--- a/src/HOL/Auth/NS_Public_Bad.thy Wed Apr 23 18:09:48 2003 +0200
+++ b/src/HOL/Auth/NS_Public_Bad.thy Fri Apr 25 11:18:14 2003 +0200
@@ -28,20 +28,20 @@
(*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 (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>)
+ \<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 (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs2\<rbrakk>
- \<Longrightarrow> Says B A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>)
+ 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 (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs3;
- Says B' A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs3\<rbrakk>
- \<Longrightarrow> Says A B (Crypt (pubK B) (Nonce NB)) # 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 knows_Spy_partsEs [elim]
declare analz_subset_parts [THEN subsetD, dest]
@@ -49,7 +49,7 @@
declare image_eq_UN [simp] (*accelerates proofs involving nested images*)
(*A "possibility property": there are traces that reach the end*)
-lemma "\<exists>NB. \<exists>evs \<in> ns_public. Says A B (Crypt (pubK B) (Nonce NB)) \<in> set evs"
+lemma "\<exists>NB. \<exists>evs \<in> ns_public. Says A B (Crypt (pubEK B) (Nonce NB)) \<in> set evs"
apply (intro exI bexI)
apply (rule_tac [2] ns_public.Nil [THEN ns_public.NS1, THEN ns_public.NS2,
THEN ns_public.NS3])
@@ -62,12 +62,12 @@
sends messages containing X! **)
(*Spy never sees another agent's private key! (unless it's bad at start)*)
-lemma Spy_see_priK [simp]:
- "evs \<in> ns_public \<Longrightarrow> (Key (priK A) \<in> parts (spies evs)) = (A \<in> bad)"
+lemma Spy_see_priEK [simp]:
+ "evs \<in> ns_public \<Longrightarrow> (Key (priEK A) \<in> parts (spies evs)) = (A \<in> bad)"
by (erule ns_public.induct, auto)
-lemma Spy_analz_priK [simp]:
- "evs \<in> ns_public \<Longrightarrow> (Key (priK A) \<in> analz (spies evs)) = (A \<in> bad)"
+lemma Spy_analz_priEK [simp]:
+ "evs \<in> ns_public \<Longrightarrow> (Key (priEK A) \<in> analz (spies evs)) = (A \<in> bad)"
by auto
@@ -77,8 +77,8 @@
is secret. (Honest users generate fresh nonces.)*)
lemma no_nonce_NS1_NS2 [rule_format]:
"evs \<in> ns_public
- \<Longrightarrow> Crypt (pubK C) \<lbrace>NA', Nonce NA\<rbrace> \<in> parts (spies evs) \<longrightarrow>
- Crypt (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace> \<in> parts (spies evs) \<longrightarrow>
+ \<Longrightarrow> Crypt (pubEK C) \<lbrace>NA', Nonce NA\<rbrace> \<in> parts (spies evs) \<longrightarrow>
+ Crypt (pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace> \<in> parts (spies evs) \<longrightarrow>
Nonce NA \<in> analz (spies evs)"
apply (erule ns_public.induct, simp_all)
apply (blast intro: analz_insertI)+
@@ -87,8 +87,8 @@
(*Unicity for NS1: nonce NA identifies agents A and B*)
lemma unique_NA:
- "\<lbrakk>Crypt(pubK B) \<lbrace>Nonce NA, Agent A \<rbrace> \<in> parts(spies evs);
- Crypt(pubK B') \<lbrace>Nonce NA, Agent A'\<rbrace> \<in> parts(spies evs);
+ "\<lbrakk>Crypt(pubEK B) \<lbrace>Nonce NA, Agent A \<rbrace> \<in> parts(spies evs);
+ Crypt(pubEK B') \<lbrace>Nonce NA, Agent A'\<rbrace> \<in> parts(spies evs);
Nonce NA \<notin> analz (spies evs); evs \<in> ns_public\<rbrakk>
\<Longrightarrow> A=A' \<and> B=B'"
apply (erule rev_mp, erule rev_mp, erule rev_mp)
@@ -102,7 +102,7 @@
The major premise "Says A B ..." makes it a dest-rule, so we use
(erule rev_mp) rather than rule_format. *)
theorem Spy_not_see_NA:
- "\<lbrakk>Says A B (Crypt(pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs;
+ "\<lbrakk>Says A B (Crypt(pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs;
A \<notin> bad; B \<notin> bad; evs \<in> ns_public\<rbrakk>
\<Longrightarrow> Nonce NA \<notin> analz (spies evs)"
apply (erule rev_mp)
@@ -115,27 +115,27 @@
to start a run, then B has sent message 2.*)
lemma A_trusts_NS2_lemma [rule_format]:
"\<lbrakk>A \<notin> bad; B \<notin> bad; evs \<in> ns_public\<rbrakk>
- \<Longrightarrow> Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace> \<in> parts (spies evs) \<longrightarrow>
- Says A B (Crypt(pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs \<longrightarrow>
- Says B A (Crypt(pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs"
+ \<Longrightarrow> Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace> \<in> parts (spies evs) \<longrightarrow>
+ Says A B (Crypt(pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs \<longrightarrow>
+ Says B A (Crypt(pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs"
apply (erule ns_public.induct)
apply (auto dest: Spy_not_see_NA unique_NA)
done
theorem A_trusts_NS2:
- "\<lbrakk>Says A B (Crypt(pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs;
- Says B' A (Crypt(pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs;
+ "\<lbrakk>Says A B (Crypt(pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs;
+ Says B' A (Crypt(pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs;
A \<notin> bad; B \<notin> bad; evs \<in> ns_public\<rbrakk>
- \<Longrightarrow> Says B A (Crypt(pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs"
+ \<Longrightarrow> Says B A (Crypt(pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs"
by (blast intro: A_trusts_NS2_lemma)
(*If the encrypted message appears then it originated with Alice in NS1*)
lemma B_trusts_NS1 [rule_format]:
"evs \<in> ns_public
- \<Longrightarrow> Crypt (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace> \<in> parts (spies evs) \<longrightarrow>
+ \<Longrightarrow> Crypt (pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace> \<in> parts (spies evs) \<longrightarrow>
Nonce NA \<notin> analz (spies evs) \<longrightarrow>
- Says A B (Crypt (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs"
+ Says A B (Crypt (pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs"
apply (erule ns_public.induct, simp_all)
(*Fake*)
apply (blast intro!: analz_insertI)
@@ -148,8 +148,8 @@
(*Unicity for NS2: nonce NB identifies nonce NA and agent A
[proof closely follows that for unique_NA] *)
lemma unique_NB [dest]:
- "\<lbrakk>Crypt(pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace> \<in> parts(spies evs);
- Crypt(pubK A') \<lbrace>Nonce NA', Nonce NB\<rbrace> \<in> parts(spies evs);
+ "\<lbrakk>Crypt(pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace> \<in> parts(spies evs);
+ Crypt(pubEK A') \<lbrace>Nonce NA', Nonce NB\<rbrace> \<in> parts(spies evs);
Nonce NB \<notin> analz (spies evs); evs \<in> ns_public\<rbrakk>
\<Longrightarrow> A=A' \<and> NA=NA'"
apply (erule rev_mp, erule rev_mp, erule rev_mp)
@@ -161,8 +161,8 @@
(*NB remains secret PROVIDED Alice never responds with round 3*)
theorem Spy_not_see_NB [dest]:
- "\<lbrakk>Says B A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs;
- \<forall>C. Says A C (Crypt (pubK C) (Nonce NB)) \<notin> set evs;
+ "\<lbrakk>Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs;
+ \<forall>C. Says A C (Crypt (pubEK C) (Nonce NB)) \<notin> set evs;
A \<notin> bad; B \<notin> bad; evs \<in> ns_public\<rbrakk>
\<Longrightarrow> Nonce NB \<notin> analz (spies evs)"
apply (erule rev_mp, erule rev_mp)
@@ -177,23 +177,23 @@
lemma B_trusts_NS3_lemma [rule_format]:
"\<lbrakk>A \<notin> bad; B \<notin> bad; evs \<in> ns_public\<rbrakk>
- \<Longrightarrow> Crypt (pubK B) (Nonce NB) \<in> parts (spies evs) \<longrightarrow>
- Says B A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs \<longrightarrow>
- (\<exists>C. Says A C (Crypt (pubK C) (Nonce NB)) \<in> set evs)"
+ \<Longrightarrow> Crypt (pubEK B) (Nonce NB) \<in> parts (spies evs) \<longrightarrow>
+ Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs \<longrightarrow>
+ (\<exists>C. Says A C (Crypt (pubEK C) (Nonce NB)) \<in> set evs)"
apply (erule ns_public.induct, auto)
by (blast intro: no_nonce_NS1_NS2)+
theorem B_trusts_NS3:
- "\<lbrakk>Says B A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs;
- Says A' B (Crypt (pubK B) (Nonce NB)) \<in> set evs;
+ "\<lbrakk>Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs;
+ Says A' B (Crypt (pubEK B) (Nonce NB)) \<in> set evs;
A \<notin> bad; B \<notin> bad; evs \<in> ns_public\<rbrakk>
- \<Longrightarrow> \<exists>C. Says A C (Crypt (pubK C) (Nonce NB)) \<in> set evs"
+ \<Longrightarrow> \<exists>C. Says A C (Crypt (pubEK C) (Nonce NB)) \<in> set evs"
by (blast intro: B_trusts_NS3_lemma)
(*Can we strengthen the secrecy theorem Spy_not_see_NB? NO*)
lemma "\<lbrakk>A \<notin> bad; B \<notin> bad; evs \<in> ns_public\<rbrakk>
- \<Longrightarrow> Says B A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs
+ \<Longrightarrow> Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs
\<longrightarrow> Nonce NB \<notin> analz (spies evs)"
apply (erule ns_public.induct, simp_all, spy_analz)
(*NS1: by freshness*)
@@ -211,14 +211,14 @@
THIS IS THE ATTACK!
Level 8
!!evs. \<lbrakk>A \<notin> bad; B \<notin> bad; evs \<in> ns_public\<rbrakk>
- \<Longrightarrow> Says B A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs \<longrightarrow>
+ \<Longrightarrow> Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs \<longrightarrow>
Nonce NB \<notin> analz (spies evs)
1. !!C B' evs3.
\<lbrakk>A \<notin> bad; B \<notin> bad; evs3 \<in> ns_public
- Says A C (Crypt (pubK C) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs3;
- Says B' A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs3;
+ Says A C (Crypt (pubEK C) \<lbrace>Nonce NA, Agent A\<rbrace>) \<in> set evs3;
+ Says B' A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs3;
C \<in> bad;
- Says B A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs3;
+ Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) \<in> set evs3;
Nonce NB \<notin> analz (spies evs3)\<rbrakk>
\<Longrightarrow> False
*)