author | paulson |
Thu, 18 Sep 1997 13:24:04 +0200 | |
changeset 3683 | aafe719dff14 |
parent 3674 | 65ec38fbb265 |
child 3730 | 6933d20f335f |
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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||
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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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||
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This file illustrates the consequences of such errors. We can still prove |
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2032 | 13 |
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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||
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open OtwayRees_Bad; |
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proof_timing:=true; |
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HOL_quantifiers := false; |
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(*A "possibility property": there are traces that reach the end*) |
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goal thy |
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"!!A B. [| 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"; |
2002 | 30 |
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 thy "!!evs. evs : otway ==> ALL A X. Says A A X ~: set evs"; |
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by (etac otway.induct 1); |
2002 | 41 |
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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||
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goal thy "!!evs. Says A' B {|N, Agent A, Agent B, X|} : set evs ==> \ |
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\ X : analz (spies evs)"; |
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by (blast_tac (!claset addSDs [Says_imp_spies RS analz.Inj]) 1); |
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qed "OR2_analz_spies"; |
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2002 | 53 |
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goal thy "!!evs. Says S' B {|N, X, Crypt (shrK B) X'|} : set evs ==> \ |
3683 | 55 |
\ X : analz (spies evs)"; |
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by (blast_tac (!claset addSDs [Says_imp_spies RS analz.Inj]) 1); |
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qed "OR4_analz_spies"; |
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2002 | 58 |
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goal thy "!!evs. 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 (!claset addSEs spies_partsEs) 1); |
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qed "Oops_parts_spies"; |
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2002 | 63 |
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(*OR2_analz... and OR4_analz... let us treat those cases using the same |
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argument as for the Fake case. This is possible for most, but not all, |
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proofs: Fake does not invent new nonces (as in OR2), and of course Fake |
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messages originate from the Spy. *) |
2002 | 68 |
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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; |
2002 | 81 |
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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 another agent's shared key! (unless it's bad at start)*) |
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goal thy |
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"!!evs. evs : otway ==> (Key (shrK A) : parts (spies evs)) = (A : bad)"; |
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by (parts_induct_tac 1); |
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by (Fake_parts_insert_tac 1); |
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by (Blast_tac 1); |
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qed "Spy_see_shrK"; |
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Addsimps [Spy_see_shrK]; |
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2002 | 94 |
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goal thy |
3683 | 96 |
"!!evs. evs : otway ==> (Key (shrK A) : analz (spies evs)) = (A : bad)"; |
2131 | 97 |
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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2002 | 100 |
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3683 | 101 |
goal thy "!!A. [| Key (shrK A) : parts (spies evs); evs : otway |] ==> A:bad"; |
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by (blast_tac (!claset addDs [Spy_see_shrK]) 1); |
2131 | 103 |
qed "Spy_see_shrK_D"; |
2002 | 104 |
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2131 | 105 |
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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2002 | 107 |
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(*Nobody can have used non-existent keys!*) |
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goal thy "!!evs. evs : otway ==> \ |
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\ Key K ~: used evs --> K ~: keysFor (parts (spies evs))"; |
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by (parts_induct_tac 1); |
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(*Fake*) |
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by (best_tac |
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(!claset addIs [impOfSubs analz_subset_parts] |
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addDs [impOfSubs (analz_subset_parts RS keysFor_mono), |
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impOfSubs (parts_insert_subset_Un RS keysFor_mono)] |
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addss (!simpset)) 1); |
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(*OR1-3*) |
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by (ALLGOALS Blast_tac); |
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qed_spec_mp "new_keys_not_used"; |
2002 | 122 |
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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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2002 | 126 |
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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 thy |
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"!!evs. [| Says Server B \ |
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\ {|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 (prove_simple_subgoals_tac 1); |
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by (Blast_tac 1); |
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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 thy |
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"!!evs. evs : otway ==> \ |
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\ ALL K KK. KK <= Compl (range shrK) --> \ |
3683 | 171 |
\ (Key K : analz (Key``KK Un (spies evs))) = \ |
172 |
\ (K : KK | Key K : analz (spies evs))"; |
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by (etac otway.induct 1); |
3683 | 174 |
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 2); |
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(*Base*) |
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by (Blast_tac 1); |
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qed_spec_mp "analz_image_freshK"; |
2002 | 183 |
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184 |
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goal thy |
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"!!evs. [| evs : otway; KAB ~: range shrK |] ==> \ |
3683 | 187 |
\ Key K : analz (insert (Key KAB) (spies evs)) = \ |
188 |
\ (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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190 |
qed "analz_insert_freshK"; |
2002 | 191 |
|
192 |
||
2131 | 193 |
(*** The Key K uniquely identifies the Server's message. **) |
2002 | 194 |
|
195 |
goal thy |
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"!!evs. 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 | 199 |
\ B=B' & NA=NA' & NB=NB' & X=X'"; |
2032 | 200 |
by (etac otway.induct 1); |
2002 | 201 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
202 |
by (Step_tac 1); |
|
203 |
(*Remaining cases: OR3 and OR4*) |
|
204 |
by (ex_strip_tac 2); |
|
3102 | 205 |
by (Blast_tac 2); |
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206 |
by (expand_case_tac "K = ?y" 1); |
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207 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
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208 |
(*...we assume X is a recent message, and handle this case by contradiction*) |
3683 | 209 |
by (blast_tac (!claset addSEs spies_partsEs |
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210 |
delrules [conjI] (*no split-up to 4 subgoals*)) 1); |
2002 | 211 |
val lemma = result(); |
212 |
||
213 |
goal thy |
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"!!evs. [| Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set evs; \ |
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215 |
\ Says Server B' {|NA',X',Crypt (shrK B') {|NB',K|}|} : set evs; \ |
2131 | 216 |
\ evs : otway |] ==> X=X' & B=B' & NA=NA' & NB=NB'"; |
2417 | 217 |
by (prove_unique_tac lemma 1); |
2002 | 218 |
qed "unique_session_keys"; |
219 |
||
220 |
||
2131 | 221 |
(*Crucial security property, but not itself enough to guarantee correctness!*) |
222 |
goal thy |
|
3683 | 223 |
"!!evs. [| A ~: bad; B ~: bad; evs : otway |] \ |
2166 | 224 |
\ ==> Says Server B \ |
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\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
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\ Crypt (shrK B) {|NB, Key K|}|} : set evs --> \ |
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227 |
\ Says B Spy {|NA, NB, Key K|} ~: set evs --> \ |
3683 | 228 |
\ Key K ~: analz (spies evs)"; |
2131 | 229 |
by (etac otway.induct 1); |
3683 | 230 |
by analz_spies_tac; |
2131 | 231 |
by (ALLGOALS |
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(asm_simp_tac (!simpset addcongs [conj_cong] |
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233 |
addsimps [analz_insert_eq, analz_insert_freshK] |
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234 |
setloop split_tac [expand_if]))); |
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235 |
(*Oops*) |
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236 |
by (blast_tac (!claset addSDs [unique_session_keys]) 4); |
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237 |
(*OR4*) |
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238 |
by (Blast_tac 3); |
2131 | 239 |
(*OR3*) |
3683 | 240 |
by (blast_tac (!claset addSEs spies_partsEs |
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241 |
addIs [impOfSubs analz_subset_parts]) 2); |
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Made proofs more concise by replacing calls to spy_analz_tac by uses of
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242 |
(*Fake*) |
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Made proofs more concise by replacing calls to spy_analz_tac by uses of
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243 |
by (spy_analz_tac 1); |
2131 | 244 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
245 |
||
246 |
goal thy |
|
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Corrected indentations and margins after the renaming of "set_of_list"
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247 |
"!!evs. [| Says Server B \ |
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248 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
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249 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
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\ Says B Spy {|NA, NB, Key K|} ~: set evs; \ |
3683 | 251 |
\ A ~: bad; B ~: bad; evs : otway |] \ |
252 |
\ ==> Key K ~: analz (spies evs)"; |
|
2131 | 253 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
3102 | 254 |
by (blast_tac (!claset addSEs [lemma]) 1); |
2131 | 255 |
qed "Spy_not_see_encrypted_key"; |
256 |
||
257 |
||
258 |
(*** Attempting to prove stronger properties ***) |
|
259 |
||
2052 | 260 |
(*Only OR1 can have caused such a part of a message to appear. |
261 |
I'm not sure why A ~= B premise is needed: OtwayRees.ML doesn't need it. |
|
262 |
Perhaps it's because OR2 has two similar-looking encrypted messages in |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
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263 |
this version.*) |
2002 | 264 |
goal thy |
3683 | 265 |
"!!evs. [| A ~: bad; A ~= B; evs : otway |] \ |
266 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (spies evs) --> \ |
|
2131 | 267 |
\ Says A B {|NA, Agent A, Agent B, \ |
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268 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs"; |
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
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269 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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270 |
by (Fake_parts_insert_tac 1); |
3102 | 271 |
by (Blast_tac 1); |
2002 | 272 |
qed_spec_mp "Crypt_imp_OR1"; |
273 |
||
274 |
||
2131 | 275 |
(*Crucial property: If the encrypted message appears, and A has used NA |
276 |
to start a run, then it originated with the Server!*) |
|
277 |
(*Only it is FALSE. Somebody could make a fake message to Server |
|
2002 | 278 |
substituting some other nonce NA' for NB.*) |
279 |
goal thy |
|
3683 | 280 |
"!!evs. [| A ~: bad; A ~= Spy; evs : otway |] \ |
281 |
\ ==> Crypt (shrK A) {|NA, Key K|} : parts (spies evs) --> \ |
|
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282 |
\ Says A B {|NA, Agent A, Agent B, \ |
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283 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
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284 |
\ : set evs --> \ |
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Changing "lost" from a parameter of protocol definitions to a constant.
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285 |
\ (EX B NB. Says Server B \ |
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Changing "lost" from a parameter of protocol definitions to a constant.
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|
286 |
\ {|NA, \ |
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Changing "lost" from a parameter of protocol definitions to a constant.
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|
287 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
3466
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Corrected indentations and margins after the renaming of "set_of_list"
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288 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs)"; |
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
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|
289 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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diff
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|
290 |
by (Fake_parts_insert_tac 1); |
2002 | 291 |
(*OR1: it cannot be a new Nonce, contradiction.*) |
3102 | 292 |
by (blast_tac (!claset addSIs [parts_insertI] |
3683 | 293 |
addSEs spies_partsEs) 1); |
2002 | 294 |
(*OR4*) |
295 |
by (REPEAT (Safe_step_tac 2)); |
|
3102 | 296 |
by (REPEAT (blast_tac (!claset addSDs [parts_cut]) 3)); |
297 |
by (blast_tac (!claset addSIs [Crypt_imp_OR1] |
|
3683 | 298 |
addEs spies_partsEs) 2); |
2131 | 299 |
(*OR3*) (** LEVEL 5 **) |
2002 | 300 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib]))); |
2052 | 301 |
by (step_tac (!claset delrules [disjCI, impCE]) 1); |
2002 | 302 |
(*The hypotheses at this point suggest an attack in which nonce NA is used |
2052 | 303 |
in two different roles: |
304 |
Says B' Server |
|
305 |
{|Nonce NAa, Agent Aa, Agent A, |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
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|
306 |
Crypt (shrK Aa) {|Nonce NAa, Agent Aa, Agent A|}, Nonce NA, |
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Swapped arguments of Crypt (for clarity and because it is conventional)
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|
307 |
Crypt (shrK A) {|Nonce NAa, Agent Aa, Agent A|}|} |
3465 | 308 |
: set evsa; |
2052 | 309 |
Says A B |
310 |
{|Nonce NA, Agent A, Agent B, |
|
2284
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|
311 |
Crypt (shrK A) {|Nonce NA, Agent A, Agent B|}|} |
3465 | 312 |
: set evsa |
2052 | 313 |
*) |
2131 | 314 |
writeln "GIVE UP! on NA_Crypt_imp_Server_msg"; |
2002 | 315 |
|
316 |
||
2052 | 317 |
(*Thus the key property A_can_trust probably fails too.*) |