--- a/src/HOL/Auth/Recur.ML Thu Dec 19 11:54:19 1996 +0100
+++ b/src/HOL/Auth/Recur.ML Thu Dec 19 11:58:39 1996 +0100
@@ -27,8 +27,8 @@
\ Agent Server|} \
\ : set_of_list evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
-by (rtac (recur.Nil RS recur.NA1 RS
- (respond.One RSN (4,recur.NA3))) 2);
+by (rtac (recur.Nil RS recur.RA1 RS
+ (respond.One RSN (4,recur.RA3))) 2);
by (ALLGOALS (simp_tac (!simpset setsolver safe_solver)));
by (REPEAT_FIRST (eq_assume_tac ORELSE' resolve_tac [refl, conjI]));
result();
@@ -42,9 +42,9 @@
\ Agent Server|} \
\ : set_of_list evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
-by (rtac (recur.Nil RS recur.NA1 RS recur.NA2 RS
- (respond.One RS respond.Cons RSN (4,recur.NA3)) RS
- recur.NA4) 2);
+by (rtac (recur.Nil RS recur.RA1 RS recur.RA2 RS
+ (respond.One RS respond.Cons RSN (4,recur.RA3)) RS
+ recur.RA4) 2);
by (REPEAT
(REPEAT_FIRST (eq_assume_tac ORELSE' resolve_tac [refl, conjI])
THEN
@@ -60,9 +60,9 @@
\ Agent Server|} \
\ : set_of_list evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
-by (rtac (recur.Nil RS recur.NA1 RS recur.NA2 RS recur.NA2 RS
+by (rtac (recur.Nil RS recur.RA1 RS recur.RA2 RS recur.RA2 RS
(respond.One RS respond.Cons RS respond.Cons RSN
- (4,recur.NA3)) RS recur.NA4 RS recur.NA4) 2);
+ (4,recur.RA3)) RS recur.RA4 RS recur.RA4) 2);
by (REPEAT (*SLOW: 37 seconds*)
(REPEAT_FIRST (eq_assume_tac ORELSE' resolve_tac [refl, conjI])
THEN
@@ -104,30 +104,30 @@
(** For reasoning about the encrypted portion of messages **)
-val NA2_analz_sees_Spy = Says_imp_sees_Spy RS analz.Inj |> standard;
+val RA2_analz_sees_Spy = Says_imp_sees_Spy RS analz.Inj |> standard;
goal thy "!!evs. Says C' B {|Agent B, X, Agent B, X', RA|} : set_of_list evs \
\ ==> RA : analz (sees lost Spy evs)";
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1);
-qed "NA4_analz_sees_Spy";
+qed "RA4_analz_sees_Spy";
-(*NA2_analz... and NA4_analz... let us treat those cases using the same
+(*RA2_analz... and RA4_analz... let us treat those cases using the same
argument as for the Fake case. This is possible for most, but not all,
- proofs: Fake does not invent new nonces (as in NA2), and of course Fake
+ proofs: Fake does not invent new nonces (as in RA2), and of course Fake
messages originate from the Spy. *)
-bind_thm ("NA2_parts_sees_Spy",
- NA2_analz_sees_Spy RS (impOfSubs analz_subset_parts));
-bind_thm ("NA4_parts_sees_Spy",
- NA4_analz_sees_Spy RS (impOfSubs analz_subset_parts));
+bind_thm ("RA2_parts_sees_Spy",
+ RA2_analz_sees_Spy RS (impOfSubs analz_subset_parts));
+bind_thm ("RA4_parts_sees_Spy",
+ RA4_analz_sees_Spy RS (impOfSubs analz_subset_parts));
(*We instantiate the variable to "lost". Leaving it as a Var makes proofs
harder to complete, since simplification does less for us.*)
val parts_Fake_tac =
let val tac = forw_inst_tac [("lost","lost")]
- in tac NA2_parts_sees_Spy 4 THEN
+ in tac RA2_parts_sees_Spy 4 THEN
forward_tac [respond_imp_responses] 5 THEN
- tac NA4_parts_sees_Spy 6
+ tac RA4_parts_sees_Spy 6
end;
(*For proving the easier theorems about X ~: parts (sees lost Spy evs) *)
@@ -159,10 +159,10 @@
"!!evs. evs : recur lost \
\ ==> (Key (shrK A) : parts (sees lost Spy evs)) = (A : lost)";
by (parts_induct_tac 1);
-(*NA2*)
+(*RA2*)
by (best_tac (!claset addSEs partsEs addSDs [parts_cut]
addss (!simpset)) 1);
-(*NA3*)
+(*RA3*)
by (fast_tac (!claset addDs [Key_in_parts_respond]
addss (!simpset addsimps [parts_insert_sees])) 1);
qed "Spy_see_shrK";
@@ -191,7 +191,7 @@
\ length evs <= i --> \
\ Key (newK2(i,j)) ~: parts (sees lost Spy evs)";
by (parts_induct_tac 1);
-(*NA2*)
+(*RA2*)
by (best_tac (!claset addSEs partsEs
addSDs [parts_cut]
addDs [Suc_leD]
@@ -201,9 +201,9 @@
impOfSubs parts_insert_subset_Un,
Suc_leD]
addss (!simpset)) 1);
-(*For NA3*)
+(*For RA3*)
by (asm_simp_tac (!simpset addsimps [parts_insert_sees]) 2);
-(*NA1-NA4*)
+(*RA1-RA4*)
by (REPEAT (best_tac (!claset addDs [Key_in_parts_respond, Suc_leD]
addss (!simpset)) 1));
qed_spec_mp "new_keys_not_seen";
@@ -235,7 +235,7 @@
goal thy "!!i. evs : recur lost ==> \
\ length evs <= i --> Nonce(newN i) ~: parts (sees lost Spy evs)";
by (parts_induct_tac 1);
-(*For NA3*)
+(*For RA3*)
by (asm_simp_tac (!simpset addsimps [parts_insert_sees]) 4);
by (deepen_tac (!claset addSDs [Says_imp_sees_Spy RS parts.Inj]
addDs [Nonce_in_parts_respond, parts_cut, Suc_leD]
@@ -245,7 +245,7 @@
impOfSubs parts_insert_subset_Un,
Suc_leD]
addss (!simpset)) 1);
-(*NA1, NA2, NA4*)
+(*RA1, RA2, RA4*)
by (REPEAT_FIRST (fast_tac (!claset
addSEs partsEs
addEs [leD RS notE]
@@ -279,13 +279,13 @@
goal thy "!!i. evs : recur lost ==> \
\ length evs <= i --> newK2(i,j) ~: keysFor (parts (sees lost Spy evs))";
by (parts_induct_tac 1);
-(*NA3*)
+(*RA3*)
by (fast_tac (!claset addDs [Key_in_keysFor_parts_respond, Suc_leD]
addss (!simpset addsimps [parts_insert_sees])) 4);
-(*NA2*)
+(*RA2*)
by (fast_tac (!claset addSEs partsEs
addDs [Suc_leD] addss (!simpset)) 3);
-(*Fake, NA1, NA4*)
+(*Fake, RA1, RA4*)
by (REPEAT
(best_tac
(!claset addDs [impOfSubs (analz_subset_parts RS keysFor_mono),
@@ -308,14 +308,14 @@
(*For proofs involving analz. We again instantiate the variable to "lost".*)
val analz_Fake_tac =
- dres_inst_tac [("lost","lost")] NA2_analz_sees_Spy 4 THEN
+ dres_inst_tac [("lost","lost")] RA2_analz_sees_Spy 4 THEN
forward_tac [respond_imp_responses] 5 THEN
- dres_inst_tac [("lost","lost")] NA4_analz_sees_Spy 6;
+ dres_inst_tac [("lost","lost")] RA4_analz_sees_Spy 6;
(** Session keys are not used to encrypt other session keys **)
-(*Version for "responses" relation. Handles case NA3 in the theorem below.
+(*Version for "responses" relation. Handles case RA3 in the theorem below.
Note that it holds for *any* set H (not just "sees lost Spy evs")
satisfying the inductive hypothesis.*)
goal thy
@@ -340,12 +340,12 @@
\ (K : newK``I | Key K : analz (sees lost Spy evs))";
by (etac recur.induct 1);
by analz_Fake_tac;
-be ssubst 4; (*NA2: DELETE needless definition of PA!*)
+be ssubst 4; (*RA2: DELETE needless definition of PA!*)
by (REPEAT_FIRST (ares_tac [allI, analz_image_newK_lemma]));
by (ALLGOALS (asm_simp_tac (!simpset addsimps [resp_analz_image_newK_lemma])));
(*Base*)
by (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1);
-(*NA4, NA2, Fake*)
+(*RA4, RA2, Fake*)
by (REPEAT (spy_analz_tac 1));
val raw_analz_image_newK = result();
qed_spec_mp "analz_image_newK";
@@ -381,12 +381,12 @@
\ (Nonce (newN i) : parts {X} --> \
\ Hash X ~: parts (sees lost Spy evs))";
be recur.induct 1;
-be ssubst 4; (*NA2: DELETE needless definition of PA!*)
+be ssubst 4; (*RA2: DELETE needless definition of PA!*)
by parts_Fake_tac;
-(*NA3 requires a further induction*)
+(*RA3 requires a further induction*)
be responses.induct 5;
by (ALLGOALS Asm_simp_tac);
-(*NA2*)
+(*RA2*)
by (best_tac (!claset addDs [Suc_leD, parts_cut]
addEs [leD RS notE,
new_nonces_not_seen RSN(2,rev_notE)]
@@ -405,7 +405,7 @@
(** The Nonce NA uniquely identifies A's message.
- This theorem applies to rounds NA1 and NA2!
+ This theorem applies to rounds RA1 and RA2!
**)
goal thy
@@ -414,15 +414,15 @@
\ Hash {|Key(shrK A), Agent A, Agent B, Nonce NA, P|} \
\ : parts (sees lost Spy evs) --> B=B' & P=P'";
be recur.induct 1;
-be ssubst 4; (*NA2: DELETE needless definition of PA!*)
-(*For better simplification of NA2*)
+be ssubst 4; (*RA2: DELETE needless definition of PA!*)
+(*For better simplification of RA2*)
by (res_inst_tac [("x1","XA")] (insert_commute RS ssubst) 4);
by parts_Fake_tac;
-(*NA3 requires a further induction*)
+(*RA3 requires a further induction*)
be responses.induct 5;
by (ALLGOALS Asm_simp_tac);
by (step_tac (!claset addSEs partsEs) 1);
-(*NA3: inductive case*)
+(*RA3: inductive case*)
by (best_tac (!claset addss (!simpset)) 5);
(*Fake*)
by (best_tac (!claset addSIs [exI]
@@ -433,13 +433,13 @@
by (fast_tac (!claset addss (!simpset)) 1);
by (ALLGOALS (simp_tac (!simpset addsimps [all_conj_distrib])));
-(*NA1: creation of new Nonce. Move assertion into global context*)
+(*RA1: creation of new Nonce. Move assertion into global context*)
by (expand_case_tac "NA = ?y" 1);
by (best_tac (!claset addSIs [exI]
addEs [Hash_new_nonces_not_seen]
addss (!simpset)) 1);
by (best_tac (!claset addss (!simpset)) 1);
-(*NA2: creation of new Nonce*)
+(*RA2: creation of new Nonce*)
by (expand_case_tac "NA = ?y" 1);
by (best_tac (!claset addSIs [exI]
addDs [parts_cut]
@@ -510,7 +510,7 @@
(*The Server does not send such messages. This theorem lets us avoid
- assuming B~=Server in NA4.*)
+ assuming B~=Server in RA4.*)
goal thy
"!!evs. evs : recur lost \
\ ==> ALL C X Y P. Says Server C {|X, Agent Server, Agent C, Y, P|} \
@@ -557,7 +557,7 @@
qed "unique_session_keys";
-(** Crucial secrecy property: Spy does not see the keys sent in msg NA3
+(** Crucial secrecy property: Spy does not see the keys sent in msg RA3
Does not in itself guarantee security: an attack could violate
the premises, e.g. by having A=Spy **)
@@ -614,24 +614,24 @@
\ Key K ~: analz (sees lost Spy evs)";
by (etac recur.induct 1);
by analz_Fake_tac;
-be ssubst 4; (*NA2: DELETE needless definition of PA!*)
+be ssubst 4; (*RA2: DELETE needless definition of PA!*)
by (ALLGOALS
(asm_simp_tac
(!simpset addsimps [not_parts_not_analz, analz_insert_Key_newK]
setloop split_tac [expand_if])));
-(*NA4*)
+(*RA4*)
by (spy_analz_tac 4);
(*Fake*)
by (spy_analz_tac 1);
by (step_tac (!claset delrules [impCE]) 1);
-(*NA2*)
+(*RA2*)
by (spy_analz_tac 1);
-(*NA3, case 2: K is an old key*)
+(*RA3, case 2: K is an old key*)
by (fast_tac (!claset addSDs [resp_analz_insert]
addSEs partsEs
addDs [Key_in_parts_respond]
addEs [Says_imp_old_keys RS less_irrefl]) 2);
-(*NA3, case 1: use lemma previously proved by induction*)
+(*RA3, case 1: use lemma previously proved by induction*)
by (fast_tac (!claset addSEs [respond_Spy_not_see_encrypted_key RSN
(2,rev_notE)]) 1);
bind_thm ("Spy_not_see_encrypted_key", result() RS mp RSN (2, rev_mp));
@@ -652,7 +652,7 @@
(**** Authenticity properties for Agents ****)
-(*Only NA1 or NA2 can have caused such a part of a message to appear.*)
+(*Only RA1 or RA2 can have caused such a part of a message to appear.*)
goal thy
"!!evs. [| Hash {|Key(shrK A), Agent A, Agent B, NA, P|} \
\ : parts (sees lost Spy evs); \
@@ -662,9 +662,9 @@
\ : set_of_list evs";
be rev_mp 1;
by (parts_induct_tac 1);
-(*NA3*)
+(*RA3*)
by (fast_tac (!claset addSDs [Hash_in_parts_respond]) 2);
-(*NA2*)
+(*RA2*)
by ((REPEAT o CHANGED) (*Push in XA*)
(res_inst_tac [("x1","XA")] (insert_commute RS ssubst) 1));
by (best_tac (!claset addSEs partsEs
@@ -692,22 +692,22 @@
in a run, then it originated with the Server!*)
goal thy
"!!evs. [| A ~: lost; A ~= Spy; evs : recur lost |] \
-\ ==> Crypt (shrK A) {|Key K, Agent B, NA|} : parts (sees lost Spy evs) \
+\ ==> Crypt (shrK A) {|Key K, Agent A', NA|} : parts (sees lost Spy evs) \
\ --> Says A B {|Hash{|Key(shrK A), Agent A, Agent B, NA, P|}, \
\ Agent A, Agent B, NA, P|} \
\ : set_of_list evs \
\ --> (EX C RC. Says Server C RC : set_of_list evs & \
-\ Crypt (shrK A) {|Key K, Agent B, NA|} : parts {RC})";
+\ Crypt (shrK A) {|Key K, Agent A', NA|} : parts {RC})";
by (parts_induct_tac 1);
-(*NA4*)
+(*RA4*)
by (best_tac (!claset addSEs [MPair_parts]
addSDs [Hash_auth_sender]
addSIs [disjI2]) 4);
-(*NA1: it cannot be a new Nonce, contradiction.*)
+(*RA1: it cannot be a new Nonce, contradiction.*)
by (fast_tac (!claset delrules [impCE]
addSEs [nonce_not_seen_now, MPair_parts]
addDs [parts.Body]) 1);
-(*NA2: it cannot be a new Nonce, contradiction.*)
+(*RA2: it cannot be a new Nonce, contradiction.*)
by ((REPEAT o CHANGED) (*Push in XA*)
(res_inst_tac [("x1","XA")] (insert_commute RS ssubst) 1));
by (deepen_tac (!claset delrules [impCE]
@@ -715,7 +715,7 @@
addSEs [MPair_parts]
addDs [parts_cut, parts.Body]
addss (!simpset)) 0 1);
-(*NA3*) (** LEVEL 5 **)
+(*RA3*) (** LEVEL 5 **)
by (REPEAT (safe_step_tac (!claset addSEs [responses_no_Hash_Server]
delrules [impCE]) 1));
by (full_simp_tac (!simpset addsimps [parts_insert_sees]) 1);
@@ -727,13 +727,13 @@
then the key really did come from the Server!*)
goal thy
"!!evs. [| Says B' A RA : set_of_list evs; \
-\ Crypt (shrK A) {|Key K, Agent B, NA|} : parts {RA}; \
+\ Crypt (shrK A) {|Key K, Agent A', NA|} : parts {RA}; \
\ Says A B {|Hash{|Key(shrK A), Agent A, Agent B, NA, P|}, \
\ Agent A, Agent B, NA, P|} \
\ : set_of_list evs; \
\ A ~: lost; A ~= Spy; evs : recur lost |] \
\ ==> EX C RC. Says Server C RC : set_of_list evs & \
-\ Crypt (shrK A) {|Key K, Agent B, NA|} : parts {RC}";
+\ Crypt (shrK A) {|Key K, Agent A', NA|} : parts {RC}";
by (best_tac (!claset addSIs [Crypt_imp_Server_msg]
addDs [Says_imp_sees_Spy RS parts.Inj RSN (2,parts_cut)]
addss (!simpset)) 1);
@@ -744,12 +744,12 @@
then the only other agent who knows the key is B.*)
goal thy
"!!evs. [| Says B' A RA : set_of_list evs; \
-\ Crypt (shrK A) {|Key K, Agent B, NA|} : parts {RA}; \
+\ Crypt (shrK A) {|Key K, Agent A', NA|} : parts {RA}; \
\ Says A B {|Hash{|Key(shrK A), Agent A, Agent B, NA, P|}, \
\ Agent A, Agent B, NA, P|} \
\ : set_of_list evs; \
-\ C ~: {A,B,Server}; \
-\ A ~: lost; B ~: lost; A ~= Spy; evs : recur lost |] \
+\ C ~: {A,A',Server}; \
+\ A ~: lost; A' ~: lost; A ~= Spy; evs : recur lost |] \
\ ==> Key K ~: analz (sees lost C evs)";
by (dtac Agent_trust 1 THEN REPEAT_FIRST assume_tac);
by (fast_tac (!claset addSEs [Agent_not_see_encrypted_key RSN(2,rev_notE)]) 1);