src/HOL/Auth/KerberosV.thy
author wenzelm
Mon Aug 31 21:28:08 2015 +0200 (2015-08-31)
changeset 61070 b72a990adfe2
parent 58889 5b7a9633cfa8
child 61830 4f5ab843cf5b
permissions -rw-r--r--
prefer symbols;
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(*  Title:      HOL/Auth/KerberosV.thy
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    Author:     Giampaolo Bella, Catania University
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*)
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section{*The Kerberos Protocol, Version V*}
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theory KerberosV imports Public begin
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text{*The "u" prefix indicates theorems referring to an updated version of the protocol. The "r" suffix indicates theorems where the confidentiality assumptions are relaxed by the corresponding arguments.*}
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abbreviation
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  Kas :: agent where
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  "Kas == Server"
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abbreviation
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  Tgs :: agent where
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  "Tgs == Friend 0"
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axiomatization where
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  Tgs_not_bad [iff]: "Tgs \<notin> bad"
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   --{*Tgs is secure --- we already know that Kas is secure*}
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definition
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 (* authKeys are those contained in an authTicket *)
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    authKeys :: "event list => key set" where
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    "authKeys evs = {authK. \<exists>A Peer Ta. 
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        Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Peer, Ta\<rbrace>,
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                     Crypt (shrK Peer) \<lbrace>Agent A, Agent Peer, Key authK, Ta\<rbrace>
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                   \<rbrace> \<in> set evs}"
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definition
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 (* A is the true creator of X if she has sent X and X never appeared on
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    the trace before this event. Recall that traces grow from head. *)
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  Issues :: "[agent, agent, msg, event list] => bool"
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             ("_ Issues _ with _ on _") where
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   "A Issues B with X on evs =
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      (\<exists>Y. Says A B Y \<in> set evs \<and> X \<in> parts {Y} \<and>
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        X \<notin> parts (spies (takeWhile (% z. z  \<noteq> Says A B Y) (rev evs))))"
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consts
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    (*Duration of the authentication key*)
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    authKlife   :: nat
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    (*Duration of the service key*)
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    servKlife   :: nat
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    (*Duration of an authenticator*)
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    authlife   :: nat
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    (*Upper bound on the time of reaction of a server*)
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    replylife   :: nat
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specification (authKlife)
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  authKlife_LB [iff]: "2 \<le> authKlife"
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    by blast
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specification (servKlife)
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  servKlife_LB [iff]: "2 + authKlife \<le> servKlife"
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    by blast
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specification (authlife)
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  authlife_LB [iff]: "Suc 0 \<le> authlife"
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    by blast
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specification (replylife)
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  replylife_LB [iff]: "Suc 0 \<le> replylife"
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    by blast
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abbreviation
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  (*The current time is just the length of the trace!*)
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  CT :: "event list=>nat" where
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  "CT == length"
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abbreviation
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  expiredAK :: "[nat, event list] => bool" where
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  "expiredAK T evs == authKlife + T < CT evs"
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abbreviation
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  expiredSK :: "[nat, event list] => bool" where
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  "expiredSK T evs == servKlife + T < CT evs"
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abbreviation
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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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abbreviation
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  valid :: "[nat, nat] => bool"  ("valid _ wrt _") where
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  "valid T1 wrt T2 == T1 <= replylife + T2"
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(*---------------------------------------------------------------------*)
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(* Predicate formalising the association between authKeys and servKeys *)
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definition AKcryptSK :: "[key, key, event list] => bool" where
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  "AKcryptSK authK servK evs ==
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     \<exists>A B tt.
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       Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, tt\<rbrace>,
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                    Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, tt\<rbrace> \<rbrace>
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         \<in> set evs"
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inductive_set kerbV :: "event list set"
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  where
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   Nil:  "[] \<in> kerbV"
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 | Fake: "\<lbrakk> evsf \<in> kerbV;  X \<in> synth (analz (spies evsf)) \<rbrakk>
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          \<Longrightarrow> Says Spy B X  # evsf \<in> kerbV"
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(*Authentication phase*)
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 | KV1:   "\<lbrakk> evs1 \<in> kerbV \<rbrakk>
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          \<Longrightarrow> Says A Kas \<lbrace>Agent A, Agent Tgs, Number (CT evs1)\<rbrace> # evs1
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          \<in> kerbV"
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   (*Unlike version IV, authTicket is not re-encrypted*)
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 | KV2:  "\<lbrakk> evs2 \<in> kerbV; Key authK \<notin> used evs2; authK \<in> symKeys;
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            Says A' Kas \<lbrace>Agent A, Agent Tgs, Number T1\<rbrace> \<in> set evs2 \<rbrakk>
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          \<Longrightarrow> Says Kas A \<lbrace>
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          Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number (CT evs2)\<rbrace>,
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        Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Number (CT evs2)\<rbrace> 
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                         \<rbrace> # evs2 \<in> kerbV"
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(* Authorisation phase *)
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 | KV3:  "\<lbrakk> evs3 \<in> kerbV; A \<noteq> Kas; A \<noteq> Tgs;
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            Says A Kas \<lbrace>Agent A, Agent Tgs, Number T1\<rbrace> \<in> set evs3;
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            Says Kas' A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>,
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                          authTicket\<rbrace> \<in> set evs3;
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            valid Ta wrt T1
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         \<rbrakk>
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          \<Longrightarrow> Says A Tgs \<lbrace>authTicket,
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                           (Crypt authK \<lbrace>Agent A, Number (CT evs3)\<rbrace>),
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                           Agent B\<rbrace> # evs3 \<in> kerbV"
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   (*Unlike version IV, servTicket is not re-encrypted*)
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 | KV4:  "\<lbrakk> evs4 \<in> kerbV; Key servK \<notin> used evs4; servK \<in> symKeys;
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            B \<noteq> Tgs;  authK \<in> symKeys;
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            Says A' Tgs \<lbrace>
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             (Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK,
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                                 Number Ta\<rbrace>),
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             (Crypt authK \<lbrace>Agent A, Number T2\<rbrace>), Agent B\<rbrace>
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                \<in> set evs4;
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            \<not> expiredAK Ta evs4;
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            \<not> expiredA T2 evs4;
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            servKlife + (CT evs4) <= authKlife + Ta
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         \<rbrakk>
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          \<Longrightarrow> Says Tgs A \<lbrace>
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             Crypt authK \<lbrace>Key servK, Agent B, Number (CT evs4)\<rbrace>,
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   Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number (CT evs4)\<rbrace> 
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                          \<rbrace> # evs4 \<in> kerbV"
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(*Service phase*)
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 | KV5:  "\<lbrakk> evs5 \<in> kerbV; authK \<in> symKeys; servK \<in> symKeys;
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            A \<noteq> Kas; A \<noteq> Tgs;
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            Says A Tgs
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                \<lbrace>authTicket, Crypt authK \<lbrace>Agent A, Number T2\<rbrace>,
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                  Agent B\<rbrace>
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              \<in> set evs5;
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            Says Tgs' A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>,
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                          servTicket\<rbrace>
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                \<in> set evs5;
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            valid Ts wrt T2 \<rbrakk>
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          \<Longrightarrow> Says A B \<lbrace>servTicket,
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                         Crypt servK \<lbrace>Agent A, Number (CT evs5)\<rbrace> \<rbrace>
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               # evs5 \<in> kerbV"
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  | KV6:  "\<lbrakk> evs6 \<in> kerbV; B \<noteq> Kas; B \<noteq> Tgs;
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            Says A' B \<lbrace>
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              (Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>),
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              (Crypt servK \<lbrace>Agent A, Number T3\<rbrace>)\<rbrace>
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            \<in> set evs6;
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            \<not> expiredSK Ts evs6;
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            \<not> expiredA T3 evs6
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         \<rbrakk>
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          \<Longrightarrow> Says B A (Crypt servK (Number Ta2))
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               # evs6 \<in> kerbV"
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(* Leaking an authK... *)
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 | Oops1:"\<lbrakk> evsO1 \<in> kerbV;  A \<noteq> Spy;
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             Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>,
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                          authTicket\<rbrace>  \<in> set evsO1;
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              expiredAK Ta evsO1 \<rbrakk>
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          \<Longrightarrow> Notes Spy \<lbrace>Agent A, Agent Tgs, Number Ta, Key authK\<rbrace>
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               # evsO1 \<in> kerbV"
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(*Leaking a servK... *)
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 | Oops2: "\<lbrakk> evsO2 \<in> kerbV;  A \<noteq> Spy;
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              Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>,
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                           servTicket\<rbrace>  \<in> set evsO2;
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              expiredSK Ts evsO2 \<rbrakk>
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          \<Longrightarrow> Notes Spy \<lbrace>Agent A, Agent B, Number Ts, Key servK\<rbrace>
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               # evsO2 \<in> kerbV"
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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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subsection{*Lemmas about lists, for reasoning about  Issues*}
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lemma spies_Says_rev: "spies (evs @ [Says A B X]) = insert X (spies evs)"
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apply (induct_tac "evs")
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apply (rename_tac [2] a b)
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apply (induct_tac [2] "a", auto)
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done
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lemma spies_Gets_rev: "spies (evs @ [Gets A X]) = spies evs"
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apply (induct_tac "evs")
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apply (rename_tac [2] a b)
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apply (induct_tac [2] "a", auto)
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done
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lemma spies_Notes_rev: "spies (evs @ [Notes A X]) =
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          (if A:bad then insert X (spies evs) else spies evs)"
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apply (induct_tac "evs")
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apply (rename_tac [2] a b)
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apply (induct_tac [2] "a", auto)
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done
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lemma spies_evs_rev: "spies evs = spies (rev evs)"
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apply (induct_tac "evs")
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apply (rename_tac [2] a b)
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apply (induct_tac [2] "a")
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apply (simp_all (no_asm_simp) add: spies_Says_rev spies_Gets_rev spies_Notes_rev)
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done
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lemmas parts_spies_evs_revD2 = spies_evs_rev [THEN equalityD2, THEN parts_mono]
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lemma spies_takeWhile: "spies (takeWhile P evs) <=  spies evs"
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apply (induct_tac "evs")
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apply (rename_tac [2] a b)
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apply (induct_tac [2] "a", auto)
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txt{* Resembles @{text"used_subset_append"} in theory Event.*}
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done
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lemmas parts_spies_takeWhile_mono = spies_takeWhile [THEN parts_mono]
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subsection{*Lemmas about @{term authKeys}*}
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lemma authKeys_empty: "authKeys [] = {}"
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  by (simp add: authKeys_def)
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lemma authKeys_not_insert:
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 "(\<forall>A Ta akey Peer.
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   ev \<noteq> Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>akey, Agent Peer, Ta\<rbrace>,
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                     Crypt (shrK Peer) \<lbrace>Agent A, Agent Peer, akey, Ta\<rbrace> \<rbrace>)
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       \<Longrightarrow> authKeys (ev # evs) = authKeys evs"
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  by (auto simp add: authKeys_def)
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lemma authKeys_insert:
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  "authKeys
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     (Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key K, Agent Peer, Number Ta\<rbrace>,
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         Crypt (shrK Peer) \<lbrace>Agent A, Agent Peer, Key K, Number Ta\<rbrace> \<rbrace> # evs)
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       = insert K (authKeys evs)"
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  by (auto simp add: authKeys_def)
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lemma authKeys_simp:
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   "K \<in> authKeys
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    (Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key K', Agent Peer, Number Ta\<rbrace>,
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        Crypt (shrK Peer) \<lbrace>Agent A, Agent Peer, Key K', Number Ta\<rbrace> \<rbrace> # evs)
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        \<Longrightarrow> K = K' | K \<in> authKeys evs"
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  by (auto simp add: authKeys_def)
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lemma authKeysI:
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   "Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key K, Agent Tgs, Number Ta\<rbrace>,
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         Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key K, Number Ta\<rbrace> \<rbrace> \<in> set evs
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        \<Longrightarrow> K \<in> authKeys evs"
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  by (auto simp add: authKeys_def)
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lemma authKeys_used: "K \<in> authKeys evs \<Longrightarrow> Key K \<in> used evs"
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  by (auto simp add: authKeys_def)
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subsection{*Forwarding Lemmas*}
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lemma Says_ticket_parts:
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     "Says S A \<lbrace>Crypt K \<lbrace>SesKey, B, TimeStamp\<rbrace>, Ticket\<rbrace>
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               \<in> set evs \<Longrightarrow> Ticket \<in> parts (spies evs)"
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by blast
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lemma Says_ticket_analz:
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     "Says S A \<lbrace>Crypt K \<lbrace>SesKey, B, TimeStamp\<rbrace>, Ticket\<rbrace>
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               \<in> set evs \<Longrightarrow> Ticket \<in> analz (spies evs)"
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by (blast dest: Says_imp_knows_Spy [THEN analz.Inj, THEN analz.Snd])
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lemma Oops_range_spies1:
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     "\<lbrakk> Says Kas A \<lbrace>Crypt KeyA \<lbrace>Key authK, Peer, Ta\<rbrace>, authTicket\<rbrace>
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           \<in> set evs ;
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         evs \<in> kerbV \<rbrakk> \<Longrightarrow> authK \<notin> range shrK & authK \<in> symKeys"
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apply (erule rev_mp)
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apply (erule kerbV.induct, auto)
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done
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lemma Oops_range_spies2:
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     "\<lbrakk> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Ts\<rbrace>, servTicket\<rbrace>
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           \<in> set evs ;
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         evs \<in> kerbV \<rbrakk> \<Longrightarrow> servK \<notin> range shrK \<and> servK \<in> symKeys"
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apply (erule rev_mp)
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apply (erule kerbV.induct, auto)
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done
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(*Spy never sees another agent's shared key! (unless it's lost at start)*)
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lemma Spy_see_shrK [simp]:
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     "evs \<in> kerbV \<Longrightarrow> (Key (shrK A) \<in> parts (spies evs)) = (A \<in> bad)"
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apply (erule kerbV.induct)
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apply (frule_tac [7] Says_ticket_parts)
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apply (frule_tac [5] Says_ticket_parts, simp_all)
paulson@18886
   317
apply (blast+)
paulson@18886
   318
done
paulson@18886
   319
paulson@18886
   320
lemma Spy_analz_shrK [simp]:
paulson@18886
   321
     "evs \<in> kerbV \<Longrightarrow> (Key (shrK A) \<in> analz (spies evs)) = (A \<in> bad)"
paulson@18886
   322
by auto
paulson@18886
   323
paulson@18886
   324
lemma Spy_see_shrK_D [dest!]:
paulson@18886
   325
     "\<lbrakk> Key (shrK A) \<in> parts (spies evs);  evs \<in> kerbV \<rbrakk> \<Longrightarrow> A:bad"
paulson@18886
   326
by (blast dest: Spy_see_shrK)
paulson@43587
   327
paulson@18886
   328
lemmas Spy_analz_shrK_D = analz_subset_parts [THEN subsetD, THEN Spy_see_shrK_D, dest!]
paulson@18886
   329
paulson@18886
   330
text{*Nobody can have used non-existent keys!*}
paulson@18886
   331
lemma new_keys_not_used [simp]:
paulson@18886
   332
    "\<lbrakk>Key K \<notin> used evs; K \<in> symKeys; evs \<in> kerbV\<rbrakk>
paulson@18886
   333
     \<Longrightarrow> K \<notin> keysFor (parts (spies evs))"
paulson@18886
   334
apply (erule rev_mp)
paulson@18886
   335
apply (erule kerbV.induct)
paulson@18886
   336
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   337
apply (frule_tac [5] Says_ticket_parts, simp_all)
paulson@18886
   338
txt{*Fake*}
paulson@18886
   339
apply (force dest!: keysFor_parts_insert)
paulson@18886
   340
txt{*Others*}
paulson@18886
   341
apply (force dest!: analz_shrK_Decrypt)+
paulson@18886
   342
done
paulson@18886
   343
paulson@18886
   344
(*Earlier, all protocol proofs declared this theorem.
paulson@18886
   345
  But few of them actually need it! (Another is Yahalom) *)
paulson@18886
   346
lemma new_keys_not_analzd:
paulson@18886
   347
 "\<lbrakk>evs \<in> kerbV; K \<in> symKeys; Key K \<notin> used evs\<rbrakk>
paulson@18886
   348
  \<Longrightarrow> K \<notin> keysFor (analz (spies evs))"
paulson@18886
   349
by (blast dest: new_keys_not_used intro: keysFor_mono [THEN subsetD])
paulson@18886
   350
paulson@18886
   351
paulson@18886
   352
paulson@18886
   353
subsection{*Regularity Lemmas*}
paulson@18886
   354
text{*These concern the form of items passed in messages*}
paulson@18886
   355
paulson@18886
   356
text{*Describes the form of all components sent by Kas*}
paulson@18886
   357
lemma Says_Kas_message_form:
paulson@18886
   358
     "\<lbrakk> Says Kas A \<lbrace>Crypt K \<lbrace>Key authK, Agent Peer, Ta\<rbrace>, authTicket\<rbrace>
paulson@18886
   359
           \<in> set evs;
paulson@18886
   360
         evs \<in> kerbV \<rbrakk>
paulson@18886
   361
      \<Longrightarrow> authK \<notin> range shrK \<and> authK \<in> authKeys evs \<and> authK \<in> symKeys \<and> 
paulson@18886
   362
  authTicket = (Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Ta\<rbrace>) \<and>
paulson@18886
   363
             K = shrK A  \<and> Peer = Tgs"
paulson@18886
   364
apply (erule rev_mp)
paulson@18886
   365
apply (erule kerbV.induct)
paulson@18886
   366
apply (simp_all (no_asm) add: authKeys_def authKeys_insert)
paulson@18886
   367
apply blast+
paulson@18886
   368
done
paulson@18886
   369
paulson@18886
   370
paulson@18886
   371
paulson@18886
   372
(*This lemma is essential for proving Says_Tgs_message_form:
paulson@18886
   373
paulson@18886
   374
  the session key authK
paulson@18886
   375
  supplied by Kas in the authentication ticket
paulson@18886
   376
  cannot be a long-term key!
paulson@18886
   377
paulson@18886
   378
  Generalised to any session keys (both authK and servK).
paulson@18886
   379
*)
paulson@18886
   380
lemma SesKey_is_session_key:
paulson@18886
   381
     "\<lbrakk> Crypt (shrK Tgs_B) \<lbrace>Agent A, Agent Tgs_B, Key SesKey, Number T\<rbrace>
paulson@18886
   382
            \<in> parts (spies evs); Tgs_B \<notin> bad;
paulson@18886
   383
         evs \<in> kerbV \<rbrakk>
paulson@18886
   384
      \<Longrightarrow> SesKey \<notin> range shrK"
paulson@18886
   385
apply (erule rev_mp)
paulson@18886
   386
apply (erule kerbV.induct)
paulson@18886
   387
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   388
apply (frule_tac [5] Says_ticket_parts, simp_all, blast)
paulson@18886
   389
done
paulson@18886
   390
paulson@18886
   391
lemma authTicket_authentic:
paulson@18886
   392
     "\<lbrakk> Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Ta\<rbrace>
paulson@18886
   393
           \<in> parts (spies evs);
paulson@18886
   394
         evs \<in> kerbV \<rbrakk>
paulson@18886
   395
      \<Longrightarrow> Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Ta\<rbrace>,
paulson@18886
   396
                 Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Ta\<rbrace>\<rbrace>
paulson@18886
   397
            \<in> set evs"
paulson@18886
   398
apply (erule rev_mp)
paulson@18886
   399
apply (erule kerbV.induct)
paulson@18886
   400
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   401
apply (frule_tac [5] Says_ticket_parts, simp_all)
paulson@18886
   402
txt{*Fake, K4*}
paulson@18886
   403
apply (blast+)
paulson@18886
   404
done
paulson@18886
   405
paulson@18886
   406
lemma authTicket_crypt_authK:
paulson@18886
   407
     "\<lbrakk> Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Number Ta\<rbrace>
paulson@18886
   408
           \<in> parts (spies evs);
paulson@18886
   409
         evs \<in> kerbV \<rbrakk>
paulson@18886
   410
      \<Longrightarrow> authK \<in> authKeys evs"
paulson@43587
   411
by (metis authKeysI authTicket_authentic)
paulson@18886
   412
paulson@18886
   413
text{*Describes the form of servK, servTicket and authK sent by Tgs*}
paulson@18886
   414
lemma Says_Tgs_message_form:
paulson@18886
   415
     "\<lbrakk> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Ts\<rbrace>, servTicket\<rbrace>
paulson@18886
   416
           \<in> set evs;
paulson@18886
   417
         evs \<in> kerbV \<rbrakk>
paulson@18886
   418
   \<Longrightarrow> B \<noteq> Tgs \<and> 
paulson@18886
   419
       servK \<notin> range shrK \<and> servK \<notin> authKeys evs \<and> servK \<in> symKeys \<and>
paulson@18886
   420
       servTicket = (Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Ts\<rbrace>) \<and>
paulson@18886
   421
       authK \<notin> range shrK \<and> authK \<in> authKeys evs \<and> authK \<in> symKeys"
paulson@18886
   422
apply (erule rev_mp)
paulson@18886
   423
apply (erule kerbV.induct)
paulson@18886
   424
apply (simp_all add: authKeys_insert authKeys_not_insert authKeys_empty authKeys_simp, blast, auto)
paulson@18886
   425
txt{*Three subcases of Message 4*}
paulson@18886
   426
apply (blast dest!: authKeys_used Says_Kas_message_form)
paulson@18886
   427
apply (blast dest!: SesKey_is_session_key)
paulson@18886
   428
apply (blast dest: authTicket_crypt_authK)
paulson@18886
   429
done
paulson@18886
   430
paulson@18886
   431
paulson@18886
   432
paulson@18886
   433
(*
paulson@18886
   434
lemma authTicket_form:
paulson@18886
   435
lemma servTicket_form:
paulson@18886
   436
lemma Says_kas_message_form:
paulson@18886
   437
lemma Says_tgs_message_form:
paulson@18886
   438
paulson@18886
   439
cannot be proved for version V, but a new proof strategy can be used in their
paulson@18886
   440
place. The new strategy merely says that both the authTicket and the servTicket
paulson@18886
   441
are in parts and in analz as soon as they appear, using lemmas Says_ticket_parts and Says_ticket_analz. 
paulson@18886
   442
The new strategy always lets the simplifier solve cases K3 and K5, saving on
paulson@18886
   443
long dedicated analyses, which seemed unavoidable. For this reason, lemma 
paulson@18886
   444
servK_notin_authKeysD is no longer needed.
paulson@18886
   445
*)
paulson@18886
   446
paulson@18886
   447
subsection{*Authenticity theorems: confirm origin of sensitive messages*}
paulson@18886
   448
paulson@18886
   449
lemma authK_authentic:
paulson@18886
   450
     "\<lbrakk> Crypt (shrK A) \<lbrace>Key authK, Peer, Ta\<rbrace>
paulson@18886
   451
           \<in> parts (spies evs);
paulson@18886
   452
         A \<notin> bad;  evs \<in> kerbV \<rbrakk>
paulson@18886
   453
      \<Longrightarrow> \<exists> AT. Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Peer, Ta\<rbrace>, AT\<rbrace>
paulson@18886
   454
            \<in> set evs"
paulson@18886
   455
apply (erule rev_mp)
paulson@18886
   456
apply (erule kerbV.induct)
paulson@18886
   457
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   458
apply (frule_tac [5] Says_ticket_parts, simp_all)
paulson@18886
   459
apply blast+
paulson@18886
   460
done
paulson@18886
   461
paulson@18886
   462
text{*If a certain encrypted message appears then it originated with Tgs*}
paulson@18886
   463
lemma servK_authentic:
paulson@18886
   464
     "\<lbrakk> Crypt authK \<lbrace>Key servK, Agent B, Ts\<rbrace>
paulson@18886
   465
           \<in> parts (spies evs);
paulson@18886
   466
         Key authK \<notin> analz (spies evs);
paulson@18886
   467
         authK \<notin> range shrK;
paulson@18886
   468
         evs \<in> kerbV \<rbrakk>
paulson@18886
   469
 \<Longrightarrow> \<exists>A ST. Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Ts\<rbrace>, ST\<rbrace>
paulson@18886
   470
       \<in> set evs"
paulson@18886
   471
apply (erule rev_mp)
paulson@18886
   472
apply (erule rev_mp)
paulson@18886
   473
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
   474
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   475
apply (frule_tac [5] Says_ticket_parts, simp_all)
paulson@18886
   476
apply blast+
paulson@18886
   477
done
paulson@18886
   478
paulson@18886
   479
lemma servK_authentic_bis:
paulson@18886
   480
     "\<lbrakk> Crypt authK \<lbrace>Key servK, Agent B, Ts\<rbrace>
paulson@18886
   481
           \<in> parts (spies evs);
paulson@18886
   482
         Key authK \<notin> analz (spies evs);
paulson@18886
   483
         B \<noteq> Tgs;
paulson@18886
   484
         evs \<in> kerbV \<rbrakk>
paulson@18886
   485
 \<Longrightarrow> \<exists>A ST. Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Ts\<rbrace>, ST\<rbrace>
paulson@18886
   486
       \<in> set evs"
paulson@18886
   487
apply (erule rev_mp)
paulson@18886
   488
apply (erule rev_mp)
paulson@18886
   489
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
   490
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   491
apply (frule_tac [5] Says_ticket_parts, simp_all, blast+)
paulson@18886
   492
done
paulson@18886
   493
paulson@18886
   494
text{*Authenticity of servK for B*}
paulson@18886
   495
lemma servTicket_authentic_Tgs:
paulson@18886
   496
     "\<lbrakk> Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Ts\<rbrace>
paulson@18886
   497
           \<in> parts (spies evs);  B \<noteq> Tgs;  B \<notin> bad;
paulson@18886
   498
         evs \<in> kerbV \<rbrakk>
paulson@18886
   499
 \<Longrightarrow> \<exists>authK.
paulson@18886
   500
       Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Ts\<rbrace>,
paulson@18886
   501
                    Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Ts\<rbrace>\<rbrace>
paulson@18886
   502
       \<in> set evs"
paulson@18886
   503
apply (erule rev_mp)
paulson@18886
   504
apply (erule kerbV.induct)
paulson@18886
   505
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   506
apply (frule_tac [5] Says_ticket_parts, simp_all, blast+)
paulson@18886
   507
done
paulson@18886
   508
paulson@18886
   509
text{*Anticipated here from next subsection*}
paulson@18886
   510
lemma K4_imp_K2:
paulson@18886
   511
"\<lbrakk> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>, servTicket\<rbrace>
paulson@18886
   512
      \<in> set evs;  evs \<in> kerbV\<rbrakk>
paulson@18886
   513
   \<Longrightarrow> \<exists>Ta. Says Kas A
paulson@18886
   514
        \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>,
paulson@18886
   515
           Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Number Ta\<rbrace> \<rbrace>
paulson@18886
   516
        \<in> set evs"
paulson@18886
   517
apply (erule rev_mp)
paulson@18886
   518
apply (erule kerbV.induct)
paulson@18886
   519
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   520
apply (frule_tac [5] Says_ticket_parts, simp_all, auto)
paulson@43587
   521
apply (metis MPair_analz Says_imp_analz_Spy analz_conj_parts authTicket_authentic)
paulson@18886
   522
done
paulson@18886
   523
paulson@18886
   524
text{*Anticipated here from next subsection*}
paulson@18886
   525
lemma u_K4_imp_K2:
paulson@18886
   526
"\<lbrakk> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>, servTicket\<rbrace>  \<in> set evs; evs \<in> kerbV\<rbrakk>
paulson@18886
   527
   \<Longrightarrow> \<exists>Ta. Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>,
paulson@18886
   528
             Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Number Ta\<rbrace> \<rbrace>
paulson@18886
   529
             \<in> set evs
paulson@18886
   530
          \<and> servKlife + Ts <= authKlife + Ta"
paulson@18886
   531
apply (erule rev_mp)
paulson@18886
   532
apply (erule kerbV.induct)
paulson@18886
   533
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   534
apply (frule_tac [5] Says_ticket_parts, simp_all, auto)
paulson@18886
   535
apply (blast dest!: Says_imp_spies [THEN parts.Inj, THEN parts.Fst, THEN authTicket_authentic])
paulson@18886
   536
done
paulson@18886
   537
paulson@18886
   538
lemma servTicket_authentic_Kas:
paulson@18886
   539
     "\<lbrakk> Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>
paulson@18886
   540
           \<in> parts (spies evs);  B \<noteq> Tgs;  B \<notin> bad;
paulson@18886
   541
         evs \<in> kerbV \<rbrakk>
paulson@18886
   542
  \<Longrightarrow> \<exists>authK Ta.
paulson@18886
   543
       Says Kas A
paulson@18886
   544
         \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>,
paulson@18886
   545
           Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Number Ta\<rbrace> \<rbrace>
paulson@18886
   546
        \<in> set evs"
paulson@43587
   547
by (metis K4_imp_K2 servTicket_authentic_Tgs)
paulson@18886
   548
paulson@18886
   549
lemma u_servTicket_authentic_Kas:
paulson@18886
   550
     "\<lbrakk> Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>
paulson@18886
   551
           \<in> parts (spies evs);  B \<noteq> Tgs;  B \<notin> bad;
paulson@18886
   552
         evs \<in> kerbV \<rbrakk>
paulson@18886
   553
  \<Longrightarrow> \<exists>authK Ta.
paulson@18886
   554
       Says Kas A
paulson@18886
   555
         \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>,
paulson@18886
   556
           Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Number Ta\<rbrace> \<rbrace>
paulson@18886
   557
        \<in> set evs \<and> 
paulson@18886
   558
      servKlife + Ts <= authKlife + Ta"
paulson@43587
   559
by (metis servTicket_authentic_Tgs u_K4_imp_K2)
paulson@18886
   560
paulson@18886
   561
lemma servTicket_authentic:
paulson@18886
   562
     "\<lbrakk> Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>
paulson@18886
   563
           \<in> parts (spies evs);  B \<noteq> Tgs;  B \<notin> bad;
paulson@18886
   564
         evs \<in> kerbV \<rbrakk>
paulson@18886
   565
 \<Longrightarrow> \<exists>Ta authK.
paulson@18886
   566
     Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>,
paulson@18886
   567
                  Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Number Ta\<rbrace> \<rbrace>  \<in> set evs
paulson@18886
   568
     \<and> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>,
paulson@18886
   569
                  Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>\<rbrace>
paulson@18886
   570
       \<in> set evs"
paulson@43587
   571
by (metis K4_imp_K2 servTicket_authentic_Tgs)
paulson@18886
   572
paulson@18886
   573
lemma u_servTicket_authentic:
paulson@18886
   574
     "\<lbrakk> Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>
paulson@18886
   575
           \<in> parts (spies evs);  B \<noteq> Tgs;  B \<notin> bad;
paulson@18886
   576
         evs \<in> kerbV \<rbrakk>
paulson@18886
   577
 \<Longrightarrow> \<exists>Ta authK.
paulson@18886
   578
     Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>,
paulson@18886
   579
                  Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Number Ta\<rbrace>\<rbrace> \<in> set evs
paulson@18886
   580
     \<and> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>,
paulson@18886
   581
                 Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>\<rbrace>
paulson@18886
   582
       \<in> set evs
paulson@18886
   583
     \<and> servKlife + Ts <= authKlife + Ta"
paulson@43587
   584
by (metis servTicket_authentic_Tgs u_K4_imp_K2)
paulson@18886
   585
paulson@18886
   586
lemma u_NotexpiredSK_NotexpiredAK:
paulson@18886
   587
     "\<lbrakk> \<not> expiredSK Ts evs; servKlife + Ts <= authKlife + Ta \<rbrakk>
paulson@18886
   588
      \<Longrightarrow> \<not> expiredAK Ta evs"
paulson@43587
   589
by (metis order_le_less_trans)
paulson@18886
   590
paulson@18886
   591
subsection{* Reliability: friendly agents send somthing if something else happened*}
paulson@18886
   592
paulson@18886
   593
lemma K3_imp_K2:
paulson@18886
   594
     "\<lbrakk> Says A Tgs
paulson@18886
   595
             \<lbrace>authTicket, Crypt authK \<lbrace>Agent A, Number T2\<rbrace>, Agent B\<rbrace>
paulson@18886
   596
           \<in> set evs;
paulson@18886
   597
         A \<notin> bad;  evs \<in> kerbV \<rbrakk>
paulson@18886
   598
      \<Longrightarrow> \<exists>Ta AT. Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Ta\<rbrace>, 
paulson@18886
   599
                               AT\<rbrace> \<in> set evs"
paulson@18886
   600
apply (erule rev_mp)
paulson@18886
   601
apply (erule kerbV.induct)
paulson@18886
   602
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   603
apply (frule_tac [5] Says_ticket_parts, simp_all, blast, blast)
paulson@18886
   604
apply (blast dest: Says_imp_spies [THEN parts.Inj, THEN parts.Fst, THEN authK_authentic])
paulson@18886
   605
done
paulson@18886
   606
paulson@18886
   607
text{*Anticipated here from next subsection. An authK is encrypted by one and only one Shared key. A servK is encrypted by one and only one authK.*}
paulson@18886
   608
lemma Key_unique_SesKey:
paulson@18886
   609
     "\<lbrakk> Crypt K  \<lbrace>Key SesKey,  Agent B, T\<rbrace>
paulson@18886
   610
           \<in> parts (spies evs);
paulson@18886
   611
         Crypt K' \<lbrace>Key SesKey,  Agent B', T'\<rbrace>
paulson@18886
   612
           \<in> parts (spies evs);  Key SesKey \<notin> analz (spies evs);
paulson@18886
   613
         evs \<in> kerbV \<rbrakk>
paulson@18886
   614
      \<Longrightarrow> K=K' \<and> B=B' \<and> T=T'"
paulson@18886
   615
apply (erule rev_mp)
paulson@18886
   616
apply (erule rev_mp)
paulson@18886
   617
apply (erule rev_mp)
paulson@18886
   618
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
   619
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   620
apply (frule_tac [5] Says_ticket_parts, simp_all)
paulson@18886
   621
txt{*Fake, K2, K4*}
paulson@18886
   622
apply (blast+)
paulson@18886
   623
done
paulson@18886
   624
paulson@18886
   625
text{*This inevitably has an existential form in version V*}
paulson@18886
   626
lemma Says_K5:
paulson@18886
   627
     "\<lbrakk> Crypt servK \<lbrace>Agent A, Number T3\<rbrace> \<in> parts (spies evs);
paulson@18886
   628
         Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>,
paulson@18886
   629
                                     servTicket\<rbrace> \<in> set evs;
paulson@18886
   630
         Key servK \<notin> analz (spies evs);
paulson@18886
   631
         A \<notin> bad; B \<notin> bad; evs \<in> kerbV \<rbrakk>
paulson@18886
   632
 \<Longrightarrow> \<exists> ST. Says A B \<lbrace>ST, Crypt servK \<lbrace>Agent A, Number T3\<rbrace>\<rbrace> \<in> set evs"
paulson@18886
   633
apply (erule rev_mp)
paulson@18886
   634
apply (erule rev_mp)
paulson@18886
   635
apply (erule rev_mp)
paulson@18886
   636
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
   637
apply (frule_tac [5] Says_ticket_parts)
paulson@18886
   638
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   639
apply (simp_all (no_asm_simp) add: all_conj_distrib)
paulson@18886
   640
apply blast
paulson@18886
   641
txt{*K3*}
paulson@18886
   642
apply (blast dest: authK_authentic Says_Kas_message_form Says_Tgs_message_form)
paulson@18886
   643
txt{*K4*}
paulson@18886
   644
apply (force dest!: Crypt_imp_keysFor)
paulson@18886
   645
txt{*K5*}
paulson@18886
   646
apply (blast dest: Key_unique_SesKey)
paulson@18886
   647
done
paulson@18886
   648
paulson@18886
   649
text{*Anticipated here from next subsection*}
paulson@18886
   650
lemma unique_CryptKey:
paulson@18886
   651
     "\<lbrakk> Crypt (shrK B)  \<lbrace>Agent A,  Agent B,  Key SesKey, T\<rbrace>
paulson@18886
   652
           \<in> parts (spies evs);
paulson@18886
   653
         Crypt (shrK B') \<lbrace>Agent A', Agent B', Key SesKey, T'\<rbrace>
paulson@18886
   654
           \<in> parts (spies evs);  Key SesKey \<notin> analz (spies evs);
paulson@18886
   655
         evs \<in> kerbV \<rbrakk>
paulson@18886
   656
      \<Longrightarrow> A=A' & B=B' & T=T'"
paulson@18886
   657
apply (erule rev_mp)
paulson@18886
   658
apply (erule rev_mp)
paulson@18886
   659
apply (erule rev_mp)
paulson@18886
   660
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
   661
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   662
apply (frule_tac [5] Says_ticket_parts, simp_all)
paulson@18886
   663
txt{*Fake, K2, K4*}
paulson@18886
   664
apply (blast+)
paulson@18886
   665
done
paulson@18886
   666
paulson@18886
   667
lemma Says_K6:
paulson@18886
   668
     "\<lbrakk> Crypt servK (Number T3) \<in> parts (spies evs);
paulson@18886
   669
         Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>,
paulson@18886
   670
                      servTicket\<rbrace> \<in> set evs;
paulson@18886
   671
         Key servK \<notin> analz (spies evs);
paulson@18886
   672
         A \<notin> bad; B \<notin> bad; evs \<in> kerbV \<rbrakk>
paulson@18886
   673
      \<Longrightarrow> Says B A (Crypt servK (Number T3)) \<in> set evs"
paulson@18886
   674
apply (frule Says_Tgs_message_form, assumption, clarify)
paulson@18886
   675
apply (erule rev_mp)
paulson@18886
   676
apply (erule rev_mp)
paulson@18886
   677
apply (erule rev_mp)
paulson@18886
   678
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
   679
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   680
apply (frule_tac [5] Says_ticket_parts)
paulson@43587
   681
apply simp_all
paulson@18886
   682
paulson@18886
   683
txt{*fake*}
paulson@18886
   684
apply blast
paulson@18886
   685
txt{*K4*}
paulson@43587
   686
apply (force dest!: Crypt_imp_keysFor)
paulson@18886
   687
txt{*K6*}
blanchet@47050
   688
apply (metis MPair_parts Says_imp_parts_knows_Spy unique_CryptKey)
paulson@18886
   689
done
paulson@18886
   690
paulson@18886
   691
text{*Needs a unicity theorem, hence moved here*}
paulson@18886
   692
lemma servK_authentic_ter:
paulson@18886
   693
 "\<lbrakk> Says Kas A
paulson@18886
   694
       \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Ta\<rbrace>, authTicket\<rbrace> \<in> set evs;
paulson@18886
   695
     Crypt authK \<lbrace>Key servK, Agent B, Ts\<rbrace>
paulson@18886
   696
       \<in> parts (spies evs);
paulson@18886
   697
     Key authK \<notin> analz (spies evs);
paulson@18886
   698
     evs \<in> kerbV \<rbrakk>
paulson@18886
   699
 \<Longrightarrow> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Ts\<rbrace>, 
paulson@18886
   700
                 Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Ts\<rbrace> \<rbrace>
paulson@18886
   701
       \<in> set evs"
paulson@18886
   702
apply (frule Says_Kas_message_form, assumption)
paulson@18886
   703
apply clarify
paulson@18886
   704
apply (erule rev_mp)
paulson@18886
   705
apply (erule rev_mp)
paulson@18886
   706
apply (erule rev_mp)
paulson@18886
   707
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
   708
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   709
apply (frule_tac [5] Says_ticket_parts, simp_all, blast)
paulson@18886
   710
txt{*K2 and K4 remain*}
paulson@18886
   711
apply (blast dest!: servK_authentic Says_Tgs_message_form authKeys_used)
paulson@18886
   712
apply (blast dest!: unique_CryptKey)
paulson@18886
   713
done
paulson@18886
   714
paulson@18886
   715
paulson@18886
   716
subsection{*Unicity Theorems*}
paulson@18886
   717
paulson@18886
   718
text{* The session key, if secure, uniquely identifies the Ticket
paulson@18886
   719
   whether authTicket or servTicket. As a matter of fact, one can read
paulson@18886
   720
   also Tgs in the place of B.                                     *}
paulson@18886
   721
paulson@18886
   722
paulson@18886
   723
lemma unique_authKeys:
paulson@18886
   724
     "\<lbrakk> Says Kas A
paulson@18886
   725
              \<lbrace>Crypt Ka \<lbrace>Key authK, Agent Tgs, Ta\<rbrace>, X\<rbrace> \<in> set evs;
paulson@18886
   726
         Says Kas A'
paulson@18886
   727
              \<lbrace>Crypt Ka' \<lbrace>Key authK, Agent Tgs, Ta'\<rbrace>, X'\<rbrace> \<in> set evs;
paulson@18886
   728
         evs \<in> kerbV \<rbrakk> \<Longrightarrow> A=A' \<and> Ka=Ka' \<and> Ta=Ta' \<and> X=X'"
paulson@18886
   729
apply (erule rev_mp)
paulson@18886
   730
apply (erule rev_mp)
paulson@18886
   731
apply (erule kerbV.induct)
paulson@18886
   732
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   733
apply (frule_tac [5] Says_ticket_parts, simp_all)
paulson@18886
   734
apply blast+
paulson@18886
   735
done
paulson@18886
   736
paulson@18886
   737
text{* servK uniquely identifies the message from Tgs *}
paulson@18886
   738
lemma unique_servKeys:
paulson@18886
   739
     "\<lbrakk> Says Tgs A
paulson@18886
   740
              \<lbrace>Crypt K \<lbrace>Key servK, Agent B, Ts\<rbrace>, X\<rbrace> \<in> set evs;
paulson@18886
   741
         Says Tgs A'
paulson@18886
   742
              \<lbrace>Crypt K' \<lbrace>Key servK, Agent B', Ts'\<rbrace>, X'\<rbrace> \<in> set evs;
paulson@18886
   743
         evs \<in> kerbV \<rbrakk> \<Longrightarrow> A=A' \<and> B=B' \<and> K=K' \<and> Ts=Ts' \<and> X=X'"
paulson@18886
   744
apply (erule rev_mp)
paulson@18886
   745
apply (erule rev_mp)
paulson@18886
   746
apply (erule kerbV.induct)
paulson@18886
   747
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   748
apply (frule_tac [5] Says_ticket_parts, simp_all)
paulson@18886
   749
apply blast+
paulson@18886
   750
done
paulson@18886
   751
paulson@18886
   752
subsection{*Lemmas About the Predicate @{term AKcryptSK}*}
paulson@18886
   753
paulson@18886
   754
lemma not_AKcryptSK_Nil [iff]: "\<not> AKcryptSK authK servK []"
paulson@18886
   755
apply (simp add: AKcryptSK_def)
paulson@18886
   756
done
paulson@18886
   757
paulson@18886
   758
lemma AKcryptSKI:
paulson@18886
   759
 "\<lbrakk> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, tt\<rbrace>, X \<rbrace> \<in> set evs;
paulson@18886
   760
     evs \<in> kerbV \<rbrakk> \<Longrightarrow> AKcryptSK authK servK evs"
paulson@43587
   761
by (metis AKcryptSK_def Says_Tgs_message_form)
paulson@18886
   762
paulson@18886
   763
lemma AKcryptSK_Says [simp]:
paulson@18886
   764
   "AKcryptSK authK servK (Says S A X # evs) =
paulson@18886
   765
     (S = Tgs \<and>
paulson@18886
   766
      (\<exists>B tt. X = \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, tt\<rbrace>,
paulson@18886
   767
                    Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, tt\<rbrace> \<rbrace>)
paulson@18886
   768
     | AKcryptSK authK servK evs)"
paulson@43587
   769
by (auto simp add: AKcryptSK_def) 
paulson@18886
   770
paulson@18886
   771
lemma AKcryptSK_Notes [simp]:
paulson@18886
   772
   "AKcryptSK authK servK (Notes A X # evs) =
paulson@18886
   773
      AKcryptSK authK servK evs"
paulson@43587
   774
by (auto simp add: AKcryptSK_def) 
paulson@18886
   775
paulson@18886
   776
(*A fresh authK cannot be associated with any other
paulson@18886
   777
  (with respect to a given trace). *)
paulson@18886
   778
lemma Auth_fresh_not_AKcryptSK:
paulson@18886
   779
     "\<lbrakk> Key authK \<notin> used evs; evs \<in> kerbV \<rbrakk>
paulson@18886
   780
      \<Longrightarrow> \<not> AKcryptSK authK servK evs"
paulson@18886
   781
apply (unfold AKcryptSK_def)
paulson@18886
   782
apply (erule rev_mp)
paulson@18886
   783
apply (erule kerbV.induct)
paulson@18886
   784
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   785
apply (frule_tac [5] Says_ticket_parts, simp_all, blast)
paulson@18886
   786
done
paulson@18886
   787
paulson@18886
   788
(*A fresh servK cannot be associated with any other
paulson@18886
   789
  (with respect to a given trace). *)
paulson@18886
   790
lemma Serv_fresh_not_AKcryptSK:
paulson@18886
   791
 "Key servK \<notin> used evs \<Longrightarrow> \<not> AKcryptSK authK servK evs"
paulson@43587
   792
by (auto simp add: AKcryptSK_def) 
paulson@18886
   793
paulson@18886
   794
lemma authK_not_AKcryptSK:
paulson@18886
   795
     "\<lbrakk> Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, tk\<rbrace>
paulson@18886
   796
           \<in> parts (spies evs);  evs \<in> kerbV \<rbrakk>
paulson@18886
   797
      \<Longrightarrow> \<not> AKcryptSK K authK evs"
paulson@18886
   798
apply (erule rev_mp)
paulson@18886
   799
apply (erule kerbV.induct)
paulson@18886
   800
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   801
apply (frule_tac [5] Says_ticket_parts, simp_all)
paulson@43587
   802
txt{*Fake,K2,K4*}
paulson@43587
   803
apply (auto simp add: AKcryptSK_def)
paulson@18886
   804
done
paulson@18886
   805
paulson@18886
   806
text{*A secure serverkey cannot have been used to encrypt others*}
paulson@18886
   807
lemma servK_not_AKcryptSK:
paulson@18886
   808
 "\<lbrakk> Crypt (shrK B) \<lbrace>Agent A, Agent B, Key SK, tt\<rbrace> \<in> parts (spies evs);
paulson@18886
   809
     Key SK \<notin> analz (spies evs);  SK \<in> symKeys;
paulson@18886
   810
     B \<noteq> Tgs;  evs \<in> kerbV \<rbrakk>
paulson@18886
   811
  \<Longrightarrow> \<not> AKcryptSK SK K evs"
paulson@18886
   812
apply (erule rev_mp)
paulson@18886
   813
apply (erule rev_mp)
paulson@18886
   814
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
   815
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   816
apply (frule_tac [5] Says_ticket_parts, simp_all, blast)
paulson@32404
   817
txt{*K4*}
paulson@43587
   818
apply (metis Auth_fresh_not_AKcryptSK MPair_parts Says_imp_parts_knows_Spy authKeys_used authTicket_crypt_authK unique_CryptKey)
paulson@18886
   819
done
paulson@18886
   820
paulson@18886
   821
text{*Long term keys are not issued as servKeys*}
paulson@18886
   822
lemma shrK_not_AKcryptSK:
paulson@18886
   823
     "evs \<in> kerbV \<Longrightarrow> \<not> AKcryptSK K (shrK A) evs"
paulson@18886
   824
apply (unfold AKcryptSK_def)
paulson@18886
   825
apply (erule kerbV.induct)
paulson@18886
   826
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   827
apply (frule_tac [5] Says_ticket_parts, auto)
paulson@18886
   828
done
paulson@18886
   829
paulson@18886
   830
text{*The Tgs message associates servK with authK and therefore not with any
paulson@18886
   831
  other key authK.*}
paulson@18886
   832
lemma Says_Tgs_AKcryptSK:
paulson@18886
   833
     "\<lbrakk> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, tt\<rbrace>, X \<rbrace>
paulson@18886
   834
           \<in> set evs;
paulson@18886
   835
         authK' \<noteq> authK;  evs \<in> kerbV \<rbrakk>
paulson@18886
   836
      \<Longrightarrow> \<not> AKcryptSK authK' servK evs"
paulson@43587
   837
by (metis AKcryptSK_def unique_servKeys)
paulson@18886
   838
paulson@18886
   839
lemma AKcryptSK_not_AKcryptSK:
paulson@18886
   840
     "\<lbrakk> AKcryptSK authK servK evs;  evs \<in> kerbV \<rbrakk>
paulson@18886
   841
      \<Longrightarrow> \<not> AKcryptSK servK K evs"
paulson@18886
   842
apply (erule rev_mp)
paulson@18886
   843
apply (erule kerbV.induct)
paulson@18886
   844
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
   845
apply (frule_tac [5] Says_ticket_parts)
paulson@18886
   846
apply (simp_all, safe)
paulson@18886
   847
txt{*K4 splits into subcases*}
paulson@18886
   848
prefer 4 apply (blast dest!: authK_not_AKcryptSK)
paulson@18886
   849
txt{*servK is fresh and so could not have been used, by
paulson@18886
   850
   @{text new_keys_not_used}*}
paulson@18886
   851
 prefer 2 
paulson@18886
   852
 apply (force dest!: Crypt_imp_invKey_keysFor simp add: AKcryptSK_def)
paulson@18886
   853
txt{*Others by freshness*}
paulson@18886
   854
apply (blast+)
paulson@18886
   855
done
paulson@18886
   856
paulson@18886
   857
lemma not_different_AKcryptSK:
paulson@18886
   858
     "\<lbrakk> AKcryptSK authK servK evs;
paulson@18886
   859
        authK' \<noteq> authK;  evs \<in> kerbV \<rbrakk>
paulson@18886
   860
      \<Longrightarrow> \<not> AKcryptSK authK' servK evs  \<and> servK \<in> symKeys"
paulson@18886
   861
apply (simp add: AKcryptSK_def)
paulson@18886
   862
apply (blast dest: unique_servKeys Says_Tgs_message_form)
paulson@18886
   863
done
paulson@18886
   864
paulson@18886
   865
text{*The only session keys that can be found with the help of session keys are
paulson@18886
   866
  those sent by Tgs in step K4.  *}
paulson@18886
   867
paulson@18886
   868
text{*We take some pains to express the property
paulson@18886
   869
  as a logical equivalence so that the simplifier can apply it.*}
paulson@18886
   870
lemma Key_analz_image_Key_lemma:
paulson@18886
   871
     "P \<longrightarrow> (Key K \<in> analz (Key`KK Un H)) \<longrightarrow> (K:KK | Key K \<in> analz H)
paulson@18886
   872
      \<Longrightarrow>
paulson@18886
   873
      P \<longrightarrow> (Key K \<in> analz (Key`KK Un H)) = (K:KK | Key K \<in> analz H)"
paulson@18886
   874
by (blast intro: analz_mono [THEN subsetD])
paulson@18886
   875
paulson@18886
   876
paulson@18886
   877
lemma AKcryptSK_analz_insert:
paulson@18886
   878
     "\<lbrakk> AKcryptSK K K' evs; K \<in> symKeys; evs \<in> kerbV \<rbrakk>
paulson@18886
   879
      \<Longrightarrow> Key K' \<in> analz (insert (Key K) (spies evs))"
paulson@18886
   880
apply (simp add: AKcryptSK_def, clarify)
paulson@18886
   881
apply (drule Says_imp_spies [THEN analz.Inj, THEN analz_insertI], auto)
paulson@18886
   882
done
paulson@18886
   883
paulson@18886
   884
lemma authKeys_are_not_AKcryptSK:
paulson@18886
   885
     "\<lbrakk> K \<in> authKeys evs Un range shrK;  evs \<in> kerbV \<rbrakk>
paulson@18886
   886
      \<Longrightarrow> \<forall>SK. \<not> AKcryptSK SK K evs \<and> K \<in> symKeys"
paulson@18886
   887
apply (simp add: authKeys_def AKcryptSK_def)
paulson@18886
   888
apply (blast dest: Says_Kas_message_form Says_Tgs_message_form)
paulson@18886
   889
done
paulson@18886
   890
paulson@18886
   891
lemma not_authKeys_not_AKcryptSK:
paulson@18886
   892
     "\<lbrakk> K \<notin> authKeys evs;
paulson@18886
   893
         K \<notin> range shrK; evs \<in> kerbV \<rbrakk>
paulson@18886
   894
      \<Longrightarrow> \<forall>SK. \<not> AKcryptSK K SK evs"
paulson@18886
   895
apply (simp add: AKcryptSK_def)
paulson@18886
   896
apply (blast dest: Says_Tgs_message_form)
paulson@18886
   897
done
paulson@18886
   898
paulson@18886
   899
paulson@18886
   900
subsection{*Secrecy Theorems*}
paulson@18886
   901
paulson@18886
   902
text{*For the Oops2 case of the next theorem*}
paulson@18886
   903
lemma Oops2_not_AKcryptSK:
paulson@18886
   904
     "\<lbrakk> evs \<in> kerbV;
paulson@18886
   905
         Says Tgs A \<lbrace>Crypt authK
paulson@18886
   906
                     \<lbrace>Key servK, Agent B, Number Ts\<rbrace>, servTicket\<rbrace>
paulson@18886
   907
           \<in> set evs \<rbrakk>
paulson@18886
   908
      \<Longrightarrow> \<not> AKcryptSK servK SK evs"
paulson@43587
   909
by (blast dest: AKcryptSKI AKcryptSK_not_AKcryptSK)
paulson@18886
   910
   
paulson@18886
   911
text{* Big simplification law for keys SK that are not crypted by keys in KK
paulson@18886
   912
 It helps prove three, otherwise hard, facts about keys. These facts are
paulson@18886
   913
 exploited as simplification laws for analz, and also "limit the damage"
paulson@18886
   914
 in case of loss of a key to the spy. See ESORICS98.*}
paulson@18886
   915
lemma Key_analz_image_Key [rule_format (no_asm)]:
paulson@18886
   916
     "evs \<in> kerbV \<Longrightarrow>
paulson@18886
   917
      (\<forall>SK KK. SK \<in> symKeys & KK <= -(range shrK) \<longrightarrow>
paulson@18886
   918
       (\<forall>K \<in> KK. \<not> AKcryptSK K SK evs)   \<longrightarrow>
paulson@18886
   919
       (Key SK \<in> analz (Key`KK Un (spies evs))) =
paulson@18886
   920
       (SK \<in> KK | Key SK \<in> analz (spies evs)))"
paulson@18886
   921
apply (erule kerbV.induct)
paulson@18886
   922
apply (frule_tac [10] Oops_range_spies2)
paulson@18886
   923
apply (frule_tac [9] Oops_range_spies1)
paulson@18886
   924
(*Used to apply Says_tgs_message form, which is no longer available. 
paulson@18886
   925
  Instead\<dots>*)
paulson@18886
   926
apply (drule_tac [7] Says_ticket_analz)
paulson@18886
   927
(*Used to apply Says_kas_message form, which is no longer available. 
paulson@18886
   928
  Instead\<dots>*)
paulson@18886
   929
apply (drule_tac [5] Says_ticket_analz)
paulson@18886
   930
apply (safe del: impI intro!: Key_analz_image_Key_lemma [THEN impI])
paulson@18886
   931
txt{*Case-splits for Oops1 and message 5: the negated case simplifies using
paulson@18886
   932
 the induction hypothesis*}
paulson@18886
   933
apply (case_tac [9] "AKcryptSK authK SK evsO1")
paulson@18886
   934
apply (case_tac [7] "AKcryptSK servK SK evs5")
paulson@18886
   935
apply (simp_all del: image_insert
paulson@18886
   936
          add: analz_image_freshK_simps AKcryptSK_Says shrK_not_AKcryptSK
paulson@18886
   937
               Oops2_not_AKcryptSK Auth_fresh_not_AKcryptSK
paulson@18886
   938
               Serv_fresh_not_AKcryptSK Says_Tgs_AKcryptSK Spy_analz_shrK)
paulson@18886
   939
txt{*Fake*} 
paulson@18886
   940
apply spy_analz
paulson@18886
   941
txt{*K2*}
paulson@18886
   942
apply blast 
paulson@18886
   943
txt{*Cases K3 and K5 solved by the simplifier thanks to the ticket being in 
paulson@18886
   944
analz - this strategy is new wrt version IV*} 
paulson@18886
   945
txt{*K4*}
paulson@18886
   946
apply (blast dest!: authK_not_AKcryptSK)
paulson@18886
   947
txt{*Oops1*}
paulson@32404
   948
apply (metis AKcryptSK_analz_insert insert_Key_singleton)
paulson@18886
   949
done
paulson@18886
   950
paulson@18886
   951
text{* First simplification law for analz: no session keys encrypt
paulson@18886
   952
authentication keys or shared keys. *}
paulson@18886
   953
lemma analz_insert_freshK1:
paulson@18886
   954
     "\<lbrakk> evs \<in> kerbV;  K \<in> authKeys evs Un range shrK;
paulson@18886
   955
        SesKey \<notin> range shrK \<rbrakk>
paulson@18886
   956
      \<Longrightarrow> (Key K \<in> analz (insert (Key SesKey) (spies evs))) =
paulson@18886
   957
          (K = SesKey | Key K \<in> analz (spies evs))"
paulson@18886
   958
apply (frule authKeys_are_not_AKcryptSK, assumption)
paulson@18886
   959
apply (simp del: image_insert
paulson@18886
   960
            add: analz_image_freshK_simps add: Key_analz_image_Key)
paulson@18886
   961
done
paulson@18886
   962
paulson@18886
   963
paulson@18886
   964
text{* Second simplification law for analz: no service keys encrypt any other keys.*}
paulson@18886
   965
lemma analz_insert_freshK2:
paulson@18886
   966
     "\<lbrakk> evs \<in> kerbV;  servK \<notin> (authKeys evs); servK \<notin> range shrK;
paulson@18886
   967
        K \<in> symKeys \<rbrakk>
paulson@18886
   968
      \<Longrightarrow> (Key K \<in> analz (insert (Key servK) (spies evs))) =
paulson@18886
   969
          (K = servK | Key K \<in> analz (spies evs))"
paulson@18886
   970
apply (frule not_authKeys_not_AKcryptSK, assumption, assumption)
paulson@18886
   971
apply (simp del: image_insert
paulson@18886
   972
            add: analz_image_freshK_simps add: Key_analz_image_Key)
paulson@18886
   973
done
paulson@18886
   974
paulson@18886
   975
paulson@18886
   976
text{* Third simplification law for analz: only one authentication key encrypts a certain service key.*}
paulson@18886
   977
paulson@18886
   978
lemma analz_insert_freshK3:
paulson@18886
   979
 "\<lbrakk> AKcryptSK authK servK evs;
paulson@18886
   980
    authK' \<noteq> authK; authK' \<notin> range shrK; evs \<in> kerbV \<rbrakk>
paulson@18886
   981
        \<Longrightarrow> (Key servK \<in> analz (insert (Key authK') (spies evs))) =
paulson@18886
   982
                (servK = authK' | Key servK \<in> analz (spies evs))"
paulson@18886
   983
apply (drule_tac authK' = authK' in not_different_AKcryptSK, blast, assumption)
paulson@18886
   984
apply (simp del: image_insert
paulson@18886
   985
            add: analz_image_freshK_simps add: Key_analz_image_Key)
paulson@18886
   986
done
paulson@18886
   987
paulson@18886
   988
lemma analz_insert_freshK3_bis:
paulson@18886
   989
 "\<lbrakk> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>, servTicket\<rbrace>
paulson@18886
   990
        \<in> set evs; 
paulson@18886
   991
     authK \<noteq> authK'; authK' \<notin> range shrK; evs \<in> kerbV \<rbrakk>
paulson@18886
   992
        \<Longrightarrow> (Key servK \<in> analz (insert (Key authK') (spies evs))) =
paulson@18886
   993
                (servK = authK' | Key servK \<in> analz (spies evs))"
paulson@18886
   994
apply (frule AKcryptSKI, assumption)
paulson@18886
   995
apply (simp add: analz_insert_freshK3)
paulson@18886
   996
done
paulson@18886
   997
paulson@18886
   998
text{*a weakness of the protocol*}
paulson@18886
   999
lemma authK_compromises_servK:
paulson@18886
  1000
     "\<lbrakk> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>, servTicket\<rbrace>
paulson@18886
  1001
        \<in> set evs;  authK \<in> symKeys;
paulson@18886
  1002
         Key authK \<in> analz (spies evs); evs \<in> kerbV \<rbrakk>
paulson@18886
  1003
      \<Longrightarrow> Key servK \<in> analz (spies evs)"
paulson@32404
  1004
  by (metis Says_imp_analz_Spy analz.Fst analz_Decrypt')
paulson@32404
  1005
paulson@18886
  1006
paulson@18886
  1007
text{*lemma @{text servK_notin_authKeysD} not needed in version V*}
paulson@18886
  1008
paulson@18886
  1009
text{*If Spy sees the Authentication Key sent in msg K2, then
paulson@18886
  1010
    the Key has expired.*}
paulson@18886
  1011
lemma Confidentiality_Kas_lemma [rule_format]:
paulson@18886
  1012
     "\<lbrakk> authK \<in> symKeys; A \<notin> bad;  evs \<in> kerbV \<rbrakk>
paulson@18886
  1013
      \<Longrightarrow> Says Kas A
paulson@18886
  1014
               \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>,
paulson@18886
  1015
          Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Number Ta\<rbrace>\<rbrace>
paulson@18886
  1016
            \<in> set evs \<longrightarrow>
paulson@18886
  1017
          Key authK \<in> analz (spies evs) \<longrightarrow>
paulson@18886
  1018
          expiredAK Ta evs"
paulson@18886
  1019
apply (erule kerbV.induct)
paulson@18886
  1020
apply (frule_tac [10] Oops_range_spies2)
paulson@18886
  1021
apply (frule_tac [9] Oops_range_spies1)
paulson@18886
  1022
apply (frule_tac [7] Says_ticket_analz)
paulson@18886
  1023
apply (frule_tac [5] Says_ticket_analz)
paulson@18886
  1024
apply (safe del: impI conjI impCE)
paulson@18886
  1025
apply (simp_all (no_asm_simp) add: Says_Kas_message_form less_SucI analz_insert_eq not_parts_not_analz analz_insert_freshK1 pushes)
paulson@18886
  1026
txt{*Fake*}
paulson@18886
  1027
apply spy_analz
paulson@18886
  1028
txt{*K2*}
paulson@18886
  1029
apply blast
paulson@18886
  1030
txt{*K4*}
paulson@18886
  1031
apply blast
paulson@18886
  1032
txt{*Oops1*}
paulson@18886
  1033
apply (blast dest!: unique_authKeys intro: less_SucI)
paulson@18886
  1034
txt{*Oops2*}
paulson@18886
  1035
apply (blast dest: Says_Tgs_message_form Says_Kas_message_form)
paulson@18886
  1036
done
paulson@18886
  1037
paulson@18886
  1038
lemma Confidentiality_Kas:
paulson@18886
  1039
     "\<lbrakk> Says Kas A
paulson@18886
  1040
              \<lbrace>Crypt Ka \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>, authTicket\<rbrace>
paulson@18886
  1041
           \<in> set evs;
paulson@18886
  1042
        \<not> expiredAK Ta evs;
paulson@18886
  1043
        A \<notin> bad;  evs \<in> kerbV \<rbrakk>
paulson@18886
  1044
      \<Longrightarrow> Key authK \<notin> analz (spies evs)"
paulson@18886
  1045
apply (blast dest: Says_Kas_message_form Confidentiality_Kas_lemma)
paulson@18886
  1046
done
paulson@18886
  1047
paulson@18886
  1048
text{*If Spy sees the Service Key sent in msg K4, then
paulson@18886
  1049
    the Key has expired.*}
paulson@18886
  1050
paulson@18886
  1051
lemma Confidentiality_lemma [rule_format]:
paulson@18886
  1052
     "\<lbrakk> Says Tgs A
wenzelm@32960
  1053
            \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>,
wenzelm@32960
  1054
              Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>\<rbrace>
wenzelm@32960
  1055
           \<in> set evs;
wenzelm@32960
  1056
        Key authK \<notin> analz (spies evs);
paulson@18886
  1057
        servK \<in> symKeys;
wenzelm@32960
  1058
        A \<notin> bad;  B \<notin> bad; evs \<in> kerbV \<rbrakk>
paulson@18886
  1059
      \<Longrightarrow> Key servK \<in> analz (spies evs) \<longrightarrow>
wenzelm@32960
  1060
          expiredSK Ts evs"
paulson@18886
  1061
apply (erule rev_mp)
paulson@18886
  1062
apply (erule rev_mp)
paulson@18886
  1063
apply (erule kerbV.induct)
paulson@43587
  1064
apply (rule_tac [9] impI)+
paulson@18886
  1065
  --{*The Oops1 case is unusual: must simplify
paulson@18886
  1066
    @{term "Authkey \<notin> analz (spies (ev#evs))"}, not letting
paulson@18886
  1067
   @{text analz_mono_contra} weaken it to
paulson@18886
  1068
   @{term "Authkey \<notin> analz (spies evs)"},
paulson@18886
  1069
  for we then conclude @{term "authK \<noteq> authKa"}.*}
paulson@18886
  1070
apply analz_mono_contra
paulson@18886
  1071
apply (frule_tac [10] Oops_range_spies2)
paulson@18886
  1072
apply (frule_tac [9] Oops_range_spies1)
paulson@18886
  1073
apply (frule_tac [7] Says_ticket_analz)
paulson@18886
  1074
apply (frule_tac [5] Says_ticket_analz)
paulson@18886
  1075
apply (safe del: impI conjI impCE)
paulson@18886
  1076
apply (simp_all add: less_SucI new_keys_not_analzd Says_Kas_message_form Says_Tgs_message_form analz_insert_eq not_parts_not_analz analz_insert_freshK1 analz_insert_freshK2 analz_insert_freshK3_bis pushes)
paulson@32404
  1077
    txt{*Fake*}
paulson@32404
  1078
    apply spy_analz
paulson@32404
  1079
   txt{*K2*}
paulson@32404
  1080
   apply (blast intro: parts_insertI less_SucI)
paulson@32404
  1081
  txt{*K4*}
paulson@32404
  1082
  apply (blast dest: authTicket_authentic Confidentiality_Kas)
paulson@32404
  1083
 txt{*Oops1*}
paulson@18886
  1084
 apply (blast dest: Says_Kas_message_form Says_Tgs_message_form intro: less_SucI)
paulson@18886
  1085
txt{*Oops2*}
paulson@32404
  1086
apply (metis Suc_le_eq linorder_linear linorder_not_le msg.simps(2) unique_servKeys)
paulson@18886
  1087
done
paulson@18886
  1088
paulson@18886
  1089
paulson@18886
  1090
text{* In the real world Tgs can't check wheter authK is secure! *}
paulson@18886
  1091
lemma Confidentiality_Tgs:
paulson@18886
  1092
     "\<lbrakk> Says Tgs A
paulson@18886
  1093
              \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>, servTicket\<rbrace>
paulson@18886
  1094
           \<in> set evs;
paulson@18886
  1095
         Key authK \<notin> analz (spies evs);
paulson@18886
  1096
         \<not> expiredSK Ts evs;
paulson@18886
  1097
         A \<notin> bad;  B \<notin> bad; evs \<in> kerbV \<rbrakk>
paulson@18886
  1098
      \<Longrightarrow> Key servK \<notin> analz (spies evs)"
paulson@43587
  1099
by (blast dest: Says_Tgs_message_form Confidentiality_lemma)
paulson@18886
  1100
paulson@18886
  1101
text{* In the real world Tgs CAN check what Kas sends! *}
paulson@18886
  1102
lemma Confidentiality_Tgs_bis:
paulson@18886
  1103
     "\<lbrakk> Says Kas A
paulson@18886
  1104
               \<lbrace>Crypt Ka \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>, authTicket\<rbrace>
paulson@18886
  1105
           \<in> set evs;
paulson@18886
  1106
         Says Tgs A
paulson@18886
  1107
              \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>, servTicket\<rbrace>
paulson@18886
  1108
           \<in> set evs;
paulson@18886
  1109
         \<not> expiredAK Ta evs; \<not> expiredSK Ts evs;
paulson@18886
  1110
         A \<notin> bad;  B \<notin> bad; evs \<in> kerbV \<rbrakk>
paulson@18886
  1111
      \<Longrightarrow> Key servK \<notin> analz (spies evs)"
paulson@43587
  1112
by (blast dest!: Confidentiality_Kas Confidentiality_Tgs)
paulson@18886
  1113
paulson@18886
  1114
text{*Most general form*}
paulson@18886
  1115
lemmas Confidentiality_Tgs_ter = authTicket_authentic [THEN Confidentiality_Tgs_bis]
paulson@18886
  1116
paulson@18886
  1117
lemmas Confidentiality_Auth_A = authK_authentic [THEN exE, THEN Confidentiality_Kas]
paulson@18886
  1118
paulson@18886
  1119
text{*Needs a confidentiality guarantee, hence moved here.
paulson@18886
  1120
      Authenticity of servK for A*}
paulson@18886
  1121
lemma servK_authentic_bis_r:
paulson@18886
  1122
     "\<lbrakk> Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>
paulson@18886
  1123
           \<in> parts (spies evs);
paulson@18886
  1124
         Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>
paulson@18886
  1125
           \<in> parts (spies evs);
paulson@18886
  1126
         \<not> expiredAK Ta evs; A \<notin> bad; evs \<in> kerbV \<rbrakk>
paulson@18886
  1127
 \<Longrightarrow> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>, 
paulson@18886
  1128
                 Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace> \<rbrace>
paulson@18886
  1129
       \<in> set evs"
paulson@43587
  1130
by (metis Confidentiality_Kas authK_authentic servK_authentic_ter)
paulson@18886
  1131
paulson@18886
  1132
lemma Confidentiality_Serv_A:
paulson@18886
  1133
     "\<lbrakk> Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>
paulson@18886
  1134
           \<in> parts (spies evs);
paulson@18886
  1135
         Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>
paulson@18886
  1136
           \<in> parts (spies evs);
paulson@18886
  1137
         \<not> expiredAK Ta evs; \<not> expiredSK Ts evs;
paulson@18886
  1138
         A \<notin> bad;  B \<notin> bad; B \<noteq> Tgs; evs \<in> kerbV \<rbrakk>
paulson@18886
  1139
      \<Longrightarrow> Key servK \<notin> analz (spies evs)"
paulson@18886
  1140
apply (drule authK_authentic, assumption, assumption)
paulson@18886
  1141
apply (blast dest: Confidentiality_Kas Says_Kas_message_form servK_authentic_ter Confidentiality_Tgs_bis)
paulson@18886
  1142
done
paulson@18886
  1143
paulson@18886
  1144
lemma Confidentiality_B:
paulson@18886
  1145
     "\<lbrakk> Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>
paulson@18886
  1146
           \<in> parts (spies evs);
paulson@18886
  1147
         Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>
paulson@18886
  1148
           \<in> parts (spies evs);
paulson@18886
  1149
         Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>
paulson@18886
  1150
           \<in> parts (spies evs);
paulson@18886
  1151
         \<not> expiredSK Ts evs; \<not> expiredAK Ta evs;
paulson@18886
  1152
         A \<notin> bad;  B \<notin> bad; B \<noteq> Tgs; evs \<in> kerbV \<rbrakk>
paulson@18886
  1153
      \<Longrightarrow> Key servK \<notin> analz (spies evs)"
paulson@18886
  1154
apply (frule authK_authentic)
paulson@18886
  1155
apply (erule_tac [3] exE)
paulson@18886
  1156
apply (frule_tac [3] Confidentiality_Kas)
paulson@18886
  1157
apply (frule_tac [6] servTicket_authentic, auto)
paulson@18886
  1158
apply (blast dest!: Confidentiality_Tgs_bis dest: Says_Kas_message_form servK_authentic unique_servKeys unique_authKeys)
paulson@18886
  1159
done
paulson@18886
  1160
paulson@18886
  1161
lemma u_Confidentiality_B:
paulson@18886
  1162
     "\<lbrakk> Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>
paulson@18886
  1163
           \<in> parts (spies evs);
paulson@18886
  1164
         \<not> expiredSK Ts evs;
paulson@18886
  1165
         A \<notin> bad;  B \<notin> bad;  B \<noteq> Tgs; evs \<in> kerbV \<rbrakk>
paulson@18886
  1166
      \<Longrightarrow> Key servK \<notin> analz (spies evs)"
paulson@43587
  1167
by (blast dest: u_servTicket_authentic u_NotexpiredSK_NotexpiredAK Confidentiality_Tgs_bis)
paulson@18886
  1168
paulson@18886
  1169
paulson@18886
  1170
paulson@18886
  1171
subsection{*Parties authentication: each party verifies "the identity of
paulson@18886
  1172
       another party who generated some data" (quoted from Neuman and Ts'o).*}
paulson@18886
  1173
paulson@18886
  1174
text{*These guarantees don't assess whether two parties agree on
paulson@18886
  1175
      the same session key: sending a message containing a key
paulson@18886
  1176
      doesn't a priori state knowledge of the key.*}
paulson@18886
  1177
paulson@18886
  1178
paulson@18886
  1179
text{*These didn't have existential form in version IV*}
paulson@18886
  1180
lemma B_authenticates_A:
paulson@18886
  1181
     "\<lbrakk> Crypt servK \<lbrace>Agent A, Number T3\<rbrace> \<in> parts (spies evs);
paulson@18886
  1182
        Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>
paulson@18886
  1183
           \<in> parts (spies evs);
paulson@18886
  1184
        Key servK \<notin> analz (spies evs);
paulson@18886
  1185
        A \<notin> bad; B \<notin> bad; B \<noteq> Tgs; evs \<in> kerbV \<rbrakk>
paulson@18886
  1186
  \<Longrightarrow> \<exists> ST. Says A B \<lbrace>ST, Crypt servK \<lbrace>Agent A, Number T3\<rbrace> \<rbrace> \<in> set evs"
paulson@43587
  1187
by (blast dest: servTicket_authentic_Tgs intro: Says_K5)
paulson@18886
  1188
paulson@18886
  1189
text{*The second assumption tells B what kind of key servK is.*}
paulson@18886
  1190
lemma B_authenticates_A_r:
paulson@18886
  1191
     "\<lbrakk> Crypt servK \<lbrace>Agent A, Number T3\<rbrace> \<in> parts (spies evs);
paulson@18886
  1192
         Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>
paulson@18886
  1193
           \<in> parts (spies evs);
paulson@18886
  1194
         Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>
paulson@18886
  1195
           \<in> parts (spies evs);
paulson@18886
  1196
         Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>
paulson@18886
  1197
           \<in> parts (spies evs);
paulson@18886
  1198
         \<not> expiredSK Ts evs; \<not> expiredAK Ta evs;
paulson@18886
  1199
         B \<noteq> Tgs; A \<notin> bad;  B \<notin> bad;  evs \<in> kerbV \<rbrakk>
paulson@18886
  1200
  \<Longrightarrow> \<exists> ST. Says A B \<lbrace>ST, Crypt servK \<lbrace>Agent A, Number T3\<rbrace> \<rbrace> \<in> set evs"
paulson@43587
  1201
by (blast intro: Says_K5 dest: Confidentiality_B servTicket_authentic_Tgs)
paulson@18886
  1202
paulson@18886
  1203
text{* @{text u_B_authenticates_A} would be the same as @{text B_authenticates_A} because the
paulson@18886
  1204
 servK confidentiality assumption is yet unrelaxed*}
paulson@18886
  1205
paulson@18886
  1206
lemma u_B_authenticates_A_r:
paulson@18886
  1207
     "\<lbrakk> Crypt servK \<lbrace>Agent A, Number T3\<rbrace> \<in> parts (spies evs);
paulson@18886
  1208
         Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>
paulson@18886
  1209
           \<in> parts (spies evs);
paulson@18886
  1210
         \<not> expiredSK Ts evs;
paulson@18886
  1211
         B \<noteq> Tgs; A \<notin> bad;  B \<notin> bad;  evs \<in> kerbV \<rbrakk>
paulson@18886
  1212
  \<Longrightarrow> \<exists> ST. Says A B \<lbrace>ST, Crypt servK \<lbrace>Agent A, Number T3\<rbrace> \<rbrace> \<in> set evs"
paulson@43587
  1213
by (blast intro: Says_K5 dest: u_Confidentiality_B servTicket_authentic_Tgs)
paulson@18886
  1214
paulson@18886
  1215
lemma A_authenticates_B:
paulson@18886
  1216
     "\<lbrakk> Crypt servK (Number T3) \<in> parts (spies evs);
paulson@18886
  1217
         Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>
paulson@18886
  1218
           \<in> parts (spies evs);
paulson@18886
  1219
         Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>
paulson@18886
  1220
           \<in> parts (spies evs);
paulson@18886
  1221
         Key authK \<notin> analz (spies evs); Key servK \<notin> analz (spies evs);
paulson@18886
  1222
         A \<notin> bad;  B \<notin> bad; evs \<in> kerbV \<rbrakk>
paulson@18886
  1223
      \<Longrightarrow> Says B A (Crypt servK (Number T3)) \<in> set evs"
paulson@32404
  1224
  by (metis authK_authentic Oops_range_spies1 Says_K6 servK_authentic u_K4_imp_K2 unique_authKeys)
paulson@18886
  1225
paulson@18886
  1226
lemma A_authenticates_B_r:
paulson@18886
  1227
     "\<lbrakk> Crypt servK (Number T3) \<in> parts (spies evs);
paulson@18886
  1228
         Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>
paulson@18886
  1229
           \<in> parts (spies evs);
paulson@18886
  1230
         Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>
paulson@18886
  1231
           \<in> parts (spies evs);
paulson@18886
  1232
         \<not> expiredAK Ta evs; \<not> expiredSK Ts evs;
paulson@18886
  1233
         A \<notin> bad;  B \<notin> bad; evs \<in> kerbV \<rbrakk>
paulson@18886
  1234
      \<Longrightarrow> Says B A (Crypt servK (Number T3)) \<in> set evs"
paulson@18886
  1235
apply (frule authK_authentic)
paulson@18886
  1236
apply (erule_tac [3] exE)
paulson@18886
  1237
apply (frule_tac [3] Says_Kas_message_form)
paulson@18886
  1238
apply (frule_tac [4] Confidentiality_Kas)
paulson@18886
  1239
apply (frule_tac [7] servK_authentic)
paulson@43587
  1240
apply auto
paulson@43587
  1241
apply (metis Confidentiality_Tgs K4_imp_K2 Says_K6 unique_authKeys) 
paulson@18886
  1242
done
paulson@18886
  1243
paulson@18886
  1244
paulson@18886
  1245
paulson@18886
  1246
subsection{*Parties' knowledge of session keys. 
paulson@18886
  1247
       An agent knows a session key if he used it to issue a cipher. These
paulson@18886
  1248
       guarantees can be interpreted both in terms of key distribution
paulson@18886
  1249
       and of non-injective agreement on the session key.*}
paulson@18886
  1250
paulson@18886
  1251
lemma Kas_Issues_A:
paulson@18886
  1252
   "\<lbrakk> Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Peer, Ta\<rbrace>, authTicket\<rbrace> \<in> set evs;
paulson@18886
  1253
      evs \<in> kerbV \<rbrakk>
paulson@18886
  1254
  \<Longrightarrow> Kas Issues A with (Crypt (shrK A) \<lbrace>Key authK, Peer, Ta\<rbrace>)
paulson@18886
  1255
          on evs"
paulson@18886
  1256
apply (simp (no_asm) add: Issues_def)
paulson@18886
  1257
apply (rule exI)
paulson@18886
  1258
apply (rule conjI, assumption)
paulson@18886
  1259
apply (simp (no_asm))
paulson@18886
  1260
apply (erule rev_mp)
paulson@18886
  1261
apply (erule kerbV.induct)
paulson@18886
  1262
apply (frule_tac [5] Says_ticket_parts)
paulson@18886
  1263
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
  1264
apply (simp_all (no_asm_simp) add: all_conj_distrib)
paulson@18886
  1265
txt{*K2*}
paulson@18886
  1266
apply (simp add: takeWhile_tail)
paulson@43587
  1267
apply (metis MPair_parts parts.Body parts_idem parts_spies_takeWhile_mono parts_trans spies_evs_rev usedI)
paulson@18886
  1268
done
paulson@18886
  1269
paulson@18886
  1270
lemma A_authenticates_and_keydist_to_Kas:
paulson@18886
  1271
  "\<lbrakk> Crypt (shrK A) \<lbrace>Key authK, Peer, Ta\<rbrace> \<in> parts (spies evs);
paulson@18886
  1272
     A \<notin> bad; evs \<in> kerbV \<rbrakk>
paulson@18886
  1273
 \<Longrightarrow> Kas Issues A with (Crypt (shrK A) \<lbrace>Key authK, Peer, Ta\<rbrace>) 
paulson@18886
  1274
          on evs"
paulson@18886
  1275
by (blast dest!: authK_authentic Kas_Issues_A)
paulson@18886
  1276
paulson@18886
  1277
lemma Tgs_Issues_A:
paulson@18886
  1278
    "\<lbrakk> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>, servTicket\<rbrace>
paulson@18886
  1279
         \<in> set evs; 
paulson@18886
  1280
       Key authK \<notin> analz (spies evs);  evs \<in> kerbV \<rbrakk>
paulson@18886
  1281
  \<Longrightarrow> Tgs Issues A with 
paulson@18886
  1282
          (Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>) on evs"
paulson@18886
  1283
apply (simp (no_asm) add: Issues_def)
paulson@18886
  1284
apply (rule exI)
paulson@18886
  1285
apply (rule conjI, assumption)
paulson@18886
  1286
apply (simp (no_asm))
paulson@18886
  1287
apply (erule rev_mp)
paulson@18886
  1288
apply (erule rev_mp)
paulson@18886
  1289
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
  1290
apply (frule_tac [5] Says_ticket_parts)
paulson@18886
  1291
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
  1292
apply (simp_all (no_asm_simp) add: all_conj_distrib)
paulson@18886
  1293
apply (simp add: takeWhile_tail)
paulson@18886
  1294
(*Last two thms installed only to derive authK \<notin> range shrK*)
paulson@18886
  1295
apply (blast dest: servK_authentic parts_spies_takeWhile_mono [THEN subsetD]
paulson@18886
  1296
      parts_spies_evs_revD2 [THEN subsetD] authTicket_authentic 
paulson@18886
  1297
      Says_Kas_message_form)
paulson@18886
  1298
done
paulson@18886
  1299
paulson@18886
  1300
lemma A_authenticates_and_keydist_to_Tgs:
paulson@18886
  1301
     "\<lbrakk> Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>
paulson@18886
  1302
           \<in> parts (spies evs);
paulson@18886
  1303
       Key authK \<notin> analz (spies evs); B \<noteq> Tgs; evs \<in> kerbV \<rbrakk>
paulson@18886
  1304
  \<Longrightarrow> \<exists>A. Tgs Issues A with 
paulson@18886
  1305
          (Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>) on evs"
paulson@18886
  1306
by (blast dest: Tgs_Issues_A servK_authentic_bis)
paulson@18886
  1307
paulson@18886
  1308
lemma B_Issues_A:
paulson@18886
  1309
     "\<lbrakk> Says B A (Crypt servK (Number T3)) \<in> set evs;
paulson@18886
  1310
         Key servK \<notin> analz (spies evs);
paulson@18886
  1311
         A \<notin> bad;  B \<notin> bad; B \<noteq> Tgs; evs \<in> kerbV \<rbrakk>
paulson@18886
  1312
      \<Longrightarrow> B Issues A with (Crypt servK (Number T3)) on evs"
paulson@18886
  1313
apply (simp (no_asm) add: Issues_def)
paulson@18886
  1314
apply (rule exI)
paulson@18886
  1315
apply (rule conjI, assumption)
paulson@18886
  1316
apply (simp (no_asm))
paulson@18886
  1317
apply (erule rev_mp)
paulson@18886
  1318
apply (erule rev_mp)
paulson@18886
  1319
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
  1320
apply (simp_all (no_asm_simp) add: all_conj_distrib)
paulson@18886
  1321
apply blast
paulson@18886
  1322
txt{*K6 requires numerous lemmas*}
paulson@18886
  1323
apply (simp add: takeWhile_tail)
paulson@18886
  1324
apply (blast intro: Says_K6 dest: servTicket_authentic 
paulson@18886
  1325
        parts_spies_takeWhile_mono [THEN subsetD] 
paulson@18886
  1326
        parts_spies_evs_revD2 [THEN subsetD])
paulson@18886
  1327
done
paulson@18886
  1328
paulson@18886
  1329
lemma A_authenticates_and_keydist_to_B:
paulson@18886
  1330
     "\<lbrakk> Crypt servK (Number T3) \<in> parts (spies evs);
paulson@18886
  1331
         Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>
paulson@18886
  1332
           \<in> parts (spies evs);
paulson@18886
  1333
         Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>
paulson@18886
  1334
           \<in> parts (spies evs);
paulson@18886
  1335
         Key authK \<notin> analz (spies evs); Key servK \<notin> analz (spies evs);
paulson@18886
  1336
         A \<notin> bad;  B \<notin> bad; B \<noteq> Tgs; evs \<in> kerbV \<rbrakk>
paulson@18886
  1337
      \<Longrightarrow> B Issues A with (Crypt servK (Number T3)) on evs"
paulson@18886
  1338
by (blast dest!: A_authenticates_B B_Issues_A)
paulson@18886
  1339
paulson@18886
  1340
paulson@18886
  1341
(*Must use \<le> rather than =, otherwise it cannot be proved inductively!*)
paulson@18886
  1342
(*This is too strong for version V but would hold for version IV if only B 
paulson@18886
  1343
  in K6 said a fresh timestamp.
paulson@18886
  1344
lemma honest_never_says_newer_timestamp:
paulson@18886
  1345
     "\<lbrakk> (CT evs) \<le> T ; Number T \<in> parts {X}; evs \<in> kerbV \<rbrakk> 
paulson@18886
  1346
     \<Longrightarrow> \<forall> A B. A \<noteq> Spy \<longrightarrow> Says A B X \<notin> set evs"
paulson@18886
  1347
apply (erule rev_mp)
paulson@18886
  1348
apply (erule kerbV.induct)
paulson@18886
  1349
apply (simp_all)
paulson@18886
  1350
apply force
paulson@18886
  1351
apply force
paulson@18886
  1352
txt{*clarifying case K3*}
paulson@18886
  1353
apply (rule impI)
paulson@18886
  1354
apply (rule impI)
paulson@18886
  1355
apply (frule Suc_leD)
paulson@18886
  1356
apply (clarify)
paulson@18886
  1357
txt{*cannot solve K3 or K5 because the spy might send CT evs as authTicket
paulson@18886
  1358
or servTicket, which the honest agent would forward*}
paulson@18886
  1359
prefer 2 apply force
paulson@18886
  1360
prefer 4 apply force
paulson@18886
  1361
prefer 4 apply force
paulson@18886
  1362
txt{*cannot solve K6 unless B updates the timestamp - rather than bouncing T3*}
paulson@18886
  1363
oops
paulson@18886
  1364
*)
paulson@18886
  1365
paulson@18886
  1366
paulson@18886
  1367
text{*But can prove a less general fact conerning only authenticators!*}
paulson@18886
  1368
lemma honest_never_says_newer_timestamp_in_auth:
paulson@18886
  1369
     "\<lbrakk> (CT evs) \<le> T; Number T \<in> parts {X}; A \<notin> bad; evs \<in> kerbV \<rbrakk> 
paulson@18886
  1370
     \<Longrightarrow> Says A B \<lbrace>Y, X\<rbrace> \<notin> set evs"
paulson@18886
  1371
apply (erule rev_mp)
paulson@18886
  1372
apply (erule kerbV.induct)
paulson@43587
  1373
apply auto
paulson@18886
  1374
done
paulson@18886
  1375
paulson@18886
  1376
lemma honest_never_says_current_timestamp_in_auth:
paulson@18886
  1377
     "\<lbrakk> (CT evs) = T; Number T \<in> parts {X}; A \<notin> bad; evs \<in> kerbV \<rbrakk> 
paulson@18886
  1378
     \<Longrightarrow> Says A B \<lbrace>Y, X\<rbrace> \<notin> set evs"
paulson@43587
  1379
by (metis honest_never_says_newer_timestamp_in_auth le_refl)
paulson@18886
  1380
paulson@18886
  1381
paulson@18886
  1382
lemma A_Issues_B:
paulson@18886
  1383
     "\<lbrakk> Says A B \<lbrace>ST, Crypt servK \<lbrace>Agent A, Number T3\<rbrace>\<rbrace> \<in> set evs;
paulson@18886
  1384
         Key servK \<notin> analz (spies evs);
paulson@18886
  1385
         B \<noteq> Tgs; A \<notin> bad;  B \<notin> bad;  evs \<in> kerbV \<rbrakk>
paulson@18886
  1386
   \<Longrightarrow> A Issues B with (Crypt servK \<lbrace>Agent A, Number T3\<rbrace>) on evs"
paulson@18886
  1387
apply (simp (no_asm) add: Issues_def)
paulson@18886
  1388
apply (rule exI)
paulson@18886
  1389
apply (rule conjI, assumption)
paulson@18886
  1390
apply (simp (no_asm))
paulson@18886
  1391
apply (erule rev_mp)
paulson@18886
  1392
apply (erule rev_mp)
paulson@18886
  1393
apply (erule kerbV.induct, analz_mono_contra)
paulson@18886
  1394
apply (frule_tac [7] Says_ticket_parts)
paulson@18886
  1395
apply (frule_tac [5] Says_ticket_parts)
paulson@18886
  1396
apply (simp_all (no_asm_simp))
paulson@18886
  1397
txt{*K5*}
paulson@18886
  1398
apply auto
paulson@18886
  1399
apply (simp add: takeWhile_tail)
paulson@18886
  1400
txt{*Level 15: case study necessary because the assumption doesn't state
paulson@18886
  1401
  the form of servTicket. The guarantee becomes stronger.*}
paulson@18886
  1402
prefer 2 apply (simp add: takeWhile_tail)
paulson@18886
  1403
(**This single command of version IV...
paulson@18886
  1404
apply (blast dest: Says_imp_spies [THEN analz.Inj, THEN analz_Decrypt']
paulson@18886
  1405
                   K3_imp_K2 K4_trustworthy'
paulson@18886
  1406
                   parts_spies_takeWhile_mono [THEN subsetD]
paulson@18886
  1407
                   parts_spies_evs_revD2 [THEN subsetD]
paulson@18886
  1408
             intro: Says_Auth)
paulson@18886
  1409
...expands as follows - including extra exE because of new form of lemmas*)
paulson@18886
  1410
apply (frule K3_imp_K2, assumption, assumption, erule exE, erule exE)
paulson@18886
  1411
apply (case_tac "Key authK \<in> analz (spies evs5)")
paulson@32404
  1412
 apply (metis Says_imp_analz_Spy analz.Fst analz_Decrypt')
paulson@18886
  1413
apply (frule K3_imp_K2, assumption, assumption, erule exE, erule exE)
paulson@18886
  1414
apply (drule Says_imp_knows_Spy [THEN parts.Inj, THEN parts.Fst])
paulson@18886
  1415
apply (frule servK_authentic_ter, blast, assumption+)
paulson@18886
  1416
apply (drule parts_spies_takeWhile_mono [THEN subsetD])
paulson@18886
  1417
apply (drule parts_spies_evs_revD2 [THEN subsetD])
paulson@18886
  1418
txt{* @{term Says_K5} closes the proof in version IV because it is clear which 
paulson@18886
  1419
servTicket an authenticator appears with in msg 5. In version V an authenticator can appear with any item that the spy could replace the servTicket with*}
paulson@43587
  1420
apply (frule Says_K5, blast)
paulson@18886
  1421
txt{*We need to state that an honest agent wouldn't send the wrong timestamp
paulson@18886
  1422
within an authenticator, wathever it is paired with*}
paulson@43587
  1423
apply (auto simp add: honest_never_says_current_timestamp_in_auth)
paulson@18886
  1424
done
paulson@18886
  1425
paulson@18886
  1426
lemma B_authenticates_and_keydist_to_A:
paulson@18886
  1427
     "\<lbrakk> Crypt servK \<lbrace>Agent A, Number T3\<rbrace> \<in> parts (spies evs);
paulson@18886
  1428
         Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>
paulson@18886
  1429
           \<in> parts (spies evs);
paulson@18886
  1430
         Key servK \<notin> analz (spies evs);
paulson@18886
  1431
         B \<noteq> Tgs; A \<notin> bad;  B \<notin> bad;  evs \<in> kerbV \<rbrakk>
paulson@18886
  1432
   \<Longrightarrow> A Issues B with (Crypt servK \<lbrace>Agent A, Number T3\<rbrace>) on evs"
paulson@18886
  1433
by (blast dest: B_authenticates_A A_Issues_B)
paulson@18886
  1434
paulson@18886
  1435
paulson@18886
  1436
paulson@18886
  1437
subsection{*
paulson@18886
  1438
Novel guarantees, never studied before. Because honest agents always say
paulson@18886
  1439
the right timestamp in authenticators, we can prove unicity guarantees based 
paulson@18886
  1440
exactly on timestamps. Classical unicity guarantees are based on nonces.
paulson@18886
  1441
Of course assuming the agent to be different from the Spy, rather than not in 
paulson@18886
  1442
bad, would suffice below. Similar guarantees must also hold of
paulson@18886
  1443
Kerberos IV.*}
paulson@18886
  1444
paulson@18886
  1445
text{*Notice that an honest agent can send the same timestamp on two
paulson@18886
  1446
different traces of the same length, but not on the same trace!*}
paulson@18886
  1447
paulson@18886
  1448
lemma unique_timestamp_authenticator1:
paulson@18886
  1449
     "\<lbrakk> Says A Kas \<lbrace>Agent A, Agent Tgs, Number T1\<rbrace> \<in> set evs;
paulson@18886
  1450
         Says A Kas' \<lbrace>Agent A, Agent Tgs', Number T1\<rbrace> \<in> set evs;
paulson@18886
  1451
         A \<notin>bad; evs \<in> kerbV \<rbrakk>
paulson@18886
  1452
  \<Longrightarrow> Kas=Kas' \<and> Tgs=Tgs'"
paulson@18886
  1453
apply (erule rev_mp, erule rev_mp)
paulson@18886
  1454
apply (erule kerbV.induct)
paulson@43587
  1455
apply (auto simp add: honest_never_says_current_timestamp_in_auth)
paulson@18886
  1456
done
paulson@18886
  1457
paulson@18886
  1458
lemma unique_timestamp_authenticator2:
paulson@18886
  1459
     "\<lbrakk> Says A Tgs \<lbrace>AT, Crypt AK \<lbrace>Agent A, Number T2\<rbrace>, Agent B\<rbrace> \<in> set evs;
paulson@18886
  1460
     Says A Tgs' \<lbrace>AT', Crypt AK' \<lbrace>Agent A, Number T2\<rbrace>, Agent B'\<rbrace> \<in> set evs;
paulson@18886
  1461
         A \<notin>bad; evs \<in> kerbV \<rbrakk>
paulson@18886
  1462
  \<Longrightarrow> Tgs=Tgs' \<and> AT=AT' \<and> AK=AK' \<and> B=B'"
paulson@18886
  1463
apply (erule rev_mp, erule rev_mp)
paulson@18886
  1464
apply (erule kerbV.induct)
paulson@43587
  1465
apply (auto simp add: honest_never_says_current_timestamp_in_auth)
paulson@18886
  1466
done
paulson@18886
  1467
paulson@18886
  1468
lemma unique_timestamp_authenticator3:
paulson@18886
  1469
     "\<lbrakk> Says A B \<lbrace>ST, Crypt SK \<lbrace>Agent A, Number T\<rbrace>\<rbrace> \<in> set evs;
paulson@18886
  1470
         Says A B' \<lbrace>ST', Crypt SK' \<lbrace>Agent A, Number T\<rbrace>\<rbrace> \<in> set evs;
paulson@18886
  1471
         A \<notin>bad; evs \<in> kerbV \<rbrakk>
paulson@18886
  1472
  \<Longrightarrow> B=B' \<and> ST=ST' \<and> SK=SK'"
paulson@18886
  1473
apply (erule rev_mp, erule rev_mp)
paulson@18886
  1474
apply (erule kerbV.induct)
paulson@18886
  1475
apply (auto simp add: honest_never_says_current_timestamp_in_auth)
paulson@18886
  1476
done
paulson@18886
  1477
paulson@18886
  1478
text{*The second part of the message is treated as an authenticator by the last
paulson@18886
  1479
simplification step, even if it is not an authenticator!*}
paulson@18886
  1480
lemma unique_timestamp_authticket:
paulson@18886
  1481
     "\<lbrakk> Says Kas A \<lbrace>X, Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key AK, T\<rbrace>\<rbrace> \<in> set evs;
paulson@18886
  1482
       Says Kas A' \<lbrace>X', Crypt (shrK Tgs') \<lbrace>Agent A', Agent Tgs', Key AK', T\<rbrace>\<rbrace> \<in> set evs;
paulson@18886
  1483
         evs \<in> kerbV \<rbrakk>
paulson@18886
  1484
  \<Longrightarrow> A=A' \<and> X=X' \<and> Tgs=Tgs' \<and> AK=AK'"
paulson@18886
  1485
apply (erule rev_mp, erule rev_mp)
paulson@18886
  1486
apply (erule kerbV.induct)
paulson@18886
  1487
apply (auto simp add: honest_never_says_current_timestamp_in_auth)
paulson@18886
  1488
done
paulson@18886
  1489
paulson@18886
  1490
text{*The second part of the message is treated as an authenticator by the last
paulson@18886
  1491
simplification step, even if it is not an authenticator!*}
paulson@18886
  1492
lemma unique_timestamp_servticket:
paulson@18886
  1493
     "\<lbrakk> Says Tgs A \<lbrace>X, Crypt (shrK B) \<lbrace>Agent A, Agent B, Key SK, T\<rbrace>\<rbrace> \<in> set evs;
paulson@18886
  1494
       Says Tgs A' \<lbrace>X', Crypt (shrK B') \<lbrace>Agent A', Agent B', Key SK', T\<rbrace>\<rbrace> \<in> set evs;
paulson@18886
  1495
         evs \<in> kerbV \<rbrakk>
paulson@18886
  1496
  \<Longrightarrow> A=A' \<and> X=X' \<and> B=B' \<and> SK=SK'"
paulson@18886
  1497
apply (erule rev_mp, erule rev_mp)
paulson@18886
  1498
apply (erule kerbV.induct)
paulson@18886
  1499
apply (auto simp add: honest_never_says_current_timestamp_in_auth)
paulson@18886
  1500
done
paulson@18886
  1501
paulson@18886
  1502
(*Uses assumption K6's assumption that B \<noteq> Kas, otherwise B should say
paulson@18886
  1503
fresh timestamp*)
paulson@18886
  1504
lemma Kas_never_says_newer_timestamp:
paulson@18886
  1505
     "\<lbrakk> (CT evs) \<le> T; Number T \<in> parts {X}; evs \<in> kerbV \<rbrakk> 
paulson@18886
  1506
     \<Longrightarrow> \<forall> A. Says Kas A X \<notin> set evs"
paulson@18886
  1507
apply (erule rev_mp)
paulson@18886
  1508
apply (erule kerbV.induct, auto)
paulson@18886
  1509
done
paulson@18886
  1510
paulson@18886
  1511
lemma Kas_never_says_current_timestamp:
paulson@18886
  1512
     "\<lbrakk> (CT evs) = T; Number T \<in> parts {X}; evs \<in> kerbV \<rbrakk> 
paulson@18886
  1513
     \<Longrightarrow> \<forall> A. Says Kas A X \<notin> set evs"
paulson@43587
  1514
by (metis Kas_never_says_newer_timestamp eq_imp_le)
paulson@18886
  1515
paulson@18886
  1516
lemma unique_timestamp_msg2:
paulson@18886
  1517
     "\<lbrakk> Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key AK, Agent Tgs, T\<rbrace>, AT\<rbrace> \<in> set evs;
paulson@18886
  1518
     Says Kas A' \<lbrace>Crypt (shrK A') \<lbrace>Key AK', Agent Tgs', T\<rbrace>, AT'\<rbrace> \<in> set evs;
paulson@18886
  1519
         evs \<in> kerbV \<rbrakk>
paulson@18886
  1520
  \<Longrightarrow> A=A' \<and> AK=AK' \<and> Tgs=Tgs' \<and> AT=AT'"
paulson@18886
  1521
apply (erule rev_mp, erule rev_mp)
paulson@18886
  1522
apply (erule kerbV.induct)
paulson@18886
  1523
apply (auto simp add: Kas_never_says_current_timestamp)
paulson@18886
  1524
done
paulson@18886
  1525
paulson@18886
  1526
(*Uses assumption K6's assumption that B \<noteq> Tgs, otherwise B should say
paulson@18886
  1527
fresh timestamp*)
paulson@18886
  1528
lemma Tgs_never_says_newer_timestamp:
paulson@18886
  1529
     "\<lbrakk> (CT evs) \<le> T; Number T \<in> parts {X}; evs \<in> kerbV \<rbrakk> 
paulson@18886
  1530
     \<Longrightarrow> \<forall> A. Says Tgs A X \<notin> set evs"
paulson@18886
  1531
apply (erule rev_mp)
paulson@18886
  1532
apply (erule kerbV.induct, auto)
paulson@18886
  1533
done
paulson@18886
  1534
paulson@18886
  1535
lemma Tgs_never_says_current_timestamp:
paulson@18886
  1536
     "\<lbrakk> (CT evs) = T; Number T \<in> parts {X}; evs \<in> kerbV \<rbrakk> 
paulson@18886
  1537
     \<Longrightarrow> \<forall> A. Says Tgs A X \<notin> set evs"
paulson@43587
  1538
by (metis Tgs_never_says_newer_timestamp eq_imp_le)
paulson@18886
  1539
paulson@18886
  1540
lemma unique_timestamp_msg4:
paulson@18886
  1541
     "\<lbrakk> Says Tgs A \<lbrace>Crypt (shrK A) \<lbrace>Key SK, Agent B, T\<rbrace>, ST\<rbrace> \<in> set evs;
paulson@18886
  1542
       Says Tgs A' \<lbrace>Crypt (shrK A') \<lbrace>Key SK', Agent B', T\<rbrace>, ST'\<rbrace> \<in> set evs;
paulson@18886
  1543
         evs \<in> kerbV \<rbrakk> 
paulson@18886
  1544
  \<Longrightarrow> A=A' \<and> SK=SK' \<and> B=B' \<and> ST=ST'"
paulson@18886
  1545
apply (erule rev_mp, erule rev_mp)
paulson@18886
  1546
apply (erule kerbV.induct)
paulson@18886
  1547
apply (auto simp add: Tgs_never_says_current_timestamp)
paulson@18886
  1548
done
paulson@18886
  1549
 
paulson@18886
  1550
end