--- a/src/HOL/Quickcheck_Examples/Needham_Schroeder_Unguided_Attacker.thy Thu Jul 12 16:22:33 2012 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,96 +0,0 @@
-theory Needham_Schroeder_Unguided_Attacker_Example
-imports Needham_Schroeder_Base
-begin
-
-inductive_set ns_public :: "event list set"
- where
- (*Initial trace is empty*)
- Nil: "[] \<in> ns_public"
-
- | Fake: "\<lbrakk>evs1 \<in> ns_public; X \<in> synth (analz (spies evs1)) \<rbrakk>
- \<Longrightarrow> Says Spy A X # evs1 \<in> ns_public"
-
- (*Alice initiates a protocol run, sending a nonce to Bob*)
- | NS1: "\<lbrakk>evs1 \<in> ns_public; Nonce NA \<notin> used evs1\<rbrakk>
- \<Longrightarrow> Says A B (Crypt (pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace>)
- # evs1 \<in> ns_public"
- (*Bob responds to Alice's message with a further nonce*)
- | NS2: "\<lbrakk>evs2 \<in> ns_public; Nonce NB \<notin> used evs2;
- Says A' B (Crypt (pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs2\<rbrakk>
- \<Longrightarrow> Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>)
- # evs2 \<in> ns_public"
-
- (*Alice proves her existence by sending NB back to Bob.*)
- | NS3: "\<lbrakk>evs3 \<in> ns_public;
- Says A B (Crypt (pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs3;
- Says B' A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs3\<rbrakk>
- \<Longrightarrow> Says A B (Crypt (pubEK B) (Nonce NB)) # evs3 \<in> ns_public"
-
-declare ListMem_iff[symmetric, code_pred_inline]
-
-lemmas [code_pred_intro] = ns_publicp.intros[folded synth'_def]
-
-code_pred [skip_proof] ns_publicp unfolding synth'_def by (rule ns_publicp.cases) fastforce+
-thm ns_publicp.equation
-
-code_pred [generator_cps] ns_publicp .
-thm ns_publicp.generator_cps_equation
-
-
-lemma "ns_publicp evs ==> \<not> (Says Alice Bob (Crypt (pubEK Bob) (Nonce NB))) : set evs"
-quickcheck[smart_exhaustive, depth = 5, timeout = 200, expect = counterexample]
-(*quickcheck[narrowing, size = 6, timeout = 200, verbose, expect = no_counterexample]*)
-oops
-
-lemma
- "\<lbrakk>ns_publicp evs\<rbrakk>
- \<Longrightarrow> Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) : set evs
- \<Longrightarrow> A \<noteq> Spy \<Longrightarrow> B \<noteq> Spy \<Longrightarrow> A \<noteq> B
- \<Longrightarrow> Nonce NB \<notin> analz (spies evs)"
-quickcheck[smart_exhaustive, depth = 6, timeout = 100, expect = no_counterexample]
-(*quickcheck[narrowing, size = 7, timeout = 200, expect = no_counterexample]*)
-oops
-
-section {* Proving the counterexample trace for validation *}
-
-lemma
- assumes "A = Alice" "B = Bob" "C = Spy" "NA = 0" "NB = 1"
- assumes "evs =
- [Says Alice Spy (Crypt (pubEK Spy) (Nonce 1)),
- Says Bob Alice (Crypt (pubEK Alice) {|Nonce 0, Nonce 1|}),
- Says Spy Bob (Crypt (pubEK Bob) {|Nonce 0, Agent Alice|}),
- Says Alice Spy (Crypt (pubEK Spy) {|Nonce 0, Agent Alice|})]" (is "_ = [?e3, ?e2, ?e1, ?e0]")
- shows "A \<noteq> Spy" "B \<noteq> Spy" "evs : ns_public" "Nonce NB : analz (knows Spy evs)"
-proof -
- from assms show "A \<noteq> Spy" by auto
- from assms show "B \<noteq> Spy" by auto
- have "[] : ns_public" by (rule Nil)
- then have first_step: "[?e0] : ns_public"
- proof (rule NS1)
- show "Nonce 0 ~: used []" by eval
- qed
- then have "[?e1, ?e0] : ns_public"
- proof (rule Fake)
- show "Crypt (pubEK Bob) {|Nonce 0, Agent Alice|} : synth (analz (knows Spy [?e0]))"
- by (intro synth.intros(2,3,4,1)) eval+
- qed
- then have "[?e2, ?e1, ?e0] : ns_public"
- proof (rule NS2)
- show "Says Spy Bob (Crypt (pubEK Bob) {|Nonce 0, Agent Alice|}) \<in> set [?e1, ?e0]" by simp
- show " Nonce 1 ~: used [?e1, ?e0]" by eval
- qed
- then show "evs : ns_public"
- unfolding assms
- proof (rule NS3)
- show " Says Alice Spy (Crypt (pubEK Spy) {|Nonce 0, Agent Alice|}) \<in> set [?e2, ?e1, ?e0]" by simp
- show "Says Bob Alice (Crypt (pubEK Alice) {|Nonce 0, Nonce 1|}) : set [?e2, ?e1, ?e0]" by simp
- qed
- from assms show "Nonce NB : analz (knows Spy evs)"
- apply simp
- apply (rule analz.intros(4))
- apply (rule analz.intros(1))
- apply (auto simp add: bad_def)
- done
-qed
-
-end
\ No newline at end of file