src/HOL/Auth/Message.ML
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(*  Title:      HOL/Auth/Message
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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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Datatypes of agents and messages;
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Inductive relations "parts", "analz" and "synth"
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*)
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val prems = goal HOL.thy "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
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by (case_tac "P" 1);
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by (ALLGOALS (asm_simp_tac (!simpset addsimps prems)));
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val expand_case = result();
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fun expand_case_tac P i =
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    res_inst_tac [("P",P)] expand_case i THEN
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    Simp_tac (i+1) THEN 
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    Simp_tac i;
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open Message;
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AddIffs (msg.inject);
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(** Inverse of keys **)
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goal thy "!!K K'. (invKey K = invKey K') = (K=K')";
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by (Step_tac 1);
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by (rtac box_equals 1);
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by (REPEAT (rtac invKey 2));
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by (Asm_simp_tac 1);
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qed "invKey_eq";
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Addsimps [invKey, invKey_eq];
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(**** keysFor operator ****)
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goalw thy [keysFor_def] "keysFor {} = {}";
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by (Fast_tac 1);
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qed "keysFor_empty";
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goalw thy [keysFor_def] "keysFor (H Un H') = keysFor H Un keysFor H'";
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by (Fast_tac 1);
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qed "keysFor_Un";
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goalw thy [keysFor_def] "keysFor (UN i. H i) = (UN i. keysFor (H i))";
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by (Fast_tac 1);
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qed "keysFor_UN";
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(*Monotonicity*)
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goalw thy [keysFor_def] "!!G H. G<=H ==> keysFor(G) <= keysFor(H)";
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by (Fast_tac 1);
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qed "keysFor_mono";
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goalw thy [keysFor_def] "keysFor (insert (Agent A) H) = keysFor H";
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by (fast_tac (!claset addss (!simpset)) 1);
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qed "keysFor_insert_Agent";
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goalw thy [keysFor_def] "keysFor (insert (Nonce N) H) = keysFor H";
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by (fast_tac (!claset addss (!simpset)) 1);
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qed "keysFor_insert_Nonce";
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goalw thy [keysFor_def] "keysFor (insert (Key K) H) = keysFor H";
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by (fast_tac (!claset addss (!simpset)) 1);
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qed "keysFor_insert_Key";
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goalw thy [keysFor_def] "keysFor (insert (Hash X) H) = keysFor H";
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by (fast_tac (!claset addss (!simpset)) 1);
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qed "keysFor_insert_Hash";
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goalw thy [keysFor_def] "keysFor (insert {|X,Y|} H) = keysFor H";
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by (fast_tac (!claset addss (!simpset)) 1);
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qed "keysFor_insert_MPair";
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goalw thy [keysFor_def]
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    "keysFor (insert (Crypt K X) H) = insert (invKey K) (keysFor H)";
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by (Auto_tac());
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qed "keysFor_insert_Crypt";
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Addsimps [keysFor_empty, keysFor_Un, keysFor_UN, 
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          keysFor_insert_Agent, keysFor_insert_Nonce, keysFor_insert_Key, 
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          keysFor_insert_Hash, keysFor_insert_MPair, keysFor_insert_Crypt];
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goalw thy [keysFor_def] "!!H. Crypt K X : H ==> invKey K : keysFor H";
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by (Fast_tac 1);
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qed "Crypt_imp_invKey_keysFor";
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(**** Inductive relation "parts" ****)
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val major::prems = 
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goal thy "[| {|X,Y|} : parts H;       \
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\            [| X : parts H; Y : parts H |] ==> P  \
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\         |] ==> P";
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by (cut_facts_tac [major] 1);
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by (resolve_tac prems 1);
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by (REPEAT (eresolve_tac [asm_rl, parts.Fst, parts.Snd] 1));
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qed "MPair_parts";
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AddIs  [parts.Inj];
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val partsEs = [MPair_parts, make_elim parts.Body];
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AddSEs partsEs;
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(*NB These two rules are UNSAFE in the formal sense, as they discard the
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     compound message.  They work well on THIS FILE, perhaps because its
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     proofs concern only atomic messages.*)
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goal thy "H <= parts(H)";
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by (Fast_tac 1);
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qed "parts_increasing";
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(*Monotonicity*)
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goalw thy parts.defs "!!G H. G<=H ==> parts(G) <= parts(H)";
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by (rtac lfp_mono 1);
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by (REPEAT (ares_tac basic_monos 1));
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qed "parts_mono";
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val parts_insertI = impOfSubs (subset_insertI RS parts_mono);
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goal thy "parts{} = {}";
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by (Step_tac 1);
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by (etac parts.induct 1);
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by (ALLGOALS Fast_tac);
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qed "parts_empty";
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Addsimps [parts_empty];
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goal thy "!!X. X: parts{} ==> P";
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by (Asm_full_simp_tac 1);
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qed "parts_emptyE";
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AddSEs [parts_emptyE];
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(*WARNING: loops if H = {Y}, therefore must not be repeated!*)
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goal thy "!!H. X: parts H ==> EX Y:H. X: parts {Y}";
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by (etac parts.induct 1);
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by (ALLGOALS Fast_tac);
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qed "parts_singleton";
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(** Unions **)
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goal thy "parts(G) Un parts(H) <= parts(G Un H)";
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by (REPEAT (ares_tac [Un_least, parts_mono, Un_upper1, Un_upper2] 1));
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val parts_Un_subset1 = result();
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goal thy "parts(G Un H) <= parts(G) Un parts(H)";
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by (rtac subsetI 1);
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by (etac parts.induct 1);
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by (ALLGOALS Fast_tac);
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val parts_Un_subset2 = result();
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goal thy "parts(G Un H) = parts(G) Un parts(H)";
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by (REPEAT (ares_tac [equalityI, parts_Un_subset1, parts_Un_subset2] 1));
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qed "parts_Un";
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goal thy "parts (insert X H) = parts {X} Un parts H";
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by (stac (read_instantiate [("A","H")] insert_is_Un) 1);
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by (simp_tac (HOL_ss addsimps [parts_Un]) 1);
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qed "parts_insert";
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(*TWO inserts to avoid looping.  This rewrite is better than nothing.
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  Not suitable for Addsimps: its behaviour can be strange.*)
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goal thy "parts (insert X (insert Y H)) = parts {X} Un parts {Y} Un parts H";
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by (simp_tac (!simpset addsimps [Un_assoc]) 1);
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by (simp_tac (!simpset addsimps [parts_insert RS sym]) 1);
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qed "parts_insert2";
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goal thy "(UN x:A. parts(H x)) <= parts(UN x:A. H x)";
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by (REPEAT (ares_tac [UN_least, parts_mono, UN_upper] 1));
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val parts_UN_subset1 = result();
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goal thy "parts(UN x:A. H x) <= (UN x:A. parts(H x))";
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by (rtac subsetI 1);
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by (etac parts.induct 1);
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by (ALLGOALS Fast_tac);
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val parts_UN_subset2 = result();
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goal thy "parts(UN x:A. H x) = (UN x:A. parts(H x))";
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by (REPEAT (ares_tac [equalityI, parts_UN_subset1, parts_UN_subset2] 1));
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qed "parts_UN";
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goal thy "parts(UN x. H x) = (UN x. parts(H x))";
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by (simp_tac (!simpset addsimps [UNION1_def, parts_UN]) 1);
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qed "parts_UN1";
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(*Added to simplify arguments to parts, analz and synth*)
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Addsimps [parts_Un, parts_UN, parts_UN1];
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goal thy "insert X (parts H) <= parts(insert X H)";
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by (fast_tac (!claset addEs [impOfSubs parts_mono]) 1);
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qed "parts_insert_subset";
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(** Idempotence and transitivity **)
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goal thy "!!H. X: parts (parts H) ==> X: parts H";
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by (etac parts.induct 1);
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by (ALLGOALS Fast_tac);
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qed "parts_partsE";
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AddSEs [parts_partsE];
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goal thy "parts (parts H) = parts H";
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by (Fast_tac 1);
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qed "parts_idem";
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Addsimps [parts_idem];
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goal thy "!!H. [| X: parts G;  G <= parts H |] ==> X: parts H";
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by (dtac parts_mono 1);
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by (Fast_tac 1);
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qed "parts_trans";
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(*Cut*)
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goal thy "!!H. [| Y: parts (insert X G);  X: parts H |] \
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\              ==> Y: parts (G Un H)";
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by (etac parts_trans 1);
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by (Auto_tac());
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qed "parts_cut";
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goal thy "!!H. X: parts H ==> parts (insert X H) = parts H";
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by (fast_tac (!claset addSDs [parts_cut]
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                      addIs  [parts_insertI] 
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                      addss (!simpset)) 1);
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qed "parts_cut_eq";
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Addsimps [parts_cut_eq];
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(** Rewrite rules for pulling out atomic messages **)
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fun parts_tac i =
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  EVERY [rtac ([subsetI, parts_insert_subset] MRS equalityI) i,
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         etac parts.induct i,
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         REPEAT (fast_tac (!claset addss (!simpset)) i)];
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goal thy "parts (insert (Agent agt) H) = insert (Agent agt) (parts H)";
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by (parts_tac 1);
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qed "parts_insert_Agent";
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goal thy "parts (insert (Nonce N) H) = insert (Nonce N) (parts H)";
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by (parts_tac 1);
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qed "parts_insert_Nonce";
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goal thy "parts (insert (Key K) H) = insert (Key K) (parts H)";
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by (parts_tac 1);
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qed "parts_insert_Key";
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goal thy "parts (insert (Hash X) H) = insert (Hash X) (parts H)";
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by (parts_tac 1);
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qed "parts_insert_Hash";
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goal thy "parts (insert (Crypt K X) H) = \
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\         insert (Crypt K X) (parts (insert X H))";
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by (rtac equalityI 1);
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by (rtac subsetI 1);
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by (etac parts.induct 1);
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by (Auto_tac());
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by (etac parts.induct 1);
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by (ALLGOALS (best_tac (!claset addIs [parts.Body])));
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qed "parts_insert_Crypt";
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goal thy "parts (insert {|X,Y|} H) = \
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\         insert {|X,Y|} (parts (insert X (insert Y H)))";
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by (rtac equalityI 1);
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by (rtac subsetI 1);
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by (etac parts.induct 1);
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by (Auto_tac());
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by (etac parts.induct 1);
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by (ALLGOALS (best_tac (!claset addIs [parts.Fst, parts.Snd])));
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qed "parts_insert_MPair";
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Addsimps [parts_insert_Agent, parts_insert_Nonce, parts_insert_Key, 
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          parts_insert_Hash, parts_insert_Crypt, parts_insert_MPair];
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goal thy "parts (Key``N) = Key``N";
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by (Auto_tac());
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by (etac parts.induct 1);
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by (Auto_tac());
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qed "parts_image_Key";
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Addsimps [parts_image_Key];
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(**** Inductive relation "analz" ****)
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val major::prems = 
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goal thy "[| {|X,Y|} : analz H;       \
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\            [| X : analz H; Y : analz H |] ==> P  \
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\         |] ==> P";
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by (cut_facts_tac [major] 1);
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by (resolve_tac prems 1);
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by (REPEAT (eresolve_tac [asm_rl, analz.Fst, analz.Snd] 1));
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qed "MPair_analz";
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AddIs  [analz.Inj];
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AddSEs [MPair_analz];      (*Perhaps it should NOT be deemed safe!*)
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AddDs  [analz.Decrypt];
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Addsimps [analz.Inj];
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goal thy "H <= analz(H)";
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by (Fast_tac 1);
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qed "analz_increasing";
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goal thy "analz H <= parts H";
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by (rtac subsetI 1);
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   307
by (etac analz.induct 1);
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by (ALLGOALS Fast_tac);
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qed "analz_subset_parts";
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bind_thm ("not_parts_not_analz", analz_subset_parts RS contra_subsetD);
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goal thy "parts (analz H) = parts H";
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by (rtac equalityI 1);
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   316
by (rtac (analz_subset_parts RS parts_mono RS subset_trans) 1);
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   317
by (Simp_tac 1);
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   318
by (fast_tac (!claset addDs [analz_increasing RS parts_mono RS subsetD]) 1);
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qed "parts_analz";
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Addsimps [parts_analz];
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goal thy "analz (parts H) = parts H";
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   323
by (Auto_tac());
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   324
by (etac analz.induct 1);
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by (Auto_tac());
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qed "analz_parts";
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Addsimps [analz_parts];
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(*Monotonicity; Lemma 1 of Lowe*)
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   330
goalw thy analz.defs "!!G H. G<=H ==> analz(G) <= analz(H)";
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by (rtac lfp_mono 1);
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   332
by (REPEAT (ares_tac basic_monos 1));
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   333
qed "analz_mono";
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val analz_insertI = impOfSubs (subset_insertI RS analz_mono);
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   336
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(** General equational properties **)
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   338
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   339
goal thy "analz{} = {}";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   340
by (Step_tac 1);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   341
by (etac analz.induct 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   342
by (ALLGOALS Fast_tac);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   343
qed "analz_empty";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   344
Addsimps [analz_empty];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   345
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   346
(*Converse fails: we can analz more from the union than from the 
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   347
  separate parts, as a key in one might decrypt a message in the other*)
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   348
goal thy "analz(G) Un analz(H) <= analz(G Un H)";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   349
by (REPEAT (ares_tac [Un_least, analz_mono, Un_upper1, Un_upper2] 1));
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   350
qed "analz_Un";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   351
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   352
goal thy "insert X (analz H) <= analz(insert X H)";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   353
by (fast_tac (!claset addEs [impOfSubs analz_mono]) 1);
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   354
qed "analz_insert";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   355
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   356
(** Rewrite rules for pulling out atomic messages **)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   357
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   358
fun analz_tac i =
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   359
  EVERY [rtac ([subsetI, analz_insert] MRS equalityI) i,
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   360
         etac analz.induct i,
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   361
         REPEAT (fast_tac (!claset addss (!simpset)) i)];
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   362
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   363
goal thy "analz (insert (Agent agt) H) = insert (Agent agt) (analz H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   364
by (analz_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   365
qed "analz_insert_Agent";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   366
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   367
goal thy "analz (insert (Nonce N) H) = insert (Nonce N) (analz H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   368
by (analz_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   369
qed "analz_insert_Nonce";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   370
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   371
goal thy "analz (insert (Hash X) H) = insert (Hash X) (analz H)";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   372
by (analz_tac 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   373
qed "analz_insert_Hash";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   374
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   375
(*Can only pull out Keys if they are not needed to decrypt the rest*)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   376
goalw thy [keysFor_def]
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   377
    "!!K. K ~: keysFor (analz H) ==>  \
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   378
\         analz (insert (Key K) H) = insert (Key K) (analz H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   379
by (analz_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   380
qed "analz_insert_Key";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   381
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   382
goal thy "analz (insert {|X,Y|} H) = \
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   383
\         insert {|X,Y|} (analz (insert X (insert Y H)))";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   384
by (rtac equalityI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   385
by (rtac subsetI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   386
by (etac analz.induct 1);
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   387
by (Auto_tac());
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   388
by (etac analz.induct 1);
2102
41a667d2c3fa Replaced excluded_middle_tac by case_tac
paulson
parents: 2068
diff changeset
   389
by (ALLGOALS
41a667d2c3fa Replaced excluded_middle_tac by case_tac
paulson
parents: 2068
diff changeset
   390
    (deepen_tac (!claset addIs [analz.Fst, analz.Snd, analz.Decrypt]) 0));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   391
qed "analz_insert_MPair";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   392
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   393
(*Can pull out enCrypted message if the Key is not known*)
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   394
goal thy "!!H. Key (invKey K) ~: analz H ==>  \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   395
\              analz (insert (Crypt K X) H) = \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   396
\              insert (Crypt K X) (analz H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   397
by (analz_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   398
qed "analz_insert_Crypt";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   399
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   400
goal thy "!!H. Key (invKey K) : analz H ==>  \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   401
\              analz (insert (Crypt K X) H) <= \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   402
\              insert (Crypt K X) (analz (insert X H))";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   403
by (rtac subsetI 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   404
by (eres_inst_tac [("za","x")] analz.induct 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   405
by (ALLGOALS (fast_tac (!claset addss (!simpset))));
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   406
val lemma1 = result();
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   407
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   408
goal thy "!!H. Key (invKey K) : analz H ==>  \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   409
\              insert (Crypt K X) (analz (insert X H)) <= \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   410
\              analz (insert (Crypt K X) H)";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   411
by (Auto_tac());
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   412
by (eres_inst_tac [("za","x")] analz.induct 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   413
by (Auto_tac());
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   414
by (best_tac (!claset addIs [subset_insertI RS analz_mono RS subsetD,
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   415
                             analz.Decrypt]) 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   416
val lemma2 = result();
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   417
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   418
goal thy "!!H. Key (invKey K) : analz H ==>  \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   419
\              analz (insert (Crypt K X) H) = \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   420
\              insert (Crypt K X) (analz (insert X H))";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   421
by (REPEAT (ares_tac [equalityI, lemma1, lemma2] 1));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   422
qed "analz_insert_Decrypt";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   423
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   424
(*Case analysis: either the message is secure, or it is not!
1946
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   425
  Effective, but can cause subgoals to blow up!
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   426
  Use with expand_if;  apparently split_tac does not cope with patterns
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   427
  such as "analz (insert (Crypt K X) H)" *)
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   428
goal thy "analz (insert (Crypt K X) H) =                \
2154
913b4fc7670a New, purely illustrative result Crypt_synth_analz
paulson
parents: 2102
diff changeset
   429
\         (if (Key (invKey K) : analz H)                \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   430
\          then insert (Crypt K X) (analz (insert X H)) \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   431
\          else insert (Crypt K X) (analz H))";
2102
41a667d2c3fa Replaced excluded_middle_tac by case_tac
paulson
parents: 2068
diff changeset
   432
by (case_tac "Key (invKey K)  : analz H " 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   433
by (ALLGOALS (asm_simp_tac (!simpset addsimps [analz_insert_Crypt, 
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   434
                                               analz_insert_Decrypt])));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   435
qed "analz_Crypt_if";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   436
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   437
Addsimps [analz_insert_Agent, analz_insert_Nonce, analz_insert_Key, 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   438
          analz_insert_Hash, analz_insert_MPair, analz_Crypt_if];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   439
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   440
(*This rule supposes "for the sake of argument" that we have the key.*)
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   441
goal thy  "analz (insert (Crypt K X) H) <=  \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   442
\          insert (Crypt K X) (analz (insert X H))";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   443
by (rtac subsetI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   444
by (etac analz.induct 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   445
by (Auto_tac());
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   446
qed "analz_insert_Crypt_subset";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   447
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   448
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   449
goal thy "analz (Key``N) = Key``N";
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   450
by (Auto_tac());
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   451
by (etac analz.induct 1);
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   452
by (Auto_tac());
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   453
qed "analz_image_Key";
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   454
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   455
Addsimps [analz_image_Key];
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   456
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   457
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   458
(** Idempotence and transitivity **)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   459
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   460
goal thy "!!H. X: analz (analz H) ==> X: analz H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   461
by (etac analz.induct 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   462
by (ALLGOALS Fast_tac);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   463
qed "analz_analzE";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   464
AddSEs [analz_analzE];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   465
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   466
goal thy "analz (analz H) = analz H";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   467
by (Fast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   468
qed "analz_idem";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   469
Addsimps [analz_idem];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   470
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   471
goal thy "!!H. [| X: analz G;  G <= analz H |] ==> X: analz H";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   472
by (dtac analz_mono 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   473
by (Fast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   474
qed "analz_trans";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   475
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   476
(*Cut; Lemma 2 of Lowe*)
1998
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   477
goal thy "!!H. [| Y: analz (insert X H);  X: analz H |] ==> Y: analz H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   478
by (etac analz_trans 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   479
by (Fast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   480
qed "analz_cut";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   481
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   482
(*Cut can be proved easily by induction on
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   483
   "!!H. Y: analz (insert X H) ==> X: analz H --> Y: analz H"
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   484
*)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   485
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   486
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   487
(** A congruence rule for "analz" **)
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   488
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   489
goal thy "!!H. [| analz G <= analz G'; analz H <= analz H' \
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   490
\              |] ==> analz (G Un H) <= analz (G' Un H')";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   491
by (Step_tac 1);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   492
by (etac analz.induct 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   493
by (ALLGOALS (best_tac (!claset addIs [analz_mono RS subsetD])));
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   494
qed "analz_subset_cong";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   495
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   496
goal thy "!!H. [| analz G = analz G'; analz H = analz H' \
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   497
\              |] ==> analz (G Un H) = analz (G' Un H')";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   498
by (REPEAT_FIRST (ares_tac [equalityI, analz_subset_cong]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   499
          ORELSE' etac equalityE));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   500
qed "analz_cong";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   501
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   502
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   503
goal thy "!!H. analz H = analz H' ==> analz(insert X H) = analz(insert X H')";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   504
by (asm_simp_tac (!simpset addsimps [insert_def] 
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   505
                           setloop (rtac analz_cong)) 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   506
qed "analz_insert_cong";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   507
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   508
(*If there are no pairs or encryptions then analz does nothing*)
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   509
goal thy "!!H. [| ALL X Y. {|X,Y|} ~: H;  ALL X K. Crypt K X ~: H |] ==> \
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   510
\         analz H = H";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   511
by (Step_tac 1);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   512
by (etac analz.induct 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   513
by (ALLGOALS Fast_tac);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   514
qed "analz_trivial";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   515
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   516
(*Helps to prove Fake cases*)
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   517
goal thy "!!X. X: analz (UN i. analz (H i)) ==> X: analz (UN i. H i)";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   518
by (etac analz.induct 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   519
by (ALLGOALS (fast_tac (!claset addEs [impOfSubs analz_mono])));
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   520
val lemma = result();
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   521
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   522
goal thy "analz (UN i. analz (H i)) = analz (UN i. H i)";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   523
by (fast_tac (!claset addIs [lemma]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   524
                      addEs [impOfSubs analz_mono]) 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   525
qed "analz_UN_analz";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   526
Addsimps [analz_UN_analz];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   527
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   528
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   529
(**** Inductive relation "synth" ****)
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   530
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   531
AddIs  synth.intrs;
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   532
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   533
(*Can only produce a nonce or key if it is already known,
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   534
  but can synth a pair or encryption from its components...*)
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   535
val mk_cases = synth.mk_cases msg.simps;
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   536
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   537
(*NO Agent_synth, as any Agent name can be synthesized*)
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   538
val Nonce_synth = mk_cases "Nonce n : synth H";
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   539
val Key_synth   = mk_cases "Key K : synth H";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   540
val Hash_synth  = mk_cases "Hash X : synth H";
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   541
val MPair_synth = mk_cases "{|X,Y|} : synth H";
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   542
val Crypt_synth = mk_cases "Crypt K X : synth H";
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   543
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   544
AddSEs [Nonce_synth, Key_synth, Hash_synth, MPair_synth, Crypt_synth];
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   545
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   546
goal thy "H <= synth(H)";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   547
by (Fast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   548
qed "synth_increasing";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   549
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   550
(*Monotonicity*)
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   551
goalw thy synth.defs "!!G H. G<=H ==> synth(G) <= synth(H)";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   552
by (rtac lfp_mono 1);
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   553
by (REPEAT (ares_tac basic_monos 1));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   554
qed "synth_mono";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   555
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   556
(** Unions **)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   557
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   558
(*Converse fails: we can synth more from the union than from the 
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   559
  separate parts, building a compound message using elements of each.*)
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   560
goal thy "synth(G) Un synth(H) <= synth(G Un H)";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   561
by (REPEAT (ares_tac [Un_least, synth_mono, Un_upper1, Un_upper2] 1));
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   562
qed "synth_Un";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   563
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   564
goal thy "insert X (synth H) <= synth(insert X H)";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   565
by (fast_tac (!claset addEs [impOfSubs synth_mono]) 1);
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   566
qed "synth_insert";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   567
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   568
(** Idempotence and transitivity **)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   569
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   570
goal thy "!!H. X: synth (synth H) ==> X: synth H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   571
by (etac synth.induct 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   572
by (ALLGOALS Fast_tac);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   573
qed "synth_synthE";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   574
AddSEs [synth_synthE];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   575
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   576
goal thy "synth (synth H) = synth H";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   577
by (Fast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   578
qed "synth_idem";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   579
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   580
goal thy "!!H. [| X: synth G;  G <= synth H |] ==> X: synth H";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   581
by (dtac synth_mono 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   582
by (Fast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   583
qed "synth_trans";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   584
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   585
(*Cut; Lemma 2 of Lowe*)
1998
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   586
goal thy "!!H. [| Y: synth (insert X H);  X: synth H |] ==> Y: synth H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   587
by (etac synth_trans 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   588
by (Fast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   589
qed "synth_cut";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   590
1946
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   591
goal thy "Agent A : synth H";
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   592
by (Fast_tac 1);
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   593
qed "Agent_synth";
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   594
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   595
goal thy "(Nonce N : synth H) = (Nonce N : H)";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   596
by (Fast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   597
qed "Nonce_synth_eq";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   598
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   599
goal thy "(Key K : synth H) = (Key K : H)";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   600
by (Fast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   601
qed "Key_synth_eq";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   602
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   603
goal thy "!!K. Key K ~: H ==> (Crypt K X : synth H) = (Crypt K X : H)";
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   604
by (Fast_tac 1);
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   605
qed "Crypt_synth_eq";
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   606
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   607
Addsimps [Agent_synth, Nonce_synth_eq, Key_synth_eq, Crypt_synth_eq];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   608
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   609
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   610
goalw thy [keysFor_def]
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   611
    "keysFor (synth H) = keysFor H Un invKey``{K. Key K : H}";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   612
by (Fast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   613
qed "keysFor_synth";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   614
Addsimps [keysFor_synth];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   615
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   616
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   617
(*** Combinations of parts, analz and synth ***)
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   618
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   619
goal thy "parts (synth H) = parts H Un synth H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   620
by (rtac equalityI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   621
by (rtac subsetI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   622
by (etac parts.induct 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   623
by (ALLGOALS
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   624
    (best_tac (!claset addIs ((synth_increasing RS parts_mono RS subsetD)
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   625
                             ::parts.intrs))));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   626
qed "parts_synth";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   627
Addsimps [parts_synth];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   628
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   629
goal thy "analz (analz G Un H) = analz (G Un H)";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   630
by (REPEAT_FIRST (resolve_tac [equalityI, analz_subset_cong]));
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   631
by (ALLGOALS Simp_tac);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   632
qed "analz_analz_Un";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   633
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   634
goal thy "analz (synth G Un H) = analz (G Un H) Un synth G";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   635
by (rtac equalityI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   636
by (rtac subsetI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   637
by (etac analz.induct 1);
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   638
by (deepen_tac (!claset addIs [impOfSubs analz_mono]) 0 5);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   639
(*Strange that best_tac just can't hack this one...*)
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   640
by (ALLGOALS (deepen_tac (!claset addIs analz.intrs) 0));
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   641
qed "analz_synth_Un";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   642
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   643
goal thy "analz (synth H) = analz H Un synth H";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   644
by (cut_inst_tac [("H","{}")] analz_synth_Un 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   645
by (Full_simp_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   646
qed "analz_synth";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   647
Addsimps [analz_analz_Un, analz_synth_Un, analz_synth];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   648
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   649
(*Hard to prove; still needed now that there's only one Spy?*)
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   650
goal thy "analz (UN i. synth (H i)) = \
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   651
\         analz (UN i. H i) Un (UN i. synth (H i))";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   652
by (rtac equalityI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   653
by (rtac subsetI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   654
by (etac analz.induct 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   655
by (best_tac
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   656
    (!claset addEs [impOfSubs synth_increasing,
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   657
                    impOfSubs analz_mono]) 5);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   658
by (Best_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   659
by (deepen_tac (!claset addIs [analz.Fst]) 0 1);
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   660
by (deepen_tac (!claset addIs [analz.Snd]) 0 1);
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   661
by (deepen_tac (!claset addSEs [analz.Decrypt]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   662
                        addIs  [analz.Decrypt]) 0 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   663
qed "analz_UN1_synth";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   664
Addsimps [analz_UN1_synth];
1929
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   665
1946
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   666
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   667
(** For reasoning about the Fake rule in traces **)
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   668
1929
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   669
goal thy "!!Y. X: G ==> parts(insert X H) <= parts G Un parts H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   670
by (rtac ([parts_mono, parts_Un_subset2] MRS subset_trans) 1);
1929
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   671
by (Fast_tac 1);
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   672
qed "parts_insert_subset_Un";
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   673
1946
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   674
(*More specifically for Fake*)
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   675
goal thy "!!H. X: synth (analz G) ==> \
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   676
\              parts (insert X H) <= synth (analz G) Un parts G Un parts H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   677
by (dtac parts_insert_subset_Un 1);
1946
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   678
by (Full_simp_tac 1);
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   679
by (Deepen_tac 0 1);
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   680
qed "Fake_parts_insert";
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   681
2061
b14a08bf61bf New theorem Crypt_Fake_parts_insert
paulson
parents: 2032
diff changeset
   682
goal thy
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   683
     "!!H. [| Crypt K Y : parts (insert X H);  X: synth (analz G);  \
2061
b14a08bf61bf New theorem Crypt_Fake_parts_insert
paulson
parents: 2032
diff changeset
   684
\             Key K ~: analz G |]                                   \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   685
\          ==> Crypt K Y : parts G Un parts H";
2061
b14a08bf61bf New theorem Crypt_Fake_parts_insert
paulson
parents: 2032
diff changeset
   686
by (dtac (impOfSubs Fake_parts_insert) 1);
2170
c5e460f1ebb4 Ran expandshort
paulson
parents: 2154
diff changeset
   687
by (assume_tac 1);
2061
b14a08bf61bf New theorem Crypt_Fake_parts_insert
paulson
parents: 2032
diff changeset
   688
by (fast_tac (!claset addDs [impOfSubs analz_subset_parts]
b14a08bf61bf New theorem Crypt_Fake_parts_insert
paulson
parents: 2032
diff changeset
   689
                      addss (!simpset)) 1);
b14a08bf61bf New theorem Crypt_Fake_parts_insert
paulson
parents: 2032
diff changeset
   690
qed "Crypt_Fake_parts_insert";
b14a08bf61bf New theorem Crypt_Fake_parts_insert
paulson
parents: 2032
diff changeset
   691
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   692
goal thy "!!H. X: synth (analz G) ==> \
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   693
\              analz (insert X H) <= synth (analz G) Un analz (G Un H)";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   694
by (rtac subsetI 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   695
by (subgoal_tac "x : analz (synth (analz G) Un H)" 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   696
by (best_tac (!claset addIs [impOfSubs (analz_mono RS synth_mono)]
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   697
                      addSEs [impOfSubs analz_mono]) 2);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   698
by (Full_simp_tac 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   699
by (Fast_tac 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   700
qed "Fake_analz_insert";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   701
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   702
goal thy "(X: analz H & X: parts H) = (X: analz H)";
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   703
by (fast_tac (!claset addDs [impOfSubs analz_subset_parts]) 1);
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   704
val analz_conj_parts = result();
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   705
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   706
goal thy "(X: analz H | X: parts H) = (X: parts H)";
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   707
by (fast_tac (!claset addDs [impOfSubs analz_subset_parts]) 1);
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   708
val analz_disj_parts = result();
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   709
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   710
AddIffs [analz_conj_parts, analz_disj_parts];
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   711
1998
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   712
(*Without this equation, other rules for synth and analz would yield
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   713
  redundant cases*)
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   714
goal thy "({|X,Y|} : synth (analz H)) = \
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   715
\         (X : synth (analz H) & Y : synth (analz H))";
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   716
by (Fast_tac 1);
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   717
qed "MPair_synth_analz";
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   718
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   719
AddIffs [MPair_synth_analz];
1929
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   720
2154
913b4fc7670a New, purely illustrative result Crypt_synth_analz
paulson
parents: 2102
diff changeset
   721
goal thy "!!K. [| Key K : analz H;  Key (invKey K) : analz H |] \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   722
\              ==> (Crypt K X : synth (analz H)) = (X : synth (analz H))";
2154
913b4fc7670a New, purely illustrative result Crypt_synth_analz
paulson
parents: 2102
diff changeset
   723
by (Fast_tac 1);
913b4fc7670a New, purely illustrative result Crypt_synth_analz
paulson
parents: 2102
diff changeset
   724
qed "Crypt_synth_analz";
913b4fc7670a New, purely illustrative result Crypt_synth_analz
paulson
parents: 2102
diff changeset
   725
1929
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   726
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   727
goal thy "!!K. X ~: synth (analz H) \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   728
\   ==> (Hash{|X,Y|} : synth (analz H)) = (Hash{|X,Y|} : analz H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   729
by (Fast_tac 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   730
qed "Hash_synth_analz";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   731
Addsimps [Hash_synth_analz];
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   732
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   733
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   734
(**** HPair: a combination of Hash and MPair ****)
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   735
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   736
(*** Freeness ***)
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   737
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   738
goalw thy [HPair_def] "Agent A ~= Hash[X] Y";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   739
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   740
qed "Agent_neq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   741
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   742
goalw thy [HPair_def] "Nonce N ~= Hash[X] Y";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   743
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   744
qed "Nonce_neq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   745
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   746
goalw thy [HPair_def] "Key K ~= Hash[X] Y";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   747
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   748
qed "Key_neq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   749
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   750
goalw thy [HPair_def] "Hash Z ~= Hash[X] Y";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   751
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   752
qed "Hash_neq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   753
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   754
goalw thy [HPair_def] "Crypt K X' ~= Hash[X] Y";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   755
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   756
qed "Crypt_neq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   757
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   758
val HPair_neqs = [Agent_neq_HPair, Nonce_neq_HPair, 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   759
                  Key_neq_HPair, Hash_neq_HPair, Crypt_neq_HPair];
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   760
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   761
AddIffs HPair_neqs;
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   762
AddIffs (HPair_neqs RL [not_sym]);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   763
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   764
goalw thy [HPair_def] "(Hash[X'] Y' = Hash[X] Y) = (X' = X & Y'=Y)";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   765
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   766
qed "HPair_eq";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   767
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   768
goalw thy [HPair_def] "({|X',Y'|} = Hash[X] Y) = (X' = Hash{|X,Y|} & Y'=Y)";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   769
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   770
qed "MPair_eq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   771
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   772
goalw thy [HPair_def] "(Hash[X] Y = {|X',Y'|}) = (X' = Hash{|X,Y|} & Y'=Y)";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   773
by (Auto_tac());
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   774
qed "HPair_eq_MPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   775
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   776
AddIffs [HPair_eq, MPair_eq_HPair, HPair_eq_MPair];
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   777
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   778
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   779
(*** Specialized laws, proved in terms of those for Hash and MPair ***)
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   780
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   781
goalw thy [HPair_def] "keysFor (insert (Hash[X] Y) H) = keysFor H";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   782
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   783
qed "keysFor_insert_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   784
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   785
goalw thy [HPair_def]
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   786
    "parts (insert (Hash[X] Y) H) = \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   787
\    insert (Hash[X] Y) (insert (Hash{|X,Y|}) (parts (insert Y H)))";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   788
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   789
qed "parts_insert_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   790
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   791
goalw thy [HPair_def]
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   792
    "analz (insert (Hash[X] Y) H) = \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   793
\    insert (Hash[X] Y) (insert (Hash{|X,Y|}) (analz (insert Y H)))";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   794
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   795
qed "analz_insert_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   796
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   797
goalw thy [HPair_def] "!!H. X ~: synth (analz H) \
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   798
\   ==> (Hash[X] Y : synth (analz H)) = \
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   799
\       (Hash {|X, Y|} : analz H & Y : synth (analz H))";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   800
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   801
by (Fast_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   802
qed "HPair_synth_analz";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   803
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   804
Addsimps [keysFor_insert_HPair, parts_insert_HPair, analz_insert_HPair, 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   805
          HPair_synth_analz, HPair_synth_analz];
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   806
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   807
1929
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   808
(*We do NOT want Crypt... messages broken up in protocols!!*)
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   809
Delrules partsEs;
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   810
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   811
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   812
(** Rewrites to push in Key and Crypt messages, so that other messages can
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   813
    be pulled out using the analz_insert rules **)
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   814
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   815
fun insComm thy x y = read_instantiate_sg (sign_of thy) [("x",x), ("y",y)] 
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   816
                          insert_commute;
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   817
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   818
val pushKeys = map (insComm thy "Key ?K") 
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   819
                   ["Agent ?C", "Nonce ?N", "Hash ?X", 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   820
                    "MPair ?X ?Y", "Crypt ?X ?K'"];
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   821
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   822
val pushCrypts = map (insComm thy "Crypt ?X ?K") 
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   823
                     ["Agent ?C", "Nonce ?N", "Hash ?X'", "MPair ?X' ?Y"];
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   824
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   825
(*Cannot be added with Addsimps -- we don't always want to re-order messages*)
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   826
val pushes = pushKeys@pushCrypts;
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   827
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   828
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   829
(*No premature instantiation of variables during simplification.
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   830
  For proving "possibility" properties.*)
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   831
fun safe_solver prems =
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   832
    match_tac (TrueI::refl::prems) ORELSE' eq_assume_tac
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   833
    ORELSE' etac FalseE;
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   834
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   835
val Fake_insert_tac = 
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   836
    dresolve_tac [impOfSubs Fake_analz_insert,
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   837
                  impOfSubs Fake_parts_insert] THEN'
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   838
    eresolve_tac [asm_rl, synth.Inj];
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   839
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   840
(*Analysis of Fake cases and of messages that forward unknown parts.
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   841
  Abstraction over i is ESSENTIAL: it delays the dereferencing of claset
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   842
  DEPENDS UPON "X" REFERRING TO THE FRADULENT MESSAGE *)
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   843
fun spy_analz_tac i =
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   844
  DETERM
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   845
   (SELECT_GOAL
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   846
     (EVERY 
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   847
      [  (*push in occurrences of X...*)
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   848
       (REPEAT o CHANGED)
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   849
           (res_inst_tac [("x1","X")] (insert_commute RS ssubst) 1),
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   850
       (*...allowing further simplifications*)
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   851
       simp_tac (!simpset setloop split_tac [expand_if]) 1,
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   852
       REPEAT (FIRSTGOAL (resolve_tac [allI,impI,notI,conjI])),
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   853
       DEPTH_SOLVE 
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   854
         (REPEAT (Fake_insert_tac 1) THEN Asm_full_simp_tac 1
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   855
          THEN
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   856
          IF_UNSOLVED (depth_tac (!claset addIs [impOfSubs analz_mono,
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   857
                                                 impOfSubs analz_subset_parts]) 2 1))
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   858
       ]) i);
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   859
2415
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   860
(** Useful in many uniqueness proofs **)
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   861
fun ex_strip_tac i = REPEAT (swap_res_tac [exI, conjI] i) THEN 
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   862
                     assume_tac (i+1);
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   863
2415
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   864
(*Apply the EX-ALL quantifification to prove uniqueness theorems in 
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   865
  their standard form*)
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   866
fun prove_unique_tac lemma = 
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   867
  EVERY' [dtac lemma,
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   868
          REPEAT o (mp_tac ORELSE' eresolve_tac [asm_rl,exE]),
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   869
          (*Duplicate the assumption*)
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   870
          forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl,
2559
06b6a499f8ae deepen_tac is NOT complete when made to apply "spec" as a safe rule\!\!
paulson
parents: 2516
diff changeset
   871
          depth_tac (!claset addSDs [spec]) 0];
2415
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   872
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   873
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   874
(*Needed occasionally with spy_analz_tac, e.g. in analz_insert_Key_newK*)
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   875
goal Set.thy "A Un (B Un A) = B Un A";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   876
by (Fast_tac 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   877
val Un_absorb3 = result();
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   878
Addsimps [Un_absorb3];