author | paulson |
Fri, 27 Jun 1997 10:47:13 +0200 | |
changeset 3466 | 30791e5a69c4 |
parent 3465 | e85c24717cad |
child 3519 | ab0a9fbed4c0 |
permissions | -rw-r--r-- |
2318 | 1 |
(* Title: HOL/Auth/NS_Public_Bad |
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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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Flawed version, vulnerable to Lowe's attack. |
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From page 260 of |
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Burrows, Abadi and Needham. A Logic of Authentication. |
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Proc. Royal Soc. 426 (1989) |
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*) |
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open NS_Public_Bad; |
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proof_timing:=true; |
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HOL_quantifiers := false; |
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AddIffs [Spy_in_lost]; |
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||
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(*Replacing the variable by a constant improves search speed by 50%!*) |
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val Says_imp_sees_Spy' = |
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read_instantiate_sg (sign_of thy) [("lost","lost")] Says_imp_sees_Spy; |
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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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3465 | 38 |
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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(** Theorems of the form X ~: parts (sees lost Spy 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 lost at start)*) |
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goal thy |
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"!!evs. evs : ns_public \ |
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\ ==> (Key (priK A) : parts (sees lost Spy evs)) = (A : lost)"; |
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by (etac ns_public.induct 1); |
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by (prove_simple_subgoals_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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goal thy |
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"!!evs. evs : ns_public \ |
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\ ==> (Key (priK A) : analz (sees lost Spy evs)) = (A : lost)"; |
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by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset)); |
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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 (sees lost Spy evs); \ |
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\ evs : ns_public |] ==> A:lost"; |
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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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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 addsimps [not_parts_not_analz] |
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setloop split_tac [expand_if])); |
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2318 | 81 |
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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. [| Nonce NA ~: analz (sees lost Spy evs); \ |
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\ Crypt (pubK B) {|Nonce NA, Agent A|} : parts (sees lost Spy evs); \ |
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\ evs : ns_public |] \ |
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\ ==> Crypt (pubK C) {|NA', Nonce NA|} ~: parts (sees lost Spy evs)"; |
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by (etac rev_mp 1); |
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by (etac rev_mp 1); |
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by (analz_induct_tac 1); |
2318 | 94 |
(*NS3*) |
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by (blast_tac (!claset addSEs partsEs) 4); |
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(*NS2*) |
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by (blast_tac (!claset addSEs partsEs) 3); |
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(*Fake*) |
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by (blast_tac (!claset addSIs [analz_insertI] |
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addDs [impOfSubs analz_subset_parts, |
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impOfSubs Fake_parts_insert]) 2); |
2318 | 102 |
(*Base*) |
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by (Blast_tac 1); |
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qed "no_nonce_NS1_NS2"; |
2318 | 105 |
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||
2480 | 107 |
(*Unicity for NS1: nonce NA identifies agents A and B*) |
2318 | 108 |
goal thy |
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"!!evs. [| Nonce NA ~: analz (sees lost Spy 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 (sees lost Spy evs) --> \ |
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\ A=A' & B=B'"; |
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by (etac rev_mp 1); |
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by (analz_induct_tac 1); |
2318 | 115 |
(*NS1*) |
2497 | 116 |
by (simp_tac (!simpset addsimps [all_conj_distrib]) 3); |
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by (expand_case_tac "NA = ?y" 3 THEN |
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REPEAT (blast_tac (!claset addSEs partsEs) 3)); |
2318 | 119 |
(*Base*) |
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by (Blast_tac 1); |
2318 | 121 |
(*Fake*) |
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by (simp_tac (!simpset addsimps [all_conj_distrib, parts_insert_sees]) 1); |
2374 | 123 |
by (step_tac (!claset addSIs [analz_insertI]) 1); |
2318 | 124 |
by (ex_strip_tac 1); |
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by (blast_tac (!claset delrules [conjI] |
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addSDs [impOfSubs Fake_parts_insert] |
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addDs [impOfSubs analz_subset_parts]) 1); |
2318 | 128 |
val lemma = result(); |
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goal thy |
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"!!evs. [| Crypt(pubK B) {|Nonce NA, Agent A|} : parts(sees lost Spy evs); \ |
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\ Crypt(pubK B') {|Nonce NA, Agent A'|} : parts(sees lost Spy evs); \ |
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\ Nonce NA ~: analz (sees lost Spy 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); |
2318 | 137 |
qed "unique_NA"; |
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139 |
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140 |
(*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 ~: lost; B ~: lost; evs : ns_public |] \ |
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\ ==> Nonce NA ~: analz (sees lost Spy evs)"; |
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145 |
by (etac rev_mp 1); |
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6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
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146 |
by (analz_induct_tac 1); |
2318 | 147 |
(*NS3*) |
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148 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS parts.Inj] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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149 |
addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)]) 4); |
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150 |
(*NS2*) |
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151 |
by (blast_tac (!claset addSEs [MPair_parts] |
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152 |
addDs [Says_imp_sees_Spy' RS parts.Inj, |
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153 |
parts.Body, unique_NA]) 3); |
2318 | 154 |
(*NS1*) |
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155 |
by (blast_tac (!claset addSEs sees_Spy_partsEs |
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Conversion to use blast_tac (with other improvements)
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|
156 |
addIs [impOfSubs analz_subset_parts]) 2); |
2318 | 157 |
(*Fake*) |
2497 | 158 |
by (spy_analz_tac 1); |
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159 |
qed "Spy_not_see_NA"; |
2318 | 160 |
|
161 |
||
162 |
(*Authentication for A: if she receives message 2 and has used NA |
|
163 |
to start a run, then B has sent message 2.*) |
|
164 |
goal thy |
|
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165 |
"!!evs. [| Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set evs; \ |
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166 |
\ Says B' A (Crypt(pubK A) {|Nonce NA, Nonce NB|}): set evs; \ |
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167 |
\ A ~: lost; B ~: lost; evs : ns_public |] \ |
3465 | 168 |
\ ==> Says B A (Crypt(pubK A) {|Nonce NA, Nonce NB|}): set evs"; |
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169 |
by (etac rev_mp 1); |
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170 |
(*prepare induction over Crypt (pubK A) {|NA,NB|} : parts H*) |
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171 |
by (etac (Says_imp_sees_Spy' RS parts.Inj RS rev_mp) 1); |
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|
172 |
by (etac ns_public.induct 1); |
2318 | 173 |
by (ALLGOALS Asm_simp_tac); |
174 |
(*NS1*) |
|
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Conversion to use blast_tac (with other improvements)
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175 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 2); |
2318 | 176 |
(*Fake*) |
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177 |
by (blast_tac (!claset addSDs [impOfSubs Fake_parts_insert] |
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178 |
addDs [Spy_not_see_NA, |
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179 |
impOfSubs analz_subset_parts]) 1); |
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180 |
(*NS2; not clear why blast_tac needs to be preceeded by Step_tac*) |
2318 | 181 |
by (Step_tac 1); |
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182 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS parts.Inj, |
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|
183 |
Spy_not_see_NA, unique_NA]) 1); |
2318 | 184 |
qed "A_trusts_NS2"; |
185 |
||
186 |
(*If the encrypted message appears then it originated with Alice in NS1*) |
|
187 |
goal thy |
|
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188 |
"!!evs. [| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (sees lost Spy evs); \ |
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189 |
\ Nonce NA ~: analz (sees lost Spy evs); \ |
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190 |
\ evs : ns_public |] \ |
3465 | 191 |
\ ==> Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set evs"; |
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Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
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192 |
by (etac rev_mp 1); |
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193 |
by (etac rev_mp 1); |
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
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parents:
2374
diff
changeset
|
194 |
by (analz_induct_tac 1); |
2318 | 195 |
(*Fake*) |
3121
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Conversion to use blast_tac (with other improvements)
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196 |
by (blast_tac (!claset addSDs [impOfSubs Fake_parts_insert] |
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|
197 |
addIs [analz_insertI] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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parents:
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diff
changeset
|
198 |
addDs [impOfSubs analz_subset_parts]) 2); |
2318 | 199 |
(*Base*) |
3121
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Conversion to use blast_tac (with other improvements)
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parents:
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diff
changeset
|
200 |
by (Blast_tac 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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parents:
2637
diff
changeset
|
201 |
qed "B_trusts_NS1"; |
2318 | 202 |
|
203 |
||
204 |
||
205 |
(**** Authenticity properties obtained from NS2 ****) |
|
206 |
||
2480 | 207 |
(*Unicity for NS2: nonce NB identifies agent A and nonce NA |
2318 | 208 |
[proof closely follows that for unique_NA] *) |
209 |
goal thy |
|
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
210 |
"!!evs. [| Nonce NB ~: analz (sees lost Spy evs); evs : ns_public |] \ |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
211 |
\ ==> EX A' NA'. ALL A NA. \ |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
212 |
\ Crypt (pubK A) {|Nonce NA, Nonce NB|} \ |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
213 |
\ : parts (sees lost Spy evs) --> A=A' & NA=NA'"; |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
214 |
by (etac rev_mp 1); |
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset
|
215 |
by (analz_induct_tac 1); |
2318 | 216 |
(*NS2*) |
2497 | 217 |
by (simp_tac (!simpset addsimps [all_conj_distrib]) 3); |
2318 | 218 |
by (expand_case_tac "NB = ?y" 3 THEN |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
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diff
changeset
|
219 |
REPEAT (blast_tac (!claset addSEs partsEs) 3)); |
2318 | 220 |
(*Base*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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parents:
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diff
changeset
|
221 |
by (Blast_tac 1); |
2318 | 222 |
(*Fake*) |
2497 | 223 |
by (simp_tac (!simpset addsimps [all_conj_distrib, parts_insert_sees]) 1); |
2374 | 224 |
by (step_tac (!claset addSIs [analz_insertI]) 1); |
2318 | 225 |
by (ex_strip_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
226 |
by (blast_tac (!claset delrules [conjI] |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2497
diff
changeset
|
227 |
addSDs [impOfSubs Fake_parts_insert] |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
228 |
addDs [impOfSubs analz_subset_parts]) 1); |
2318 | 229 |
val lemma = result(); |
230 |
||
231 |
goal thy |
|
232 |
"!!evs. [| Crypt(pubK A) {|Nonce NA, Nonce NB|} : parts(sees lost Spy evs); \ |
|
233 |
\ Crypt(pubK A'){|Nonce NA', Nonce NB|} : parts(sees lost Spy evs); \ |
|
234 |
\ Nonce NB ~: analz (sees lost Spy evs); \ |
|
235 |
\ evs : ns_public |] \ |
|
236 |
\ ==> A=A' & NA=NA'"; |
|
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset
|
237 |
by (prove_unique_tac lemma 1); |
2318 | 238 |
qed "unique_NB"; |
239 |
||
240 |
||
241 |
(*NB remains secret PROVIDED Alice never responds with round 3*) |
|
242 |
goal thy |
|
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
243 |
"!!evs.[| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
244 |
\ (ALL C. Says A C (Crypt (pubK C) (Nonce NB)) ~: set evs); \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
245 |
\ A ~: lost; B ~: lost; evs : ns_public |] \ |
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
246 |
\ ==> Nonce NB ~: analz (sees lost Spy evs)"; |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
247 |
by (etac rev_mp 1); |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
248 |
by (etac rev_mp 1); |
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset
|
249 |
by (analz_induct_tac 1); |
2318 | 250 |
(*NS1*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
251 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 2); |
2318 | 252 |
(*Fake*) |
2497 | 253 |
by (spy_analz_tac 1); |
2318 | 254 |
(*NS2 and NS3*) |
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
255 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
256 |
by (step_tac (!claset delrules [allI]) 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
257 |
by (Blast_tac 5); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
258 |
(*NS3*) |
3440
22db7a9cbb52
Deleted spurious reference to Spy_not_see_NB, which by chance was defined
paulson
parents:
3121
diff
changeset
|
259 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS parts.Inj, unique_NB]) 4); |
2318 | 260 |
(*NS2*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
261 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 3); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
262 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
263 |
addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)]) 2); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
264 |
by (blast_tac (!claset addSIs [impOfSubs analz_subset_parts]) 1); |
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
265 |
qed "Spy_not_see_NB"; |
2318 | 266 |
|
267 |
||
268 |
||
269 |
(*Authentication for B: if he receives message 3 and has used NB |
|
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
270 |
in message 2, then A has sent message 3--to somebody....*) |
2318 | 271 |
goal thy |
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
272 |
"!!evs. [| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
273 |
\ : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
274 |
\ Says A' B (Crypt (pubK B) (Nonce NB)): set evs; \ |
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
275 |
\ A ~: lost; B ~: lost; evs : ns_public |] \ |
3465 | 276 |
\ ==> EX C. Says A C (Crypt (pubK C) (Nonce NB)) : set evs"; |
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
277 |
by (etac rev_mp 1); |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
278 |
(*prepare induction over Crypt (pubK B) NB : parts H*) |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
279 |
by (etac (Says_imp_sees_Spy' RS parts.Inj RS rev_mp) 1); |
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset
|
280 |
by (analz_induct_tac 1); |
2318 | 281 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib]))); |
282 |
(*NS1*) |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
283 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 2); |
2318 | 284 |
(*Fake*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
285 |
by (blast_tac (!claset addSDs [impOfSubs Fake_parts_insert] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
286 |
addDs [Spy_not_see_NB, |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
287 |
impOfSubs analz_subset_parts]) 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
288 |
(*NS3; not clear why blast_tac needs to be preceeded by Step_tac*) |
2318 | 289 |
by (Step_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
290 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS parts.Inj, |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
291 |
Spy_not_see_NB, unique_NB]) 1); |
2318 | 292 |
qed "B_trusts_NS3"; |
293 |
||
294 |
||
295 |
(*Can we strengthen the secrecy theorem? NO*) |
|
296 |
goal thy |
|
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
297 |
"!!evs. [| A ~: lost; B ~: lost; evs : ns_public |] \ |
3465 | 298 |
\ ==> Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs \ |
2318 | 299 |
\ --> Nonce NB ~: analz (sees lost Spy evs)"; |
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset
|
300 |
by (analz_induct_tac 1); |
2318 | 301 |
(*NS1*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
302 |
by (blast_tac (!claset addSEs partsEs |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
303 |
addSDs [Says_imp_sees_Spy' RS parts.Inj]) 2); |
2318 | 304 |
(*Fake*) |
2497 | 305 |
by (spy_analz_tac 1); |
2318 | 306 |
(*NS2 and NS3*) |
307 |
by (Step_tac 1); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
308 |
by (blast_tac (!claset addSIs [impOfSubs analz_subset_parts, usedI]) 1); |
2318 | 309 |
(*NS2*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
310 |
by (blast_tac (!claset addSEs partsEs |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
311 |
addSDs [Says_imp_sees_Spy' RS parts.Inj]) 2); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
312 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
313 |
addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)]) 1); |
2318 | 314 |
(*NS3*) |
315 |
by (forw_inst_tac [("A'","A")] (Says_imp_sees_Spy' RS parts.Inj RS unique_NB) 1 |
|
316 |
THEN REPEAT (eresolve_tac [asm_rl, Says_imp_sees_Spy' RS parts.Inj] 1)); |
|
317 |
by (Step_tac 1); |
|
318 |
||
319 |
(* |
|
320 |
THIS IS THE ATTACK! |
|
321 |
Level 9 |
|
322 |
!!evs. [| A ~: lost; B ~: lost; evs : ns_public |] |
|
323 |
==> Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) |
|
3465 | 324 |
: set evs --> |
2318 | 325 |
Nonce NB ~: analz (sees lost Spy evs) |
326 |
1. !!evs Aa Ba B' NAa NBa evsa. |
|
327 |
[| A ~: lost; B ~: lost; evsa : ns_public; A ~= Ba; |
|
3465 | 328 |
Says B' A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evsa; |
329 |
Says A Ba (Crypt (pubK Ba) {|Nonce NA, Agent A|}) : set evsa; |
|
2318 | 330 |
Ba : lost; |
3465 | 331 |
Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evsa; |
2318 | 332 |
Nonce NB ~: analz (sees lost Spy evsa) |] |
333 |
==> False |
|
334 |
*) |
|
335 |
||
336 |
||
337 |