# HG changeset patch # User paulson # Date 843493317 -7200 # Node ID ed423882c6a9ec2cd54aea16c5727bae614a9afc # Parent 974167c1d2c4c81f09da990958ab86d088b29ec4 Bad version of Otway-Rees and the new attack on it diff -r 974167c1d2c4 -r ed423882c6a9 src/HOL/Auth/OtwayRees_Bad.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Auth/OtwayRees_Bad.ML Mon Sep 23 17:41:57 1996 +0200 @@ -0,0 +1,668 @@ +(* Title: HOL/Auth/OtwayRees_Bad + ID: $Id$ + Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1996 University of Cambridge + +Inductive relation "otway" for the Otway-Rees protocol. + +The FAULTY version omitting encryption of Nonce NB, as suggested on page 247 of + Burrows, Abadi and Needham. A Logic of Authentication. + Proc. Royal Soc. 426 (1989) + +This file illustrates the consequences of such errors. We can still prove +impressive-looking properties such as Enemy_not_see_encrypted_key, yet the +protocol is open to a middleperson attack. Attempting to prove some key lemmas +indicates the possibility of this attack. +*) + +open OtwayRees_Bad; + +proof_timing:=true; +HOL_quantifiers := false; + + +(*Weak liveness: there are traces that reach the end*) +goal thy + "!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ +\ ==> EX K. EX NA. EX evs: otway. \ +\ Says B A {|Nonce NA, Crypt {|Nonce NA, Key K|} (shrK A)|} \ +\ : set_of_list evs"; +by (REPEAT (resolve_tac [exI,bexI] 1)); +br (otway.Nil RS otway.OR1 RS otway.OR2 RS otway.OR3 RS otway.OR4) 2; +by (ALLGOALS (simp_tac (!simpset setsolver safe_solver))); +by (REPEAT_FIRST (resolve_tac [refl, conjI])); +by (ALLGOALS (fast_tac (!claset addss (!simpset setsolver safe_solver)))); +result(); + + +(**** Inductive proofs about otway ****) + +(*The Enemy can see more than anybody else, except for their initial state*) +goal thy + "!!evs. evs : otway ==> \ +\ sees A evs <= initState A Un sees Enemy evs"; +be otway.induct 1; +by (ALLGOALS (fast_tac (!claset addDs [sees_Says_subset_insert RS subsetD] + addss (!simpset)))); +qed "sees_agent_subset_sees_Enemy"; + + +(*Nobody sends themselves messages*) +goal thy "!!evs. evs : otway ==> ALL A X. Says A A X ~: set_of_list evs"; +be otway.induct 1; +by (Auto_tac()); +qed_spec_mp "not_Says_to_self"; +Addsimps [not_Says_to_self]; +AddSEs [not_Says_to_self RSN (2, rev_notE)]; + + +(** For reasoning about the encrypted portion of messages **) + +goal thy "!!evs. Says A' B {|N, Agent A, Agent B, X|} : set_of_list evs ==> \ +\ X : analz (sees Enemy evs)"; +by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj]) 1); +qed "OR2_analz_sees_Enemy"; + +goal thy "!!evs. Says S B {|N, X, X'|} : set_of_list evs ==> \ +\ X : analz (sees Enemy evs)"; +by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj]) 1); +qed "OR4_analz_sees_Enemy"; + +goal thy "!!evs. Says B' A {|N, Crypt {|N,K|} K'|} : set_of_list evs ==> \ +\ K : parts (sees Enemy evs)"; +by (fast_tac (!claset addSEs partsEs + addSDs [Says_imp_sees_Enemy RS parts.Inj]) 1); +qed "Reveal_parts_sees_Enemy"; + +(*OR2_analz... and OR4_analz... let us treat those cases using the same + argument as for the Fake case. This is possible for most, but not all, + proofs: Fake does not invent new nonces (as in OR2), and of course Fake + messages originate from the Enemy. *) + +val parts_Fake_tac = + dtac (OR2_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 4 THEN + dtac (OR4_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 6 THEN + dtac Reveal_parts_sees_Enemy 7; + + +(** Theorems of the form X ~: parts (sees Enemy evs) imply that NOBODY + sends messages containing X! **) + +(*Enemy never sees another agent's shared key! (unless it is leaked at start)*) +goal thy + "!!evs. [| evs : otway; A ~: bad |] \ +\ ==> Key (shrK A) ~: parts (sees Enemy evs)"; +be otway.induct 1; +by parts_Fake_tac; +by (Auto_tac()); +(*Deals with Fake message*) +by (best_tac (!claset addDs [impOfSubs analz_subset_parts, + impOfSubs Fake_parts_insert]) 1); +qed "Enemy_not_see_shrK"; + +bind_thm ("Enemy_not_analz_shrK", + [analz_subset_parts, Enemy_not_see_shrK] MRS contra_subsetD); + +Addsimps [Enemy_not_see_shrK, Enemy_not_analz_shrK]; + +(*We go to some trouble to preserve R in the 3rd and 4th subgoals + As usual fast_tac cannot be used because it uses the equalities too soon*) +val major::prems = +goal thy "[| Key (shrK A) : parts (sees Enemy evs); \ +\ evs : otway; \ +\ A:bad ==> R \ +\ |] ==> R"; +br ccontr 1; +br ([major, Enemy_not_see_shrK] MRS rev_notE) 1; +by (swap_res_tac prems 2); +by (ALLGOALS (fast_tac (!claset addIs prems))); +qed "Enemy_see_shrK_E"; + +bind_thm ("Enemy_analz_shrK_E", + analz_subset_parts RS subsetD RS Enemy_see_shrK_E); + +AddSEs [Enemy_see_shrK_E, Enemy_analz_shrK_E]; + + +(*** Future keys can't be seen or used! ***) + +(*Nobody can have SEEN keys that will be generated in the future. + This has to be proved anew for each protocol description, + but should go by similar reasoning every time. Hardest case is the + standard Fake rule. + The Union over C is essential for the induction! *) +goal thy "!!evs. evs : otway ==> \ +\ length evs <= length evs' --> \ +\ Key (newK evs') ~: (UN C. parts (sees C evs))"; +be otway.induct 1; +by parts_Fake_tac; +(*auto_tac does not work here, as it performs safe_tac first*) +by (ALLGOALS Asm_simp_tac); +by (REPEAT_FIRST (best_tac (!claset addDs [impOfSubs analz_subset_parts, + impOfSubs parts_insert_subset_Un, + Suc_leD] + addss (!simpset)))); +val lemma = result(); + +(*Variant needed for the main theorem below*) +goal thy + "!!evs. [| evs : otway; length evs <= length evs' |] \ +\ ==> Key (newK evs') ~: parts (sees C evs)"; +by (fast_tac (!claset addDs [lemma]) 1); +qed "new_keys_not_seen"; +Addsimps [new_keys_not_seen]; + +(*Another variant: old messages must contain old keys!*) +goal thy + "!!evs. [| Says A B X : set_of_list evs; \ +\ Key (newK evt) : parts {X}; \ +\ evs : otway \ +\ |] ==> length evt < length evs"; +br ccontr 1; +by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Enemy] + addIs [impOfSubs parts_mono, leI]) 1); +qed "Says_imp_old_keys"; + + +(*** Future nonces can't be seen or used! [proofs resemble those above] ***) + +goal thy "!!evs. evs : otway ==> \ +\ length evs <= length evs' --> \ +\ Nonce (newN evs') ~: (UN C. parts (sees C evs))"; +be otway.induct 1; +(*auto_tac does not work here, as it performs safe_tac first*) +by (ALLGOALS (asm_simp_tac (!simpset addsimps [de_Morgan_disj] + addcongs [conj_cong]))); +by (REPEAT_FIRST (fast_tac (!claset (*60 seconds???*) + addSEs [MPair_parts] + addDs [Says_imp_sees_Enemy RS parts.Inj, + impOfSubs analz_subset_parts, + impOfSubs parts_insert_subset_Un, + Suc_leD] + addss (!simpset)))); +val lemma = result(); + +(*Variant needed for the main theorem below*) +goal thy + "!!evs. [| evs : otway; length evs <= length evs' |] \ +\ ==> Nonce (newN evs') ~: parts (sees C evs)"; +by (fast_tac (!claset addDs [lemma]) 1); +qed "new_nonces_not_seen"; +Addsimps [new_nonces_not_seen]; + +(*Another variant: old messages must contain old nonces!*) +goal thy + "!!evs. [| Says A B X : set_of_list evs; \ +\ Nonce (newN evt) : parts {X}; \ +\ evs : otway \ +\ |] ==> length evt < length evs"; +br ccontr 1; +by (fast_tac (!claset addSDs [new_nonces_not_seen, Says_imp_sees_Enemy] + addIs [impOfSubs parts_mono, leI]) 1); +qed "Says_imp_old_nonces"; + + +(*Nobody can have USED keys that will be generated in the future. + ...very like new_keys_not_seen*) +goal thy "!!evs. evs : otway ==> \ +\ length evs <= length evs' --> \ +\ newK evs' ~: keysFor (UN C. parts (sees C evs))"; +be otway.induct 1; +by parts_Fake_tac; +by (ALLGOALS Asm_simp_tac); +(*OR1 and OR3*) +by (EVERY (map (fast_tac (!claset addDs [Suc_leD] addss (!simpset))) [4,2])); +(*Fake, OR2, OR4: these messages send unknown (X) components*) +by (EVERY + (map + (best_tac + (!claset addDs [impOfSubs (analz_subset_parts RS keysFor_mono), + impOfSubs (parts_insert_subset_Un RS keysFor_mono), + Suc_leD] + addEs [new_keys_not_seen RS not_parts_not_analz RSN(2,rev_notE)] + addss (!simpset))) + [3,2,1])); +(*Reveal: dummy message*) +by (best_tac (!claset addEs [new_keys_not_seen RSN(2,rev_notE)] + addIs [less_SucI, impOfSubs keysFor_mono] + addss (!simpset addsimps [le_def])) 1); +val lemma = result(); + +goal thy + "!!evs. [| evs : otway; length evs <= length evs' |] \ +\ ==> newK evs' ~: keysFor (parts (sees C evs))"; +by (fast_tac (!claset addSDs [lemma] addss (!simpset)) 1); +qed "new_keys_not_used"; + +bind_thm ("new_keys_not_analzd", + [analz_subset_parts RS keysFor_mono, + new_keys_not_used] MRS contra_subsetD); + +Addsimps [new_keys_not_used, new_keys_not_analzd]; + + +(** Lemmas concerning the form of items passed in messages **) + + +(**** + The following is to prove theorems of the form + + Key K : analz (insert (Key (newK evt)) (sees Enemy evs)) ==> + Key K : analz (sees Enemy evs) + + A more general formula must be proved inductively. + +****) + + +(*NOT useful in this form, but it says that session keys are not used + to encrypt messages containing other keys, in the actual protocol. + We require that agents should behave like this subsequently also.*) +goal thy + "!!evs. evs : otway ==> \ +\ (Crypt X (newK evt)) : parts (sees Enemy evs) & \ +\ Key K : parts {X} --> Key K : parts (sees Enemy evs)"; +be otway.induct 1; +by parts_Fake_tac; +by (ALLGOALS (asm_simp_tac (!simpset addsimps pushes))); +(*Deals with Faked messages*) +by (best_tac (!claset addSEs partsEs + addDs [impOfSubs analz_subset_parts, + impOfSubs parts_insert_subset_Un] + addss (!simpset)) 2); +(*Base case and Reveal*) +by (Auto_tac()); +result(); + + +(** Specialized rewriting for this proof **) + +Delsimps [image_insert]; +Addsimps [image_insert RS sym]; + +Delsimps [image_Un]; +Addsimps [image_Un RS sym]; + +goal thy "insert (Key (newK x)) (sees A evs) = \ +\ Key `` (newK``{x}) Un (sees A evs)"; +by (Fast_tac 1); +val insert_Key_singleton = result(); + +goal thy "insert (Key (f x)) (Key``(f``E) Un C) = \ +\ Key `` (f `` (insert x E)) Un C"; +by (Fast_tac 1); +val insert_Key_image = result(); + + +(*This lets us avoid analyzing the new message -- unless we have to!*) +(*NEEDED??*) +goal thy "synth (analz (sees Enemy evs)) <= \ +\ synth (analz (sees Enemy (Says A B X # evs)))"; +by (Simp_tac 1); +br (subset_insertI RS analz_mono RS synth_mono) 1; +qed "synth_analz_thin"; + +AddIs [impOfSubs synth_analz_thin]; + + + +(** Session keys are not used to encrypt other session keys **) + +(*Describes the form of Key K when the following message is sent. The use of + "parts" strengthens the induction hyp for proving the Fake case. The + assumptions on A are needed to prevent its being a Faked message. (Based + on NS_Shared/Says_S_message_form) *) +goal thy + "!!evs. evs: otway ==> \ +\ Crypt {|N, Key K|} (shrK A) : parts (sees Enemy evs) & \ +\ A ~: bad --> \ +\ (EX evt:otway. K = newK evt)"; +be otway.induct 1; +by parts_Fake_tac; +by (Auto_tac()); +(*Deals with Fake message*) +by (best_tac (!claset addDs [impOfSubs analz_subset_parts, + impOfSubs Fake_parts_insert]) 1); +val lemma = result() RS mp; + + +(*EITHER describes the form of Key K when the following message is sent, + OR reduces it to the Fake case.*) +goal thy + "!!evs. [| Says B' A {|N, Crypt {|N, Key K|} (shrK A)|} : set_of_list evs; \ +\ evs : otway |] \ +\ ==> (EX evt:otway. K = newK evt) | Key K : analz (sees Enemy evs)"; +by (excluded_middle_tac "A : bad" 1); +by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj] + addss (!simpset)) 2); +by (forward_tac [lemma] 1); +by (fast_tac (!claset addEs partsEs + addSDs [Says_imp_sees_Enemy RS parts.Inj]) 1); +by (Fast_tac 1); +qed "Reveal_message_form"; + + +(*Lemma for the trivial direction of the if-and-only-if*) +goal thy + "!!evs. (Key K : analz (Key``nE Un sEe)) --> \ +\ (K : nE | Key K : analz sEe) ==> \ +\ (Key K : analz (Key``nE Un sEe)) = (K : nE | Key K : analz sEe)"; +by (fast_tac (!claset addSEs [impOfSubs analz_mono]) 1); +val lemma = result(); + + +(*The equality makes the induction hypothesis easier to apply*) +goal thy + "!!evs. evs : otway ==> \ +\ ALL K E. (Key K : analz (Key``(newK``E) Un (sees Enemy evs))) = \ +\ (K : newK``E | Key K : analz (sees Enemy evs))"; +be otway.induct 1; +bd OR2_analz_sees_Enemy 4; +bd OR4_analz_sees_Enemy 6; +bd Reveal_message_form 7; +by (REPEAT_FIRST (ares_tac [allI, lemma])); +by (REPEAT ((eresolve_tac [bexE, disjE] ORELSE' hyp_subst_tac) 7)); +by (ALLGOALS (*Takes 28 secs*) + (asm_simp_tac + (!simpset addsimps ([insert_Key_singleton, insert_Key_image, pushKey_newK] + @ pushes) + setloop split_tac [expand_if]))); +(** LEVEL 7 **) +(*Reveal case 2, OR4, OR2, Fake*) +by (EVERY (map enemy_analz_tac [7,5,3,2])); +(*Reveal case 1, OR3, Base*) +by (Auto_tac()); +qed_spec_mp "analz_image_newK"; + + +goal thy + "!!evs. evs : otway ==> \ +\ Key K : analz (insert (Key (newK evt)) (sees Enemy evs)) = \ +\ (K = newK evt | Key K : analz (sees Enemy evs))"; +by (asm_simp_tac (HOL_ss addsimps [pushKey_newK, analz_image_newK, + insert_Key_singleton]) 1); +by (Fast_tac 1); +qed "analz_insert_Key_newK"; + + +(*Describes the form of K and NA when the Server sends this message.*) +goal thy + "!!evs. [| Says Server B \ +\ {|NA, Crypt {|NA, K|} (shrK A), \ +\ Crypt {|NB, K|} (shrK B)|} : set_of_list evs; \ +\ evs : otway |] \ +\ ==> (EX evt:otway. K = Key(newK evt)) & \ +\ (EX i. NA = Nonce i)"; +be rev_mp 1; +be otway.induct 1; +by (ALLGOALS (fast_tac (!claset addIs [less_SucI] addss (!simpset)))); +qed "Says_Server_message_form"; + + +(*Crucial security property, but not itself enough to guarantee correctness! + The need for quantification over N, C seems to indicate the problem. + Omitting the Reveal message from the description deprives us of even + this clue. *) +goal thy + "!!evs. [| A ~: bad; B ~: bad; evs : otway; evt : otway |] \ +\ ==> Says Server B \ +\ {|Nonce NA, Crypt {|Nonce NA, Key(newK evt)|} (shrK A), \ +\ Crypt {|NB, Key(newK evt)|} (shrK B)|} : set_of_list evs --> \ +\ (ALL N C. Says C Enemy {|N, Key(newK evt)|} ~: set_of_list evs) --> \ +\ Key(newK evt) ~: analz (sees Enemy evs)"; +be otway.induct 1; +bd OR2_analz_sees_Enemy 4; +bd OR4_analz_sees_Enemy 6; +bd Reveal_message_form 7; +by (REPEAT_FIRST (eresolve_tac [asm_rl, bexE, disjE] ORELSE' hyp_subst_tac)); +by (ALLGOALS + (asm_full_simp_tac + (!simpset addsimps ([analz_subset_parts RS contra_subsetD, + analz_insert_Key_newK] @ pushes) + setloop split_tac [expand_if]))); +(** LEVEL 6 **) +(*Reveal case 1*) +by (Fast_tac 5); +(*OR3*) +by (fast_tac (!claset addSIs [parts_insertI] + addEs [Says_imp_old_keys RS less_irrefl] + addss (!simpset)) 3); +(*Reveal case 2, OR4, OR2, Fake*) +br conjI 3; +by (REPEAT (enemy_analz_tac 1)); +val lemma = result() RS mp RS mp RSN(2,rev_notE); + + + +(*WEAK VERSION: NEED TO ELIMINATE QUANTIFICATION OVER N, C!!*) +goal thy + "!!evs. [| Says Server B \ +\ {|NA, Crypt {|NA, K|} (shrK A), \ +\ Crypt {|NB, K|} (shrK B)|} : set_of_list evs; \ +\ (ALL N C. Says C Enemy {|N, K|} ~: set_of_list evs); \ +\ A ~: bad; B ~: bad; evs : otway |] \ +\ ==> K ~: analz (sees Enemy evs)"; +by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); +by (fast_tac (!claset addSEs [lemma]) 1); +qed "Enemy_not_see_encrypted_key"; + + +(*** Attempting to prove stronger properties ***) + +(** The Key K uniquely identifies the Server's message. **) + +fun ex_strip_tac i = REPEAT (ares_tac [exI, conjI] i) THEN assume_tac (i+1); + +goal thy + "!!evs. evs : otway ==> \ +\ EX A' B' NA' NB'. ALL A B NA NB. \ +\ Says Server B \ +\ {|NA, Crypt {|NA, K|} (shrK A), \ +\ Crypt {|NB, K|} (shrK B)|} : set_of_list evs --> \ +\ A=A' & B=B' & NA=NA' & NB=NB'"; +be otway.induct 1; +by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); +by (Step_tac 1); +(*Remaining cases: OR3 and OR4*) +by (ex_strip_tac 2); +by (Fast_tac 2); +by (excluded_middle_tac "K = Key(newK evsa)" 1); +by (Asm_simp_tac 1); +by (REPEAT (ares_tac [refl,exI,impI,conjI] 1)); +(*...we assume X is a very new message, and handle this case by contradiction*) +by (fast_tac (!claset addEs [Says_imp_old_keys RS less_irrefl] + delrules [conjI] (*prevent split-up into 4 subgoals*) + addss (!simpset addsimps [parts_insertI])) 1); +val lemma = result(); + + +goal thy + "!!evs. [| Says Server B \ +\ {|NA, Crypt {|NA, K|} (shrK A), \ +\ Crypt {|NB, K|} (shrK B)|} \ +\ : set_of_list evs; \ +\ Says Server B' \ +\ {|NA', Crypt {|NA', K|} (shrK A'), \ +\ Crypt {|NB', K|} (shrK B')|} \ +\ : set_of_list evs; \ +\ evs : otway |] \ +\ ==> A=A' & B=B' & NA=NA' & NB=NB'"; +bd lemma 1; +by (REPEAT (etac exE 1)); +(*Duplicate the assumption*) +by (forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl 1); +by (fast_tac (!claset addSDs [spec]) 1); +qed "unique_session_keys"; + + +(*Could probably remove the A ~= B premise using another induction*) +goal thy + "!!evs. [| A ~: bad; A ~= B; evs : otway |] \ +\ ==> Crypt {|NA, Agent A, Agent B|} (shrK A) \ +\ : parts (sees Enemy evs) --> \ +\ Says A B {|NA, Agent A, Agent B, \ +\ Crypt {|NA, Agent A, Agent B|} (shrK A)|} \ +\ : set_of_list evs"; +be otway.induct 1; +by parts_Fake_tac; +by (ALLGOALS Asm_simp_tac); +(*Fake*) +by (best_tac (!claset addSDs [impOfSubs analz_subset_parts, + impOfSubs Fake_parts_insert]) 2); +by (Auto_tac()); +qed_spec_mp "Crypt_imp_OR1"; + + +(*This key property is FALSE. Somebody could make a fake message to Server + substituting some other nonce NA' for NB.*) +goal thy + "!!evs. [| A ~: bad; evs : otway |] \ +\ ==> Crypt {|Nonce NA, Key K|} (shrK A) : parts (sees Enemy evs) --> \ +\ Says A B {|Nonce NA, Agent A, Agent B, \ +\ Crypt {|Nonce NA, Agent A, Agent B|} (shrK A)|} \ +\ : set_of_list evs --> \ +\ (EX B NB. Says Server B \ +\ {|Nonce NA, \ +\ Crypt {|Nonce NA, Key K|} (shrK A), \ +\ Crypt {|Nonce NB, Key K|} (shrK B)|} \ +\ : set_of_list evs)"; +be otway.induct 1; +fun ftac rl = forward_tac [rl]; +by ( + ftac (OR2_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 4 THEN + ftac (OR4_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 6 THEN + ftac Reveal_parts_sees_Enemy 7); + +(* by parts_Fake_tac; ?*) +by (ALLGOALS Asm_simp_tac); +(*Fake*) +by (best_tac (!claset addSDs [impOfSubs analz_subset_parts, + impOfSubs Fake_parts_insert]) 1); +(*OR1: it cannot be a new Nonce, contradiction.*) +by (fast_tac (!claset addSIs [parts_insertI] + addSEs partsEs + addEs [Says_imp_old_nonces RS less_irrefl] + addss (!simpset)) 1); +(*OR3 and OR4*) (** LEVEL 5 **) +(*OR4*) +by (REPEAT (Safe_step_tac 2)); +by (best_tac (!claset addSDs [parts_cut]) 3); +by (best_tac (!claset addSDs [parts_cut]) 3); +by (forward_tac [Crypt_imp_OR1] 2); +by (fast_tac (!claset addEs partsEs + addSDs [Says_imp_sees_Enemy RS parts.Inj]) 4); +by (REPEAT (Fast_tac 2)); +(*OR3*) (** LEVEL 11 **) +by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib]))); +fr impI; +by (REPEAT (etac conjE 1 ORELSE hyp_subst_tac 1)); +fr impI; +(*The hypotheses at this point suggest an attack in which nonce NA is used + in two different places*) +writeln "GIVE UP!"; + + + +(*What can A deduce from receipt of OR4? This too is probably FALSE*) +goal thy + "!!evs. [| A ~: bad; evs : otway |] \ +\ ==> ALL B' NA K B. \ +\ Says B' A {|Nonce NA, Crypt {|Nonce NA, Key K|} (shrK A)|} \ +\ : set_of_list evs --> \ +\ Says A B {|Nonce NA, Agent A, Agent B, \ +\ Crypt {|Nonce NA, Agent A, Agent B|} (shrK A)|} \ +\ : set_of_list evs --> \ +\ (EX NB. Says Server B \ +\ {|Nonce NA, \ +\ Crypt {|Nonce NA, Key K|} (shrK A), \ +\ Crypt {|Nonce NB, Key K|} (shrK B)|} \ +\ : set_of_list evs)"; +be otway.induct 1; +by (ALLGOALS (asm_simp_tac (!simpset addcongs [conj_cong]))); +(*OR2*) +by (Fast_tac 3); +(*OR1: it cannot be a new Nonce, contradiction.*) +by (fast_tac (!claset addSIs [parts_insertI] + addEs [Says_imp_old_nonces RS less_irrefl] + addss (!simpset)) 2); +by (ALLGOALS + (asm_simp_tac (!simpset addsimps [all_conj_distrib, de_Morgan_disj, de_Morgan_conj]))); +(*Fake, OR4*) (** LEVEL 5 **) +by (step_tac (!claset delrules [MPair_analz]) 1); +by (ALLGOALS Asm_simp_tac); +by (fast_tac (!claset addSDs [spec]) 4); +by (forward_tac [Crypt_imp_OR1] 3); +by (fast_tac (!claset addEs partsEs + addSDs [Says_imp_sees_Enemy RS parts.Inj]) 5); +by (REPEAT (Fast_tac 3)); +(** LEVEL 11 **) +(*Fake (??) and OR4*) + + +by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib, ex_disj_distrib, de_Morgan_disj, de_Morgan_conj]))); + + +(*** Session keys are issued at most once, and identify the principals ***) + +(** First, two lemmas for the Fake, OR2 and OR4 cases **) + +goal thy + "!!evs. [| X : synth (analz (sees Enemy evs)); \ +\ Crypt X' (shrK C) : parts{X}; \ +\ C ~: bad; evs : otway |] \ +\ ==> Crypt X' (shrK C) : parts (sees Enemy evs)"; +by (best_tac (!claset addSEs [impOfSubs analz_subset_parts] + addDs [impOfSubs parts_insert_subset_Un] + addss (!simpset)) 1); +qed "Crypt_Fake_parts"; + +goal thy + "!!evs. [| Crypt X' K : parts (sees A evs); evs : otway |] \ +\ ==> EX S S' Y. Says S S' Y : set_of_list evs & \ +\ Crypt X' K : parts {Y}"; +bd parts_singleton 1; +by (fast_tac (!claset addSDs [seesD] addss (!simpset)) 1); +qed "Crypt_parts_singleton"; + +(*The Key K uniquely identifies a pair of senders in the message encrypted by + C, but if C=Enemy then he could send all sorts of nonsense.*) +goal thy + "!!evs. evs : otway ==> \ +\ EX A B. ALL C. \ +\ C ~: bad --> \ +\ (ALL S S' X. Says S S' X : set_of_list evs --> \ +\ (EX NA. Crypt {|NA, Key K|} (shrK C) : parts{X}) --> C=A | C=B)"; +by (Simp_tac 1); +be otway.induct 1; +bd OR2_analz_sees_Enemy 4; +bd OR4_analz_sees_Enemy 6; +by (ALLGOALS + (asm_simp_tac (!simpset addsimps [all_conj_distrib, imp_conj_distrib]))); +by (REPEAT_FIRST (etac exE)); +(*OR4*) +by (ex_strip_tac 4); +by (fast_tac (!claset addSDs [synth.Inj RS Crypt_Fake_parts, + Crypt_parts_singleton]) 4); +(*OR3: Case split propagates some context to other subgoal...*) + (** LEVEL 8 **) +by (excluded_middle_tac "K = newK evsa" 3); +by (Asm_simp_tac 3); +by (REPEAT (ares_tac [exI] 3)); +(*...we prove this case by contradiction: the key is too new!*) +by (fast_tac (!claset addIs [parts_insertI] + addSEs partsEs + addEs [Says_imp_old_keys RS less_irrefl] + addss (!simpset)) 3); +(*OR2*) (** LEVEL 12 **) +(*enemy_analz_tac just does not work here: it is an entirely different proof!*) +by (ex_strip_tac 2); +by (res_inst_tac [("x1","X")] (insert_commute RS ssubst) 2); +by (Simp_tac 2); +by (fast_tac (!claset addSDs [synth.Inj RS Crypt_Fake_parts, + Crypt_parts_singleton]) 2); +(*Fake*) (** LEVEL 16 **) +by (ex_strip_tac 1); +by (fast_tac (!claset addSDs [Crypt_Fake_parts, Crypt_parts_singleton]) 1); +qed "unique_session_keys2"; + + diff -r 974167c1d2c4 -r ed423882c6a9 src/HOL/Auth/OtwayRees_Bad.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Auth/OtwayRees_Bad.thy Mon Sep 23 17:41:57 1996 +0200 @@ -0,0 +1,79 @@ +(* Title: HOL/Auth/OtwayRees_Bad + ID: $Id$ + Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1996 University of Cambridge + +Inductive relation "otway" for the Otway-Rees protocol. + +The FAULTY version omitting encryption of Nonce NB, as suggested on page 247 of + Burrows, Abadi and Needham. A Logic of Authentication. + Proc. Royal Soc. 426 (1989) +*) + +OtwayRees_Bad = Shared + + +consts otway :: "event list set" +inductive otway + intrs + (*Initial trace is empty*) + Nil "[]: otway" + + (*The enemy MAY say anything he CAN say. We do not expect him to + invent new nonces here, but he can also use NS1. Common to + all similar protocols.*) + Fake "[| evs: otway; B ~= Enemy; X: synth (analz (sees Enemy evs)) |] + ==> Says Enemy B X # evs : otway" + + (*Alice initiates a protocol run*) + OR1 "[| evs: otway; A ~= B; B ~= Server |] + ==> Says A B {|Nonce (newN evs), Agent A, Agent B, + Crypt {|Nonce (newN evs), Agent A, Agent B|} + (shrK A) |} + # evs : otway" + + (*Bob's response to Alice's message. Bob doesn't know who + the sender is, hence the A' in the sender field. + We modify the published protocol by NOT encrypting NB.*) + OR2 "[| evs: otway; B ~= Server; + Says A' B {|Nonce NA, Agent A, Agent B, X|} : set_of_list evs |] + ==> Says B Server + {|Nonce NA, Agent A, Agent B, X, Nonce (newN evs), + Crypt {|Nonce NA, Agent A, Agent B|} (shrK B)|} + # evs : otway" + + (*The Server receives Bob's message and checks that the three NAs + match. Then he sends a new session key to Bob with a packet for + forwarding to Alice.*) + OR3 "[| evs: otway; B ~= Server; + Says B' Server + {|Nonce NA, Agent A, Agent B, + Crypt {|Nonce NA, Agent A, Agent B|} (shrK A), + Nonce NB, + Crypt {|Nonce NA, Agent A, Agent B|} (shrK B)|} + : set_of_list evs |] + ==> Says Server B + {|Nonce NA, + Crypt {|Nonce NA, Key (newK evs)|} (shrK A), + Crypt {|Nonce NB, Key (newK evs)|} (shrK B)|} + # evs : otway" + + (*Bob receives the Server's (?) message and compares the Nonces with + those in the message he previously sent the Server.*) + OR4 "[| evs: otway; A ~= B; B ~= Server; + Says S B {|Nonce NA, X, Crypt {|Nonce NB, Key K|} (shrK B)|} + : set_of_list evs; + Says B Server {|Nonce NA, Agent A, Agent B, X', Nonce NB, X''|} + : set_of_list evs |] + ==> Says B A {|Nonce NA, X|} # evs : otway" + + (*This message models possible leaks of session keys. Alice's Nonce + identifies the protocol run.*) + Reveal "[| evs: otway; A ~= Enemy; + Says B' A {|Nonce NA, Crypt {|Nonce NA, Key K|} (shrK A)|} + : set_of_list evs; + Says A B {|Nonce NA, Agent A, Agent B, + Crypt {|Nonce NA, Agent A, Agent B|} (shrK A)|} + : set_of_list evs |] + ==> Says A Enemy {|Nonce NA, Key K|} # evs : otway" + +end