--- a/src/HOL/Auth/Yahalom2.ML Wed Mar 10 10:42:40 1999 +0100
+++ b/src/HOL/Auth/Yahalom2.ML Wed Mar 10 10:42:57 1999 +0100
@@ -12,7 +12,7 @@
Proc. Royal Soc. 426 (1989)
*)
-AddEs spies_partsEs;
+AddEs knows_Spy_partsEs;
AddDs [impOfSubs analz_subset_parts];
AddDs [impOfSubs Fake_parts_insert];
@@ -21,58 +21,74 @@
Goal "EX X NB K. EX evs: yahalom. \
\ Says A B {|X, Crypt K (Nonce NB)|} : set evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
-by (rtac (yahalom.Nil RS yahalom.YM1 RS yahalom.YM2 RS yahalom.YM3 RS
- yahalom.YM4) 2);
+by (rtac (yahalom.Nil RS
+ yahalom.YM1 RS yahalom.Reception RS
+ yahalom.YM2 RS yahalom.Reception RS
+ yahalom.YM3 RS yahalom.Reception RS yahalom.YM4) 2);
by possibility_tac;
result();
+Goal "[| Gets B X : set evs; evs : yahalom |] ==> EX A. Says A B X : set evs";
+by (etac rev_mp 1);
+by (etac yahalom.induct 1);
+by Auto_tac;
+qed "Gets_imp_Says";
+
+(*Must be proved separately for each protocol*)
+Goal "[| Gets B X : set evs; evs : yahalom |] ==> X : knows Spy evs";
+by (blast_tac (claset() addSDs [Gets_imp_Says, Says_imp_knows_Spy]) 1);
+qed"Gets_imp_knows_Spy";
+AddDs [Gets_imp_knows_Spy RS parts.Inj];
+
(**** Inductive proofs about yahalom ****)
(** For reasoning about the encrypted portion of messages **)
(*Lets us treat YM4 using a similar argument as for the Fake case.*)
-Goal "Says S A {|NB, Crypt (shrK A) Y, X|} : set evs ==> \
-\ X : analz (spies evs)";
-by (blast_tac (claset() addSDs [Says_imp_spies RS analz.Inj]) 1);
-qed "YM4_analz_spies";
+Goal "[| Gets A {|NB, Crypt (shrK A) Y, X|} : set evs; evs : yahalom |] \
+\ ==> X : analz (knows Spy evs)";
+by (blast_tac (claset() addSDs [Gets_imp_knows_Spy RS analz.Inj]) 1);
+qed "YM4_analz_knows_Spy";
-bind_thm ("YM4_parts_spies",
- YM4_analz_spies RS (impOfSubs analz_subset_parts));
+bind_thm ("YM4_parts_knows_Spy",
+ YM4_analz_knows_Spy RS (impOfSubs analz_subset_parts));
-(*Relates to both YM4 and Oops*)
-Goal "Says S A {|NB, Crypt (shrK A) {|B,K,NA|}, X|} : set evs ==> \
-\ K : parts (spies evs)";
-by (Blast_tac 1);
-qed "YM4_Key_parts_spies";
+(*For Oops*)
+Goal "Says Server A {|NB, Crypt (shrK A) {|B,K,NA|}, X|} : set evs \
+\ ==> K : parts (knows Spy evs)";
+by (blast_tac (claset() addSEs partsEs
+ addSDs [Says_imp_knows_Spy RS parts.Inj]) 1);
+qed "YM4_Key_parts_knows_Spy";
-(*For proving the easier theorems about X ~: parts (spies evs).*)
-fun parts_spies_tac i =
- forward_tac [YM4_Key_parts_spies] (i+6) THEN
- forward_tac [YM4_parts_spies] (i+5) THEN
- prove_simple_subgoals_tac i;
+(*For proving the easier theorems about X ~: parts (knows Spy evs).*)
+fun parts_knows_Spy_tac i =
+ EVERY
+ [forward_tac [YM4_Key_parts_knows_Spy] (i+7),
+ forward_tac [YM4_parts_knows_Spy] (i+6), assume_tac (i+6),
+ prove_simple_subgoals_tac i];
(*Induction for regularity theorems. If induction formula has the form
- X ~: analz (spies evs) --> ... then it shortens the proof by discarding
- needless information about analz (insert X (spies evs)) *)
+ X ~: analz (knows Spy evs) --> ... then it shortens the proof by discarding
+ needless information about analz (insert X (knows Spy evs)) *)
fun parts_induct_tac i =
etac yahalom.induct i
THEN
REPEAT (FIRSTGOAL analz_mono_contra_tac)
- THEN parts_spies_tac i;
+ THEN parts_knows_Spy_tac i;
-(** Theorems of the form X ~: parts (spies evs) imply that NOBODY
+(** Theorems of the form X ~: parts (knows Spy evs) imply that NOBODY
sends messages containing X! **)
(*Spy never sees another agent's shared key! (unless it's bad at start)*)
-Goal "evs : yahalom ==> (Key (shrK A) : parts (spies evs)) = (A : bad)";
+Goal "evs : yahalom ==> (Key (shrK A) : parts (knows Spy evs)) = (A : bad)";
by (parts_induct_tac 1);
by (ALLGOALS Blast_tac);
qed "Spy_see_shrK";
Addsimps [Spy_see_shrK];
-Goal "evs : yahalom ==> (Key (shrK A) : analz (spies evs)) = (A : bad)";
+Goal "evs : yahalom ==> (Key (shrK A) : analz (knows Spy evs)) = (A : bad)";
by Auto_tac;
qed "Spy_analz_shrK";
Addsimps [Spy_analz_shrK];
@@ -83,7 +99,7 @@
(*Nobody can have used non-existent keys! Needed to apply analz_insert_Key*)
Goal "evs : yahalom ==> \
-\ Key K ~: used evs --> K ~: keysFor (parts (spies evs))";
+\ Key K ~: used evs --> K ~: keysFor (parts (knows Spy evs))";
by (parts_induct_tac 1);
(*YM4: Key K is not fresh!*)
by (Blast_tac 3);
@@ -112,18 +128,18 @@
(*For proofs involving analz.*)
-val analz_spies_tac =
- dtac YM4_analz_spies 6 THEN
- forward_tac [Says_Server_message_form] 7 THEN
- assume_tac 7 THEN
- REPEAT ((etac conjE ORELSE' hyp_subst_tac) 7);
+val analz_knows_Spy_tac =
+ dtac YM4_analz_knows_Spy 7 THEN assume_tac 7 THEN
+ forward_tac [Says_Server_message_form] 8 THEN
+ assume_tac 8 THEN
+ REPEAT ((etac conjE ORELSE' hyp_subst_tac) 8);
(****
The following is to prove theorems of the form
- Key K : analz (insert (Key KAB) (spies evs)) ==>
- Key K : analz (spies evs)
+ Key K : analz (insert (Key KAB) (knows Spy evs)) ==>
+ Key K : analz (knows Spy evs)
A more general formula must be proved inductively.
@@ -133,10 +149,10 @@
Goal "evs : yahalom ==> \
\ ALL K KK. KK <= - (range shrK) --> \
-\ (Key K : analz (Key``KK Un (spies evs))) = \
-\ (K : KK | Key K : analz (spies evs))";
+\ (Key K : analz (Key``KK Un (knows Spy evs))) = \
+\ (K : KK | Key K : analz (knows Spy evs))";
by (etac yahalom.induct 1);
-by analz_spies_tac;
+by analz_knows_Spy_tac;
by (REPEAT_FIRST (resolve_tac [allI, impI]));
by (REPEAT_FIRST (rtac analz_image_freshK_lemma));
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss));
@@ -145,8 +161,8 @@
qed_spec_mp "analz_image_freshK";
Goal "[| evs : yahalom; KAB ~: range shrK |] ==> \
-\ Key K : analz (insert (Key KAB) (spies evs)) = \
-\ (K = KAB | Key K : analz (spies evs))";
+\ Key K : analz (insert (Key KAB) (knows Spy evs)) = \
+\ (K = KAB | Key K : analz (knows Spy evs))";
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1);
qed "analz_insert_freshK";
@@ -187,9 +203,9 @@
\ Crypt (shrK B) {|Agent A, Agent B, Key K, nb|}|} \
\ : set evs --> \
\ Notes Spy {|na, nb, Key K|} ~: set evs --> \
-\ Key K ~: analz (spies evs)";
+\ Key K ~: analz (knows Spy evs)";
by (etac yahalom.induct 1);
-by analz_spies_tac;
+by analz_knows_Spy_tac;
by (ALLGOALS
(asm_simp_tac
(simpset() addsimps split_ifs
@@ -211,7 +227,7 @@
\ : set evs; \
\ Notes Spy {|na, nb, Key K|} ~: set evs; \
\ A ~: bad; B ~: bad; evs : yahalom |] \
-\ ==> Key K ~: analz (spies evs)";
+\ ==> Key K ~: analz (knows Spy evs)";
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1);
by (blast_tac (claset() addSEs [lemma]) 1);
qed "Spy_not_see_encrypted_key";
@@ -222,7 +238,7 @@
(*If the encrypted message appears then it originated with the Server.
May now apply Spy_not_see_encrypted_key, subject to its conditions.*)
Goal "[| Crypt (shrK A) {|Agent B, Key K, na|} \
-\ : parts (spies evs); \
+\ : parts (knows Spy evs); \
\ A ~: bad; evs : yahalom |] \
\ ==> EX nb. Says Server A \
\ {|nb, Crypt (shrK A) {|Agent B, Key K, na|}, \
@@ -234,10 +250,10 @@
qed "A_trusts_YM3";
(*The obvious combination of A_trusts_YM3 with Spy_not_see_encrypted_key*)
-Goal "[| Crypt (shrK A) {|Agent B, Key K, na|} : parts (spies evs); \
+Goal "[| Crypt (shrK A) {|Agent B, Key K, na|} : parts (knows Spy evs); \
\ ALL nb. Notes Spy {|na, nb, Key K|} ~: set evs; \
\ A ~: bad; B ~: bad; evs : yahalom |] \
-\ ==> Key K ~: analz (spies evs)";
+\ ==> Key K ~: analz (knows Spy evs)";
by (blast_tac (claset() addSDs [A_trusts_YM3, Spy_not_see_encrypted_key]) 1);
qed "A_gets_good_key";
@@ -247,7 +263,7 @@
(*B knows, by the first part of A's message, that the Server distributed
the key for A and B, and has associated it with NB.*)
Goal "[| Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|} \
-\ : parts (spies evs); \
+\ : parts (knows Spy evs); \
\ B ~: bad; evs : yahalom |] \
\ ==> EX NA. Says Server A \
\ {|Nonce NB, \
@@ -265,7 +281,7 @@
(*What can B deduce from receipt of YM4? Stronger and simpler than Yahalom
because we do not have to show that NB is secret. *)
-Goal "[| Says A' B {|Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}, \
+Goal "[| Gets B {|Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}, \
\ X|} \
\ : set evs; \
\ A ~: bad; B ~: bad; evs : yahalom |] \
@@ -279,12 +295,12 @@
(*The obvious combination of B_trusts_YM4 with Spy_not_see_encrypted_key*)
-Goal "[| Says A' B {|Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}, \
+Goal "[| Gets B {|Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}, \
\ X|} \
\ : set evs; \
\ ALL na. Notes Spy {|na, Nonce NB, Key K|} ~: set evs; \
\ A ~: bad; B ~: bad; evs : yahalom |] \
-\ ==> Key K ~: analz (spies evs)";
+\ ==> Key K ~: analz (knows Spy evs)";
by (blast_tac (claset() addSDs [B_trusts_YM4, Spy_not_see_encrypted_key]) 1);
qed "B_gets_good_key";
@@ -293,7 +309,7 @@
(*** Authenticating B to A ***)
(*The encryption in message YM2 tells us it cannot be faked.*)
-Goal "[| Crypt (shrK B) {|Agent A, Nonce NA|} : parts (spies evs); \
+Goal "[| Crypt (shrK B) {|Agent A, Nonce NA|} : parts (knows Spy evs); \
\ B ~: bad; evs : yahalom \
\ |] ==> EX NB. Says B Server {|Agent B, Nonce NB, \
\ Crypt (shrK B) {|Agent A, Nonce NA|}|} \
@@ -324,9 +340,9 @@
val lemma = result();
(*If A receives YM3 then B has used nonce NA (and therefore is alive)*)
-Goal "[| Says S A {|nb, Crypt (shrK A) {|Agent B, Key K, Nonce NA|}, X|} \
+Goal "[| Gets A {|nb, Crypt (shrK A) {|Agent B, Key K, Nonce NA|}, X|} \
\ : set evs; \
-\ A ~: bad; B ~: bad; evs : yahalom |] \
+\ A ~: bad; B ~: bad; evs : yahalom |] \
\==> EX nb'. Says B Server \
\ {|Agent B, nb', Crypt (shrK B) {|Agent A, Nonce NA|}|} \
\ : set evs";
@@ -338,13 +354,13 @@
(*Assuming the session key is secure, if both certificates are present then
A has said NB. We can't be sure about the rest of A's message, but only
- NB matters for freshness. Note that Key K ~: analz (spies evs) must be
+ NB matters for freshness. Note that Key K ~: analz (knows Spy evs) must be
the FIRST antecedent of the induction formula.*)
Goal "evs : yahalom \
-\ ==> Key K ~: analz (spies evs) --> \
-\ Crypt K (Nonce NB) : parts (spies evs) --> \
+\ ==> Key K ~: analz (knows Spy evs) --> \
+\ Crypt K (Nonce NB) : parts (knows Spy evs) --> \
\ Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|} \
-\ : parts (spies evs) --> \
+\ : parts (knows Spy evs) --> \
\ B ~: bad --> \
\ (EX X. Says A B {|X, Crypt K (Nonce NB)|} : set evs)";
by (parts_induct_tac 1);
@@ -356,6 +372,7 @@
by (asm_simp_tac (simpset() addsimps [ex_disj_distrib]) 1);
(*yes: delete a useless induction hypothesis; apply unicity of session keys*)
by (thin_tac "?P-->?Q" 1);
+by (forward_tac [Gets_imp_Says] 1 THEN assume_tac 1);
by (not_bad_tac "Aa" 1);
by (blast_tac (claset() addSDs [A_trusts_YM3, B_trusts_YM4_shrK]
addDs [unique_session_keys]) 1);
@@ -365,12 +382,12 @@
(*If B receives YM4 then A has used nonce NB (and therefore is alive).
Moreover, A associates K with NB (thus is talking about the same run).
Other premises guarantee secrecy of K.*)
-Goal "[| Says A' B {|Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}, \
+Goal "[| Gets B {|Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}, \
\ Crypt K (Nonce NB)|} : set evs; \
\ (ALL NA. Notes Spy {|Nonce NA, Nonce NB, Key K|} ~: set evs); \
\ A ~: bad; B ~: bad; evs : yahalom |] \
\ ==> EX X. Says A B {|X, Crypt K (Nonce NB)|} : set evs";
-by (subgoal_tac "Key K ~: analz (spies evs)" 1);
+by (subgoal_tac "Key K ~: analz (knows Spy evs)" 1);
by (blast_tac (claset() addIs [Auth_A_to_B_lemma]) 1);
by (blast_tac (claset() addDs [Spy_not_see_encrypted_key,
B_trusts_YM4_shrK]) 1);