--- a/src/HOL/Auth/NS_Public_Bad.ML Thu Jul 02 17:27:35 1998 +0200
+++ b/src/HOL/Auth/NS_Public_Bad.ML Thu Jul 02 17:48:11 1998 +0200
@@ -23,9 +23,8 @@
AddIffs [Spy_in_bad];
(*A "possibility property": there are traces that reach the end*)
-Goal
- "!!A B. A ~= B ==> EX NB. EX evs: ns_public. \
-\ Says A B (Crypt (pubK B) (Nonce NB)) : set evs";
+Goal "A ~= B ==> EX NB. EX evs: ns_public. \
+\ Says A B (Crypt (pubK B) (Nonce NB)) : set evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
by (rtac (ns_public.Nil RS ns_public.NS1 RS ns_public.NS2 RS ns_public.NS3) 2);
by possibility_tac;
@@ -35,7 +34,7 @@
(**** Inductive proofs about ns_public ****)
(*Nobody sends themselves messages*)
-Goal "!!evs. evs : ns_public ==> ALL A X. Says A A X ~: set evs";
+Goal "evs : ns_public ==> ALL A X. Says A A X ~: set evs";
by (etac ns_public.induct 1);
by Auto_tac;
qed_spec_mp "not_Says_to_self";
@@ -58,15 +57,13 @@
sends messages containing X! **)
(*Spy never sees another agent's private key! (unless it's bad at start)*)
-Goal
- "!!A. evs: ns_public ==> (Key (priK A) : parts (spies evs)) = (A : bad)";
+Goal "evs: ns_public ==> (Key (priK A) : parts (spies evs)) = (A : bad)";
by (parts_induct_tac 1);
by (Blast_tac 1);
qed "Spy_see_priK";
Addsimps [Spy_see_priK];
-Goal
- "!!A. evs: ns_public ==> (Key (priK A) : analz (spies evs)) = (A : bad)";
+Goal "evs: ns_public ==> (Key (priK A) : analz (spies evs)) = (A : bad)";
by Auto_tac;
qed "Spy_analz_priK";
Addsimps [Spy_analz_priK];
@@ -79,9 +76,8 @@
(*It is impossible to re-use a nonce in both NS1 and NS2, provided the nonce
is secret. (Honest users generate fresh nonces.)*)
-Goal
- "!!evs. [| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \
-\ Nonce NA ~: analz (spies evs); evs : ns_public |] \
+Goal "[| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \
+\ Nonce NA ~: analz (spies evs); evs : ns_public |] \
\ ==> Crypt (pubK C) {|NA', Nonce NA|} ~: parts (spies evs)";
by (etac rev_mp 1);
by (etac rev_mp 1);
@@ -94,11 +90,10 @@
(*Unicity for NS1: nonce NA identifies agents A and B*)
-Goal
- "!!evs. [| Nonce NA ~: analz (spies evs); evs : ns_public |] \
+Goal "[| Nonce NA ~: analz (spies evs); evs : ns_public |] \
\ ==> EX A' B'. ALL A B. \
-\ Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs) --> \
-\ A=A' & B=B'";
+\ Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs) --> \
+\ A=A' & B=B'";
by (etac rev_mp 1);
by (parts_induct_tac 1);
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib])));
@@ -109,12 +104,11 @@
by (Blast_tac 1);
val lemma = result();
-Goal
- "!!evs. [| Crypt(pubK B) {|Nonce NA, Agent A|} : parts(spies evs); \
-\ Crypt(pubK B') {|Nonce NA, Agent A'|} : parts(spies evs); \
-\ Nonce NA ~: analz (spies evs); \
-\ evs : ns_public |] \
-\ ==> A=A' & B=B'";
+Goal "[| Crypt(pubK B) {|Nonce NA, Agent A|} : parts(spies evs); \
+\ Crypt(pubK B') {|Nonce NA, Agent A'|} : parts(spies evs); \
+\ Nonce NA ~: analz (spies evs); \
+\ evs : ns_public |] \
+\ ==> A=A' & B=B'";
by (prove_unique_tac lemma 1);
qed "unique_NA";
@@ -126,10 +120,9 @@
(*Secrecy: Spy does not see the nonce sent in msg NS1 if A and B are secure*)
-Goal
- "!!evs. [| Says A B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set evs; \
-\ A ~: bad; B ~: bad; evs : ns_public |] \
-\ ==> Nonce NA ~: analz (spies evs)";
+Goal "[| Says A B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set evs; \
+\ A ~: bad; B ~: bad; evs : ns_public |] \
+\ ==> Nonce NA ~: analz (spies evs)";
by (etac rev_mp 1);
by (analz_induct_tac 1);
(*NS3*)
@@ -145,11 +138,10 @@
(*Authentication for A: if she receives message 2 and has used NA
to start a run, then B has sent message 2.*)
-Goal
- "!!evs. [| Says A B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set evs; \
-\ Says B' A (Crypt(pubK A) {|Nonce NA, Nonce NB|}): set evs; \
-\ A ~: bad; B ~: bad; evs : ns_public |] \
-\ ==> Says B A (Crypt(pubK A) {|Nonce NA, Nonce NB|}): set evs";
+Goal "[| Says A B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set evs; \
+\ Says B' A (Crypt(pubK A) {|Nonce NA, Nonce NB|}): set evs; \
+\ A ~: bad; B ~: bad; evs : ns_public |] \
+\ ==> Says B A (Crypt(pubK A) {|Nonce NA, Nonce NB|}): set evs";
by (etac rev_mp 1);
(*prepare induction over Crypt (pubK A) {|NA,NB|} : parts H*)
by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1);
@@ -166,11 +158,10 @@
(*If the encrypted message appears then it originated with Alice in NS1*)
-Goal
- "!!evs. [| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \
-\ Nonce NA ~: analz (spies evs); \
-\ evs : ns_public |] \
-\ ==> Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set evs";
+Goal "[| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \
+\ Nonce NA ~: analz (spies evs); \
+\ evs : ns_public |] \
+\==> Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set evs";
by (etac rev_mp 1);
by (etac rev_mp 1);
by (parts_induct_tac 1);
@@ -183,11 +174,10 @@
(*Unicity for NS2: nonce NB identifies nonce NA and agent A
[proof closely follows that for unique_NA] *)
-Goal
- "!!evs. [| Nonce NB ~: analz (spies evs); evs : ns_public |] \
+Goal "[| Nonce NB ~: analz (spies evs); evs : ns_public |] \
\ ==> EX A' NA'. ALL A NA. \
-\ Crypt (pubK A) {|Nonce NA, Nonce NB|} : parts (spies evs) \
-\ --> A=A' & NA=NA'";
+\ Crypt (pubK A) {|Nonce NA, Nonce NB|} : parts (spies evs) \
+\ --> A=A' & NA=NA'";
by (etac rev_mp 1);
by (parts_induct_tac 1);
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib])));
@@ -197,22 +187,20 @@
by (Blast_tac 1);
val lemma = result();
-Goal
- "!!evs. [| Crypt(pubK A) {|Nonce NA, Nonce NB|} : parts(spies evs); \
-\ Crypt(pubK A'){|Nonce NA', Nonce NB|} : parts(spies evs); \
-\ Nonce NB ~: analz (spies evs); \
-\ evs : ns_public |] \
-\ ==> A=A' & NA=NA'";
+Goal "[| Crypt(pubK A) {|Nonce NA, Nonce NB|} : parts(spies evs); \
+\ Crypt(pubK A'){|Nonce NA', Nonce NB|} : parts(spies evs); \
+\ Nonce NB ~: analz (spies evs); \
+\ evs : ns_public |] \
+\ ==> A=A' & NA=NA'";
by (prove_unique_tac lemma 1);
qed "unique_NB";
(*NB remains secret PROVIDED Alice never responds with round 3*)
-Goal
- "!!evs.[| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs; \
-\ ALL C. Says A C (Crypt (pubK C) (Nonce NB)) ~: set evs; \
-\ A ~: bad; B ~: bad; evs : ns_public |] \
-\ ==> Nonce NB ~: analz (spies evs)";
+Goal "[| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs; \
+\ ALL C. Says A C (Crypt (pubK C) (Nonce NB)) ~: set evs; \
+\ A ~: bad; B ~: bad; evs : ns_public |] \
+\ ==> Nonce NB ~: analz (spies evs)";
by (etac rev_mp 1);
by (etac rev_mp 1);
by (analz_induct_tac 1);
@@ -232,11 +220,10 @@
(*Authentication for B: if he receives message 3 and has used NB
in message 2, then A has sent message 3--to somebody....*)
-Goal
- "!!evs. [| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs; \
-\ Says A' B (Crypt (pubK B) (Nonce NB)): set evs; \
-\ A ~: bad; B ~: bad; evs : ns_public |] \
-\ ==> EX C. Says A C (Crypt (pubK C) (Nonce NB)) : set evs";
+Goal "[| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs; \
+\ Says A' B (Crypt (pubK B) (Nonce NB)): set evs; \
+\ A ~: bad; B ~: bad; evs : ns_public |] \
+\ ==> EX C. Says A C (Crypt (pubK C) (Nonce NB)) : set evs";
by (etac rev_mp 1);
(*prepare induction over Crypt (pubK B) NB : parts H*)
by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1);
@@ -254,10 +241,9 @@
(*Can we strengthen the secrecy theorem? NO*)
-Goal
- "!!evs. [| A ~: bad; B ~: bad; evs : ns_public |] \
+Goal "[| A ~: bad; B ~: bad; evs : ns_public |] \
\ ==> Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs \
-\ --> Nonce NB ~: analz (spies evs)";
+\ --> Nonce NB ~: analz (spies evs)";
by (analz_induct_tac 1);
by (ALLGOALS Clarify_tac);
(*NS2: by freshness and unicity of NB*)