author | nipkow |
Tue, 09 Jan 2001 15:29:17 +0100 | |
changeset 10833 | c0844a30ea4e |
parent 7499 | 23e090051cb8 |
child 11104 | f2024fed9f0c |
permissions | -rw-r--r-- |
2449 | 1 |
(* Title: HOL/Auth/Recur |
2 |
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 "recur" for the Recursive Authentication protocol. |
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*) |
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Pretty.setdepth 30; |
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5359 | 11 |
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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(** Possibility properties: traces that reach the end |
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ONE theorem would be more elegant and faster! |
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By induction on a list of agents (no repetitions) |
2449 | 19 |
**) |
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2449 | 22 |
(*Simplest case: Alice goes directly to the server*) |
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Goal "EX K NA. EX evs: recur. \ |
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\ Says Server A {|Crypt (shrK A) {|Key K, Agent Server, Nonce NA|}, \ |
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\ END|} : set evs"; |
2449 | 26 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
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by (rtac (recur.Nil RS recur.RA1 RS (respond.One RSN (3,recur.RA3))) 2); |
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by possibility_tac; |
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result(); |
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(*Case two: Alice, Bob and the server*) |
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Goal "EX K. EX NA. EX evs: recur. \ |
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\ Says B A {|Crypt (shrK A) {|Key K, Agent B, Nonce NA|}, \ |
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\ END|} : set evs"; |
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by (cut_facts_tac [Nonce_supply2, Key_supply2] 1); |
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by (REPEAT (eresolve_tac [exE, conjE] 1)); |
2449 | 38 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
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by (rtac (recur.Nil RS recur.RA1 RS recur.RA2 RS |
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(respond.One RS respond.Cons RSN (3,recur.RA3)) RS |
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recur.RA4) 2); |
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by basic_possibility_tac; |
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by (DEPTH_SOLVE (eresolve_tac [asm_rl, less_not_refl2, less_not_refl3] 1)); |
2449 | 44 |
result(); |
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(*Case three: Alice, Bob, Charlie and the server |
2533 | 48 |
TOO SLOW to run every time! |
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Goal "EX K. EX NA. EX evs: recur. \ |
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\ Says B A {|Crypt (shrK A) {|Key K, Agent B, Nonce NA|}, \ |
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\ END|} : set evs"; |
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by (cut_facts_tac [Nonce_supply3, Key_supply3] 1); |
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by (REPEAT (eresolve_tac [exE, conjE] 1)); |
2449 | 54 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
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by (rtac (recur.Nil RS recur.RA1 RS recur.RA2 RS recur.RA2 RS |
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(respond.One RS respond.Cons RS respond.Cons RSN |
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(3,recur.RA3)) RS recur.RA4 RS recur.RA4) 2); |
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(*SLOW: 33 seconds*) |
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by basic_possibility_tac; |
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by (DEPTH_SOLVE (swap_res_tac [refl, conjI, disjCI] 1 |
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ORELSE |
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eresolve_tac [asm_rl, less_not_refl2, less_not_refl3] 1)); |
2449 | 63 |
result(); |
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****************) |
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(**** Inductive proofs about recur ****) |
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Goal "(PA,RB,KAB) : respond evs ==> Key KAB : parts{RB}"; |
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by (etac respond.induct 1); |
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by (ALLGOALS Simp_tac); |
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qed "respond_Key_in_parts"; |
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Goal "(PA,RB,KAB) : respond evs ==> Key KAB ~: used evs"; |
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by (etac respond.induct 1); |
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by (REPEAT (assume_tac 1)); |
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qed "respond_imp_not_used"; |
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Goal "[| Key K : parts {RB}; (PB,RB,K') : respond evs |] \ |
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\ ==> Key K ~: used evs"; |
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by (etac rev_mp 1); |
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by (etac respond.induct 1); |
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by (auto_tac(claset() addDs [Key_not_used, respond_imp_not_used], |
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simpset())); |
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qed_spec_mp "Key_in_parts_respond"; |
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(*Simple inductive reasoning about responses*) |
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Goal "(PA,RB,KAB) : respond evs ==> RB : responses evs"; |
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by (etac respond.induct 1); |
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by (REPEAT (ares_tac (respond_imp_not_used::responses.intrs) 1)); |
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qed "respond_imp_responses"; |
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(** For reasoning about the encrypted portion of messages **) |
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val RA2_analz_spies = Says_imp_spies RS analz.Inj |> standard; |
2449 | 97 |
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Goal "Says C' B {|Crypt K X, X', RA|} : set evs ==> RA : analz (spies evs)"; |
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by (blast_tac (claset() addSDs [Says_imp_spies RS analz.Inj]) 1); |
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qed "RA4_analz_spies"; |
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(*RA2_analz... and RA4_analz... let us treat those cases using the same |
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argument as for the Fake case. This is possible for most, but not all, |
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proofs: Fake does not invent new nonces (as in RA2), and of course Fake |
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messages originate from the Spy. *) |
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bind_thm ("RA2_parts_spies", |
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RA2_analz_spies RS (impOfSubs analz_subset_parts)); |
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bind_thm ("RA4_parts_spies", |
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RA4_analz_spies RS (impOfSubs analz_subset_parts)); |
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2449 | 111 |
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(*For proving the easier theorems about X ~: parts (spies evs).*) |
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fun parts_induct_tac i = |
5359 | 114 |
EVERY [etac recur.induct i, |
7499 | 115 |
ftac RA4_parts_spies (i+5), |
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ftac respond_imp_responses (i+4), |
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ftac RA2_parts_spies (i+3), |
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5359 | 118 |
prove_simple_subgoals_tac i]; |
2449 | 119 |
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120 |
||
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(** Theorems of the form X ~: parts (spies evs) imply that NOBODY |
2449 | 122 |
sends messages containing X! **) |
123 |
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(** Spy never sees another agent's shared key! (unless it's bad at start) **) |
2449 | 126 |
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Goal "evs : recur ==> (Key (shrK A) : parts (spies evs)) = (A : bad)"; |
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by (parts_induct_tac 1); |
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by Auto_tac; |
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(*RA3*) |
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by (auto_tac (claset() addDs [Key_in_parts_respond], |
132 |
simpset() addsimps [parts_insert_spies])); |
|
2449 | 133 |
qed "Spy_see_shrK"; |
134 |
Addsimps [Spy_see_shrK]; |
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||
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Goal "evs : recur ==> (Key (shrK A) : analz (spies evs)) = (A : bad)"; |
5359 | 137 |
by Auto_tac; |
2449 | 138 |
qed "Spy_analz_shrK"; |
139 |
Addsimps [Spy_analz_shrK]; |
|
140 |
||
4471 | 141 |
AddSDs [Spy_see_shrK RSN (2, rev_iffD1), |
142 |
Spy_analz_shrK RSN (2, rev_iffD1)]; |
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(** Nobody can have used non-existent keys! **) |
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(*The special case of H={} has the same proof*) |
5359 | 148 |
Goal "[| K : keysFor (parts (insert RB H)); RB : responses evs |] \ |
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\ ==> K : range shrK | K : keysFor (parts H)"; |
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by (etac rev_mp 1); |
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by (etac responses.induct 1); |
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by Auto_tac; |
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qed_spec_mp "Key_in_keysFor_parts"; |
2449 | 154 |
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155 |
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5359 | 156 |
Goal "evs : recur ==> Key K ~: used evs --> K ~: keysFor (parts (spies evs))"; |
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by (parts_induct_tac 1); |
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158 |
(*RA3*) |
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by (blast_tac (claset() addSDs [Key_in_keysFor_parts]) 2); |
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(*Fake*) |
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by (blast_tac (claset() addSDs [keysFor_parts_insert]) 1); |
2449 | 162 |
qed_spec_mp "new_keys_not_used"; |
163 |
||
164 |
||
165 |
bind_thm ("new_keys_not_analzd", |
|
166 |
[analz_subset_parts RS keysFor_mono, |
|
167 |
new_keys_not_used] MRS contra_subsetD); |
|
168 |
||
169 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
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170 |
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171 |
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172 |
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173 |
(*** Proofs involving analz ***) |
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174 |
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175 |
(*For proofs involving analz.*) |
3683 | 176 |
val analz_spies_tac = |
177 |
dtac RA2_analz_spies 4 THEN |
|
7499 | 178 |
ftac respond_imp_responses 5 THEN |
3683 | 179 |
dtac RA4_analz_spies 6; |
2449 | 180 |
|
181 |
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182 |
(** Session keys are not used to encrypt other session keys **) |
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183 |
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184 |
(*Version for "responses" relation. Handles case RA3 in the theorem below. |
3683 | 185 |
Note that it holds for *any* set H (not just "spies evs") |
2449 | 186 |
satisfying the inductive hypothesis.*) |
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187 |
Goal "[| RB : responses evs; \ |
5492 | 188 |
\ ALL K KK. KK <= - (range shrK) --> \ |
10833 | 189 |
\ (Key K : analz (Key`KK Un H)) = \ |
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190 |
\ (K : KK | Key K : analz H) |] \ |
5492 | 191 |
\ ==> ALL K KK. KK <= - (range shrK) --> \ |
10833 | 192 |
\ (Key K : analz (insert RB (Key`KK Un H))) = \ |
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193 |
\ (K : KK | Key K : analz (insert RB H))"; |
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194 |
by (etac responses.induct 1); |
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195 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
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qed "resp_analz_image_freshK_lemma"; |
2449 | 197 |
|
198 |
(*Version for the protocol. Proof is almost trivial, thanks to the lemma.*) |
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199 |
Goal "evs : recur ==> \ |
5492 | 200 |
\ ALL K KK. KK <= - (range shrK) --> \ |
10833 | 201 |
\ (Key K : analz (Key`KK Un (spies evs))) = \ |
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202 |
\ (K : KK | Key K : analz (spies evs))"; |
2449 | 203 |
by (etac recur.induct 1); |
3683 | 204 |
by analz_spies_tac; |
2516
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|
205 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
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|
206 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma)); |
2516
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|
207 |
by (ALLGOALS |
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|
208 |
(asm_simp_tac |
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|
209 |
(analz_image_freshK_ss addsimps [resp_analz_image_freshK_lemma]))); |
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|
210 |
(*Fake*) |
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|
211 |
by (spy_analz_tac 1); |
2516
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|
212 |
val raw_analz_image_freshK = result(); |
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|
213 |
qed_spec_mp "analz_image_freshK"; |
2449 | 214 |
|
215 |
||
3683 | 216 |
(*Instance of the lemma with H replaced by (spies evs): |
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217 |
[| RB : responses evs; evs : recur; |] |
5492 | 218 |
==> KK <= - (range shrK) --> |
10833 | 219 |
Key K : analz (insert RB (Key`KK Un spies evs)) = |
3683 | 220 |
(K : KK | Key K : analz (insert RB (spies evs))) |
2449 | 221 |
*) |
2516
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|
222 |
bind_thm ("resp_analz_image_freshK", |
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|
223 |
raw_analz_image_freshK RSN |
3961 | 224 |
(2, resp_analz_image_freshK_lemma) RS spec RS spec RS mp); |
2449 | 225 |
|
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|
226 |
Goal "[| evs : recur; KAB ~: range shrK |] ==> \ |
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|
227 |
\ Key K : analz (insert (Key KAB) (spies evs)) = \ |
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|
228 |
\ (K = KAB | Key K : analz (spies evs))"; |
2516
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|
229 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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|
230 |
qed "analz_insert_freshK"; |
2449 | 231 |
|
232 |
||
2516
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|
233 |
(*Everything that's hashed is already in past traffic. *) |
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|
234 |
Goal "[| Hash {|Key(shrK A), X|} : parts (spies evs); \ |
5359 | 235 |
\ evs : recur; A ~: bad |] ==> X : parts (spies evs)"; |
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|
236 |
by (etac rev_mp 1); |
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|
237 |
by (parts_induct_tac 1); |
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|
238 |
(*RA3 requires a further induction*) |
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|
239 |
by (etac responses.induct 2); |
2449 | 240 |
by (ALLGOALS Asm_simp_tac); |
241 |
(*Fake*) |
|
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|
242 |
by (blast_tac (claset() addIs [parts_insertI]) 1); |
2550
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|
243 |
qed "Hash_imp_body"; |
2449 | 244 |
|
245 |
||
246 |
(** The Nonce NA uniquely identifies A's message. |
|
2516
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|
247 |
This theorem applies to steps RA1 and RA2! |
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|
248 |
|
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|
249 |
Unicity is not used in other proofs but is desirable in its own right. |
2449 | 250 |
**) |
251 |
||
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|
252 |
Goal "[| evs : recur; A ~: bad |] \ |
2560 | 253 |
\ ==> EX B' P'. ALL B P. \ |
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|
254 |
\ Hash {|Key(shrK A), Agent A, B, NA, P|} : parts (spies evs) \ |
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|
255 |
\ --> B=B' & P=P'"; |
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|
256 |
by (parts_induct_tac 1); |
5359 | 257 |
by (Blast_tac 1); |
2516
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|
258 |
by (etac responses.induct 3); |
4091 | 259 |
by (ALLGOALS (simp_tac (simpset() addsimps [all_conj_distrib]))); |
260 |
by (clarify_tac (claset() addSEs partsEs) 1); |
|
2516
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|
261 |
(*RA1,2: creation of new Nonce. Move assertion into global context*) |
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|
262 |
by (ALLGOALS (expand_case_tac "NA = ?y")); |
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|
263 |
by (REPEAT_FIRST (ares_tac [exI])); |
5359 | 264 |
by (REPEAT (blast_tac (claset() addSDs [Hash_imp_body]) 1)); |
2449 | 265 |
val lemma = result(); |
266 |
||
5076 | 267 |
Goalw [HPair_def] |
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|
268 |
"[| Hash[Key(shrK A)] {|Agent A, B,NA,P|} : parts (spies evs); \ |
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|
269 |
\ Hash[Key(shrK A)] {|Agent A, B',NA,P'|} : parts (spies evs); \ |
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|
270 |
\ evs : recur; A ~: bad |] \ |
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|
271 |
\ ==> B=B' & P=P'"; |
2481 | 272 |
by (REPEAT (eresolve_tac partsEs 1)); |
2449 | 273 |
by (prove_unique_tac lemma 1); |
274 |
qed "unique_NA"; |
|
275 |
||
276 |
||
277 |
(*** Lemmas concerning the Server's response |
|
278 |
(relations "respond" and "responses") |
|
279 |
***) |
|
280 |
||
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|
281 |
Goal "[| RB : responses evs; evs : recur |] \ |
3683 | 282 |
\ ==> (Key (shrK B) : analz (insert RB (spies evs))) = (B:bad)"; |
2516
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|
283 |
by (etac responses.induct 1); |
2449 | 284 |
by (ALLGOALS |
285 |
(asm_simp_tac |
|
2516
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|
286 |
(analz_image_freshK_ss addsimps [Spy_analz_shrK, |
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|
287 |
resp_analz_image_freshK]))); |
2449 | 288 |
qed "shrK_in_analz_respond"; |
289 |
Addsimps [shrK_in_analz_respond]; |
|
290 |
||
291 |
||
5492 | 292 |
Goal "[| RB : responses evs; \ |
293 |
\ ALL K KK. KK <= - (range shrK) --> \ |
|
10833 | 294 |
\ (Key K : analz (Key`KK Un H)) = \ |
5492 | 295 |
\ (K : KK | Key K : analz H) |] \ |
296 |
\ ==> (Key K : analz (insert RB H)) --> \ |
|
5114
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|
297 |
\ (Key K : parts{RB} | Key K : analz H)"; |
2516
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|
298 |
by (etac responses.induct 1); |
2449 | 299 |
by (ALLGOALS |
300 |
(asm_simp_tac |
|
2516
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|
301 |
(analz_image_freshK_ss addsimps [resp_analz_image_freshK_lemma]))); |
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|
302 |
(*Simplification using two distinct treatments of "image"*) |
4091 | 303 |
by (simp_tac (simpset() addsimps [parts_insert2]) 1); |
304 |
by (blast_tac (claset() delrules [allE]) 1); |
|
2449 | 305 |
qed "resp_analz_insert_lemma"; |
306 |
||
307 |
bind_thm ("resp_analz_insert", |
|
2516
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|
308 |
raw_analz_image_freshK RSN |
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|
309 |
(2, resp_analz_insert_lemma) RSN(2, rev_mp)); |
2449 | 310 |
|
311 |
||
2516
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|
312 |
(*The last key returned by respond indeed appears in a certificate*) |
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|
313 |
Goal "(Hash[Key(shrK A)] {|Agent A, B, NA, P|}, RA, K) : respond evs \ |
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|
314 |
\ ==> Crypt (shrK A) {|Key K, B, NA|} : parts {RA}"; |
2516
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changeset
|
315 |
by (etac respond.elim 1); |
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changeset
|
316 |
by (ALLGOALS Asm_full_simp_tac); |
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|
317 |
qed "respond_certificate"; |
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|
318 |
|
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|
319 |
|
5359 | 320 |
Goal "(PB,RB,KXY) : respond evs \ |
321 |
\ ==> EX A' B'. ALL A B N. \ |
|
322 |
\ Crypt (shrK A) {|Key K, Agent B, N|} : parts {RB} \ |
|
323 |
\ --> (A'=A & B'=B) | (A'=B & B'=A)"; |
|
2516
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changeset
|
324 |
by (etac respond.induct 1); |
4091 | 325 |
by (ALLGOALS (asm_full_simp_tac (simpset() addsimps [all_conj_distrib]))); |
2449 | 326 |
(*Base case*) |
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Conversion to use blast_tac (with other improvements)
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2637
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|
327 |
by (Blast_tac 1); |
3730 | 328 |
by Safe_tac; |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
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2533
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changeset
|
329 |
by (expand_case_tac "K = KBC" 1); |
2516
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paulson
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changeset
|
330 |
by (dtac respond_Key_in_parts 1); |
4091 | 331 |
by (blast_tac (claset() addSIs [exI] |
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4556
diff
changeset
|
332 |
addDs [Key_in_parts_respond]) 1); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
333 |
by (expand_case_tac "K = KAB" 1); |
2449 | 334 |
by (REPEAT (ares_tac [exI] 2)); |
335 |
by (ex_strip_tac 1); |
|
2516
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changeset
|
336 |
by (dtac respond_certificate 1); |
5359 | 337 |
by (Blast_tac 1); |
2449 | 338 |
val lemma = result(); |
339 |
||
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|
340 |
Goal "[| Crypt (shrK A) {|Key K, Agent B, N|} : parts {RB}; \ |
5359 | 341 |
\ Crypt (shrK A') {|Key K, Agent B', N'|} : parts {RB}; \ |
342 |
\ (PB,RB,KXY) : respond evs |] \ |
|
343 |
\ ==> (A'=A & B'=B) | (A'=B & B'=A)"; |
|
2560 | 344 |
by (prove_unique_tac lemma 1); |
2449 | 345 |
qed "unique_session_keys"; |
346 |
||
347 |
||
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Extensive tidying and simplification, largely stemming from
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diff
changeset
|
348 |
(** Crucial secrecy property: Spy does not see the keys sent in msg RA3 |
2449 | 349 |
Does not in itself guarantee security: an attack could violate |
350 |
the premises, e.g. by having A=Spy **) |
|
351 |
||
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|
352 |
Goal "[| (PB,RB,KAB) : respond evs; evs : recur |] \ |
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|
353 |
\ ==> ALL A A' N. A ~: bad & A' ~: bad --> \ |
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|
354 |
\ Crypt (shrK A) {|Key K, Agent A', N|} : parts{RB} --> \ |
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|
355 |
\ Key K ~: analz (insert RB (spies evs))"; |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
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diff
changeset
|
356 |
by (etac respond.induct 1); |
7499 | 357 |
by (ftac respond_imp_responses 2); |
358 |
by (ftac respond_imp_not_used 2); |
|
3961 | 359 |
by (ALLGOALS (*6 seconds*) |
2449 | 360 |
(asm_simp_tac |
3961 | 361 |
(analz_image_freshK_ss |
4831 | 362 |
addsimps split_ifs |
3961 | 363 |
addsimps |
364 |
[shrK_in_analz_respond, resp_analz_image_freshK, parts_insert2]))); |
|
4091 | 365 |
by (ALLGOALS (simp_tac (simpset() addsimps [ex_disj_distrib]))); |
3681 | 366 |
(** LEVEL 5 **) |
5359 | 367 |
by (Blast_tac 1); |
3961 | 368 |
by (REPEAT_FIRST (resolve_tac [allI, conjI, impI])); |
369 |
by (ALLGOALS Clarify_tac); |
|
4091 | 370 |
by (blast_tac (claset() addSDs [resp_analz_insert] |
7057
b9ddbb925939
tweaked proofs to handle new freeness reasoning for data c onstructors
paulson
parents:
5535
diff
changeset
|
371 |
addIs [impOfSubs analz_subset_parts]) 3); |
b9ddbb925939
tweaked proofs to handle new freeness reasoning for data c onstructors
paulson
parents:
5535
diff
changeset
|
372 |
by (blast_tac (claset() addSDs [respond_certificate]) 2); |
3961 | 373 |
by (Asm_full_simp_tac 1); |
374 |
(*by unicity, either B=Aa or B=A', a contradiction if B: bad*) |
|
375 |
by (blast_tac |
|
4091 | 376 |
(claset() addSEs [MPair_parts] |
3961 | 377 |
addDs [parts.Body, |
378 |
respond_certificate RSN (2, unique_session_keys)]) 1); |
|
2533 | 379 |
qed_spec_mp "respond_Spy_not_see_session_key"; |
2449 | 380 |
|
381 |
||
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|
382 |
Goal "[| Crypt (shrK A) {|Key K, Agent A', N|} : parts (spies evs); \ |
c729d4c299c1
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diff
changeset
|
383 |
\ A ~: bad; A' ~: bad; evs : recur |] \ |
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Deleted leading parameters thanks to new Goal command
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5076
diff
changeset
|
384 |
\ ==> Key K ~: analz (spies evs)"; |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
385 |
by (etac rev_mp 1); |
2449 | 386 |
by (etac recur.induct 1); |
3683 | 387 |
by analz_spies_tac; |
2449 | 388 |
by (ALLGOALS |
389 |
(asm_simp_tac |
|
5535 | 390 |
(simpset() addsimps split_ifs @ [analz_insert_eq, analz_insert_freshK]))); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
391 |
(*RA4*) |
2533 | 392 |
by (spy_analz_tac 5); |
393 |
(*RA2*) |
|
394 |
by (spy_analz_tac 3); |
|
2449 | 395 |
(*Fake*) |
2533 | 396 |
by (spy_analz_tac 2); |
397 |
(*Base*) |
|
7057
b9ddbb925939
tweaked proofs to handle new freeness reasoning for data c onstructors
paulson
parents:
5535
diff
changeset
|
398 |
by (Force_tac 1); |
2533 | 399 |
(*RA3 remains*) |
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4552
diff
changeset
|
400 |
by (simp_tac (simpset() addsimps [parts_insert_spies]) 1); |
4091 | 401 |
by (safe_tac (claset() delrules [impCE])); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
402 |
(*RA3, case 2: K is an old key*) |
4091 | 403 |
by (blast_tac (claset() addSDs [resp_analz_insert] |
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4552
diff
changeset
|
404 |
addSEs partsEs |
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4552
diff
changeset
|
405 |
addDs [Key_in_parts_respond]) 2); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
406 |
(*RA3, case 1: use lemma previously proved by induction*) |
4091 | 407 |
by (blast_tac (claset() addSEs [respond_Spy_not_see_session_key RSN |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
408 |
(2,rev_notE)]) 1); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
409 |
qed "Spy_not_see_session_key"; |
2449 | 410 |
|
411 |
(**** Authenticity properties for Agents ****) |
|
412 |
||
2481 | 413 |
(*The response never contains Hashes*) |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
414 |
Goal "[| Hash {|Key (shrK B), M|} : parts (insert RB H); \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
415 |
\ (PB,RB,K) : respond evs |] \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
416 |
\ ==> Hash {|Key (shrK B), M|} : parts H"; |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
417 |
by (etac rev_mp 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
418 |
by (etac (respond_imp_responses RS responses.induct) 1); |
4477
b3e5857d8d99
New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents:
4471
diff
changeset
|
419 |
by Auto_tac; |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
420 |
qed "Hash_in_parts_respond"; |
2481 | 421 |
|
2533 | 422 |
(*Only RA1 or RA2 can have caused such a part of a message to appear. |
423 |
This result is of no use to B, who cannot verify the Hash. Moreover, |
|
424 |
it can say nothing about how recent A's message is. It might later be |
|
425 |
used to prove B's presence to A at the run's conclusion.*) |
|
5076 | 426 |
Goalw [HPair_def] |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
427 |
"[| Hash {|Key(shrK A), Agent A, Agent B, NA, P|} : parts(spies evs); \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
428 |
\ A ~: bad; evs : recur |] \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
429 |
\ ==> Says A B (Hash[Key(shrK A)] {|Agent A, Agent B, NA, P|}) : set evs"; |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
430 |
by (etac rev_mp 1); |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
431 |
by (parts_induct_tac 1); |
5359 | 432 |
by (Blast_tac 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
433 |
(*RA3*) |
4091 | 434 |
by (blast_tac (claset() addSDs [Hash_in_parts_respond]) 1); |
2449 | 435 |
qed_spec_mp "Hash_auth_sender"; |
436 |
||
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
437 |
(** These two results subsume (for all agents) the guarantees proved |
2449 | 438 |
separately for A and B in the Otway-Rees protocol. |
439 |
**) |
|
440 |
||
441 |
||
2533 | 442 |
(*Certificates can only originate with the Server.*) |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
443 |
Goal "[| Crypt (shrK A) Y : parts (spies evs); \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
444 |
\ A ~: bad; evs : recur |] \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
445 |
\ ==> EX C RC. Says Server C RC : set evs & \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
446 |
\ Crypt (shrK A) Y : parts {RC}"; |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
447 |
by (etac rev_mp 1); |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
448 |
by (parts_induct_tac 1); |
5359 | 449 |
by (Blast_tac 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
450 |
(*RA4*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
451 |
by (Blast_tac 4); |
2455
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
452 |
(*RA3*) |
4091 | 453 |
by (full_simp_tac (simpset() addsimps [parts_insert_spies]) 3 |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
454 |
THEN Blast_tac 3); |
2455
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
455 |
(*RA1*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
456 |
by (Blast_tac 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
457 |
(*RA2: it cannot be a new Nonce, contradiction.*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
458 |
by (Blast_tac 1); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
459 |
qed "Cert_imp_Server_msg"; |