--- a/src/HOL/Auth/OtwayRees_Bad.thy Thu Oct 09 18:20:14 2003 +0200
+++ b/src/HOL/Auth/OtwayRees_Bad.thy Fri Oct 10 11:13:29 2003 +0200
@@ -22,39 +22,39 @@
consts otway :: "event list set"
inductive "otway"
intros
- (*Initial trace is empty*)
- Nil: "[] \<in> otway"
+ Nil: --{*The empty trace*}
+ "[] \<in> otway"
- (*The spy MAY say anything he CAN say. We do not expect him to
- invent new nonces here, but he can also use NS1. Common to
- all similar protocols.*)
- Fake: "[| evsf \<in> otway; X \<in> synth (analz (knows Spy evsf)) |]
+ Fake: --{*The Spy may say anything he can say. The sender field is correct,
+ but agents don't use that information.*}
+ "[| evsf \<in> otway; X \<in> synth (analz (knows Spy evsf)) |]
==> Says Spy B X # evsf \<in> otway"
- (*A message that has been sent can be received by the
- intended recipient.*)
- Reception: "[| evsr \<in> otway; Says A B X \<in>set evsr |]
+
+ Reception: --{*A message that has been sent can be received by the
+ intended recipient.*}
+ "[| evsr \<in> otway; Says A B X \<in>set evsr |]
==> Gets B X # evsr \<in> otway"
- (*Alice initiates a protocol run*)
- OR1: "[| evs1 \<in> otway; Nonce NA \<notin> used evs1 |]
+ OR1: --{*Alice initiates a protocol run*}
+ "[| evs1 \<in> otway; Nonce NA \<notin> used evs1 |]
==> Says A B {|Nonce NA, Agent A, Agent B,
Crypt (shrK A) {|Nonce NA, Agent A, Agent B|} |}
# evs1 \<in> otway"
- (*Bob's response to Alice's message.
- This variant of the protocol does NOT encrypt NB.*)
- OR2: "[| evs2 \<in> otway; Nonce NB \<notin> used evs2;
+ OR2: --{*Bob's response to Alice's message.
+ This variant of the protocol does NOT encrypt NB.*}
+ "[| evs2 \<in> otway; Nonce NB \<notin> used evs2;
Gets B {|Nonce NA, Agent A, Agent B, X|} \<in> set evs2 |]
==> Says B Server
{|Nonce NA, Agent A, Agent B, X, Nonce NB,
Crypt (shrK B) {|Nonce NA, Agent A, Agent B|}|}
# evs2 \<in> otway"
- (*The Server receives Bob's message and checks that the three NAs
+ OR3: --{*The Server receives Bob's message and checks that the three NAs
match. Then he sends a new session key to Bob with a packet for
- forwarding to Alice.*)
- OR3: "[| evs3 \<in> otway; Key KAB \<notin> used evs3;
+ forwarding to Alice.*}
+ "[| evs3 \<in> otway; Key KAB \<notin> used evs3;
Gets Server
{|Nonce NA, Agent A, Agent B,
Crypt (shrK A) {|Nonce NA, Agent A, Agent B|},
@@ -67,10 +67,10 @@
Crypt (shrK B) {|Nonce NB, Key KAB|}|}
# evs3 \<in> otway"
- (*Bob receives the Server's (?) message and compares the Nonces with
- those in the message he previously sent the Server.
- Need B ~= Server because we allow messages to self.*)
- OR4: "[| evs4 \<in> otway; B ~= Server;
+ OR4: --{*Bob receives the Server's (?) message and compares the Nonces with
+ those in the message he previously sent the Server.
+ Need @{term "B \<noteq> Server"} because we allow messages to self.*}
+ "[| evs4 \<in> otway; B \<noteq> Server;
Says B Server {|Nonce NA, Agent A, Agent B, X', Nonce NB,
Crypt (shrK B) {|Nonce NA, Agent A, Agent B|}|}
\<in> set evs4;
@@ -78,9 +78,9 @@
\<in> set evs4 |]
==> Says B A {|Nonce NA, X|} # evs4 \<in> otway"
- (*This message models possible leaks of session keys. The nonces
- identify the protocol run.*)
- Oops: "[| evso \<in> otway;
+ Oops: --{*This message models possible leaks of session keys. The nonces
+ identify the protocol run.*}
+ "[| evso \<in> otway;
Says Server B {|Nonce NA, X, Crypt (shrK B) {|Nonce NB, Key K|}|}
\<in> set evso |]
==> Notes Spy {|Nonce NA, Nonce NB, Key K|} # evso \<in> otway"
@@ -91,7 +91,7 @@
declare analz_into_parts [dest]
declare Fake_parts_insert_in_Un [dest]
-(*A "possibility property": there are traces that reach the end*)
+text{*A "possibility property": there are traces that reach the end*}
lemma "[| B \<noteq> Server; Key K \<notin> used [] |]
==> \<exists>NA. \<exists>evs \<in> otway.
Says B A {|Nonce NA, Crypt (shrK A) {|Nonce NA, Key K|}|}
@@ -111,10 +111,7 @@
done
-(**** Inductive proofs about otway ****)
-
-
-(** For reasoning about the encrypted portion of messages **)
+subsection{*For reasoning about the encrypted portion of messages *}
lemma OR2_analz_knows_Spy:
"[| Gets B {|N, Agent A, Agent B, X|} \<in> set evs; evs \<in> otway |]
@@ -131,20 +128,20 @@
==> K \<in> parts (knows Spy evs)"
by blast
-(*Forwarding lemma: see comments in OtwayRees.thy*)
+text{*Forwarding lemma: see comments in OtwayRees.thy*}
lemmas OR2_parts_knows_Spy =
OR2_analz_knows_Spy [THEN analz_into_parts, standard]
-(** Theorems of the form X \<notin> parts (knows Spy evs) imply that NOBODY
- sends messages containing X! **)
+text{*Theorems of the form @{term "X \<notin> parts (spies evs)"} imply that
+NOBODY sends messages containing X! *}
-(*Spy never sees a good agent's shared key!*)
+text{*Spy never sees a good agent's shared key!*}
lemma Spy_see_shrK [simp]:
"evs \<in> otway ==> (Key (shrK A) \<in> parts (knows Spy evs)) = (A \<in> bad)"
-apply (erule otway.induct, force,
- drule_tac [4] OR2_parts_knows_Spy, simp_all, blast+)
-done
+by (erule otway.induct, force,
+ drule_tac [4] OR2_parts_knows_Spy, simp_all, blast+)
+
lemma Spy_analz_shrK [simp]:
"evs \<in> otway ==> (Key (shrK A) \<in> analz (knows Spy evs)) = (A \<in> bad)"
@@ -155,10 +152,10 @@
by (blast dest: Spy_see_shrK)
-(*** Proofs involving analz ***)
+subsection{*Proofs involving analz *}
-(*Describes the form of K and NA when the Server sends this message. Also
- for Oops case.*)
+text{*Describes the form of K and NA when the Server sends this message. Also
+ for Oops case.*}
lemma Says_Server_message_form:
"[| Says Server B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} \<in> set evs;
evs \<in> otway |]
@@ -178,9 +175,9 @@
****)
-(** Session keys are not used to encrypt other session keys **)
+text{*Session keys are not used to encrypt other session keys*}
-(*The equality makes the induction hypothesis easier to apply*)
+text{*The equality makes the induction hypothesis easier to apply*}
lemma analz_image_freshK [rule_format]:
"evs \<in> otway ==>
\<forall>K KK. KK <= -(range shrK) -->
@@ -199,8 +196,7 @@
by (simp only: analz_image_freshK analz_image_freshK_simps)
-(*** The Key K uniquely identifies the Server's message. **)
-
+text{*The Key K uniquely identifies the Server's message. *}
lemma unique_session_keys:
"[| Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} \<in> set evs;
Says Server B' {|NA',X',Crypt (shrK B') {|NB',K|}|} \<in> set evs;
@@ -208,14 +204,13 @@
apply (erule rev_mp)
apply (erule rev_mp)
apply (erule otway.induct, simp_all)
-(*Remaining cases: OR3 and OR4*)
-apply blast+
+apply blast+ --{*OR3 and OR4*}
done
-(** Crucial secrecy property: Spy does not see the keys sent in msg OR3
+subsection{*Crucial secrecy property: Spy does not see the keys sent in msg OR3
Does not in itself guarantee security: an attack could violate
- the premises, e.g. by having A=Spy **)
+ the premises, e.g. by having @{term "A=Spy"} *}
lemma secrecy_lemma:
"[| A \<notin> bad; B \<notin> bad; evs \<in> otway |]
@@ -228,9 +223,9 @@
apply (frule_tac [7] Says_Server_message_form)
apply (drule_tac [6] OR4_analz_knows_Spy)
apply (drule_tac [4] OR2_analz_knows_Spy)
-apply (simp_all add: analz_insert_eq analz_insert_freshK pushes, spy_analz) (*Fake*)
-(*OR3, OR4, Oops*)
-apply (blast dest: unique_session_keys)+
+apply (simp_all add: analz_insert_eq analz_insert_freshK pushes)
+apply spy_analz --{*Fake*}
+apply (blast dest: unique_session_keys)+ --{*OR3, OR4, Oops*}
done
@@ -244,26 +239,25 @@
by (blast dest: Says_Server_message_form secrecy_lemma)
-(*** Attempting to prove stronger properties ***)
+subsection{*Attempting to prove stronger properties *}
-(*Only OR1 can have caused such a part of a message to appear.
- The premise A \<noteq> B prevents OR2's similar-looking cryptogram from being
- picked up. Original Otway-Rees doesn't need it.*)
+text{*Only OR1 can have caused such a part of a message to appear. The premise
+ @{term "A \<noteq> B"} prevents OR2's similar-looking cryptogram from being picked
+ up. Original Otway-Rees doesn't need it.*}
lemma Crypt_imp_OR1 [rule_format]:
"[| A \<notin> bad; A \<noteq> B; evs \<in> otway |]
==> Crypt (shrK A) {|NA, Agent A, Agent B|} \<in> parts (knows Spy evs) -->
Says A B {|NA, Agent A, Agent B,
Crypt (shrK A) {|NA, Agent A, Agent B|}|} \<in> set evs"
-apply (erule otway.induct, force,
- drule_tac [4] OR2_parts_knows_Spy, simp_all, blast+)
-done
+by (erule otway.induct, force,
+ drule_tac [4] OR2_parts_knows_Spy, simp_all, blast+)
-(*Crucial property: If the encrypted message appears, and A has used NA
+text{*Crucial property: If the encrypted message appears, and A has used NA
to start a run, then it originated with the Server!
- The premise A \<noteq> B allows use of Crypt_imp_OR1*)
-(*Only it is FALSE. Somebody could make a fake message to Server
- substituting some other nonce NA' for NB.*)
+ The premise @{term "A \<noteq> B"} allows use of @{text Crypt_imp_OR1}*}
+text{*Only it is FALSE. Somebody could make a fake message to Server
+ substituting some other nonce NA' for NB.*}
lemma "[| A \<notin> bad; A \<noteq> B; evs \<in> otway |]
==> Crypt (shrK A) {|NA, Key K|} \<in> parts (knows Spy evs) -->
Says A B {|NA, Agent A, Agent B,
@@ -275,15 +269,12 @@
Crypt (shrK B) {|NB, Key K|}|} \<in> set evs)"
apply (erule otway.induct, force,
drule_tac [4] OR2_parts_knows_Spy, simp_all)
-(*Fake*)
-apply blast
-(*OR1: it cannot be a new Nonce, contradiction.*)
-apply blast
-(*OR3 and OR4*)
+apply blast --{*Fake*}
+apply blast --{*OR1: it cannot be a new Nonce, contradiction.*}
+txt{*OR3 and OR4*}
apply (simp_all add: ex_disj_distrib)
-(*OR4*)
-prefer 2 apply (blast intro!: Crypt_imp_OR1)
-(*OR3*)
+ prefer 2 apply (blast intro!: Crypt_imp_OR1) --{*OR4*}
+txt{*OR3*}
apply clarify
(*The hypotheses at this point suggest an attack in which nonce NB is used
in two different roles: