author | paulson |
Tue, 01 Jul 1997 17:59:36 +0200 | |
changeset 3483 | 6988394a6008 |
parent 3466 | 30791e5a69c4 |
child 3516 | 470626799511 |
permissions | -rw-r--r-- |
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(* 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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||
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Inductive relation "recur" for the Recursive Authentication protocol. |
|
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*) |
|
8 |
||
9 |
open Recur; |
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||
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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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||
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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 lost. \ |
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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(); |
33 |
||
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||
35 |
(*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 lost. \ |
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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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||
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||
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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 lost. \ |
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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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****************) |
2449 | 74 |
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(**** Inductive proofs about recur ****) |
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76 |
||
77 |
(*Monotonicity*) |
|
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goal thy "!!evs. lost' <= lost ==> recur lost' <= recur lost"; |
|
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by (rtac subsetI 1); |
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80 |
by (etac recur.induct 1); |
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by (REPEAT_FIRST |
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(blast_tac (!claset addIs (impOfSubs(sees_mono RS analz_mono RS synth_mono) |
2449 | 83 |
:: recur.intrs)))); |
84 |
qed "recur_mono"; |
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||
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(*Nobody sends themselves messages*) |
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goal thy "!!evs. evs : recur lost ==> ALL A X. Says A A X ~: set evs"; |
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by (etac recur.induct 1); |
89 |
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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|
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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], |
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!simpset)); |
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qed_spec_mp "Key_in_parts_respond"; |
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|
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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"; |
120 |
||
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(** For reasoning about the encrypted portion of messages **) |
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||
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val RA2_analz_sees_Spy = Says_imp_sees_Spy RS analz.Inj |> standard; |
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3465 | 126 |
goal thy "!!evs. Says C' B {|Crypt K X, X', RA|} : set evs \ |
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\ ==> RA : analz (sees lost Spy evs)"; |
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128 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1); |
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qed "RA4_analz_sees_Spy"; |
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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. *) |
135 |
||
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bind_thm ("RA2_parts_sees_Spy", |
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RA2_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
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bind_thm ("RA4_parts_sees_Spy", |
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RA4_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
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|
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(*For proving the easier theorems about X ~: parts (sees lost Spy evs). |
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142 |
We instantiate the variable to "lost" since leaving it as a Var would |
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143 |
interfere with simplification.*) |
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144 |
val parts_induct_tac = |
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let val tac = forw_inst_tac [("lost","lost")] |
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146 |
in etac recur.induct 1 THEN |
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147 |
tac RA2_parts_sees_Spy 4 THEN |
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etac subst 4 (*RA2: DELETE needless definition of PA!*) THEN |
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149 |
forward_tac [respond_imp_responses] 5 THEN |
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150 |
tac RA4_parts_sees_Spy 6 THEN |
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151 |
prove_simple_subgoals_tac 1 |
2449 | 152 |
end; |
153 |
||
154 |
||
155 |
(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY |
|
156 |
sends messages containing X! **) |
|
157 |
||
158 |
||
159 |
(** Spy never sees another agent's long-term key (unless initially lost) **) |
|
160 |
||
161 |
goal thy |
|
162 |
"!!evs. evs : recur lost \ |
|
163 |
\ ==> (Key (shrK A) : parts (sees lost Spy evs)) = (A : lost)"; |
|
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164 |
by parts_induct_tac; |
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165 |
by (Fake_parts_insert_tac 1); |
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166 |
by (ALLGOALS |
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167 |
(asm_simp_tac (!simpset addsimps [parts_insert2, parts_insert_sees]))); |
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168 |
(*RA3*) |
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169 |
by (blast_tac (!claset addDs [Key_in_parts_respond]) 2); |
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170 |
(*RA2*) |
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171 |
by (blast_tac (!claset addSEs partsEs addDs [parts_cut]) 1); |
2449 | 172 |
qed "Spy_see_shrK"; |
173 |
Addsimps [Spy_see_shrK]; |
|
174 |
||
175 |
goal thy |
|
176 |
"!!evs. evs : recur lost \ |
|
177 |
\ ==> (Key (shrK A) : analz (sees lost Spy evs)) = (A : lost)"; |
|
178 |
by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset)); |
|
179 |
qed "Spy_analz_shrK"; |
|
180 |
Addsimps [Spy_analz_shrK]; |
|
181 |
||
182 |
goal thy "!!A. [| Key (shrK A) : parts (sees lost Spy evs); \ |
|
183 |
\ evs : recur lost |] ==> A:lost"; |
|
3121
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Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
184 |
by (blast_tac (!claset addDs [Spy_see_shrK]) 1); |
2449 | 185 |
qed "Spy_see_shrK_D"; |
186 |
||
187 |
bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D); |
|
188 |
AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D]; |
|
189 |
||
190 |
||
2516
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changeset
|
191 |
|
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changeset
|
192 |
(** Nobody can have used non-existent keys! **) |
2449 | 193 |
|
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paulson
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changeset
|
194 |
goal thy |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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changeset
|
195 |
"!!evs. [| K : keysFor (parts {RB}); (PB,RB,K') : respond evs |] \ |
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paulson
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changeset
|
196 |
\ ==> K : range shrK"; |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
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changeset
|
197 |
by (etac rev_mp 1); |
4d68fbe6378b
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paulson
parents:
2485
diff
changeset
|
198 |
by (etac (respond_imp_responses RS responses.induct) 1); |
2449 | 199 |
by (Auto_tac()); |
2516
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2485
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changeset
|
200 |
qed_spec_mp "Key_in_keysFor_parts"; |
2449 | 201 |
|
202 |
||
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
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2485
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changeset
|
203 |
goal thy "!!evs. evs : recur lost ==> \ |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
204 |
\ Key K ~: used evs --> K ~: keysFor (parts (sees lost Spy evs))"; |
3121
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Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
205 |
by parts_induct_tac; |
2451
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Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
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changeset
|
206 |
(*RA3*) |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
207 |
by (best_tac (!claset addDs [Key_in_keysFor_parts] |
3207 | 208 |
addss (!simpset addsimps [parts_insert_sees])) 2); |
2516
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paulson
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changeset
|
209 |
(*Fake*) |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
210 |
by (best_tac |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
211 |
(!claset addIs [impOfSubs analz_subset_parts] |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
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changeset
|
212 |
addDs [impOfSubs (analz_subset_parts RS keysFor_mono), |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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changeset
|
213 |
impOfSubs (parts_insert_subset_Un RS keysFor_mono)] |
3207 | 214 |
addss (!simpset)) 1); |
2449 | 215 |
qed_spec_mp "new_keys_not_used"; |
216 |
||
217 |
||
218 |
bind_thm ("new_keys_not_analzd", |
|
219 |
[analz_subset_parts RS keysFor_mono, |
|
220 |
new_keys_not_used] MRS contra_subsetD); |
|
221 |
||
222 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
|
223 |
||
224 |
||
225 |
||
226 |
(*** Proofs involving analz ***) |
|
227 |
||
228 |
(*For proofs involving analz. We again instantiate the variable to "lost".*) |
|
3121
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Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
229 |
val analz_sees_tac = |
2485
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Simplification of some proofs, especially by eliminating
paulson
parents:
2481
diff
changeset
|
230 |
etac subst 4 (*RA2: DELETE needless definition of PA!*) THEN |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
231 |
dres_inst_tac [("lost","lost")] RA2_analz_sees_Spy 4 THEN |
2449 | 232 |
forward_tac [respond_imp_responses] 5 THEN |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
233 |
dres_inst_tac [("lost","lost")] RA4_analz_sees_Spy 6; |
2449 | 234 |
|
235 |
||
236 |
(** Session keys are not used to encrypt other session keys **) |
|
237 |
||
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
238 |
(*Version for "responses" relation. Handles case RA3 in the theorem below. |
2449 | 239 |
Note that it holds for *any* set H (not just "sees lost Spy evs") |
240 |
satisfying the inductive hypothesis.*) |
|
241 |
goal thy |
|
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
242 |
"!!evs. [| RB : responses evs; \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
243 |
\ 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
|
244 |
\ (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
|
245 |
\ (K : KK | Key K : analz H) |] \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
246 |
\ ==> 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
|
247 |
\ (Key K : analz (insert RB (Key``KK Un H))) = \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
248 |
\ (K : KK | Key K : analz (insert RB H))"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
249 |
by (etac responses.induct 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
250 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
251 |
qed "resp_analz_image_freshK_lemma"; |
2449 | 252 |
|
253 |
(*Version for the protocol. Proof is almost trivial, thanks to the lemma.*) |
|
254 |
goal thy |
|
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
255 |
"!!evs. evs : recur lost ==> \ |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
256 |
\ 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
|
257 |
\ (Key K : analz (Key``KK Un (sees lost Spy evs))) = \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
258 |
\ (K : KK | Key K : analz (sees lost Spy evs))"; |
2449 | 259 |
by (etac recur.induct 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
260 |
by analz_sees_tac; |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
261 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
262 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
263 |
by (ALLGOALS |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
264 |
(asm_simp_tac |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
265 |
(analz_image_freshK_ss addsimps [resp_analz_image_freshK_lemma]))); |
2449 | 266 |
(*Base*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
267 |
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
|
268 |
(*Fake*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
269 |
by (spy_analz_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
270 |
val raw_analz_image_freshK = result(); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
271 |
qed_spec_mp "analz_image_freshK"; |
2449 | 272 |
|
273 |
||
274 |
(*Instance of the lemma with H replaced by (sees lost Spy evs): |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
275 |
[| RB : responses evs; evs : recur lost; |] |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
276 |
==> KK <= Compl (range shrK) --> |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
277 |
Key K : analz (insert RB (Key``KK Un sees lost Spy evs)) = |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
278 |
(K : KK | Key K : analz (insert RB (sees lost Spy evs))) |
2449 | 279 |
*) |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
280 |
bind_thm ("resp_analz_image_freshK", |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
281 |
raw_analz_image_freshK RSN |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
282 |
(2, resp_analz_image_freshK_lemma) RS spec RS spec); |
2449 | 283 |
|
284 |
goal thy |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
285 |
"!!evs. [| evs : recur lost; KAB ~: range shrK |] ==> \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
286 |
\ Key K : analz (insert (Key KAB) (sees lost Spy evs)) = \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
287 |
\ (K = KAB | Key K : analz (sees lost Spy evs))"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
288 |
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
paulson
parents:
2485
diff
changeset
|
289 |
qed "analz_insert_freshK"; |
2449 | 290 |
|
291 |
||
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
292 |
(*Everything that's hashed is already in past traffic. *) |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
293 |
goal thy "!!evs. [| Hash {|Key(shrK A), X|} : parts (sees lost Spy evs); \ |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
294 |
\ evs : recur lost; A ~: lost |] \ |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
295 |
\ ==> X : parts (sees lost Spy evs)"; |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
296 |
by (etac rev_mp 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
297 |
by parts_induct_tac; |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
298 |
(*RA3 requires a further induction*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
299 |
by (etac responses.induct 2); |
2449 | 300 |
by (ALLGOALS Asm_simp_tac); |
301 |
(*Fake*) |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
302 |
by (simp_tac (!simpset addsimps [parts_insert_sees]) 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
303 |
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
|
304 |
qed "Hash_imp_body"; |
2449 | 305 |
|
306 |
||
307 |
(** The Nonce NA uniquely identifies A's message. |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
308 |
This theorem applies to steps RA1 and RA2! |
2455
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
309 |
|
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
310 |
Unicity is not used in other proofs but is desirable in its own right. |
2449 | 311 |
**) |
312 |
||
313 |
goal thy |
|
2560 | 314 |
"!!evs. [| evs : recur lost; A ~: lost |] \ |
315 |
\ ==> EX B' P'. ALL B P. \ |
|
316 |
\ Hash {|Key(shrK A), Agent A, B, NA, P|} : parts (sees lost Spy evs) \ |
|
317 |
\ --> B=B' & P=P'"; |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
318 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
319 |
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
|
320 |
by (etac responses.induct 3); |
2485
c4368c967c56
Simplification of some proofs, especially by eliminating
paulson
parents:
2481
diff
changeset
|
321 |
by (ALLGOALS (simp_tac (!simpset addsimps [all_conj_distrib]))); |
2449 | 322 |
by (step_tac (!claset addSEs partsEs) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
323 |
(*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
|
324 |
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
|
325 |
by (REPEAT_FIRST (ares_tac [exI])); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
326 |
by (REPEAT (blast_tac (!claset addSDs [Hash_imp_body] |
3483
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
327 |
addSEs sees_Spy_partsEs) 1)); |
2449 | 328 |
val lemma = result(); |
329 |
||
2481 | 330 |
goalw thy [HPair_def] |
3483
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
331 |
"!!A.[| Hash[Key(shrK A)] {|Agent A, B,NA,P|} : parts(sees lost Spy evs); \ |
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
332 |
\ Hash[Key(shrK A)] {|Agent A, B',NA,P'|} : parts(sees lost Spy evs); \ |
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
333 |
\ evs : recur lost; A ~: lost |] \ |
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
334 |
\ ==> B=B' & P=P'"; |
2481 | 335 |
by (REPEAT (eresolve_tac partsEs 1)); |
2449 | 336 |
by (prove_unique_tac lemma 1); |
337 |
qed "unique_NA"; |
|
338 |
||
339 |
||
340 |
(*** Lemmas concerning the Server's response |
|
341 |
(relations "respond" and "responses") |
|
342 |
***) |
|
343 |
||
344 |
goal thy |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
345 |
"!!evs. [| RB : responses evs; evs : recur lost |] \ |
2449 | 346 |
\ ==> (Key (shrK B) : analz (insert RB (sees lost Spy evs))) = (B:lost)"; |
2516
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 [Spy_analz_shrK, |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
351 |
resp_analz_image_freshK]))); |
2449 | 352 |
qed "shrK_in_analz_respond"; |
353 |
Addsimps [shrK_in_analz_respond]; |
|
354 |
||
355 |
||
356 |
goal thy |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
357 |
"!!evs. [| RB : responses evs; \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
358 |
\ 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
|
359 |
\ (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
|
360 |
\ (K : KK | Key K : analz H) |] \ |
3483
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
361 |
\ ==> (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
|
362 |
\ (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
|
363 |
by (etac responses.induct 1); |
2449 | 364 |
by (ALLGOALS |
365 |
(asm_simp_tac |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
366 |
(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
|
367 |
(*Simplification using two distinct treatments of "image"*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
368 |
by (simp_tac (!simpset addsimps [parts_insert2]) 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
369 |
by (blast_tac (!claset delrules [allE]) 1); |
2449 | 370 |
qed "resp_analz_insert_lemma"; |
371 |
||
372 |
bind_thm ("resp_analz_insert", |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
373 |
raw_analz_image_freshK RSN |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
374 |
(2, resp_analz_insert_lemma) RSN(2, rev_mp)); |
2449 | 375 |
|
376 |
||
377 |
(*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
|
378 |
assuming B~=Server in RA4.*) |
2449 | 379 |
goal thy |
3483
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
380 |
"!!evs. evs : recur lost \ |
6988394a6008
Tidying; also simplified the lemma Says_Server_not
paulson
parents:
3466
diff
changeset
|
381 |
\ ==> ALL C X Y. Says Server C {|X, Agent Server, Y|} ~: set evs"; |
2449 | 382 |
by (etac recur.induct 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
383 |
by (etac (respond.induct) 5); |
2449 | 384 |
by (Auto_tac()); |
385 |
qed_spec_mp "Says_Server_not"; |
|
386 |
AddSEs [Says_Server_not RSN (2,rev_notE)]; |
|
387 |
||
388 |
||
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
389 |
(*The last key returned by respond indeed appears in a certificate*) |
2449 | 390 |
goal thy |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
391 |
"!!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
|
392 |
\ ==> 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
|
393 |
by (etac respond.elim 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
394 |
by (ALLGOALS Asm_full_simp_tac); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
395 |
qed "respond_certificate"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
396 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
397 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
398 |
goal thy |
2560 | 399 |
"!!K'. (PB,RB,KXY) : respond evs \ |
400 |
\ ==> EX A' B'. ALL A B N. \ |
|
2449 | 401 |
\ Crypt (shrK A) {|Key K, Agent B, N|} : parts {RB} \ |
402 |
\ --> (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
|
403 |
by (etac respond.induct 1); |
2449 | 404 |
by (ALLGOALS (asm_full_simp_tac (!simpset addsimps [all_conj_distrib]))); |
405 |
(*Base case*) |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
406 |
by (Blast_tac 1); |
2449 | 407 |
by (Step_tac 1); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
408 |
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
|
409 |
by (dtac respond_Key_in_parts 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
410 |
by (blast_tac (!claset addSIs [exI] |
2449 | 411 |
addSEs partsEs |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
412 |
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
|
413 |
by (expand_case_tac "K = KAB" 1); |
2449 | 414 |
by (REPEAT (ares_tac [exI] 2)); |
415 |
by (ex_strip_tac 1); |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
416 |
by (dtac respond_certificate 1); |
2449 | 417 |
by (Fast_tac 1); |
418 |
val lemma = result(); |
|
419 |
||
420 |
goal thy |
|
2560 | 421 |
"!!RB. [| Crypt (shrK A) {|Key K, Agent B, N|} : parts {RB}; \ |
2449 | 422 |
\ Crypt (shrK A') {|Key K, Agent B', N'|} : parts {RB}; \ |
2560 | 423 |
\ (PB,RB,KXY) : respond evs |] \ |
2449 | 424 |
\ ==> (A'=A & B'=B) | (A'=B & B'=A)"; |
2560 | 425 |
by (prove_unique_tac lemma 1); |
2449 | 426 |
qed "unique_session_keys"; |
427 |
||
428 |
||
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
429 |
(** Crucial secrecy property: Spy does not see the keys sent in msg RA3 |
2449 | 430 |
Does not in itself guarantee security: an attack could violate |
431 |
the premises, e.g. by having A=Spy **) |
|
432 |
||
433 |
goal thy |
|
2533 | 434 |
"!!evs. [| (PB,RB,KAB) : respond evs; evs : recur lost |] \ |
435 |
\ ==> ALL A A' N. A ~: lost & A' ~: lost --> \ |
|
2449 | 436 |
\ Crypt (shrK A) {|Key K, Agent A', N|} : parts{RB} --> \ |
437 |
\ Key K ~: analz (insert RB (sees lost Spy evs))"; |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
438 |
by (etac respond.induct 1); |
2449 | 439 |
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
|
440 |
by (forward_tac [respond_imp_not_used] 2); |
2533 | 441 |
by (ALLGOALS (*23 seconds*) |
2449 | 442 |
(asm_simp_tac |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
443 |
(analz_image_freshK_ss addsimps |
2533 | 444 |
[shrK_in_analz_respond, resp_analz_image_freshK, parts_insert2]))); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
445 |
by (ALLGOALS Simp_tac); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
446 |
by (blast_tac (!claset addIs [impOfSubs analz_subset_parts]) 1); |
2449 | 447 |
by (step_tac (!claset addSEs [MPair_parts]) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
448 |
(** LEVEL 7 **) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
449 |
by (blast_tac (!claset addSDs [resp_analz_insert, Key_in_parts_respond] |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
450 |
addDs [impOfSubs analz_subset_parts]) 4); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
451 |
by (blast_tac (!claset addSDs [respond_certificate]) 3); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
452 |
by (blast_tac (!claset addSEs partsEs |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
453 |
addDs [Key_in_parts_respond]) 2); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
454 |
by (dtac unique_session_keys 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
455 |
by (etac respond_certificate 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
456 |
by (assume_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
457 |
by (Blast_tac 1); |
2533 | 458 |
qed_spec_mp "respond_Spy_not_see_session_key"; |
2449 | 459 |
|
460 |
||
461 |
goal thy |
|
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
462 |
"!!evs. [| Crypt (shrK A) {|Key K, Agent A', N|} \ |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
463 |
\ : parts (sees lost Spy evs); \ |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
464 |
\ A ~: lost; A' ~: lost; evs : recur lost |] \ |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
465 |
\ ==> Key K ~: analz (sees lost Spy evs)"; |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
466 |
by (etac rev_mp 1); |
2449 | 467 |
by (etac recur.induct 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
468 |
by analz_sees_tac; |
2449 | 469 |
by (ALLGOALS |
470 |
(asm_simp_tac |
|
2533 | 471 |
(!simpset addsimps [parts_insert_sees, analz_insert_freshK] |
2449 | 472 |
setloop split_tac [expand_if]))); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
473 |
(*RA4*) |
2533 | 474 |
by (spy_analz_tac 5); |
475 |
(*RA2*) |
|
476 |
by (spy_analz_tac 3); |
|
2449 | 477 |
(*Fake*) |
2533 | 478 |
by (spy_analz_tac 2); |
479 |
(*Base*) |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
480 |
by (Blast_tac 1); |
2533 | 481 |
(*RA3 remains*) |
2449 | 482 |
by (step_tac (!claset delrules [impCE]) 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
483 |
(*RA3, case 2: K is an old key*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
484 |
by (blast_tac (!claset addSDs [resp_analz_insert] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
485 |
addSEs partsEs |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
486 |
addDs [Key_in_parts_respond]) 2); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
487 |
(*RA3, case 1: use lemma previously proved by induction*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
488 |
by (blast_tac (!claset addSEs [respond_Spy_not_see_session_key RSN |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
489 |
(2,rev_notE)]) 1); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
490 |
qed "Spy_not_see_session_key"; |
2449 | 491 |
|
492 |
||
493 |
goal thy |
|
2533 | 494 |
"!!evs. [| Crypt (shrK A) {|Key K, Agent A', N|} \ |
495 |
\ : parts(sees lost Spy evs); \ |
|
496 |
\ C ~: {A,A',Server}; \ |
|
497 |
\ A ~: lost; A' ~: lost; evs : recur lost |] \ |
|
2449 | 498 |
\ ==> Key K ~: analz (sees lost C evs)"; |
499 |
by (rtac (subset_insertI RS sees_mono RS analz_mono RS contra_subsetD) 1); |
|
500 |
by (rtac (sees_lost_agent_subset_sees_Spy RS analz_mono RS contra_subsetD) 1); |
|
2533 | 501 |
by (FIRSTGOAL (rtac Spy_not_see_session_key)); |
502 |
by (REPEAT_FIRST |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
503 |
(blast_tac |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
504 |
(!claset addIs (map impOfSubs [recur_mono, parts_mono, sees_mono])))); |
2533 | 505 |
qed "Agent_not_see_session_key"; |
2449 | 506 |
|
507 |
||
508 |
(**** Authenticity properties for Agents ****) |
|
509 |
||
2481 | 510 |
(*The response never contains Hashes*) |
511 |
goal thy |
|
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
512 |
"!!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
|
513 |
\ (PB,RB,K) : respond evs |] \ |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
514 |
\ ==> 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
|
515 |
by (etac rev_mp 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
516 |
by (etac (respond_imp_responses RS responses.induct) 1); |
2481 | 517 |
by (Auto_tac()); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
518 |
qed "Hash_in_parts_respond"; |
2481 | 519 |
|
2533 | 520 |
(*Only RA1 or RA2 can have caused such a part of a message to appear. |
521 |
This result is of no use to B, who cannot verify the Hash. Moreover, |
|
522 |
it can say nothing about how recent A's message is. It might later be |
|
523 |
used to prove B's presence to A at the run's conclusion.*) |
|
2481 | 524 |
goalw thy [HPair_def] |
2449 | 525 |
"!!evs. [| Hash {|Key(shrK A), Agent A, Agent B, NA, P|} \ |
526 |
\ : parts (sees lost Spy evs); \ |
|
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
527 |
\ A ~: lost; evs : recur lost |] \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
528 |
\ ==> 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
|
529 |
by (etac rev_mp 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
530 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
531 |
by (Fake_parts_insert_tac 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
532 |
(*RA3*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
533 |
by (blast_tac (!claset addSDs [Hash_in_parts_respond]) 1); |
2449 | 534 |
qed_spec_mp "Hash_auth_sender"; |
535 |
||
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2485
diff
changeset
|
536 |
(** These two results subsume (for all agents) the guarantees proved |
2449 | 537 |
separately for A and B in the Otway-Rees protocol. |
538 |
**) |
|
539 |
||
540 |
||
2533 | 541 |
(*Certificates can only originate with the Server.*) |
2449 | 542 |
goal thy |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
543 |
"!!evs. [| Crypt (shrK A) Y : parts (sees lost Spy evs); \ |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
544 |
\ A ~: lost; A ~= Spy; evs : recur lost |] \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
545 |
\ ==> 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
|
546 |
\ Crypt (shrK A) Y : parts {RC}"; |
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
547 |
by (etac rev_mp 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
548 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
549 |
by (Fake_parts_insert_tac 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
550 |
(*RA4*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
551 |
by (Blast_tac 4); |
2455
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
552 |
(*RA3*) |
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
553 |
by (full_simp_tac (!simpset addsimps [parts_insert_sees]) 3 |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
554 |
THEN Blast_tac 3); |
2455
9c4444bfd44e
Simplification and generalization of the guarantees.
paulson
parents:
2451
diff
changeset
|
555 |
(*RA1*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
556 |
by (Blast_tac 1); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
557 |
(*RA2: it cannot be a new Nonce, contradiction.*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
558 |
by (Blast_tac 1); |
2550
8d8344bcf98a
Re-ordering of certificates so that session keys appear in decreasing order
paulson
parents:
2533
diff
changeset
|
559 |
qed "Cert_imp_Server_msg"; |