author | paulson |
Fri, 27 Jun 1997 10:47:13 +0200 | |
changeset 3466 | 30791e5a69c4 |
parent 3465 | e85c24717cad |
child 3516 | 470626799511 |
permissions | -rw-r--r-- |
1941 | 1 |
(* Title: HOL/Auth/OtwayRees |
2 |
ID: $Id$ |
|
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
|
4 |
Copyright 1996 University of Cambridge |
|
5 |
||
6 |
Inductive relation "otway" for the Otway-Rees protocol. |
|
7 |
||
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Version that encrypts Nonce NB |
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|
1941 | 10 |
From page 244 of |
11 |
Burrows, Abadi and Needham. A Logic of Authentication. |
|
12 |
Proc. Royal Soc. 426 (1989) |
|
13 |
*) |
|
14 |
||
15 |
open OtwayRees; |
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16 |
||
17 |
proof_timing:=true; |
|
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HOL_quantifiers := false; |
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19 |
||
3102 | 20 |
(*Replacing the variable by a constant improves search speed by 50%!*) |
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val Says_imp_sees_Spy' = read_instantiate [("lost","lost")] Says_imp_sees_Spy; |
3102 | 22 |
|
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23 |
|
2328 | 24 |
(*A "possibility property": there are traces that reach the end*) |
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goal thy |
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"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
2032 | 27 |
\ ==> EX K. EX NA. EX evs: otway lost. \ |
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\ Says B A {|Nonce NA, Crypt (shrK A) {|Nonce NA, Key K|}|} \ |
3465 | 29 |
\ : set evs"; |
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30 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
2032 | 31 |
by (rtac (otway.Nil RS otway.OR1 RS otway.OR2 RS otway.OR3 RS otway.OR4) 2); |
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by possibility_tac; |
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result(); |
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|
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|
1941 | 36 |
(**** Inductive proofs about otway ****) |
37 |
||
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(*Monotonicity*) |
2032 | 39 |
goal thy "!!evs. lost' <= lost ==> otway lost' <= otway lost"; |
40 |
by (rtac subsetI 1); |
|
41 |
by (etac otway.induct 1); |
|
3102 | 42 |
by (ALLGOALS |
43 |
(blast_tac (!claset addIs (impOfSubs(sees_mono RS analz_mono RS synth_mono) |
|
2032 | 44 |
:: otway.intrs)))); |
45 |
qed "otway_mono"; |
|
46 |
||
1941 | 47 |
(*Nobody sends themselves messages*) |
3465 | 48 |
goal thy "!!evs. evs : otway lost ==> ALL A X. Says A A X ~: set evs"; |
2032 | 49 |
by (etac otway.induct 1); |
1941 | 50 |
by (Auto_tac()); |
51 |
qed_spec_mp "not_Says_to_self"; |
|
52 |
Addsimps [not_Says_to_self]; |
|
53 |
AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
|
54 |
||
55 |
||
56 |
(** For reasoning about the encrypted portion of messages **) |
|
57 |
||
3465 | 58 |
goal thy "!!evs. Says A' B {|N, Agent A, Agent B, X|} : set evs \ |
2135 | 59 |
\ ==> X : analz (sees lost Spy evs)"; |
3102 | 60 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS analz.Inj]) 1); |
2032 | 61 |
qed "OR2_analz_sees_Spy"; |
1941 | 62 |
|
3465 | 63 |
goal thy "!!evs. Says S' B {|N, X, Crypt (shrK B) X'|} : set evs \ |
2135 | 64 |
\ ==> X : analz (sees lost Spy evs)"; |
3102 | 65 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS analz.Inj]) 1); |
2032 | 66 |
qed "OR4_analz_sees_Spy"; |
1941 | 67 |
|
3465 | 68 |
goal thy "!!evs. Says Server B {|NA, X, Crypt K' {|NB,K|}|} : set evs \ |
2135 | 69 |
\ ==> K : parts (sees lost Spy evs)"; |
3102 | 70 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
2135 | 71 |
qed "Oops_parts_sees_Spy"; |
1941 | 72 |
|
73 |
(*OR2_analz... and OR4_analz... let us treat those cases using the same |
|
1964 | 74 |
argument as for the Fake case. This is possible for most, but not all, |
75 |
proofs: Fake does not invent new nonces (as in OR2), and of course Fake |
|
2032 | 76 |
messages originate from the Spy. *) |
1964 | 77 |
|
2032 | 78 |
bind_thm ("OR2_parts_sees_Spy", |
79 |
OR2_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
|
80 |
bind_thm ("OR4_parts_sees_Spy", |
|
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OR4_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
|
82 |
||
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(*For proving the easier theorems about X ~: parts (sees lost Spy evs). |
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84 |
We instantiate the variable to "lost" since leaving it as a Var would |
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85 |
interfere with simplification.*) |
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val parts_induct_tac = |
2032 | 87 |
let val tac = forw_inst_tac [("lost","lost")] |
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in etac otway.induct 1 THEN |
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tac OR2_parts_sees_Spy 4 THEN |
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tac OR4_parts_sees_Spy 6 THEN |
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tac Oops_parts_sees_Spy 7 THEN |
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prove_simple_subgoals_tac 1 |
2032 | 93 |
end; |
1941 | 94 |
|
95 |
||
2032 | 96 |
(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY |
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sends messages containing X! **) |
1941 | 98 |
|
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99 |
|
2064 | 100 |
(*Spy never sees another agent's shared key! (unless it's lost at start)*) |
1941 | 101 |
goal thy |
2135 | 102 |
"!!evs. evs : otway lost \ |
103 |
\ ==> (Key (shrK A) : parts (sees lost Spy evs)) = (A : lost)"; |
|
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by parts_induct_tac; |
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by (Fake_parts_insert_tac 1); |
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by (Blast_tac 1); |
2135 | 107 |
qed "Spy_see_shrK"; |
108 |
Addsimps [Spy_see_shrK]; |
|
1941 | 109 |
|
2135 | 110 |
goal thy |
111 |
"!!evs. evs : otway lost \ |
|
112 |
\ ==> (Key (shrK A) : analz (sees lost Spy evs)) = (A : lost)"; |
|
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by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset)); |
|
114 |
qed "Spy_analz_shrK"; |
|
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Addsimps [Spy_analz_shrK]; |
|
1941 | 116 |
|
2135 | 117 |
goal thy "!!A. [| Key (shrK A) : parts (sees lost Spy evs); \ |
118 |
\ evs : otway lost |] ==> A:lost"; |
|
3102 | 119 |
by (blast_tac (!claset addDs [Spy_see_shrK]) 1); |
2135 | 120 |
qed "Spy_see_shrK_D"; |
1941 | 121 |
|
2135 | 122 |
bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D); |
123 |
AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D]; |
|
1941 | 124 |
|
125 |
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(*Nobody can have used non-existent keys!*) |
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goal thy "!!evs. evs : otway lost ==> \ |
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\ Key K ~: used evs --> K ~: keysFor (parts (sees lost Spy evs))"; |
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by parts_induct_tac; |
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130 |
(*Fake*) |
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131 |
by (best_tac |
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132 |
(!claset addIs [impOfSubs analz_subset_parts] |
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addDs [impOfSubs (analz_subset_parts RS keysFor_mono), |
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134 |
impOfSubs (parts_insert_subset_Un RS keysFor_mono)] |
3207 | 135 |
addss (!simpset)) 1); |
3102 | 136 |
by (ALLGOALS Blast_tac); |
2160 | 137 |
qed_spec_mp "new_keys_not_used"; |
1941 | 138 |
|
139 |
bind_thm ("new_keys_not_analzd", |
|
2032 | 140 |
[analz_subset_parts RS keysFor_mono, |
141 |
new_keys_not_used] MRS contra_subsetD); |
|
1941 | 142 |
|
143 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
|
144 |
||
145 |
||
2064 | 146 |
|
147 |
(*** Proofs involving analz ***) |
|
148 |
||
2135 | 149 |
(*Describes the form of K and NA when the Server sends this message. Also |
150 |
for Oops case.*) |
|
2064 | 151 |
goal thy |
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152 |
"!!evs. [| Says Server B \ |
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153 |
\ {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
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154 |
\ evs : otway lost |] \ |
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155 |
\ ==> K ~: range shrK & (EX i. NA = Nonce i) & (EX j. NB = Nonce j)"; |
2135 | 156 |
by (etac rev_mp 1); |
157 |
by (etac otway.induct 1); |
|
3102 | 158 |
by (ALLGOALS Simp_tac); |
159 |
by (ALLGOALS Blast_tac); |
|
2135 | 160 |
qed "Says_Server_message_form"; |
2064 | 161 |
|
162 |
||
163 |
(*For proofs involving analz. We again instantiate the variable to "lost".*) |
|
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164 |
val analz_sees_tac = |
2064 | 165 |
dres_inst_tac [("lost","lost")] OR2_analz_sees_Spy 4 THEN |
166 |
dres_inst_tac [("lost","lost")] OR4_analz_sees_Spy 6 THEN |
|
2135 | 167 |
forw_inst_tac [("lost","lost")] Says_Server_message_form 7 THEN |
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168 |
assume_tac 7 THEN |
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169 |
REPEAT ((eresolve_tac [exE, conjE] ORELSE' hyp_subst_tac) 7); |
1941 | 170 |
|
171 |
||
172 |
(**** |
|
173 |
The following is to prove theorems of the form |
|
174 |
||
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175 |
Key K : analz (insert (Key KAB) (sees lost Spy evs)) ==> |
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176 |
Key K : analz (sees lost Spy evs) |
1941 | 177 |
|
178 |
A more general formula must be proved inductively. |
|
179 |
****) |
|
180 |
||
181 |
||
182 |
(** Session keys are not used to encrypt other session keys **) |
|
183 |
||
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184 |
(*The equality makes the induction hypothesis easier to apply*) |
1941 | 185 |
goal thy |
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186 |
"!!evs. evs : otway lost ==> \ |
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187 |
\ ALL K KK. KK <= Compl (range shrK) --> \ |
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188 |
\ (Key K : analz (Key``KK Un (sees lost Spy evs))) = \ |
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189 |
\ (K : KK | Key K : analz (sees lost Spy evs))"; |
2032 | 190 |
by (etac otway.induct 1); |
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191 |
by analz_sees_tac; |
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192 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
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193 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
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194 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
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195 |
(*Fake*) |
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196 |
by (spy_analz_tac 2); |
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197 |
(*Base*) |
3102 | 198 |
by (Blast_tac 1); |
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199 |
qed_spec_mp "analz_image_freshK"; |
1941 | 200 |
|
201 |
||
202 |
goal thy |
|
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203 |
"!!evs. [| evs : otway lost; KAB ~: range shrK |] ==> \ |
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204 |
\ Key K : analz (insert (Key KAB) (sees lost Spy evs)) = \ |
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205 |
\ (K = KAB | Key K : analz (sees lost Spy evs))"; |
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206 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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207 |
qed "analz_insert_freshK"; |
1941 | 208 |
|
209 |
||
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210 |
(*** The Key K uniquely identifies the Server's message. **) |
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211 |
|
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212 |
goal thy |
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213 |
"!!evs. evs : otway lost ==> \ |
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214 |
\ EX B' NA' NB' X'. ALL B NA NB X. \ |
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215 |
\ Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set evs --> \ |
2135 | 216 |
\ B=B' & NA=NA' & NB=NB' & X=X'"; |
2032 | 217 |
by (etac otway.induct 1); |
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218 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
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|
219 |
by (Step_tac 1); |
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|
220 |
(*Remaining cases: OR3 and OR4*) |
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|
221 |
by (ex_strip_tac 2); |
3102 | 222 |
by (Best_tac 2); |
2064 | 223 |
by (expand_case_tac "K = ?y" 1); |
224 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
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|
225 |
(*...we assume X is a recent message, and handle this case by contradiction*) |
3102 | 226 |
by (blast_tac (!claset addSEs sees_Spy_partsEs |
227 |
delrules [conjI] (*no split-up into 4 subgoals*)) 1); |
|
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|
228 |
val lemma = result(); |
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|
229 |
|
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|
230 |
goal thy |
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|
231 |
"!!evs. [| Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} \ |
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|
232 |
\ : set evs; \ |
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|
233 |
\ Says Server B' {|NA',X',Crypt (shrK B') {|NB',K|}|} \ |
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|
234 |
\ : set evs; \ |
2135 | 235 |
\ evs : otway lost |] ==> X=X' & B=B' & NA=NA' & NB=NB'"; |
2417 | 236 |
by (prove_unique_tac lemma 1); |
2014
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|
237 |
qed "unique_session_keys"; |
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|
238 |
|
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changeset
|
239 |
|
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|
240 |
|
2048 | 241 |
(**** Authenticity properties relating to NA ****) |
2014
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|
242 |
|
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diff
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|
243 |
(*Only OR1 can have caused such a part of a message to appear.*) |
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changeset
|
244 |
goal thy |
2064 | 245 |
"!!evs. [| A ~: lost; evs : otway lost |] \ |
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|
246 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} \ |
2064 | 247 |
\ : parts (sees lost Spy evs) --> \ |
248 |
\ Says A B {|NA, Agent A, Agent B, \ |
|
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|
249 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
3465 | 250 |
\ : set evs"; |
3121
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|
251 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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parents:
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diff
changeset
|
252 |
by (Fake_parts_insert_tac 1); |
2014
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Correction of protocol; addition of Reveal message; proofs of
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|
253 |
qed_spec_mp "Crypt_imp_OR1"; |
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diff
changeset
|
254 |
|
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parents:
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diff
changeset
|
255 |
|
2064 | 256 |
(** The Nonce NA uniquely identifies A's message. **) |
2014
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parents:
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changeset
|
257 |
|
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diff
changeset
|
258 |
goal thy |
2032 | 259 |
"!!evs. [| evs : otway lost; A ~: lost |] \ |
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|
260 |
\ ==> EX B'. ALL B. \ |
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diff
changeset
|
261 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (sees lost Spy evs) \ |
2048 | 262 |
\ --> B = B'"; |
3121
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Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
263 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
264 |
by (Fake_parts_insert_tac 1); |
2064 | 265 |
by (simp_tac (!simpset addsimps [all_conj_distrib]) 1); |
2026
0df5a96bf77e
Last working version prior to introduction of "lost"
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diff
changeset
|
266 |
(*OR1: creation of new Nonce. Move assertion into global context*) |
2064 | 267 |
by (expand_case_tac "NA = ?y" 1); |
3102 | 268 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
2014
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Correction of protocol; addition of Reveal message; proofs of
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parents:
1999
diff
changeset
|
269 |
val lemma = result(); |
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parents:
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diff
changeset
|
270 |
|
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diff
changeset
|
271 |
goal thy |
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changeset
|
272 |
"!!evs.[| Crypt (shrK A) {|NA, Agent A, Agent B|}: parts(sees lost Spy evs); \ |
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|
273 |
\ Crypt (shrK A) {|NA, Agent A, Agent C|}: parts(sees lost Spy evs); \ |
2048 | 274 |
\ evs : otway lost; A ~: lost |] \ |
2014
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Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
275 |
\ ==> B = C"; |
2417 | 276 |
by (prove_unique_tac lemma 1); |
2048 | 277 |
qed "unique_NA"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
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parents:
1999
diff
changeset
|
278 |
|
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diff
changeset
|
279 |
|
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Correction of protocol; addition of Reveal message; proofs of
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diff
changeset
|
280 |
(*It is impossible to re-use a nonce in both OR1 and OR2. This holds because |
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parents:
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diff
changeset
|
281 |
OR2 encrypts Nonce NB. It prevents the attack that can occur in the |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
282 |
over-simplified version of this protocol: see OtwayRees_Bad.*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
283 |
goal thy |
2328 | 284 |
"!!evs. [| A ~: lost; evs : otway lost |] \ |
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paulson
parents:
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diff
changeset
|
285 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} \ |
2328 | 286 |
\ : parts (sees lost Spy evs) --> \ |
2284
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Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
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changeset
|
287 |
\ Crypt (shrK A) {|NA', NA, Agent A', Agent A|} \ |
2032 | 288 |
\ ~: parts (sees lost Spy evs)"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
289 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
290 |
by (Fake_parts_insert_tac 1); |
3102 | 291 |
by (REPEAT (blast_tac (!claset addSEs sees_Spy_partsEs |
292 |
addSDs [impOfSubs parts_insert_subset_Un]) 1)); |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
293 |
qed_spec_mp"no_nonce_OR1_OR2"; |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
294 |
|
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paulson
parents:
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diff
changeset
|
295 |
|
2053 | 296 |
(*Crucial property: If the encrypted message appears, and A has used NA |
297 |
to start a run, then it originated with the Server!*) |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
298 |
goal thy |
2048 | 299 |
"!!evs. [| A ~: lost; A ~= Spy; evs : otway lost |] \ |
2284
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Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
300 |
\ ==> Crypt (shrK A) {|NA, Key K|} : parts (sees lost Spy evs) \ |
2048 | 301 |
\ --> Says A B {|NA, Agent A, Agent B, \ |
2284
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paulson
parents:
2264
diff
changeset
|
302 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
3466
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Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
303 |
\ : set evs --> \ |
2048 | 304 |
\ (EX NB. Says Server B \ |
305 |
\ {|NA, \ |
|
2284
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Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
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diff
changeset
|
306 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
307 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 308 |
\ : set evs)"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
309 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
310 |
by (Fake_parts_insert_tac 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
311 |
(*OR1: it cannot be a new Nonce, contradiction.*) |
3102 | 312 |
by (blast_tac (!claset addSIs [parts_insertI] addSEs sees_Spy_partsEs) 1); |
2064 | 313 |
(*OR3 and OR4*) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
314 |
(*OR4*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
315 |
by (REPEAT (Safe_step_tac 2)); |
3102 | 316 |
by (REPEAT (blast_tac (!claset addSDs [parts_cut]) 3)); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
317 |
by (fast_tac (!claset addSIs [Crypt_imp_OR1] |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
318 |
addEs sees_Spy_partsEs) 2); |
2064 | 319 |
(*OR3*) (** LEVEL 5 **) |
320 |
by (asm_simp_tac (!simpset addsimps [ex_disj_distrib]) 1); |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
321 |
by (step_tac (!claset delrules [disjCI, impCE]) 1); |
3102 | 322 |
by (blast_tac (!claset addSEs [MPair_parts] |
323 |
addSDs [Says_imp_sees_Spy' RS parts.Inj] |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
324 |
addEs [no_nonce_OR1_OR2 RSN (2, rev_notE)] |
2048 | 325 |
delrules [conjI] (*stop split-up into 4 subgoals*)) 2); |
3102 | 326 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj] |
2048 | 327 |
addSEs [MPair_parts] |
3102 | 328 |
addIs [unique_NA]) 1); |
2048 | 329 |
qed_spec_mp "NA_Crypt_imp_Server_msg"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
330 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
331 |
|
2053 | 332 |
(*Corollary: if A receives B's OR4 message and the nonce NA agrees |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
333 |
then the key really did come from the Server! CANNOT prove this of the |
2048 | 334 |
bad form of this protocol, even though we can prove |
2032 | 335 |
Spy_not_see_encrypted_key*) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
336 |
goal thy |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
337 |
"!!evs. [| Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
338 |
\ : set evs; \ |
2053 | 339 |
\ Says A B {|NA, Agent A, Agent B, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
340 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
341 |
\ : set evs; \ |
2053 | 342 |
\ A ~: lost; A ~= Spy; evs : otway lost |] \ |
343 |
\ ==> EX NB. Says Server B \ |
|
2048 | 344 |
\ {|NA, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
345 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
346 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 347 |
\ : set evs"; |
3102 | 348 |
by (blast_tac (!claset addSIs [NA_Crypt_imp_Server_msg] |
349 |
addEs sees_Spy_partsEs) 1); |
|
2328 | 350 |
qed "A_trusts_OR4"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
351 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
352 |
|
2048 | 353 |
(** Crucial secrecy property: Spy does not see the keys sent in msg OR3 |
354 |
Does not in itself guarantee security: an attack could violate |
|
355 |
the premises, e.g. by having A=Spy **) |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
356 |
|
1941 | 357 |
goal thy |
2166 | 358 |
"!!evs. [| A ~: lost; B ~: lost; evs : otway lost |] \ |
2048 | 359 |
\ ==> Says Server B \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
360 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
361 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs --> \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
362 |
\ Says B Spy {|NA, NB, Key K|} ~: set evs --> \ |
2048 | 363 |
\ Key K ~: analz (sees lost Spy evs)"; |
2032 | 364 |
by (etac otway.induct 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
365 |
by analz_sees_tac; |
1964 | 366 |
by (ALLGOALS |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
367 |
(asm_simp_tac (!simpset addcongs [conj_cong] |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
368 |
addsimps [analz_insert_eq, not_parts_not_analz, |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
369 |
analz_insert_freshK] |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
370 |
setloop split_tac [expand_if]))); |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
371 |
(*Oops*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
372 |
by (blast_tac (!claset addSDs [unique_session_keys]) 4); |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
373 |
(*OR4*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
374 |
by (Blast_tac 3); |
1941 | 375 |
(*OR3*) |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
376 |
by (blast_tac (!claset addSEs sees_Spy_partsEs |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
377 |
addIs [impOfSubs analz_subset_parts]) 2); |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
378 |
(*Fake*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
379 |
by (spy_analz_tac 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
380 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
381 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
382 |
goal thy |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
383 |
"!!evs. [| Says Server B \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
384 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
385 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
386 |
\ Says B Spy {|NA, NB, Key K|} ~: set evs; \ |
2032 | 387 |
\ A ~: lost; B ~: lost; evs : otway lost |] \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
388 |
\ ==> Key K ~: analz (sees lost Spy evs)"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
389 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
3102 | 390 |
by (blast_tac (!claset addSEs [lemma]) 1); |
2032 | 391 |
qed "Spy_not_see_encrypted_key"; |
392 |
||
1945 | 393 |
|
2032 | 394 |
goal thy |
2048 | 395 |
"!!evs. [| C ~: {A,B,Server}; \ |
396 |
\ Says Server B \ |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
397 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
398 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
399 |
\ Says B Spy {|NA, NB, Key K|} ~: set evs; \ |
2032 | 400 |
\ A ~: lost; B ~: lost; evs : otway lost |] \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
401 |
\ ==> Key K ~: analz (sees lost C evs)"; |
2032 | 402 |
by (rtac (subset_insertI RS sees_mono RS analz_mono RS contra_subsetD) 1); |
403 |
by (rtac (sees_lost_agent_subset_sees_Spy RS analz_mono RS contra_subsetD) 1); |
|
404 |
by (FIRSTGOAL (rtac Spy_not_see_encrypted_key)); |
|
3102 | 405 |
by (REPEAT_FIRST (blast_tac (!claset addIs [otway_mono RS subsetD]))); |
2032 | 406 |
qed "Agent_not_see_encrypted_key"; |
1945 | 407 |
|
408 |
||
2048 | 409 |
(**** Authenticity properties relating to NB ****) |
410 |
||
411 |
(*Only OR2 can have caused such a part of a message to appear. We do not |
|
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
412 |
know anything about X: it does NOT have to have the right form.*) |
2048 | 413 |
goal thy |
414 |
"!!evs. [| B ~: lost; evs : otway lost |] \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
415 |
\ ==> Crypt (shrK B) {|NA, NB, Agent A, Agent B|} \ |
2048 | 416 |
\ : parts (sees lost Spy evs) --> \ |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
417 |
\ (EX X. Says B Server \ |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
418 |
\ {|NA, Agent A, Agent B, X, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
419 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|} \ |
3465 | 420 |
\ : set evs)"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
421 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
422 |
by (Fake_parts_insert_tac 1); |
3102 | 423 |
by (ALLGOALS Blast_tac); |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
424 |
bind_thm ("Crypt_imp_OR2", result() RSN (2,rev_mp) RS exE); |
2048 | 425 |
|
426 |
||
427 |
(** The Nonce NB uniquely identifies B's message. **) |
|
428 |
||
429 |
goal thy |
|
430 |
"!!evs. [| evs : otway lost; B ~: lost |] \ |
|
2064 | 431 |
\ ==> EX NA' A'. ALL NA A. \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
432 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} : parts(sees lost Spy evs) \ |
2048 | 433 |
\ --> NA = NA' & A = A'"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
434 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
435 |
by (Fake_parts_insert_tac 1); |
2064 | 436 |
by (simp_tac (!simpset addsimps [all_conj_distrib]) 1); |
2048 | 437 |
(*OR2: creation of new Nonce. Move assertion into global context*) |
2064 | 438 |
by (expand_case_tac "NB = ?y" 1); |
3102 | 439 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
2048 | 440 |
val lemma = result(); |
441 |
||
442 |
goal thy |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
443 |
"!!evs.[| Crypt (shrK B) {|NA, NB, Agent A, Agent B|} \ |
2048 | 444 |
\ : parts(sees lost Spy evs); \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
445 |
\ Crypt (shrK B) {|NC, NB, Agent C, Agent B|} \ |
2048 | 446 |
\ : parts(sees lost Spy evs); \ |
447 |
\ evs : otway lost; B ~: lost |] \ |
|
448 |
\ ==> NC = NA & C = A"; |
|
2417 | 449 |
by (prove_unique_tac lemma 1); |
2048 | 450 |
qed "unique_NB"; |
451 |
||
452 |
||
453 |
(*If the encrypted message appears, and B has used Nonce NB, |
|
454 |
then it originated with the Server!*) |
|
455 |
goal thy |
|
456 |
"!!evs. [| B ~: lost; B ~= Spy; evs : otway lost |] \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
457 |
\ ==> Crypt (shrK B) {|NB, Key K|} : parts (sees lost Spy evs) \ |
2048 | 458 |
\ --> (ALL X'. Says B Server \ |
459 |
\ {|NA, Agent A, Agent B, X', \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
460 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
461 |
\ : set evs \ |
2048 | 462 |
\ --> Says Server B \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
463 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
464 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 465 |
\ : set evs)"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
466 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
467 |
by (Fake_parts_insert_tac 1); |
2048 | 468 |
(*OR1: it cannot be a new Nonce, contradiction.*) |
3102 | 469 |
by (blast_tac (!claset addSIs [parts_insertI] addSEs sees_Spy_partsEs) 1); |
2048 | 470 |
(*OR4*) |
3102 | 471 |
by (blast_tac (!claset addSEs [MPair_parts, Crypt_imp_OR2]) 2); |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
472 |
(*OR3*) |
2048 | 473 |
by (step_tac (!claset delrules [disjCI, impCE]) 1); |
3102 | 474 |
by (blast_tac (!claset delrules [conjI] (*stop split-up*)) 3); |
475 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj] |
|
476 |
addSEs [MPair_parts] |
|
477 |
addDs [unique_NB]) 2); |
|
478 |
by (blast_tac (!claset addSEs [MPair_parts, no_nonce_OR1_OR2 RSN (2, rev_notE)] |
|
479 |
addSDs [Says_imp_sees_Spy' RS parts.Inj] |
|
480 |
delrules [conjI, impCE] (*stop split-up*)) 1); |
|
2048 | 481 |
qed_spec_mp "NB_Crypt_imp_Server_msg"; |
482 |
||
483 |
||
484 |
(*Guarantee for B: if it gets a message with matching NB then the Server |
|
485 |
has sent the correct message.*) |
|
486 |
goal thy |
|
487 |
"!!evs. [| B ~: lost; B ~= Spy; evs : otway lost; \ |
|
2837
dee1c7f1f576
Trivial renamings (for consistency with CSFW papers)
paulson
parents:
2637
diff
changeset
|
488 |
\ Says S' B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
489 |
\ : set evs; \ |
2048 | 490 |
\ Says B Server {|NA, Agent A, Agent B, X', \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
491 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
492 |
\ : set evs |] \ |
2048 | 493 |
\ ==> Says Server B \ |
494 |
\ {|NA, \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
495 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
496 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 497 |
\ : set evs"; |
3102 | 498 |
by (blast_tac (!claset addSIs [NB_Crypt_imp_Server_msg] |
499 |
addSEs sees_Spy_partsEs) 1); |
|
2328 | 500 |
qed "B_trusts_OR3"; |
2048 | 501 |
|
502 |
||
2328 | 503 |
B_trusts_OR3 RS Spy_not_see_encrypted_key; |
2048 | 504 |
|
505 |
||
1945 | 506 |
goal thy |
2214 | 507 |
"!!evs. [| B ~: lost; evs : otway lost |] \ |
508 |
\ ==> Says Server B \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
509 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
510 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs --> \ |
2214 | 511 |
\ (EX X. Says B Server {|NA, Agent A, Agent B, X, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
512 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \ |
3465 | 513 |
\ : set evs)"; |
2032 | 514 |
by (etac otway.induct 1); |
3102 | 515 |
by (ALLGOALS Asm_simp_tac); |
516 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS parts.Inj] |
|
517 |
addSEs [MPair_parts, Crypt_imp_OR2]) 3); |
|
518 |
by (ALLGOALS Blast_tac); |
|
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
519 |
bind_thm ("OR3_imp_OR2", result() RSN (2,rev_mp) RS exE); |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
520 |
|
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
521 |
|
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
522 |
(*After getting and checking OR4, agent A can trust that B has been active. |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
523 |
We could probably prove that X has the expected form, but that is not |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
524 |
strictly necessary for authentication.*) |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
525 |
goal thy |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
526 |
"!!evs. [| Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
527 |
\ Says A B {|NA, Agent A, Agent B, \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
528 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
529 |
\ A ~: lost; A ~= Spy; B ~: lost; evs : otway lost |] \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
530 |
\ ==> EX NB X. Says B Server {|NA, Agent A, Agent B, X, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
531 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |}\ |
3465 | 532 |
\ : set evs"; |
3102 | 533 |
by (blast_tac (!claset addSDs [A_trusts_OR4] |
534 |
addSEs [OR3_imp_OR2]) 1); |
|
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
535 |
qed "A_auths_B"; |