--- a/src/HOL/UNITY/NSP_Bad.ML Mon Mar 05 12:31:31 2001 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,288 +0,0 @@
-(* Title: HOL/Auth/NSP_Bad
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1996 University of Cambridge
-
-Inductive relation "ns_public" for the Needham-Schroeder Public-Key protocol.
-Flawed version, vulnerable to Lowe's attack.
-
-From page 260 of
- Burrows, Abadi and Needham. A Logic of Authentication.
- Proc. Royal Soc. 426 (1989)
-*)
-
-fun impOfAlways th =
- rulify (th RS Always_includes_reachable RS subsetD RS CollectD);
-
-AddEs spies_partsEs;
-AddDs [impOfSubs analz_subset_parts];
-AddDs [impOfSubs Fake_parts_insert];
-
-(*For other theories, e.g. Mutex and Lift, using AddIffs slows proofs down.
- Here, it facilitates re-use of the Auth proofs.*)
-
-AddIffs (map simp_of_act [Fake_def, NS1_def, NS2_def, NS3_def]);
-
-Addsimps [Nprg_def RS def_prg_simps];
-
-
-(*A "possibility property": there are traces that reach the end.
- Replace by LEADSTO proof!*)
-Goal "A ~= B ==> EX NB. EX s: reachable Nprg. \
-\ Says A B (Crypt (pubK B) (Nonce NB)) : set s";
-by (REPEAT (resolve_tac [exI,bexI] 1));
-by (res_inst_tac [("act", "NS3")] reachable.Acts 2);
-by (res_inst_tac [("act", "NS2")] reachable.Acts 3);
-by (res_inst_tac [("act", "NS1")] reachable.Acts 4);
-by (rtac reachable.Init 5);
-by (ALLGOALS (asm_simp_tac (simpset() addsimps [Nprg_def])));
-by (REPEAT_FIRST (rtac exI ));
-by possibility_tac;
-result();
-
-
-(**** Inductive proofs about ns_public ****)
-
-(*can be used to simulate analz_mono_contra_tac
-val analz_impI = read_instantiate_sg (sign_of thy)
- [("P", "?Y ~: analz (spies ?evs)")] impI;
-
-val spies_Says_analz_contraD =
- spies_subset_spies_Says RS analz_mono RS contra_subsetD;
-
-by (rtac analz_impI 2);
-by (auto_tac (claset() addSDs [spies_Says_analz_contraD], simpset()));
-*)
-
-fun ns_constrains_tac i =
- SELECT_GOAL
- (EVERY [REPEAT (etac Always_ConstrainsI 1),
- REPEAT (resolve_tac [StableI, stableI,
- constrains_imp_Constrains] 1),
- rtac constrainsI 1,
- Full_simp_tac 1,
- REPEAT (FIRSTGOAL (etac disjE)),
- ALLGOALS (clarify_tac (claset() delrules [impI,impCE])),
- REPEAT (FIRSTGOAL analz_mono_contra_tac),
- ALLGOALS Asm_simp_tac]) i;
-
-(*Tactic for proving secrecy theorems*)
-val ns_induct_tac =
- (SELECT_GOAL o EVERY)
- [rtac AlwaysI 1,
- Force_tac 1,
- (*"reachable" gets in here*)
- rtac (Always_reachable RS Always_ConstrainsI RS StableI) 1,
- ns_constrains_tac 1];
-
-
-(** Theorems of the form X ~: parts (spies evs) imply that NOBODY
- sends messages containing X! **)
-
-(*Spy never sees another agent's private key! (unless it's bad at start)*)
-Goal "Nprg : Always {s. (Key (priK A) : parts (spies s)) = (A : bad)}";
-by (ns_induct_tac 1);
-by (Blast_tac 1);
-qed "Spy_see_priK";
-Addsimps [impOfAlways Spy_see_priK];
-
-Goal "Nprg : Always {s. (Key (priK A) : analz (spies s)) = (A : bad)}";
-by (rtac (Always_reachable RS Always_weaken) 1);
-by Auto_tac;
-qed "Spy_analz_priK";
-Addsimps [impOfAlways Spy_analz_priK];
-
-(**
-AddSDs [Spy_see_priK RSN (2, rev_iffD1),
- Spy_analz_priK RSN (2, rev_iffD1)];
-**)
-
-
-(**** Authenticity properties obtained from NS2 ****)
-
-(*It is impossible to re-use a nonce in both NS1 and NS2, provided the nonce
- is secret. (Honest users generate fresh nonces.)*)
-Goal
- "Nprg \
-\ : Always {s. Nonce NA ~: analz (spies s) --> \
-\ Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies s) --> \
-\ Crypt (pubK C) {|NA', Nonce NA|} ~: parts (spies s)}";
-by (ns_induct_tac 1);
-by (ALLGOALS Blast_tac);
-qed "no_nonce_NS1_NS2";
-
-(*Adding it to the claset slows down proofs...*)
-val nonce_NS1_NS2_E = impOfAlways no_nonce_NS1_NS2 RSN (2, rev_notE);
-
-
-(*Unicity for NS1: nonce NA identifies agents A and B*)
-Goal "Nprg \
-\ : Always {s. Nonce NA ~: analz (spies s) --> \
-\ Crypt(pubK B) {|Nonce NA, Agent A|} : parts(spies s) --> \
-\ Crypt(pubK B') {|Nonce NA, Agent A'|} : parts(spies s) --> \
-\ A=A' & B=B'}";
-by (ns_induct_tac 1);
-by Auto_tac;
-(*Fake, NS1 are non-trivial*)
-val unique_NA_lemma = result();
-
-(*Unicity for NS1: nonce NA identifies agents A and B*)
-Goal "[| Crypt(pubK B) {|Nonce NA, Agent A|} : parts(spies s); \
-\ Crypt(pubK B') {|Nonce NA, Agent A'|} : parts(spies s); \
-\ Nonce NA ~: analz (spies s); \
-\ s : reachable Nprg |] \
-\ ==> A=A' & B=B'";
-by (blast_tac (claset() addDs [impOfAlways unique_NA_lemma]) 1);
-qed "unique_NA";
-
-
-(*Secrecy: Spy does not see the nonce sent in msg NS1 if A and B are secure*)
-Goal "[| A ~: bad; B ~: bad |] \
-\ ==> Nprg : Always \
-\ {s. Says A B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set s \
-\ --> Nonce NA ~: analz (spies s)}";
-by (ns_induct_tac 1);
-(*NS3*)
-by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 4);
-(*NS2*)
-by (blast_tac (claset() addDs [unique_NA]) 3);
-(*NS1*)
-by (Blast_tac 2);
-(*Fake*)
-by (spy_analz_tac 1);
-qed "Spy_not_see_NA";
-
-
-(*Authentication for A: if she receives message 2 and has used NA
- to start a run, then B has sent message 2.*)
-val prems =
-goal thy "[| A ~: bad; B ~: bad |] \
-\ ==> Nprg : Always \
-\ {s. Says A B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set s & \
-\ Crypt(pubK A) {|Nonce NA, Nonce NB|} : parts (knows Spy s) \
-\ --> Says B A (Crypt(pubK A) {|Nonce NA, Nonce NB|}): set s}";
- (*insert an invariant for use in some of the subgoals*)
-by (cut_facts_tac ([prems MRS Spy_not_see_NA] @ prems) 1);
-by (ns_induct_tac 1);
-by (ALLGOALS Clarify_tac);
-(*NS2*)
-by (blast_tac (claset() addDs [unique_NA]) 3);
-(*NS1*)
-by (Blast_tac 2);
-(*Fake*)
-by (Blast_tac 1);
-qed "A_trusts_NS2";
-
-
-(*If the encrypted message appears then it originated with Alice in NS1*)
-Goal "Nprg : Always \
-\ {s. Nonce NA ~: analz (spies s) --> \
-\ Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies s) \
-\ --> Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set s}";
-by (ns_induct_tac 1);
-by (Blast_tac 1);
-qed "B_trusts_NS1";
-
-
-
-(**** Authenticity properties obtained from NS2 ****)
-
-(*Unicity for NS2: nonce NB identifies nonce NA and agent A
- [proof closely follows that for unique_NA] *)
-Goal
- "Nprg \
-\ : Always {s. Nonce NB ~: analz (spies s) --> \
-\ Crypt (pubK A) {|Nonce NA, Nonce NB|} : parts (spies s) --> \
-\ Crypt(pubK A'){|Nonce NA', Nonce NB|} : parts(spies s) --> \
-\ A=A' & NA=NA'}";
-by (ns_induct_tac 1);
-by Auto_tac;
-(*Fake, NS2 are non-trivial*)
-val unique_NB_lemma = result();
-
-Goal "[| Crypt(pubK A) {|Nonce NA, Nonce NB|} : parts(spies s); \
-\ Crypt(pubK A'){|Nonce NA', Nonce NB|} : parts(spies s); \
-\ Nonce NB ~: analz (spies s); \
-\ s : reachable Nprg |] \
-\ ==> A=A' & NA=NA'";
-by (blast_tac (claset() addDs [impOfAlways unique_NB_lemma]) 1);
-qed "unique_NB";
-
-
-(*NB remains secret PROVIDED Alice never responds with round 3*)
-Goal "[| A ~: bad; B ~: bad |] \
-\ ==> Nprg : Always \
-\ {s. Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set s & \
-\ (ALL C. Says A C (Crypt (pubK C) (Nonce NB)) ~: set s) \
-\ --> Nonce NB ~: analz (spies s)}";
-by (ns_induct_tac 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib])));
-by (ALLGOALS Clarify_tac);
-(*NS3: because NB determines A*)
-by (blast_tac (claset() addDs [unique_NB]) 4);
-(*NS2: by freshness and unicity of NB*)
-by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 3);
-(*NS1: by freshness*)
-by (Blast_tac 2);
-(*Fake*)
-by (spy_analz_tac 1);
-qed "Spy_not_see_NB";
-
-
-
-(*Authentication for B: if he receives message 3 and has used NB
- in message 2, then A has sent message 3--to somebody....*)
-val prems =
-goal thy "[| A ~: bad; B ~: bad |] \
-\ ==> Nprg : Always \
-\ {s. Crypt (pubK B) (Nonce NB) : parts (spies s) & \
-\ Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set s \
-\ --> (EX C. Says A C (Crypt (pubK C) (Nonce NB)) : set s)}";
- (*insert an invariant for use in some of the subgoals*)
-by (cut_facts_tac ([prems MRS Spy_not_see_NB] @ prems) 1);
-by (ns_induct_tac 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsimps [ex_disj_distrib])));
-by (ALLGOALS Clarify_tac);
-(*NS3: because NB determines A (this use of unique_NB is more robust) *)
-by (blast_tac (claset() addIs [unique_NB RS conjunct1]) 3);
-(*NS1: by freshness*)
-by (Blast_tac 2);
-(*Fake*)
-by (Blast_tac 1);
-qed "B_trusts_NS3";
-
-
-(*Can we strengthen the secrecy theorem? NO*)
-Goal "[| A ~: bad; B ~: bad |] \
-\ ==> Nprg : Always \
-\ {s. Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set s \
-\ --> Nonce NB ~: analz (spies s)}";
-by (ns_induct_tac 1);
-by (ALLGOALS Clarify_tac);
-(*NS2: by freshness and unicity of NB*)
-by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 3);
-(*NS1: by freshness*)
-by (Blast_tac 2);
-(*Fake*)
-by (spy_analz_tac 1);
-(*NS3: unicity of NB identifies A and NA, but not B*)
-by (forw_inst_tac [("A'","A")] (Says_imp_spies RS parts.Inj RS unique_NB) 1
- THEN REPEAT (eresolve_tac [asm_rl, Says_imp_spies RS parts.Inj] 1));
-by Auto_tac;
-by (rename_tac "s B' C" 1);
-
-(*
-THIS IS THE ATTACK!
-[| A ~: bad; B ~: bad |]
-==> Nprg
- : Always
- {s. Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set s -->
- Nonce NB ~: analz (knows Spy s)}
- 1. !!s B' C.
- [| A ~: bad; B ~: bad; s : reachable Nprg;
- Says A C (Crypt (pubK C) {|Nonce NA, Agent A|}) : set s;
- Says B' A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set s;
- C : bad; Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set s;
- Nonce NB ~: analz (knows Spy s) |]
- ==> False
-*)