# HG changeset patch # User paulson # Date 845631794 -7200 # Node ID 81c8d46edfa3e8aebb8b9610c4eefe9334d67c70 # Parent d01151e66cd450e0618ad6e2a984c7c273b37093 New version of Yahalom, as recommended on p 259 of BAN paper diff -r d01151e66cd4 -r 81c8d46edfa3 src/HOL/Auth/Yahalom2.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Auth/Yahalom2.ML Fri Oct 18 11:43:14 1996 +0200 @@ -0,0 +1,456 @@ +(* Title: HOL/Auth/Yahalom2 + ID: $Id$ + Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1996 University of Cambridge + +Inductive relation "yahalom" for the Yahalom protocol, Variant 2. + +This version trades encryption of NB for additional explicitness in YM3. + +From page 259 of + Burrows, Abadi and Needham. A Logic of Authentication. + Proc. Royal Soc. 426 (1989) +*) + +open Yahalom2; + +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 X NB K. EX evs: yahalom lost. \ +\ Says A B {|X, Crypt (Nonce NB) K|} : set_of_list evs"; +by (REPEAT (resolve_tac [exI,bexI] 1)); +by (rtac (yahalom.Nil RS yahalom.YM1 RS yahalom.YM2 RS yahalom.YM3 RS yahalom.YM4) 2); +by (ALLGOALS (simp_tac (!simpset setsolver safe_solver))); +by (ALLGOALS Fast_tac); +result(); + + +(**** Inductive proofs about yahalom ****) + +(*Monotonicity*) +goal thy "!!evs. lost' <= lost ==> yahalom lost' <= yahalom lost"; +by (rtac subsetI 1); +by (etac yahalom.induct 1); +by (REPEAT_FIRST + (best_tac (!claset addIs (impOfSubs (sees_mono RS analz_mono RS synth_mono) + :: yahalom.intrs)))); +qed "yahalom_mono"; + + +(*Nobody sends themselves messages*) +goal thy "!!evs. evs: yahalom lost ==> ALL A X. Says A A X ~: set_of_list evs"; +by (etac yahalom.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 **) + +(*Lets us treat YM4 using a similar argument as for the Fake case.*) +goal thy "!!evs. Says S A {|NB, Crypt Y (shrK A), 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 "YM4_analz_sees_Spy"; + +bind_thm ("YM4_parts_sees_Spy", + YM4_analz_sees_Spy RS (impOfSubs analz_subset_parts)); + +(*Relates to both YM4 and Revl*) +goal thy "!!evs. Says S A {|NB, Crypt {|B, K, NA|} (shrK A), X|} \ +\ : 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 "YM4_Key_parts_sees_Spy"; + +(*We instantiate the variable to "lost". Leaving it as a Var makes proofs + harder: the simplifier does less.*) +val parts_Fake_tac = + forw_inst_tac [("lost","lost")] YM4_parts_sees_Spy 6 THEN + forw_inst_tac [("lost","lost")] YM4_Key_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 yahalom.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 is leaked at start)*) +goal thy + "!!evs. [| evs : yahalom 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 : yahalom 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 : yahalom 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 : yahalom 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 : yahalom 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"; + + +(*Nobody can have USED keys that will be generated in the future. + ...very like new_keys_not_seen*) +goal thy "!!evs. evs : yahalom lost ==> \ +\ length evs <= length evs' --> \ +\ newK evs' ~: keysFor (UN C. parts (sees lost C evs))"; +by (parts_induct_tac 1); +by (dresolve_tac [YM4_Key_parts_sees_Spy] 5); + +(*YM1, YM2 and YM3*) +by (EVERY (map (fast_tac (!claset addDs [Suc_leD] addss (!simpset))) [4,3,2])); +(*Fake and YM4: these messages send unknown (X) components*) +by (stac insert_commute 2); +by (Simp_tac 2); +(*YM4: the only way K could have been used is if it had been seen, + contradicting new_keys_not_seen*) +by (REPEAT + (best_tac + (!claset addDs [impOfSubs analz_subset_parts, + impOfSubs (analz_subset_parts RS keysFor_mono), + impOfSubs (parts_insert_subset_Un RS keysFor_mono), + Suc_leD] + addEs [new_keys_not_seen RSN(2,rev_notE)] + addss (!simpset)) 1)); +val lemma = result(); + +goal thy + "!!evs. [| evs : yahalom 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]; + + +(*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: yahalom lost ==> \ +\ Crypt {|B, Key K, NA|} (shrK A) : parts (sees lost Spy evs) \ +\ --> A ~: lost --> (EX evt: yahalom 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 S A {|NB, Crypt {|B, Key K, NA|} (shrK A), X|} \ +\ : set_of_list evs; \ +\ evs : yahalom lost |] \ +\ ==> (EX evt: yahalom 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_imp_sees_Spy RS analz.Inj] + addss (!simpset)) 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")] YM4_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. + +****) + +(** Session keys are not used to encrypt other session keys **) + +goal thy + "!!evs. evs : yahalom 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 yahalom.induct 1); +by analz_Fake_tac; +by (REPEAT_FIRST (resolve_tac [allI, analz_image_newK_lemma])); +by (REPEAT ((eresolve_tac [bexE, disjE] ORELSE' hyp_subst_tac) 8)); +by (ALLGOALS (*Takes 26 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, YM4, Fake*) +by (EVERY (map spy_analz_tac [6, 4, 2])); +(*Reveal case 1, YM3, Base*) +by (REPEAT (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1)); +qed_spec_mp "analz_image_newK"; + +goal thy + "!!evs. evs : yahalom 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. **) + +goal thy + "!!evs. evs : yahalom lost ==> \ +\ EX A' B' NA' NB'. ALL A B NA NB. \ +\ Says Server A \ +\ {|NB, Crypt {|Agent B, Key K, NA|} (shrK A), \ +\ Crypt {|Agent A, Key K, NB, NB|} (shrK B)|} \ +\ : set_of_list evs --> A=A' & B=B' & NA=NA' & NB=NB'"; +by (etac yahalom.induct 1); +by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); +by (Step_tac 1); +(*Remaining case: YM3*) +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 A \ +\ {|NB, Crypt {|Agent B, Key K, NA|} (shrK A), \ +\ Crypt {|Agent A, Key K, NB, NB|} (shrK B)|} \ +\ : set_of_list evs; \ +\ Says Server A' \ +\ {|NB', Crypt {|Agent B', Key K, NA'|} (shrK A'), \ +\ Crypt {|Agent A', Key K, NB', NB'|} (shrK B')|} \ +\ : set_of_list evs; \ +\ evs : yahalom 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"; + + +(*If the encrypted message appears then it originated with the Server*) +goal thy + "!!evs. [| Crypt {|Agent B, Key K, Nonce NA|} (shrK A) \ +\ : parts (sees lost Spy evs); \ +\ A ~: lost; evs : yahalom lost |] \ +\ ==> EX NB. Says Server A \ +\ {|NB, Crypt {|Agent B, Key K, Nonce NA|} (shrK A), \ +\ Crypt {|Agent A, Key K, NB, NB|} (shrK B)|} \ +\ : set_of_list evs"; +by (etac rev_mp 1); +by (parts_induct_tac 1); +by (Fast_tac 1); +qed "A_trust_YM3"; + + +(*Describes the form of K when the Server sends this message.*) +goal thy + "!!evs. [| Says Server A \ +\ {|NB, Crypt {|Agent B, K, NA|} (shrK A), \ +\ Crypt {|Agent A, K, NB, NB|} (shrK B)|} \ +\ : set_of_list evs; \ +\ evs : yahalom lost |] \ +\ ==> (EX evt: yahalom lost. K = Key(newK evt))"; +by (etac rev_mp 1); +by (etac yahalom.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 YM3 **) + +goal thy + "!!evs. [| A ~: lost; B ~: lost; \ +\ evs : yahalom lost; evt : yahalom lost |] \ +\ ==> Says Server A \ +\ {|NB, Crypt {|Agent B, Key K, NA|} (shrK A), \ +\ Crypt {|Agent A, Key K, NB, NB|} (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 yahalom.induct 1); +by analz_Fake_tac; +by (REPEAT_FIRST (eresolve_tac [asm_rl, bexE, disjE] ORELSE' hyp_subst_tac)); +by (ALLGOALS + (asm_simp_tac + (!simpset addsimps ([analz_subset_parts RS contra_subsetD, + analz_insert_Key_newK] @ pushes) + setloop split_tac [expand_if]))); +(*YM3*) +by (fast_tac (!claset addIs [parts_insertI] + addEs [Says_imp_old_keys RS less_irrefl] + addss (!simpset)) 2); +(*Reveal case 2, OR4, Fake*) +by (REPEAT_FIRST (resolve_tac [conjI, impI] ORELSE' spy_analz_tac)); +(*Reveal case 1*) (** LEVEL 6 **) +by (case_tac "Aa : lost" 1); +(*But this contradicts Key K ~: analz (sees lost Spy evsa) *) +by (dtac (Says_imp_sees_Spy RS analz.Inj) 1); +by (fast_tac (!claset addSDs [analz.Decrypt] addss (!simpset)) 1); +(*So now we have Aa ~: lost *) +bd (Says_imp_sees_Spy RS parts.Inj) 1; +by (fast_tac (!claset delrules [disjE] + addSEs [MPair_parts] + addDs [A_trust_YM3, unique_session_keys] + addss (!simpset)) 1); +val lemma = result() RS mp RS mp RSN(2,rev_notE); + + +(*Final version: Server's message in the most abstract form*) +goal thy + "!!evs. [| Says Server A \ +\ {|NB, Crypt {|Agent B, K, NA|} (shrK A), \ +\ Crypt {|Agent A, K, NB, NB|} (shrK B)|} \ +\ : set_of_list evs; \ +\ Says A Spy {|NA, K|} ~: set_of_list evs; \ +\ A ~: lost; B ~: lost; evs : yahalom 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 A \ +\ {|NB, Crypt {|Agent B, K, NA|} (shrK A), \ +\ Crypt {|Agent A, K, NB, NB|} (shrK B)|} \ +\ : set_of_list evs; \ +\ Says A Spy {|NA, K|} ~: set_of_list evs; \ +\ A ~: lost; B ~: lost; evs : yahalom 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 [yahalom_mono RS subsetD]))); +qed "Agent_not_see_encrypted_key"; + + +(*** Security Guarantee for B upon receiving YM4 ***) + +(*B knows, by the first part of A's message, that the Server distributed + the key for A and B. But this part says nothing about nonces.*) +goal thy + "!!evs. [| Crypt {|Agent A, Key K, Nonce NB, Nonce NB|} (shrK B) \ +\ : parts (sees lost Spy evs); \ +\ B ~: lost; evs : yahalom lost |] \ +\ ==> EX NA. Says Server A \ +\ {|Nonce NB, \ +\ Crypt {|Agent B, Key K, Nonce NA|} (shrK A), \ +\ Crypt {|Agent A, Key K, Nonce NB, Nonce NB|} (shrK B)|}\ +\ : set_of_list evs"; +by (etac rev_mp 1); +by (parts_induct_tac 1); +(*YM3*) +by (Fast_tac 1); +qed "B_trusts_YM4_shrK"; + +(*With this variant we don't bother to use the 2nd part of YM4 at all, since + Nonce NB is available in the first part. However the 2nd part does assure B + of A's existence.*) + +(*What can B deduce from receipt of YM4? Note how the two components of + the message contribute to a single conclusion about the Server's message.*) +goal thy + "!!evs. [| Says A' B {|Crypt {|Agent A, Key K, Nonce NB, Nonce NB|} (shrK B), \ +\ Crypt (Nonce NB) K|} : set_of_list evs; \ +\ ALL N N'. Says A Spy {|N,N', Key K|} ~: set_of_list evs; \ +\ A ~: lost; B ~: lost; evs : yahalom lost |] \ +\ ==> EX NA. Says Server A \ +\ {|Nonce NB, \ +\ Crypt {|Agent B, Key K, Nonce NA|} (shrK A), \ +\ Crypt {|Agent A, Key K, Nonce NB, Nonce NB|} (shrK B)|}\ +\ : set_of_list evs"; +be (Says_imp_sees_Spy RS parts.Inj RS MPair_parts) 1; +by (fast_tac (!claset addSDs [B_trusts_YM4_shrK]) 1); +qed "B_trust_YM4"; diff -r d01151e66cd4 -r 81c8d46edfa3 src/HOL/Auth/Yahalom2.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Auth/Yahalom2.thy Fri Oct 18 11:43:14 1996 +0200 @@ -0,0 +1,72 @@ +(* Title: HOL/Auth/Yahalom + ID: $Id$ + Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1996 University of Cambridge + +Inductive relation "yahalom" for the Yahalom protocol, Variant 2. + +This version trades encryption of NB for additional explicitness in YM3. + +From page 259 of + Burrows, Abadi and Needham. A Logic of Authentication. + Proc. Royal Soc. 426 (1989) +*) + +Yahalom2 = Shared + + +consts yahalom :: "agent set => event list set" +inductive "yahalom lost" + intrs + (*Initial trace is empty*) + Nil "[]: yahalom 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: yahalom lost; B ~= Spy; + X: synth (analz (sees lost Spy evs)) |] + ==> Says Spy B X # evs : yahalom lost" + + (*Alice initiates a protocol run*) + YM1 "[| evs: yahalom lost; A ~= B |] + ==> Says A B {|Agent A, Nonce (newN evs)|} # evs : yahalom lost" + + (*Bob's response to Alice's message. Bob doesn't know who + the sender is, hence the A' in the sender field.*) + YM2 "[| evs: yahalom lost; B ~= Server; + Says A' B {|Agent A, Nonce NA|} : set_of_list evs |] + ==> Says B Server + {|Agent B, Nonce (newN evs), + Crypt {|Agent A, Nonce NA|} (shrK B)|} + # evs : yahalom lost" + + (*The Server receives Bob's message. He responds by sending a + new session key to Alice, with a packet for forwarding to Bob.*) + YM3 "[| evs: yahalom lost; A ~= Server; + Says B' Server + {|Agent B, Nonce NB, Crypt {|Agent A, Nonce NA|} (shrK B)|} + : set_of_list evs |] + ==> Says Server A + {|Nonce NB, + Crypt {|Agent B, Key (newK evs), Nonce NA|} (shrK A), + Crypt {|Agent A, Key (newK evs), Nonce NB, Nonce NB|} (shrK B)|} + # evs : yahalom lost" + + (*Alice receives the Server's (?) message, checks her Nonce, and + uses the new session key to send Bob his Nonce.*) + YM4 "[| evs: yahalom lost; A ~= B; + Says S A {|Nonce NB, Crypt {|Agent B, Key K, Nonce NA|} (shrK A), + X|} + : set_of_list evs; + Says A B {|Agent A, Nonce NA|} : set_of_list evs |] + ==> Says A B {|X, Crypt (Nonce NB) K|} # evs : yahalom lost" + + (*This message models possible leaks of session keys. The Nonce NA + identifies the protocol run. We can't be sure about NB.*) + Revl "[| evs: yahalom lost; A ~= Spy; + Says S A {|Nonce NB, Crypt {|Agent B, Key K, Nonce NA|} (shrK A), + X|} + : set_of_list evs |] + ==> Says A Spy {|Nonce NA, Key K|} # evs : yahalom lost" + +end