# HG changeset patch # User paulson # Date 844965634 -7200 # Node ID 307ebbbec86258b05df25d17c947aed1df2618e4 # Parent e2ec077ac90d856ae3832896b9163987f9bcb99c Abadi and Needham's variant of Otway-Rees diff -r e2ec077ac90d -r 307ebbbec862 src/HOL/Auth/OtwayRees_AN.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Auth/OtwayRees_AN.ML Thu Oct 10 18:40:34 1996 +0200 @@ -0,0 +1,536 @@ +(* Title: HOL/Auth/OtwayRees + ID: $Id$ + Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1996 University of Cambridge + +Inductive relation "otway" for the Otway-Rees protocol. + +Simplified version with minimal encryption but explicit messages + +From page 11 of + Abadi and Needham. Prudent Engineering Practice for Cryptographic Protocols. + IEEE Trans. SE 22 (1), 1996 +*) + +open OtwayRees_AN; + +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 lost. \ +\ Says B A (Crypt {|Nonce NA, Agent A, Agent B, Key K|} (shrK A)) \ +\ : set_of_list evs"; +by (REPEAT (resolve_tac [exI,bexI] 1)); +by (rtac (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 (REPEAT_FIRST (fast_tac (!claset addss (!simpset setsolver safe_solver)))); +result(); + + +(**** Inductive proofs about otway ****) + +goal thy "!!evs. lost' <= lost ==> otway lost' <= otway lost"; +by (rtac subsetI 1); +by (etac otway.induct 1); +by (REPEAT_FIRST + (best_tac (!claset addIs (impOfSubs (sees_mono RS analz_mono RS synth_mono) + :: otway.intrs)))); +qed "otway_mono"; + +(*Nobody sends themselves messages*) +goal thy "!!evs. evs : otway lost ==> ALL A X. Says A A X ~: set_of_list evs"; +by (etac 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 S B {|X, X'|} : set_of_list evs ==> \ +\ X : analz (sees lost Spy evs)"; +by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1); +qed "OR4_analz_sees_Spy"; + +goal thy "!!evs. Says B' A (Crypt {|N,Agent A,B,K|} K') : set_of_list evs ==> \ +\ K : parts (sees lost Spy evs)"; +by (fast_tac (!claset addSEs partsEs + addSDs [Says_imp_sees_Spy RS parts.Inj]) 1); +qed "Reveal_parts_sees_Spy"; + +(*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 Spy. *) + +bind_thm ("OR4_parts_sees_Spy", + OR4_analz_sees_Spy RS (impOfSubs analz_subset_parts)); + +(*We instantiate the variable to "lost". Leaving it as a Var makes proofs + harder to complete, since simplification does less for us.*) +val parts_Fake_tac = + forw_inst_tac [("lost","lost")] OR4_parts_sees_Spy 6 THEN + forw_inst_tac [("lost","lost")] Reveal_parts_sees_Spy 7; + +(*For proving the easier theorems about X ~: parts (sees lost Spy evs) *) +fun parts_induct_tac i = SELECT_GOAL + (DETERM (etac otway.induct 1 THEN parts_Fake_tac THEN + (*Fake message*) + TRY (best_tac (!claset addDs [impOfSubs analz_subset_parts, + impOfSubs Fake_parts_insert] + addss (!simpset)) 2)) THEN + (*Base case*) + fast_tac (!claset addss (!simpset)) 1 THEN + ALLGOALS Asm_simp_tac) i; + +(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY + sends messages containing X! **) + +(*Spy never sees another agent's shared key! (unless it's lost at start)*) +goal thy + "!!evs. [| evs : otway lost; A ~: lost |] \ +\ ==> Key (shrK A) ~: parts (sees lost Spy evs)"; +by (parts_induct_tac 1); +by (Auto_tac()); +qed "Spy_not_see_shrK"; + +bind_thm ("Spy_not_analz_shrK", + [analz_subset_parts, Spy_not_see_shrK] MRS contra_subsetD); + +Addsimps [Spy_not_see_shrK, Spy_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 lost Spy evs); \ +\ evs : otway lost; \ +\ A:lost ==> R \ +\ |] ==> R"; +by (rtac ccontr 1); +by (rtac ([major, Spy_not_see_shrK] MRS rev_notE) 1); +by (swap_res_tac prems 2); +by (ALLGOALS (fast_tac (!claset addIs prems))); +qed "Spy_see_shrK_E"; + +bind_thm ("Spy_analz_shrK_E", + analz_subset_parts RS subsetD RS Spy_see_shrK_E); + +AddSEs [Spy_see_shrK_E, Spy_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 lost ==> \ +\ length evs <= length evs' --> \ +\ Key (newK evs') ~: (UN C. parts (sees lost C evs))"; +by (parts_induct_tac 1); +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 lost; length evs <= length evs' |] \ +\ ==> Key (newK evs') ~: parts (sees lost 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 lost \ +\ |] ==> length evt < length evs"; +by (rtac ccontr 1); +by (dtac leI 1); +by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Spy] + 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 lost ==> \ +\ length evs <= length evt --> \ +\ Nonce (newN evt) ~: (UN C. parts (sees lost C evs))"; +by (etac 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_Spy 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 lost; length evs <= length evs' |] \ +\ ==> Nonce (newN evs') ~: parts (sees lost 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 lost \ +\ |] ==> length evt < length evs"; +by (rtac ccontr 1); +by (dtac leI 1); +by (fast_tac (!claset addSDs [new_nonces_not_seen, Says_imp_sees_Spy] + 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 lost ==> \ +\ length evs <= length evs' --> \ +\ newK evs' ~: keysFor (UN C. parts (sees lost C evs))"; +by (parts_induct_tac 1); +(*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 lost; length evs <= length evs' |] \ +\ ==> newK evs' ~: keysFor (parts (sees lost 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]; + + + +(*** Proofs involving analz ***) + +(*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 + assumption A ~: lost prevents its being a Faked message. (Based + on NS_Shared/Says_S_message_form) *) +goal thy + "!!evs. evs: otway lost ==> \ +\ Crypt {|N, Agent A, B, Key K|} (shrK A) : parts (sees lost Spy evs) \ +\ --> A ~: lost --> (EX evt: otway lost. K = newK evt)"; +by (parts_induct_tac 1); +by (Auto_tac()); +qed_spec_mp "Reveal_message_lemma"; + +(*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 (Crypt {|N, Agent A, B, Key K|} (shrK A)) \ +\ : set_of_list evs; \ +\ evs : otway lost |] \ +\ ==> (EX evt: otway lost. K = newK evt) \ +\ | Key K : analz (sees lost Spy evs)"; +br (Reveal_message_lemma RS disjCI) 1; +ba 1; +by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj] + addDs [impOfSubs analz_subset_parts]) 1); +by (fast_tac (!claset addSDs [Says_Crypt_lost]) 1); +qed "Reveal_message_form"; + + +(*For proofs involving analz. We again instantiate the variable to "lost".*) +val analz_Fake_tac = + dres_inst_tac [("lost","lost")] OR4_analz_sees_Spy 6 THEN + forw_inst_tac [("lost","lost")] Reveal_message_form 7; + + +(**** + The following is to prove theorems of the form + + Key K : analz (insert (Key (newK evt)) (sees lost Spy evs)) ==> + Key K : analz (sees lost Spy 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 lost ==> \ +\ (Crypt X (newK evt)) : parts (sees lost Spy evs) & \ +\ Key K : parts {X} --> Key K : parts (sees lost Spy evs)"; +by (etac otway.induct 1); +by parts_Fake_tac; +by (ALLGOALS Asm_simp_tac); +(*Deals with Faked messages*) +by (best_tac (!claset addSEs partsEs + addDs [impOfSubs parts_insert_subset_Un] + addss (!simpset)) 2); +(*Base case and Reveal*) +by (Auto_tac()); +result(); + + +(** Session keys are not used to encrypt other session keys **) + +(*The equality makes the induction hypothesis easier to apply*) +goal thy + "!!evs. evs : otway lost ==> \ +\ ALL K E. (Key K : analz (Key``(newK``E) Un (sees lost Spy evs))) = \ +\ (K : newK``E | Key K : analz (sees lost Spy evs))"; +by (etac otway.induct 1); +by analz_Fake_tac; +by (REPEAT_FIRST (ares_tac [allI, analz_image_newK_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 5 **) +(*Reveal case 2, OR4, OR2, Fake*) +by (EVERY (map spy_analz_tac [6, 4, 2])); +(*Reveal case 1, OR3, Base*) +by (REPEAT (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1)); +qed_spec_mp "analz_image_newK"; + + +goal thy + "!!evs. evs : otway lost ==> \ +\ Key K : analz (insert (Key (newK evt)) (sees lost Spy evs)) = \ +\ (K = newK evt | Key K : analz (sees lost Spy 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"; + + +(*** 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 lost ==> \ +\ EX A' B' NA' NB'. ALL A B NA NB. \ +\ Says Server B \ +\ {|Crypt {|NA, Agent A, Agent B, K|} (shrK A), \ +\ Crypt {|NB, Agent A, Agent B, K|} (shrK B)|} : set_of_list evs \ +\ --> A=A' & B=B' & NA=NA' & NB=NB'"; +by (etac 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 (expand_case_tac "K = ?y" 1); +by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); +(*...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 \ +\ {|Crypt {|NA, Agent A, Agent B, K|} (shrK A), \ +\ Crypt {|NB, Agent A, Agent B, K|} (shrK B)|} \ +\ : set_of_list evs; \ +\ Says Server B' \ +\ {|Crypt {|NA', Agent A', Agent B', K|} (shrK A'), \ +\ Crypt {|NB', Agent A', Agent B', K|} (shrK B')|} \ +\ : set_of_list evs; \ +\ evs : otway lost |] \ +\ ==> A=A' & B=B' & NA=NA' & NB=NB'"; +by (dtac 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"; + + + +(**** Authenticity properties relating to NA ****) + +(*If the encrypted message appears then it originated with the Server!*) +goal thy + "!!evs. [| A ~: lost; evs : otway lost |] \ +\ ==> Crypt {|NA, Agent A, Agent B, Key K|} (shrK A) \ +\ : parts (sees lost Spy evs) \ +\ --> (EX NB. Says Server B \ +\ {|Crypt {|NA, Agent A, Agent B, Key K|} (shrK A), \ +\ Crypt {|NB, Agent A, Agent B, Key K|} (shrK B)|} \ +\ : set_of_list evs)"; +by (parts_induct_tac 1); +by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib]))); +(*OR3*) +by (Fast_tac 1); +qed_spec_mp "NA_Crypt_imp_Server_msg"; + + +(*Corollary: 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 + Spy_not_see_encrypted_key*) +goal thy + "!!evs. [| Says B' A (Crypt {|NA, Agent A, Agent B, Key K|} (shrK A)) \ +\ : set_of_list evs; \ +\ A ~: lost; evs : otway lost |] \ +\ ==> EX NB. Says Server B \ +\ {|Crypt {|NA, Agent A, Agent B, Key K|} (shrK A), \ +\ Crypt {|NB, Agent A, Agent B, Key K|} (shrK B)|} \ +\ : set_of_list evs"; +by (fast_tac (!claset addSIs [NA_Crypt_imp_Server_msg] + addEs partsEs + addDs [Says_imp_sees_Spy RS parts.Inj]) 1); +qed "A_trust_OR4"; + + +(*Describes the form of K and NA when the Server sends this message.*) +goal thy + "!!evs. [| Says Server B \ +\ {|Crypt {|NA, Agent A, Agent B, K|} (shrK A), \ +\ Crypt {|NB, Agent A, Agent B, K|} (shrK B)|} : set_of_list evs; \ +\ evs : otway lost |] \ +\ ==> (EX evt: otway lost. K = Key(newK evt)) & \ +\ (EX i. NA = Nonce i) & \ +\ (EX j. NB = Nonce j)"; +by (etac rev_mp 1); +by (etac otway.induct 1); +by (ALLGOALS (fast_tac (!claset addss (!simpset)))); +qed "Says_Server_message_form"; + + +(** Crucial secrecy property: Spy does not see the keys sent in msg OR3 + Does not in itself guarantee security: an attack could violate + the premises, e.g. by having A=Spy **) + +goal thy + "!!evs. [| A ~: lost; B ~: lost; evs : otway lost; evt : otway lost |] \ +\ ==> Says Server B \ +\ {|Crypt {|NA, Agent A, Agent B, Key K|} (shrK A), \ +\ Crypt {|NB, Agent A, Agent B, Key K|} (shrK B)|} \ +\ : set_of_list evs --> \ +\ Says A Spy {|NA, Key K|} ~: set_of_list evs --> \ +\ Key K ~: analz (sees lost Spy evs)"; +by (etac otway.induct 1); +by analz_Fake_tac; +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 4 **) +(*OR3*) +by (fast_tac (!claset addSIs [parts_insertI] + addEs [Says_imp_old_keys RS less_irrefl] + addss (!simpset addsimps [parts_insert2])) 2); +(*Reveal case 2, OR4, Fake*) +by (REPEAT_FIRST (resolve_tac [conjI, impI] ORELSE' spy_analz_tac)); +(*Reveal case 1*) (** LEVEL 6 **) +by (excluded_middle_tac "Aa : lost" 1); +(*But this contradicts Key K ~: analz (sees lost Spy evsa) *) +by (dtac (Says_imp_sees_Spy RS analz.Inj) 2); +by (fast_tac (!claset addSDs [analz.Decrypt] addss (!simpset)) 2); +(*So now we have Aa ~: lost *) +by (dtac A_trust_OR4 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 \ +\ {|Crypt {|NA, Agent A, Agent B, K|} (shrK A), \ +\ Crypt {|NB, Agent A, Agent B, K|} (shrK B)|} : set_of_list evs; \ +\ Says A Spy {|NA, K|} ~: set_of_list evs; \ +\ A ~: lost; B ~: lost; evs : otway lost |] \ +\ ==> K ~: analz (sees lost Spy evs)"; +by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); +by (fast_tac (!claset addSEs [lemma]) 1); +qed "Spy_not_see_encrypted_key"; + + +goal thy + "!!evs. [| C ~: {A,B,Server}; \ +\ Says Server B \ +\ {|Crypt {|NA, Agent A, Agent B, K|} (shrK A), \ +\ Crypt {|NB, Agent A, Agent B, K|} (shrK B)|} : set_of_list evs; \ +\ Says A Spy {|NA, K|} ~: set_of_list evs; \ +\ A ~: lost; B ~: lost; evs : otway lost |] \ +\ ==> K ~: analz (sees lost C evs)"; +by (rtac (subset_insertI RS sees_mono RS analz_mono RS contra_subsetD) 1); +by (rtac (sees_lost_agent_subset_sees_Spy RS analz_mono RS contra_subsetD) 1); +by (FIRSTGOAL (rtac Spy_not_see_encrypted_key)); +by (REPEAT_FIRST (fast_tac (!claset addIs [otway_mono RS subsetD]))); +qed "Agent_not_see_encrypted_key"; + + +(**** Authenticity properties relating to NB ****) + +(*If the encrypted message appears then it originated with the Server!*) +goal thy + "!!evs. [| B ~: lost; evs : otway lost |] \ +\ ==> Crypt {|NB, Agent A, Agent B, Key K|} (shrK B) \ +\ : parts (sees lost Spy evs) \ +\ --> (EX NA. Says Server B \ +\ {|Crypt {|NA, Agent A, Agent B, Key K|} (shrK A), \ +\ Crypt {|NB, Agent A, Agent B, Key K|} (shrK B)|} \ +\ : set_of_list evs)"; +by (parts_induct_tac 1); +by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib]))); +(*OR3*) +by (Fast_tac 1); +qed_spec_mp "NB_Crypt_imp_Server_msg"; + + +(*Guarantee for B: if it gets a message with matching NB then the Server + has sent the correct message.*) +goal thy + "!!evs. [| B ~: lost; evs : otway lost; \ +\ Says S B {|X, Crypt {|NB, Agent A, Agent B, Key K|} (shrK B)|} \ +\ : set_of_list evs |] \ +\ ==> EX NA. Says Server B \ +\ {|Crypt {|NA, Agent A, Agent B, Key K|} (shrK A), \ +\ Crypt {|NB, Agent A, Agent B, Key K|} (shrK B)|} \ +\ : set_of_list evs"; +by (fast_tac (!claset addSIs [NB_Crypt_imp_Server_msg] + addEs partsEs + addDs [Says_imp_sees_Spy RS parts.Inj]) 1); +qed "B_trust_OR3"; diff -r e2ec077ac90d -r 307ebbbec862 src/HOL/Auth/OtwayRees_AN.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Auth/OtwayRees_AN.thy Thu Oct 10 18:40:34 1996 +0200 @@ -0,0 +1,70 @@ +(* Title: HOL/Auth/OtwayRees + ID: $Id$ + Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1996 University of Cambridge + +Inductive relation "otway" for the Otway-Rees protocol. + +Simplified version with minimal encryption but explicit messages + +From page 11 of + Abadi and Needham. Prudent Engineering Practice for Cryptographic Protocols. + IEEE Trans. SE 22 (1), 1996 +*) + +OtwayRees_AN = Shared + + +consts otway :: "agent set => event list set" +inductive "otway lost" + intrs + (*Initial trace is empty*) + Nil "[]: otway lost" + + (*The spy 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 lost; B ~= Spy; + X: synth (analz (sees lost Spy evs)) |] + ==> Says Spy B X # evs : otway lost" + + (*Alice initiates a protocol run*) + OR1 "[| evs: otway lost; A ~= B; B ~= Server |] + ==> Says A B {|Agent A, Agent B, Nonce (newN evs)|} + # evs : otway lost" + + (*Bob's response to Alice's message. Bob doesn't know who + the sender is, hence the A' in the sender field.*) + OR2 "[| evs: otway lost; B ~= Server; + Says A' B {|Agent A, Agent B, Nonce NA|} : set_of_list evs |] + ==> Says B Server {|Agent A, Agent B, Nonce NA, Nonce (newN evs)|} + # evs : otway lost" + + (*The Server receives Bob's message. Then he sends a new + session key to Bob with a packet for forwarding to Alice.*) + OR3 "[| evs: otway lost; B ~= Server; A ~= B; + Says B' Server {|Agent A, Agent B, Nonce NA, Nonce NB|} + : set_of_list evs |] + ==> Says Server B + {|Crypt {|Nonce NA, Agent A, Agent B, Key(newK evs)|} (shrK A), + Crypt {|Nonce NB, Agent A, Agent B, Key(newK evs)|} (shrK B)|} + # evs : otway lost" + + (*Bob receives the Server's (?) message and compares the Nonces with + those in the message he previously sent the Server.*) + OR4 "[| evs: otway lost; A ~= B; B ~= Server; + Says S B {|X, + Crypt {|Nonce NB, Agent A, Agent B, Key K|} (shrK B)|} + : set_of_list evs; + Says B Server {|Agent A, Agent B, Nonce NA, Nonce NB|} + : set_of_list evs |] + ==> Says B A X # evs : otway lost" + + (*This message models possible leaks of session keys. Alice's Nonce + identifies the protocol run.*) + Revl "[| evs: otway lost; A ~= Spy; + Says B' A (Crypt {|Nonce NA, Agent A, Agent B, Key K|} (shrK A)) + : set_of_list evs; + Says A B {|Agent A, Agent B, Nonce NA|} : set_of_list evs |] + ==> Says A Spy {|Nonce NA, Key K|} # evs : otway lost" + +end