author | paulson |
Fri, 13 Dec 1996 11:00:44 +0100 | |
changeset 2378 | fc103154ad8f |
parent 2375 | 14539397fc04 |
child 2417 | 95f275c8476e |
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 |
||
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
8 |
Version that encrypts Nonce NB |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
9 |
|
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; |
|
16 |
||
17 |
proof_timing:=true; |
|
18 |
HOL_quantifiers := false; |
|
2135 | 19 |
Pretty.setdepth 15; |
1941 | 20 |
|
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
21 |
|
2328 | 22 |
(*A "possibility property": there are traces that reach the end*) |
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
23 |
goal thy |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
24 |
"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
2032 | 25 |
\ ==> EX K. EX NA. EX evs: otway lost. \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
26 |
\ Says B A {|Nonce NA, Crypt (shrK A) {|Nonce NA, Key K|}|} \ |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
27 |
\ : set_of_list evs"; |
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
28 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
2032 | 29 |
by (rtac (otway.Nil RS otway.OR1 RS otway.OR2 RS otway.OR3 RS otway.OR4) 2); |
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
30 |
by (ALLGOALS (simp_tac (!simpset setsolver safe_solver))); |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
31 |
by (REPEAT_FIRST (resolve_tac [refl, conjI])); |
2104
f5c9a91e4b50
Replaced excluded_middle_tac by case_tac; tidied proofs
paulson
parents:
2071
diff
changeset
|
32 |
by (REPEAT_FIRST (fast_tac (!claset addss (!simpset setsolver safe_solver)))); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
33 |
result(); |
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
34 |
|
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
35 |
|
1941 | 36 |
(**** Inductive proofs about otway ****) |
37 |
||
2104
f5c9a91e4b50
Replaced excluded_middle_tac by case_tac; tidied proofs
paulson
parents:
2071
diff
changeset
|
38 |
(*Monotonicity*) |
2032 | 39 |
goal thy "!!evs. lost' <= lost ==> otway lost' <= otway lost"; |
40 |
by (rtac subsetI 1); |
|
41 |
by (etac otway.induct 1); |
|
42 |
by (REPEAT_FIRST |
|
43 |
(best_tac (!claset addIs (impOfSubs (sees_mono RS analz_mono RS synth_mono) |
|
44 |
:: otway.intrs)))); |
|
45 |
qed "otway_mono"; |
|
46 |
||
1941 | 47 |
(*Nobody sends themselves messages*) |
2032 | 48 |
goal thy "!!evs. evs : otway lost ==> ALL A X. Says A A X ~: set_of_list evs"; |
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 |
||
2135 | 58 |
goal thy "!!evs. Says A' B {|N, Agent A, Agent B, X|} : set_of_list evs \ |
59 |
\ ==> X : analz (sees lost Spy evs)"; |
|
2032 | 60 |
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1); |
61 |
qed "OR2_analz_sees_Spy"; |
|
1941 | 62 |
|
2135 | 63 |
goal thy "!!evs. Says S B {|N, X, X'|} : set_of_list evs \ |
64 |
\ ==> X : analz (sees lost Spy evs)"; |
|
2032 | 65 |
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1); |
66 |
qed "OR4_analz_sees_Spy"; |
|
1941 | 67 |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
68 |
goal thy "!!evs. Says Server B {|NA, X, Crypt K' {|NB,K|}|} : set_of_list evs \ |
2135 | 69 |
\ ==> K : parts (sees lost Spy evs)"; |
1941 | 70 |
by (fast_tac (!claset addSEs partsEs |
2032 | 71 |
addSDs [Says_imp_sees_Spy RS parts.Inj]) 1); |
2135 | 72 |
qed "Oops_parts_sees_Spy"; |
1941 | 73 |
|
74 |
(*OR2_analz... and OR4_analz... let us treat those cases using the same |
|
1964 | 75 |
argument as for the Fake case. This is possible for most, but not all, |
76 |
proofs: Fake does not invent new nonces (as in OR2), and of course Fake |
|
2032 | 77 |
messages originate from the Spy. *) |
1964 | 78 |
|
2032 | 79 |
bind_thm ("OR2_parts_sees_Spy", |
80 |
OR2_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
|
81 |
bind_thm ("OR4_parts_sees_Spy", |
|
82 |
OR4_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
|
83 |
||
84 |
(*We instantiate the variable to "lost". Leaving it as a Var makes proofs |
|
85 |
harder to complete, since simplification does less for us.*) |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
86 |
val parts_Fake_tac = |
2032 | 87 |
let val tac = forw_inst_tac [("lost","lost")] |
88 |
in tac OR2_parts_sees_Spy 4 THEN |
|
89 |
tac OR4_parts_sees_Spy 6 THEN |
|
2135 | 90 |
tac Oops_parts_sees_Spy 7 |
2032 | 91 |
end; |
1941 | 92 |
|
2064 | 93 |
(*For proving the easier theorems about X ~: parts (sees lost Spy evs) *) |
94 |
fun parts_induct_tac i = SELECT_GOAL |
|
95 |
(DETERM (etac otway.induct 1 THEN parts_Fake_tac THEN |
|
2171 | 96 |
(*Fake message*) |
97 |
TRY (best_tac (!claset addDs [impOfSubs analz_subset_parts, |
|
98 |
impOfSubs Fake_parts_insert] |
|
2064 | 99 |
addss (!simpset)) 2)) THEN |
100 |
(*Base case*) |
|
101 |
fast_tac (!claset addss (!simpset)) 1 THEN |
|
102 |
ALLGOALS Asm_simp_tac) i; |
|
1941 | 103 |
|
2032 | 104 |
(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
105 |
sends messages containing X! **) |
1941 | 106 |
|
2064 | 107 |
(*Spy never sees another agent's shared key! (unless it's lost at start)*) |
1941 | 108 |
goal thy |
2135 | 109 |
"!!evs. evs : otway lost \ |
110 |
\ ==> (Key (shrK A) : parts (sees lost Spy evs)) = (A : lost)"; |
|
2064 | 111 |
by (parts_induct_tac 1); |
1941 | 112 |
by (Auto_tac()); |
2135 | 113 |
qed "Spy_see_shrK"; |
114 |
Addsimps [Spy_see_shrK]; |
|
1941 | 115 |
|
2135 | 116 |
goal thy |
117 |
"!!evs. evs : otway lost \ |
|
118 |
\ ==> (Key (shrK A) : analz (sees lost Spy evs)) = (A : lost)"; |
|
119 |
by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset)); |
|
120 |
qed "Spy_analz_shrK"; |
|
121 |
Addsimps [Spy_analz_shrK]; |
|
1941 | 122 |
|
2135 | 123 |
goal thy "!!A. [| Key (shrK A) : parts (sees lost Spy evs); \ |
124 |
\ evs : otway lost |] ==> A:lost"; |
|
125 |
by (fast_tac (!claset addDs [Spy_see_shrK]) 1); |
|
126 |
qed "Spy_see_shrK_D"; |
|
1941 | 127 |
|
2135 | 128 |
bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D); |
129 |
AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D]; |
|
1941 | 130 |
|
131 |
||
132 |
(*** Future keys can't be seen or used! ***) |
|
133 |
||
2160 | 134 |
(*Nobody can have SEEN keys that will be generated in the future. *) |
2032 | 135 |
goal thy "!!evs. evs : otway lost ==> \ |
1941 | 136 |
\ length evs <= length evs' --> \ |
2160 | 137 |
\ Key (newK evs') ~: parts (sees lost Spy evs)"; |
2064 | 138 |
by (parts_induct_tac 1); |
2264
f298678bd54a
Weaking of injectivity assumptions for newK and newN:
paulson
parents:
2214
diff
changeset
|
139 |
by (REPEAT_FIRST (best_tac (!claset addEs [leD RS notE] |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
140 |
addDs [impOfSubs analz_subset_parts, |
2032 | 141 |
impOfSubs parts_insert_subset_Un, |
142 |
Suc_leD] |
|
143 |
addss (!simpset)))); |
|
2160 | 144 |
qed_spec_mp "new_keys_not_seen"; |
1941 | 145 |
Addsimps [new_keys_not_seen]; |
146 |
||
2160 | 147 |
(*Variant: old messages must contain old keys!*) |
1941 | 148 |
goal thy |
149 |
"!!evs. [| Says A B X : set_of_list evs; \ |
|
150 |
\ Key (newK evt) : parts {X}; \ |
|
2032 | 151 |
\ evs : otway lost \ |
1941 | 152 |
\ |] ==> length evt < length evs"; |
2032 | 153 |
by (rtac ccontr 1); |
154 |
by (dtac leI 1); |
|
155 |
by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Spy] |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
156 |
addIs [impOfSubs parts_mono]) 1); |
1941 | 157 |
qed "Says_imp_old_keys"; |
158 |
||
159 |
||
2160 | 160 |
(*** Future nonces can't be seen or used! ***) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
161 |
|
2032 | 162 |
goal thy "!!evs. evs : otway lost ==> \ |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
163 |
\ length evs <= length evt --> \ |
2160 | 164 |
\ Nonce (newN evt) ~: parts (sees lost Spy evs)"; |
165 |
by (parts_induct_tac 1); |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
166 |
by (REPEAT_FIRST (fast_tac (!claset |
2032 | 167 |
addSEs partsEs |
2375 | 168 |
addSDs [Says_imp_sees_Spy RS parts.Inj] |
169 |
addEs [leD RS notE] |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
170 |
addDs [impOfSubs analz_subset_parts, |
2032 | 171 |
impOfSubs parts_insert_subset_Un, |
172 |
Suc_leD] |
|
173 |
addss (!simpset)))); |
|
2160 | 174 |
qed_spec_mp "new_nonces_not_seen"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
175 |
Addsimps [new_nonces_not_seen]; |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
176 |
|
2160 | 177 |
(*Variant: old messages must contain old nonces!*) |
178 |
goal thy "!!evs. [| Says A B X : set_of_list evs; \ |
|
179 |
\ Nonce (newN evt) : parts {X}; \ |
|
180 |
\ evs : otway lost \ |
|
181 |
\ |] ==> length evt < length evs"; |
|
2032 | 182 |
by (rtac ccontr 1); |
183 |
by (dtac leI 1); |
|
184 |
by (fast_tac (!claset addSDs [new_nonces_not_seen, Says_imp_sees_Spy] |
|
185 |
addIs [impOfSubs parts_mono]) 1); |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
186 |
qed "Says_imp_old_nonces"; |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
187 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
188 |
|
1941 | 189 |
(*Nobody can have USED keys that will be generated in the future. |
190 |
...very like new_keys_not_seen*) |
|
2160 | 191 |
goal thy "!!evs. evs : otway lost ==> \ |
1941 | 192 |
\ length evs <= length evs' --> \ |
2160 | 193 |
\ newK evs' ~: keysFor (parts (sees lost Spy evs))"; |
2064 | 194 |
by (parts_induct_tac 1); |
1941 | 195 |
(*OR1 and OR3*) |
196 |
by (EVERY (map (fast_tac (!claset addDs [Suc_leD] addss (!simpset))) [4,2])); |
|
197 |
(*Fake, OR2, OR4: these messages send unknown (X) components*) |
|
2104
f5c9a91e4b50
Replaced excluded_middle_tac by case_tac; tidied proofs
paulson
parents:
2071
diff
changeset
|
198 |
by (REPEAT |
f5c9a91e4b50
Replaced excluded_middle_tac by case_tac; tidied proofs
paulson
parents:
2071
diff
changeset
|
199 |
(best_tac |
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
200 |
(!claset addDs [impOfSubs (analz_subset_parts RS keysFor_mono), |
2032 | 201 |
impOfSubs (parts_insert_subset_Un RS keysFor_mono), |
202 |
Suc_leD] |
|
203 |
addEs [new_keys_not_seen RS not_parts_not_analz RSN(2,rev_notE)] |
|
2104
f5c9a91e4b50
Replaced excluded_middle_tac by case_tac; tidied proofs
paulson
parents:
2071
diff
changeset
|
204 |
addss (!simpset)) 1)); |
2160 | 205 |
qed_spec_mp "new_keys_not_used"; |
1941 | 206 |
|
207 |
bind_thm ("new_keys_not_analzd", |
|
2032 | 208 |
[analz_subset_parts RS keysFor_mono, |
209 |
new_keys_not_used] MRS contra_subsetD); |
|
1941 | 210 |
|
211 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
|
212 |
||
213 |
||
2064 | 214 |
|
215 |
(*** Proofs involving analz ***) |
|
216 |
||
2135 | 217 |
(*Describes the form of K and NA when the Server sends this message. Also |
218 |
for Oops case.*) |
|
2064 | 219 |
goal thy |
2135 | 220 |
"!!evs. [| Says Server B \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
221 |
\ {|NA, X, Crypt (shrK B) {|NB, K|}|} : set_of_list evs; \ |
2135 | 222 |
\ evs : otway lost |] \ |
223 |
\ ==> (EX evt: otway lost. K = Key(newK evt)) & \ |
|
224 |
\ (EX i. NA = Nonce i) & (EX j. NB = Nonce j)"; |
|
225 |
by (etac rev_mp 1); |
|
226 |
by (etac otway.induct 1); |
|
227 |
by (ALLGOALS (fast_tac (!claset addss (!simpset)))); |
|
228 |
qed "Says_Server_message_form"; |
|
2064 | 229 |
|
230 |
||
231 |
(*For proofs involving analz. We again instantiate the variable to "lost".*) |
|
232 |
val analz_Fake_tac = |
|
233 |
dres_inst_tac [("lost","lost")] OR2_analz_sees_Spy 4 THEN |
|
234 |
dres_inst_tac [("lost","lost")] OR4_analz_sees_Spy 6 THEN |
|
2135 | 235 |
forw_inst_tac [("lost","lost")] Says_Server_message_form 7 THEN |
236 |
assume_tac 7 THEN Full_simp_tac 7 THEN |
|
237 |
REPEAT ((eresolve_tac [bexE, exE, conjE] ORELSE' hyp_subst_tac) 7); |
|
1941 | 238 |
|
239 |
||
240 |
(**** |
|
241 |
The following is to prove theorems of the form |
|
242 |
||
2032 | 243 |
Key K : analz (insert (Key (newK evt)) (sees lost Spy evs)) ==> |
244 |
Key K : analz (sees lost Spy evs) |
|
1941 | 245 |
|
246 |
A more general formula must be proved inductively. |
|
247 |
****) |
|
248 |
||
249 |
||
250 |
(** Session keys are not used to encrypt other session keys **) |
|
251 |
||
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
252 |
(*The equality makes the induction hypothesis easier to apply*) |
1941 | 253 |
goal thy |
2032 | 254 |
"!!evs. evs : otway lost ==> \ |
255 |
\ ALL K E. (Key K : analz (Key``(newK``E) Un (sees lost Spy evs))) = \ |
|
256 |
\ (K : newK``E | Key K : analz (sees lost Spy evs))"; |
|
257 |
by (etac otway.induct 1); |
|
2064 | 258 |
by analz_Fake_tac; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
259 |
by (REPEAT_FIRST (ares_tac [allI, analz_image_newK_lemma])); |
2375 | 260 |
by (ALLGOALS (*Takes 12 secs*) |
1941 | 261 |
(asm_simp_tac |
262 |
(!simpset addsimps ([insert_Key_singleton, insert_Key_image, pushKey_newK] |
|
2032 | 263 |
@ pushes) |
1941 | 264 |
setloop split_tac [expand_if]))); |
2135 | 265 |
(*OR4, OR2, Fake*) |
266 |
by (EVERY (map spy_analz_tac [5,3,2])); |
|
267 |
(*Oops, OR3, Base*) |
|
2064 | 268 |
by (REPEAT (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1)); |
1941 | 269 |
qed_spec_mp "analz_image_newK"; |
270 |
||
271 |
||
272 |
goal thy |
|
2032 | 273 |
"!!evs. evs : otway lost ==> \ |
274 |
\ Key K : analz (insert (Key (newK evt)) (sees lost Spy evs)) = \ |
|
275 |
\ (K = newK evt | Key K : analz (sees lost Spy evs))"; |
|
1941 | 276 |
by (asm_simp_tac (HOL_ss addsimps [pushKey_newK, analz_image_newK, |
2032 | 277 |
insert_Key_singleton]) 1); |
1941 | 278 |
by (Fast_tac 1); |
279 |
qed "analz_insert_Key_newK"; |
|
280 |
||
281 |
||
2026
0df5a96bf77e
Last working version prior to introduction of "lost"
paulson
parents:
2014
diff
changeset
|
282 |
(*** The Key K uniquely identifies the Server's message. **) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
283 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
284 |
goal thy |
2135 | 285 |
"!!evs. evs : otway lost ==> \ |
286 |
\ EX B' NA' NB' X'. ALL B NA NB X. \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
287 |
\ Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set_of_list evs --> \ |
2135 | 288 |
\ B=B' & NA=NA' & NB=NB' & X=X'"; |
2032 | 289 |
by (etac otway.induct 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
290 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
291 |
by (Step_tac 1); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
292 |
(*Remaining cases: OR3 and OR4*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
293 |
by (ex_strip_tac 2); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
294 |
by (Fast_tac 2); |
2064 | 295 |
by (expand_case_tac "K = ?y" 1); |
296 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
297 |
(*...we assume X is a very new message, and handle this case by contradiction*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
298 |
by (fast_tac (!claset addEs [Says_imp_old_keys RS less_irrefl] |
2032 | 299 |
delrules [conjI] (*prevent split-up into 4 subgoals*) |
300 |
addss (!simpset addsimps [parts_insertI])) 1); |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
301 |
val lemma = result(); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
302 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
303 |
goal thy |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
304 |
"!!evs. [| Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} \ |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
305 |
\ : set_of_list evs; \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
306 |
\ Says Server B' {|NA',X',Crypt (shrK B') {|NB',K|}|} \ |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
307 |
\ : set_of_list evs; \ |
2135 | 308 |
\ evs : otway lost |] ==> X=X' & B=B' & NA=NA' & NB=NB'"; |
2032 | 309 |
by (dtac lemma 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
310 |
by (REPEAT (etac exE 1)); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
311 |
(*Duplicate the assumption*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
312 |
by (forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl 1); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
313 |
by (fast_tac (!claset addSDs [spec]) 1); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
314 |
qed "unique_session_keys"; |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
315 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
316 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
317 |
|
2048 | 318 |
(**** Authenticity properties relating to NA ****) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
319 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
320 |
(*Only OR1 can have caused such a part of a message to appear.*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
321 |
goal thy |
2064 | 322 |
"!!evs. [| A ~: lost; evs : otway lost |] \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
323 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} \ |
2064 | 324 |
\ : parts (sees lost Spy evs) --> \ |
325 |
\ 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
|
326 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
327 |
\ : set_of_list evs"; |
2064 | 328 |
by (parts_induct_tac 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
329 |
qed_spec_mp "Crypt_imp_OR1"; |
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 |
|
2064 | 332 |
(** The Nonce NA uniquely identifies A's message. **) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
333 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
334 |
goal thy |
2032 | 335 |
"!!evs. [| evs : otway lost; A ~: lost |] \ |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
336 |
\ ==> EX B'. ALL B. \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
337 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (sees lost Spy evs) \ |
2048 | 338 |
\ --> B = B'"; |
2064 | 339 |
by (parts_induct_tac 1); |
340 |
by (simp_tac (!simpset addsimps [all_conj_distrib]) 1); |
|
2026
0df5a96bf77e
Last working version prior to introduction of "lost"
paulson
parents:
2014
diff
changeset
|
341 |
(*OR1: creation of new Nonce. Move assertion into global context*) |
2064 | 342 |
by (expand_case_tac "NA = ?y" 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
343 |
by (best_tac (!claset addSEs partsEs |
2032 | 344 |
addEs [new_nonces_not_seen RSN(2,rev_notE)]) 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
345 |
val lemma = result(); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
346 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
347 |
goal thy |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
348 |
"!!evs.[| Crypt (shrK A) {|NA, Agent A, Agent B|}: parts(sees lost Spy evs); \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
349 |
\ Crypt (shrK A) {|NA, Agent A, Agent C|}: parts(sees lost Spy evs); \ |
2048 | 350 |
\ evs : otway lost; A ~: lost |] \ |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
351 |
\ ==> B = C"; |
2032 | 352 |
by (dtac lemma 1); |
353 |
by (assume_tac 1); |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
354 |
by (etac exE 1); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
355 |
(*Duplicate the assumption*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
356 |
by (forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl 1); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
357 |
by (fast_tac (!claset addSDs [spec]) 1); |
2048 | 358 |
qed "unique_NA"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
359 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
360 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
361 |
val nonce_not_seen_now = le_refl RSN (2, new_nonces_not_seen) RSN (2,rev_notE); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
362 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
363 |
(*It is impossible to re-use a nonce in both OR1 and OR2. This holds because |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
364 |
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
|
365 |
over-simplified version of this protocol: see OtwayRees_Bad.*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
366 |
goal thy |
2328 | 367 |
"!!evs. [| A ~: lost; evs : otway lost |] \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
368 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} \ |
2328 | 369 |
\ : parts (sees lost Spy evs) --> \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
370 |
\ Crypt (shrK A) {|NA', NA, Agent A', Agent A|} \ |
2032 | 371 |
\ ~: parts (sees lost Spy evs)"; |
2071
0debdc018d26
Put in a simpler and *much* faster proof of no_nonce_OR1_OR2
paulson
parents:
2064
diff
changeset
|
372 |
by (parts_induct_tac 1); |
0debdc018d26
Put in a simpler and *much* faster proof of no_nonce_OR1_OR2
paulson
parents:
2064
diff
changeset
|
373 |
by (REPEAT (fast_tac (!claset addSEs (partsEs@[nonce_not_seen_now]) |
2026
0df5a96bf77e
Last working version prior to introduction of "lost"
paulson
parents:
2014
diff
changeset
|
374 |
addSDs [impOfSubs parts_insert_subset_Un] |
2071
0debdc018d26
Put in a simpler and *much* faster proof of no_nonce_OR1_OR2
paulson
parents:
2064
diff
changeset
|
375 |
addss (!simpset)) 1)); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
376 |
qed_spec_mp"no_nonce_OR1_OR2"; |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
377 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
378 |
|
2053 | 379 |
(*Crucial property: If the encrypted message appears, and A has used NA |
380 |
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
|
381 |
goal thy |
2048 | 382 |
"!!evs. [| A ~: lost; A ~= Spy; evs : otway lost |] \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
383 |
\ ==> Crypt (shrK A) {|NA, Key K|} : parts (sees lost Spy evs) \ |
2048 | 384 |
\ --> 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
|
385 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
2048 | 386 |
\ : set_of_list evs --> \ |
387 |
\ (EX NB. Says Server B \ |
|
388 |
\ {|NA, \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
389 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
390 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
391 |
\ : set_of_list evs)"; |
2064 | 392 |
by (parts_induct_tac 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
393 |
(*OR1: it cannot be a new Nonce, contradiction.*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
394 |
by (fast_tac (!claset addSIs [parts_insertI] |
2032 | 395 |
addSEs partsEs |
396 |
addEs [Says_imp_old_nonces RS less_irrefl] |
|
397 |
addss (!simpset)) 1); |
|
2064 | 398 |
(*OR3 and OR4*) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
399 |
(*OR4*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
400 |
by (REPEAT (Safe_step_tac 2)); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
401 |
by (REPEAT (best_tac (!claset addSDs [parts_cut]) 3)); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
402 |
by (fast_tac (!claset addSIs [Crypt_imp_OR1] |
2032 | 403 |
addEs partsEs |
404 |
addDs [Says_imp_sees_Spy RS parts.Inj]) 2); |
|
2064 | 405 |
(*OR3*) (** LEVEL 5 **) |
406 |
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
|
407 |
by (step_tac (!claset delrules [disjCI, impCE]) 1); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
408 |
by (fast_tac (!claset addSEs [MPair_parts] |
2032 | 409 |
addSDs [Says_imp_sees_Spy RS parts.Inj] |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
410 |
addEs [no_nonce_OR1_OR2 RSN (2, rev_notE)] |
2048 | 411 |
delrules [conjI] (*stop split-up into 4 subgoals*)) 2); |
412 |
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS parts.Inj] |
|
413 |
addSEs [MPair_parts] |
|
414 |
addEs [unique_NA]) 1); |
|
415 |
qed_spec_mp "NA_Crypt_imp_Server_msg"; |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
416 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
417 |
|
2053 | 418 |
(*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
|
419 |
then the key really did come from the Server! CANNOT prove this of the |
2048 | 420 |
bad form of this protocol, even though we can prove |
2032 | 421 |
Spy_not_see_encrypted_key*) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
422 |
goal thy |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
423 |
"!!evs. [| Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} \ |
2053 | 424 |
\ : set_of_list evs; \ |
425 |
\ 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
|
426 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
2053 | 427 |
\ : set_of_list evs; \ |
428 |
\ A ~: lost; A ~= Spy; evs : otway lost |] \ |
|
429 |
\ ==> EX NB. Says Server B \ |
|
2048 | 430 |
\ {|NA, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
431 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
432 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
2053 | 433 |
\ : set_of_list evs"; |
2048 | 434 |
by (fast_tac (!claset addSIs [NA_Crypt_imp_Server_msg] |
2032 | 435 |
addEs partsEs |
436 |
addDs [Says_imp_sees_Spy RS parts.Inj]) 1); |
|
2328 | 437 |
qed "A_trusts_OR4"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
438 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
439 |
|
2048 | 440 |
(** Crucial secrecy property: Spy does not see the keys sent in msg OR3 |
441 |
Does not in itself guarantee security: an attack could violate |
|
442 |
the premises, e.g. by having A=Spy **) |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
443 |
|
1941 | 444 |
goal thy |
2166 | 445 |
"!!evs. [| A ~: lost; B ~: lost; evs : otway lost |] \ |
2048 | 446 |
\ ==> Says Server B \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
447 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
448 |
\ Crypt (shrK B) {|NB, Key K|}|} : set_of_list evs --> \ |
2135 | 449 |
\ Says B Spy {|NA, NB, Key K|} ~: set_of_list evs --> \ |
2048 | 450 |
\ Key K ~: analz (sees lost Spy evs)"; |
2032 | 451 |
by (etac otway.induct 1); |
2064 | 452 |
by analz_Fake_tac; |
1964 | 453 |
by (ALLGOALS |
2375 | 454 |
(asm_simp_tac (!simpset addsimps ([not_parts_not_analz, |
455 |
analz_insert_Key_newK] @ pushes) |
|
456 |
setloop split_tac [expand_if]))); |
|
1941 | 457 |
(*OR3*) |
2166 | 458 |
by (fast_tac (!claset addEs [Says_imp_old_keys RS less_irrefl] |
2048 | 459 |
addss (!simpset addsimps [parts_insert2])) 3); |
2135 | 460 |
(*OR4, OR2, Fake*) |
2375 | 461 |
by (REPEAT_FIRST spy_analz_tac); |
2135 | 462 |
(*Oops*) (** LEVEL 5 **) |
463 |
by (fast_tac (!claset delrules [disjE] |
|
2171 | 464 |
addDs [unique_session_keys] addss (!simpset)) 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
465 |
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
|
466 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
467 |
goal thy |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
468 |
"!!evs. [| Says Server B \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
469 |
\ {|NA, Crypt (shrK A) {|NA, K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
470 |
\ Crypt (shrK B) {|NB, K|}|} : set_of_list evs; \ |
2135 | 471 |
\ Says B Spy {|NA, NB, K|} ~: set_of_list evs; \ |
2032 | 472 |
\ A ~: lost; B ~: lost; evs : otway lost |] \ |
473 |
\ ==> K ~: analz (sees lost Spy evs)"; |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
474 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
475 |
by (fast_tac (!claset addSEs [lemma]) 1); |
2032 | 476 |
qed "Spy_not_see_encrypted_key"; |
477 |
||
1945 | 478 |
|
2032 | 479 |
goal thy |
2048 | 480 |
"!!evs. [| C ~: {A,B,Server}; \ |
481 |
\ Says Server B \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
482 |
\ {|NA, Crypt (shrK A) {|NA, K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
483 |
\ Crypt (shrK B) {|NB, K|}|} : set_of_list evs; \ |
2135 | 484 |
\ Says B Spy {|NA, NB, K|} ~: set_of_list evs; \ |
2032 | 485 |
\ A ~: lost; B ~: lost; evs : otway lost |] \ |
486 |
\ ==> K ~: analz (sees lost C evs)"; |
|
487 |
by (rtac (subset_insertI RS sees_mono RS analz_mono RS contra_subsetD) 1); |
|
488 |
by (rtac (sees_lost_agent_subset_sees_Spy RS analz_mono RS contra_subsetD) 1); |
|
489 |
by (FIRSTGOAL (rtac Spy_not_see_encrypted_key)); |
|
490 |
by (REPEAT_FIRST (fast_tac (!claset addIs [otway_mono RS subsetD]))); |
|
491 |
qed "Agent_not_see_encrypted_key"; |
|
1945 | 492 |
|
493 |
||
2048 | 494 |
(**** Authenticity properties relating to NB ****) |
495 |
||
496 |
(*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
|
497 |
know anything about X: it does NOT have to have the right form.*) |
2048 | 498 |
goal thy |
499 |
"!!evs. [| B ~: lost; evs : otway lost |] \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
500 |
\ ==> Crypt (shrK B) {|NA, NB, Agent A, Agent B|} \ |
2048 | 501 |
\ : parts (sees lost Spy evs) --> \ |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
502 |
\ (EX X. Says B Server \ |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
503 |
\ {|NA, Agent A, Agent B, X, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
504 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|} \ |
2048 | 505 |
\ : set_of_list evs)"; |
2064 | 506 |
by (parts_induct_tac 1); |
507 |
by (auto_tac (!claset, !simpset addcongs [conj_cong])); |
|
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
508 |
bind_thm ("Crypt_imp_OR2", result() RSN (2,rev_mp) RS exE); |
2048 | 509 |
|
510 |
||
511 |
(** The Nonce NB uniquely identifies B's message. **) |
|
512 |
||
513 |
goal thy |
|
514 |
"!!evs. [| evs : otway lost; B ~: lost |] \ |
|
2064 | 515 |
\ ==> EX NA' A'. ALL NA A. \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
516 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} : parts(sees lost Spy evs) \ |
2048 | 517 |
\ --> NA = NA' & A = A'"; |
2064 | 518 |
by (parts_induct_tac 1); |
519 |
by (simp_tac (!simpset addsimps [all_conj_distrib]) 1); |
|
2048 | 520 |
(*OR2: creation of new Nonce. Move assertion into global context*) |
2064 | 521 |
by (expand_case_tac "NB = ?y" 1); |
2048 | 522 |
by (fast_tac (!claset addSEs (nonce_not_seen_now::partsEs)) 1); |
523 |
val lemma = result(); |
|
524 |
||
525 |
goal thy |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
526 |
"!!evs.[| Crypt (shrK B) {|NA, NB, Agent A, Agent B|} \ |
2048 | 527 |
\ : parts(sees lost Spy evs); \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
528 |
\ Crypt (shrK B) {|NC, NB, Agent C, Agent B|} \ |
2048 | 529 |
\ : parts(sees lost Spy evs); \ |
530 |
\ evs : otway lost; B ~: lost |] \ |
|
531 |
\ ==> NC = NA & C = A"; |
|
532 |
by (dtac lemma 1); |
|
533 |
by (assume_tac 1); |
|
534 |
by (REPEAT (etac exE 1)); |
|
535 |
(*Duplicate the assumption*) |
|
536 |
by (forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl 1); |
|
537 |
by (fast_tac (!claset addSDs [spec]) 1); |
|
538 |
qed "unique_NB"; |
|
539 |
||
540 |
||
541 |
(*If the encrypted message appears, and B has used Nonce NB, |
|
542 |
then it originated with the Server!*) |
|
543 |
goal thy |
|
544 |
"!!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
|
545 |
\ ==> Crypt (shrK B) {|NB, Key K|} : parts (sees lost Spy evs) \ |
2048 | 546 |
\ --> (ALL X'. Says B Server \ |
547 |
\ {|NA, Agent A, Agent B, X', \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
548 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|} \ |
2048 | 549 |
\ : set_of_list evs \ |
550 |
\ --> Says Server B \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
551 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
552 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
2048 | 553 |
\ : set_of_list evs)"; |
2064 | 554 |
by (parts_induct_tac 1); |
2048 | 555 |
(*OR1: it cannot be a new Nonce, contradiction.*) |
556 |
by (fast_tac (!claset addSIs [parts_insertI] |
|
557 |
addSEs partsEs |
|
558 |
addEs [Says_imp_old_nonces RS less_irrefl] |
|
559 |
addss (!simpset)) 1); |
|
560 |
(*OR4*) |
|
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
561 |
by (fast_tac (!claset addSEs [MPair_parts, Crypt_imp_OR2]) 2); |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
562 |
(*OR3*) |
2048 | 563 |
by (step_tac (!claset delrules [disjCI, impCE]) 1); |
564 |
by (fast_tac (!claset delrules [conjI] (*stop split-up*)) 3); |
|
565 |
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS parts.Inj] |
|
566 |
addSEs [MPair_parts] |
|
567 |
addDs [unique_NB]) 2); |
|
568 |
by (fast_tac (!claset addSEs [MPair_parts] |
|
569 |
addSDs [Says_imp_sees_Spy RS parts.Inj] |
|
570 |
addSEs [no_nonce_OR1_OR2 RSN (2, rev_notE)] |
|
571 |
delrules [conjI, impCE] (*stop split-up*)) 1); |
|
572 |
qed_spec_mp "NB_Crypt_imp_Server_msg"; |
|
573 |
||
574 |
||
575 |
(*Guarantee for B: if it gets a message with matching NB then the Server |
|
576 |
has sent the correct message.*) |
|
577 |
goal thy |
|
578 |
"!!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
|
579 |
\ Says S B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} \ |
2048 | 580 |
\ : set_of_list evs; \ |
581 |
\ 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
|
582 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \ |
2048 | 583 |
\ : set_of_list evs |] \ |
584 |
\ ==> Says Server B \ |
|
585 |
\ {|NA, \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
586 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
587 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
2048 | 588 |
\ : set_of_list evs"; |
589 |
by (fast_tac (!claset addSIs [NB_Crypt_imp_Server_msg] |
|
590 |
addEs partsEs |
|
591 |
addDs [Says_imp_sees_Spy RS parts.Inj]) 1); |
|
2328 | 592 |
qed "B_trusts_OR3"; |
2048 | 593 |
|
594 |
||
2328 | 595 |
B_trusts_OR3 RS Spy_not_see_encrypted_key; |
2048 | 596 |
|
597 |
||
1945 | 598 |
goal thy |
2214 | 599 |
"!!evs. [| B ~: lost; evs : otway lost |] \ |
600 |
\ ==> Says Server B \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
601 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
602 |
\ Crypt (shrK B) {|NB, Key K|}|} : set_of_list evs --> \ |
2214 | 603 |
\ (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
|
604 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \ |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
605 |
\ : set_of_list evs)"; |
2032 | 606 |
by (etac otway.induct 1); |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
607 |
by (Auto_tac()); |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
608 |
by (dtac (Says_imp_sees_Spy RS parts.Inj) 1); |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
609 |
by (fast_tac (!claset addSEs [MPair_parts, Crypt_imp_OR2]) 1); |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
610 |
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
|
611 |
|
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
612 |
|
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
613 |
(*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
|
614 |
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
|
615 |
strictly necessary for authentication.*) |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
616 |
goal thy |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
617 |
"!!evs. [| Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} \ |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
618 |
\ : set_of_list evs; \ |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
619 |
\ 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
|
620 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
621 |
\ : set_of_list evs; \ |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
622 |
\ A ~: lost; A ~= Spy; B ~: lost; evs : otway lost |] \ |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
623 |
\ ==> 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
|
624 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |}\ |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
625 |
\ : set_of_list evs"; |
2328 | 626 |
by (fast_tac (!claset addSDs [A_trusts_OR4] |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
627 |
addSEs [OR3_imp_OR2]) 1); |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
628 |
qed "A_auths_B"; |