author | wenzelm |
Thu, 28 Sep 2006 23:42:35 +0200 | |
changeset 20768 | 1d478c2d621f |
parent 16417 | 9bc16273c2d4 |
child 21404 | eb85850d3eb7 |
permissions | -rw-r--r-- |
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(* Title: HOL/Auth/ZhouGollmann |
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ID: $Id$ |
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Author: Giampaolo Bella and L C Paulson, Cambridge Univ Computer Lab |
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Copyright 2003 University of Cambridge |
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|
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The protocol of |
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Jianying Zhou and Dieter Gollmann, |
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A Fair Non-Repudiation Protocol, |
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Security and Privacy 1996 (Oakland) |
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55-61 |
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*) |
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|
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theory ZhouGollmann imports Public begin |
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abbreviation |
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TTP :: agent |
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"TTP == Server" |
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f_sub :: nat |
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"f_sub == 5" |
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f_nro :: nat |
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"f_nro == 2" |
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f_nrr :: nat |
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"f_nrr == 3" |
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f_con :: nat |
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"f_con == 4" |
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|
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constdefs |
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broken :: "agent set" |
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--{*the compromised honest agents; TTP is included as it's not allowed to |
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use the protocol*} |
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"broken == bad - {Spy}" |
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declare broken_def [simp] |
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consts zg :: "event list set" |
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inductive zg |
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intros |
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Nil: "[] \<in> zg" |
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Fake: "[| evsf \<in> zg; X \<in> synth (analz (spies evsf)) |] |
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==> Says Spy B X # evsf \<in> zg" |
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Reception: "[| evsr \<in> zg; Says A B X \<in> set evsr |] ==> Gets B X # evsr \<in> zg" |
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(*L is fresh for honest agents. |
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We don't require K to be fresh because we don't bother to prove secrecy! |
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We just assume that the protocol's objective is to deliver K fairly, |
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rather than to keep M secret.*) |
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ZG1: "[| evs1 \<in> zg; Nonce L \<notin> used evs1; C = Crypt K (Number m); |
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K \<in> symKeys; |
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NRO = Crypt (priK A) {|Number f_nro, Agent B, Nonce L, C|}|] |
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==> Says A B {|Number f_nro, Agent B, Nonce L, C, NRO|} # evs1 \<in> zg" |
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(*B must check that NRO is A's signature to learn the sender's name*) |
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ZG2: "[| evs2 \<in> zg; |
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Gets B {|Number f_nro, Agent B, Nonce L, C, NRO|} \<in> set evs2; |
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NRO = Crypt (priK A) {|Number f_nro, Agent B, Nonce L, C|}; |
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NRR = Crypt (priK B) {|Number f_nrr, Agent A, Nonce L, C|}|] |
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==> Says B A {|Number f_nrr, Agent A, Nonce L, NRR|} # evs2 \<in> zg" |
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(*A must check that NRR is B's signature to learn the sender's name; |
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without spy, the matching label would be enough*) |
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ZG3: "[| evs3 \<in> zg; C = Crypt K M; K \<in> symKeys; |
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Says A B {|Number f_nro, Agent B, Nonce L, C, NRO|} \<in> set evs3; |
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Gets A {|Number f_nrr, Agent A, Nonce L, NRR|} \<in> set evs3; |
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NRR = Crypt (priK B) {|Number f_nrr, Agent A, Nonce L, C|}; |
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sub_K = Crypt (priK A) {|Number f_sub, Agent B, Nonce L, Key K|}|] |
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==> Says A TTP {|Number f_sub, Agent B, Nonce L, Key K, sub_K|} |
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# evs3 \<in> zg" |
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(*TTP checks that sub_K is A's signature to learn who issued K, then |
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gives credentials to A and B. The Notes event models the availability of |
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the credentials, but the act of fetching them is not modelled. We also |
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give con_K to the Spy. This makes the threat model more dangerous, while |
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also allowing lemma @{text Crypt_used_imp_spies} to omit the condition |
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@{term "K \<noteq> priK TTP"}. *) |
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ZG4: "[| evs4 \<in> zg; K \<in> symKeys; |
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Gets TTP {|Number f_sub, Agent B, Nonce L, Key K, sub_K|} |
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\<in> set evs4; |
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sub_K = Crypt (priK A) {|Number f_sub, Agent B, Nonce L, Key K|}; |
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con_K = Crypt (priK TTP) {|Number f_con, Agent A, Agent B, |
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Nonce L, Key K|}|] |
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==> Says TTP Spy con_K |
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# |
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Notes TTP {|Number f_con, Agent A, Agent B, Nonce L, Key K, con_K|} |
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# evs4 \<in> zg" |
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declare Says_imp_knows_Spy [THEN analz.Inj, dest] |
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declare Fake_parts_insert_in_Un [dest] |
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declare analz_into_parts [dest] |
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declare symKey_neq_priEK [simp] |
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declare symKey_neq_priEK [THEN not_sym, simp] |
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text{*A "possibility property": there are traces that reach the end*} |
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lemma "[|A \<noteq> B; TTP \<noteq> A; TTP \<noteq> B; K \<in> symKeys|] ==> |
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\<exists>L. \<exists>evs \<in> zg. |
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Notes TTP {|Number f_con, Agent A, Agent B, Nonce L, Key K, |
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Crypt (priK TTP) {|Number f_con, Agent A, Agent B, Nonce L, Key K|} |} |
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\<in> set evs" |
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apply (intro exI bexI) |
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apply (rule_tac [2] zg.Nil |
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[THEN zg.ZG1, THEN zg.Reception [of _ A B], |
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THEN zg.ZG2, THEN zg.Reception [of _ B A], |
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THEN zg.ZG3, THEN zg.Reception [of _ A TTP], |
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THEN zg.ZG4]) |
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apply (possibility, auto) |
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done |
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subsection {*Basic Lemmas*} |
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lemma Gets_imp_Says: |
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"[| Gets B X \<in> set evs; evs \<in> zg |] ==> \<exists>A. Says A B X \<in> set evs" |
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apply (erule rev_mp) |
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apply (erule zg.induct, auto) |
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done |
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lemma Gets_imp_knows_Spy: |
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"[| Gets B X \<in> set evs; evs \<in> zg |] ==> X \<in> spies evs" |
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by (blast dest!: Gets_imp_Says Says_imp_knows_Spy) |
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text{*Lets us replace proofs about @{term "used evs"} by simpler proofs |
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about @{term "parts (spies evs)"}.*} |
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lemma Crypt_used_imp_spies: |
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"[| Crypt K X \<in> used evs; evs \<in> zg |] |
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==> Crypt K X \<in> parts (spies evs)" |
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apply (erule rev_mp) |
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apply (erule zg.induct) |
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apply (simp_all add: parts_insert_knows_A) |
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done |
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|
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lemma Notes_TTP_imp_Gets: |
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"[|Notes TTP {|Number f_con, Agent A, Agent B, Nonce L, Key K, con_K |} |
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\<in> set evs; |
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sub_K = Crypt (priK A) {|Number f_sub, Agent B, Nonce L, Key K|}; |
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evs \<in> zg|] |
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==> Gets TTP {|Number f_sub, Agent B, Nonce L, Key K, sub_K|} \<in> set evs" |
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apply (erule rev_mp) |
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apply (erule zg.induct, auto) |
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done |
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|
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text{*For reasoning about C, which is encrypted in message ZG2*} |
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lemma ZG2_msg_in_parts_spies: |
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"[|Gets B {|F, B', L, C, X|} \<in> set evs; evs \<in> zg|] |
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==> C \<in> parts (spies evs)" |
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by (blast dest: Gets_imp_Says) |
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|
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(*classical regularity lemma on priK*) |
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lemma Spy_see_priK [simp]: |
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"evs \<in> zg ==> (Key (priK A) \<in> parts (spies evs)) = (A \<in> bad)" |
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apply (erule zg.induct) |
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apply (frule_tac [5] ZG2_msg_in_parts_spies, auto) |
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done |
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|
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text{*So that blast can use it too*} |
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declare Spy_see_priK [THEN [2] rev_iffD1, dest!] |
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|
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lemma Spy_analz_priK [simp]: |
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"evs \<in> zg ==> (Key (priK A) \<in> analz (spies evs)) = (A \<in> bad)" |
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by auto |
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|
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|
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subsection{*About NRO: Validity for @{term B}*} |
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|
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text{*Below we prove that if @{term NRO} exists then @{term A} definitely |
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sent it, provided @{term A} is not broken.*} |
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|
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text{*Strong conclusion for a good agent*} |
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lemma NRO_validity_good: |
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"[|NRO = Crypt (priK A) {|Number f_nro, Agent B, Nonce L, C|}; |
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NRO \<in> parts (spies evs); |
|
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A \<notin> bad; evs \<in> zg |] |
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==> Says A B {|Number f_nro, Agent B, Nonce L, C, NRO|} \<in> set evs" |
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apply clarify |
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apply (erule rev_mp) |
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apply (erule zg.induct) |
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apply (frule_tac [5] ZG2_msg_in_parts_spies, auto) |
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done |
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|
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lemma NRO_sender: |
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"[|Says A' B {|n, b, l, C, Crypt (priK A) X|} \<in> set evs; evs \<in> zg|] |
|
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==> A' \<in> {A,Spy}" |
|
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apply (erule rev_mp) |
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apply (erule zg.induct, simp_all) |
|
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done |
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|
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text{*Holds also for @{term "A = Spy"}!*} |
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theorem NRO_validity: |
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"[|Gets B {|Number f_nro, Agent B, Nonce L, C, NRO|} \<in> set evs; |
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NRO = Crypt (priK A) {|Number f_nro, Agent B, Nonce L, C|}; |
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A \<notin> broken; evs \<in> zg |] |
|
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==> Says A B {|Number f_nro, Agent B, Nonce L, C, NRO|} \<in> set evs" |
|
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apply (drule Gets_imp_Says, assumption) |
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apply clarify |
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apply (frule NRO_sender, auto) |
|
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txt{*We are left with the case where the sender is @{term Spy} and not |
204 |
equal to @{term A}, because @{term "A \<notin> bad"}. |
|
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Thus theorem @{text NRO_validity_good} applies.*} |
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apply (blast dest: NRO_validity_good [OF refl]) |
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done |
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|
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|
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subsection{*About NRR: Validity for @{term A}*} |
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|
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text{*Below we prove that if @{term NRR} exists then @{term B} definitely |
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sent it, provided @{term B} is not broken.*} |
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|
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text{*Strong conclusion for a good agent*} |
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lemma NRR_validity_good: |
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"[|NRR = Crypt (priK B) {|Number f_nrr, Agent A, Nonce L, C|}; |
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NRR \<in> parts (spies evs); |
|
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B \<notin> bad; evs \<in> zg |] |
|
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==> Says B A {|Number f_nrr, Agent A, Nonce L, NRR|} \<in> set evs" |
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apply clarify |
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apply (erule rev_mp) |
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apply (erule zg.induct) |
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apply (frule_tac [5] ZG2_msg_in_parts_spies, auto) |
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done |
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|
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lemma NRR_sender: |
228 |
"[|Says B' A {|n, a, l, Crypt (priK B) X|} \<in> set evs; evs \<in> zg|] |
|
229 |
==> B' \<in> {B,Spy}" |
|
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apply (erule rev_mp) |
|
231 |
apply (erule zg.induct, simp_all) |
|
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done |
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|
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text{*Holds also for @{term "B = Spy"}!*} |
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theorem NRR_validity: |
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"[|Says B' A {|Number f_nrr, Agent A, Nonce L, NRR|} \<in> set evs; |
237 |
NRR = Crypt (priK B) {|Number f_nrr, Agent A, Nonce L, C|}; |
|
238 |
B \<notin> broken; evs \<in> zg|] |
|
239 |
==> Says B A {|Number f_nrr, Agent A, Nonce L, NRR|} \<in> set evs" |
|
240 |
apply clarify |
|
241 |
apply (frule NRR_sender, auto) |
|
242 |
txt{*We are left with the case where @{term "B' = Spy"} and @{term "B' \<noteq> B"}, |
|
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i.e. @{term "B \<notin> bad"}, when we can apply @{text NRR_validity_good}.*} |
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apply (blast dest: NRR_validity_good [OF refl]) |
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done |
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|
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|
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subsection{*Proofs About @{term sub_K}*} |
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|
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text{*Below we prove that if @{term sub_K} exists then @{term A} definitely |
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sent it, provided @{term A} is not broken. *} |
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|
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text{*Strong conclusion for a good agent*} |
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lemma sub_K_validity_good: |
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"[|sub_K = Crypt (priK A) {|Number f_sub, Agent B, Nonce L, Key K|}; |
256 |
sub_K \<in> parts (spies evs); |
|
257 |
A \<notin> bad; evs \<in> zg |] |
|
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==> Says A TTP {|Number f_sub, Agent B, Nonce L, Key K, sub_K|} \<in> set evs" |
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apply clarify |
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apply (erule rev_mp) |
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apply (erule zg.induct) |
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apply (frule_tac [5] ZG2_msg_in_parts_spies, simp_all) |
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txt{*Fake*} |
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apply (blast dest!: Fake_parts_sing_imp_Un) |
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done |
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|
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lemma sub_K_sender: |
268 |
"[|Says A' TTP {|n, b, l, k, Crypt (priK A) X|} \<in> set evs; evs \<in> zg|] |
|
269 |
==> A' \<in> {A,Spy}" |
|
270 |
apply (erule rev_mp) |
|
271 |
apply (erule zg.induct, simp_all) |
|
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done |
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|
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text{*Holds also for @{term "A = Spy"}!*} |
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theorem sub_K_validity: |
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"[|Gets TTP {|Number f_sub, Agent B, Nonce L, Key K, sub_K|} \<in> set evs; |
14741 | 277 |
sub_K = Crypt (priK A) {|Number f_sub, Agent B, Nonce L, Key K|}; |
278 |
A \<notin> broken; evs \<in> zg |] |
|
279 |
==> Says A TTP {|Number f_sub, Agent B, Nonce L, Key K, sub_K|} \<in> set evs" |
|
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apply (drule Gets_imp_Says, assumption) |
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apply clarify |
282 |
apply (frule sub_K_sender, auto) |
|
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txt{*We are left with the case where the sender is @{term Spy} and not |
284 |
equal to @{term A}, because @{term "A \<notin> bad"}. |
|
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Thus theorem @{text sub_K_validity_good} applies.*} |
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apply (blast dest: sub_K_validity_good [OF refl]) |
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done |
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|
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|
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|
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subsection{*Proofs About @{term con_K}*} |
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|
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text{*Below we prove that if @{term con_K} exists, then @{term TTP} has it, |
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and therefore @{term A} and @{term B}) can get it too. Moreover, we know |
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that @{term A} sent @{term sub_K}*} |
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|
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lemma con_K_validity: |
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"[|con_K \<in> used evs; |
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con_K = Crypt (priK TTP) |
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{|Number f_con, Agent A, Agent B, Nonce L, Key K|}; |
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evs \<in> zg |] |
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==> Notes TTP {|Number f_con, Agent A, Agent B, Nonce L, Key K, con_K|} |
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\<in> set evs" |
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|
304 |
apply clarify |
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apply (erule rev_mp) |
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apply (erule zg.induct) |
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apply (frule_tac [5] ZG2_msg_in_parts_spies, simp_all) |
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txt{*Fake*} |
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apply (blast dest!: Fake_parts_sing_imp_Un) |
14741 | 310 |
txt{*ZG2*} |
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apply (blast dest: parts_cut) |
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312 |
done |
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313 |
|
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text{*If @{term TTP} holds @{term con_K} then @{term A} sent |
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@{term sub_K}. We assume that @{term A} is not broken. Importantly, nothing |
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needs to be assumed about the form of @{term con_K}!*} |
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lemma Notes_TTP_imp_Says_A: |
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"[|Notes TTP {|Number f_con, Agent A, Agent B, Nonce L, Key K, con_K|} |
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\<in> set evs; |
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sub_K = Crypt (priK A) {|Number f_sub, Agent B, Nonce L, Key K|}; |
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A \<notin> broken; evs \<in> zg|] |
14741 | 322 |
==> Says A TTP {|Number f_sub, Agent B, Nonce L, Key K, sub_K|} \<in> set evs" |
323 |
apply clarify |
|
324 |
apply (erule rev_mp) |
|
325 |
apply (erule zg.induct) |
|
326 |
apply (frule_tac [5] ZG2_msg_in_parts_spies, simp_all) |
|
327 |
txt{*ZG4*} |
|
15047 | 328 |
apply clarify |
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329 |
apply (rule sub_K_validity, auto) |
14741 | 330 |
done |
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|
331 |
|
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text{*If @{term con_K} exists, then @{term A} sent @{term sub_K}. We again |
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|
333 |
assume that @{term A} is not broken. *} |
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|
334 |
theorem B_sub_K_validity: |
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|
335 |
"[|con_K \<in> used evs; |
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|
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con_K = Crypt (priK TTP) {|Number f_con, Agent A, Agent B, |
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Nonce L, Key K|}; |
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|
338 |
sub_K = Crypt (priK A) {|Number f_sub, Agent B, Nonce L, Key K|}; |
14741 | 339 |
A \<notin> broken; evs \<in> zg|] |
340 |
==> Says A TTP {|Number f_sub, Agent B, Nonce L, Key K, sub_K|} \<in> set evs" |
|
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|
341 |
by (blast dest: con_K_validity Notes_TTP_imp_Says_A) |
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|
342 |
|
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|
343 |
|
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|
344 |
subsection{*Proving fairness*} |
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|
345 |
|
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|
346 |
text{*Cannot prove that, if @{term B} has NRO, then @{term A} has her NRR. |
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|
347 |
It would appear that @{term B} has a small advantage, though it is |
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|
348 |
useless to win disputes: @{term B} needs to present @{term con_K} as well.*} |
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|
349 |
|
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|
350 |
text{*Strange: unicity of the label protects @{term A}?*} |
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|
351 |
lemma A_unicity: |
2e31b8cc8788
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|
352 |
"[|NRO = Crypt (priK A) {|Number f_nro, Agent B, Nonce L, Crypt K M|}; |
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|
353 |
NRO \<in> parts (spies evs); |
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|
354 |
Says A B {|Number f_nro, Agent B, Nonce L, Crypt K M', NRO'|} |
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|
355 |
\<in> set evs; |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
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|
356 |
A \<notin> bad; evs \<in> zg |] |
2e31b8cc8788
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|
357 |
==> M'=M" |
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|
358 |
apply clarify |
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paulson
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changeset
|
359 |
apply (erule rev_mp) |
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|
360 |
apply (erule rev_mp) |
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|
361 |
apply (erule zg.induct) |
2e31b8cc8788
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parents:
diff
changeset
|
362 |
apply (frule_tac [5] ZG2_msg_in_parts_spies, auto) |
2e31b8cc8788
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parents:
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|
363 |
txt{*ZG1: freshness*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
364 |
apply (blast dest: parts.Body) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
365 |
done |
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changeset
|
366 |
|
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|
367 |
|
2e31b8cc8788
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|
368 |
text{*Fairness lemma: if @{term sub_K} exists, then @{term A} holds |
2e31b8cc8788
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paulson
parents:
diff
changeset
|
369 |
NRR. Relies on unicity of labels.*} |
2e31b8cc8788
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parents:
diff
changeset
|
370 |
lemma sub_K_implies_NRR: |
14741 | 371 |
"[| NRO = Crypt (priK A) {|Number f_nro, Agent B, Nonce L, Crypt K M|}; |
372 |
NRR = Crypt (priK B) {|Number f_nrr, Agent A, Nonce L, Crypt K M|}; |
|
373 |
sub_K \<in> parts (spies evs); |
|
14145
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|
374 |
NRO \<in> parts (spies evs); |
2e31b8cc8788
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changeset
|
375 |
sub_K = Crypt (priK A) {|Number f_sub, Agent B, Nonce L, Key K|}; |
2e31b8cc8788
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paulson
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changeset
|
376 |
A \<notin> bad; evs \<in> zg |] |
2e31b8cc8788
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paulson
parents:
diff
changeset
|
377 |
==> Gets A {|Number f_nrr, Agent A, Nonce L, NRR|} \<in> set evs" |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
378 |
apply clarify |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
379 |
apply (erule rev_mp) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
380 |
apply (erule rev_mp) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
381 |
apply (erule zg.induct) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
382 |
apply (frule_tac [5] ZG2_msg_in_parts_spies, simp_all) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
383 |
txt{*Fake*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
384 |
apply blast |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
385 |
txt{*ZG1: freshness*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
386 |
apply (blast dest: parts.Body) |
14741 | 387 |
txt{*ZG3*} |
14145
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
388 |
apply (blast dest: A_unicity [OF refl]) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
389 |
done |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
390 |
|
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
391 |
|
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
392 |
lemma Crypt_used_imp_L_used: |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
393 |
"[| Crypt (priK TTP) {|F, A, B, L, K|} \<in> used evs; evs \<in> zg |] |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
394 |
==> L \<in> used evs" |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
395 |
apply (erule rev_mp) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
396 |
apply (erule zg.induct, auto) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
397 |
txt{*Fake*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
398 |
apply (blast dest!: Fake_parts_sing_imp_Un) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
399 |
txt{*ZG2: freshness*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
400 |
apply (blast dest: parts.Body) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
401 |
done |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
402 |
|
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
403 |
|
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
404 |
text{*Fairness for @{term A}: if @{term con_K} and @{term NRO} exist, |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
405 |
then @{term A} holds NRR. @{term A} must be uncompromised, but there is no |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
406 |
assumption about @{term B}.*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
407 |
theorem A_fairness_NRO: |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
408 |
"[|con_K \<in> used evs; |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
409 |
NRO \<in> parts (spies evs); |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
410 |
con_K = Crypt (priK TTP) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
411 |
{|Number f_con, Agent A, Agent B, Nonce L, Key K|}; |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
412 |
NRO = Crypt (priK A) {|Number f_nro, Agent B, Nonce L, Crypt K M|}; |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
413 |
NRR = Crypt (priK B) {|Number f_nrr, Agent A, Nonce L, Crypt K M|}; |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
414 |
A \<notin> bad; evs \<in> zg |] |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
415 |
==> Gets A {|Number f_nrr, Agent A, Nonce L, NRR|} \<in> set evs" |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
416 |
apply clarify |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
417 |
apply (erule rev_mp) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
418 |
apply (erule rev_mp) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
419 |
apply (erule zg.induct) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
420 |
apply (frule_tac [5] ZG2_msg_in_parts_spies, simp_all) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
421 |
txt{*Fake*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
422 |
apply (simp add: parts_insert_knows_A) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
423 |
apply (blast dest: Fake_parts_sing_imp_Un) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
424 |
txt{*ZG1*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
425 |
apply (blast dest: Crypt_used_imp_L_used) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
426 |
txt{*ZG2*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
427 |
apply (blast dest: parts_cut) |
14741 | 428 |
txt{*ZG4*} |
429 |
apply (blast intro: sub_K_implies_NRR [OF refl] |
|
14145
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
430 |
dest: Gets_imp_knows_Spy [THEN parts.Inj]) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
431 |
done |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
432 |
|
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
433 |
text{*Fairness for @{term B}: NRR exists at all, then @{term B} holds NRO. |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
434 |
@{term B} must be uncompromised, but there is no assumption about @{term |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
435 |
A}. *} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
436 |
theorem B_fairness_NRR: |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
437 |
"[|NRR \<in> used evs; |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
438 |
NRR = Crypt (priK B) {|Number f_nrr, Agent A, Nonce L, C|}; |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
439 |
NRO = Crypt (priK A) {|Number f_nro, Agent B, Nonce L, C|}; |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
440 |
B \<notin> bad; evs \<in> zg |] |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
441 |
==> Gets B {|Number f_nro, Agent B, Nonce L, C, NRO|} \<in> set evs" |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
442 |
apply clarify |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
443 |
apply (erule rev_mp) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
444 |
apply (erule zg.induct) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
445 |
apply (frule_tac [5] ZG2_msg_in_parts_spies, simp_all) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
446 |
txt{*Fake*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
447 |
apply (blast dest!: Fake_parts_sing_imp_Un) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
448 |
txt{*ZG2*} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
449 |
apply (blast dest: parts_cut) |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
450 |
done |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
451 |
|
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
452 |
|
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
453 |
text{*If @{term con_K} exists at all, then @{term B} can get it, by @{text |
15068
58d216b32199
minor tweaks to go with the new version of the Accountability paper
paulson
parents:
15047
diff
changeset
|
454 |
con_K_validity}. Cannot conclude that also NRO is available to @{term B}, |
14145
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
455 |
because if @{term A} were unfair, @{term A} could build message 3 without |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
456 |
building message 1, which contains NRO. *} |
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
457 |
|
2e31b8cc8788
ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents:
diff
changeset
|
458 |
end |