--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Auth/Public_lemmas.ML Tue Feb 13 16:02:53 2001 +0100
@@ -0,0 +1,180 @@
+(* Title: HOL/Auth/Public_lemmas
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1996 University of Cambridge
+
+Theory of Public Keys (common to all symmetric-key protocols)
+
+Server keys; initial states of agents; new nonces and keys; function "sees"
+*)
+
+val inj_pubK = thm "inj_pubK";
+val priK_neq_pubK = thm "priK_neq_pubK";
+
+(*** Basic properties of pubK & priK ***)
+
+AddIffs [inj_pubK RS inj_eq];
+
+Goal "(priK A = priK B) = (A=B)";
+by Safe_tac;
+by (dres_inst_tac [("f","invKey")] arg_cong 1);
+by (Full_simp_tac 1);
+qed "priK_inj_eq";
+
+AddIffs [priK_inj_eq];
+AddIffs [priK_neq_pubK, priK_neq_pubK RS not_sym];
+
+Goalw [isSymKey_def] "~ isSymKey (pubK A)";
+by (Simp_tac 1);
+qed "not_isSymKey_pubK";
+
+Goalw [isSymKey_def] "~ isSymKey (priK A)";
+by (Simp_tac 1);
+qed "not_isSymKey_priK";
+
+AddIffs [not_isSymKey_pubK, not_isSymKey_priK];
+
+
+(** "Image" equations that hold for injective functions **)
+
+Goal "(invKey x : invKey`A) = (x:A)";
+by Auto_tac;
+qed "invKey_image_eq";
+
+(*holds because invKey is injective*)
+Goal "(pubK x : pubK`A) = (x:A)";
+by Auto_tac;
+qed "pubK_image_eq";
+
+Goal "(priK x ~: pubK`A)";
+by Auto_tac;
+qed "priK_pubK_image_eq";
+Addsimps [invKey_image_eq, pubK_image_eq, priK_pubK_image_eq];
+
+
+(** Rewrites should not refer to initState(Friend i)
+ -- not in normal form! **)
+
+Goalw [keysFor_def] "keysFor (parts (initState C)) = {}";
+by (induct_tac "C" 1);
+by (auto_tac (claset() addIs [range_eqI], simpset()));
+qed "keysFor_parts_initState";
+Addsimps [keysFor_parts_initState];
+
+
+(*** Function "spies" ***)
+
+(*Agents see their own private keys!*)
+Goal "Key (priK A) : initState A";
+by (induct_tac "A" 1);
+by Auto_tac;
+qed "priK_in_initState";
+AddIffs [priK_in_initState];
+
+(*All public keys are visible*)
+Goal "Key (pubK A) : spies evs";
+by (induct_tac "evs" 1);
+by (ALLGOALS (asm_simp_tac
+ (simpset() addsimps [imageI, knows_Cons]
+ addsplits [expand_event_case])));
+qed_spec_mp "spies_pubK";
+
+(*Spy sees private keys of bad agents!*)
+Goal "A: bad ==> Key (priK A) : spies evs";
+by (induct_tac "evs" 1);
+by (ALLGOALS (asm_simp_tac
+ (simpset() addsimps [imageI, knows_Cons]
+ addsplits [expand_event_case])));
+qed "Spy_spies_bad";
+
+AddIffs [spies_pubK, spies_pubK RS analz.Inj];
+AddSIs [Spy_spies_bad];
+
+
+(*For not_bad_tac*)
+Goal "[| Crypt (pubK A) X : analz (spies evs); A: bad |] \
+\ ==> X : analz (spies evs)";
+by (blast_tac (claset() addSDs [analz.Decrypt]) 1);
+qed "Crypt_Spy_analz_bad";
+
+(*Prove that the agent is uncompromised by the confidentiality of
+ a component of a message she's said.*)
+fun not_bad_tac s =
+ case_tac ("(" ^ s ^ ") : bad") THEN'
+ SELECT_GOAL
+ (REPEAT_DETERM (dtac (Says_imp_spies RS analz.Inj) 1) THEN
+ REPEAT_DETERM (etac MPair_analz 1) THEN
+ THEN_BEST_FIRST
+ (dres_inst_tac [("A", s)] Crypt_Spy_analz_bad 1 THEN assume_tac 1)
+ (has_fewer_prems 1, size_of_thm)
+ Safe_tac);
+
+
+(*** Fresh nonces ***)
+
+Goal "Nonce N ~: parts (initState B)";
+by (induct_tac "B" 1);
+by Auto_tac;
+qed "Nonce_notin_initState";
+AddIffs [Nonce_notin_initState];
+
+Goal "Nonce N ~: used []";
+by (simp_tac (simpset() addsimps [used_Nil]) 1);
+qed "Nonce_notin_used_empty";
+Addsimps [Nonce_notin_used_empty];
+
+
+(*** Supply fresh nonces for possibility theorems. ***)
+
+(*In any trace, there is an upper bound N on the greatest nonce in use.*)
+Goal "EX N. ALL n. N<=n --> Nonce n ~: used evs";
+by (induct_tac "evs" 1);
+by (res_inst_tac [("x","0")] exI 1);
+by (ALLGOALS (asm_simp_tac
+ (simpset() addsimps [used_Cons]
+ addsplits [expand_event_case])));
+by Safe_tac;
+by (ALLGOALS (rtac (msg_Nonce_supply RS exE)));
+by (ALLGOALS (blast_tac (claset() addSEs [add_leE])));
+val lemma = result();
+
+Goal "EX N. Nonce N ~: used evs";
+by (rtac (lemma RS exE) 1);
+by (Blast_tac 1);
+qed "Nonce_supply1";
+
+Goal "Nonce (@ N. Nonce N ~: used evs) ~: used evs";
+by (rtac (lemma RS exE) 1);
+by (rtac someI 1);
+by (Fast_tac 1);
+qed "Nonce_supply";
+
+(*Tactic for possibility theorems*)
+fun possibility_tac st = st |>
+ REPEAT (*omit used_Says so that Nonces start from different traces!*)
+ (ALLGOALS (simp_tac (simpset() delsimps [used_Says]))
+ THEN
+ REPEAT_FIRST (eq_assume_tac ORELSE'
+ resolve_tac [refl, conjI, Nonce_supply]));
+
+
+(*** Specialized rewriting for the analz_image_... theorems ***)
+
+Goal "insert (Key K) H = Key ` {K} Un H";
+by (Blast_tac 1);
+qed "insert_Key_singleton";
+
+Goal "insert (Key K) (Key`KK Un C) = Key ` (insert K KK) Un C";
+by (Blast_tac 1);
+qed "insert_Key_image";
+
+(*Reverse the normal simplification of "image" to build up (not break down)
+ the set of keys. Based on analz_image_freshK_ss, but simpler.*)
+val analz_image_keys_ss =
+ simpset() delsimps [image_insert, image_Un]
+ delsimps [imp_disjL] (*reduces blow-up*)
+ addsimps [image_insert RS sym, image_Un RS sym,
+ rangeI,
+ insert_Key_singleton,
+ insert_Key_image, Un_assoc RS sym];
+