author  nipkow 
Fri, 24 Nov 2000 16:49:27 +0100  
changeset 10519  ade64af4c57c 
parent 8054  2ce57ef2a4aa 
permissions  rwrr 
2318  1 
(* 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 

5 

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Inductive relation "ns_public" for the NeedhamSchroeder PublicKey protocol. 

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Version incorporating Lowe's fix (inclusion of B's identify in round 2). 

8 
*) 

9 

4470  10 
AddEs spies_partsEs; 
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AddDs [impOfSubs analz_subset_parts]; 

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AddDs [impOfSubs Fake_parts_insert]; 

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3683  14 
AddIffs [Spy_in_bad]; 
2318  15 

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Addsimps [image_eq_UN]; (*accelerates proofs involving nested images*) 
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2318  18 
(*A "possibility property": there are traces that reach the end*) 
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Goal 
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"EX NB. EX evs: ns_public. Says A B (Crypt (pubK B) (Nonce NB)) : set evs"; 
2318  21 
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; 
2318  24 
result(); 
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26 

27 
(**** Inductive proofs about ns_public ****) 

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(*Induction for regularity theorems. If induction formula has the form 
3683  30 
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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3683  40 
(** Theorems of the form X ~: parts (spies evs) imply that NOBODY 
2318  41 
sends messages containing X! **) 
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3683  43 
(*Spy never sees another agent's private key! (unless it's bad at start)*) 
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Goal "evs: ns_public ==> (Key (priK A) : parts (spies evs)) = (A : bad)"; 
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by (parts_induct_tac 1); 
4470  46 
by (Blast_tac 1); 
2318  47 
qed "Spy_see_priK"; 
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Addsimps [Spy_see_priK]; 

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Goal "evs: ns_public ==> (Key (priK A) : analz (spies evs)) = (A : bad)"; 
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by Auto_tac; 
2318  52 
qed "Spy_analz_priK"; 
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Addsimps [Spy_analz_priK]; 

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4470  55 
AddSDs [Spy_see_priK RSN (2, rev_iffD1), 
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Spy_analz_priK RSN (2, rev_iffD1)]; 

2318  57 

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(**** Authenticity properties obtained from NS2 ****) 
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(*It is impossible to reuse 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 "[ Crypt (pubK B) {Nonce NA, Agent A} : parts (spies evs); \ 
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\ Nonce NA ~: analz (spies evs); evs : ns_public ] \ 
3683  65 
\ ==> 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); 
4470  69 
by (ALLGOALS Blast_tac); 
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qed "no_nonce_NS1_NS2"; 
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4470  72 
(*Adding it to the claset slows down proofs...*) 
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val nonce_NS1_NS2_E = no_nonce_NS1_NS2 RSN (2, rev_notE); 

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(*Unicity for NS1: nonce NA identifies agents A and B*) 
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Goal "[ Nonce NA ~: analz (spies evs); evs : ns_public ] \ 
3709  78 
\ ==> 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 (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); 
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(*NS1*) 
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by (expand_case_tac "NA = ?y" 2 THEN Blast_tac 2); 
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(*Fake*) 
3709  87 
by (Clarify_tac 1); 
4470  88 
by (Blast_tac 1); 
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val lemma = result(); 
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Goal "[ 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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(*Tactic for proving secrecy theorems*) 
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fun analz_induct_tac i = 
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etac ns_public.induct i THEN 
4686  103 
ALLGOALS Asm_simp_tac; 
2318  104 

105 

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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 "[ 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); 
2318  112 
(*NS3*) 
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by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 4); 
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(*NS2*) 
4470  115 
by (blast_tac (claset() addDs [unique_NA]) 3); 
2318  116 
(*NS1*) 
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by (Blast_tac 2); 
2318  118 
(*Fake*) 
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by (spy_analz_tac 1); 
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qed "Spy_not_see_NA"; 
2318  121 

122 

123 
(*Authentication for A: if she receives message 2 and has used NA 

124 
to start a run, then B has sent message 2.*) 

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Goal "[ 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*) 
3683  133 
by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1); 
2318  134 
by (etac ns_public.induct 1); 
135 
by (ALLGOALS Asm_simp_tac); 

136 
(*NS1*) 

4470  137 
by (Blast_tac 2); 
2318  138 
(*Fake*) 
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by (blast_tac (claset() addDs [Spy_not_see_NA]) 1); 
2318  140 
qed "A_trusts_NS2"; 
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2318  143 
(*If the encrypted message appears then it originated with Alice in NS1*) 
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Goal "[ 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 (Blast_tac 1); 
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qed "B_trusts_NS1"; 
2318  153 

154 

155 

156 
(**** Authenticity properties obtained from NS2 ****) 

157 

2480  158 
(*Unicity for NS2: nonce NB identifies nonce NA and agents A, B 
2318  159 
[unicity of B makes Lowe's fix work] 
160 
[proof closely follows that for unique_NA] *) 

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Goal "[ 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) \ 
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\ > 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 (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); 
2318  168 
(*NS2*) 
4470  169 
by (expand_case_tac "NB = ?y" 2 THEN Blast_tac 2); 
2318  170 
(*Fake*) 
3709  171 
by (Clarify_tac 1); 
4470  172 
by (Blast_tac 1); 
2318  173 
val lemma = result(); 
174 

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Goal "[ 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); \ 
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\ Nonce NB ~: analz (spies evs); \ 
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\ evs : ns_public ] \ 
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\ ==> A=A' & NA=NA' & B=B'"; 
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by (prove_unique_tac lemma 1); 
2318  183 
qed "unique_NB"; 
184 

4470  185 
AddDs [unique_NB]; 
186 

2318  187 

188 
(*Secrecy: Spy does not see the nonce sent in msg NS2 if A and B are secure*) 

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Goal "[ 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 ] \ 
3683  192 
\ ==> Nonce NB ~: analz (spies evs)"; 
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by (etac rev_mp 1); 
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by (analz_induct_tac 1); 
2318  195 
(*NS3*) 
4470  196 
by (Blast_tac 4); 
3709  197 
(*NS2: by freshness and unicity of NB*) 
4470  198 
by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 3); 
2318  199 
(*NS1*) 
4470  200 
by (Blast_tac 2); 
2318  201 
(*Fake*) 
2497  202 
by (spy_analz_tac 1); 
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qed "Spy_not_see_NB"; 
2318  204 

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AddDs [Spy_not_see_NB]; 
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2318  207 

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(*Authentication for B: if he receives message 3 and has used NB 

209 
in message 2, then A has sent message 3.*) 

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Goal "[ Says B A (Crypt (pubK A) {Nonce NA, Nonce NB, Agent B}) \ 
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\ : set evs; \ 
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\ Says A' B (Crypt (pubK B) (Nonce NB)): set evs; \ 
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\ A ~: bad; B ~: bad; evs : ns_public ] \ 
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\ ==> Says A B (Crypt (pubK B) (Nonce NB)) : set evs"; 
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by (etac rev_mp 1); 
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(*prepare induction over Crypt (pubK B) NB : parts H*) 
3683  217 
by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1); 
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by (parts_induct_tac 1); 
3709  219 
by (ALLGOALS Clarify_tac); 
4470  220 
by (ALLGOALS Blast_tac); 
2318  221 
qed "B_trusts_NS3"; 
222 

223 

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(**** Overall guarantee for B*) 

225 

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(*Matches only NS2, not NS1 (or NS3)*) 
3683  227 
val Says_imp_spies' = 
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read_instantiate [("X","Crypt ?K {?XX,?YY,?ZZ}")] Says_imp_spies; 

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(*If B receives NS3 and the nonce NB agrees with the nonce he joined with 
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NA, then A initiated the run using NA. SAME proof as B_trusts_NS3!*) 
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Goal "[ Says B A (Crypt (pubK A) {Nonce NA, Nonce NB, Agent B}) \ 
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\ : set evs; \ 
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\ Says A' B (Crypt (pubK B) (Nonce NB)): set evs; \ 
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\ A ~: bad; B ~: bad; 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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(*prepare induction over Crypt (pubK B) {NB} : parts H*) 
3683  240 
by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1); 
2318  241 
by (etac ns_public.induct 1); 
242 
by (ALLGOALS Asm_simp_tac); 

3709  243 
by (ALLGOALS Clarify_tac); 
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(*NS3 holds because NB determines A and NA*) 
245 
by (ALLGOALS Blast_tac); 

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qed "B_trusts_protocol"; 
2318  247 