# HG changeset patch # User paulson # Date 843495691 -7200 # Node ID 5be4c8ca7b25f6d66872dac1ea0ca81702634cef # Parent 4b7a432fb3ed24cfeea5dbb41f5049cbfe160168 Correction of protocol; addition of Reveal message; proofs of correctness in its presence diff -r 4b7a432fb3ed -r 5be4c8ca7b25 src/HOL/Auth/OtwayRees.ML --- a/src/HOL/Auth/OtwayRees.ML Mon Sep 23 18:20:43 1996 +0200 +++ b/src/HOL/Auth/OtwayRees.ML Mon Sep 23 18:21:31 1996 +0200 @@ -5,30 +5,42 @@ Inductive relation "otway" for the Otway-Rees protocol. +Version that encrypts Nonce NB + From page 244 of Burrows, Abadi and Needham. A Logic of Authentication. Proc. Royal Soc. 426 (1989) *) + +(*MAY DELETE**) +Delsimps [parts_insert_sees]; +AddIffs [le_refl]; +val disj_cong = + let val th = prove_goal HOL.thy + "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))" + (fn _=> [fast_tac HOL_cs 1]) + in standard (impI RSN (2, th RS mp RS mp)) end; + + open OtwayRees; proof_timing:=true; HOL_quantifiers := false; -(** Weak liveness: there are traces that reach the end **) - +(*Weak liveness: there are traces that reach the end*) goal thy "!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ -\ ==> EX K. EX evs: otway. \ -\ Says A B (Crypt (Agent A) K) : set_of_list evs"; +\ ==> 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 RS - otway.OR5) 2; +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)))); -qed "weak_liveness"; +result(); (**** Inductive proofs about otway ****) @@ -51,13 +63,6 @@ Addsimps [not_Says_to_self]; AddSEs [not_Says_to_self RSN (2, rev_notE)]; -goal thy "!!evs. evs : otway ==> Notes A X ~: set_of_list evs"; -be otway.induct 1; -by (Auto_tac()); -qed "not_Notes"; -Addsimps [not_Notes]; -AddSEs [not_Notes RSN (2, rev_notE)]; - (** For reasoning about the encrypted portion of messages **) @@ -75,26 +80,28 @@ \ K : parts (sees Enemy evs)"; by (fast_tac (!claset addSEs partsEs addSDs [Says_imp_sees_Enemy RS parts.Inj]) 1); -qed "OR5_parts_sees_Enemy"; +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 OR2_OR4_tac = - dtac (OR2_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 4 THEN - dtac (OR4_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 6; +val parts_Fake_tac = + forward_tac [OR2_analz_sees_Enemy RS (impOfSubs analz_subset_parts)] 4 THEN + forward_tac [OR4_analz_sees_Enemy RS (impOfSubs analz_subset_parts)] 6 THEN + forward_tac [Reveal_parts_sees_Enemy] 7; -(*** Shared keys are not betrayed ***) +(** 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 OR2_OR4_tac; +by parts_Fake_tac; by (Auto_tac()); (*Deals with Fake message*) by (best_tac (!claset addDs [impOfSubs analz_subset_parts, @@ -131,13 +138,12 @@ 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 length comparison, and Union over C, are essential for the - induction! *) + 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 OR2_OR4_tac; +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, @@ -161,19 +167,58 @@ \ evs : otway \ \ |] ==> length evt < length evs"; br ccontr 1; +bd leI 1; by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Enemy] - addIs [impOfSubs parts_mono, leI]) 1); + addIs [impOfSubs parts_mono]) 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 evt --> \ +\ Nonce (newN evt) ~: (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 [ parts_insert2] + addcongs [disj_cong]))); +by (REPEAT_FIRST (fast_tac (!claset + addSEs partsEs + addSDs [Says_imp_sees_Enemy RS parts.Inj] + 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' |] \ +\ ==> 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; +bd leI 1; +by (fast_tac (!claset addSDs [new_nonces_not_seen, Says_imp_sees_Enemy] + addIs [impOfSubs parts_mono]) 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 OR2_OR4_tac; -bd OR5_parts_sees_Enemy 7; +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])); @@ -187,7 +232,7 @@ addEs [new_keys_not_seen RS not_parts_not_analz RSN(2,rev_notE)] addss (!simpset))) [3,2,1])); -(*OR5: dummy message*) +(*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); @@ -228,14 +273,14 @@ \ (Crypt X (newK evt)) : parts (sees Enemy evs) & \ \ Key K : parts {X} --> Key K : parts (sees Enemy evs)"; be otway.induct 1; -by OR2_OR4_tac; +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 OR5*) +(*Base case and Reveal*) by (Auto_tac()); result(); @@ -273,6 +318,40 @@ (** 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)) --> \ @@ -282,6 +361,7 @@ 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))) = \ @@ -289,18 +369,19 @@ be otway.induct 1; bd OR2_analz_sees_Enemy 4; bd OR4_analz_sees_Enemy 6; -by (REPEAT_FIRST (resolve_tac [allI, lemma])); -by (ALLGOALS (*Takes 35 secs*) +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]))); -(*OR4, OR2, Fake*) -by (EVERY (map enemy_analz_tac [5,3,2])); -(*OR3*) -by (Fast_tac 2); -(*Base case*) -by (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1); +(** 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"; @@ -314,14 +395,235 @@ qed "analz_insert_Key_newK"; -(*Describes the form *and age* of K when the following message is sent*) +(** 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"; + + + +(**** Towards proving stronger authenticity properties ****) + +(*Only OR1 can have caused such a part of a message to appear.*) +goal thy + "!!evs. [| A ~: bad; 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"; + + +(** The Nonce NA uniquely identifies A's message. **) + +goal thy + "!!evs. [| evs : otway; A ~: bad |] \ +\ ==> EX B'. ALL B. \ +\ Crypt {|NA, Agent A, Agent B|} (shrK A) : parts (sees Enemy evs) --> \ +\ B = B'"; +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); +(*Base case*) +by (fast_tac (!claset addss (!simpset)) 1); +by (Step_tac 1); +(*OR1: creation of new Nonce*) +by (excluded_middle_tac "NA = Nonce (newN evsa)" 1); +by (Asm_simp_tac 1); +by (Fast_tac 1); +by (best_tac (!claset addSEs partsEs + addEs [new_nonces_not_seen RSN(2,rev_notE)]) 1); +val lemma = result(); + +goal thy + "!!evs.[| Crypt {|NA, Agent A, Agent B|} (shrK A) : parts (sees Enemy evs); \ +\ Crypt {|NA, Agent A, Agent C|} (shrK A) : parts (sees Enemy evs); \ +\ evs : otway; A ~: bad |] \ +\ ==> B = C"; +bd lemma 1; +ba 1; +by (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_OR1_nonce"; + + +val nonce_not_seen_now = le_refl RSN (2, new_nonces_not_seen) RSN (2,rev_notE); + +(*It is impossible to re-use a nonce in both OR1 and OR2. This holds because + OR2 encrypts Nonce NB. It prevents the attack that can occur in the + over-simplified version of this protocol: see OtwayRees_Bad.*) +goal thy + "!!evs. [| A ~: bad; evs : otway |] \ +\ ==> Crypt {|NA, Agent A, Agent B|} (shrK A) \ +\ : parts (sees Enemy evs) --> \ +\ Crypt {|NA', NA, Agent A', Agent A|} (shrK A) \ +\ ~: parts (sees Enemy evs)"; +be otway.induct 1; +by (ALLGOALS (asm_simp_tac (!simpset addsimps [parts_insert2]))); +(*It is hard to generate this proof in a reasonable amount of time*) +by (step_tac (!claset addSEs [MPair_parts, nonce_not_seen_now] + addSDs [Says_imp_sees_Enemy RS parts.Inj]) 1); +by (REPEAT_FIRST (fast_tac (!claset (*40 seconds??*) + addSDs [impOfSubs analz_subset_parts, + impOfSubs parts_insert_subset_Un] + addss (!simpset)))); +by (REPEAT_FIRST (fast_tac (!claset + addSEs (partsEs@[nonce_not_seen_now]) + addSDs [impOfSubs analz_subset_parts, + impOfSubs parts_insert_subset_Un] + addss (!simpset)))); +qed_spec_mp"no_nonce_OR1_OR2"; + + + +(*If the encrypted message appears, and A has used Nonce NA to start a run, + then it originated with the Server!*) +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 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 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 (REPEAT (best_tac (!claset addSDs [parts_cut]) 3)); +by (fast_tac (!claset addSIs [Crypt_imp_OR1] + addEs partsEs + addDs [Says_imp_sees_Enemy RS parts.Inj]) 2); +(*OR3*) (** LEVEL 8 **) +by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib]))); +by (step_tac (!claset delrules [disjCI, impCE]) 1); +by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS parts.Inj] + addSEs [MPair_parts] + addEs [unique_OR1_nonce]) 1); +by (fast_tac (!claset addSEs [MPair_parts] + addSDs [Says_imp_sees_Enemy RS parts.Inj] + addEs [no_nonce_OR1_OR2 RSN (2, rev_notE)] + delrules [conjI] (*stop split-up into 4 subgoals*)) 1); +qed_spec_mp "Crypt_imp_Server_msg"; + + +(*Crucial property: if A receives B's OR4 message and the nonce NA agrees + then the key really did come from the Server! CANNOT prove this of the + bad form of this protocol, even though we can prove + Enemy_not_see_encrypted_key*) +goal thy + "!!evs. [| A ~: bad; evs : otway |] \ +\ ==> 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); +(*Fake, OR4*) (** LEVEL 4 **) +by (step_tac (!claset delrules [impCE]) 1); +by (ALLGOALS Asm_simp_tac); +by (Fast_tac 4); +by (fast_tac (!claset addSIs [Crypt_imp_OR1] + addEs partsEs + addDs [Says_imp_sees_Enemy RS parts.Inj]) 3); +(** LEVEL 8 **) +(*Still subcases of Fake and OR4*) +by (fast_tac (!claset addSIs [Crypt_imp_Server_msg] + addDs [impOfSubs analz_subset_parts]) 1); +by (fast_tac (!claset addSIs [Crypt_imp_Server_msg] + addEs partsEs + addDs [Says_imp_sees_Enemy RS parts.Inj]) 1); +val lemma = result(); + +val OR4_imp_Says_Server_A = + lemma RSN (2, rev_mp) RS mp |> standard; + + + +(*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) & \ -\ length evt < length evs) & \ +\ ==> (EX evt:otway. K = Key(newK evt)) & \ \ (EX i. NA = Nonce i)"; be rev_mp 1; be otway.induct 1; @@ -329,31 +631,52 @@ qed "Says_Server_message_form"; -(*Crucial secrecy property: Enemy does not see the keys sent in msg OR3*) +(** Crucial secrecy property: Enemy does not see the keys sent in msg OR3 **) + goal thy - "!!evs. [| Says Server A \ -\ {|NA, Crypt {|NA, K|} (shrK B), \ -\ Crypt {|NB, K|} (shrK A)|} : set_of_list evs; \ -\ A ~: bad; B ~: bad; evs : otway |] ==> \ -\ K ~: analz (sees Enemy evs)"; -be rev_mp 1; + "!!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 --> \ +\ Says A Enemy {|Nonce NA, 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; -by (ALLGOALS Asm_simp_tac); -(*Next 3 steps infer that K has the form "Key (newK evs'" ... *) -by (REPEAT_FIRST (resolve_tac [conjI, impI])); -by (TRYALL (forward_tac [Says_Server_message_form] THEN' assume_tac)); -by (REPEAT_FIRST (eresolve_tac [bexE, exE, conjE] ORELSE' hyp_subst_tac)); +by (forward_tac [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]))); -(*OR4, OR2, Fake*) -by (EVERY (map enemy_analz_tac [4,2,1])); +(** LEVEL 6 **) (*OR3*) -by (fast_tac (!claset addSEs [less_irrefl]) 1); +by (fast_tac (!claset addSIs [parts_insertI] + addEs [Says_imp_old_keys RS less_irrefl] + addss (!simpset)) 3); +(*Reveal case 2, OR4, OR2, Fake*) +by (REPEAT_FIRST (resolve_tac [conjI, impI] ORELSE' enemy_analz_tac)); +(*Reveal case 1*) (** LEVEL 8 **) +by (excluded_middle_tac "Aa : bad" 1); +(*But this contradicts Key(newK evt) ~: analz (sees Enemy evsa) *) +bd (Says_imp_sees_Enemy RS analz.Inj) 2; +by (fast_tac (!claset addSDs [analz.Decrypt] addss (!simpset)) 2); +(*So now we have Aa ~: bad *) +by (dresolve_tac [OR4_imp_Says_Server_A] 1); +by (REPEAT (assume_tac 1)); +by (fast_tac (!claset addDs [unique_session_keys] addss (!simpset)) 1); +val lemma = result() RS mp RS mp RSN(2,rev_notE); + +goal thy + "!!evs. [| Says Server B \ +\ {|NA, Crypt {|NA, K|} (shrK A), \ +\ Crypt {|NB, K|} (shrK B)|} : set_of_list evs; \ +\ Says A Enemy {|NA, 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"; @@ -380,8 +703,6 @@ by (fast_tac (!claset addSDs [seesD] addss (!simpset)) 1); qed "Crypt_parts_singleton"; -fun ex_strip_tac i = REPEAT (ares_tac [exI, conjI] i) THEN assume_tac (i+1); - (*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 @@ -407,7 +728,7 @@ 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 [impOfSubs (subset_insertI RS parts_mono)] +by (fast_tac (!claset addIs [parts_insertI] addSEs partsEs addEs [Says_imp_old_keys RS less_irrefl] addss (!simpset)) 3); @@ -421,6 +742,5 @@ (*Fake*) (** LEVEL 16 **) by (ex_strip_tac 1); by (fast_tac (!claset addSDs [Crypt_Fake_parts, Crypt_parts_singleton]) 1); -qed "unique_session_keys"; +qed "key_identifies_senders"; -(*It seems strange but this theorem is NOT needed to prove the main result!*) diff -r 4b7a432fb3ed -r 5be4c8ca7b25 src/HOL/Auth/OtwayRees.thy --- a/src/HOL/Auth/OtwayRees.thy Mon Sep 23 18:20:43 1996 +0200 +++ b/src/HOL/Auth/OtwayRees.thy Mon Sep 23 18:21:31 1996 +0200 @@ -5,6 +5,8 @@ Inductive relation "otway" for the Otway-Rees protocol. +Version that encrypts Nonce NB + From page 244 of Burrows, Abadi and Needham. A Logic of Authentication. Proc. Royal Soc. 426 (1989) @@ -25,10 +27,10 @@ ==> Says Enemy B X # evs : otway" (*Alice initiates a protocol run*) - OR1 "[| evs: otway; A ~= B |] + 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) |} + Crypt {|Nonce (newN evs), Agent A, Agent B|} + (shrK A) |} # evs : otway" (*Bob's response to Alice's message. Bob doesn't know who @@ -37,8 +39,9 @@ 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)|} + {|Nonce NA, Agent A, Agent B, X, + Crypt {|Nonce NA, Nonce (newN evs), + Agent A, Agent B|} (shrK B)|} # evs : otway" (*The Server receives Bob's message and checks that the three NAs @@ -48,8 +51,7 @@ 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)|} + Crypt {|Nonce NA, Nonce NB, Agent A, Agent B|} (shrK B)|} : set_of_list evs |] ==> Says Server B {|Nonce NA, @@ -59,19 +61,23 @@ (*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; + 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''|} + Says B Server {|Nonce NA, Agent A, Agent B, X', + Crypt {|Nonce NA, Nonce NB, Agent A, Agent B|} + (shrK B)|} : set_of_list evs |] - ==> (Says B A {|Nonce NA, X|}) # evs : otway" + ==> Says B A {|Nonce NA, X|} # evs : otway" - (*Alice checks her Nonce, then sends a dummy message to Bob, - using the new session key.*) - OR5 "[| evs: otway; - 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, X|} : set_of_list evs |] - ==> Says A B (Crypt (Agent A) K) # 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