author | paulson |
Mon, 14 Jul 1997 12:47:21 +0200 | |
changeset 3519 | ab0a9fbed4c0 |
parent 3516 | 470626799511 |
child 3543 | 82f33248d89d |
permissions | -rw-r--r-- |
2090 | 1 |
(* Title: HOL/Auth/OtwayRees |
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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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Simplified version with minimal encryption but explicit messages |
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From page 11 of |
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Abadi and Needham. Prudent Engineering Practice for Cryptographic Protocols. |
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IEEE Trans. SE 22 (1), 1996 |
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*) |
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open OtwayRees_AN; |
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proof_timing:=true; |
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HOL_quantifiers := false; |
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2331 | 21 |
(*A "possibility property": there are traces that reach the end*) |
2090 | 22 |
goal thy |
2331 | 23 |
"!!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 (Crypt (shrK A) {|Nonce NA, Agent A, Agent B, Key K|}) \ |
3465 | 26 |
\ : set evs"; |
2090 | 27 |
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; |
2090 | 30 |
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"; |
2090 | 37 |
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 thy "!!evs. Says S' B {|X, Crypt(shrK B) X'|} : set evs ==> \ |
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\ X : analz (sees Spy evs)"; |
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by (blast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1); |
2090 | 49 |
qed "OR4_analz_sees_Spy"; |
50 |
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goal thy "!!evs. Says Server B {|X, Crypt K' {|NB, a, Agent B, K|}|} \ |
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\ : set evs ==> K : parts (sees Spy evs)"; |
3102 | 53 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
2131 | 54 |
qed "Oops_parts_sees_Spy"; |
2090 | 55 |
|
2131 | 56 |
(*OR4_analz_sees_Spy lets 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, |
2131 | 58 |
proofs, since Fake messages originate from the Spy. *) |
2090 | 59 |
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bind_thm ("OR4_parts_sees_Spy", |
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OR4_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
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||
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(*For proving the easier theorems about X ~: parts (sees Spy 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_sees_Spy] (i+6) THEN |
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forward_tac [OR4_parts_sees_Spy] (i+5) THEN |
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prove_simple_subgoals_tac i; |
2090 | 69 |
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||
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(** Theorems of the form X ~: parts (sees Spy 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 lost at start)*) |
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goal thy |
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"!!evs. evs : otway ==> (Key (shrK A) : parts (sees Spy evs)) = (A : lost)"; |
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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); |
2131 | 80 |
qed "Spy_see_shrK"; |
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Addsimps [Spy_see_shrK]; |
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2090 | 82 |
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2131 | 83 |
goal thy |
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"!!evs. evs : otway ==> (Key (shrK A) : analz (sees Spy evs)) = (A : lost)"; |
2131 | 85 |
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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2090 | 88 |
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goal thy "!!A. [| Key (shrK A) : parts (sees Spy evs); \ |
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\ evs : otway |] ==> A:lost"; |
3102 | 91 |
by (blast_tac (!claset addDs [Spy_see_shrK]) 1); |
2131 | 92 |
qed "Spy_see_shrK_D"; |
2090 | 93 |
|
2131 | 94 |
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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2090 | 96 |
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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 (sees Spy 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)] |
3207 | 107 |
addss (!simpset)) 1); |
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(*OR3*) |
3102 | 109 |
by (Blast_tac 1); |
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qed_spec_mp "new_keys_not_used"; |
2090 | 111 |
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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.*) |
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goal thy |
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"!!evs. [| Says Server B \ |
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\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
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\ : 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)"; |
2131 | 130 |
by (etac rev_mp 1); |
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by (etac otway.induct 1); |
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3102 | 132 |
by (ALLGOALS Asm_simp_tac); |
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by (Blast_tac 1); |
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2131 | 134 |
qed "Says_Server_message_form"; |
2090 | 135 |
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||
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(*For proofs involving analz.*) |
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val analz_sees_tac = |
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dtac OR4_analz_sees_Spy 6 THEN |
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forward_tac [Says_Server_message_form] 7 THEN |
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assume_tac 7 THEN |
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REPEAT ((eresolve_tac [exE, conjE] ORELSE' hyp_subst_tac) 7); |
2090 | 143 |
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145 |
(**** |
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The following is to prove theorems of the form |
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||
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Key K : analz (insert (Key KAB) (sees Spy evs)) ==> |
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Key K : analz (sees Spy evs) |
2090 | 150 |
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A more general formula must be proved inductively. |
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****) |
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154 |
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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) --> \ |
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\ (Key K : analz (Key``KK Un (sees Spy evs))) = \ |
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\ (K : KK | Key K : analz (sees Spy evs))"; |
2090 | 163 |
by (etac otway.induct 1); |
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by analz_sees_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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168 |
(*Fake*) |
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by (spy_analz_tac 2); |
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170 |
(*Base*) |
3102 | 171 |
by (Blast_tac 1); |
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qed_spec_mp "analz_image_freshK"; |
2090 | 173 |
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174 |
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175 |
goal thy |
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"!!evs. [| evs : otway; KAB ~: range shrK |] ==> \ |
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\ Key K : analz (insert (Key KAB) (sees Spy evs)) = \ |
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178 |
\ (K = KAB | Key K : analz (sees Spy evs))"; |
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179 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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180 |
qed "analz_insert_freshK"; |
2090 | 181 |
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182 |
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183 |
(*** The Key K uniquely identifies the Server's message. **) |
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184 |
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185 |
goal thy |
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186 |
"!!evs. evs : otway ==> \ |
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\ EX A' B' NA' NB'. ALL A B NA NB. \ |
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188 |
\ Says Server B \ |
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189 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, K|}, \ |
3465 | 190 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, K|}|} : set evs \ |
2090 | 191 |
\ --> A=A' & B=B' & NA=NA' & NB=NB'"; |
192 |
by (etac otway.induct 1); |
|
193 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
|
194 |
by (Step_tac 1); |
|
195 |
(*Remaining cases: OR3 and OR4*) |
|
196 |
by (ex_strip_tac 2); |
|
3102 | 197 |
by (Blast_tac 2); |
2090 | 198 |
by (expand_case_tac "K = ?y" 1); |
199 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
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200 |
(*...we assume X is a recent message and handle this case by contradiction*) |
3102 | 201 |
by (blast_tac (!claset addSEs sees_Spy_partsEs |
202 |
delrules[conjI] (*prevent splitup into 4 subgoals*)) 1); |
|
2090 | 203 |
val lemma = result(); |
204 |
||
205 |
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206 |
goal thy |
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207 |
"!!evs. [| Says Server B \ |
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208 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, K|}, \ |
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\ Crypt (shrK B) {|NB, Agent A, Agent B, K|}|} \ |
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210 |
\ : set evs; \ |
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\ Says Server B' \ |
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212 |
\ {|Crypt (shrK A') {|NA', Agent A', Agent B', K|}, \ |
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\ Crypt (shrK B') {|NB', Agent A', Agent B', K|}|} \ |
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\ : set evs; \ |
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215 |
\ evs : otway |] \ |
2090 | 216 |
\ ==> A=A' & B=B' & NA=NA' & NB=NB'"; |
2417 | 217 |
by (prove_unique_tac lemma 1); |
2090 | 218 |
qed "unique_session_keys"; |
219 |
||
220 |
||
221 |
||
222 |
(**** Authenticity properties relating to NA ****) |
|
223 |
||
224 |
(*If the encrypted message appears then it originated with the Server!*) |
|
225 |
goal thy |
|
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226 |
"!!evs. [| A ~: lost; evs : otway |] \ |
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227 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B, Key K|} \ |
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228 |
\ : parts (sees Spy evs) \ |
2331 | 229 |
\ --> (EX NB. Says Server B \ |
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230 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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231 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
3465 | 232 |
\ : set evs)"; |
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233 |
by (parts_induct_tac 1); |
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234 |
by (Fake_parts_insert_tac 1); |
2090 | 235 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib]))); |
236 |
(*OR3*) |
|
3102 | 237 |
by (Blast_tac 1); |
2090 | 238 |
qed_spec_mp "NA_Crypt_imp_Server_msg"; |
239 |
||
240 |
||
2454 | 241 |
(*Corollary: if A receives B's OR4 message then it originated with the Server. |
242 |
Freshness may be inferred from nonce NA.*) |
|
2090 | 243 |
goal thy |
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244 |
"!!evs. [| Says B' A (Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}) \ |
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245 |
\ : set evs; \ |
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246 |
\ A ~: lost; evs : otway |] \ |
2090 | 247 |
\ ==> EX NB. Says Server B \ |
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248 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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249 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
3465 | 250 |
\ : set evs"; |
3102 | 251 |
by (blast_tac (!claset addSIs [NA_Crypt_imp_Server_msg] |
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252 |
addEs sees_Spy_partsEs) 1); |
2331 | 253 |
qed "A_trusts_OR4"; |
2090 | 254 |
|
255 |
||
256 |
(** Crucial secrecy property: Spy does not see the keys sent in msg OR3 |
|
257 |
Does not in itself guarantee security: an attack could violate |
|
258 |
the premises, e.g. by having A=Spy **) |
|
259 |
||
260 |
goal thy |
|
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261 |
"!!evs. [| A ~: lost; B ~: lost; evs : otway |] \ |
2090 | 262 |
\ ==> Says Server B \ |
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263 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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|
264 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
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265 |
\ : set evs --> \ |
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266 |
\ Says B Spy {|NA, NB, Key K|} ~: set evs --> \ |
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267 |
\ Key K ~: analz (sees Spy evs)"; |
2090 | 268 |
by (etac otway.induct 1); |
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269 |
by analz_sees_tac; |
2090 | 270 |
by (ALLGOALS |
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|
271 |
(asm_simp_tac (!simpset addcongs [conj_cong] |
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|
272 |
addsimps [analz_insert_eq, not_parts_not_analz, |
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273 |
analz_insert_freshK] |
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|
274 |
setloop split_tac [expand_if]))); |
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275 |
(*Oops*) |
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276 |
by (blast_tac (!claset addSDs [unique_session_keys]) 4); |
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|
277 |
(*OR4*) |
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|
278 |
by (Blast_tac 3); |
2090 | 279 |
(*OR3*) |
3102 | 280 |
by (blast_tac (!claset addSEs sees_Spy_partsEs |
281 |
addIs [impOfSubs analz_subset_parts]) 2); |
|
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282 |
(*Fake*) |
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|
283 |
by (spy_analz_tac 1); |
2090 | 284 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
285 |
||
286 |
goal thy |
|
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287 |
"!!evs. [| Says Server B \ |
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|
288 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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|
289 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
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290 |
\ : set evs; \ |
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|
291 |
\ Says B Spy {|NA, NB, Key K|} ~: set evs; \ |
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292 |
\ A ~: lost; B ~: lost; evs : otway |] \ |
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|
293 |
\ ==> Key K ~: analz (sees Spy evs)"; |
2090 | 294 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
2891 | 295 |
by (blast_tac (!claset addSEs [lemma]) 1); |
2090 | 296 |
qed "Spy_not_see_encrypted_key"; |
297 |
||
298 |
||
299 |
(**** Authenticity properties relating to NB ****) |
|
300 |
||
301 |
(*If the encrypted message appears then it originated with the Server!*) |
|
302 |
goal thy |
|
3519
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changeset
|
303 |
"!!evs. [| B ~: lost; evs : otway |] \ |
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changeset
|
304 |
\ ==> Crypt (shrK B) {|NB, Agent A, Agent B, Key K|} \ |
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changeset
|
305 |
\ : parts (sees Spy evs) \ |
2090 | 306 |
\ --> (EX NA. Says Server B \ |
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|
307 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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changeset
|
308 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
3465 | 309 |
\ : set evs)"; |
3519
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changeset
|
310 |
by (parts_induct_tac 1); |
3121
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Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
311 |
by (Fake_parts_insert_tac 1); |
2090 | 312 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib]))); |
313 |
(*OR3*) |
|
3102 | 314 |
by (Blast_tac 1); |
2090 | 315 |
qed_spec_mp "NB_Crypt_imp_Server_msg"; |
316 |
||
317 |
||
2454 | 318 |
(*Guarantee for B: if it gets a well-formed certificate then the Server |
319 |
has sent the correct message in round 3.*) |
|
2090 | 320 |
goal thy |
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
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changeset
|
321 |
"!!evs. [| B ~: lost; evs : otway; \ |
2837
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Trivial renamings (for consistency with CSFW papers)
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|
322 |
\ Says S' B {|X, Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
3466
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Corrected indentations and margins after the renaming of "set_of_list"
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|
323 |
\ : set evs |] \ |
2106 | 324 |
\ ==> EX NA. Says Server B \ |
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|
325 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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changeset
|
326 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
3465 | 327 |
\ : set evs"; |
3102 | 328 |
by (blast_tac (!claset addSIs [NB_Crypt_imp_Server_msg] |
329 |
addEs sees_Spy_partsEs) 1); |
|
2331 | 330 |
qed "B_trusts_OR3"; |