src/HOL/Auth/OtwayRees.thy
author paulson <lp15@cam.ac.uk>
Wed, 26 Apr 2017 15:53:35 +0100
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(*  Title:      HOL/Auth/OtwayRees.thy
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1996  University of Cambridge
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*)
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section\<open>The Original Otway-Rees Protocol\<close>
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theory OtwayRees imports Public begin
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text\<open>From page 244 of
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  Burrows, Abadi and Needham (1989).  A Logic of Authentication.
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  Proc. Royal Soc. 426
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This is the original version, which encrypts Nonce NB.\<close>
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inductive_set otway :: "event list set"
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  where
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         (*Initial trace is empty*)
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   Nil:  "[] \<in> otway"
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         (*The spy MAY say anything he CAN say.  We do not expect him to
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           invent new nonces here, but he can also use NS1.  Common to
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           all similar protocols.*)
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 | Fake: "\<lbrakk>evsf \<in> otway;  X \<in> synth (analz (knows Spy evsf)) \<rbrakk>
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          \<Longrightarrow> Says Spy B X  # evsf \<in> otway"
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         (*A message that has been sent can be received by the
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           intended recipient.*)
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 | Reception: "\<lbrakk>evsr \<in> otway;  Says A B X \<in>set evsr\<rbrakk>
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               \<Longrightarrow> Gets B X # evsr \<in> otway"
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         (*Alice initiates a protocol run*)
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 | OR1:  "\<lbrakk>evs1 \<in> otway;  Nonce NA \<notin> used evs1\<rbrakk>
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          \<Longrightarrow> Says A B \<lbrace>Nonce NA, Agent A, Agent B,
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                         Crypt (shrK A) \<lbrace>Nonce NA, Agent A, Agent B\<rbrace> \<rbrace>
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                 # evs1 \<in> otway"
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         (*Bob's response to Alice's message.  Note that NB is encrypted.*)
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 | OR2:  "\<lbrakk>evs2 \<in> otway;  Nonce NB \<notin> used evs2;
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             Gets B \<lbrace>Nonce NA, Agent A, Agent B, X\<rbrace> : set evs2\<rbrakk>
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          \<Longrightarrow> Says B Server
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                  \<lbrace>Nonce NA, Agent A, Agent B, X,
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                    Crypt (shrK B)
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                      \<lbrace>Nonce NA, Nonce NB, Agent A, Agent B\<rbrace>\<rbrace>
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                 # evs2 \<in> otway"
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         (*The Server receives Bob's message and checks that the three NAs
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           match.  Then he sends a new session key to Bob with a packet for
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           forwarding to Alice.*)
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 | OR3:  "\<lbrakk>evs3 \<in> otway;  Key KAB \<notin> used evs3;
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             Gets Server
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                  \<lbrace>Nonce NA, Agent A, Agent B,
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                    Crypt (shrK A) \<lbrace>Nonce NA, Agent A, Agent B\<rbrace>,
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                    Crypt (shrK B) \<lbrace>Nonce NA, Nonce NB, Agent A, Agent B\<rbrace>\<rbrace>
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               : set evs3\<rbrakk>
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          \<Longrightarrow> Says Server B
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                  \<lbrace>Nonce NA,
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                    Crypt (shrK A) \<lbrace>Nonce NA, Key KAB\<rbrace>,
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                    Crypt (shrK B) \<lbrace>Nonce NB, Key KAB\<rbrace>\<rbrace>
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                 # evs3 \<in> otway"
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         (*Bob receives the Server's (?) message and compares the Nonces with
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           those in the message he previously sent the Server.
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           Need B \<noteq> Server because we allow messages to self.*)
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 | OR4:  "\<lbrakk>evs4 \<in> otway;  B \<noteq> Server;
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             Says B Server \<lbrace>Nonce NA, Agent A, Agent B, X',
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                             Crypt (shrK B)
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                                   \<lbrace>Nonce NA, Nonce NB, Agent A, Agent B\<rbrace>\<rbrace>
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               : set evs4;
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             Gets B \<lbrace>Nonce NA, X, Crypt (shrK B) \<lbrace>Nonce NB, Key K\<rbrace>\<rbrace>
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               : set evs4\<rbrakk>
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          \<Longrightarrow> Says B A \<lbrace>Nonce NA, X\<rbrace> # evs4 \<in> otway"
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         (*This message models possible leaks of session keys.  The nonces
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           identify the protocol run.*)
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 | Oops: "\<lbrakk>evso \<in> otway;
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             Says Server B \<lbrace>Nonce NA, X, Crypt (shrK B) \<lbrace>Nonce NB, Key K\<rbrace>\<rbrace>
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               : set evso\<rbrakk>
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          \<Longrightarrow> Notes Spy \<lbrace>Nonce NA, Nonce NB, Key K\<rbrace> # evso \<in> otway"
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declare Says_imp_analz_Spy [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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text\<open>A "possibility property": there are traces that reach the end\<close>
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lemma "\<lbrakk>B \<noteq> Server; Key K \<notin> used []\<rbrakk>
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      \<Longrightarrow> \<exists>evs \<in> otway.
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             Says B A \<lbrace>Nonce NA, Crypt (shrK A) \<lbrace>Nonce NA, Key K\<rbrace>\<rbrace>
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               \<in> set evs"
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apply (intro exI bexI)
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apply (rule_tac [2] otway.Nil
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                    [THEN otway.OR1, THEN otway.Reception,
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                     THEN otway.OR2, THEN otway.Reception,
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                     THEN otway.OR3, THEN otway.Reception, THEN otway.OR4]) 
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apply (possibility, simp add: used_Cons) 
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done
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lemma Gets_imp_Says [dest!]:
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     "\<lbrakk>Gets B X \<in> set evs; evs \<in> otway\<rbrakk> \<Longrightarrow> \<exists>A. Says A B X \<in> set evs"
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apply (erule rev_mp)
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apply (erule otway.induct, auto)
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done
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(** For reasoning about the encrypted portion of messages **)
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lemma OR2_analz_knows_Spy:
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     "\<lbrakk>Gets B \<lbrace>N, Agent A, Agent B, X\<rbrace> \<in> set evs;  evs \<in> otway\<rbrakk>
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      \<Longrightarrow> X \<in> analz (knows Spy evs)"
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by blast
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lemma OR4_analz_knows_Spy:
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     "\<lbrakk>Gets B \<lbrace>N, X, Crypt (shrK B) X'\<rbrace> \<in> set evs;  evs \<in> otway\<rbrakk>
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      \<Longrightarrow> X \<in> analz (knows Spy evs)"
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by blast
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(*These lemmas assist simplification by removing forwarded X-variables.
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  We can replace them by rewriting with parts_insert2 and proving using
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  dest: parts_cut, but the proofs become more difficult.*)
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lemmas OR2_parts_knows_Spy =
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    OR2_analz_knows_Spy [THEN analz_into_parts]
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(*There could be OR4_parts_knows_Spy and Oops_parts_knows_Spy, but for
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  some reason proofs work without them!*)
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text\<open>Theorems of the form @{term "X \<notin> parts (spies evs)"} imply that
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NOBODY sends messages containing X!\<close>
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text\<open>Spy never sees a good agent's shared key!\<close>
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lemma Spy_see_shrK [simp]:
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     "evs \<in> otway \<Longrightarrow> (Key (shrK A) \<in> parts (knows Spy evs)) = (A \<in> bad)"
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by (erule otway.induct, force,
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    drule_tac [4] OR2_parts_knows_Spy, simp_all, blast+)
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lemma Spy_analz_shrK [simp]:
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     "evs \<in> otway \<Longrightarrow> (Key (shrK A) \<in> analz (knows Spy evs)) = (A \<in> bad)"
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by auto
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lemma Spy_see_shrK_D [dest!]:
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     "\<lbrakk>Key (shrK A) \<in> parts (knows Spy evs);  evs \<in> otway\<rbrakk> \<Longrightarrow> A \<in> bad"
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by (blast dest: Spy_see_shrK)
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subsection\<open>Towards Secrecy: Proofs Involving @{term analz}\<close>
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(*Describes the form of K and NA when the Server sends this message.  Also
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  for Oops case.*)
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lemma Says_Server_message_form:
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     "\<lbrakk>Says Server B \<lbrace>NA, X, Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace> \<in> set evs;
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         evs \<in> otway\<rbrakk>
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      \<Longrightarrow> K \<notin> range shrK & (\<exists>i. NA = Nonce i) & (\<exists>j. NB = Nonce j)"
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by (erule rev_mp, erule otway.induct, simp_all)
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(****
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 The following is to prove theorems of the form
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  Key K \<in> analz (insert (Key KAB) (knows Spy evs)) \<Longrightarrow>
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  Key K \<in> analz (knows Spy evs)
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 A more general formula must be proved inductively.
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****)
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text\<open>Session keys are not used to encrypt other session keys\<close>
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text\<open>The equality makes the induction hypothesis easier to apply\<close>
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lemma analz_image_freshK [rule_format]:
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 "evs \<in> otway \<Longrightarrow>
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   \<forall>K KK. KK <= -(range shrK) -->
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          (Key K \<in> analz (Key`KK Un (knows Spy evs))) =
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          (K \<in> KK | Key K \<in> analz (knows Spy evs))"
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apply (erule otway.induct)
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apply (frule_tac [8] Says_Server_message_form)
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apply (drule_tac [7] OR4_analz_knows_Spy)
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apply (drule_tac [5] OR2_analz_knows_Spy, analz_freshK, spy_analz, auto) 
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done
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lemma analz_insert_freshK:
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  "\<lbrakk>evs \<in> otway;  KAB \<notin> range shrK\<rbrakk> \<Longrightarrow>
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      (Key K \<in> analz (insert (Key KAB) (knows Spy evs))) =
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      (K = KAB | Key K \<in> analz (knows Spy evs))"
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by (simp only: analz_image_freshK analz_image_freshK_simps)
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text\<open>The Key K uniquely identifies the Server's  message.\<close>
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lemma unique_session_keys:
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     "\<lbrakk>Says Server B \<lbrace>NA, X, Crypt (shrK B) \<lbrace>NB, K\<rbrace>\<rbrace>   \<in> set evs;
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         Says Server B' \<lbrace>NA',X',Crypt (shrK B') \<lbrace>NB',K\<rbrace>\<rbrace> \<in> set evs;
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         evs \<in> otway\<rbrakk> \<Longrightarrow> X=X' & B=B' & NA=NA' & NB=NB'"
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apply (erule rev_mp)
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apply (erule rev_mp)
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apply (erule otway.induct, simp_all)
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apply blast+  \<comment>\<open>OR3 and OR4\<close>
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done
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subsection\<open>Authenticity properties relating to NA\<close>
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text\<open>Only OR1 can have caused such a part of a message to appear.\<close>
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lemma Crypt_imp_OR1 [rule_format]:
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 "\<lbrakk>A \<notin> bad;  evs \<in> otway\<rbrakk>
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  \<Longrightarrow> Crypt (shrK A) \<lbrace>NA, Agent A, Agent B\<rbrace> \<in> parts (knows Spy evs) -->
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      Says A B \<lbrace>NA, Agent A, Agent B,
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                 Crypt (shrK A) \<lbrace>NA, Agent A, Agent B\<rbrace>\<rbrace>
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        \<in> set evs"
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by (erule otway.induct, force,
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    drule_tac [4] OR2_parts_knows_Spy, simp_all, blast+)
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lemma Crypt_imp_OR1_Gets:
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     "\<lbrakk>Gets B \<lbrace>NA, Agent A, Agent B,
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                  Crypt (shrK A) \<lbrace>NA, Agent A, Agent B\<rbrace>\<rbrace> \<in> set evs;
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         A \<notin> bad; evs \<in> otway\<rbrakk>
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       \<Longrightarrow> Says A B \<lbrace>NA, Agent A, Agent B,
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                      Crypt (shrK A) \<lbrace>NA, Agent A, Agent B\<rbrace>\<rbrace>
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             \<in> set evs"
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by (blast dest: Crypt_imp_OR1)
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   223
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text\<open>The Nonce NA uniquely identifies A's message\<close>
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lemma unique_NA:
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     "\<lbrakk>Crypt (shrK A) \<lbrace>NA, Agent A, Agent B\<rbrace> \<in> parts (knows Spy evs);
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         Crypt (shrK A) \<lbrace>NA, Agent A, Agent C\<rbrace> \<in> parts (knows Spy evs);
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         evs \<in> otway;  A \<notin> bad\<rbrakk>
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      \<Longrightarrow> B = C"
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apply (erule rev_mp, erule rev_mp)
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apply (erule otway.induct, force,
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       drule_tac [4] OR2_parts_knows_Spy, simp_all, blast+)
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done
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   235
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   236
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text\<open>It is impossible to re-use a nonce in both OR1 and OR2.  This holds because
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  OR2 encrypts Nonce NB.  It prevents the attack that can occur in the
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  over-simplified version of this protocol: see \<open>OtwayRees_Bad\<close>.\<close>
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   240
lemma no_nonce_OR1_OR2:
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   "\<lbrakk>Crypt (shrK A) \<lbrace>NA, Agent A, Agent B\<rbrace> \<in> parts (knows Spy evs);
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       A \<notin> bad;  evs \<in> otway\<rbrakk>
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   243
    \<Longrightarrow> Crypt (shrK A) \<lbrace>NA', NA, Agent A', Agent A\<rbrace> \<notin> parts (knows Spy evs)"
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   244
apply (erule rev_mp)
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apply (erule otway.induct, force,
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   246
       drule_tac [4] OR2_parts_knows_Spy, simp_all, blast+)
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done
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   248
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text\<open>Crucial property: If the encrypted message appears, and A has used NA
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  to start a run, then it originated with the Server!\<close>
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   251
lemma NA_Crypt_imp_Server_msg [rule_format]:
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   252
     "\<lbrakk>A \<notin> bad;  evs \<in> otway\<rbrakk>
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      \<Longrightarrow> Says A B \<lbrace>NA, Agent A, Agent B,
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                     Crypt (shrK A) \<lbrace>NA, Agent A, Agent B\<rbrace>\<rbrace> \<in> set evs -->
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          Crypt (shrK A) \<lbrace>NA, Key K\<rbrace> \<in> parts (knows Spy evs)
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          --> (\<exists>NB. Says Server B
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                         \<lbrace>NA,
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   258
                           Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>,
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                           Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace> \<in> set evs)"
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apply (erule otway.induct, force,
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       drule_tac [4] OR2_parts_knows_Spy, simp_all, blast)
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   262
  subgoal \<comment>\<open>OR1: by freshness\<close>
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   263
    by blast  
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   264
  subgoal \<comment>\<open>OR3\<close>
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   265
    by (blast dest!: no_nonce_OR1_OR2 intro: unique_NA)
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   266
  subgoal \<comment>\<open>OR4\<close>
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   267
    by (blast intro!: Crypt_imp_OR1) 
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paulson
parents: 11230
diff changeset
   268
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   269
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   270
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
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parents: 58889
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   271
text\<open>Corollary: if A receives B's OR4 message and the nonce NA agrees
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   272
  then the key really did come from the Server!  CANNOT prove this of the
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   273
  bad form of this protocol, even though we can prove
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   274
  \<open>Spy_not_see_encrypted_key\<close>\<close>
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paulson
parents: 11230
diff changeset
   275
lemma A_trusts_OR4:
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parents: 61956
diff changeset
   276
     "\<lbrakk>Says A  B \<lbrace>NA, Agent A, Agent B,
61956
38b73f7940af more symbols;
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parents: 61830
diff changeset
   277
                     Crypt (shrK A) \<lbrace>NA, Agent A, Agent B\<rbrace>\<rbrace> \<in> set evs;
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   278
         Says B' A \<lbrace>NA, Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>\<rbrace> \<in> set evs;
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paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   279
     A \<notin> bad;  evs \<in> otway\<rbrakk>
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paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   280
  \<Longrightarrow> \<exists>NB. Says Server B
61956
38b73f7940af more symbols;
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parents: 61830
diff changeset
   281
               \<lbrace>NA,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   282
                 Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   283
                 Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   284
                 \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   285
by (blast intro!: NA_Crypt_imp_Server_msg)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   286
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   287
61830
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wenzelm
parents: 58889
diff changeset
   288
text\<open>Crucial secrecy property: Spy does not see the keys sent in msg OR3
11251
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paulson
parents: 11230
diff changeset
   289
    Does not in itself guarantee security: an attack could violate
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   290
    the premises, e.g. by having @{term "A=Spy"}\<close>
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a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   291
lemma secrecy_lemma:
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parents: 61956
diff changeset
   292
 "\<lbrakk>A \<notin> bad;  B \<notin> bad;  evs \<in> otway\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   293
  \<Longrightarrow> Says Server B
61956
38b73f7940af more symbols;
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parents: 61830
diff changeset
   294
        \<lbrace>NA, Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   295
          Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace> \<in> set evs -->
38b73f7940af more symbols;
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parents: 61830
diff changeset
   296
      Notes Spy \<lbrace>NA, NB, Key K\<rbrace> \<notin> set evs -->
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   297
      Key K \<notin> analz (knows Spy evs)"
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paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   298
  apply (erule otway.induct, force, simp_all)
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   299
  subgoal \<comment>\<open>Fake\<close>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   300
    by spy_analz
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   301
  subgoal \<comment>\<open>OR2\<close>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   302
    by (drule OR2_analz_knows_Spy) (auto simp: analz_insert_eq)
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   303
  subgoal \<comment>\<open>OR3\<close>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   304
    by (auto simp add: analz_insert_freshK pushes)
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   305
  subgoal \<comment>\<open>OR4\<close>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   306
    by (drule OR4_analz_knows_Spy) (auto simp: analz_insert_eq)
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   307
  subgoal \<comment>\<open>Oops\<close>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   308
    by (auto simp add: Says_Server_message_form analz_insert_freshK unique_session_keys)
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   309
  done
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a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   310
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   311
theorem Spy_not_see_encrypted_key:
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paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   312
     "\<lbrakk>Says Server B
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   313
          \<lbrace>NA, Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   314
                Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace> \<in> set evs;
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   315
         Notes Spy \<lbrace>NA, NB, Key K\<rbrace> \<notin> set evs;
63975
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paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   316
         A \<notin> bad;  B \<notin> bad;  evs \<in> otway\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   317
      \<Longrightarrow> Key K \<notin> analz (knows Spy evs)"
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   318
by (blast dest: Says_Server_message_form secrecy_lemma)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   319
61830
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wenzelm
parents: 58889
diff changeset
   320
text\<open>This form is an immediate consequence of the previous result.  It is 
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   321
similar to the assertions established by other methods.  It is equivalent
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   322
to the previous result in that the Spy already has @{term analz} and
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   323
@{term synth} at his disposal.  However, the conclusion 
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   324
@{term "Key K \<notin> knows Spy evs"} appears not to be inductive: all the cases
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   325
other than Fake are trivial, while Fake requires 
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   326
@{term "Key K \<notin> analz (knows Spy evs)"}.\<close>
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   327
lemma Spy_not_know_encrypted_key:
63975
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paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   328
     "\<lbrakk>Says Server B
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   329
          \<lbrace>NA, Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   330
                Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace> \<in> set evs;
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   331
         Notes Spy \<lbrace>NA, NB, Key K\<rbrace> \<notin> set evs;
63975
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paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   332
         A \<notin> bad;  B \<notin> bad;  evs \<in> otway\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   333
      \<Longrightarrow> Key K \<notin> knows Spy evs"
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   334
by (blast dest: Spy_not_see_encrypted_key)
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   335
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   336
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   337
text\<open>A's guarantee.  The Oops premise quantifies over NB because A cannot know
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   338
  what it is.\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   339
lemma A_gets_good_key:
63975
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paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   340
     "\<lbrakk>Says A  B \<lbrace>NA, Agent A, Agent B,
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   341
                     Crypt (shrK A) \<lbrace>NA, Agent A, Agent B\<rbrace>\<rbrace> \<in> set evs;
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   342
         Says B' A \<lbrace>NA, Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>\<rbrace> \<in> set evs;
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   343
         \<forall>NB. Notes Spy \<lbrace>NA, NB, Key K\<rbrace> \<notin> set evs;
63975
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paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   344
         A \<notin> bad;  B \<notin> bad;  evs \<in> otway\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   345
      \<Longrightarrow> Key K \<notin> analz (knows Spy evs)"
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   346
by (blast dest!: A_trusts_OR4 Spy_not_see_encrypted_key)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   347
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   348
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   349
subsection\<open>Authenticity properties relating to NB\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   350
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   351
text\<open>Only OR2 can have caused such a part of a message to appear.  We do not
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   352
  know anything about X: it does NOT have to have the right form.\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   353
lemma Crypt_imp_OR2:
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   354
     "\<lbrakk>Crypt (shrK B) \<lbrace>NA, NB, Agent A, Agent B\<rbrace> \<in> parts (knows Spy evs);
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   355
         B \<notin> bad;  evs \<in> otway\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   356
      \<Longrightarrow> \<exists>X. Says B Server
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   357
                 \<lbrace>NA, Agent A, Agent B, X,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   358
                   Crypt (shrK B) \<lbrace>NA, NB, Agent A, Agent B\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   359
                 \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   360
apply (erule rev_mp)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   361
apply (erule otway.induct, force,
13507
febb8e5d2a9d tidying of Isar scripts
paulson
parents: 11655
diff changeset
   362
       drule_tac [4] OR2_parts_knows_Spy, simp_all, blast+)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   363
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   364
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   365
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   366
text\<open>The Nonce NB uniquely identifies B's  message\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   367
lemma unique_NB:
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   368
     "\<lbrakk>Crypt (shrK B) \<lbrace>NA, NB, Agent A, Agent B\<rbrace> \<in> parts(knows Spy evs);
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   369
         Crypt (shrK B) \<lbrace>NC, NB, Agent C, Agent B\<rbrace> \<in> parts(knows Spy evs);
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   370
           evs \<in> otway;  B \<notin> bad\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   371
         \<Longrightarrow> NC = NA & C = A"
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   372
apply (erule rev_mp, erule rev_mp)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   373
apply (erule otway.induct, force,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   374
       drule_tac [4] OR2_parts_knows_Spy, simp_all)
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   375
apply blast+  \<comment>\<open>Fake, OR2\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   376
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   377
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   378
text\<open>If the encrypted message appears, and B has used Nonce NB,
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   379
  then it originated with the Server!  Quite messy proof.\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   380
lemma NB_Crypt_imp_Server_msg [rule_format]:
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   381
 "\<lbrakk>B \<notin> bad;  evs \<in> otway\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   382
  \<Longrightarrow> Crypt (shrK B) \<lbrace>NB, Key K\<rbrace> \<in> parts (knows Spy evs)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   383
      --> (\<forall>X'. Says B Server
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   384
                     \<lbrace>NA, Agent A, Agent B, X',
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   385
                       Crypt (shrK B) \<lbrace>NA, NB, Agent A, Agent B\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   386
           \<in> set evs
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   387
           --> Says Server B
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   388
                \<lbrace>NA, Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   389
                      Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   390
                    \<in> set evs)"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   391
apply simp
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   392
apply (erule otway.induct, force, simp_all)
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   393
  subgoal \<comment>\<open>Fake\<close>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   394
    by blast 
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   395
  subgoal \<comment>\<open>OR2\<close>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   396
    by (force dest!: OR2_parts_knows_Spy)
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   397
  subgoal \<comment>\<open>OR3\<close>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   398
    by (blast dest: unique_NB dest!: no_nonce_OR1_OR2)  \<comment>\<open>OR3\<close>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   399
  subgoal \<comment>\<open>OR4\<close>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   400
    by (blast dest!: Crypt_imp_OR2) 
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   401
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   402
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   403
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   404
text\<open>Guarantee for B: if it gets a message with matching NB then the Server
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   405
  has sent the correct message.\<close>
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   406
theorem B_trusts_OR3:
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   407
     "\<lbrakk>Says B Server \<lbrace>NA, Agent A, Agent B, X',
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   408
                         Crypt (shrK B) \<lbrace>NA, NB, Agent A, Agent B\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   409
           \<in> set evs;
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   410
         Gets B \<lbrace>NA, X, Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace> \<in> set evs;
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   411
         B \<notin> bad;  evs \<in> otway\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   412
      \<Longrightarrow> Says Server B
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   413
               \<lbrace>NA,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   414
                 Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   415
                 Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   416
                 \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   417
by (blast intro!: NB_Crypt_imp_Server_msg)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   418
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   419
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   420
text\<open>The obvious combination of \<open>B_trusts_OR3\<close> with 
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   421
      \<open>Spy_not_see_encrypted_key\<close>\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   422
lemma B_gets_good_key:
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   423
     "\<lbrakk>Says B Server \<lbrace>NA, Agent A, Agent B, X',
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   424
                         Crypt (shrK B) \<lbrace>NA, NB, Agent A, Agent B\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   425
           \<in> set evs;
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   426
         Gets B \<lbrace>NA, X, Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace> \<in> set evs;
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   427
         Notes Spy \<lbrace>NA, NB, Key K\<rbrace> \<notin> set evs;
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   428
         A \<notin> bad;  B \<notin> bad;  evs \<in> otway\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   429
      \<Longrightarrow> Key K \<notin> analz (knows Spy evs)"
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   430
by (blast dest!: B_trusts_OR3 Spy_not_see_encrypted_key)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   431
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   432
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   433
lemma OR3_imp_OR2:
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   434
     "\<lbrakk>Says Server B
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   435
              \<lbrace>NA, Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   436
                Crypt (shrK B) \<lbrace>NB, Key K\<rbrace>\<rbrace> \<in> set evs;
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   437
         B \<notin> bad;  evs \<in> otway\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   438
  \<Longrightarrow> \<exists>X. Says B Server \<lbrace>NA, Agent A, Agent B, X,
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   439
                            Crypt (shrK B) \<lbrace>NA, NB, Agent A, Agent B\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   440
              \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   441
apply (erule rev_mp)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   442
apply (erule otway.induct, simp_all)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   443
apply (blast dest!: Crypt_imp_OR2)+
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   444
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   445
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   446
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   447
text\<open>After getting and checking OR4, agent A can trust that B has been active.
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   448
  We could probably prove that X has the expected form, but that is not
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 58889
diff changeset
   449
  strictly necessary for authentication.\<close>
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   450
theorem A_auths_B:
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   451
     "\<lbrakk>Says B' A \<lbrace>NA, Crypt (shrK A) \<lbrace>NA, Key K\<rbrace>\<rbrace> \<in> set evs;
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   452
         Says A  B \<lbrace>NA, Agent A, Agent B,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   453
                     Crypt (shrK A) \<lbrace>NA, Agent A, Agent B\<rbrace>\<rbrace> \<in> set evs;
63975
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   454
         A \<notin> bad;  B \<notin> bad;  evs \<in> otway\<rbrakk>
6728b5007ad0 Trying out "subgoal", and no more [| |]
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   455
  \<Longrightarrow> \<exists>NB X. Says B Server \<lbrace>NA, Agent A, Agent B, X,
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   456
                               Crypt (shrK B)  \<lbrace>NA, NB, Agent A, Agent B\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   457
                 \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   458
by (blast dest!: A_trusts_OR4 OR3_imp_OR2)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11230
diff changeset
   459
1941
f97a6e5b6375 Initial working proof of Otway-Rees protocol
paulson
parents:
diff changeset
   460
end