey, Agent B, Tt, \ |
|
697 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|}|}\ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
698 |
\ \\<in> parts (spies evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
699 |
\ Key ServKey \\<notin> analz (spies evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
700 |
\ B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
701 |
\ ==> ServKey \\<notin> AuthKeys evs"; |
6452 | 702 |
by (etac rev_mp 1); |
703 |
by (etac rev_mp 1); |
|
704 |
by (asm_full_simp_tac (simpset() addsimps [AuthKeys_def]) 1); |
|
705 |
by (parts_induct_tac 1); |
|
11222 | 706 |
by (ALLGOALS Blast_tac); |
11288 | 707 |
qed "ServKey_notin_AuthKeysD"; |
6452 | 708 |
|
709 |
||
710 |
(** If Spy sees the Authentication Key sent in msg K2, then |
|
711 |
the Key has expired **) |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
712 |
Goal "[| A \\<notin> bad; evs \\<in> kerberos |] \ |
6452 | 713 |
\ ==> Says Kas A \ |
714 |
\ (Crypt (shrK A) \ |
|
715 |
\ {|Key AuthKey, Agent Tgs, Number Tk, \ |
|
716 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
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changeset
|
717 |
\ \\<in> set evs --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
718 |
\ Key AuthKey \\<in> analz (spies evs) --> \ |
6452 | 719 |
\ ExpirAuth Tk evs"; |
720 |
by (etac kerberos.induct 1); |
|
721 |
by analz_sees_tac; |
|
722 |
by (ALLGOALS |
|
723 |
(asm_simp_tac |
|
11288 | 724 |
(simpset() addsimps [Says_Kas_message_form, less_SucI, |
725 |
analz_insert_eq, not_parts_not_analz, |
|
726 |
analz_insert_freshK1] @ pushes))); |
|
6452 | 727 |
(*Fake*) |
728 |
by (spy_analz_tac 1); |
|
729 |
(*K2*) |
|
11222 | 730 |
by (Blast_tac 1); |
6452 | 731 |
(*K4*) |
11222 | 732 |
by (Blast_tac 1); |
6452 | 733 |
(*Level 8: K5*) |
11288 | 734 |
by (blast_tac (claset() addDs [ServKey_notin_AuthKeysD, Says_Kas_message_form] |
6452 | 735 |
addIs [less_SucI]) 1); |
736 |
(*Oops1*) |
|
11222 | 737 |
by (blast_tac (claset() addSDs [unique_AuthKeys] addIs [less_SucI]) 1); |
6452 | 738 |
(*Oops2*) |
739 |
by (blast_tac (claset() addDs [Says_Tgs_message_form, |
|
740 |
Says_Kas_message_form]) 1); |
|
741 |
val lemma = result() RS mp RS mp RSN(1,rev_notE); |
|
742 |
||
743 |
||
744 |
Goal "[| Says Kas A \ |
|
745 |
\ (Crypt Ka {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}) \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
746 |
\ \\<in> set evs; \ |
6452 | 747 |
\ ~ ExpirAuth Tk evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
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diff
changeset
|
748 |
\ A \\<notin> bad; evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
749 |
\ ==> Key AuthKey \\<notin> analz (spies evs)"; |
11222 | 750 |
by (blast_tac (claset() addDs [Says_Kas_message_form, lemma]) 1); |
6452 | 751 |
qed "Confidentiality_Kas"; |
752 |
||
753 |
||
754 |
(********************** Guarantees for Tgs *****************************) |
|
755 |
||
756 |
(** If Spy sees the Service Key sent in msg K4, then |
|
757 |
the Key has expired **) |
|
11288 | 758 |
Goal "[| Says Tgs A \ |
6452 | 759 |
\ (Crypt AuthKey \ |
760 |
\ {|Key ServKey, Agent B, Number Tt, \ |
|
761 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|}|})\ |
|
11288 | 762 |
\ \\<in> set evs; \ |
763 |
\ Key AuthKey \\<notin> analz (spies evs); \ |
|
764 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
|
765 |
\ ==> Key ServKey \\<in> analz (spies evs) --> \ |
|
6452 | 766 |
\ ExpirServ Tt evs"; |
11288 | 767 |
by (etac rev_mp 1); |
768 |
by (etac rev_mp 1); |
|
6452 | 769 |
by (etac kerberos.induct 1); |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
770 |
(*The Oops1 case is unusual: must simplify Authkey \\<notin> analz (spies (ev#evs)) |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
771 |
rather than weakening it to Authkey \\<notin> analz (spies evs), for we then |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
772 |
conclude AuthKey \\<noteq> AuthKeya.*) |
6452 | 773 |
by (Clarify_tac 9); |
774 |
by analz_sees_tac; |
|
775 |
by (rotate_tac ~1 11); |
|
776 |
by (ALLGOALS |
|
777 |
(asm_full_simp_tac |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
778 |
(simpset() addsimps [less_SucI, new_keys_not_analzd, |
8741
61bc5ed22b62
removal of less_SucI, le_SucI from default simpset
paulson
parents:
7499
diff
changeset
|
779 |
Says_Kas_message_form, Says_Tgs_message_form, |
61bc5ed22b62
removal of less_SucI, le_SucI from default simpset
paulson
parents:
7499
diff
changeset
|
780 |
analz_insert_eq, not_parts_not_analz, |
11288 | 781 |
analz_insert_freshK1, analz_insert_freshK2, |
782 |
analz_insert_freshK3] |
|
8741
61bc5ed22b62
removal of less_SucI, le_SucI from default simpset
paulson
parents:
7499
diff
changeset
|
783 |
@ pushes))); |
6452 | 784 |
(*Fake*) |
785 |
by (spy_analz_tac 1); |
|
786 |
(*K2*) |
|
11288 | 787 |
by (blast_tac (claset() addIs [parts_insertI, less_SucI]) 1); |
6452 | 788 |
(*K4*) |
11222 | 789 |
by (blast_tac (claset() addDs [A_trusts_AuthTicket, Confidentiality_Kas]) 1); |
6452 | 790 |
by (ALLGOALS Clarify_tac); |
791 |
(*Oops2*) |
|
792 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj, |
|
793 |
Key_unique_SesKey] addIs [less_SucI]) 3); |
|
11222 | 794 |
(** Level 10 **) |
6452 | 795 |
(*Oops1*) |
11288 | 796 |
by (blast_tac (claset() addDs [Says_Kas_message_form, Says_Tgs_message_form] |
797 |
addIs [less_SucI]) 2); |
|
798 |
(*K5. Not clear how this step could be integrated with the main |
|
799 |
simplification step.*) |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
800 |
by (thin_tac "Says Aa Tgs ?X \\<in> set ?evs" 1); |
6452 | 801 |
by (forward_tac [Says_imp_spies RS parts.Inj RS ServKey_notin_AuthKeysD] 1); |
802 |
by (assume_tac 1 THEN Blast_tac 1 THEN assume_tac 1); |
|
803 |
by (rotate_tac ~1 1); |
|
804 |
by (asm_full_simp_tac (simpset() addsimps [analz_insert_freshK2]) 1); |
|
11222 | 805 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj, Key_unique_SesKey] |
806 |
addIs [less_SucI]) 1); |
|
11288 | 807 |
qed_spec_mp "Confidentiality_lemma"; |
6452 | 808 |
|
809 |
||
810 |
(* In the real world Tgs can't check wheter AuthKey is secure! *) |
|
11288 | 811 |
Goal "[| Says Tgs A \ |
6452 | 812 |
\ (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
11288 | 813 |
\ \\<in> set evs; \ |
814 |
\ Key AuthKey \\<notin> analz (spies evs); \ |
|
815 |
\ ~ ExpirServ Tt evs; \ |
|
816 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
|
817 |
\ ==> Key ServKey \\<notin> analz (spies evs)"; |
|
818 |
by (blast_tac |
|
819 |
(claset() addDs [Says_Tgs_message_form, Confidentiality_lemma]) 1); |
|
6452 | 820 |
qed "Confidentiality_Tgs1"; |
821 |
||
822 |
(* In the real world Tgs CAN check what Kas sends! *) |
|
11288 | 823 |
Goal "[| Says Kas A \ |
6452 | 824 |
\ (Crypt Ka {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}) \ |
11288 | 825 |
\ \\<in> set evs; \ |
826 |
\ Says Tgs A \ |
|
6452 | 827 |
\ (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
11288 | 828 |
\ \\<in> set evs; \ |
829 |
\ ~ ExpirAuth Tk evs; ~ ExpirServ Tt evs; \ |
|
830 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
|
831 |
\ ==> Key ServKey \\<notin> analz (spies evs)"; |
|
6452 | 832 |
by (blast_tac (claset() addSDs [Confidentiality_Kas, |
833 |
Confidentiality_Tgs1]) 1); |
|
834 |
qed "Confidentiality_Tgs2"; |
|
835 |
||
836 |
(*Most general form*) |
|
837 |
val Confidentiality_Tgs3 = A_trusts_AuthTicket RS Confidentiality_Tgs2; |
|
838 |
||
839 |
||
840 |
(********************** Guarantees for Alice *****************************) |
|
841 |
||
842 |
val Confidentiality_Auth_A = A_trusts_AuthKey RS Confidentiality_Kas; |
|
843 |
||
844 |
Goal |
|
845 |
"[| Says Kas A \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
846 |
\ (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Tk, AuthTicket|}) \\<in> set evs;\ |
6452 | 847 |
\ Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
848 |
\ \\<in> parts (spies evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
849 |
\ Key AuthKey \\<notin> analz (spies evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
850 |
\ evs \\<in> kerberos |] \ |
6452 | 851 |
\==> Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Tt, ServTicket|})\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
852 |
\ \\<in> set evs"; |
7499 | 853 |
by (ftac Says_Kas_message_form 1 THEN assume_tac 1); |
6452 | 854 |
by (etac rev_mp 1); |
855 |
by (etac rev_mp 1); |
|
856 |
by (etac rev_mp 1); |
|
857 |
by (parts_induct_tac 1); |
|
11222 | 858 |
by (Blast_tac 1); |
6452 | 859 |
(*K2 and K4 remain*) |
11222 | 860 |
by (blast_tac (claset() addSDs [unique_CryptKey]) 2); |
6452 | 861 |
by (blast_tac (claset() addSDs [A_trusts_K4, Says_Tgs_message_form, |
862 |
AuthKeys_used]) 1); |
|
863 |
qed "A_trusts_K4_bis"; |
|
864 |
||
865 |
||
866 |
Goal "[| Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|} \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
867 |
\ \\<in> parts (spies evs); \ |
6452 | 868 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
869 |
\ \\<in> parts (spies evs); \ |
6452 | 870 |
\ ~ ExpirAuth Tk evs; ~ ExpirServ Tt evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
871 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
872 |
\ ==> Key ServKey \\<notin> analz (spies evs)"; |
6452 | 873 |
by (dtac A_trusts_AuthKey 1); |
874 |
by (assume_tac 1); |
|
875 |
by (assume_tac 1); |
|
876 |
by (blast_tac (claset() addDs [Confidentiality_Kas, |
|
877 |
Says_Kas_message_form, |
|
878 |
A_trusts_K4_bis, Confidentiality_Tgs2]) 1); |
|
879 |
qed "Confidentiality_Serv_A"; |
|
880 |
||
881 |
||
882 |
(********************** Guarantees for Bob *****************************) |
|
883 |
(* Theorems for the refined model have suffix "refined" *) |
|
884 |
||
885 |
Goal |
|
886 |
"[| Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|})\ |
|
11288 | 887 |
\ \\<in> set evs; evs \\<in> kerberos|] \ |
888 |
\ ==> \\<exists>Tk. Says Kas A \ |
|
889 |
\ (Crypt (shrK A) \ |
|
890 |
\ {|Key AuthKey, Agent Tgs, Number Tk,\ |
|
6452 | 891 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
11288 | 892 |
\ \\<in> set evs"; |
6452 | 893 |
by (etac rev_mp 1); |
894 |
by (parts_induct_tac 1); |
|
895 |
by Auto_tac; |
|
896 |
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj RS parts.Fst RS |
|
11288 | 897 |
A_trusts_AuthTicket]) 1); |
6452 | 898 |
qed "K4_imp_K2"; |
899 |
||
900 |
Goal |
|
901 |
"[| Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|})\ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
902 |
\ \\<in> set evs; evs \\<in> kerberos|] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
903 |
\ ==> \\<exists>Tk. (Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk,\ |
6452 | 904 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
905 |
\ \\<in> set evs \ |
6452 | 906 |
\ & ServLife + Tt <= AuthLife + Tk)"; |
907 |
by (etac rev_mp 1); |
|
908 |
by (parts_induct_tac 1); |
|
909 |
by Auto_tac; |
|
910 |
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj RS parts.Fst RS |
|
11288 | 911 |
A_trusts_AuthTicket]) 1); |
6452 | 912 |
qed "K4_imp_K2_refined"; |
913 |
||
914 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|} \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
915 |
\ \\<in> parts (spies evs); B \\<noteq> Tgs; B \\<notin> bad; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
916 |
\ evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
917 |
\==> \\<exists>AuthKey. \ |
6452 | 918 |
\ Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Tt, \ |
919 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Tt|}|}) \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
920 |
\ \\<in> set evs"; |
6452 | 921 |
by (etac rev_mp 1); |
922 |
by (parts_induct_tac 1); |
|
11222 | 923 |
by (ALLGOALS Blast_tac); |
6452 | 924 |
qed "B_trusts_ServKey"; |
925 |
||
926 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
927 |
\ \\<in> parts (spies evs); B \\<noteq> Tgs; B \\<notin> bad; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
928 |
\ evs \\<in> kerberos |] \ |
11288 | 929 |
\ ==> \\<exists>AuthKey Tk. \ |
930 |
\ Says Kas A \ |
|
931 |
\ (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk,\ |
|
932 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
933 |
\ \\<in> set evs"; |
|
6452 | 934 |
by (blast_tac (claset() addSDs [B_trusts_ServKey, K4_imp_K2]) 1); |
935 |
qed "B_trusts_ServTicket_Kas"; |
|
936 |
||
937 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
11288 | 938 |
\ \\<in> parts (spies evs); B \\<noteq> Tgs; B \\<notin> bad; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
939 |
\ evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
940 |
\ ==> \\<exists>AuthKey Tk. (Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk,\ |
6452 | 941 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
942 |
\ \\<in> set evs \ |
6452 | 943 |
\ & ServLife + Tt <= AuthLife + Tk)"; |
944 |
by (blast_tac (claset() addSDs [B_trusts_ServKey,K4_imp_K2_refined]) 1); |
|
945 |
qed "B_trusts_ServTicket_Kas_refined"; |
|
946 |
||
947 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
11288 | 948 |
\ \\<in> parts (spies evs); B \\<noteq> Tgs; B \\<notin> bad; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
949 |
\ evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
950 |
\==> \\<exists>Tk AuthKey. \ |
6452 | 951 |
\ Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, \ |
952 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
953 |
\ \\<in> set evs \ |
6452 | 954 |
\ & Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, \ |
955 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|}|}) \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
956 |
\ \\<in> set evs"; |
11222 | 957 |
by (blast_tac (claset() addDs [B_trusts_ServKey, K4_imp_K2]) 1); |
6452 | 958 |
qed "B_trusts_ServTicket"; |
959 |
||
960 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
11288 | 961 |
\ \\<in> parts (spies evs); B \\<noteq> Tgs; B \\<notin> bad; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
962 |
\ evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
963 |
\==> \\<exists>Tk AuthKey. \ |
6452 | 964 |
\ (Says Kas A (Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, \ |
965 |
\ Crypt (shrK Tgs) {|Agent A, Agent Tgs, Key AuthKey, Number Tk|}|})\ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
966 |
\ \\<in> set evs \ |
6452 | 967 |
\ & Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, \ |
968 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|}|}) \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
969 |
\ \\<in> set evs \ |
6452 | 970 |
\ & ServLife + Tt <= AuthLife + Tk)"; |
11222 | 971 |
by (blast_tac (claset() addDs [B_trusts_ServKey, K4_imp_K2_refined]) 1); |
6452 | 972 |
qed "B_trusts_ServTicket_refined"; |
973 |
||
974 |
||
975 |
Goal "[| ~ ExpirServ Tt evs; ServLife + Tt <= AuthLife + Tk |] \ |
|
11288 | 976 |
\ ==> ~ ExpirAuth Tk evs"; |
6452 | 977 |
by (blast_tac (claset() addDs [leI,le_trans] addEs [leE]) 1); |
978 |
qed "NotExpirServ_NotExpirAuth_refined"; |
|
979 |
||
980 |
||
981 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
982 |
\ \\<in> parts (spies evs); \ |
6452 | 983 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
984 |
\ \\<in> parts (spies evs); \ |
6452 | 985 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
986 |
\ \\<in> parts (spies evs); \ |
6452 | 987 |
\ ~ ExpirServ Tt evs; ~ ExpirAuth Tk evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
988 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
989 |
\ ==> Key ServKey \\<notin> analz (spies evs)"; |
7499 | 990 |
by (ftac A_trusts_AuthKey 1); |
991 |
by (ftac Confidentiality_Kas 3); |
|
992 |
by (ftac B_trusts_ServTicket 6); |
|
11222 | 993 |
by (blast_tac (claset() addSDs [Confidentiality_Tgs2] |
994 |
addDs [Says_Kas_message_form, A_trusts_K4, |
|
995 |
unique_ServKeys, unique_AuthKeys]) 9); |
|
6452 | 996 |
by (ALLGOALS assume_tac); |
997 |
(* |
|
11222 | 998 |
The proof above is fast. It can be done in one command in 50 secs: |
6452 | 999 |
by (blast_tac (claset() addDs [A_trusts_AuthKey, A_trusts_K4, |
1000 |
Says_Kas_message_form, B_trusts_ServTicket, |
|
1001 |
unique_ServKeys, unique_AuthKeys, |
|
1002 |
Confidentiality_Kas, |
|
1003 |
Confidentiality_Tgs2]) 1); |
|
1004 |
*) |
|
1005 |
qed "Confidentiality_B"; |
|
1006 |
||
1007 |
||
1008 |
(*Most general form -- only for refined model! *) |
|
1009 |
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1010 |
\ \\<in> parts (spies evs); \ |
6452 | 1011 |
\ ~ ExpirServ Tt evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1012 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1013 |
\ ==> Key ServKey \\<notin> analz (spies evs)"; |
6452 | 1014 |
by (blast_tac (claset() addDs [B_trusts_ServTicket_refined, |
1015 |
NotExpirServ_NotExpirAuth_refined, |
|
1016 |
Confidentiality_Tgs2]) 1); |
|
1017 |
qed "Confidentiality_B_refined"; |
|
1018 |
||
1019 |
||
1020 |
(********************** Authenticity theorems *****************************) |
|
1021 |
||
1022 |
(***1. Session Keys authenticity: they originated with servers.***) |
|
1023 |
||
1024 |
(*Authenticity of AuthKey for A: "A_trusts_AuthKey"*) |
|
1025 |
||
1026 |
(*Authenticity of ServKey for A: "A_trusts_ServKey"*) |
|
1027 |
Goal "[| Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|} \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1028 |
\ \\<in> parts (spies evs); \ |
6452 | 1029 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1030 |
\ \\<in> parts (spies evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1031 |
\ ~ ExpirAuth Tk evs; A \\<notin> bad; evs \\<in> kerberos |] \ |
6452 | 1032 |
\==>Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|})\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1033 |
\ \\<in> set evs"; |
11222 | 1034 |
by (blast_tac (claset() addDs [A_trusts_AuthKey, Confidentiality_Auth_A, |
1035 |
A_trusts_K4_bis]) 1); |
|
6452 | 1036 |
qed "A_trusts_ServKey"; |
1037 |
(*Note: requires a temporal check*) |
|
1038 |
||
1039 |
||
1040 |
(*Authenticity of ServKey for B: "B_trusts_ServKey"*) |
|
1041 |
||
1042 |
(***2. Parties authenticity: each party verifies "the identity of |
|
1043 |
another party who generated some data" (quoted from Neuman & Ts'o).***) |
|
1044 |
||
1045 |
(*These guarantees don't assess whether two parties agree on |
|
1046 |
the same session key: sending a message containing a key |
|
1047 |
doesn't a priori state knowledge of the key.***) |
|
1048 |
||
1049 |
(*B checks authenticity of A: theorems "A_Authenticity", |
|
1050 |
"A_authenticity_refined" *) |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1051 |
Goal "[| Crypt ServKey {|Agent A, Number Ta|} \\<in> parts (spies evs); \ |
6452 | 1052 |
\ Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1053 |
\ ServTicket|}) \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1054 |
\ Key ServKey \\<notin> analz (spies evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1055 |
\ A \\<notin> bad; B \\<notin> bad; evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1056 |
\==> Says A B {|ServTicket, Crypt ServKey {|Agent A, Number Ta|}|} \\<in> set evs"; |
6452 | 1057 |
by (etac rev_mp 1); |
1058 |
by (etac rev_mp 1); |
|
1059 |
by (etac rev_mp 1); |
|
1060 |
by (etac kerberos.induct 1); |
|
7499 | 1061 |
by (ftac Says_ticket_in_parts_spies 5); |
1062 |
by (ftac Says_ticket_in_parts_spies 7); |
|
6452 | 1063 |
by (REPEAT (FIRSTGOAL analz_mono_contra_tac)); |
1064 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
|
11222 | 1065 |
by (Blast_tac 1); |
6452 | 1066 |
(*K3*) |
11222 | 1067 |
by (blast_tac (claset() addDs [A_trusts_AuthKey, |
6452 | 1068 |
Says_Kas_message_form, |
1069 |
Says_Tgs_message_form]) 1); |
|
1070 |
(*K4*) |
|
1071 |
by (force_tac (claset() addSDs [Crypt_imp_keysFor], simpset()) 1); |
|
1072 |
(*K5*) |
|
11222 | 1073 |
by (blast_tac (claset() addDs [Key_unique_SesKey]) 1); |
6452 | 1074 |
qed "Says_Auth"; |
1075 |
||
1076 |
(*The second assumption tells B what kind of key ServKey is.*) |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1077 |
Goal "[| Crypt ServKey {|Agent A, Number Ta|} \\<in> parts (spies evs); \ |
6452 | 1078 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1079 |
\ \\<in> parts (spies evs); \ |
6452 | 1080 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1081 |
\ \\<in> parts (spies evs); \ |
6452 | 1082 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1083 |
\ \\<in> parts (spies evs); \ |
6452 | 1084 |
\ ~ ExpirServ Tt evs; ~ ExpirAuth Tk evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1085 |
\ B \\<noteq> Tgs; A \\<notin> bad; B \\<notin> bad; evs \\<in> kerberos |] \ |
6452 | 1086 |
\ ==> Says A B {|Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|},\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1087 |
\ Crypt ServKey {|Agent A, Number Ta|} |} \\<in> set evs"; |
11222 | 1088 |
by (blast_tac (claset() addIs [Says_Auth] |
1089 |
addDs [Confidentiality_B, Key_unique_SesKey, |
|
1090 |
B_trusts_ServKey]) 1); |
|
6452 | 1091 |
qed "A_Authenticity"; |
1092 |
||
1093 |
(*Stronger form in the refined model*) |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1094 |
Goal "[| Crypt ServKey {|Agent A, Number Ta2|} \\<in> parts (spies evs); \ |
6452 | 1095 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1096 |
\ \\<in> parts (spies evs); \ |
6452 | 1097 |
\ ~ ExpirServ Tt evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1098 |
\ B \\<noteq> Tgs; A \\<notin> bad; B \\<notin> bad; evs \\<in> kerberos |] \ |
6452 | 1099 |
\ ==> Says A B {|Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|},\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1100 |
\ Crypt ServKey {|Agent A, Number Ta2|} |} \\<in> set evs"; |
11222 | 1101 |
by (blast_tac (claset() addDs [Confidentiality_B_refined, B_trusts_ServKey, |
1102 |
Key_unique_SesKey] |
|
1103 |
addIs [Says_Auth]) 1); |
|
6452 | 1104 |
qed "A_Authenticity_refined"; |
1105 |
||
1106 |
||
1107 |
(*A checks authenticity of B: theorem "B_authenticity"*) |
|
1108 |
||
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1109 |
Goal "[| Crypt ServKey (Number Ta) \\<in> parts (spies evs); \ |
6452 | 1110 |
\ Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, Number Tt, \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1111 |
\ ServTicket|}) \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1112 |
\ Key ServKey \\<notin> analz (spies evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1113 |
\ A \\<notin> bad; B \\<notin> bad; evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1114 |
\ ==> Says B A (Crypt ServKey (Number Ta)) \\<in> set evs"; |
6452 | 1115 |
by (etac rev_mp 1); |
1116 |
by (etac rev_mp 1); |
|
1117 |
by (etac rev_mp 1); |
|
1118 |
by (etac kerberos.induct 1); |
|
7499 | 1119 |
by (ftac Says_ticket_in_parts_spies 5); |
1120 |
by (ftac Says_ticket_in_parts_spies 7); |
|
6452 | 1121 |
by (REPEAT (FIRSTGOAL analz_mono_contra_tac)); |
1122 |
by (ALLGOALS Asm_simp_tac); |
|
11222 | 1123 |
by (Blast_tac 1); |
6452 | 1124 |
by (force_tac (claset() addSDs [Crypt_imp_keysFor], simpset()) 1); |
1125 |
by (Clarify_tac 1); |
|
7499 | 1126 |
by (ftac Says_Tgs_message_form 1 THEN assume_tac 1); |
6452 | 1127 |
by (Clarify_tac 1); (*PROOF FAILED if omitted*) |
11222 | 1128 |
by (blast_tac (claset() addDs [unique_CryptKey]) 1); |
6452 | 1129 |
qed "Says_K6"; |
1130 |
||
1131 |
Goal "[| Crypt AuthKey {|Key ServKey, Agent B, T, ServTicket|} \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1132 |
\ \\<in> parts (spies evs); \ |
11288 | 1133 |
\ Key AuthKey \\<notin> analz (spies evs); AuthKey \\<notin> range shrK; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1134 |
\ evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1135 |
\ ==> \\<exists>A. Says Tgs A (Crypt AuthKey {|Key ServKey, Agent B, T, ServTicket|})\ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1136 |
\ \\<in> set evs"; |
6452 | 1137 |
by (etac rev_mp 1); |
1138 |
by (etac rev_mp 1); |
|
1139 |
by (parts_induct_tac 1); |
|
11288 | 1140 |
by (ALLGOALS Blast_tac); |
6452 | 1141 |
qed "K4_trustworthy"; |
1142 |
||
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1143 |
Goal "[| Crypt ServKey (Number Ta) \\<in> parts (spies evs); \ |
6452 | 1144 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1145 |
\ \\<in> parts (spies evs); \ |
6452 | 1146 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1147 |
\ \\<in> parts (spies evs); \ |
6452 | 1148 |
\ ~ ExpirAuth Tk evs; ~ ExpirServ Tt evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1149 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1150 |
\ ==> Says B A (Crypt ServKey (Number Ta)) \\<in> set evs"; |
7499 | 1151 |
by (ftac A_trusts_AuthKey 1); |
1152 |
by (ftac Says_Kas_message_form 3); |
|
1153 |
by (ftac Confidentiality_Kas 4); |
|
1154 |
by (ftac K4_trustworthy 7); |
|
6452 | 1155 |
by (Blast_tac 8); |
1156 |
by (etac exE 9); |
|
7499 | 1157 |
by (ftac K4_imp_K2 9); |
11222 | 1158 |
(*Yes the proof's a mess, but I don't know how to improve it.*) |
1159 |
by (blast_tac (claset() addDs [Key_unique_SesKey] |
|
6452 | 1160 |
addSIs [Says_K6] |
11222 | 1161 |
addDs [Confidentiality_Tgs1]) 10); |
6452 | 1162 |
by (ALLGOALS assume_tac); |
1163 |
qed "B_Authenticity"; |
|
1164 |
||
1165 |
||
1166 |
(***3. Parties' knowledge of session keys. A knows a session key if she |
|
1167 |
used it to build a cipher.***) |
|
1168 |
||
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1169 |
Goal "[| Says B A (Crypt ServKey (Number Ta)) \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1170 |
\ Key ServKey \\<notin> analz (spies evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1171 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
6452 | 1172 |
\ ==> B Issues A with (Crypt ServKey (Number Ta)) on evs"; |
1173 |
by (simp_tac (simpset() addsimps [Issues_def]) 1); |
|
1174 |
by (rtac exI 1); |
|
1175 |
by (rtac conjI 1); |
|
1176 |
by (assume_tac 1); |
|
1177 |
by (Simp_tac 1); |
|
1178 |
by (etac rev_mp 1); |
|
1179 |
by (etac rev_mp 1); |
|
1180 |
by (etac kerberos.induct 1); |
|
7499 | 1181 |
by (ftac Says_ticket_in_parts_spies 5); |
1182 |
by (ftac Says_ticket_in_parts_spies 7); |
|
6452 | 1183 |
by (REPEAT (FIRSTGOAL analz_mono_contra_tac)); |
1184 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
|
11222 | 1185 |
by (Blast_tac 1); |
6452 | 1186 |
(*K6 requires numerous lemmas*) |
1187 |
by (asm_full_simp_tac (simpset() addsimps [takeWhile_tail]) 1); |
|
1188 |
by (blast_tac (claset() addDs [B_trusts_ServTicket, |
|
1189 |
impOfSubs parts_spies_takeWhile_mono, |
|
1190 |
impOfSubs parts_spies_evs_revD2] |
|
11222 | 1191 |
addIs [Says_K6]) 1); |
6452 | 1192 |
qed "B_Knows_B_Knows_ServKey_lemma"; |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1193 |
(*Key ServKey \\<notin> analz (spies evs) could be relaxed by Confidentiality_B |
6452 | 1194 |
but this is irrelevant because B knows what he knows! *) |
1195 |
||
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1196 |
Goal "[| Says B A (Crypt ServKey (Number Ta)) \\<in> set evs; \ |
6452 | 1197 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|}\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1198 |
\ \\<in> parts (spies evs);\ |
6452 | 1199 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1200 |
\ \\<in> parts (spies evs);\ |
6452 | 1201 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1202 |
\ \\<in> parts (spies evs); \ |
6452 | 1203 |
\ ~ ExpirServ Tt evs; ~ ExpirAuth Tk evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1204 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
6452 | 1205 |
\ ==> B Issues A with (Crypt ServKey (Number Ta)) on evs"; |
1206 |
by (blast_tac (claset() addSDs [Confidentiality_B, |
|
11288 | 1207 |
B_Knows_B_Knows_ServKey_lemma]) 1); |
6452 | 1208 |
qed "B_Knows_B_Knows_ServKey"; |
1209 |
||
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1210 |
Goal "[| Says B A (Crypt ServKey (Number Ta)) \\<in> set evs; \ |
6452 | 1211 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|}\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1212 |
\ \\<in> parts (spies evs);\ |
6452 | 1213 |
\ ~ ExpirServ Tt evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1214 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
6452 | 1215 |
\ ==> B Issues A with (Crypt ServKey (Number Ta)) on evs"; |
1216 |
by (blast_tac (claset() addSDs [Confidentiality_B_refined, |
|
1217 |
B_Knows_B_Knows_ServKey_lemma]) 1); |
|
1218 |
qed "B_Knows_B_Knows_ServKey_refined"; |
|
1219 |
||
1220 |
||
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1221 |
Goal "[| Crypt ServKey (Number Ta) \\<in> parts (spies evs); \ |
6452 | 1222 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1223 |
\ \\<in> parts (spies evs); \ |
6452 | 1224 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1225 |
\ \\<in> parts (spies evs); \ |
6452 | 1226 |
\ ~ ExpirAuth Tk evs; ~ ExpirServ Tt evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1227 |
\ A \\<notin> bad; B \\<notin> bad; B \\<noteq> Tgs; evs \\<in> kerberos |] \ |
6452 | 1228 |
\ ==> B Issues A with (Crypt ServKey (Number Ta)) on evs"; |
1229 |
by (blast_tac (claset() addSDs [B_Authenticity, Confidentiality_Serv_A, |
|
1230 |
B_Knows_B_Knows_ServKey_lemma]) 1); |
|
1231 |
qed "A_Knows_B_Knows_ServKey"; |
|
1232 |
||
1233 |
Goal "[| Says A Tgs \ |
|
1234 |
\ {|AuthTicket, Crypt AuthKey {|Agent A, Number Ta|}, Agent B|}\ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1235 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1236 |
\ A \\<notin> bad; evs \\<in> kerberos |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1237 |
\ ==> \\<exists>Tk. Says Kas A (Crypt (shrK A) \ |
6452 | 1238 |
\ {|Key AuthKey, Agent Tgs, Tk, AuthTicket|}) \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1239 |
\ \\<in> set evs"; |
6452 | 1240 |
by (etac rev_mp 1); |
1241 |
by (parts_induct_tac 1); |
|
11222 | 1242 |
by (Blast_tac 1); |
6452 | 1243 |
by (Blast_tac 1); |
1244 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj RS |
|
1245 |
A_trusts_AuthKey]) 1); |
|
1246 |
qed "K3_imp_K2"; |
|
1247 |
||
1248 |
Goal "[| Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1249 |
\ \\<in> parts (spies evs); \ |
6452 | 1250 |
\ Says Kas A (Crypt (shrK A) \ |
1251 |
\ {|Key AuthKey, Agent Tgs, Tk, AuthTicket|}) \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1252 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1253 |
\ Key AuthKey \\<notin> analz (spies evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1254 |
\ B \\<noteq> Tgs; A \\<notin> bad; B \\<notin> bad; evs \\<in> kerberos |] \ |
6452 | 1255 |
\ ==> Says Tgs A (Crypt AuthKey \ |
1256 |
\ {|Key ServKey, Agent B, Number Tt, ServTicket|}) \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1257 |
\ \\<in> set evs"; |
6452 | 1258 |
by (etac rev_mp 1); |
1259 |
by (etac rev_mp 1); |
|
1260 |
by (etac rev_mp 1); |
|
1261 |
by (parts_induct_tac 1); |
|
11222 | 1262 |
by (Blast_tac 1); |
6452 | 1263 |
by (force_tac (claset() addSDs [Crypt_imp_keysFor], simpset()) 1); |
1264 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj RS parts.Fst RS |
|
1265 |
A_trusts_AuthTicket, unique_AuthKeys]) 1); |
|
1266 |
qed "K4_trustworthy'"; |
|
1267 |
||
1268 |
Goal "[| Says A B {|ServTicket, Crypt ServKey {|Agent A, Number Ta|}|} \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1269 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1270 |
\ Key ServKey \\<notin> analz (spies evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1271 |
\ B \\<noteq> Tgs; A \\<notin> bad; B \\<notin> bad; evs \\<in> kerberos |] \ |
6452 | 1272 |
\ ==> A Issues B with (Crypt ServKey {|Agent A, Number Ta|}) on evs"; |
1273 |
by (simp_tac (simpset() addsimps [Issues_def]) 1); |
|
1274 |
by (rtac exI 1); |
|
1275 |
by (rtac conjI 1); |
|
1276 |
by (assume_tac 1); |
|
1277 |
by (Simp_tac 1); |
|
1278 |
by (etac rev_mp 1); |
|
1279 |
by (etac rev_mp 1); |
|
1280 |
by (etac kerberos.induct 1); |
|
7499 | 1281 |
by (ftac Says_ticket_in_parts_spies 5); |
1282 |
by (ftac Says_ticket_in_parts_spies 7); |
|
6452 | 1283 |
by (REPEAT (FIRSTGOAL analz_mono_contra_tac)); |
1284 |
by (ALLGOALS Asm_simp_tac); |
|
1285 |
by (Clarify_tac 1); |
|
1286 |
(*K6*) |
|
1287 |
by Auto_tac; |
|
1288 |
by (asm_full_simp_tac (simpset() addsimps [takeWhile_tail]) 1); |
|
1289 |
(*Level 15: case study necessary because the assumption doesn't state |
|
1290 |
the form of ServTicket. The guarantee becomes stronger.*) |
|
11222 | 1291 |
by (blast_tac (claset() addDs [Says_imp_spies RS analz.Inj RS analz_Decrypt', |
1292 |
K3_imp_K2, K4_trustworthy', |
|
6452 | 1293 |
impOfSubs parts_spies_takeWhile_mono, |
1294 |
impOfSubs parts_spies_evs_revD2] |
|
11222 | 1295 |
addIs [Says_Auth]) 1); |
6452 | 1296 |
by (asm_full_simp_tac (simpset() addsimps [takeWhile_tail]) 1); |
1297 |
qed "A_Knows_A_Knows_ServKey_lemma"; |
|
1298 |
||
1299 |
Goal "[| Says A B {|ServTicket, Crypt ServKey {|Agent A, Number Ta|}|} \ |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1300 |
\ \\<in> set evs; \ |
6452 | 1301 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|}\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1302 |
\ \\<in> parts (spies evs);\ |
6452 | 1303 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|}\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1304 |
\ \\<in> parts (spies evs); \ |
6452 | 1305 |
\ ~ ExpirAuth Tk evs; ~ ExpirServ Tt evs;\ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1306 |
\ B \\<noteq> Tgs; A \\<notin> bad; B \\<notin> bad; evs \\<in> kerberos |] \ |
6452 | 1307 |
\ ==> A Issues B with (Crypt ServKey {|Agent A, Number Ta|}) on evs"; |
1308 |
by (blast_tac (claset() addSDs [Confidentiality_Serv_A, |
|
1309 |
A_Knows_A_Knows_ServKey_lemma]) 1); |
|
1310 |
qed "A_Knows_A_Knows_ServKey"; |
|
1311 |
||
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1312 |
Goal "[| Crypt ServKey {|Agent A, Number Ta|} \\<in> parts (spies evs); \ |
6452 | 1313 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1314 |
\ \\<in> parts (spies evs); \ |
6452 | 1315 |
\ Crypt AuthKey {|Key ServKey, Agent B, Number Tt, ServTicket|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1316 |
\ \\<in> parts (spies evs); \ |
6452 | 1317 |
\ Crypt (shrK A) {|Key AuthKey, Agent Tgs, Number Tk, AuthTicket|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1318 |
\ \\<in> parts (spies evs); \ |
6452 | 1319 |
\ ~ ExpirServ Tt evs; ~ ExpirAuth Tk evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1320 |
\ B \\<noteq> Tgs; A \\<notin> bad; B \\<notin> bad; evs \\<in> kerberos |] \ |
6452 | 1321 |
\ ==> A Issues B with (Crypt ServKey {|Agent A, Number Ta|}) on evs"; |
1322 |
by (blast_tac (claset() addDs [A_Authenticity, Confidentiality_B, |
|
1323 |
A_Knows_A_Knows_ServKey_lemma]) 1); |
|
1324 |
qed "B_Knows_A_Knows_ServKey"; |
|
1325 |
||
1326 |
||
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1327 |
Goal "[| Crypt ServKey {|Agent A, Number Ta|} \\<in> parts (spies evs); \ |
6452 | 1328 |
\ Crypt (shrK B) {|Agent A, Agent B, Key ServKey, Number Tt|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1329 |
\ \\<in> parts (spies evs); \ |
6452 | 1330 |
\ ~ ExpirServ Tt evs; \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11104
diff
changeset
|
1331 |
\ B \\<noteq> Tgs; A \\<notin> bad; B \\<notin> bad; evs \\<in> kerberos |] \ |
6452 | 1332 |
\ ==> A Issues B with (Crypt ServKey {|Agent A, Number Ta|}) on evs"; |
1333 |
by (blast_tac (claset() addDs [A_Authenticity_refined, |
|
1334 |
Confidentiality_B_refined, |
|
1335 |
A_Knows_A_Knows_ServKey_lemma]) 1); |
|
1336 |
qed "B_Knows_A_Knows_ServKey_refined"; |