author | paulson |
Thu, 11 Sep 1997 12:22:31 +0200 | |
changeset 3667 | 42a726e008ce |
parent 3544 | 6ae62d55a620 |
child 3673 | 3b06747c3f37 |
permissions | -rw-r--r-- |
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(* Title: HOL/Auth/Public |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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Theory of Public Keys (common to all symmetric-key protocols) |
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Server keys; initial states of agents; new nonces and keys; function "sees" |
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*) |
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open Public; |
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(*** Basic properties of pubK & priK ***) |
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AddIffs [inj_pubK RS inj_eq]; |
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goal thy "!!A B. (priK A = priK B) = (A=B)"; |
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by (Step_tac 1); |
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by (dres_inst_tac [("f","invKey")] arg_cong 1); |
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by (Full_simp_tac 1); |
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qed "priK_inj_eq"; |
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AddIffs [priK_inj_eq]; |
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AddIffs [priK_neq_pubK, priK_neq_pubK RS not_sym]; |
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goalw thy [isSymKey_def] "~ isSymKey (pubK A)"; |
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by (Simp_tac 1); |
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qed "not_isSymKey_pubK"; |
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goalw thy [isSymKey_def] "~ isSymKey (priK A)"; |
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by (Simp_tac 1); |
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qed "not_isSymKey_priK"; |
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AddIffs [not_isSymKey_pubK, not_isSymKey_priK]; |
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(** Rewrites should not refer to initState(Friend i) |
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-- not in normal form! **) |
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goalw thy [keysFor_def] "keysFor (parts (initState C)) = {}"; |
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by (induct_tac "C" 1); |
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by (auto_tac (!claset addIs [range_eqI], !simpset)); |
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qed "keysFor_parts_initState"; |
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Addsimps [keysFor_parts_initState]; |
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(*** Function "sees" ***) |
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(*Agents see their own private keys!*) |
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goal thy "A ~= Spy --> Key (priK A) : sees A evs"; |
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by (induct_tac "evs" 1); |
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by (induct_tac "A" 1); |
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by (ALLGOALS (asm_simp_tac (!simpset addsimps [sees_Cons]))); |
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qed_spec_mp "sees_own_priK"; |
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(*All public keys are visible to all*) |
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goal thy "Key (pubK A) : sees B evs"; |
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by (induct_tac "evs" 1); |
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by (induct_tac "B" 1); |
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by (ALLGOALS (asm_simp_tac (!simpset addsimps [sees_Cons]))); |
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by (Auto_tac ()); |
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qed_spec_mp "sees_pubK"; |
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(*Spy sees private keys of agents!*) |
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goal thy "!!A. A: lost ==> Key (priK A) : sees Spy evs"; |
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by (induct_tac "evs" 1); |
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by (ALLGOALS (asm_simp_tac (!simpset addsimps [sees_Cons]))); |
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by (Blast_tac 1); |
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qed "Spy_sees_lost"; |
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AddIffs [sees_pubK, sees_pubK RS analz.Inj]; |
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AddSIs [sees_own_priK, Spy_sees_lost]; |
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(*For not_lost_tac*) |
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goal thy "!!A. [| Crypt (pubK A) X : analz (sees Spy evs); A: lost |] \ |
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\ ==> X : analz (sees Spy evs)"; |
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by (blast_tac (!claset addSDs [analz.Decrypt]) 1); |
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qed "Crypt_Spy_analz_lost"; |
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(*Prove that the agent is uncompromised by the confidentiality of |
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a component of a message she's said.*) |
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fun not_lost_tac s = |
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case_tac ("(" ^ s ^ ") : lost") THEN' |
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SELECT_GOAL |
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(REPEAT_DETERM (dtac (Says_imp_sees_Spy RS analz.Inj) 1) THEN |
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REPEAT_DETERM (etac MPair_analz 1) THEN |
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THEN_BEST_FIRST |
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(dres_inst_tac [("A", s)] Crypt_Spy_analz_lost 1 THEN assume_tac 1) |
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(has_fewer_prems 1, size_of_thm) |
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(Step_tac 1)); |
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(*** Fresh nonces ***) |
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goal thy "Nonce N ~: parts (initState B)"; |
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by (induct_tac "B" 1); |
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by (Auto_tac ()); |
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qed "Nonce_notin_initState"; |
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AddIffs [Nonce_notin_initState]; |
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goal thy "Nonce N ~: used []"; |
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by (simp_tac (!simpset addsimps [used_def]) 1); |
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qed "Nonce_notin_used_empty"; |
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Addsimps [Nonce_notin_used_empty]; |
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(*** Supply fresh nonces for possibility theorems. ***) |
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goalw thy [used_def] "EX N. ALL n. N<=n --> Nonce n ~: used evs"; |
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by (induct_tac "evs" 1); |
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by (res_inst_tac [("x","0")] exI 1); |
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by (Step_tac 1); |
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by (Full_simp_tac 1); |
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(*Inductive step*) |
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by (induct_tac "a" 1); |
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by (ALLGOALS (full_simp_tac |
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(!simpset delsimps [sees_Notes] |
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addsimps [UN_parts_sees_Says, |
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UN_parts_sees_Notes]))); |
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by (ALLGOALS (rtac (msg_Nonce_supply RS exE))); |
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by (ALLGOALS (blast_tac (!claset addSEs [add_leE]))); |
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val lemma = result(); |
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goal thy "Nonce (@ N. Nonce N ~: used evs) ~: used evs"; |
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by (rtac (lemma RS exE) 1); |
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by (rtac selectI 1); |
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by (Fast_tac 1); |
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qed "Nonce_supply"; |
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(*Tactic for possibility theorems*) |
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fun possibility_tac st = st |> |
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REPEAT (*omit used_Says so that Nonces, Keys start from different traces!*) |
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(ALLGOALS (simp_tac (!simpset delsimps [used_Says] setSolver safe_solver)) |
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THEN |
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REPEAT_FIRST (eq_assume_tac ORELSE' |
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resolve_tac [refl, conjI, Nonce_supply])); |
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(*** Specialized rewriting for the analz_image_... theorems ***) |
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goal thy "insert (Key K) H = Key `` {K} Un H"; |
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by (Blast_tac 1); |
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qed "insert_Key_singleton"; |
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goal thy "insert (Key K) (Key``KK Un C) = Key `` (insert K KK) Un C"; |
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by (Blast_tac 1); |
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qed "insert_Key_image"; |
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(*Reverse the normal simplification of "image" to build up (not break down) |
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the set of keys. Based on analz_image_freshK_ss, but simpler.*) |
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val analz_image_keys_ss = |
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!simpset delsimps [image_insert, image_Un] |
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addsimps [image_insert RS sym, image_Un RS sym, |
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rangeI, |
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insert_Key_singleton, |
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insert_Key_image, Un_assoc RS sym] |
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setloop split_tac [expand_if]; |
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