author | wenzelm |
Mon, 03 Nov 1997 12:24:13 +0100 | |
changeset 4091 | 771b1f6422a8 |
parent 3961 | 6a8996fb7d99 |
child 4422 | 21238c9d363e |
permissions | -rw-r--r-- |
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(* Title: HOL/Auth/Recur |
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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 "recur" for the Recursive Authentication protocol. |
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*) |
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open Recur; |
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proof_timing:=true; |
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HOL_quantifiers := false; |
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Pretty.setdepth 30; |
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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) |
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**) |
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||
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(*Simplest case: Alice goes directly to the server*) |
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goal thy |
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"!!A. A ~= Server \ |
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\ ==> 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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\ Agent Server|} : set evs"; |
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by (REPEAT (resolve_tac [exI,bexI] 1)); |
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by (rtac (recur.Nil RS recur.RA1 RS |
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(respond.One RSN (4,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 thy |
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"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
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\ ==> 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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\ Agent Server|} : 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)); |
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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 (4,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, |
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less_not_refl2 RS not_sym] 1)); |
2449 | 50 |
result(); |
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(*Case three: Alice, Bob, Charlie and the server |
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TOO SLOW to run every time! |
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goal thy |
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"!!A B. [| A ~= B; B ~= C; A ~= Server; B ~= Server; C ~= Server |] \ |
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\ ==> 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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\ Agent Server|} : 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)); |
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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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(4,recur.RA3)) RS recur.RA4 RS recur.RA4) 2); |
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(*SLOW: 70 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, |
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less_not_refl2 RS not_sym] 1)); |
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result(); |
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****************) |
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(**** Inductive proofs about recur ****) |
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(*Nobody sends themselves messages*) |
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goal thy "!!evs. evs : recur ==> ALL A X. Says A A X ~: set evs"; |
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by (etac recur.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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goal thy "!!evs. (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 thy "!!evs. (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 thy |
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"!!evs. [| 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], |
103 |
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 thy "!!evs. (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"; |
111 |
||
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||
113 |
(** For reasoning about the encrypted portion of messages **) |
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||
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val RA2_analz_spies = Says_imp_spies RS analz.Inj |> standard; |
2449 | 116 |
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goal thy "!!evs. Says C' B {|Crypt K X, X', RA|} : set evs \ |
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\ ==> 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. *) |
126 |
||
3683 | 127 |
bind_thm ("RA2_parts_spies", |
128 |
RA2_analz_spies RS (impOfSubs analz_subset_parts)); |
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129 |
bind_thm ("RA4_parts_spies", |
|
130 |
RA4_analz_spies RS (impOfSubs analz_subset_parts)); |
|
2449 | 131 |
|
3683 | 132 |
(*For proving the easier theorems about X ~: parts (spies evs).*) |
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fun parts_induct_tac i = |
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etac recur.induct i THEN |
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forward_tac [RA2_parts_spies] (i+3) THEN |
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etac subst (i+3) (*RA2: DELETE needless definition of PA!*) THEN |
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forward_tac [respond_imp_responses] (i+4) THEN |
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forward_tac [RA4_parts_spies] (i+5) THEN |
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139 |
prove_simple_subgoals_tac i; |
2449 | 140 |
|
141 |
||
3683 | 142 |
(** Theorems of the form X ~: parts (spies evs) imply that NOBODY |
2449 | 143 |
sends messages containing X! **) |
144 |
||
145 |
||
3683 | 146 |
(** Spy never sees another agent's shared key! (unless it's bad at start) **) |
2449 | 147 |
|
148 |
goal thy |
|
3683 | 149 |
"!!evs. evs : recur ==> (Key (shrK A) : parts (spies evs)) = (A : bad)"; |
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150 |
by (parts_induct_tac 1); |
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151 |
by (Fake_parts_insert_tac 1); |
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152 |
by (ALLGOALS |
4091 | 153 |
(asm_simp_tac (simpset() addsimps [parts_insert2, parts_insert_spies]))); |
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154 |
(*RA3*) |
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by (blast_tac (claset() addDs [Key_in_parts_respond]) 2); |
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156 |
(*RA2*) |
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by (blast_tac (claset() addSEs partsEs addDs [parts_cut]) 1); |
2449 | 158 |
qed "Spy_see_shrK"; |
159 |
Addsimps [Spy_see_shrK]; |
|
160 |
||
161 |
goal thy |
|
3683 | 162 |
"!!evs. evs : recur ==> (Key (shrK A) : analz (spies evs)) = (A : bad)"; |
4091 | 163 |
by (auto_tac(claset() addDs [impOfSubs analz_subset_parts], simpset())); |
2449 | 164 |
qed "Spy_analz_shrK"; |
165 |
Addsimps [Spy_analz_shrK]; |
|
166 |
||
3683 | 167 |
goal thy "!!A. [| Key (shrK A) : parts (spies evs); evs : recur |] ==> A:bad"; |
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by (blast_tac (claset() addDs [Spy_see_shrK]) 1); |
2449 | 169 |
qed "Spy_see_shrK_D"; |
170 |
||
171 |
bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D); |
|
172 |
AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D]; |
|
173 |
||
174 |
||
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175 |
|
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176 |
(** Nobody can have used non-existent keys! **) |
2449 | 177 |
|
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goal thy |
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179 |
"!!evs. [| K : keysFor (parts {RB}); (PB,RB,K') : respond evs |] \ |
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180 |
\ ==> K : range shrK"; |
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181 |
by (etac rev_mp 1); |
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182 |
by (etac (respond_imp_responses RS responses.induct) 1); |
2449 | 183 |
by (Auto_tac()); |
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184 |
qed_spec_mp "Key_in_keysFor_parts"; |
2449 | 185 |
|
186 |
||
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goal thy "!!evs. evs : recur ==> \ |
3683 | 188 |
\ Key K ~: used evs --> K ~: keysFor (parts (spies evs))"; |
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189 |
by (parts_induct_tac 1); |
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|
190 |
(*RA3*) |
4091 | 191 |
by (best_tac (claset() addDs [Key_in_keysFor_parts] |
192 |
addss (simpset() addsimps [parts_insert_spies])) 2); |
|
2516
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|
193 |
(*Fake*) |
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paulson
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diff
changeset
|
194 |
by (best_tac |
4091 | 195 |
(claset() addSDs [impOfSubs (parts_insert_subset_Un RS keysFor_mono)] |
3961 | 196 |
addIs [impOfSubs analz_subset_parts] |
197 |
addDs [impOfSubs (analz_subset_parts RS keysFor_mono)] |
|
4091 | 198 |
addss (simpset())) 1); |
2449 | 199 |
qed_spec_mp "new_keys_not_used"; |
200 |
||
201 |
||
202 |
bind_thm ("new_keys_not_analzd", |
|
203 |
[analz_subset_parts RS keysFor_mono, |
|
204 |
new_keys_not_used] MRS contra_subsetD); |
|
205 |
||
206 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
|
207 |
||
208 |
||
209 |
||
210 |
(*** Proofs involving analz ***) |
|
211 |
||
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|
212 |
(*For proofs involving analz.*) |
3683 | 213 |
val analz_spies_tac = |
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Simplification of some proofs, especially by eliminating
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|
214 |
etac subst 4 (*RA2: DELETE needless definition of PA!*) THEN |
3683 | 215 |
dtac RA2_analz_spies 4 THEN |
2449 | 216 |
forward_tac [respond_imp_responses] 5 THEN |
3683 | 217 |
dtac RA4_analz_spies 6; |
2449 | 218 |
|
219 |
||
220 |
(** Session keys are not used to encrypt other session keys **) |
|
221 |
||
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|
222 |
(*Version for "responses" relation. Handles case RA3 in the theorem below. |
3683 | 223 |
Note that it holds for *any* set H (not just "spies evs") |
2449 | 224 |
satisfying the inductive hypothesis.*) |
225 |
goal thy |
|
2516
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changeset
|
226 |
"!!evs. [| RB : responses evs; \ |
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|
227 |
\ ALL K KK. KK <= Compl (range shrK) --> \ |
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|
228 |
\ (Key K : analz (Key``KK Un H)) = \ |
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|
229 |
\ (K : KK | Key K : analz H) |] \ |
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changeset
|
230 |
\ ==> ALL K KK. KK <= Compl (range shrK) --> \ |
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changeset
|
231 |
\ (Key K : analz (insert RB (Key``KK Un H))) = \ |
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|
232 |
\ (K : KK | Key K : analz (insert RB H))"; |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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changeset
|
233 |
by (etac responses.induct 1); |
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2485
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changeset
|
234 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
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|
235 |
qed "resp_analz_image_freshK_lemma"; |
2449 | 236 |
|
237 |
(*Version for the protocol. Proof is almost trivial, thanks to the lemma.*) |
|
238 |
goal thy |
|
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|
239 |
"!!evs. evs : recur ==> \ |
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|
240 |
\ ALL K KK. KK <= Compl (range shrK) --> \ |
3683 | 241 |
\ (Key K : analz (Key``KK Un (spies evs))) = \ |
242 |
\ (K : KK | Key K : analz (spies evs))"; |
|
2449 | 243 |
by (etac recur.induct 1); |
3683 | 244 |
by analz_spies_tac; |
2516
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changeset
|
245 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
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2485
diff
changeset
|
246 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
4d68fbe6378b
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|
247 |
by (ALLGOALS |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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2485
diff
changeset
|
248 |
(asm_simp_tac |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
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2485
diff
changeset
|
249 |
(analz_image_freshK_ss addsimps [resp_analz_image_freshK_lemma]))); |
2449 | 250 |
(*Base*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
251 |
by (Blast_tac 1); |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
252 |
(*Fake*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
253 |
by (spy_analz_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
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diff
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|
254 |
val raw_analz_image_freshK = result(); |
4d68fbe6378b
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diff
changeset
|
255 |
qed_spec_mp "analz_image_freshK"; |
2449 | 256 |
|
257 |
||
3683 | 258 |
(*Instance of the lemma with H replaced by (spies evs): |
3519
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|
259 |
[| RB : responses evs; evs : recur; |] |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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2485
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changeset
|
260 |
==> KK <= Compl (range shrK) --> |
3683 | 261 |
Key K : analz (insert RB (Key``KK Un spies evs)) = |
262 |
(K : KK | Key K : analz (insert RB (spies evs))) |
|
2449 | 263 |
*) |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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2485
diff
changeset
|
264 |
bind_thm ("resp_analz_image_freshK", |
4d68fbe6378b
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2485
diff
changeset
|
265 |
raw_analz_image_freshK RSN |
3961 | 266 |
(2, resp_analz_image_freshK_lemma) RS spec RS spec RS mp); |
2449 | 267 |
|
268 |
goal thy |
|
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
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3516
diff
changeset
|
269 |
"!!evs. [| evs : recur; KAB ~: range shrK |] ==> \ |
3683 | 270 |
\ Key K : analz (insert (Key KAB) (spies evs)) = \ |
271 |
\ (K = KAB | Key K : analz (spies evs))"; |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
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parents:
2485
diff
changeset
|
272 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
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diff
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|
273 |
qed "analz_insert_freshK"; |
2449 | 274 |
|
275 |
||
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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2485
diff
changeset
|
276 |
(*Everything that's hashed is already in past traffic. *) |
3683 | 277 |
goal thy "!!evs. [| Hash {|Key(shrK A), X|} : parts (spies evs); \ |
278 |
\ evs : recur; A ~: bad |] \ |
|
279 |
\ ==> X : parts (spies evs)"; |
|
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
280 |
by (etac rev_mp 1); |
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
281 |
by (parts_induct_tac 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
282 |
(*RA3 requires a further induction*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
283 |
by (etac responses.induct 2); |
2449 | 284 |
by (ALLGOALS Asm_simp_tac); |
285 |
(*Fake*) |
|
4091 | 286 |
by (simp_tac (simpset() addsimps [parts_insert_spies]) 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
287 |
by (Fake_parts_insert_tac 1); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
288 |
qed "Hash_imp_body"; |
2449 | 289 |
|
290 |
||
291 |
(** The Nonce NA uniquely identifies A's message. |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
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parents:
2485
diff
changeset
|
292 |
This theorem applies to steps RA1 and RA2! |
2455
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
293 |
|
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
294 |
Unicity is not used in other proofs but is desirable in its own right. |
2449 | 295 |
**) |
296 |
||
297 |
goal thy |
|
3683 | 298 |
"!!evs. [| evs : recur; A ~: bad |] \ |
2560 | 299 |
\ ==> EX B' P'. ALL B P. \ |
3683 | 300 |
\ Hash {|Key(shrK A), Agent A, B, NA, P|} : parts (spies evs) \ |
2560 | 301 |
\ --> B=B' & P=P'"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
302 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
303 |
by (Fake_parts_insert_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
304 |
by (etac responses.induct 3); |
4091 | 305 |
by (ALLGOALS (simp_tac (simpset() addsimps [all_conj_distrib]))); |
306 |
by (clarify_tac (claset() addSEs partsEs) 1); |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
307 |
(*RA1,2: creation of new Nonce. Move assertion into global context*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
308 |
by (ALLGOALS (expand_case_tac "NA = ?y")); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
309 |
by (REPEAT_FIRST (ares_tac [exI])); |
4091 | 310 |
by (REPEAT (blast_tac (claset() addSDs [Hash_imp_body] |
3683 | 311 |
addSEs spies_partsEs) 1)); |
2449 | 312 |
val lemma = result(); |
313 |
||
2481 | 314 |
goalw thy [HPair_def] |
3683 | 315 |
"!!A.[| Hash[Key(shrK A)] {|Agent A, B,NA,P|} : parts(spies evs); \ |
316 |
\ Hash[Key(shrK A)] {|Agent A, B',NA,P'|} : parts(spies evs); \ |
|
317 |
\ evs : recur; A ~: bad |] \ |
|
3483
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
318 |
\ ==> B=B' & P=P'"; |
2481 | 319 |
by (REPEAT (eresolve_tac partsEs 1)); |
2449 | 320 |
by (prove_unique_tac lemma 1); |
321 |
qed "unique_NA"; |
|
322 |
||
323 |
||
324 |
(*** Lemmas concerning the Server's response |
|
325 |
(relations "respond" and "responses") |
|
326 |
***) |
|
327 |
||
328 |
goal thy |
|
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
329 |
"!!evs. [| RB : responses evs; evs : recur |] \ |
3683 | 330 |
\ ==> (Key (shrK B) : analz (insert RB (spies evs))) = (B:bad)"; |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
331 |
by (etac responses.induct 1); |
2449 | 332 |
by (ALLGOALS |
333 |
(asm_simp_tac |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
334 |
(analz_image_freshK_ss addsimps [Spy_analz_shrK, |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
335 |
resp_analz_image_freshK]))); |
2449 | 336 |
qed "shrK_in_analz_respond"; |
337 |
Addsimps [shrK_in_analz_respond]; |
|
338 |
||
339 |
||
340 |
goal thy |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
341 |
"!!evs. [| RB : responses evs; \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
342 |
\ ALL K KK. KK <= Compl (range shrK) --> \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
343 |
\ (Key K : analz (Key``KK Un H)) = \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
344 |
\ (K : KK | Key K : analz H) |] \ |
3483
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
345 |
\ ==> (Key K : analz (insert RB H)) --> \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
346 |
\ (Key K : parts{RB} | Key K : analz H)"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
347 |
by (etac responses.induct 1); |
2449 | 348 |
by (ALLGOALS |
349 |
(asm_simp_tac |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
350 |
(analz_image_freshK_ss addsimps [resp_analz_image_freshK_lemma]))); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
351 |
(*Simplification using two distinct treatments of "image"*) |
4091 | 352 |
by (simp_tac (simpset() addsimps [parts_insert2]) 1); |
353 |
by (blast_tac (claset() delrules [allE]) 1); |
|
2449 | 354 |
qed "resp_analz_insert_lemma"; |
355 |
||
356 |
bind_thm ("resp_analz_insert", |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
357 |
raw_analz_image_freshK RSN |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
358 |
(2, resp_analz_insert_lemma) RSN(2, rev_mp)); |
2449 | 359 |
|
360 |
||
361 |
(*The Server does not send such messages. This theorem lets us avoid |
|
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
362 |
assuming B~=Server in RA4.*) |
2449 | 363 |
goal thy |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
364 |
"!!evs. evs : recur \ |
3483
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
365 |
\ ==> ALL C X Y. Says Server C {|X, Agent Server, Y|} ~: set evs"; |
2449 | 366 |
by (etac recur.induct 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
367 |
by (etac (respond.induct) 5); |
2449 | 368 |
by (Auto_tac()); |
369 |
qed_spec_mp "Says_Server_not"; |
|
370 |
AddSEs [Says_Server_not RSN (2,rev_notE)]; |
|
371 |
||
372 |
||
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
373 |
(*The last key returned by respond indeed appears in a certificate*) |
2449 | 374 |
goal thy |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
375 |
"!!K. (Hash[Key(shrK A)] {|Agent A, B, NA, P|}, RA, K) : respond evs \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
376 |
\ ==> Crypt (shrK A) {|Key K, B, NA|} : parts {RA}"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
377 |
by (etac respond.elim 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
378 |
by (ALLGOALS Asm_full_simp_tac); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
379 |
qed "respond_certificate"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
380 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
381 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
382 |
goal thy |
2560 | 383 |
"!!K'. (PB,RB,KXY) : respond evs \ |
384 |
\ ==> EX A' B'. ALL A B N. \ |
|
2449 | 385 |
\ Crypt (shrK A) {|Key K, Agent B, N|} : parts {RB} \ |
386 |
\ --> (A'=A & B'=B) | (A'=B & B'=A)"; |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
387 |
by (etac respond.induct 1); |
4091 | 388 |
by (ALLGOALS (asm_full_simp_tac (simpset() addsimps [all_conj_distrib]))); |
2449 | 389 |
(*Base case*) |
3121
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Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
390 |
by (Blast_tac 1); |
3730 | 391 |
by Safe_tac; |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
392 |
by (expand_case_tac "K = KBC" 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
393 |
by (dtac respond_Key_in_parts 1); |
4091 | 394 |
by (blast_tac (claset() addSIs [exI] |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
395 |
addSEs partsEs |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
396 |
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
|
397 |
by (expand_case_tac "K = KAB" 1); |
2449 | 398 |
by (REPEAT (ares_tac [exI] 2)); |
399 |
by (ex_strip_tac 1); |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
400 |
by (dtac respond_certificate 1); |
2449 | 401 |
by (Fast_tac 1); |
402 |
val lemma = result(); |
|
403 |
||
404 |
goal thy |
|
2560 | 405 |
"!!RB. [| Crypt (shrK A) {|Key K, Agent B, N|} : parts {RB}; \ |
2449 | 406 |
\ Crypt (shrK A') {|Key K, Agent B', N'|} : parts {RB}; \ |
2560 | 407 |
\ (PB,RB,KXY) : respond evs |] \ |
2449 | 408 |
\ ==> (A'=A & B'=B) | (A'=B & B'=A)"; |
2560 | 409 |
by (prove_unique_tac lemma 1); |
2449 | 410 |
qed "unique_session_keys"; |
411 |
||
412 |
||
2451
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Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
413 |
(** Crucial secrecy property: Spy does not see the keys sent in msg RA3 |
2449 | 414 |
Does not in itself guarantee security: an attack could violate |
415 |
the premises, e.g. by having A=Spy **) |
|
416 |
||
417 |
goal thy |
|
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
418 |
"!!evs. [| (PB,RB,KAB) : respond evs; evs : recur |] \ |
3683 | 419 |
\ ==> ALL A A' N. A ~: bad & A' ~: bad --> \ |
2449 | 420 |
\ Crypt (shrK A) {|Key K, Agent A', N|} : parts{RB} --> \ |
3683 | 421 |
\ Key K ~: analz (insert RB (spies evs))"; |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
422 |
by (etac respond.induct 1); |
2449 | 423 |
by (forward_tac [respond_imp_responses] 2); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
424 |
by (forward_tac [respond_imp_not_used] 2); |
3961 | 425 |
by (ALLGOALS (*6 seconds*) |
2449 | 426 |
(asm_simp_tac |
3961 | 427 |
(analz_image_freshK_ss |
428 |
addsimps expand_ifs |
|
429 |
addsimps |
|
430 |
[shrK_in_analz_respond, resp_analz_image_freshK, parts_insert2]))); |
|
4091 | 431 |
by (ALLGOALS (simp_tac (simpset() addsimps [ex_disj_distrib]))); |
3681 | 432 |
(** LEVEL 5 **) |
4091 | 433 |
by (blast_tac (claset() addIs [impOfSubs analz_subset_parts]) 1); |
3961 | 434 |
by (REPEAT_FIRST (resolve_tac [allI, conjI, impI])); |
435 |
by (ALLGOALS Clarify_tac); |
|
4091 | 436 |
by (blast_tac (claset() addSDs [resp_analz_insert] |
3961 | 437 |
addIs [impOfSubs analz_subset_parts]) 2); |
4091 | 438 |
by (blast_tac (claset() addSDs [respond_certificate]) 1); |
3961 | 439 |
by (Asm_full_simp_tac 1); |
440 |
(*by unicity, either B=Aa or B=A', a contradiction if B: bad*) |
|
441 |
by (blast_tac |
|
4091 | 442 |
(claset() addSEs [MPair_parts] |
3961 | 443 |
addDs [parts.Body, |
444 |
respond_certificate RSN (2, unique_session_keys)]) 1); |
|
2533 | 445 |
qed_spec_mp "respond_Spy_not_see_session_key"; |
2449 | 446 |
|
447 |
||
448 |
goal thy |
|
3683 | 449 |
"!!evs. [| Crypt (shrK A) {|Key K, Agent A', N|} : parts (spies evs); \ |
3730 | 450 |
\ A ~: bad; A' ~: bad; evs : recur |] \ |
3683 | 451 |
\ ==> Key K ~: analz (spies evs)"; |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
452 |
by (etac rev_mp 1); |
2449 | 453 |
by (etac recur.induct 1); |
3683 | 454 |
by analz_spies_tac; |
2449 | 455 |
by (ALLGOALS |
456 |
(asm_simp_tac |
|
4091 | 457 |
(simpset() addsimps (expand_ifs @ |
3961 | 458 |
[analz_insert_eq, parts_insert_spies, |
459 |
analz_insert_freshK])))); |
|
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
460 |
(*RA4*) |
2533 | 461 |
by (spy_analz_tac 5); |
462 |
(*RA2*) |
|
463 |
by (spy_analz_tac 3); |
|
2449 | 464 |
(*Fake*) |
2533 | 465 |
by (spy_analz_tac 2); |
466 |
(*Base*) |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
467 |
by (Blast_tac 1); |
2533 | 468 |
(*RA3 remains*) |
4091 | 469 |
by (safe_tac (claset() delrules [impCE])); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
470 |
(*RA3, case 2: K is an old key*) |
4091 | 471 |
by (blast_tac (claset() addSDs [resp_analz_insert] |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
472 |
addSEs partsEs |
3730 | 473 |
addDs [Key_in_parts_respond]) 2); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
474 |
(*RA3, case 1: use lemma previously proved by induction*) |
4091 | 475 |
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
|
476 |
(2,rev_notE)]) 1); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
477 |
qed "Spy_not_see_session_key"; |
2449 | 478 |
|
479 |
||
480 |
(**** Authenticity properties for Agents ****) |
|
481 |
||
2481 | 482 |
(*The response never contains Hashes*) |
483 |
goal thy |
|
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
484 |
"!!evs. [| Hash {|Key (shrK B), M|} : parts (insert RB H); \ |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
485 |
\ (PB,RB,K) : respond evs |] \ |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
486 |
\ ==> Hash {|Key (shrK B), M|} : parts H"; |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
487 |
by (etac rev_mp 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
488 |
by (etac (respond_imp_responses RS responses.induct) 1); |
2481 | 489 |
by (Auto_tac()); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
490 |
qed "Hash_in_parts_respond"; |
2481 | 491 |
|
2533 | 492 |
(*Only RA1 or RA2 can have caused such a part of a message to appear. |
493 |
This result is of no use to B, who cannot verify the Hash. Moreover, |
|
494 |
it can say nothing about how recent A's message is. It might later be |
|
495 |
used to prove B's presence to A at the run's conclusion.*) |
|
2481 | 496 |
goalw thy [HPair_def] |
3683 | 497 |
"!!evs. [| Hash {|Key(shrK A), Agent A, Agent B, NA, P|} : parts(spies evs); \ |
498 |
\ A ~: bad; evs : recur |] \ |
|
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
499 |
\ ==> 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
|
500 |
by (etac rev_mp 1); |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
501 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
502 |
by (Fake_parts_insert_tac 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
503 |
(*RA3*) |
4091 | 504 |
by (blast_tac (claset() addSDs [Hash_in_parts_respond]) 1); |
2449 | 505 |
qed_spec_mp "Hash_auth_sender"; |
506 |
||
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
507 |
(** These two results subsume (for all agents) the guarantees proved |
2449 | 508 |
separately for A and B in the Otway-Rees protocol. |
509 |
**) |
|
510 |
||
511 |
||
2533 | 512 |
(*Certificates can only originate with the Server.*) |
2449 | 513 |
goal thy |
3683 | 514 |
"!!evs. [| Crypt (shrK A) Y : parts (spies evs); \ |
515 |
\ A ~: bad; A ~= Spy; evs : recur |] \ |
|
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
516 |
\ ==> EX C RC. Says Server C RC : set evs & \ |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
517 |
\ Crypt (shrK A) Y : parts {RC}"; |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
518 |
by (etac rev_mp 1); |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
519 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
520 |
by (Fake_parts_insert_tac 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
521 |
(*RA4*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
522 |
by (Blast_tac 4); |
2455
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
523 |
(*RA3*) |
4091 | 524 |
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
|
525 |
THEN Blast_tac 3); |
2455
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
526 |
(*RA1*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
527 |
by (Blast_tac 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
528 |
(*RA2: it cannot be a new Nonce, contradiction.*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
529 |
by (Blast_tac 1); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
530 |
qed "Cert_imp_Server_msg"; |