# HG changeset patch # User paulson # Date 845631761 -7200 # Node ID d01151e66cd450e0618ad6e2a984c7c273b37093 # Parent fabc35243ceab2ebddafbe677059b6f89d768fe9 Addition of Reveal message diff -r fabc35243cea -r d01151e66cd4 src/HOL/Auth/Yahalom.ML --- a/src/HOL/Auth/Yahalom.ML Fri Oct 18 11:42:17 1996 +0200 +++ b/src/HOL/Auth/Yahalom.ML Fri Oct 18 11:42:41 1996 +0200 @@ -8,8 +8,6 @@ From page 257 of Burrows, Abadi and Needham. A Logic of Authentication. Proc. Royal Soc. 426 (1989) - -DEFINE parts_induct_tac AS IN OtwayRees *) open Yahalom; @@ -33,6 +31,7 @@ (**** Inductive proofs about yahalom ****) +(*Monotonicity*) goal thy "!!evs. lost' <= lost ==> yahalom lost' <= yahalom lost"; by (rtac subsetI 1); by (etac yahalom.induct 1); @@ -59,30 +58,44 @@ 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 {|Crypt {|B, K, NA, NB|} (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_parts_sees_Spy"; +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 lost another agent's shared key! (unless it is leaked at start)*) +(*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 (etac yahalom.induct 1); -by (dtac (YM4_analz_sees_Spy RS synth.Inj) 6); -by (ALLGOALS Asm_simp_tac); -by (stac insert_commute 3); +by (parts_induct_tac 1); by (Auto_tac()); -(*Fake and YM4 are similar*) -by (ALLGOALS (best_tac (!claset addSDs [impOfSubs analz_subset_parts, - impOfSubs Fake_parts_insert]))); qed "Spy_not_see_shrK"; bind_thm ("Spy_not_analz_shrK", @@ -115,13 +128,11 @@ 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 : yahalom lost ==> \ \ length evs <= length evs' --> \ \ Key (newK evs') ~: (UN C. parts (sees lost C evs))"; -by (etac yahalom.induct 1); -by (dtac (YM4_analz_sees_Spy RS synth.Inj) 6); +by (parts_induct_tac 1); by (REPEAT_FIRST (best_tac (!claset addDs [impOfSubs analz_subset_parts, impOfSubs parts_insert_subset_Un, Suc_leD] @@ -154,10 +165,9 @@ goal thy "!!evs. evs : yahalom lost ==> \ \ length evs <= length evs' --> \ \ newK evs' ~: keysFor (UN C. parts (sees lost C evs))"; -by (etac yahalom.induct 1); -by (forward_tac [YM4_parts_sees_Spy] 6); -by (dtac (YM4_analz_sees_Spy RS synth.Inj) 6); -by (ALLGOALS Asm_full_simp_tac); +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*) @@ -165,14 +175,14 @@ 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 (ALLGOALS +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)))); + addss (!simpset)) 1)); val lemma = result(); goal thy @@ -188,7 +198,40 @@ Addsimps [new_keys_not_used, new_keys_not_analzd]; -(** Lemmas concerning the form of items passed in messages **) +(*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, NB|} (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 {|Crypt {|B, Key K, NA, NB|} (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; (**** @@ -210,14 +253,12 @@ \ (Crypt X (newK evt)) : parts (sees lost Spy evs) & \ \ Key K : parts {X} --> Key K : parts (sees lost Spy evs)"; by (etac yahalom.induct 1); -by (dtac (YM4_analz_sees_Spy RS synth.Inj) 6); +by parts_Fake_tac; by (ALLGOALS Asm_simp_tac); (*Deals with Faked messages*) -by (EVERY - (map (best_tac (!claset addSEs partsEs - addDs [impOfSubs parts_insert_subset_Un] - addss (!simpset))) - [3,2])); +by (best_tac (!claset addSEs partsEs + addDs [impOfSubs parts_insert_subset_Un] + addss (!simpset)) 2); (*Base case*) by (Auto_tac()); result(); @@ -230,21 +271,19 @@ \ 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 (dtac YM4_analz_sees_Spy 6); +by analz_Fake_tac; by (REPEAT_FIRST (resolve_tac [allI, analz_image_newK_lemma])); -by (ALLGOALS +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]))); -(*YM4*) -by (spy_analz_tac 4); -(*YM3*) -by (Fast_tac 3); -(*Fake case*) -by (spy_analz_tac 2); -(*Base case*) -by (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1); +(** 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 @@ -257,12 +296,66 @@ 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 \ +\ {|Crypt {|Agent B, Key K, NA, NB|} (shrK A), \ +\ Crypt {|Agent A, Key K|} (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 \ +\ {|Crypt {|Agent B, Key K, NA, NB|} (shrK A), \ +\ Crypt {|Agent A, Key K|} (shrK B)|} \ +\ : set_of_list evs; \ +\ Says Server A' \ +\ {|Crypt {|Agent B', Key K, NA', NB'|} (shrK A'), \ +\ Crypt {|Agent A', Key K|} (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, NA, NB|} (shrK A) \ +\ : parts (sees lost Spy evs); \ +\ A ~: lost; evs : yahalom lost |] \ +\ ==> Says Server A \ +\ {|Crypt {|Agent B, Key K, NA, NB|} (shrK A), \ +\ Crypt {|Agent A, Key K|} (shrK B)|} \ +\ : set_of_list evs"; +by (etac rev_mp 1); +by (parts_induct_tac 1); +qed "A_trust_YM3"; + + (*Describes the form of K when the Server sends this message.*) goal thy "!!evs. [| Says Server A \ \ {|Crypt {|Agent B, K, NA, NB|} (shrK A), \ \ Crypt {|Agent A, K|} (shrK B)|} : set_of_list evs; \ -\ evs : yahalom lost |] \ +\ evs : yahalom lost |] \ \ ==> (EX evt: yahalom lost. K = Key(newK evt))"; by (etac rev_mp 1); by (etac yahalom.induct 1); @@ -270,8 +363,7 @@ qed "Says_Server_message_form"; -(** Crucial secrecy property: Spy does not see the keys sent in msg YM3 - As with Otway-Rees, proof does not need uniqueness of session keys. **) +(** Crucial secrecy property: Spy does not see the keys sent in msg YM3 **) goal thy "!!evs. [| A ~: lost; B ~: lost; \ @@ -279,32 +371,44 @@ \ ==> Says Server A \ \ {|Crypt {|Agent B, Key K, NA, NB|} (shrK A), \ \ Crypt {|Agent A, Key K|} (shrK B)|} \ -\ : set_of_list evs --> \ +\ : set_of_list evs --> \ +\ Says A Spy {|NA, NB, Key K|} ~: set_of_list evs --> \ \ Key K ~: analz (sees lost Spy evs)"; by (etac yahalom.induct 1); -by (dtac YM4_analz_sees_Spy 6); +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]))); -(*YM4*) -by (spy_analz_tac 3); (*YM3*) by (fast_tac (!claset addIs [parts_insertI] addEs [Says_imp_old_keys RS less_irrefl] addss (!simpset)) 2); -(*Fake*) (** LEVEL 10 **) -by (spy_analz_tac 1); -val lemma = result() RS mp RSN(2,rev_notE); +(*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 \ + "!!evs. [| Says Server A \ \ {|Crypt {|Agent B, K, NA, NB|} (shrK A), \ \ Crypt {|Agent A, K|} (shrK B)|} : set_of_list evs; \ -\ A ~: lost; B ~: lost; evs : yahalom lost |] ==> \ +\ Says A Spy {|NA, NB, 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); @@ -316,6 +420,7 @@ \ Says Server A \ \ {|Crypt {|Agent B, K, NA, NB|} (shrK A), \ \ Crypt {|Agent A, K|} (shrK B)|} : set_of_list evs; \ +\ Says A Spy {|NA, NB, 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); @@ -325,8 +430,10 @@ qed "Agent_not_see_encrypted_key"; -(** Towards proofs of stronger authenticity properties **) +(*** 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|} (shrK B) : parts (sees lost Spy evs); \ \ B ~: lost; evs : yahalom lost |] \ @@ -336,46 +443,62 @@ \ Crypt {|Agent A, Key K|} (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"; + +(*B knows, by the second part of A's message, that the Server distributed + the key quoting nonce NB. This part says nothing about agent names.*) +goal thy + "!!evs. evs : yahalom lost \ +\ ==> Key K ~: analz (sees lost Spy evs) --> \ +\ Crypt (Nonce NB) K : parts (sees lost Spy evs) --> \ +\ (EX A B NA. Says Server A \ +\ {|Crypt {|Agent B, Key K, \ +\ Nonce NA, Nonce NB|} (shrK A), \ +\ Crypt {|Agent A, Key K|} (shrK B)|} \ +\ : set_of_list evs)"; by (etac yahalom.induct 1); -by (dtac (YM4_analz_sees_Spy RS synth.Inj) 6); -by (ALLGOALS Asm_simp_tac); -(*YM3*) -by (Fast_tac 3); -(*Base case*) +by parts_Fake_tac; by (fast_tac (!claset addss (!simpset)) 1); -(*Prepare YM4*) -by (stac insert_commute 2 THEN Simp_tac 2); -(*Fake and YM4 are similar*) -by (ALLGOALS (best_tac (!claset addSDs [impOfSubs analz_subset_parts, - impOfSubs Fake_parts_insert]))); -qed "Crypt_imp_Server_msg"; +by (TRYALL (rtac impI)); +by (REPEAT_FIRST + (dtac (sees_subset_sees_Says RS analz_mono RS contra_subsetD))); +by (ALLGOALS Asm_simp_tac); +(*Fake, YM3, YM4*) +by (fast_tac (!claset addSDs [Crypt_Fake_parts_insert] + addDs [impOfSubs analz_subset_parts]) 1); +by (Fast_tac 1); +(*YM4*) +by (Step_tac 1); +by (case_tac "A : 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); +by (fast_tac (!claset addDs [Says_imp_sees_Spy RS parts.Inj RS parts.Fst RS + A_trust_YM3]) 1); +val B_trusts_YM4_newK = result() RS mp RSN (2, rev_mp); - -(*What can B deduce from receipt of YM4? NOT THAT THE NONCES AGREE. Cf the - BAN paper page 259. "If A chose to replay an old key to B in message 4, - B could not detect the fraud." *) +(*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. + It's annoying that the "Says A Spy" assumption must quantify over + ALL POSSIBLE nonces instead of our particular NB. Perhaps a different + proof of B_trusts_YM4_newK could eliminate this problem.*) goal thy "!!evs. [| Says A' B {|Crypt {|Agent A, Key K|} (shrK B), \ \ Crypt (Nonce NB) K|} : set_of_list evs; \ -\ B ~: lost; evs : yahalom lost |] \ -\ ==> EX NA NB. Says Server A \ +\ 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 \ \ {|Crypt {|Agent B, Key K, \ \ Nonce NA, Nonce NB|} (shrK A), \ \ Crypt {|Agent A, Key K|} (shrK B)|} \ \ : set_of_list evs"; -by (etac rev_mp 1); -by (etac yahalom.induct 1); -by (dtac YM4_analz_sees_Spy 6); -by (ALLGOALS Asm_simp_tac); -by (ALLGOALS (fast_tac (!claset addSDs [impOfSubs analz_subset_parts RS - Crypt_imp_Server_msg]))); -qed "YM4_imp_Says_Server_A"; - -goal thy - "!!evs. [| Says A' B {|Crypt {|Agent A, Key K|} (shrK B), \ -\ Crypt (Nonce NB) K|} : set_of_list evs; \ -\ A ~: lost; B ~: lost; evs : yahalom lost |] \ -\ ==> Key K ~: analz (sees lost Spy evs)"; -by (fast_tac (!claset addSDs [YM4_imp_Says_Server_A, - Spy_not_see_encrypted_key]) 1); -qed "B_gets_secure_key"; +be (Says_imp_sees_Spy RS parts.Inj RS MPair_parts) 1; +bd B_trusts_YM4_shrK 1; +bd B_trusts_YM4_newK 3; +by (REPEAT_FIRST (eresolve_tac [asm_rl, exE])); +by (fast_tac (!claset addDs [unique_session_keys]) 2); +by (fast_tac (!claset addDs [Spy_not_see_encrypted_key]) 1); +qed "B_trust_YM4"; diff -r fabc35243cea -r d01151e66cd4 src/HOL/Auth/Yahalom.thy --- a/src/HOL/Auth/Yahalom.thy Fri Oct 18 11:42:17 1996 +0200 +++ b/src/HOL/Auth/Yahalom.thy Fri Oct 18 11:42:41 1996 +0200 @@ -59,4 +59,12 @@ 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 Nonces + identify the protocol run.*) + Revl "[| evs: yahalom lost; A ~= Spy; + Says S A {|Crypt {|Agent B, Key K, Nonce NA, Nonce NB|} (shrK A), + X|} + : set_of_list evs |] + ==> Says A Spy {|Nonce NA, Nonce NB, Key K|} # evs : yahalom lost" + end