author | wenzelm |
Fri, 19 Dec 1997 10:28:33 +0100 | |
changeset 4449 | df30e75f670f |
parent 4422 | 21238c9d363e |
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permissions | -rw-r--r-- |
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(* Title: HOL/Auth/NS_Public |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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Inductive relation "ns_public" for the Needham-Schroeder Public-Key protocol. |
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Version incorporating Lowe's fix (inclusion of B's identify in round 2). |
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*) |
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open NS_Public; |
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set proof_timing; |
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HOL_quantifiers := false; |
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AddIffs [Spy_in_bad]; |
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(*A "possibility property": there are traces that reach the end*) |
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goal thy |
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"!!A B. A ~= B ==> EX NB. EX evs: ns_public. \ |
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\ Says A B (Crypt (pubK B) (Nonce NB)) : set evs"; |
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by (REPEAT (resolve_tac [exI,bexI] 1)); |
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by (rtac (ns_public.Nil RS ns_public.NS1 RS ns_public.NS2 RS ns_public.NS3) 2); |
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by possibility_tac; |
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result(); |
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(**** Inductive proofs about ns_public ****) |
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(*Nobody sends themselves messages*) |
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goal thy "!!evs. evs : ns_public ==> ALL A X. Says A A X ~: set evs"; |
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by (etac ns_public.induct 1); |
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by (Auto_tac()); |
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qed_spec_mp "not_Says_to_self"; |
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Addsimps [not_Says_to_self]; |
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AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
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(*Induction for regularity theorems. If induction formula has the form |
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X ~: analz (spies evs) --> ... then it shortens the proof by discarding |
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needless information about analz (insert X (spies evs)) *) |
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fun parts_induct_tac i = |
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etac ns_public.induct i |
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THEN |
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REPEAT (FIRSTGOAL analz_mono_contra_tac) |
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THEN |
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prove_simple_subgoals_tac i; |
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|
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(** Theorems of the form X ~: parts (spies evs) imply that NOBODY |
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sends messages containing X! **) |
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(*Spy never sees another agent's private key! (unless it's bad at start)*) |
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goal thy |
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"!!A. evs: ns_public ==> (Key (priK A) : parts (spies evs)) = (A : bad)"; |
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by (parts_induct_tac 1); |
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by (Fake_parts_insert_tac 1); |
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qed "Spy_see_priK"; |
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Addsimps [Spy_see_priK]; |
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AddDs [impOfSubs analz_subset_parts]; |
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AddDs [Says_imp_spies RS parts.Inj]; |
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AddDs [impOfSubs Fake_parts_insert]; |
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goal thy |
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"!!A. evs: ns_public ==> (Key (priK A) : analz (spies evs)) = (A : bad)"; |
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by (Auto_tac()); |
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qed "Spy_analz_priK"; |
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Addsimps [Spy_analz_priK]; |
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goal thy "!!A. [| Key (priK A) : parts (spies evs); \ |
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\ evs : ns_public |] ==> A:bad"; |
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by (blast_tac (claset() addDs [Spy_see_priK]) 1); |
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qed "Spy_see_priK_D"; |
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bind_thm ("Spy_analz_priK_D", analz_subset_parts RS subsetD RS Spy_see_priK_D); |
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AddSDs [Spy_see_priK_D, Spy_analz_priK_D]; |
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(**** Authenticity properties obtained from NS2 ****) |
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(*It is impossible to re-use a nonce in both NS1 and NS2, provided the nonce |
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is secret. (Honest users generate fresh nonces.)*) |
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goal thy |
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"!!evs. [| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \ |
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\ Nonce NA ~: analz (spies evs); \ |
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\ evs : ns_public |] \ |
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\ ==> Crypt (pubK C) {|NA', Nonce NA, Agent D|} ~: parts (spies evs)"; |
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by (etac rev_mp 1); |
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by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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(*NS3*) |
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by (blast_tac (claset() addSEs partsEs) 3); |
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(*NS2*) |
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by (blast_tac (claset() addSEs partsEs) 2); |
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by (Fake_parts_insert_tac 1); |
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qed "no_nonce_NS1_NS2"; |
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(*Unicity for NS1: nonce NA identifies agents A and B*) |
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goal thy |
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"!!evs. [| Nonce NA ~: analz (spies evs); evs : ns_public |] \ |
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\ ==> EX A' B'. ALL A B. \ |
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\ Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs) --> \ |
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\ A=A' & B=B'"; |
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by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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by (ALLGOALS |
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(asm_simp_tac (simpset() addsimps [all_conj_distrib, parts_insert_spies]))); |
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(*NS1*) |
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by (expand_case_tac "NA = ?y" 2 THEN blast_tac (claset() addSEs partsEs) 2); |
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(*Fake*) |
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by (Clarify_tac 1); |
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by (ex_strip_tac 1); |
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by (Fake_parts_insert_tac 1); |
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val lemma = result(); |
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goal thy |
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"!!evs. [| Crypt(pubK B) {|Nonce NA, Agent A|} : parts(spies evs); \ |
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\ Crypt(pubK B') {|Nonce NA, Agent A'|} : parts(spies evs); \ |
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\ Nonce NA ~: analz (spies evs); \ |
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\ evs : ns_public |] \ |
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\ ==> A=A' & B=B'"; |
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by (prove_unique_tac lemma 1); |
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qed "unique_NA"; |
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|
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(*Tactic for proving secrecy theorems*) |
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fun analz_induct_tac i = |
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etac ns_public.induct i THEN |
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ALLGOALS (asm_simp_tac |
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(simpset() addsplits [expand_if])); |
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(*Secrecy: Spy does not see the nonce sent in msg NS1 if A and B are secure*) |
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goal thy |
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"!!evs. [| Says A B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set evs; \ |
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\ A ~: bad; B ~: bad; evs : ns_public |] \ |
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\ ==> Nonce NA ~: analz (spies evs)"; |
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by (etac rev_mp 1); |
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by (analz_induct_tac 1); |
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(*NS3*) |
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by (blast_tac (claset() addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)]) 4); |
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(*NS2*) |
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by (blast_tac (claset() addSEs [MPair_parts] |
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addDs [parts.Body, unique_NA]) 3); |
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(*NS1*) |
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by (blast_tac (claset() addSEs spies_partsEs) 2); |
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(*Fake*) |
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by (spy_analz_tac 1); |
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qed "Spy_not_see_NA"; |
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(*Authentication for A: if she receives message 2 and has used NA |
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to start a run, then B has sent message 2.*) |
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goal thy |
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"!!evs. [| Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set evs; \ |
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\ Says B' A (Crypt(pubK A) {|Nonce NA, Nonce NB, Agent B|}) \ |
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\ : set evs; \ |
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\ A ~: bad; B ~: bad; evs : ns_public |] \ |
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\ ==> Says B A (Crypt(pubK A) {|Nonce NA, Nonce NB, Agent B|}) \ |
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\ : set evs"; |
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by (etac rev_mp 1); |
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(*prepare induction over Crypt (pubK A) {|NA,NB,B|} : parts H*) |
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by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1); |
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by (etac ns_public.induct 1); |
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by (ALLGOALS Asm_simp_tac); |
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(*NS1*) |
|
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by (blast_tac (claset() addSEs spies_partsEs) 2); |
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(*Fake*) |
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by (blast_tac (claset() addDs [Spy_not_see_NA]) 1); |
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qed "A_trusts_NS2"; |
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(*If the encrypted message appears then it originated with Alice in NS1*) |
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goal thy |
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"!!evs. [| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \ |
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\ Nonce NA ~: analz (spies evs); \ |
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\ evs : ns_public |] \ |
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\ ==> Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set evs"; |
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by (etac rev_mp 1); |
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by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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by (Fake_parts_insert_tac 1); |
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qed "B_trusts_NS1"; |
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(**** Authenticity properties obtained from NS2 ****) |
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||
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(*Unicity for NS2: nonce NB identifies nonce NA and agents A, B |
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[unicity of B makes Lowe's fix work] |
191 |
[proof closely follows that for unique_NA] *) |
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goal thy |
|
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"!!evs. [| Nonce NB ~: analz (spies evs); evs : ns_public |] \ |
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\ ==> EX A' NA' B'. ALL A NA B. \ |
|
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\ Crypt (pubK A) {|Nonce NA, Nonce NB, Agent B|} : parts (spies evs) \ |
196 |
\ --> A=A' & NA=NA' & B=B'"; |
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by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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by (ALLGOALS |
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(asm_simp_tac (simpset() addsimps [all_conj_distrib, |
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201 |
parts_insert_spies]))); |
2318 | 202 |
(*NS2*) |
4091 | 203 |
by (expand_case_tac "NB = ?y" 2 THEN blast_tac (claset() addSEs partsEs) 2); |
2318 | 204 |
(*Fake*) |
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by (Clarify_tac 1); |
2318 | 206 |
by (ex_strip_tac 1); |
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by (Fake_parts_insert_tac 1); |
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val lemma = result(); |
209 |
||
210 |
goal thy |
|
211 |
"!!evs. [| Crypt(pubK A) {|Nonce NA, Nonce NB, Agent B|} \ |
|
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\ : parts(spies evs); \ |
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\ Crypt(pubK A') {|Nonce NA', Nonce NB, Agent B'|} \ |
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\ : parts(spies evs); \ |
215 |
\ Nonce NB ~: analz (spies evs); \ |
|
2318 | 216 |
\ evs : ns_public |] \ |
217 |
\ ==> A=A' & NA=NA' & B=B'"; |
|
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by (prove_unique_tac lemma 1); |
2318 | 219 |
qed "unique_NB"; |
220 |
||
221 |
||
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(*Secrecy: Spy does not see the nonce sent in msg NS2 if A and B are secure*) |
|
223 |
goal thy |
|
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224 |
"!!evs. [| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB, Agent B|}) \ |
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\ : set evs; \ |
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\ A ~: bad; B ~: bad; evs : ns_public |] \ |
227 |
\ ==> Nonce NB ~: analz (spies evs)"; |
|
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228 |
by (etac rev_mp 1); |
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229 |
by (analz_induct_tac 1); |
2318 | 230 |
(*NS3*) |
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by (blast_tac (claset() addDs [unique_NB]) 4); |
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(*NS2: by freshness and unicity of NB*) |
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by (blast_tac (claset() addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)] |
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234 |
addEs partsEs) 3); |
2318 | 235 |
(*NS1*) |
4091 | 236 |
by (blast_tac (claset() addSEs spies_partsEs) 2); |
2318 | 237 |
(*Fake*) |
2497 | 238 |
by (spy_analz_tac 1); |
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239 |
qed "Spy_not_see_NB"; |
2318 | 240 |
|
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241 |
AddDs [Spy_not_see_NB]; |
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242 |
|
2318 | 243 |
|
244 |
(*Authentication for B: if he receives message 3 and has used NB |
|
245 |
in message 2, then A has sent message 3.*) |
|
246 |
goal thy |
|
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247 |
"!!evs. [| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB, Agent B|}) \ |
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248 |
\ : set evs; \ |
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249 |
\ Says A' B (Crypt (pubK B) (Nonce NB)): set evs; \ |
4197 | 250 |
\ A ~: bad; B ~: bad; evs : ns_public |] \ |
3465 | 251 |
\ ==> Says A B (Crypt (pubK B) (Nonce NB)) : set evs"; |
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252 |
by (etac rev_mp 1); |
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253 |
(*prepare induction over Crypt (pubK B) NB : parts H*) |
3683 | 254 |
by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1); |
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255 |
by (parts_induct_tac 1); |
3709 | 256 |
by (ALLGOALS Clarify_tac); |
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257 |
(*NS3: because NB determines A*) |
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258 |
by (blast_tac (claset() addDs [unique_NB]) 3); |
3709 | 259 |
(*NS1: by freshness*) |
4091 | 260 |
by (blast_tac (claset() addSEs spies_partsEs) 2); |
2318 | 261 |
(*Fake*) |
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262 |
by (Blast_tac 1); |
2318 | 263 |
qed "B_trusts_NS3"; |
264 |
||
265 |
||
266 |
(**** Overall guarantee for B*) |
|
267 |
||
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268 |
(*Matches only NS2, not NS1 (or NS3)*) |
3683 | 269 |
val Says_imp_spies' = |
270 |
read_instantiate [("X","Crypt ?K {|?XX,?YY,?ZZ|}")] Says_imp_spies; |
|
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271 |
|
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272 |
|
2318 | 273 |
(*If B receives NS3 and the nonce NB agrees with the nonce he joined with |
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274 |
NA, then A initiated the run using NA. SAME proof as B_trusts_NS3!*) |
2318 | 275 |
goal thy |
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276 |
"!!evs. [| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB, Agent B|}) \ |
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277 |
\ : set evs; \ |
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278 |
\ Says A' B (Crypt (pubK B) (Nonce NB)): set evs; \ |
3683 | 279 |
\ A ~: bad; B ~: bad; evs : ns_public |] \ |
3465 | 280 |
\ ==> Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set evs"; |
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281 |
by (etac rev_mp 1); |
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282 |
(*prepare induction over Crypt (pubK B) {|NB|} : parts H*) |
3683 | 283 |
by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1); |
2318 | 284 |
by (etac ns_public.induct 1); |
285 |
by (ALLGOALS Asm_simp_tac); |
|
3709 | 286 |
by (ALLGOALS Clarify_tac); |
4197 | 287 |
(*NS3: because NB determines A and NA*) |
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288 |
by (blast_tac (claset() addDs [unique_NB]) 3); |
2318 | 289 |
(*NS1*) |
4091 | 290 |
by (blast_tac (claset() addSEs spies_partsEs) 2); |
2318 | 291 |
(*Fake*) |
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292 |
by (Blast_tac 1); |
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|
293 |
qed "B_trusts_protocol"; |
2318 | 294 |