author | paulson |
Mon, 01 Dec 1997 12:52:18 +0100 | |
changeset 4331 | 34bb65b037dd |
parent 4267 | cdc193e38925 |
child 4422 | 21238c9d363e |
permissions | -rw-r--r-- |
1934 | 1 |
(* Title: HOL/Auth/NS_Shared |
2 |
ID: $Id$ |
|
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
|
4 |
Copyright 1996 University of Cambridge |
|
5 |
||
6 |
Inductive relation "ns_shared" for Needham-Schroeder Shared-Key protocol. |
|
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||
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From page 247 of |
|
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Burrows, Abadi and Needham. A Logic of Authentication. |
|
10 |
Proc. Royal Soc. 426 (1989) |
|
11 |
*) |
|
12 |
||
13 |
open NS_Shared; |
|
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||
1943 | 15 |
proof_timing:=true; |
1997 | 16 |
HOL_quantifiers := false; |
17 |
||
18 |
||
2323 | 19 |
(*A "possibility property": there are traces that reach the end*) |
1997 | 20 |
goal thy |
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"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
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22 |
\ ==> EX N K. EX evs: ns_shared. \ |
3465 | 23 |
\ Says A B (Crypt K {|Nonce N, Nonce N|}) : set evs"; |
1997 | 24 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
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by (rtac (ns_shared.Nil RS ns_shared.NS1 RS ns_shared.NS2 RS |
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ns_shared.NS3 RS ns_shared.NS4 RS ns_shared.NS5) 2); |
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by possibility_tac; |
2015 | 28 |
result(); |
29 |
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goal thy |
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"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
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32 |
\ ==> EX evs: ns_shared. \ |
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\ Says A B (Crypt ?K {|Nonce ?N, Nonce ?N|}) : set evs"; |
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34 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
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35 |
by (rtac (ns_shared.Nil RS ns_shared.NS1 RS ns_shared.NS2 RS |
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ns_shared.NS3 RS ns_shared.NS4 RS ns_shared.NS5) 2); |
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by possibility_tac; |
1943 | 38 |
|
1934 | 39 |
(**** Inductive proofs about ns_shared ****) |
40 |
||
41 |
(*Nobody sends themselves messages*) |
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goal thy "!!evs. evs : ns_shared ==> ALL A X. Says A A X ~: set evs"; |
2032 | 43 |
by (etac ns_shared.induct 1); |
1934 | 44 |
by (Auto_tac()); |
45 |
qed_spec_mp "not_Says_to_self"; |
|
46 |
Addsimps [not_Says_to_self]; |
|
47 |
AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
|
48 |
||
1943 | 49 |
(*For reasoning about the encrypted portion of message NS3*) |
3465 | 50 |
goal thy "!!evs. Says S A (Crypt KA {|N, B, K, X|}) : set evs \ |
3683 | 51 |
\ ==> X : parts (spies evs)"; |
4091 | 52 |
by (blast_tac (claset() addSEs spies_partsEs) 1); |
3683 | 53 |
qed "NS3_msg_in_parts_spies"; |
2032 | 54 |
|
2070 | 55 |
goal thy |
3465 | 56 |
"!!evs. Says Server A (Crypt (shrK A) {|NA, B, K, X|}) : set evs \ |
3683 | 57 |
\ ==> K : parts (spies evs)"; |
4091 | 58 |
by (blast_tac (claset() addSEs spies_partsEs) 1); |
3683 | 59 |
qed "Oops_parts_spies"; |
2070 | 60 |
|
3683 | 61 |
(*For proving the easier theorems about X ~: parts (spies evs).*) |
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fun parts_induct_tac i = |
4331 | 63 |
EVERY [etac ns_shared.induct i, |
64 |
REPEAT (FIRSTGOAL analz_mono_contra_tac), |
|
65 |
forward_tac [Oops_parts_spies] (i+7), |
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forward_tac [NS3_msg_in_parts_spies] (i+4), |
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prove_simple_subgoals_tac i]; |
|
2070 | 68 |
|
1934 | 69 |
|
3683 | 70 |
(** Theorems of the form X ~: parts (spies evs) imply that NOBODY |
2015 | 71 |
sends messages containing X! **) |
1934 | 72 |
|
3683 | 73 |
(*Spy never sees another agent's shared key! (unless it's bad at start)*) |
1934 | 74 |
goal thy |
3683 | 75 |
"!!evs. evs : ns_shared ==> (Key (shrK A) : parts (spies evs)) = (A : bad)"; |
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by (parts_induct_tac 1); |
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77 |
by (Fake_parts_insert_tac 1); |
3961 | 78 |
by (ALLGOALS Blast_tac); |
2131 | 79 |
qed "Spy_see_shrK"; |
80 |
Addsimps [Spy_see_shrK]; |
|
1934 | 81 |
|
2131 | 82 |
goal thy |
3683 | 83 |
"!!evs. evs : ns_shared ==> (Key (shrK A) : analz (spies evs)) = (A : bad)"; |
4091 | 84 |
by (auto_tac(claset() addDs [impOfSubs analz_subset_parts], simpset())); |
2131 | 85 |
qed "Spy_analz_shrK"; |
86 |
Addsimps [Spy_analz_shrK]; |
|
1934 | 87 |
|
3683 | 88 |
goal thy "!!A. [| Key (shrK A) : parts (spies evs); \ |
89 |
\ evs : ns_shared |] ==> A:bad"; |
|
4091 | 90 |
by (blast_tac (claset() addDs [Spy_see_shrK]) 1); |
2131 | 91 |
qed "Spy_see_shrK_D"; |
1934 | 92 |
|
2131 | 93 |
bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D); |
94 |
AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D]; |
|
1934 | 95 |
|
2070 | 96 |
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97 |
(*Nobody can have used non-existent keys!*) |
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goal thy "!!evs. evs : ns_shared ==> \ |
3683 | 99 |
\ Key K ~: used evs --> K ~: keysFor (parts (spies evs))"; |
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100 |
by (parts_induct_tac 1); |
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101 |
(*Fake*) |
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by (best_tac |
4091 | 103 |
(claset() addSDs [impOfSubs (parts_insert_subset_Un RS keysFor_mono)] |
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addIs [impOfSubs analz_subset_parts] |
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addDs [impOfSubs (analz_subset_parts RS keysFor_mono)] |
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addss (simpset())) 1); |
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107 |
(*NS2, NS4, NS5*) |
4091 | 108 |
by (ALLGOALS (blast_tac (claset() addSEs spies_partsEs))); |
2160 | 109 |
qed_spec_mp "new_keys_not_used"; |
1934 | 110 |
|
111 |
bind_thm ("new_keys_not_analzd", |
|
2032 | 112 |
[analz_subset_parts RS keysFor_mono, |
113 |
new_keys_not_used] MRS contra_subsetD); |
|
1934 | 114 |
|
115 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
|
116 |
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117 |
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118 |
(** Lemmas concerning the form of items passed in messages **) |
|
119 |
||
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(*Describes the form of K, X and K' when the Server sends this message.*) |
1934 | 121 |
goal thy |
3683 | 122 |
"!!evs. [| Says Server A (Crypt K' {|N, Agent B, Key K, X|}) : set evs; \ |
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123 |
\ evs : ns_shared |] \ |
4267 | 124 |
\ ==> K ~: range shrK & \ |
125 |
\ X = (Crypt (shrK B) {|Key K, Agent A|}) & \ |
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126 |
\ K' = shrK A"; |
2032 | 127 |
by (etac rev_mp 1); |
128 |
by (etac ns_shared.induct 1); |
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129 |
by (Auto_tac()); |
1934 | 130 |
qed "Says_Server_message_form"; |
131 |
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132 |
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2070 | 133 |
(*If the encrypted message appears then it originated with the Server*) |
1934 | 134 |
goal thy |
3683 | 135 |
"!!evs. [| Crypt (shrK A) {|NA, Agent B, Key K, X|} : parts (spies evs); \ |
4267 | 136 |
\ A ~: bad; evs : ns_shared |] \ |
137 |
\ ==> Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|}) \ |
|
3651 | 138 |
\ : set evs"; |
2070 | 139 |
by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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141 |
by (Fake_parts_insert_tac 1); |
2323 | 142 |
qed "A_trusts_NS2"; |
1934 | 143 |
|
1965 | 144 |
|
4331 | 145 |
goal thy |
146 |
"!!evs. [| Crypt (shrK A) {|NA, Agent B, Key K, X|} : parts (spies evs); \ |
|
147 |
\ A ~: bad; evs : ns_shared |] \ |
|
148 |
\ ==> K ~: range shrK & X = (Crypt (shrK B) {|Key K, Agent A|})"; |
|
149 |
by (blast_tac (claset() addSDs [A_trusts_NS2, Says_Server_message_form]) 1); |
|
150 |
qed "cert_A_form"; |
|
151 |
||
152 |
||
1965 | 153 |
(*EITHER describes the form of X when the following message is sent, |
154 |
OR reduces it to the Fake case. |
|
155 |
Use Says_Server_message_form if applicable.*) |
|
1934 | 156 |
goal thy |
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157 |
"!!evs. [| Says S A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|}) \ |
3651 | 158 |
\ : set evs; \ |
159 |
\ evs : ns_shared |] \ |
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160 |
\ ==> (K ~: range shrK & X = (Crypt (shrK B) {|Key K, Agent A|})) \ |
3683 | 161 |
\ | X : analz (spies evs)"; |
162 |
by (case_tac "A : bad" 1); |
|
4091 | 163 |
by (fast_tac (claset() addSDs [Says_imp_spies RS analz.Inj] |
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164 |
addss (simpset())) 1); |
4331 | 165 |
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj, cert_A_form]) 1); |
1934 | 166 |
qed "Says_S_message_form"; |
167 |
||
168 |
||
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169 |
(*For proofs involving analz.*) |
3683 | 170 |
val analz_spies_tac = |
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171 |
forward_tac [Says_Server_message_form] 8 THEN |
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172 |
forward_tac [Says_S_message_form] 5 THEN |
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173 |
REPEAT_FIRST (eresolve_tac [asm_rl, conjE, disjE] ORELSE' hyp_subst_tac); |
2131 | 174 |
|
1934 | 175 |
|
176 |
(**** |
|
177 |
The following is to prove theorems of the form |
|
178 |
||
3683 | 179 |
Key K : analz (insert (Key KAB) (spies evs)) ==> |
180 |
Key K : analz (spies evs) |
|
1934 | 181 |
|
182 |
A more general formula must be proved inductively. |
|
183 |
****) |
|
184 |
||
185 |
||
186 |
(*NOT useful in this form, but it says that session keys are not used |
|
187 |
to encrypt messages containing other keys, in the actual protocol. |
|
188 |
We require that agents should behave like this subsequently also.*) |
|
189 |
goal thy |
|
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190 |
"!!evs. [| evs : ns_shared; Kab ~: range shrK |] ==> \ |
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191 |
\ (Crypt KAB X) : parts (spies evs) & \ |
3683 | 192 |
\ Key K : parts {X} --> Key K : parts (spies evs)"; |
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193 |
by (parts_induct_tac 1); |
1934 | 194 |
(*Deals with Faked messages*) |
4091 | 195 |
by (blast_tac (claset() addSEs partsEs |
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196 |
addDs [impOfSubs parts_insert_subset_Un]) 1); |
1965 | 197 |
(*Base, NS4 and NS5*) |
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198 |
by (Auto_tac()); |
1934 | 199 |
result(); |
200 |
||
201 |
||
202 |
(** Session keys are not used to encrypt other session keys **) |
|
203 |
||
2015 | 204 |
(*The equality makes the induction hypothesis easier to apply*) |
1934 | 205 |
goal thy |
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206 |
"!!evs. evs : ns_shared ==> \ |
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|
207 |
\ ALL K KK. KK <= Compl (range shrK) --> \ |
3683 | 208 |
\ (Key K : analz (Key``KK Un (spies evs))) = \ |
209 |
\ (K : KK | Key K : analz (spies evs))"; |
|
2032 | 210 |
by (etac ns_shared.induct 1); |
3683 | 211 |
by analz_spies_tac; |
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212 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
3961 | 213 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma)); |
214 |
(*Takes 9 secs*) |
|
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215 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
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216 |
(*Fake*) |
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217 |
by (spy_analz_tac 2); |
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218 |
(*Base*) |
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219 |
by (Blast_tac 1); |
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220 |
qed_spec_mp "analz_image_freshK"; |
1934 | 221 |
|
222 |
||
223 |
goal thy |
|
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|
224 |
"!!evs. [| evs : ns_shared; KAB ~: range shrK |] ==> \ |
3683 | 225 |
\ Key K : analz (insert (Key KAB) (spies evs)) = \ |
226 |
\ (K = KAB | Key K : analz (spies evs))"; |
|
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|
227 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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|
228 |
qed "analz_insert_freshK"; |
1934 | 229 |
|
230 |
||
2558 | 231 |
(** The session key K uniquely identifies the message **) |
1965 | 232 |
|
1934 | 233 |
goal thy |
4267 | 234 |
"!!evs. evs : ns_shared ==> \ |
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|
235 |
\ EX A' NA' B' X'. ALL A NA B X. \ |
3683 | 236 |
\ Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|}) : set evs \ |
237 |
\ --> A=A' & NA=NA' & B=B' & X=X'"; |
|
2032 | 238 |
by (etac ns_shared.induct 1); |
4091 | 239 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
3730 | 240 |
by Safe_tac; |
2070 | 241 |
(*NS3*) |
242 |
by (ex_strip_tac 2); |
|
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|
243 |
by (Blast_tac 2); |
2070 | 244 |
(*NS2: it can't be a new key*) |
245 |
by (expand_case_tac "K = ?y" 1); |
|
246 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
4237
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247 |
by (blast_tac (claset() delrules [conjI] (*prevent splitup into 4 subgoals*) |
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248 |
addSEs spies_partsEs) 1); |
1934 | 249 |
val lemma = result(); |
250 |
||
251 |
(*In messages of this form, the session key uniquely identifies the rest*) |
|
252 |
goal thy |
|
4237
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253 |
"!!evs. [| Says Server A \ |
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254 |
\ (Crypt (shrK A) {|NA, Agent B, Key K, X|}) : set evs; \ |
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255 |
\ Says Server A' \ |
3683 | 256 |
\ (Crypt (shrK A') {|NA', Agent B', Key K, X'|}) : set evs; \ |
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257 |
\ evs : ns_shared |] ==> A=A' & NA=NA' & B=B' & X = X'"; |
2451
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|
258 |
by (prove_unique_tac lemma 1); |
1934 | 259 |
qed "unique_session_keys"; |
260 |
||
261 |
||
2032 | 262 |
(** Crucial secrecy property: Spy does not see the keys sent in msg NS2 **) |
2015 | 263 |
|
1934 | 264 |
goal thy |
3961 | 265 |
"!!evs. [| A ~: bad; B ~: bad; evs : ns_shared |] \ |
2015 | 266 |
\ ==> Says Server A \ |
2284
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267 |
\ (Crypt (shrK A) {|NA, Agent B, Key K, \ |
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268 |
\ Crypt (shrK B) {|Key K, Agent A|}|}) \ |
3466
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|
269 |
\ : set evs --> \ |
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270 |
\ (ALL NB. Says A Spy {|NA, NB, Key K|} ~: set evs) --> \ |
3683 | 271 |
\ Key K ~: analz (spies evs)"; |
2032 | 272 |
by (etac ns_shared.induct 1); |
3683 | 273 |
by analz_spies_tac; |
1934 | 274 |
by (ALLGOALS |
2015 | 275 |
(asm_simp_tac |
4091 | 276 |
(simpset() addsimps ([analz_insert_eq, analz_insert_freshK] @ |
4237
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|
277 |
pushes @ expand_ifs)))); |
3451
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|
278 |
(*Oops*) |
4091 | 279 |
by (blast_tac (claset() addDs [unique_session_keys]) 5); |
3679 | 280 |
(*NS3, replay sub-case*) |
3451
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281 |
by (Blast_tac 4); |
1934 | 282 |
(*NS2*) |
4091 | 283 |
by (blast_tac (claset() addSEs spies_partsEs |
4237
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284 |
addIs [parts_insertI, |
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|
285 |
impOfSubs analz_subset_parts]) 2); |
3451
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Made proofs more concise by replacing calls to spy_analz_tac by uses of
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|
286 |
(*Fake*) |
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Made proofs more concise by replacing calls to spy_analz_tac by uses of
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|
287 |
by (spy_analz_tac 1); |
3679 | 288 |
(*NS3, Server sub-case*) (**LEVEL 6 **) |
4091 | 289 |
by (clarify_tac (claset() delrules [impCE]) 1); |
3683 | 290 |
by (forward_tac [Says_imp_spies RS parts.Inj RS A_trusts_NS2] 1); |
2170 | 291 |
by (assume_tac 2); |
4091 | 292 |
by (blast_tac (claset() addDs [Says_imp_spies RS analz.Inj RS |
3683 | 293 |
Crypt_Spy_analz_bad]) 1); |
4091 | 294 |
by (blast_tac (claset() addDs [unique_session_keys]) 1); |
2070 | 295 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
2015 | 296 |
|
297 |
||
298 |
(*Final version: Server's message in the most abstract form*) |
|
299 |
goal thy |
|
4237
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300 |
"!!evs. [| Says Server A \ |
4331 | 301 |
\ (Crypt K' {|NA, Agent B, Key K, X|}) : set evs; \ |
302 |
\ ALL NB. Says A Spy {|NA, NB, Key K|} ~: set evs; \ |
|
3683 | 303 |
\ A ~: bad; B ~: bad; evs : ns_shared \ |
304 |
\ |] ==> Key K ~: analz (spies evs)"; |
|
2015 | 305 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
4091 | 306 |
by (blast_tac (claset() addSDs [lemma]) 1); |
2032 | 307 |
qed "Spy_not_see_encrypted_key"; |
308 |
||
309 |
||
2070 | 310 |
(**** Guarantees available at various stages of protocol ***) |
311 |
||
3651 | 312 |
A_trusts_NS2 RS Spy_not_see_encrypted_key; |
2070 | 313 |
|
314 |
||
315 |
(*If the encrypted message appears then it originated with the Server*) |
|
316 |
goal thy |
|
4237
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|
317 |
"!!evs. [| Crypt (shrK B) {|Key K, Agent A|} : parts (spies evs); \ |
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|
318 |
\ B ~: bad; evs : ns_shared |] \ |
2070 | 319 |
\ ==> EX NA. Says Server A \ |
2284
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changeset
|
320 |
\ (Crypt (shrK A) {|NA, Agent B, Key K, \ |
80ebd1a213fd
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diff
changeset
|
321 |
\ Crypt (shrK B) {|Key K, Agent A|}|}) \ |
3465 | 322 |
\ : set evs"; |
2070 | 323 |
by (etac rev_mp 1); |
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
paulson
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changeset
|
324 |
by (parts_induct_tac 1); |
3121
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Conversion to use blast_tac (with other improvements)
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|
325 |
by (Fake_parts_insert_tac 1); |
2070 | 326 |
(*Fake case*) |
3121
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Conversion to use blast_tac (with other improvements)
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changeset
|
327 |
by (ALLGOALS Blast_tac); |
2323 | 328 |
qed "B_trusts_NS3"; |
2070 | 329 |
|
330 |
||
331 |
goal thy |
|
4331 | 332 |
"!!evs. [| Crypt K (Nonce NB) : parts (spies evs); \ |
333 |
\ Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|}) \ |
|
334 |
\ : set evs; \ |
|
335 |
\ Key K ~: analz (spies evs); \ |
|
336 |
\ evs : ns_shared |] \ |
|
337 |
\ ==> Says B A (Crypt K (Nonce NB)) : set evs"; |
|
338 |
by (etac rev_mp 1); |
|
339 |
by (etac rev_mp 1); |
|
340 |
by (etac rev_mp 1); |
|
341 |
by (parts_induct_tac 1); |
|
4267 | 342 |
(*NS3*) |
343 |
by (Blast_tac 3); |
|
344 |
by (Fake_parts_insert_tac 1); |
|
345 |
(*NS2: contradiction from the assumptions |
|
4331 | 346 |
Key K ~: used evs2 and Crypt K (Nonce NB) : parts (spies evs2) *) |
347 |
by (blast_tac (claset() addSEs [new_keys_not_used RSN (2,rev_notE)] |
|
348 |
addSDs [Crypt_imp_keysFor]) 1); |
|
349 |
(**LEVEL 7**) |
|
350 |
(*NS4*) |
|
351 |
by (Clarify_tac 1); |
|
352 |
by (not_bad_tac "Ba" 1); |
|
4091 | 353 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj RS B_trusts_NS3, |
4331 | 354 |
unique_session_keys]) 1); |
355 |
qed "A_trusts_NS4_lemma"; |
|
2103 | 356 |
|
4331 | 357 |
|
358 |
(*This version no longer assumes that K is secure*) |
|
2103 | 359 |
goal thy |
4267 | 360 |
"!!evs. [| Crypt K (Nonce NB) : parts (spies evs); \ |
4331 | 361 |
\ Crypt (shrK A) {|NA, Agent B, Key K, X|} : parts (spies evs); \ |
3466
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Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
362 |
\ ALL NB. Says A Spy {|NA, NB, Key K|} ~: set evs; \ |
4267 | 363 |
\ A ~: bad; B ~: bad; evs : ns_shared |] \ |
3465 | 364 |
\ ==> Says B A (Crypt K (Nonce NB)) : set evs"; |
4331 | 365 |
by (blast_tac (claset() addSIs [A_trusts_NS2, A_trusts_NS4_lemma] |
4267 | 366 |
addSEs [Spy_not_see_encrypted_key RSN (2,rev_notE)]) 1); |
2323 | 367 |
qed "A_trusts_NS4"; |
4331 | 368 |
|
369 |
||
370 |
(*If the session key has been used in NS4 then somebody has forwarded |
|
371 |
component X in some instance of NS4. Perhaps an interesting property, |
|
372 |
but not needed (after all) for the proofs below.*) |
|
373 |
goal thy |
|
374 |
"!!evs. [| Crypt K (Nonce NB) : parts (spies evs); \ |
|
375 |
\ Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|}) \ |
|
376 |
\ : set evs; \ |
|
377 |
\ Key K ~: analz (spies evs); \ |
|
378 |
\ evs : ns_shared |] \ |
|
379 |
\ ==> EX A'. Says A' B X : set evs"; |
|
380 |
by (etac rev_mp 1); |
|
381 |
by (etac rev_mp 1); |
|
382 |
by (etac rev_mp 1); |
|
383 |
by (parts_induct_tac 1); |
|
384 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [ex_disj_distrib]))); |
|
385 |
by (ALLGOALS Clarify_tac); |
|
386 |
by (Fake_parts_insert_tac 1); |
|
387 |
(**LEVEL 7**) |
|
388 |
(*NS2*) |
|
389 |
by (blast_tac (claset() addSEs [new_keys_not_used RSN (2,rev_notE)] |
|
390 |
addSDs [Crypt_imp_keysFor]) 1); |
|
391 |
(*NS4*) |
|
392 |
by (not_bad_tac "Ba" 1); |
|
393 |
by (Asm_full_simp_tac 1); |
|
394 |
by (forward_tac [Says_imp_spies RS parts.Inj RS B_trusts_NS3] 1); |
|
395 |
by (ALLGOALS Clarify_tac); |
|
396 |
by (blast_tac (claset() addDs [unique_session_keys]) 1); |
|
397 |
qed "NS4_implies_NS3"; |
|
398 |
||
399 |
||
400 |
goal thy |
|
401 |
"!!evs. [| B ~: bad; evs : ns_shared |] \ |
|
402 |
\ ==> Key K ~: analz (spies evs) --> \ |
|
403 |
\ Says Server A \ |
|
404 |
\ (Crypt (shrK A) {|NA, Agent B, Key K, \ |
|
405 |
\ Crypt (shrK B) {|Key K, Agent A|}|}) \ |
|
406 |
\ : set evs --> \ |
|
407 |
\ Says B A (Crypt K (Nonce NB)) : set evs --> \ |
|
408 |
\ Crypt K {|Nonce NB, Nonce NB|} : parts (spies evs) --> \ |
|
409 |
\ Says A B (Crypt K {|Nonce NB, Nonce NB|}) : set evs"; |
|
410 |
by (parts_induct_tac 1); |
|
411 |
(*NS4*) |
|
412 |
by (blast_tac (claset() addSEs spies_partsEs) 4); |
|
413 |
(*NS3*) |
|
414 |
by (blast_tac (claset() addSDs [Says_imp_spies RS parts.Inj, cert_A_form]) 3); |
|
415 |
(*NS2*) |
|
416 |
by (blast_tac (claset() addSEs [new_keys_not_used RSN (2,rev_notE)] |
|
417 |
addSDs [Crypt_imp_keysFor]) 2); |
|
418 |
by (Fake_parts_insert_tac 1); |
|
419 |
(**LEVEL 5**) |
|
420 |
(*NS5*) |
|
421 |
by (Clarify_tac 1); |
|
422 |
by (not_bad_tac "Aa" 1); |
|
423 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj RS A_trusts_NS2, |
|
424 |
unique_session_keys]) 1); |
|
425 |
val lemma = result(); |
|
426 |
||
427 |
||
428 |
(*Very strong Oops condition reveals protocol's weakness*) |
|
429 |
goal thy |
|
430 |
"!!evs. [| Crypt K {|Nonce NB, Nonce NB|} : parts (spies evs); \ |
|
431 |
\ Says B A (Crypt K (Nonce NB)) : set evs; \ |
|
432 |
\ Crypt (shrK B) {|Key K, Agent A|} : parts (spies evs); \ |
|
433 |
\ ALL NA NB. Says A Spy {|NA, NB, Key K|} ~: set evs; \ |
|
434 |
\ A ~: bad; B ~: bad; evs : ns_shared |] \ |
|
435 |
\ ==> Says A B (Crypt K {|Nonce NB, Nonce NB|}) : set evs"; |
|
436 |
by (dtac B_trusts_NS3 1); |
|
437 |
by (ALLGOALS Clarify_tac); |
|
438 |
by (blast_tac (claset() addSIs [normalize_thm [RSspec, RSmp] lemma] |
|
439 |
addSEs [Spy_not_see_encrypted_key RSN (2,rev_notE)]) 1); |
|
440 |
qed "B_trusts_NS5"; |