author | paulson |
Thu, 06 Aug 1998 15:48:13 +0200 | |
changeset 5278 | a903b66822e2 |
parent 5223 | 4cb05273f764 |
child 5421 | 01fc8d6a40f2 |
permissions | -rw-r--r-- |
2002 | 1 |
(* Title: HOL/Auth/OtwayRees_Bad |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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Inductive relation "otway" for the Otway-Rees protocol. |
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||
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The FAULTY version omitting encryption of Nonce NB, as suggested on page 247 of |
|
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Burrows, Abadi and Needham. A Logic of Authentication. |
|
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Proc. Royal Soc. 426 (1989) |
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This file illustrates the consequences of such errors. We can still prove |
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impressive-looking properties such as Spy_not_see_encrypted_key, yet the |
2002 | 14 |
protocol is open to a middleperson attack. Attempting to prove some key lemmas |
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indicates the possibility of this attack. |
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*) |
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AddEs spies_partsEs; |
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AddDs [impOfSubs analz_subset_parts]; |
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AddDs [impOfSubs Fake_parts_insert]; |
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(*A "possibility property": there are traces that reach the end*) |
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Goal "[| A ~= B; A ~= Server; B ~= Server |] \ |
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\ ==> EX K. EX NA. EX evs: otway. \ |
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\ Says B A {|Nonce NA, Crypt (shrK A) {|Nonce NA, Key K|}|} \ |
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\ : set evs"; |
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by (REPEAT (resolve_tac [exI,bexI] 1)); |
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by (rtac (otway.Nil RS otway.OR1 RS otway.OR2 RS otway.OR3 RS otway.OR4) 2); |
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by possibility_tac; |
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result(); |
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(**** Inductive proofs about otway ****) |
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(*Nobody sends themselves messages*) |
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Goal "evs : otway ==> ALL A X. Says A A X ~: set evs"; |
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by (etac otway.induct 1); |
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by Auto_tac; |
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qed_spec_mp "not_Says_to_self"; |
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Addsimps [not_Says_to_self]; |
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AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
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(** For reasoning about the encrypted portion of messages **) |
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Goal "Says A' B {|N, Agent A, Agent B, X|} : set evs \ |
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\ ==> X : analz (spies evs)"; |
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by (dtac (Says_imp_spies RS analz.Inj) 1); |
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by (Blast_tac 1); |
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qed "OR2_analz_spies"; |
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Goal "Says S' B {|N, X, Crypt (shrK B) X'|} : set evs \ |
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\ ==> X : analz (spies evs)"; |
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by (dtac (Says_imp_spies RS analz.Inj) 1); |
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by (Blast_tac 1); |
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qed "OR4_analz_spies"; |
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Goal "Says Server B {|NA, X, Crypt K' {|NB,K|}|} : set evs \ |
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\ ==> K : parts (spies evs)"; |
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by (Blast_tac 1); |
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qed "Oops_parts_spies"; |
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bind_thm ("OR2_parts_spies", |
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OR2_analz_spies RS (impOfSubs analz_subset_parts)); |
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bind_thm ("OR4_parts_spies", |
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OR4_analz_spies RS (impOfSubs analz_subset_parts)); |
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(*For proving the easier theorems about X ~: parts (spies evs).*) |
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fun parts_induct_tac i = |
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etac otway.induct i THEN |
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forward_tac [Oops_parts_spies] (i+6) THEN |
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forward_tac [OR4_parts_spies] (i+5) THEN |
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forward_tac [OR2_parts_spies] (i+3) THEN |
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prove_simple_subgoals_tac i; |
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(** Theorems of the form X ~: parts (spies evs) imply that NOBODY |
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sends messages containing X! **) |
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(*Spy never sees a good agent's shared key!*) |
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Goal "evs : otway ==> (Key (shrK A) : parts (spies evs)) = (A : 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 : otway ==> (Key (shrK A) : analz (spies evs)) = (A : bad)"; |
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by (auto_tac(claset() addDs [impOfSubs analz_subset_parts], simpset())); |
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qed "Spy_analz_shrK"; |
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Addsimps [Spy_analz_shrK]; |
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AddSDs [Spy_see_shrK RSN (2, rev_iffD1), |
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Spy_analz_shrK RSN (2, rev_iffD1)]; |
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(*Nobody can have used non-existent keys!*) |
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Goal "evs : otway ==> Key K ~: used evs --> K ~: keysFor (parts (spies evs))"; |
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by (parts_induct_tac 1); |
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(*Fake*) |
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by (blast_tac (claset() addSDs [keysFor_parts_insert]) 1); |
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(*OR2, OR3*) |
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by (ALLGOALS Blast_tac); |
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qed_spec_mp "new_keys_not_used"; |
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bind_thm ("new_keys_not_analzd", |
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[analz_subset_parts RS keysFor_mono, |
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new_keys_not_used] MRS contra_subsetD); |
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Addsimps [new_keys_not_used, new_keys_not_analzd]; |
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(*** Proofs involving analz ***) |
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(*Describes the form of K and NA when the Server sends this message. Also |
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for Oops case.*) |
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Goal "[| Says Server B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
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\ evs : otway |] \ |
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\ ==> K ~: range shrK & (EX i. NA = Nonce i) & (EX j. NB = Nonce j)"; |
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by (etac rev_mp 1); |
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by (etac otway.induct 1); |
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by (ALLGOALS Simp_tac); |
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by (ALLGOALS Blast_tac); |
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qed "Says_Server_message_form"; |
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(*For proofs involving analz.*) |
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val analz_spies_tac = |
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dtac OR2_analz_spies 4 THEN |
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dtac OR4_analz_spies 6 THEN |
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forward_tac [Says_Server_message_form] 7 THEN assume_tac 7 THEN |
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REPEAT ((eresolve_tac [exE, conjE] ORELSE' hyp_subst_tac) 7); |
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(**** |
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The following is to prove theorems of the form |
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Key K : analz (insert (Key KAB) (spies evs)) ==> |
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Key K : analz (spies evs) |
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A more general formula must be proved inductively. |
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****) |
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(** Session keys are not used to encrypt other session keys **) |
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(*The equality makes the induction hypothesis easier to apply*) |
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Goal "evs : otway ==> \ |
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\ ALL K KK. KK <= Compl (range shrK) --> \ |
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\ (Key K : analz (Key``KK Un (spies evs))) = \ |
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\ (K : KK | Key K : analz (spies evs))"; |
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by (etac otway.induct 1); |
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by analz_spies_tac; |
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by (REPEAT_FIRST (resolve_tac [allI, impI])); |
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by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
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by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
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(*Fake*) |
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by (spy_analz_tac 1); |
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qed_spec_mp "analz_image_freshK"; |
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Goal "[| evs : otway; KAB ~: range shrK |] ==> \ |
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\ Key K : analz (insert (Key KAB) (spies evs)) = \ |
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\ (K = KAB | Key K : analz (spies evs))"; |
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by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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qed "analz_insert_freshK"; |
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(*** The Key K uniquely identifies the Server's message. **) |
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Goal "evs : otway ==> \ |
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\ EX B' NA' NB' X'. ALL B NA NB X. \ |
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\ Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set evs --> \ |
2131 | 175 |
\ B=B' & NA=NA' & NB=NB' & X=X'"; |
2032 | 176 |
by (etac otway.induct 1); |
4091 | 177 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
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by (ALLGOALS Clarify_tac); |
2002 | 179 |
(*Remaining cases: OR3 and OR4*) |
180 |
by (ex_strip_tac 2); |
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by (Best_tac 2); (*Blast_tac's too slow (in reconstruction)*) |
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by (expand_case_tac "K = ?y" 1); |
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by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
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(*...we assume X is a recent message, and handle this case by contradiction*) |
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by (blast_tac (claset() addSEs spies_partsEs) 1); |
2002 | 186 |
val lemma = result(); |
187 |
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Goal "[| Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set evs; \ |
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189 |
\ Says Server B' {|NA',X',Crypt (shrK B') {|NB',K|}|} : set evs; \ |
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190 |
\ evs : otway |] ==> X=X' & B=B' & NA=NA' & NB=NB'"; |
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by (prove_unique_tac lemma 1); |
2002 | 192 |
qed "unique_session_keys"; |
193 |
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(** Crucial secrecy property: Spy does not see the keys sent in msg OR3 |
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196 |
Does not in itself guarantee security: an attack could violate |
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the premises, e.g. by having A=Spy **) |
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198 |
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199 |
Goal "[| A ~: bad; B ~: bad; evs : otway |] \ |
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200 |
\ ==> Says Server B \ |
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201 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
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202 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs --> \ |
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203 |
\ Notes Spy {|NA, NB, Key K|} ~: set evs --> \ |
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204 |
\ Key K ~: analz (spies evs)"; |
2131 | 205 |
by (etac otway.induct 1); |
3683 | 206 |
by analz_spies_tac; |
2131 | 207 |
by (ALLGOALS |
4091 | 208 |
(asm_simp_tac (simpset() addcongs [conj_cong] |
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addsimps [analz_insert_eq, analz_insert_freshK] |
4831 | 210 |
addsimps (pushes@split_ifs)))); |
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211 |
(*Oops*) |
4091 | 212 |
by (blast_tac (claset() addSDs [unique_session_keys]) 4); |
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213 |
(*OR4*) |
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by (Blast_tac 3); |
2131 | 215 |
(*OR3*) |
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by (Blast_tac 2); |
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217 |
(*Fake*) |
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218 |
by (spy_analz_tac 1); |
2131 | 219 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
220 |
||
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221 |
Goal "[| Says Server B \ |
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222 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
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223 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
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224 |
\ Notes Spy {|NA, NB, Key K|} ~: set evs; \ |
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225 |
\ A ~: bad; B ~: bad; evs : otway |] \ |
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226 |
\ ==> Key K ~: analz (spies evs)"; |
2131 | 227 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
4091 | 228 |
by (blast_tac (claset() addSEs [lemma]) 1); |
2131 | 229 |
qed "Spy_not_see_encrypted_key"; |
230 |
||
231 |
||
232 |
(*** Attempting to prove stronger properties ***) |
|
233 |
||
2052 | 234 |
(*Only OR1 can have caused such a part of a message to appear. |
235 |
I'm not sure why A ~= B premise is needed: OtwayRees.ML doesn't need it. |
|
236 |
Perhaps it's because OR2 has two similar-looking encrypted messages in |
|
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237 |
this version.*) |
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238 |
Goal "[| A ~: bad; A ~= B; evs : otway |] \ |
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239 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (spies evs) --> \ |
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240 |
\ Says A B {|NA, Agent A, Agent B, \ |
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241 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs"; |
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242 |
by (parts_induct_tac 1); |
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243 |
by (ALLGOALS Blast_tac); |
2002 | 244 |
qed_spec_mp "Crypt_imp_OR1"; |
245 |
||
246 |
||
2131 | 247 |
(*Crucial property: If the encrypted message appears, and A has used NA |
248 |
to start a run, then it originated with the Server!*) |
|
249 |
(*Only it is FALSE. Somebody could make a fake message to Server |
|
2002 | 250 |
substituting some other nonce NA' for NB.*) |
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251 |
Goal "[| A ~: bad; evs : otway |] \ |
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252 |
\ ==> Crypt (shrK A) {|NA, Key K|} : parts (spies evs) --> \ |
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253 |
\ Says A B {|NA, Agent A, Agent B, \ |
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254 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
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255 |
\ : set evs --> \ |
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256 |
\ (EX B NB. Says Server B \ |
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257 |
\ {|NA, \ |
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258 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
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259 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs)"; |
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260 |
by (parts_induct_tac 1); |
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261 |
(*Fake*) |
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262 |
by (Blast_tac 1); |
2002 | 263 |
(*OR1: it cannot be a new Nonce, contradiction.*) |
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264 |
by (Blast_tac 1); |
3730 | 265 |
(*OR3 and OR4*) |
4091 | 266 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [ex_disj_distrib]))); |
3730 | 267 |
by (ALLGOALS Clarify_tac); |
2002 | 268 |
(*OR4*) |
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269 |
by (blast_tac (claset() addSIs [Crypt_imp_OR1]) 2); |
2131 | 270 |
(*OR3*) (** LEVEL 5 **) |
3730 | 271 |
(*The hypotheses at this point suggest an attack in which nonce NB is used |
2052 | 272 |
in two different roles: |
273 |
Says B' Server |
|
3730 | 274 |
{|Nonce NA, Agent Aa, Agent A, |
275 |
Crypt (shrK Aa) {|Nonce NA, Agent Aa, Agent A|}, Nonce NB, |
|
276 |
Crypt (shrK A) {|Nonce NA, Agent Aa, Agent A|}|} |
|
277 |
: set evs3; |
|
2052 | 278 |
Says A B |
3730 | 279 |
{|Nonce NB, Agent A, Agent B, |
280 |
Crypt (shrK A) {|Nonce NB, Agent A, Agent B|}|} |
|
281 |
: set evs3; |
|
2052 | 282 |
*) |
2131 | 283 |
writeln "GIVE UP! on NA_Crypt_imp_Server_msg"; |
2002 | 284 |
|
285 |
||
2052 | 286 |
(*Thus the key property A_can_trust probably fails too.*) |