src/HOL/Auth/Yahalom.thy
author paulson <lp15@cam.ac.uk>
Mon, 24 Oct 2016 14:31:05 +0100
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permissions -rw-r--r--
"subgoal" examples
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(*  Title:      HOL/Auth/Yahalom.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 Yahalom Protocol\<close>
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theory Yahalom imports Public begin
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text\<open>From page 257 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 theory has the prototypical example of a secrecy relation, KeyCryptNonce.
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\<close>
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inductive_set yahalom :: "event list set"
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  where
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         (*Initial trace is empty*)
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   Nil:  "[] \<in> yahalom"
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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> yahalom;  X \<in> synth (analz (knows Spy evsf))\<rbrakk>
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          \<Longrightarrow> Says Spy B X  # evsf \<in> yahalom"
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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> yahalom;  Says A B X \<in> set evsr\<rbrakk>
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               \<Longrightarrow> Gets B X # evsr \<in> yahalom"
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         (*Alice initiates a protocol run*)
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 | YM1:  "\<lbrakk>evs1 \<in> yahalom;  Nonce NA \<notin> used evs1\<rbrakk>
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          \<Longrightarrow> Says A B \<lbrace>Agent A, Nonce NA\<rbrace> # evs1 \<in> yahalom"
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         (*Bob's response to Alice's message.*)
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 | YM2:  "\<lbrakk>evs2 \<in> yahalom;  Nonce NB \<notin> used evs2;
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             Gets B \<lbrace>Agent A, Nonce NA\<rbrace> \<in> set evs2\<rbrakk>
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          \<Longrightarrow> Says B Server 
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                  \<lbrace>Agent B, Crypt (shrK B) \<lbrace>Agent A, Nonce NA, Nonce NB\<rbrace>\<rbrace>
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                # evs2 \<in> yahalom"
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         (*The Server receives Bob's message.  He responds by sending a
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            new session key to Alice, with a packet for forwarding to Bob.*)
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 | YM3:  "\<lbrakk>evs3 \<in> yahalom;  Key KAB \<notin> used evs3;  KAB \<in> symKeys;
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             Gets Server 
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                  \<lbrace>Agent B, Crypt (shrK B) \<lbrace>Agent A, Nonce NA, Nonce NB\<rbrace>\<rbrace>
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               \<in> set evs3\<rbrakk>
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          \<Longrightarrow> Says Server A
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                   \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key KAB, Nonce NA, Nonce NB\<rbrace>,
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                     Crypt (shrK B) \<lbrace>Agent A, Key KAB\<rbrace>\<rbrace>
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                # evs3 \<in> yahalom"
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 | YM4:  
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       \<comment>\<open>Alice receives the Server's (?) message, checks her Nonce, and
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           uses the new session key to send Bob his Nonce.  The premise
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           @{term "A \<noteq> Server"} is needed for \<open>Says_Server_not_range\<close>.
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           Alice can check that K is symmetric by its length.\<close>
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         "\<lbrakk>evs4 \<in> yahalom;  A \<noteq> Server;  K \<in> symKeys;
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             Gets A \<lbrace>Crypt(shrK A) \<lbrace>Agent B, Key K, Nonce NA, Nonce NB\<rbrace>, X\<rbrace>
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                \<in> set evs4;
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             Says A B \<lbrace>Agent A, Nonce NA\<rbrace> \<in> set evs4\<rbrakk>
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          \<Longrightarrow> Says A B \<lbrace>X, Crypt K (Nonce NB)\<rbrace> # evs4 \<in> yahalom"
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         (*This message models possible leaks of session keys.  The Nonces
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           identify the protocol run.  Quoting Server here ensures they are
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           correct.*)
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 | Oops: "\<lbrakk>evso \<in> yahalom;  
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             Says Server A \<lbrace>Crypt (shrK A)
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                                   \<lbrace>Agent B, Key K, Nonce NA, Nonce NB\<rbrace>,
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                             X\<rbrace>  \<in> set evso\<rbrakk>
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          \<Longrightarrow> Notes Spy \<lbrace>Nonce NA, Nonce NB, Key K\<rbrace> # evso \<in> yahalom"
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definition KeyWithNonce :: "[key, nat, event list] => bool" where
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  "KeyWithNonce K NB evs ==
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     \<exists>A B na X. 
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       Says Server A \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, na, Nonce NB\<rbrace>, X\<rbrace>
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         \<in> set evs"
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declare Says_imp_analz_Spy [dest]
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declare parts.Body  [dest]
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declare Fake_parts_insert_in_Un  [dest]
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declare analz_into_parts [dest]
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text\<open>A "possibility property": there are traces that reach the end\<close>
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lemma "\<lbrakk>A \<noteq> Server; K \<in> symKeys; Key K \<notin> used []\<rbrakk>
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      \<Longrightarrow> \<exists>X NB. \<exists>evs \<in> yahalom.
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             Says A B \<lbrace>X, Crypt K (Nonce NB)\<rbrace> \<in> set evs"
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apply (intro exI bexI)
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apply (rule_tac [2] yahalom.Nil
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                    [THEN yahalom.YM1, THEN yahalom.Reception,
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                     THEN yahalom.YM2, THEN yahalom.Reception,
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                     THEN yahalom.YM3, THEN yahalom.Reception,
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                     THEN yahalom.YM4])
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apply (possibility, simp add: used_Cons)
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done
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subsection\<open>Regularity Lemmas for Yahalom\<close>
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lemma Gets_imp_Says:
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     "\<lbrakk>Gets B X \<in> set evs; evs \<in> yahalom\<rbrakk> \<Longrightarrow> \<exists>A. Says A B X \<in> set evs"
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by (erule rev_mp, erule yahalom.induct, auto)
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text\<open>Must be proved separately for each protocol\<close>
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lemma Gets_imp_knows_Spy:
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     "\<lbrakk>Gets B X \<in> set evs; evs \<in> yahalom\<rbrakk>  \<Longrightarrow> X \<in> knows Spy evs"
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by (blast dest!: Gets_imp_Says Says_imp_knows_Spy)
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lemmas Gets_imp_analz_Spy = Gets_imp_knows_Spy [THEN analz.Inj]
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declare Gets_imp_analz_Spy [dest]
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text\<open>Lets us treat YM4 using a similar argument as for the Fake case.\<close>
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lemma YM4_analz_knows_Spy:
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     "\<lbrakk>Gets A \<lbrace>Crypt (shrK A) Y, X\<rbrace> \<in> set evs;  evs \<in> yahalom\<rbrakk>
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      \<Longrightarrow> X \<in> analz (knows Spy evs)"
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by blast
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lemmas YM4_parts_knows_Spy =
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       YM4_analz_knows_Spy [THEN analz_into_parts]
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text\<open>For Oops\<close>
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lemma YM4_Key_parts_knows_Spy:
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     "Says Server A \<lbrace>Crypt (shrK A) \<lbrace>B,K,NA,NB\<rbrace>, X\<rbrace> \<in> set evs
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      \<Longrightarrow> K \<in> parts (knows Spy evs)"
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  by (metis parts.Body parts.Fst parts.Snd  Says_imp_knows_Spy parts.Inj)
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text\<open>Theorems of the form @{term "X \<notin> parts (knows Spy evs)"} imply 
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that 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> yahalom \<Longrightarrow> (Key (shrK A) \<in> parts (knows Spy evs)) = (A \<in> bad)"
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by (erule yahalom.induct, force,
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    drule_tac [6] YM4_parts_knows_Spy, simp_all, blast+)
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lemma Spy_analz_shrK [simp]:
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     "evs \<in> yahalom \<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> yahalom\<rbrakk> \<Longrightarrow> A \<in> bad"
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by (blast dest: Spy_see_shrK)
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text\<open>Nobody can have used non-existent keys!
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    Needed to apply \<open>analz_insert_Key\<close>\<close>
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lemma new_keys_not_used [simp]:
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    "\<lbrakk>Key K \<notin> used evs; K \<in> symKeys; evs \<in> yahalom\<rbrakk>
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     \<Longrightarrow> K \<notin> keysFor (parts (spies evs))"
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apply (erule rev_mp)
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apply (erule yahalom.induct, force,
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       frule_tac [6] YM4_parts_knows_Spy, simp_all)
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txt\<open>Fake\<close>
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apply (force dest!: keysFor_parts_insert, auto)
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done
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text\<open>Earlier, all protocol proofs declared this theorem.
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  But only a few proofs need it, e.g. Yahalom and Kerberos IV.\<close>
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lemma new_keys_not_analzd:
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 "\<lbrakk>K \<in> symKeys; evs \<in> yahalom; Key K \<notin> used evs\<rbrakk>
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  \<Longrightarrow> K \<notin> keysFor (analz (knows Spy evs))"
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by (blast dest: new_keys_not_used intro: keysFor_mono [THEN subsetD])
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text\<open>Describes the form of K when the Server sends this message.  Useful for
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  Oops as well as main secrecy property.\<close>
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lemma Says_Server_not_range [simp]:
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     "\<lbrakk>Says Server A \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, na, nb\<rbrace>, X\<rbrace>
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           \<in> set evs;   evs \<in> yahalom\<rbrakk>
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      \<Longrightarrow> K \<notin> range shrK"
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by (erule rev_mp, erule yahalom.induct, simp_all)
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subsection\<open>Secrecy Theorems\<close>
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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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lemma analz_image_freshK [rule_format]:
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 "evs \<in> yahalom \<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 yahalom.induct,
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       drule_tac [7] YM4_analz_knows_Spy, analz_freshK, spy_analz, blast)
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apply (simp only: Says_Server_not_range analz_image_freshK_simps)
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apply safe
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done
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lemma analz_insert_freshK:
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     "\<lbrakk>evs \<in> yahalom;  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 A
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          \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, na, nb\<rbrace>, X\<rbrace> \<in> set evs;
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        Says Server A'
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          \<lbrace>Crypt (shrK A') \<lbrace>Agent B', Key K, na', nb'\<rbrace>, X'\<rbrace> \<in> set evs;
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        evs \<in> yahalom\<rbrakk>
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     \<Longrightarrow> A=A' & B=B' & na=na' & nb=nb'"
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apply (erule rev_mp, erule rev_mp)
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apply (erule yahalom.induct, simp_all)
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txt\<open>YM3, by freshness, and YM4\<close>
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apply blast+
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done
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text\<open>Crucial secrecy property: Spy does not see the keys sent in msg YM3\<close>
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lemma secrecy_lemma:
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     "\<lbrakk>A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom\<rbrakk>
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      \<Longrightarrow> Says Server A
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            \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, na, nb\<rbrace>,
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              Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace>\<rbrace>
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           \<in> set evs -->
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          Notes Spy \<lbrace>na, nb, Key K\<rbrace> \<notin> set evs -->
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          Key K \<notin> analz (knows Spy evs)"
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apply (erule yahalom.induct, force,
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       drule_tac [6] YM4_analz_knows_Spy)
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apply (simp_all add: pushes analz_insert_eq analz_insert_freshK) 
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  subgoal --\<open>Fake\<close> by spy_analz
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  subgoal --\<open>YM3\<close> by blast   
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  subgoal --\<open>Oops\<close> by  (blast dest: unique_session_keys)   
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done
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text\<open>Final version\<close>
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lemma Spy_not_see_encrypted_key:
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     "\<lbrakk>Says Server A
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            \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, na, nb\<rbrace>,
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              Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace>\<rbrace>
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           \<in> set evs;
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         Notes Spy \<lbrace>na, nb, Key K\<rbrace> \<notin> set evs;
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         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom\<rbrakk>
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      \<Longrightarrow> Key K \<notin> analz (knows Spy evs)"
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by (blast dest: secrecy_lemma)
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subsubsection\<open>Security Guarantee for A upon receiving YM3\<close>
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text\<open>If the encrypted message appears then it originated with the Server\<close>
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lemma A_trusts_YM3:
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     "\<lbrakk>Crypt (shrK A) \<lbrace>Agent B, Key K, na, nb\<rbrace> \<in> parts (knows Spy evs);
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         A \<notin> bad;  evs \<in> yahalom\<rbrakk>
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       \<Longrightarrow> Says Server A
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            \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, na, nb\<rbrace>,
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              Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace>\<rbrace>
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           \<in> set evs"
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apply (erule rev_mp)
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apply (erule yahalom.induct, force,
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       frule_tac [6] YM4_parts_knows_Spy, simp_all)
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txt\<open>Fake, YM3\<close>
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apply blast+
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done
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text\<open>The obvious combination of \<open>A_trusts_YM3\<close> with
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  \<open>Spy_not_see_encrypted_key\<close>\<close>
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lemma A_gets_good_key:
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     "\<lbrakk>Crypt (shrK A) \<lbrace>Agent B, Key K, na, nb\<rbrace> \<in> parts (knows Spy evs);
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         Notes Spy \<lbrace>na, nb, Key K\<rbrace> \<notin> set evs;
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         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom\<rbrakk>
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   277
      \<Longrightarrow> Key K \<notin> analz (knows Spy evs)"
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  by (metis A_trusts_YM3 secrecy_lemma)
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subsubsection\<open>Security Guarantees for B upon receiving YM4\<close>
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text\<open>B knows, by the first part of A's message, that the Server distributed
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  the key for A and B.  But this part says nothing about nonces.\<close>
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lemma B_trusts_YM4_shrK:
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   286
     "\<lbrakk>Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace> \<in> parts (knows Spy evs);
464420ba7f74 "subgoal" examples
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   287
         B \<notin> bad;  evs \<in> yahalom\<rbrakk>
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   288
      \<Longrightarrow> \<exists>NA NB. Says Server A
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                      \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K,
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                                         Nonce NA, Nonce NB\<rbrace>,
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                        Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace>\<rbrace>
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                     \<in> set evs"
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apply (erule rev_mp)
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apply (erule yahalom.induct, force,
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       frule_tac [6] YM4_parts_knows_Spy, simp_all)
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txt\<open>Fake, YM3\<close>
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apply blast+
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done
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text\<open>B knows, by the second part of A's message, that the Server
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  distributed the key quoting nonce NB.  This part says nothing about
664434175578 fixed document;
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  agent names.  Secrecy of NB is crucial.  Note that @{term "Nonce NB
664434175578 fixed document;
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  \<notin> analz(knows Spy evs)"} must be the FIRST antecedent of the
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  induction formula.\<close>
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lemma B_trusts_YM4_newK [rule_format]:
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     "\<lbrakk>Crypt K (Nonce NB) \<in> parts (knows Spy evs);
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   308
        Nonce NB \<notin> analz (knows Spy evs);  evs \<in> yahalom\<rbrakk>
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      \<Longrightarrow> \<exists>A B NA. Says Server A
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                      \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, Nonce NA, Nonce NB\<rbrace>,
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                        Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace>\<rbrace>
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                     \<in> set evs"
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apply (erule rev_mp, erule rev_mp)
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apply (erule yahalom.induct, force,
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   315
       frule_tac [6] YM4_parts_knows_Spy)
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paulson <lp15@cam.ac.uk>
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diff changeset
   316
         apply (analz_mono_contra, simp_all)
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paulson <lp15@cam.ac.uk>
parents: 61956
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   317
  subgoal --\<open>Fake\<close> by blast
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paulson <lp15@cam.ac.uk>
parents: 61956
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   318
  subgoal --\<open>YM3\<close> by blast   
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   319
txt\<open>YM4.  A is uncompromised because NB is secure
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   320
  A's certificate guarantees the existence of the Server message\<close>
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   321
apply (blast dest!: Gets_imp_Says Crypt_Spy_analz_bad
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             dest: Says_imp_spies
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   323
                   parts.Inj [THEN parts.Fst, THEN A_trusts_YM3])
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   324
done
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   325
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
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diff changeset
   326
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   327
subsubsection\<open>Towards proving secrecy of Nonce NB\<close>
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   328
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   329
text\<open>Lemmas about the predicate KeyWithNonce\<close>
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   330
14207
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   331
lemma KeyWithNonceI:
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   332
 "Says Server A
61956
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diff changeset
   333
          \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, na, Nonce NB\<rbrace>, X\<rbrace>
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paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   334
        \<in> set evs \<Longrightarrow> KeyWithNonce K NB evs"
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paulson
parents: 11185
diff changeset
   335
by (unfold KeyWithNonce_def, blast)
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paulson
parents: 11185
diff changeset
   336
14207
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   337
lemma KeyWithNonce_Says [simp]:
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   338
   "KeyWithNonce K NB (Says S A X # evs) =
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parents: 11185
diff changeset
   339
      (Server = S &
61956
38b73f7940af more symbols;
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   340
       (\<exists>B n X'. X = \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, n, Nonce NB\<rbrace>, X'\<rbrace>)
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paulson
parents: 11185
diff changeset
   341
      | KeyWithNonce K NB evs)"
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paulson
parents: 11185
diff changeset
   342
by (simp add: KeyWithNonce_def, blast)
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paulson
parents: 11185
diff changeset
   343
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
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diff changeset
   344
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   345
lemma KeyWithNonce_Notes [simp]:
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   346
   "KeyWithNonce K NB (Notes A X # evs) = KeyWithNonce K NB evs"
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   347
by (simp add: KeyWithNonce_def)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   348
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   349
lemma KeyWithNonce_Gets [simp]:
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   350
   "KeyWithNonce K NB (Gets A X # evs) = KeyWithNonce K NB evs"
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paulson
parents: 11185
diff changeset
   351
by (simp add: KeyWithNonce_def)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   352
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   353
text\<open>A fresh key cannot be associated with any nonce
4f5ab843cf5b isabelle update_cartouches -c -t;
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parents: 59807
diff changeset
   354
  (with respect to a given trace).\<close>
14207
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paulson
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   355
lemma fresh_not_KeyWithNonce:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   356
     "Key K \<notin> used evs \<Longrightarrow> ~ KeyWithNonce K NB evs"
11251
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paulson
parents: 11185
diff changeset
   357
by (unfold KeyWithNonce_def, blast)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   358
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   359
text\<open>The Server message associates K with NB' and therefore not with any
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   360
  other nonce NB.\<close>
14207
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paulson
parents: 14200
diff changeset
   361
lemma Says_Server_KeyWithNonce:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   362
 "\<lbrakk>Says Server A \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, na, Nonce NB'\<rbrace>, X\<rbrace>
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   363
       \<in> set evs;
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   364
     NB \<noteq> NB';  evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   365
  \<Longrightarrow> ~ KeyWithNonce K NB evs"
11251
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paulson
parents: 11185
diff changeset
   366
by (unfold KeyWithNonce_def, blast dest: unique_session_keys)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   367
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   368
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   369
text\<open>The only nonces that can be found with the help of session keys are
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   370
  those distributed as nonce NB by the Server.  The form of the theorem
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   371
  recalls \<open>analz_image_freshK\<close>, but it is much more complicated.\<close>
11251
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paulson
parents: 11185
diff changeset
   372
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   373
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   374
text\<open>As with \<open>analz_image_freshK\<close>, we take some pains to express the 
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   375
  property as a logical equivalence so that the simplifier can apply it.\<close>
11251
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paulson
parents: 11185
diff changeset
   376
lemma Nonce_secrecy_lemma:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   377
     "P --> (X \<in> analz (G Un H)) --> (X \<in> analz H)  \<Longrightarrow>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   378
      P --> (X \<in> analz (G Un H)) = (X \<in> analz H)"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   379
by (blast intro: analz_mono [THEN subsetD])
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   380
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   381
lemma Nonce_secrecy:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   382
     "evs \<in> yahalom \<Longrightarrow>
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   383
      (\<forall>KK. KK <= - (range shrK) -->
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   384
           (\<forall>K \<in> KK. K \<in> symKeys --> ~ KeyWithNonce K NB evs)   -->
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   385
           (Nonce NB \<in> analz (Key`KK Un (knows Spy evs))) =
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   386
           (Nonce NB \<in> analz (knows Spy evs)))"
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   387
apply (erule yahalom.induct,
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   388
       frule_tac [7] YM4_analz_knows_Spy)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   389
apply (safe del: allI impI intro!: Nonce_secrecy_lemma [THEN impI, THEN allI])
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   390
apply (simp_all del: image_insert image_Un
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   391
       add: analz_image_freshK_simps split_ifs
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   392
            all_conj_distrib ball_conj_distrib
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   393
            analz_image_freshK fresh_not_KeyWithNonce
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   394
            imp_disj_not1               (*Moves NBa\<noteq>NB to the front*)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   395
            Says_Server_KeyWithNonce)
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   396
txt\<open>For Oops, simplification proves @{prop "NBa\<noteq>NB"}.  By
17411
664434175578 fixed document;
wenzelm
parents: 16417
diff changeset
   397
  @{term Says_Server_KeyWithNonce}, we get @{prop "~ KeyWithNonce K NB
664434175578 fixed document;
wenzelm
parents: 16417
diff changeset
   398
  evs"}; then simplification can apply the induction hypothesis with
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   399
  @{term "KK = {K}"}.\<close>
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   400
  subgoal --\<open>Fake\<close> by spy_analz
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   401
  subgoal --\<open>YM2\<close> by blast
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   402
  subgoal --\<open>YM3\<close> by blast
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   403
  subgoal --\<open>YM4: If @{prop "A \<in> bad"} then @{term NBa} is known, therefore @{prop "NBa \<noteq> NB"}.\<close>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   404
    by (metis A_trusts_YM3 Gets_imp_analz_Spy Gets_imp_knows_Spy KeyWithNonce_def
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   405
        Spy_analz_shrK analz.Fst analz.Snd analz_shrK_Decrypt parts.Fst parts.Inj)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   406
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   407
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   408
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   409
text\<open>Version required below: if NB can be decrypted using a session key then
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   410
   it was distributed with that key.  The more general form above is required
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   411
   for the induction to carry through.\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   412
lemma single_Nonce_secrecy:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   413
     "\<lbrakk>Says Server A
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   414
          \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key KAB, na, Nonce NB'\<rbrace>, X\<rbrace>
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   415
         \<in> set evs;
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   416
         NB \<noteq> NB';  KAB \<notin> range shrK;  evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   417
      \<Longrightarrow> (Nonce NB \<in> analz (insert (Key KAB) (knows Spy evs))) =
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   418
          (Nonce NB \<in> analz (knows Spy evs))"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   419
by (simp_all del: image_insert image_Un imp_disjL
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   420
             add: analz_image_freshK_simps split_ifs
13507
febb8e5d2a9d tidying of Isar scripts
paulson
parents: 11655
diff changeset
   421
                  Nonce_secrecy Says_Server_KeyWithNonce)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   422
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   423
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   424
subsubsection\<open>The Nonce NB uniquely identifies B's message.\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   425
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   426
lemma unique_NB:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   427
     "\<lbrakk>Crypt (shrK B) \<lbrace>Agent A, Nonce NA, nb\<rbrace> \<in> parts (knows Spy evs);
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   428
         Crypt (shrK B') \<lbrace>Agent A', Nonce NA', nb\<rbrace> \<in> parts (knows Spy evs);
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   429
        evs \<in> yahalom;  B \<notin> bad;  B' \<notin> bad\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   430
      \<Longrightarrow> NA' = NA & A' = A & B' = B"
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   431
apply (erule rev_mp, erule rev_mp)
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   432
apply (erule yahalom.induct, force,
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   433
       frule_tac [6] YM4_parts_knows_Spy, simp_all)
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   434
txt\<open>Fake, and YM2 by freshness\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   435
apply blast+
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   436
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   437
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   438
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   439
text\<open>Variant useful for proving secrecy of NB.  Because nb is assumed to be
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   440
  secret, we no longer must assume B, B' not bad.\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   441
lemma Says_unique_NB:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   442
     "\<lbrakk>Says C S   \<lbrace>X,  Crypt (shrK B) \<lbrace>Agent A, Nonce NA, nb\<rbrace>\<rbrace>
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   443
           \<in> set evs;
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   444
         Gets S' \<lbrace>X', Crypt (shrK B') \<lbrace>Agent A', Nonce NA', nb\<rbrace>\<rbrace>
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   445
           \<in> set evs;
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   446
         nb \<notin> analz (knows Spy evs);  evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   447
      \<Longrightarrow> NA' = NA & A' = A & B' = B"
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   448
by (blast dest!: Gets_imp_Says Crypt_Spy_analz_bad
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   449
          dest: Says_imp_spies unique_NB parts.Inj analz.Inj)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   450
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   451
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   452
subsubsection\<open>A nonce value is never used both as NA and as NB\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   453
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   454
lemma no_nonce_YM1_YM2:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   455
     "\<lbrakk>Crypt (shrK B') \<lbrace>Agent A', Nonce NB, nb'\<rbrace> \<in> parts(knows Spy evs);
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   456
        Nonce NB \<notin> analz (knows Spy evs);  evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   457
  \<Longrightarrow> Crypt (shrK B)  \<lbrace>Agent A, na, Nonce NB\<rbrace> \<notin> parts(knows Spy evs)"
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   458
apply (erule rev_mp, erule rev_mp)
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   459
apply (erule yahalom.induct, force,
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   460
       frule_tac [6] YM4_parts_knows_Spy)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   461
apply (analz_mono_contra, simp_all)
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   462
txt\<open>Fake, YM2\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   463
apply blast+
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   464
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   465
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   466
text\<open>The Server sends YM3 only in response to YM2.\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   467
lemma Says_Server_imp_YM2:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   468
     "\<lbrakk>Says Server A \<lbrace>Crypt (shrK A) \<lbrace>Agent B, k, na, nb\<rbrace>, X\<rbrace> \<in> set evs;
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   469
         evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   470
      \<Longrightarrow> Gets Server \<lbrace>Agent B, Crypt (shrK B) \<lbrace>Agent A, na, nb\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   471
             \<in> set evs"
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   472
by (erule rev_mp, erule yahalom.induct, auto)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   473
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   474
text\<open>A vital theorem for B, that nonce NB remains secure from the Spy.\<close>
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   475
theorem Spy_not_see_NB :
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   476
     "\<lbrakk>Says B Server
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   477
                \<lbrace>Agent B, Crypt (shrK B) \<lbrace>Agent A, Nonce NA, Nonce NB\<rbrace>\<rbrace>
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 32377
diff changeset
   478
           \<in> set evs;
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   479
         (\<forall>k. Notes Spy \<lbrace>Nonce NA, Nonce NB, k\<rbrace> \<notin> set evs);
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   480
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   481
      \<Longrightarrow> Nonce NB \<notin> analz (knows Spy evs)"
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   482
apply (erule rev_mp, erule rev_mp)
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   483
apply (erule yahalom.induct, force,
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   484
       frule_tac [6] YM4_analz_knows_Spy)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   485
apply (simp_all add: split_ifs pushes new_keys_not_analzd analz_insert_eq
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   486
                     analz_insert_freshK)
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   487
  subgoal --\<open>Fake\<close> by spy_analz
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   488
  subgoal --\<open>YM1: NB=NA is impossible anyway, but NA is secret because it is fresh!\<close> by blast
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   489
  subgoal --\<open>YM2\<close> by blast
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   490
  subgoal --\<open>YM3: because no NB can also be an NA\<close> 
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   491
    by (blast dest!: no_nonce_YM1_YM2 dest: Gets_imp_Says Says_unique_NB)
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   492
  subgoal --\<open>YM4: key K is visible to Spy, contradicting session key secrecy theorem\<close>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   493
    --\<open>Case analysis on whether Aa is bad;
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   494
            use \<open>Says_unique_NB\<close> to identify message components: @{term "Aa=A"}, @{term "Ba=B"}\<close>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   495
    apply clarify
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   496
    apply (blast dest!: Says_unique_NB analz_shrK_Decrypt
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   497
                        parts.Inj [THEN parts.Fst, THEN A_trusts_YM3]
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   498
                 dest: Gets_imp_Says Says_imp_spies Says_Server_imp_YM2
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   499
                       Spy_not_see_encrypted_key)
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   500
    done
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   501
  subgoal --\<open>Oops case: if the nonce is betrayed now, show that the Oops event is
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   502
    covered by the quantified Oops assumption.\<close>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   503
    apply clarsimp
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   504
    apply (metis Says_Server_imp_YM2 Gets_imp_Says Says_Server_not_range Says_unique_NB no_nonce_YM1_YM2 parts.Snd single_Nonce_secrecy spies_partsEs(1))
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   505
    done
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   506
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   507
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   508
text\<open>B's session key guarantee from YM4.  The two certificates contribute to a
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   509
  single conclusion about the Server's message.  Note that the "Notes Spy"
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   510
  assumption must quantify over \<open>\<forall>\<close> POSSIBLE keys instead of our particular K.
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   511
  If this run is broken and the spy substitutes a certificate containing an
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   512
  old key, B has no means of telling.\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   513
lemma B_trusts_YM4:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   514
     "\<lbrakk>Gets B \<lbrace>Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace>,
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   515
                  Crypt K (Nonce NB)\<rbrace> \<in> set evs;
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   516
         Says B Server
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   517
           \<lbrace>Agent B, Crypt (shrK B) \<lbrace>Agent A, Nonce NA, Nonce NB\<rbrace>\<rbrace>
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   518
           \<in> set evs;
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   519
         \<forall>k. Notes Spy \<lbrace>Nonce NA, Nonce NB, k\<rbrace> \<notin> set evs;
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   520
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   521
       \<Longrightarrow> Says Server A
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   522
                   \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   523
                             Nonce NA, Nonce NB\<rbrace>,
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   524
                     Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   525
             \<in> set evs"
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   526
by (blast dest: Spy_not_see_NB Says_unique_NB
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   527
                Says_Server_imp_YM2 B_trusts_YM4_newK)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   528
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   529
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   530
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   531
text\<open>The obvious combination of \<open>B_trusts_YM4\<close> with 
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   532
  \<open>Spy_not_see_encrypted_key\<close>\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   533
lemma B_gets_good_key:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   534
     "\<lbrakk>Gets B \<lbrace>Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace>,
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   535
                  Crypt K (Nonce NB)\<rbrace> \<in> set evs;
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   536
         Says B Server
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   537
           \<lbrace>Agent B, Crypt (shrK B) \<lbrace>Agent A, Nonce NA, Nonce NB\<rbrace>\<rbrace>
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   538
           \<in> set evs;
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   539
         \<forall>k. Notes Spy \<lbrace>Nonce NA, Nonce NB, k\<rbrace> \<notin> set evs;
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   540
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   541
      \<Longrightarrow> Key K \<notin> analz (knows Spy evs)"
32367
a508148f7c25 Removal of redundant settings of unification trace and search bounds.
paulson
parents: 23746
diff changeset
   542
  by (metis B_trusts_YM4 Spy_not_see_encrypted_key)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   543
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   544
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   545
subsection\<open>Authenticating B to A\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   546
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   547
text\<open>The encryption in message YM2 tells us it cannot be faked.\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   548
lemma B_Said_YM2 [rule_format]:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   549
     "\<lbrakk>Crypt (shrK B) \<lbrace>Agent A, Nonce NA, nb\<rbrace> \<in> parts (knows Spy evs);
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   550
        evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   551
      \<Longrightarrow> B \<notin> bad -->
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   552
          Says B Server \<lbrace>Agent B, Crypt (shrK B) \<lbrace>Agent A, Nonce NA, nb\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   553
            \<in> set evs"
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   554
apply (erule rev_mp, erule yahalom.induct, force,
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   555
       frule_tac [6] YM4_parts_knows_Spy, simp_all)
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   556
txt\<open>Fake\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   557
apply blast
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   558
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   559
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   560
text\<open>If the server sends YM3 then B sent YM2\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   561
lemma YM3_auth_B_to_A_lemma:
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   562
     "\<lbrakk>Says Server A \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, Nonce NA, nb\<rbrace>, X\<rbrace>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   563
       \<in> set evs;  evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   564
      \<Longrightarrow> B \<notin> bad -->
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   565
          Says B Server \<lbrace>Agent B, Crypt (shrK B) \<lbrace>Agent A, Nonce NA, nb\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   566
            \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   567
apply (erule rev_mp, erule yahalom.induct, simp_all)
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   568
txt\<open>YM3, YM4\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   569
apply (blast dest!: B_Said_YM2)+
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   570
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   571
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   572
text\<open>If A receives YM3 then B has used nonce NA (and therefore is alive)\<close>
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   573
theorem YM3_auth_B_to_A:
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   574
     "\<lbrakk>Gets A \<lbrace>Crypt (shrK A) \<lbrace>Agent B, Key K, Nonce NA, nb\<rbrace>, X\<rbrace>
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   575
           \<in> set evs;
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   576
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   577
      \<Longrightarrow> Says B Server \<lbrace>Agent B, Crypt (shrK B) \<lbrace>Agent A, Nonce NA, nb\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   578
       \<in> set evs"
32367
a508148f7c25 Removal of redundant settings of unification trace and search bounds.
paulson
parents: 23746
diff changeset
   579
  by (metis A_trusts_YM3 Gets_imp_analz_Spy YM3_auth_B_to_A_lemma analz.Fst
a508148f7c25 Removal of redundant settings of unification trace and search bounds.
paulson
parents: 23746
diff changeset
   580
         not_parts_not_analz)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   581
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   582
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   583
subsection\<open>Authenticating A to B using the certificate 
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   584
  @{term "Crypt K (Nonce NB)"}\<close>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   585
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   586
text\<open>Assuming the session key is secure, if both certificates are present then
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   587
  A has said NB.  We can't be sure about the rest of A's message, but only
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   588
  NB matters for freshness.\<close>
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   589
theorem A_Said_YM3_lemma [rule_format]:
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   590
     "evs \<in> yahalom
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   591
      \<Longrightarrow> Key K \<notin> analz (knows Spy evs) -->
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   592
          Crypt K (Nonce NB) \<in> parts (knows Spy evs) -->
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   593
          Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace> \<in> parts (knows Spy evs) -->
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   594
          B \<notin> bad -->
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   595
          (\<exists>X. Says A B \<lbrace>X, Crypt K (Nonce NB)\<rbrace> \<in> set evs)"
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   596
apply (erule yahalom.induct, force,
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   597
       frule_tac [6] YM4_parts_knows_Spy)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   598
apply (analz_mono_contra, simp_all)
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   599
  subgoal --\<open>Fake\<close> by blast
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   600
  subgoal --\<open>YM3 because the message @{term "Crypt K (Nonce NB)"} could not exist\<close>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   601
     by (force dest!: Crypt_imp_keysFor)
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   602
   subgoal --\<open>YM4: was @{term "Crypt K (Nonce NB)"} the very last message? If not, use the induction hypothesis,
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   603
               otherwise by unicity of session keys\<close>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   604
     by (blast dest!: Gets_imp_Says A_trusts_YM3 B_trusts_YM4_shrK Crypt_Spy_analz_bad
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   605
             dest: Says_imp_knows_Spy [THEN parts.Inj] unique_session_keys)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   606
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   607
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   608
text\<open>If B receives YM4 then A has used nonce NB (and therefore is alive).
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   609
  Moreover, A associates K with NB (thus is talking about the same run).
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59807
diff changeset
   610
  Other premises guarantee secrecy of K.\<close>
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   611
theorem YM4_imp_A_Said_YM3 [rule_format]:
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   612
     "\<lbrakk>Gets B \<lbrace>Crypt (shrK B) \<lbrace>Agent A, Key K\<rbrace>,
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   613
                  Crypt K (Nonce NB)\<rbrace> \<in> set evs;
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   614
         Says B Server
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   615
           \<lbrace>Agent B, Crypt (shrK B) \<lbrace>Agent A, Nonce NA, Nonce NB\<rbrace>\<rbrace>
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   616
           \<in> set evs;
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   617
         (\<forall>NA k. Notes Spy \<lbrace>Nonce NA, Nonce NB, k\<rbrace> \<notin> set evs);
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   618
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom\<rbrakk>
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   619
      \<Longrightarrow> \<exists>X. Says A B \<lbrace>X, Crypt K (Nonce NB)\<rbrace> \<in> set evs"
32367
a508148f7c25 Removal of redundant settings of unification trace and search bounds.
paulson
parents: 23746
diff changeset
   620
by (metis A_Said_YM3_lemma B_gets_good_key Gets_imp_analz_Spy YM4_parts_knows_Spy analz.Fst not_parts_not_analz)
64364
464420ba7f74 "subgoal" examples
paulson <lp15@cam.ac.uk>
parents: 61956
diff changeset
   621
1985
84cf16192e03 Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff changeset
   622
end