author | paulson |
Mon, 29 Sep 1997 11:47:01 +0200 | |
changeset 3730 | 6933d20f335f |
parent 3683 | aafe719dff14 |
child 3919 | c036caebfc75 |
permissions | -rw-r--r-- |
1934 | 1 |
(* Title: HOL/Auth/NS_Shared |
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ID: $Id$ |
|
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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Inductive relation "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. |
|
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Proc. Royal Soc. 426 (1989) |
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*) |
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||
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open NS_Shared; |
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||
1943 | 15 |
proof_timing:=true; |
1997 | 16 |
HOL_quantifiers := false; |
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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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\ ==> 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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\ ==> EX evs: ns_shared. \ |
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\ Says A B (Crypt ?K {|Nonce ?N, Nonce ?N|}) : set evs"; |
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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; |
1943 | 38 |
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1934 | 39 |
(**** Inductive proofs about ns_shared ****) |
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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"; |
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46 |
Addsimps [not_Says_to_self]; |
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AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
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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)"; |
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by (blast_tac (!claset addSEs spies_partsEs) 1); |
|
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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)"; |
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by (blast_tac (!claset addSEs spies_partsEs) 1); |
|
59 |
qed "Oops_parts_spies"; |
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2070 | 60 |
|
3683 | 61 |
(*For proving the easier theorems about X ~: parts (spies evs).*) |
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fun parts_induct_tac i = |
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etac ns_shared.induct i THEN |
3683 | 64 |
forward_tac [Oops_parts_spies] (i+7) THEN |
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dtac NS3_msg_in_parts_spies (i+4) THEN |
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prove_simple_subgoals_tac i; |
2070 | 67 |
|
1934 | 68 |
|
3683 | 69 |
(** Theorems of the form X ~: parts (spies evs) imply that NOBODY |
2015 | 70 |
sends messages containing X! **) |
1934 | 71 |
|
3683 | 72 |
(*Spy never sees another agent's shared key! (unless it's bad at start)*) |
1934 | 73 |
goal thy |
3683 | 74 |
"!!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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by (Fake_parts_insert_tac 1); |
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by (Blast_tac 1); |
2131 | 78 |
qed "Spy_see_shrK"; |
79 |
Addsimps [Spy_see_shrK]; |
|
1934 | 80 |
|
2131 | 81 |
goal thy |
3683 | 82 |
"!!evs. evs : ns_shared ==> (Key (shrK A) : analz (spies evs)) = (A : bad)"; |
2131 | 83 |
by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset)); |
84 |
qed "Spy_analz_shrK"; |
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Addsimps [Spy_analz_shrK]; |
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1934 | 86 |
|
3683 | 87 |
goal thy "!!A. [| Key (shrK A) : parts (spies evs); \ |
88 |
\ evs : ns_shared |] ==> A:bad"; |
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by (blast_tac (!claset addDs [Spy_see_shrK]) 1); |
2131 | 90 |
qed "Spy_see_shrK_D"; |
1934 | 91 |
|
2131 | 92 |
bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D); |
93 |
AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D]; |
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1934 | 94 |
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2070 | 95 |
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(*Nobody can have used non-existent keys!*) |
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goal thy "!!evs. evs : ns_shared ==> \ |
3683 | 98 |
\ Key K ~: used evs --> K ~: keysFor (parts (spies evs))"; |
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by (parts_induct_tac 1); |
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(*Fake*) |
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by (best_tac |
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(!claset addIs [impOfSubs analz_subset_parts] |
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addDs [impOfSubs (analz_subset_parts RS keysFor_mono), |
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impOfSubs (parts_insert_subset_Un RS keysFor_mono)] |
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addss (!simpset)) 1); |
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(*NS2, NS4, NS5*) |
3683 | 107 |
by (ALLGOALS (blast_tac (!claset addSEs spies_partsEs))); |
2160 | 108 |
qed_spec_mp "new_keys_not_used"; |
1934 | 109 |
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bind_thm ("new_keys_not_analzd", |
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2032 | 111 |
[analz_subset_parts RS keysFor_mono, |
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new_keys_not_used] MRS contra_subsetD); |
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1934 | 113 |
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Addsimps [new_keys_not_used, new_keys_not_analzd]; |
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(** Lemmas concerning the form of items passed in messages **) |
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(*Describes the form of K, X and K' when the Server sends this message.*) |
1934 | 120 |
goal thy |
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"!!evs. [| Says Server A (Crypt K' {|N, Agent B, Key K, X|}) : set evs; \ |
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\ evs : ns_shared |] \ |
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\ ==> K ~: range shrK & \ |
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\ X = (Crypt (shrK B) {|Key K, Agent A|}) & \ |
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\ K' = shrK A"; |
2032 | 126 |
by (etac rev_mp 1); |
127 |
by (etac ns_shared.induct 1); |
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by (Auto_tac()); |
1934 | 129 |
qed "Says_Server_message_form"; |
130 |
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(*If the encrypted message appears then it originated with the Server*) |
1934 | 133 |
goal thy |
3683 | 134 |
"!!evs. [| Crypt (shrK A) {|NA, Agent B, Key K, X|} : parts (spies evs); \ |
135 |
\ A ~: bad; evs : ns_shared |] \ |
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3651 | 136 |
\ ==> Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|}) \ |
137 |
\ : set evs"; |
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2070 | 138 |
by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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by (Fake_parts_insert_tac 1); |
2323 | 141 |
qed "A_trusts_NS2"; |
1934 | 142 |
|
1965 | 143 |
|
144 |
(*EITHER describes the form of X when the following message is sent, |
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OR reduces it to the Fake case. |
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146 |
Use Says_Server_message_form if applicable.*) |
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1934 | 147 |
goal thy |
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"!!evs. [| Says S A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|}) \ |
3651 | 149 |
\ : set evs; \ |
150 |
\ evs : ns_shared |] \ |
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151 |
\ ==> (K ~: range shrK & X = (Crypt (shrK B) {|Key K, Agent A|})) \ |
3683 | 152 |
\ | X : analz (spies evs)"; |
153 |
by (case_tac "A : bad" 1); |
|
154 |
by (fast_tac (!claset addSDs [Says_imp_spies RS analz.Inj] |
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155 |
addss (!simpset)) 1); |
3683 | 156 |
by (forward_tac [Says_imp_spies RS parts.Inj] 1); |
3651 | 157 |
by (blast_tac (!claset addSDs [A_trusts_NS2, Says_Server_message_form]) 1); |
1934 | 158 |
qed "Says_S_message_form"; |
159 |
||
160 |
||
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161 |
(*For proofs involving analz.*) |
3683 | 162 |
val analz_spies_tac = |
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forward_tac [Says_Server_message_form] 8 THEN |
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164 |
forward_tac [Says_S_message_form] 5 THEN |
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165 |
REPEAT_FIRST (eresolve_tac [asm_rl, conjE, disjE] ORELSE' hyp_subst_tac); |
2131 | 166 |
|
1934 | 167 |
|
168 |
(**** |
|
169 |
The following is to prove theorems of the form |
|
170 |
||
3683 | 171 |
Key K : analz (insert (Key KAB) (spies evs)) ==> |
172 |
Key K : analz (spies evs) |
|
1934 | 173 |
|
174 |
A more general formula must be proved inductively. |
|
175 |
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176 |
****) |
|
177 |
||
178 |
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179 |
(*NOT useful in this form, but it says that session keys are not used |
|
180 |
to encrypt messages containing other keys, in the actual protocol. |
|
181 |
We require that agents should behave like this subsequently also.*) |
|
182 |
goal thy |
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183 |
"!!evs. [| evs : ns_shared; Kab ~: range shrK |] ==> \ |
3683 | 184 |
\ (Crypt KAB X) : parts (spies evs) & \ |
185 |
\ Key K : parts {X} --> Key K : parts (spies evs)"; |
|
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186 |
by (parts_induct_tac 1); |
1934 | 187 |
(*Deals with Faked messages*) |
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188 |
by (blast_tac (!claset addSEs partsEs |
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189 |
addDs [impOfSubs parts_insert_subset_Un]) 1); |
1965 | 190 |
(*Base, NS4 and NS5*) |
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191 |
by (Auto_tac()); |
1934 | 192 |
result(); |
193 |
||
194 |
||
195 |
(** Session keys are not used to encrypt other session keys **) |
|
196 |
||
2015 | 197 |
(*The equality makes the induction hypothesis easier to apply*) |
1934 | 198 |
goal thy |
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199 |
"!!evs. evs : ns_shared ==> \ |
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200 |
\ ALL K KK. KK <= Compl (range shrK) --> \ |
3683 | 201 |
\ (Key K : analz (Key``KK Un (spies evs))) = \ |
202 |
\ (K : KK | Key K : analz (spies evs))"; |
|
2032 | 203 |
by (etac ns_shared.induct 1); |
3683 | 204 |
by analz_spies_tac; |
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205 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
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206 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
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207 |
(*Takes 24 secs*) |
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|
208 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
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209 |
(*Fake*) |
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210 |
by (spy_analz_tac 2); |
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211 |
(*Base*) |
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212 |
by (Blast_tac 1); |
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213 |
qed_spec_mp "analz_image_freshK"; |
1934 | 214 |
|
215 |
||
216 |
goal thy |
|
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217 |
"!!evs. [| evs : ns_shared; KAB ~: range shrK |] ==> \ |
3683 | 218 |
\ Key K : analz (insert (Key KAB) (spies evs)) = \ |
219 |
\ (K = KAB | Key K : analz (spies evs))"; |
|
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|
220 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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|
221 |
qed "analz_insert_freshK"; |
1934 | 222 |
|
223 |
||
2558 | 224 |
(** The session key K uniquely identifies the message **) |
1965 | 225 |
|
1934 | 226 |
goal thy |
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227 |
"!!evs. evs : ns_shared ==> \ |
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|
228 |
\ EX A' NA' B' X'. ALL A NA B X. \ |
3683 | 229 |
\ Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|}) : set evs \ |
230 |
\ --> A=A' & NA=NA' & B=B' & X=X'"; |
|
2032 | 231 |
by (etac ns_shared.induct 1); |
2070 | 232 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
3730 | 233 |
by Safe_tac; |
2070 | 234 |
(*NS3*) |
235 |
by (ex_strip_tac 2); |
|
3121
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Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
236 |
by (Blast_tac 2); |
2070 | 237 |
(*NS2: it can't be a new key*) |
238 |
by (expand_case_tac "K = ?y" 1); |
|
239 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
240 |
by (blast_tac (!claset delrules [conjI] (*prevent split-up into 4 subgoals*) |
3683 | 241 |
addSEs spies_partsEs) 1); |
1934 | 242 |
val lemma = result(); |
243 |
||
244 |
(*In messages of this form, the session key uniquely identifies the rest*) |
|
245 |
goal thy |
|
2070 | 246 |
"!!evs. [| Says Server A \ |
3683 | 247 |
\ (Crypt (shrK A) {|NA, Agent B, Key K, X|}) : set evs; \ |
2070 | 248 |
\ Says Server A' \ |
3683 | 249 |
\ (Crypt (shrK A') {|NA', Agent B', Key K, X'|}) : set evs; \ |
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
250 |
\ evs : ns_shared |] ==> A=A' & NA=NA' & B=B' & X = X'"; |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2374
diff
changeset
|
251 |
by (prove_unique_tac lemma 1); |
1934 | 252 |
qed "unique_session_keys"; |
253 |
||
254 |
||
2032 | 255 |
(** Crucial secrecy property: Spy does not see the keys sent in msg NS2 **) |
2015 | 256 |
|
1934 | 257 |
goal thy |
3683 | 258 |
"!!evs. [| A ~: bad; B ~: bad; evs : ns_shared |] \ |
2015 | 259 |
\ ==> Says Server A \ |
2284
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Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
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diff
changeset
|
260 |
\ (Crypt (shrK A) {|NA, Agent B, Key K, \ |
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parents:
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diff
changeset
|
261 |
\ Crypt (shrK B) {|Key K, Agent A|}|}) \ |
3466
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Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
262 |
\ : set evs --> \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
263 |
\ (ALL NB. Says A Spy {|NA, NB, Key K|} ~: set evs) --> \ |
3683 | 264 |
\ Key K ~: analz (spies evs)"; |
2032 | 265 |
by (etac ns_shared.induct 1); |
3683 | 266 |
by analz_spies_tac; |
1934 | 267 |
by (ALLGOALS |
2015 | 268 |
(asm_simp_tac |
3675
70dd312b70b2
Deleted the redundant simprule not_parts_not_analz
paulson
parents:
3651
diff
changeset
|
269 |
(!simpset addsimps ([analz_insert_eq, analz_insert_freshK] @ pushes) |
1934 | 270 |
setloop split_tac [expand_if]))); |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
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diff
changeset
|
271 |
(*Oops*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3441
diff
changeset
|
272 |
by (blast_tac (!claset addDs [unique_session_keys]) 5); |
3679 | 273 |
(*NS3, replay sub-case*) |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3441
diff
changeset
|
274 |
by (Blast_tac 4); |
1934 | 275 |
(*NS2*) |
3683 | 276 |
by (blast_tac (!claset addSEs spies_partsEs |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3441
diff
changeset
|
277 |
addIs [parts_insertI, impOfSubs analz_subset_parts]) 2); |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3441
diff
changeset
|
278 |
(*Fake*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3441
diff
changeset
|
279 |
by (spy_analz_tac 1); |
3679 | 280 |
(*NS3, Server sub-case*) (**LEVEL 6 **) |
3730 | 281 |
by (clarify_tac (!claset delrules [impCE]) 1); |
3683 | 282 |
by (forward_tac [Says_imp_spies RS parts.Inj RS A_trusts_NS2] 1); |
2170 | 283 |
by (assume_tac 2); |
3683 | 284 |
by (blast_tac (!claset addDs [Says_imp_spies RS analz.Inj RS |
285 |
Crypt_Spy_analz_bad]) 1); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
286 |
by (blast_tac (!claset addDs [unique_session_keys]) 1); |
2070 | 287 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
2015 | 288 |
|
289 |
||
290 |
(*Final version: Server's message in the most abstract form*) |
|
291 |
goal thy |
|
2070 | 292 |
"!!evs. [| Says Server A \ |
3466
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Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
293 |
\ (Crypt K' {|NA, Agent B, Key K, X|}) : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
294 |
\ (ALL NB. Says A Spy {|NA, NB, Key K|} ~: set evs); \ |
3683 | 295 |
\ A ~: bad; B ~: bad; evs : ns_shared \ |
296 |
\ |] ==> Key K ~: analz (spies evs)"; |
|
2015 | 297 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
298 |
by (blast_tac (!claset addSDs [lemma]) 1); |
2032 | 299 |
qed "Spy_not_see_encrypted_key"; |
300 |
||
301 |
||
2070 | 302 |
(**** Guarantees available at various stages of protocol ***) |
303 |
||
3651 | 304 |
A_trusts_NS2 RS Spy_not_see_encrypted_key; |
2070 | 305 |
|
306 |
||
307 |
(*If the encrypted message appears then it originated with the Server*) |
|
308 |
goal thy |
|
3683 | 309 |
"!!evs. [| Crypt (shrK B) {|Key K, Agent A|} : parts (spies evs); \ |
310 |
\ B ~: bad; evs : ns_shared |] \ |
|
2070 | 311 |
\ ==> EX NA. Says Server A \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
312 |
\ (Crypt (shrK A) {|NA, Agent B, Key K, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
313 |
\ Crypt (shrK B) {|Key K, Agent A|}|}) \ |
3465 | 314 |
\ : set evs"; |
2070 | 315 |
by (etac rev_mp 1); |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
316 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
317 |
by (Fake_parts_insert_tac 1); |
2070 | 318 |
(*Fake case*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
319 |
by (ALLGOALS Blast_tac); |
2323 | 320 |
qed "B_trusts_NS3"; |
2070 | 321 |
|
322 |
||
323 |
goal thy |
|
3683 | 324 |
"!!evs. [| B ~: bad; evs : ns_shared |] \ |
325 |
\ ==> Key K ~: analz (spies evs) --> \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
326 |
\ Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|}) \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
327 |
\ : set evs --> \ |
3683 | 328 |
\ Crypt K (Nonce NB) : parts (spies evs) --> \ |
3465 | 329 |
\ Says B A (Crypt K (Nonce NB)) : set evs"; |
2070 | 330 |
by (etac ns_shared.induct 1); |
331 |
by (forward_tac [Says_S_message_form] 5 THEN assume_tac 5); |
|
3683 | 332 |
by (dtac NS3_msg_in_parts_spies 5); |
333 |
by (forward_tac [Oops_parts_spies] 8); |
|
2103 | 334 |
by (TRYALL (rtac impI)); |
335 |
by (REPEAT_FIRST |
|
3683 | 336 |
(dtac (spies_subset_spies_Says RS analz_mono RS contra_subsetD))); |
2103 | 337 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
338 |
(**LEVEL 7**) |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
339 |
by (blast_tac (!claset addSDs [Crypt_Fake_parts_insert] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
340 |
addDs [impOfSubs analz_subset_parts]) 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
341 |
by (Blast_tac 2); |
2103 | 342 |
by (REPEAT_FIRST (rtac impI ORELSE' etac conjE ORELSE' hyp_subst_tac)); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
343 |
(*Subgoal 1: contradiction from the assumptions |
3683 | 344 |
Key K ~: used evsa and Crypt K (Nonce NB) : parts (spies evsa) *) |
2170 | 345 |
by (dtac Crypt_imp_invKey_keysFor 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
346 |
(**LEVEL 11**) |
2070 | 347 |
by (Asm_full_simp_tac 1); |
2170 | 348 |
by (rtac disjI1 1); |
2070 | 349 |
by (thin_tac "?PP-->?QQ" 1); |
3683 | 350 |
by (case_tac "Ba : bad" 1); |
351 |
by (blast_tac (!claset addDs [Says_imp_spies RS parts.Inj RS B_trusts_NS3, |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
352 |
unique_session_keys]) 2); |
3683 | 353 |
by (blast_tac (!claset addDs [Says_imp_spies RS analz.Inj RS |
354 |
Crypt_Spy_analz_bad]) 1); |
|
2103 | 355 |
val lemma = result(); |
356 |
||
357 |
goal thy |
|
3683 | 358 |
"!!evs. [| Crypt K (Nonce NB) : parts (spies evs); \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
359 |
\ Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|}) \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
360 |
\ : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
361 |
\ ALL NB. Says A Spy {|NA, NB, Key K|} ~: set evs; \ |
3683 | 362 |
\ A ~: bad; B ~: bad; evs : ns_shared |] \ |
3465 | 363 |
\ ==> Says B A (Crypt K (Nonce NB)) : set evs"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
364 |
by (blast_tac (!claset addSIs [lemma RS mp RS mp RS mp] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
365 |
addSEs [Spy_not_see_encrypted_key RSN (2,rev_notE)]) 1); |
2323 | 366 |
qed "A_trusts_NS4"; |