--- a/src/HOL/Auth/WooLam.thy Wed Apr 11 11:53:54 2001 +0200
+++ b/src/HOL/Auth/WooLam.thy Thu Apr 12 12:45:05 2001 +0200
@@ -14,52 +14,166 @@
Computer Security Foundations Workshop, 1996.
*)
-WooLam = Shared +
+theory WooLam = Shared:
-consts woolam :: event list set
+consts woolam :: "event list set"
inductive woolam
- intrs
+ intros
(*Initial trace is empty*)
- Nil "[] \\<in> woolam"
+ Nil: "[] \<in> woolam"
(** These rules allow agents to send messages to themselves **)
(*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> woolam; X \\<in> synth (analz (spies evsf)) |]
- ==> Says Spy B X # evsf \\<in> woolam"
+ Fake: "[| evsf \<in> woolam; X \<in> synth (analz (spies evsf)) |]
+ ==> Says Spy B X # evsf \<in> woolam"
(*Alice initiates a protocol run*)
- WL1 "[| evs1 \\<in> woolam |]
- ==> Says A B (Agent A) # evs1 \\<in> woolam"
+ WL1: "evs1 \<in> woolam ==> Says A B (Agent A) # evs1 \<in> woolam"
(*Bob responds to Alice's message with a challenge.*)
- WL2 "[| evs2 \\<in> woolam; Says A' B (Agent A) \\<in> set evs2 |]
- ==> Says B A (Nonce NB) # evs2 \\<in> woolam"
+ WL2: "[| evs2 \<in> woolam; Says A' B (Agent A) \<in> set evs2 |]
+ ==> Says B A (Nonce NB) # evs2 \<in> woolam"
(*Alice responds to Bob's challenge by encrypting NB with her key.
B is *not* properly determined -- Alice essentially broadcasts
her reply.*)
- WL3 "[| evs3 \\<in> woolam;
- Says A B (Agent A) \\<in> set evs3;
- Says B' A (Nonce NB) \\<in> set evs3 |]
- ==> Says A B (Crypt (shrK A) (Nonce NB)) # evs3 \\<in> woolam"
+ WL3: "[| evs3 \<in> woolam;
+ Says A B (Agent A) \<in> set evs3;
+ Says B' A (Nonce NB) \<in> set evs3 |]
+ ==> Says A B (Crypt (shrK A) (Nonce NB)) # evs3 \<in> woolam"
(*Bob forwards Alice's response to the Server. NOTE: usually
the messages are shown in chronological order, for clarity.
But here, exchanging the two events would cause the lemma
WL4_analz_spies to pick up the wrong assumption!*)
- WL4 "[| evs4 \\<in> woolam;
- Says A' B X \\<in> set evs4;
- Says A'' B (Agent A) \\<in> set evs4 |]
- ==> Says B Server {|Agent A, Agent B, X|} # evs4 \\<in> woolam"
+ WL4: "[| evs4 \<in> woolam;
+ Says A' B X \<in> set evs4;
+ Says A'' B (Agent A) \<in> set evs4 |]
+ ==> Says B Server {|Agent A, Agent B, X|} # evs4 \<in> woolam"
(*Server decrypts Alice's response for Bob.*)
- WL5 "[| evs5 \\<in> woolam;
+ WL5: "[| evs5 \<in> woolam;
Says B' Server {|Agent A, Agent B, Crypt (shrK A) (Nonce NB)|}
- \\<in> set evs5 |]
+ \<in> set evs5 |]
==> Says Server B (Crypt (shrK B) {|Agent A, Nonce NB|})
- # evs5 \\<in> woolam"
+ # evs5 \<in> woolam"
+
+
+declare Says_imp_knows_Spy [THEN analz.Inj, dest]
+declare parts.Body [dest]
+declare analz_into_parts [dest]
+declare Fake_parts_insert_in_Un [dest]
+
+
+(*A "possibility property": there are traces that reach the end*)
+lemma "\<exists>NB. \<exists>evs \<in> woolam.
+ Says Server B (Crypt (shrK B) {|Agent A, Nonce NB|}) \<in> set evs"
+apply (intro exI bexI)
+apply (rule_tac [2] woolam.Nil
+ [THEN woolam.WL1, THEN woolam.WL2, THEN woolam.WL3,
+ THEN woolam.WL4, THEN woolam.WL5])
+apply possibility
+done
+
+(*Could prove forwarding lemmas for WL4, but we do not need them!*)
+
+(**** Inductive proofs about woolam ****)
+
+(** Theorems of the form X \<notin> parts (spies evs) imply that NOBODY
+ sends messages containing X! **)
+
+(*Spy never sees a good agent's shared key!*)
+lemma Spy_see_shrK [simp]:
+ "evs \<in> woolam ==> (Key (shrK A) \<in> parts (spies evs)) = (A \<in> bad)"
+apply (erule woolam.induct, force, simp_all)
+apply blast+
+done
+
+lemma Spy_analz_shrK [simp]:
+ "evs \<in> woolam ==> (Key (shrK A) \<in> analz (spies evs)) = (A \<in> bad)"
+by auto
+
+lemma Spy_see_shrK_D [dest!]:
+ "[|Key (shrK A) \<in> parts (knows Spy evs); evs \<in> woolam|] ==> A \<in> bad"
+by (blast dest: Spy_see_shrK)
+
+
+(**** Autheticity properties for Woo-Lam ****)
+
+(*** WL4 ***)
+
+(*If the encrypted message appears then it originated with Alice*)
+lemma NB_Crypt_imp_Alice_msg:
+ "[| Crypt (shrK A) (Nonce NB) \<in> parts (spies evs);
+ A \<notin> bad; evs \<in> woolam |]
+ ==> \<exists>B. Says A B (Crypt (shrK A) (Nonce NB)) \<in> set evs"
+apply (erule rev_mp, erule woolam.induct, force, simp_all)
+apply blast+
+done
+
+(*Guarantee for Server: if it gets a message containing a certificate from
+ Alice, then she originated that certificate. But we DO NOT know that B
+ ever saw it: the Spy may have rerouted the message to the Server.*)
+lemma Server_trusts_WL4 [dest]:
+ "[| Says B' Server {|Agent A, Agent B, Crypt (shrK A) (Nonce NB)|}
+ \<in> set evs;
+ A \<notin> bad; evs \<in> woolam |]
+ ==> \<exists>B. Says A B (Crypt (shrK A) (Nonce NB)) \<in> set evs"
+by (blast intro!: NB_Crypt_imp_Alice_msg)
+
+
+(*** WL5 ***)
+
+(*Server sent WL5 only if it received the right sort of message*)
+lemma Server_sent_WL5 [dest]:
+ "[| Says Server B (Crypt (shrK B) {|Agent A, NB|}) \<in> set evs;
+ evs \<in> woolam |]
+ ==> \<exists>B'. Says B' Server {|Agent A, Agent B, Crypt (shrK A) NB|}
+ \<in> set evs"
+apply (erule rev_mp, erule woolam.induct, force, simp_all)
+apply blast+
+done
+
+(*If the encrypted message appears then it originated with the Server!*)
+lemma NB_Crypt_imp_Server_msg [rule_format]:
+ "[| Crypt (shrK B) {|Agent A, NB|} \<in> parts (spies evs);
+ B \<notin> bad; evs \<in> woolam |]
+ ==> Says Server B (Crypt (shrK B) {|Agent A, NB|}) \<in> set evs"
+apply (erule rev_mp, erule woolam.induct, force, simp_all)
+apply blast+
+done
+
+(*Guarantee for B. If B gets the Server's certificate then A has encrypted
+ the nonce using her key. This event can be no older than the nonce itself.
+ But A may have sent the nonce to some other agent and it could have reached
+ the Server via the Spy.*)
+lemma B_trusts_WL5:
+ "[| Says S B (Crypt (shrK B) {|Agent A, Nonce NB|}): set evs;
+ A \<notin> bad; B \<notin> bad; evs \<in> woolam |]
+ ==> \<exists>B. Says A B (Crypt (shrK A) (Nonce NB)) \<in> set evs"
+by (blast dest!: NB_Crypt_imp_Server_msg)
+
+
+(*B only issues challenges in response to WL1. Not used.*)
+lemma B_said_WL2:
+ "[| Says B A (Nonce NB) \<in> set evs; B \<noteq> Spy; evs \<in> woolam |]
+ ==> \<exists>A'. Says A' B (Agent A) \<in> set evs"
+apply (erule rev_mp, erule woolam.induct, force, simp_all)
+apply blast+
+done
+
+
+(**CANNOT be proved because A doesn't know where challenges come from...*)
+lemma "[| A \<notin> bad; B \<noteq> Spy; evs \<in> woolam |]
+ ==> Crypt (shrK A) (Nonce NB) \<in> parts (spies evs) &
+ Says B A (Nonce NB) \<in> set evs
+ --> Says A B (Crypt (shrK A) (Nonce NB)) \<in> set evs"
+apply (erule rev_mp, erule woolam.induct, force, simp_all)
+apply blast
+apply auto
+oops
end