author | nipkow |
Thu, 24 Sep 2009 17:25:42 +0200 | |
changeset 32676 | b1c85a117dec |
parent 23746 | a455e69c31cc |
child 32960 | 69916a850301 |
permissions | -rw-r--r-- |
18886 | 1 |
(* ID: $Id$ |
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Author: Giampaolo Bella, Catania University |
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*) |
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header{*The Kerberos Protocol, BAN Version, with Gets event*} |
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theory Kerberos_BAN_Gets imports Public begin |
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text{*From page 251 of |
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Burrows, Abadi and Needham (1989). A Logic of Authentication. |
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Proc. Royal Soc. 426 |
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Confidentiality (secrecy) and authentication properties rely on |
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temporal checks: strong guarantees in a little abstracted - but |
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very realistic - model. |
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*} |
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(* Temporal modelization: session keys can be leaked |
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ONLY when they have expired *) |
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consts |
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(*Duration of the session key*) |
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sesKlife :: nat |
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(*Duration of the authenticator*) |
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authlife :: nat |
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text{*The ticket should remain fresh for two journeys on the network at least*} |
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text{*The Gets event causes longer traces for the protocol to reach its end*} |
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specification (sesKlife) |
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sesKlife_LB [iff]: "4 \<le> sesKlife" |
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by blast |
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text{*The authenticator only for one journey*} |
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text{*The Gets event causes longer traces for the protocol to reach its end*} |
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specification (authlife) |
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authlife_LB [iff]: "2 \<le> authlife" |
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by blast |
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abbreviation |
21404
eb85850d3eb7
more robust syntax for definition/abbreviation/notation;
wenzelm
parents:
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CT :: "event list=>nat" where |
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"CT == length" |
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eb85850d3eb7
more robust syntax for definition/abbreviation/notation;
wenzelm
parents:
20768
diff
changeset
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abbreviation |
eb85850d3eb7
more robust syntax for definition/abbreviation/notation;
wenzelm
parents:
20768
diff
changeset
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expiredK :: "[nat, event list] => bool" where |
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"expiredK T evs == sesKlife + T < CT evs" |
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|
21404
eb85850d3eb7
more robust syntax for definition/abbreviation/notation;
wenzelm
parents:
20768
diff
changeset
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abbreviation |
eb85850d3eb7
more robust syntax for definition/abbreviation/notation;
wenzelm
parents:
20768
diff
changeset
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expiredA :: "[nat, event list] => bool" where |
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"expiredA T evs == authlife + T < CT evs" |
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constdefs |
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(* Yields the subtrace of a given trace from its beginning to a given event *) |
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before :: "[event, event list] => event list" ("before _ on _") |
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"before ev on evs == takeWhile (% z. z ~= ev) (rev evs)" |
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(* States than an event really appears only once on a trace *) |
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Unique :: "[event, event list] => bool" ("Unique _ on _") |
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"Unique ev on evs == |
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ev \<notin> set (tl (dropWhile (% z. z \<noteq> ev) evs))" |
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inductive_set bankerb_gets :: "event list set" |
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where |
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Nil: "[] \<in> bankerb_gets" |
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| Fake: "\<lbrakk> evsf \<in> bankerb_gets; X \<in> synth (analz (knows Spy evsf)) \<rbrakk> |
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\<Longrightarrow> Says Spy B X # evsf \<in> bankerb_gets" |
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| Reception: "\<lbrakk> evsr\<in> bankerb_gets; Says A B X \<in> set evsr \<rbrakk> |
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\<Longrightarrow> Gets B X # evsr \<in> bankerb_gets" |
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| BK1: "\<lbrakk> evs1 \<in> bankerb_gets \<rbrakk> |
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\<Longrightarrow> Says A Server \<lbrace>Agent A, Agent B\<rbrace> # evs1 |
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\<in> bankerb_gets" |
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| BK2: "\<lbrakk> evs2 \<in> bankerb_gets; Key K \<notin> used evs2; K \<in> symKeys; |
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Gets Server \<lbrace>Agent A, Agent B\<rbrace> \<in> set evs2 \<rbrakk> |
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\<Longrightarrow> Says Server A |
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(Crypt (shrK A) |
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\<lbrace>Number (CT evs2), Agent B, Key K, |
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(Crypt (shrK B) \<lbrace>Number (CT evs2), Agent A, Key K\<rbrace>)\<rbrace>) |
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# evs2 \<in> bankerb_gets" |
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| BK3: "\<lbrakk> evs3 \<in> bankerb_gets; |
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Gets A (Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) |
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\<in> set evs3; |
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Says A Server \<lbrace>Agent A, Agent B\<rbrace> \<in> set evs3; |
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\<not> expiredK Tk evs3 \<rbrakk> |
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\<Longrightarrow> Says A B \<lbrace>Ticket, Crypt K \<lbrace>Agent A, Number (CT evs3)\<rbrace> \<rbrace> |
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# evs3 \<in> bankerb_gets" |
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| BK4: "\<lbrakk> evs4 \<in> bankerb_gets; |
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Gets B \<lbrace>(Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>), |
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(Crypt K \<lbrace>Agent A, Number Ta\<rbrace>) \<rbrace>: set evs4; |
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\<not> expiredK Tk evs4; \<not> expiredA Ta evs4 \<rbrakk> |
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\<Longrightarrow> Says B A (Crypt K (Number Ta)) # evs4 |
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\<in> bankerb_gets" |
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(*Old session keys may become compromised*) |
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| Oops: "\<lbrakk> evso \<in> bankerb_gets; |
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Says Server A (Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) |
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\<in> set evso; |
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expiredK Tk evso \<rbrakk> |
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\<Longrightarrow> Notes Spy \<lbrace>Number Tk, Key K\<rbrace> # evso \<in> bankerb_gets" |
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declare Says_imp_knows_Spy [THEN parts.Inj, dest] |
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declare parts.Body [dest] |
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declare analz_into_parts [dest] |
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declare Fake_parts_insert_in_Un [dest] |
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declare knows_Spy_partsEs [elim] |
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text{*A "possibility property": there are traces that reach the end.*} |
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lemma "\<lbrakk>Key K \<notin> used []; K \<in> symKeys\<rbrakk> |
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\<Longrightarrow> \<exists>Timestamp. \<exists>evs \<in> bankerb_gets. |
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Says B A (Crypt K (Number Timestamp)) |
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\<in> set evs" |
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apply (cut_tac sesKlife_LB) |
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apply (cut_tac authlife_LB) |
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apply (intro exI bexI) |
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apply (rule_tac [2] |
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bankerb_gets.Nil [THEN bankerb_gets.BK1, THEN bankerb_gets.Reception, |
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THEN bankerb_gets.BK2, THEN bankerb_gets.Reception, |
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THEN bankerb_gets.BK3, THEN bankerb_gets.Reception, |
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THEN bankerb_gets.BK4]) |
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apply (possibility, simp_all (no_asm_simp) add: used_Cons) |
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done |
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text{*Lemmas about reception invariant: if a message is received it certainly |
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was sent*} |
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lemma Gets_imp_Says : |
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"\<lbrakk> Gets B X \<in> set evs; evs \<in> bankerb_gets \<rbrakk> \<Longrightarrow> \<exists>A. Says A B X \<in> set evs" |
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apply (erule rev_mp) |
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apply (erule bankerb_gets.induct) |
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apply auto |
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done |
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lemma Gets_imp_knows_Spy: |
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"\<lbrakk> Gets B X \<in> set evs; evs \<in> bankerb_gets \<rbrakk> \<Longrightarrow> X \<in> knows Spy evs" |
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apply (blast dest!: Gets_imp_Says Says_imp_knows_Spy) |
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done |
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lemma Gets_imp_knows_Spy_parts[dest]: |
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"\<lbrakk> Gets B X \<in> set evs; evs \<in> bankerb_gets \<rbrakk> \<Longrightarrow> X \<in> parts (knows Spy evs)" |
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apply (blast dest: Gets_imp_knows_Spy [THEN parts.Inj]) |
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done |
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lemma Gets_imp_knows: |
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"\<lbrakk> Gets B X \<in> set evs; evs \<in> bankerb_gets \<rbrakk> \<Longrightarrow> X \<in> knows B evs" |
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apply (case_tac "B = Spy") |
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apply (blast dest!: Gets_imp_knows_Spy) |
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apply (blast dest!: Gets_imp_knows_agents) |
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done |
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lemma Gets_imp_knows_analz: |
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"\<lbrakk> Gets B X \<in> set evs; evs \<in> bankerb_gets \<rbrakk> \<Longrightarrow> X \<in> analz (knows B evs)" |
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apply (blast dest: Gets_imp_knows [THEN analz.Inj]) |
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done |
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text{*Lemmas for reasoning about predicate "before"*} |
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lemma used_Says_rev: "used (evs @ [Says A B X]) = parts {X} \<union> (used evs)"; |
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apply (induct_tac "evs") |
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apply simp |
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apply (induct_tac "a") |
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apply auto |
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done |
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lemma used_Notes_rev: "used (evs @ [Notes A X]) = parts {X} \<union> (used evs)"; |
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apply (induct_tac "evs") |
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apply simp |
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apply (induct_tac "a") |
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apply auto |
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done |
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lemma used_Gets_rev: "used (evs @ [Gets B X]) = used evs"; |
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apply (induct_tac "evs") |
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apply simp |
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apply (induct_tac "a") |
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apply auto |
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done |
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lemma used_evs_rev: "used evs = used (rev evs)" |
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apply (induct_tac "evs") |
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apply simp |
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apply (induct_tac "a") |
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apply (simp add: used_Says_rev) |
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apply (simp add: used_Gets_rev) |
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apply (simp add: used_Notes_rev) |
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done |
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lemma used_takeWhile_used [rule_format]: |
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"x : used (takeWhile P X) --> x : used X" |
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apply (induct_tac "X") |
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apply simp |
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apply (induct_tac "a") |
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apply (simp_all add: used_Nil) |
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apply (blast dest!: initState_into_used)+ |
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done |
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lemma set_evs_rev: "set evs = set (rev evs)" |
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apply auto |
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done |
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lemma takeWhile_void [rule_format]: |
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"x \<notin> set evs \<longrightarrow> takeWhile (\<lambda>z. z \<noteq> x) evs = evs" |
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apply auto |
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done |
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(**** Inductive proofs about bankerb_gets ****) |
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text{*Forwarding Lemma for reasoning about the encrypted portion of message BK3*} |
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lemma BK3_msg_in_parts_knows_Spy: |
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"\<lbrakk>Gets A (Crypt KA \<lbrace>Timestamp, B, K, X\<rbrace>) \<in> set evs; evs \<in> bankerb_gets \<rbrakk> |
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\<Longrightarrow> X \<in> parts (knows Spy evs)" |
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apply blast |
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done |
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lemma Oops_parts_knows_Spy: |
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"Says Server A (Crypt (shrK A) \<lbrace>Timestamp, B, K, X\<rbrace>) \<in> set evs |
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\<Longrightarrow> K \<in> parts (knows Spy evs)" |
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apply blast |
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done |
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text{*Spy never sees another agent's shared key! (unless it's bad at start)*} |
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lemma Spy_see_shrK [simp]: |
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"evs \<in> bankerb_gets \<Longrightarrow> (Key (shrK A) \<in> parts (knows Spy evs)) = (A \<in> bad)" |
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apply (erule bankerb_gets.induct) |
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apply (frule_tac [8] Oops_parts_knows_Spy) |
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apply (frule_tac [6] BK3_msg_in_parts_knows_Spy, simp_all, blast+) |
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done |
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lemma Spy_analz_shrK [simp]: |
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"evs \<in> bankerb_gets \<Longrightarrow> (Key (shrK A) \<in> analz (knows Spy evs)) = (A \<in> bad)" |
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by auto |
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lemma Spy_see_shrK_D [dest!]: |
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"\<lbrakk> Key (shrK A) \<in> parts (knows Spy evs); |
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evs \<in> bankerb_gets \<rbrakk> \<Longrightarrow> A:bad" |
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by (blast dest: Spy_see_shrK) |
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lemmas Spy_analz_shrK_D = analz_subset_parts [THEN subsetD, THEN Spy_see_shrK_D, dest!] |
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text{*Nobody can have used non-existent keys!*} |
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lemma new_keys_not_used [simp]: |
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"\<lbrakk>Key K \<notin> used evs; K \<in> symKeys; evs \<in> bankerb_gets\<rbrakk> |
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\<Longrightarrow> K \<notin> keysFor (parts (knows Spy evs))" |
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apply (erule rev_mp) |
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apply (erule bankerb_gets.induct) |
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apply (frule_tac [8] Oops_parts_knows_Spy) |
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apply (frule_tac [6] BK3_msg_in_parts_knows_Spy, simp_all) |
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txt{*Fake*} |
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apply (force dest!: keysFor_parts_insert) |
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txt{*BK2, BK3, BK4*} |
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apply (force dest!: analz_shrK_Decrypt)+ |
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done |
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subsection{* Lemmas concerning the form of items passed in messages *} |
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text{*Describes the form of K, X and K' when the Server sends this message.*} |
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lemma Says_Server_message_form: |
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"\<lbrakk> Says Server A (Crypt K' \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) |
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\<in> set evs; evs \<in> bankerb_gets \<rbrakk> |
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\<Longrightarrow> K' = shrK A & K \<notin> range shrK & |
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Ticket = (Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>) & |
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Key K \<notin> used(before |
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Says Server A (Crypt K' \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) |
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on evs) & |
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Tk = CT(before |
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Says Server A (Crypt K' \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) |
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on evs)" |
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apply (unfold before_def) |
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apply (erule rev_mp) |
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apply (erule bankerb_gets.induct, simp_all) |
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txt{*We need this simplification only for Message 2*} |
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apply (simp (no_asm) add: takeWhile_tail) |
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apply auto |
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txt{*Two subcases of Message 2. Subcase: used before*} |
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apply (blast dest: used_evs_rev [THEN equalityD2, THEN contra_subsetD] |
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used_takeWhile_used) |
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txt{*subcase: CT before*} |
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apply (fastsimp dest!: set_evs_rev [THEN equalityD2, THEN contra_subsetD, THEN takeWhile_void]) |
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done |
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text{*If the encrypted message appears then it originated with the Server |
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PROVIDED that A is NOT compromised! |
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This allows A to verify freshness of the session key. |
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*} |
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lemma Kab_authentic: |
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"\<lbrakk> Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace> |
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\<in> parts (knows Spy evs); |
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A \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
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\<Longrightarrow> Says Server A (Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace>) |
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\<in> set evs" |
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apply (erule rev_mp) |
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apply (erule bankerb_gets.induct) |
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apply (frule_tac [8] Oops_parts_knows_Spy) |
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apply (frule_tac [6] BK3_msg_in_parts_knows_Spy, simp_all, blast) |
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done |
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text{*If the TICKET appears then it originated with the Server*} |
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text{*FRESHNESS OF THE SESSION KEY to B*} |
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lemma ticket_authentic: |
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"\<lbrakk> Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace> \<in> parts (knows Spy evs); |
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B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
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\<Longrightarrow> Says Server A |
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(Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, |
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Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>\<rbrace>) |
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\<in> set evs" |
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apply (erule rev_mp) |
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apply (erule bankerb_gets.induct) |
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apply (frule_tac [8] Oops_parts_knows_Spy) |
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apply (frule_tac [6] BK3_msg_in_parts_knows_Spy, simp_all, blast) |
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done |
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text{*EITHER describes the form of X when the following message is sent, |
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OR reduces it to the Fake case. |
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Use @{text Says_Server_message_form} if applicable.*} |
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lemma Gets_Server_message_form: |
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"\<lbrakk> Gets A (Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace>) |
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\<in> set evs; |
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evs \<in> bankerb_gets \<rbrakk> |
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\<Longrightarrow> (K \<notin> range shrK & X = (Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>)) |
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| X \<in> analz (knows Spy evs)" |
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apply (case_tac "A \<in> bad") |
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apply (force dest!: Gets_imp_knows_Spy [THEN analz.Inj]) |
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apply (blast dest!: Kab_authentic Says_Server_message_form) |
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done |
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text{*Reliability guarantees: honest agents act as we expect*} |
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lemma BK3_imp_Gets: |
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"\<lbrakk> Says A B \<lbrace>Ticket, Crypt K \<lbrace>Agent A, Number Ta\<rbrace>\<rbrace> \<in> set evs; |
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A \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
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\<Longrightarrow> \<exists> Tk. Gets A (Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) |
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\<in> set evs" |
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apply (erule rev_mp) |
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apply (erule bankerb_gets.induct) |
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apply auto |
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done |
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lemma BK4_imp_Gets: |
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"\<lbrakk> Says B A (Crypt K (Number Ta)) \<in> set evs; |
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B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
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\<Longrightarrow> \<exists> Tk. Gets B \<lbrace>Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>, |
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Crypt K \<lbrace>Agent A, Number Ta\<rbrace>\<rbrace> \<in> set evs" |
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apply (erule rev_mp) |
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apply (erule bankerb_gets.induct) |
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apply auto |
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done |
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lemma Gets_A_knows_K: |
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"\<lbrakk> Gets A (Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) \<in> set evs; |
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evs \<in> bankerb_gets \<rbrakk> |
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\<Longrightarrow> Key K \<in> analz (knows A evs)" |
|
372 |
apply (force dest: Gets_imp_knows_analz) |
|
373 |
done |
|
374 |
||
375 |
lemma Gets_B_knows_K: |
|
376 |
"\<lbrakk> Gets B \<lbrace>Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>, |
|
377 |
Crypt K \<lbrace>Agent A, Number Ta\<rbrace>\<rbrace> \<in> set evs; |
|
378 |
evs \<in> bankerb_gets \<rbrakk> |
|
379 |
\<Longrightarrow> Key K \<in> analz (knows B evs)" |
|
380 |
apply (force dest: Gets_imp_knows_analz) |
|
381 |
done |
|
382 |
||
383 |
||
384 |
(**** |
|
385 |
The following is to prove theorems of the form |
|
386 |
||
387 |
Key K \<in> analz (insert (Key KAB) (knows Spy evs)) \<Longrightarrow> |
|
388 |
Key K \<in> analz (knows Spy evs) |
|
389 |
||
390 |
A more general formula must be proved inductively. |
|
391 |
||
392 |
****) |
|
393 |
||
394 |
||
395 |
text{* Session keys are not used to encrypt other session keys *} |
|
396 |
lemma analz_image_freshK [rule_format (no_asm)]: |
|
397 |
"evs \<in> bankerb_gets \<Longrightarrow> |
|
398 |
\<forall>K KK. KK \<subseteq> - (range shrK) \<longrightarrow> |
|
399 |
(Key K \<in> analz (Key`KK Un (knows Spy evs))) = |
|
400 |
(K \<in> KK | Key K \<in> analz (knows Spy evs))" |
|
401 |
apply (erule bankerb_gets.induct) |
|
402 |
apply (drule_tac [8] Says_Server_message_form) |
|
403 |
apply (erule_tac [6] Gets_Server_message_form [THEN disjE], analz_freshK, spy_analz, auto) |
|
404 |
done |
|
405 |
||
406 |
||
407 |
lemma analz_insert_freshK: |
|
408 |
"\<lbrakk> evs \<in> bankerb_gets; KAB \<notin> range shrK \<rbrakk> \<Longrightarrow> |
|
409 |
(Key K \<in> analz (insert (Key KAB) (knows Spy evs))) = |
|
410 |
(K = KAB | Key K \<in> analz (knows Spy evs))" |
|
411 |
by (simp only: analz_image_freshK analz_image_freshK_simps) |
|
412 |
||
413 |
||
414 |
text{* The session key K uniquely identifies the message *} |
|
415 |
lemma unique_session_keys: |
|
416 |
"\<lbrakk> Says Server A |
|
417 |
(Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace>) \<in> set evs; |
|
418 |
Says Server A' |
|
419 |
(Crypt (shrK A') \<lbrace>Number Tk', Agent B', Key K, X'\<rbrace>) \<in> set evs; |
|
420 |
evs \<in> bankerb_gets \<rbrakk> \<Longrightarrow> A=A' & Tk=Tk' & B=B' & X = X'" |
|
421 |
apply (erule rev_mp) |
|
422 |
apply (erule rev_mp) |
|
423 |
apply (erule bankerb_gets.induct) |
|
424 |
apply (frule_tac [8] Oops_parts_knows_Spy) |
|
425 |
apply (frule_tac [6] BK3_msg_in_parts_knows_Spy, simp_all) |
|
426 |
txt{*BK2: it can't be a new key*} |
|
427 |
apply blast |
|
428 |
done |
|
429 |
||
430 |
lemma unique_session_keys_Gets: |
|
431 |
"\<lbrakk> Gets A |
|
432 |
(Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace>) \<in> set evs; |
|
433 |
Gets A |
|
434 |
(Crypt (shrK A) \<lbrace>Number Tk', Agent B', Key K, X'\<rbrace>) \<in> set evs; |
|
435 |
A \<notin> bad; evs \<in> bankerb_gets \<rbrakk> \<Longrightarrow> Tk=Tk' & B=B' & X = X'" |
|
436 |
apply (blast dest!: Kab_authentic unique_session_keys) |
|
437 |
done |
|
438 |
||
439 |
||
440 |
lemma Server_Unique: |
|
441 |
"\<lbrakk> Says Server A |
|
442 |
(Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) \<in> set evs; |
|
443 |
evs \<in> bankerb_gets \<rbrakk> \<Longrightarrow> |
|
444 |
Unique Says Server A (Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) |
|
445 |
on evs" |
|
446 |
apply (erule rev_mp, erule bankerb_gets.induct, simp_all add: Unique_def) |
|
447 |
apply blast |
|
448 |
done |
|
449 |
||
450 |
||
451 |
||
452 |
subsection{*Non-temporal guarantees, explicitly relying on non-occurrence of |
|
453 |
oops events - refined below by temporal guarantees*} |
|
454 |
||
455 |
text{*Non temporal treatment of confidentiality*} |
|
456 |
||
457 |
text{* Lemma: the session key sent in msg BK2 would be lost by oops |
|
458 |
if the spy could see it! *} |
|
459 |
lemma lemma_conf [rule_format (no_asm)]: |
|
460 |
"\<lbrakk> A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
461 |
\<Longrightarrow> Says Server A |
|
462 |
(Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, |
|
463 |
Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>\<rbrace>) |
|
464 |
\<in> set evs \<longrightarrow> |
|
465 |
Key K \<in> analz (knows Spy evs) \<longrightarrow> Notes Spy \<lbrace>Number Tk, Key K\<rbrace> \<in> set evs" |
|
466 |
apply (erule bankerb_gets.induct) |
|
467 |
apply (frule_tac [8] Says_Server_message_form) |
|
468 |
apply (frule_tac [6] Gets_Server_message_form [THEN disjE]) |
|
469 |
apply (simp_all (no_asm_simp) add: analz_insert_eq analz_insert_freshK pushes) |
|
470 |
txt{*Fake*} |
|
471 |
apply spy_analz |
|
472 |
txt{*BK2*} |
|
473 |
apply (blast intro: parts_insertI) |
|
474 |
txt{*BK3*} |
|
475 |
apply (case_tac "Aa \<in> bad") |
|
476 |
prefer 2 apply (blast dest: Kab_authentic unique_session_keys) |
|
477 |
apply (blast dest: Gets_imp_knows_Spy [THEN analz.Inj] Crypt_Spy_analz_bad elim!: MPair_analz) |
|
478 |
txt{*Oops*} |
|
479 |
apply (blast dest: unique_session_keys) |
|
480 |
done |
|
481 |
||
482 |
||
483 |
text{*Confidentiality for the Server: Spy does not see the keys sent in msg BK2 |
|
484 |
as long as they have not expired.*} |
|
485 |
lemma Confidentiality_S: |
|
486 |
"\<lbrakk> Says Server A |
|
487 |
(Crypt K' \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) \<in> set evs; |
|
488 |
Notes Spy \<lbrace>Number Tk, Key K\<rbrace> \<notin> set evs; |
|
489 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets |
|
490 |
\<rbrakk> \<Longrightarrow> Key K \<notin> analz (knows Spy evs)" |
|
491 |
apply (frule Says_Server_message_form, assumption) |
|
492 |
apply (blast intro: lemma_conf) |
|
493 |
done |
|
494 |
||
495 |
text{*Confidentiality for Alice*} |
|
496 |
lemma Confidentiality_A: |
|
497 |
"\<lbrakk> Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace> \<in> parts (knows Spy evs); |
|
498 |
Notes Spy \<lbrace>Number Tk, Key K\<rbrace> \<notin> set evs; |
|
499 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets |
|
500 |
\<rbrakk> \<Longrightarrow> Key K \<notin> analz (knows Spy evs)" |
|
501 |
by (blast dest!: Kab_authentic Confidentiality_S) |
|
502 |
||
503 |
text{*Confidentiality for Bob*} |
|
504 |
lemma Confidentiality_B: |
|
505 |
"\<lbrakk> Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace> |
|
506 |
\<in> parts (knows Spy evs); |
|
507 |
Notes Spy \<lbrace>Number Tk, Key K\<rbrace> \<notin> set evs; |
|
508 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets |
|
509 |
\<rbrakk> \<Longrightarrow> Key K \<notin> analz (knows Spy evs)" |
|
510 |
by (blast dest!: ticket_authentic Confidentiality_S) |
|
511 |
||
512 |
||
513 |
text{*Non temporal treatment of authentication*} |
|
514 |
||
515 |
text{*Lemmas @{text lemma_A} and @{text lemma_B} in fact are common to both temporal and non-temporal treatments*} |
|
516 |
lemma lemma_A [rule_format]: |
|
517 |
"\<lbrakk> A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
518 |
\<Longrightarrow> |
|
519 |
Key K \<notin> analz (knows Spy evs) \<longrightarrow> |
|
520 |
Says Server A (Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace>) |
|
521 |
\<in> set evs \<longrightarrow> |
|
522 |
Crypt K \<lbrace>Agent A, Number Ta\<rbrace> \<in> parts (knows Spy evs) \<longrightarrow> |
|
523 |
Says A B \<lbrace>X, Crypt K \<lbrace>Agent A, Number Ta\<rbrace>\<rbrace> |
|
524 |
\<in> set evs" |
|
525 |
apply (erule bankerb_gets.induct) |
|
526 |
apply (frule_tac [8] Oops_parts_knows_Spy) |
|
527 |
apply (frule_tac [6] Gets_Server_message_form) |
|
528 |
apply (frule_tac [7] BK3_msg_in_parts_knows_Spy, analz_mono_contra) |
|
529 |
apply (simp_all (no_asm_simp) add: all_conj_distrib) |
|
530 |
txt{*Fake*} |
|
531 |
apply blast |
|
532 |
txt{*BK2*} |
|
533 |
apply (force dest: Crypt_imp_invKey_keysFor) |
|
534 |
txt{*BK3*} |
|
535 |
apply (blast dest: Kab_authentic unique_session_keys) |
|
536 |
done |
|
537 |
lemma lemma_B [rule_format]: |
|
538 |
"\<lbrakk> B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
539 |
\<Longrightarrow> Key K \<notin> analz (knows Spy evs) \<longrightarrow> |
|
540 |
Says Server A (Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace>) |
|
541 |
\<in> set evs \<longrightarrow> |
|
542 |
Crypt K (Number Ta) \<in> parts (knows Spy evs) \<longrightarrow> |
|
543 |
Says B A (Crypt K (Number Ta)) \<in> set evs" |
|
544 |
apply (erule bankerb_gets.induct) |
|
545 |
apply (frule_tac [8] Oops_parts_knows_Spy) |
|
546 |
apply (frule_tac [6] Gets_Server_message_form) |
|
547 |
apply (drule_tac [7] BK3_msg_in_parts_knows_Spy, analz_mono_contra) |
|
548 |
apply (simp_all (no_asm_simp) add: all_conj_distrib) |
|
549 |
txt{*Fake*} |
|
550 |
apply blast |
|
551 |
txt{*BK2*} |
|
552 |
apply (force dest: Crypt_imp_invKey_keysFor) |
|
553 |
txt{*BK4*} |
|
554 |
apply (blast dest: ticket_authentic unique_session_keys |
|
555 |
Gets_imp_knows_Spy [THEN analz.Inj] Crypt_Spy_analz_bad) |
|
556 |
done |
|
557 |
||
558 |
||
559 |
text{*The "r" suffix indicates theorems where the confidentiality assumptions are relaxed by the corresponding arguments.*} |
|
560 |
||
561 |
text{*Authentication of A to B*} |
|
562 |
lemma B_authenticates_A_r: |
|
563 |
"\<lbrakk> Crypt K \<lbrace>Agent A, Number Ta\<rbrace> \<in> parts (knows Spy evs); |
|
564 |
Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace> \<in> parts (knows Spy evs); |
|
565 |
Notes Spy \<lbrace>Number Tk, Key K\<rbrace> \<notin> set evs; |
|
566 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
567 |
\<Longrightarrow> Says A B \<lbrace>Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>, |
|
568 |
Crypt K \<lbrace>Agent A, Number Ta\<rbrace>\<rbrace> \<in> set evs" |
|
569 |
by (blast dest!: ticket_authentic |
|
570 |
intro!: lemma_A |
|
571 |
elim!: Confidentiality_S [THEN [2] rev_notE]) |
|
572 |
||
573 |
text{*Authentication of B to A*} |
|
574 |
lemma A_authenticates_B_r: |
|
575 |
"\<lbrakk> Crypt K (Number Ta) \<in> parts (knows Spy evs); |
|
576 |
Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace> \<in> parts (knows Spy evs); |
|
577 |
Notes Spy \<lbrace>Number Tk, Key K\<rbrace> \<notin> set evs; |
|
578 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
579 |
\<Longrightarrow> Says B A (Crypt K (Number Ta)) \<in> set evs" |
|
580 |
by (blast dest!: Kab_authentic |
|
581 |
intro!: lemma_B elim!: Confidentiality_S [THEN [2] rev_notE]) |
|
582 |
||
583 |
lemma B_authenticates_A: |
|
584 |
"\<lbrakk> Crypt K \<lbrace>Agent A, Number Ta\<rbrace> \<in> parts (spies evs); |
|
585 |
Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace> \<in> parts (spies evs); |
|
586 |
Key K \<notin> analz (spies evs); |
|
587 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
588 |
\<Longrightarrow> Says A B \<lbrace>Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>, |
|
589 |
Crypt K \<lbrace>Agent A, Number Ta\<rbrace>\<rbrace> \<in> set evs" |
|
590 |
apply (blast dest!: ticket_authentic intro!: lemma_A) |
|
591 |
done |
|
592 |
||
593 |
lemma A_authenticates_B: |
|
594 |
"\<lbrakk> Crypt K (Number Ta) \<in> parts (spies evs); |
|
595 |
Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace> \<in> parts (spies evs); |
|
596 |
Key K \<notin> analz (spies evs); |
|
597 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
598 |
\<Longrightarrow> Says B A (Crypt K (Number Ta)) \<in> set evs" |
|
599 |
apply (blast dest!: Kab_authentic intro!: lemma_B) |
|
600 |
done |
|
601 |
||
602 |
||
603 |
subsection{*Temporal guarantees, relying on a temporal check that insures that |
|
604 |
no oops event occurred. These are available in the sense of goal availability*} |
|
605 |
||
606 |
||
607 |
text{*Temporal treatment of confidentiality*} |
|
608 |
||
609 |
text{* Lemma: the session key sent in msg BK2 would be EXPIRED |
|
610 |
if the spy could see it! *} |
|
611 |
lemma lemma_conf_temporal [rule_format (no_asm)]: |
|
612 |
"\<lbrakk> A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
613 |
\<Longrightarrow> Says Server A |
|
614 |
(Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, |
|
615 |
Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>\<rbrace>) |
|
616 |
\<in> set evs \<longrightarrow> |
|
617 |
Key K \<in> analz (knows Spy evs) \<longrightarrow> expiredK Tk evs" |
|
618 |
apply (erule bankerb_gets.induct) |
|
619 |
apply (frule_tac [8] Says_Server_message_form) |
|
620 |
apply (frule_tac [6] Gets_Server_message_form [THEN disjE]) |
|
621 |
apply (simp_all (no_asm_simp) add: less_SucI analz_insert_eq analz_insert_freshK pushes) |
|
622 |
txt{*Fake*} |
|
623 |
apply spy_analz |
|
624 |
txt{*BK2*} |
|
625 |
apply (blast intro: parts_insertI less_SucI) |
|
626 |
txt{*BK3*} |
|
627 |
apply (case_tac "Aa \<in> bad") |
|
628 |
prefer 2 apply (blast dest: Kab_authentic unique_session_keys) |
|
629 |
apply (blast dest: Gets_imp_knows_Spy [THEN analz.Inj] Crypt_Spy_analz_bad elim!: MPair_analz intro: less_SucI) |
|
630 |
txt{*Oops: PROOF FAILS if unsafe intro below*} |
|
631 |
apply (blast dest: unique_session_keys intro!: less_SucI) |
|
632 |
done |
|
633 |
||
634 |
||
635 |
text{*Confidentiality for the Server: Spy does not see the keys sent in msg BK2 |
|
636 |
as long as they have not expired.*} |
|
637 |
lemma Confidentiality_S_temporal: |
|
638 |
"\<lbrakk> Says Server A |
|
639 |
(Crypt K' \<lbrace>Number T, Agent B, Key K, X\<rbrace>) \<in> set evs; |
|
640 |
\<not> expiredK T evs; |
|
641 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets |
|
642 |
\<rbrakk> \<Longrightarrow> Key K \<notin> analz (knows Spy evs)" |
|
643 |
apply (frule Says_Server_message_form, assumption) |
|
644 |
apply (blast intro: lemma_conf_temporal) |
|
645 |
done |
|
646 |
||
647 |
text{*Confidentiality for Alice*} |
|
648 |
lemma Confidentiality_A_temporal: |
|
649 |
"\<lbrakk> Crypt (shrK A) \<lbrace>Number T, Agent B, Key K, X\<rbrace> \<in> parts (knows Spy evs); |
|
650 |
\<not> expiredK T evs; |
|
651 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets |
|
652 |
\<rbrakk> \<Longrightarrow> Key K \<notin> analz (knows Spy evs)" |
|
653 |
by (blast dest!: Kab_authentic Confidentiality_S_temporal) |
|
654 |
||
655 |
text{*Confidentiality for Bob*} |
|
656 |
lemma Confidentiality_B_temporal: |
|
657 |
"\<lbrakk> Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace> |
|
658 |
\<in> parts (knows Spy evs); |
|
659 |
\<not> expiredK Tk evs; |
|
660 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets |
|
661 |
\<rbrakk> \<Longrightarrow> Key K \<notin> analz (knows Spy evs)" |
|
662 |
by (blast dest!: ticket_authentic Confidentiality_S_temporal) |
|
663 |
||
664 |
||
665 |
text{*Temporal treatment of authentication*} |
|
666 |
||
667 |
text{*Authentication of A to B*} |
|
668 |
lemma B_authenticates_A_temporal: |
|
669 |
"\<lbrakk> Crypt K \<lbrace>Agent A, Number Ta\<rbrace> \<in> parts (knows Spy evs); |
|
670 |
Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace> |
|
671 |
\<in> parts (knows Spy evs); |
|
672 |
\<not> expiredK Tk evs; |
|
673 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
674 |
\<Longrightarrow> Says A B \<lbrace>Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>, |
|
675 |
Crypt K \<lbrace>Agent A, Number Ta\<rbrace>\<rbrace> \<in> set evs" |
|
676 |
by (blast dest!: ticket_authentic |
|
677 |
intro!: lemma_A |
|
678 |
elim!: Confidentiality_S_temporal [THEN [2] rev_notE]) |
|
679 |
||
680 |
text{*Authentication of B to A*} |
|
681 |
lemma A_authenticates_B_temporal: |
|
682 |
"\<lbrakk> Crypt K (Number Ta) \<in> parts (knows Spy evs); |
|
683 |
Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, X\<rbrace> |
|
684 |
\<in> parts (knows Spy evs); |
|
685 |
\<not> expiredK Tk evs; |
|
686 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
687 |
\<Longrightarrow> Says B A (Crypt K (Number Ta)) \<in> set evs" |
|
688 |
by (blast dest!: Kab_authentic |
|
689 |
intro!: lemma_B elim!: Confidentiality_S_temporal [THEN [2] rev_notE]) |
|
690 |
||
691 |
||
692 |
subsection{*Combined guarantees of key distribution and non-injective agreement on the session keys*} |
|
693 |
||
694 |
lemma B_authenticates_and_keydist_to_A: |
|
695 |
"\<lbrakk> Gets B \<lbrace>Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>, |
|
696 |
Crypt K \<lbrace>Agent A, Number Ta\<rbrace>\<rbrace> \<in> set evs; |
|
697 |
Key K \<notin> analz (spies evs); |
|
698 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
699 |
\<Longrightarrow> Says A B \<lbrace>Crypt (shrK B) \<lbrace>Number Tk, Agent A, Key K\<rbrace>, |
|
700 |
Crypt K \<lbrace>Agent A, Number Ta\<rbrace>\<rbrace> \<in> set evs |
|
701 |
\<and> Key K \<in> analz (knows A evs)" |
|
702 |
apply (blast dest: B_authenticates_A BK3_imp_Gets Gets_A_knows_K) |
|
703 |
done |
|
704 |
||
705 |
lemma A_authenticates_and_keydist_to_B: |
|
706 |
"\<lbrakk> Gets A (Crypt (shrK A) \<lbrace>Number Tk, Agent B, Key K, Ticket\<rbrace>) \<in> set evs; |
|
707 |
Gets A (Crypt K (Number Ta)) \<in> set evs; |
|
708 |
Key K \<notin> analz (spies evs); |
|
709 |
A \<notin> bad; B \<notin> bad; evs \<in> bankerb_gets \<rbrakk> |
|
710 |
\<Longrightarrow> Says B A (Crypt K (Number Ta)) \<in> set evs |
|
711 |
\<and> Key K \<in> analz (knows B evs)" |
|
712 |
apply (blast dest: A_authenticates_B BK4_imp_Gets Gets_B_knows_K) |
|
713 |
done |
|
714 |
||
715 |
||
716 |
||
717 |
||
718 |
||
719 |
end |