author | paulson |
Tue, 22 Jul 1997 11:26:02 +0200 | |
changeset 3543 | 82f33248d89d |
parent 3519 | ab0a9fbed4c0 |
child 3674 | 65ec38fbb265 |
permissions | -rw-r--r-- |
1941 | 1 |
(* Title: HOL/Auth/OtwayRees |
2 |
ID: $Id$ |
|
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
|
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Copyright 1996 University of Cambridge |
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||
6 |
Inductive relation "otway" for the Otway-Rees protocol. |
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Version that encrypts Nonce NB |
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|
1941 | 10 |
From page 244 of |
11 |
Burrows, Abadi and Needham. A Logic of Authentication. |
|
12 |
Proc. Royal Soc. 426 (1989) |
|
13 |
*) |
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||
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open OtwayRees; |
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||
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proof_timing:=true; |
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HOL_quantifiers := false; |
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1996
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2328 | 21 |
(*A "possibility property": there are traces that reach the end*) |
1996
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goal thy |
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23 |
"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
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24 |
\ ==> EX K. EX NA. EX evs: otway. \ |
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25 |
\ Says B A {|Nonce NA, Crypt (shrK A) {|Nonce NA, Key K|}|} \ |
3465 | 26 |
\ : set evs"; |
1996
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27 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
2032 | 28 |
by (rtac (otway.Nil RS otway.OR1 RS otway.OR2 RS otway.OR3 RS otway.OR4) 2); |
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by possibility_tac; |
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30 |
result(); |
1996
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Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
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31 |
|
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|
1941 | 33 |
(**** Inductive proofs about otway ****) |
34 |
||
35 |
(*Nobody sends themselves messages*) |
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goal thy "!!evs. evs : otway ==> ALL A X. Says A A X ~: set evs"; |
2032 | 37 |
by (etac otway.induct 1); |
1941 | 38 |
by (Auto_tac()); |
39 |
qed_spec_mp "not_Says_to_self"; |
|
40 |
Addsimps [not_Says_to_self]; |
|
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AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
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42 |
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43 |
||
44 |
(** For reasoning about the encrypted portion of messages **) |
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||
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goal thy "!!evs. Says A' B {|N, Agent A, Agent B, X|} : set evs \ |
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\ ==> X : analz (sees Spy evs)"; |
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48 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1); |
2032 | 49 |
qed "OR2_analz_sees_Spy"; |
1941 | 50 |
|
3465 | 51 |
goal thy "!!evs. Says S' B {|N, X, Crypt (shrK B) X'|} : set evs \ |
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\ ==> X : analz (sees Spy evs)"; |
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53 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1); |
2032 | 54 |
qed "OR4_analz_sees_Spy"; |
1941 | 55 |
|
3465 | 56 |
goal thy "!!evs. Says Server B {|NA, X, Crypt K' {|NB,K|}|} : set evs \ |
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\ ==> K : parts (sees Spy evs)"; |
3102 | 58 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
2135 | 59 |
qed "Oops_parts_sees_Spy"; |
1941 | 60 |
|
61 |
(*OR2_analz... and OR4_analz... let us treat those cases using the same |
|
1964 | 62 |
argument as for the Fake case. This is possible for most, but not all, |
63 |
proofs: Fake does not invent new nonces (as in OR2), and of course Fake |
|
2032 | 64 |
messages originate from the Spy. *) |
1964 | 65 |
|
2032 | 66 |
bind_thm ("OR2_parts_sees_Spy", |
67 |
OR2_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
|
68 |
bind_thm ("OR4_parts_sees_Spy", |
|
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OR4_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
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70 |
||
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(*For proving the easier theorems about X ~: parts (sees Spy evs).*) |
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72 |
fun parts_induct_tac i = |
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etac otway.induct i THEN |
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forward_tac [Oops_parts_sees_Spy] (i+6) THEN |
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forward_tac [OR4_parts_sees_Spy] (i+5) THEN |
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forward_tac [OR2_parts_sees_Spy] (i+3) THEN |
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77 |
prove_simple_subgoals_tac i; |
1941 | 78 |
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79 |
||
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(** Theorems of the form X ~: parts (sees Spy evs) imply that NOBODY |
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sends messages containing X! **) |
1941 | 82 |
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83 |
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2064 | 84 |
(*Spy never sees another agent's shared key! (unless it's lost at start)*) |
1941 | 85 |
goal thy |
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86 |
"!!evs. evs : otway ==> (Key (shrK A) : parts (sees Spy evs)) = (A : lost)"; |
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by (parts_induct_tac 1); |
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by (Fake_parts_insert_tac 1); |
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89 |
by (Blast_tac 1); |
2135 | 90 |
qed "Spy_see_shrK"; |
91 |
Addsimps [Spy_see_shrK]; |
|
1941 | 92 |
|
2135 | 93 |
goal thy |
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94 |
"!!evs. evs : otway ==> (Key (shrK A) : analz (sees Spy evs)) = (A : lost)"; |
2135 | 95 |
by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset)); |
96 |
qed "Spy_analz_shrK"; |
|
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Addsimps [Spy_analz_shrK]; |
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1941 | 98 |
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goal thy "!!A. [| Key (shrK A) : parts (sees Spy evs); \ |
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\ evs : otway |] ==> A:lost"; |
3102 | 101 |
by (blast_tac (!claset addDs [Spy_see_shrK]) 1); |
2135 | 102 |
qed "Spy_see_shrK_D"; |
1941 | 103 |
|
2135 | 104 |
bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D); |
105 |
AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D]; |
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1941 | 106 |
|
107 |
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108 |
(*Nobody can have used non-existent keys!*) |
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goal thy "!!evs. evs : otway ==> \ |
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110 |
\ Key K ~: used evs --> K ~: keysFor (parts (sees Spy evs))"; |
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111 |
by (parts_induct_tac 1); |
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112 |
(*Fake*) |
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by (best_tac |
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114 |
(!claset addIs [impOfSubs analz_subset_parts] |
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115 |
addDs [impOfSubs (analz_subset_parts RS keysFor_mono), |
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116 |
impOfSubs (parts_insert_subset_Un RS keysFor_mono)] |
3207 | 117 |
addss (!simpset)) 1); |
3102 | 118 |
by (ALLGOALS Blast_tac); |
2160 | 119 |
qed_spec_mp "new_keys_not_used"; |
1941 | 120 |
|
121 |
bind_thm ("new_keys_not_analzd", |
|
2032 | 122 |
[analz_subset_parts RS keysFor_mono, |
123 |
new_keys_not_used] MRS contra_subsetD); |
|
1941 | 124 |
|
125 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
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126 |
||
127 |
||
2064 | 128 |
|
129 |
(*** Proofs involving analz ***) |
|
130 |
||
2135 | 131 |
(*Describes the form of K and NA when the Server sends this message. Also |
132 |
for Oops case.*) |
|
2064 | 133 |
goal thy |
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134 |
"!!evs. [| Says Server B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
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135 |
\ evs : otway |] \ |
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136 |
\ ==> K ~: range shrK & (EX i. NA = Nonce i) & (EX j. NB = Nonce j)"; |
2135 | 137 |
by (etac rev_mp 1); |
138 |
by (etac otway.induct 1); |
|
3102 | 139 |
by (ALLGOALS Simp_tac); |
140 |
by (ALLGOALS Blast_tac); |
|
2135 | 141 |
qed "Says_Server_message_form"; |
2064 | 142 |
|
143 |
||
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144 |
(*For proofs involving analz.*) |
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145 |
val analz_sees_tac = |
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146 |
dtac OR2_analz_sees_Spy 4 THEN |
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dtac OR4_analz_sees_Spy 6 THEN |
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148 |
forward_tac [Says_Server_message_form] 7 THEN |
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149 |
assume_tac 7 THEN |
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150 |
REPEAT ((eresolve_tac [exE, conjE] ORELSE' hyp_subst_tac) 7); |
1941 | 151 |
|
152 |
||
153 |
(**** |
|
154 |
The following is to prove theorems of the form |
|
155 |
||
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156 |
Key K : analz (insert (Key KAB) (sees Spy evs)) ==> |
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157 |
Key K : analz (sees Spy evs) |
1941 | 158 |
|
159 |
A more general formula must be proved inductively. |
|
160 |
****) |
|
161 |
||
162 |
||
163 |
(** Session keys are not used to encrypt other session keys **) |
|
164 |
||
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165 |
(*The equality makes the induction hypothesis easier to apply*) |
1941 | 166 |
goal thy |
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167 |
"!!evs. evs : otway ==> \ |
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168 |
\ ALL K KK. KK <= Compl (range shrK) --> \ |
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169 |
\ (Key K : analz (Key``KK Un (sees Spy evs))) = \ |
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170 |
\ (K : KK | Key K : analz (sees Spy evs))"; |
2032 | 171 |
by (etac otway.induct 1); |
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172 |
by analz_sees_tac; |
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173 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
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174 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
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175 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
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176 |
(*Fake*) |
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177 |
by (spy_analz_tac 2); |
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178 |
(*Base*) |
3102 | 179 |
by (Blast_tac 1); |
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180 |
qed_spec_mp "analz_image_freshK"; |
1941 | 181 |
|
182 |
||
183 |
goal thy |
|
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184 |
"!!evs. [| evs : otway; KAB ~: range shrK |] ==> \ |
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185 |
\ Key K : analz (insert (Key KAB) (sees Spy evs)) = \ |
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186 |
\ (K = KAB | Key K : analz (sees Spy evs))"; |
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187 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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188 |
qed "analz_insert_freshK"; |
1941 | 189 |
|
190 |
||
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191 |
(*** The Key K uniquely identifies the Server's message. **) |
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192 |
|
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193 |
goal thy |
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194 |
"!!evs. evs : otway ==> \ |
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195 |
\ EX B' NA' NB' X'. ALL B NA NB X. \ |
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196 |
\ Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set evs --> \ |
2135 | 197 |
\ B=B' & NA=NA' & NB=NB' & X=X'"; |
2032 | 198 |
by (etac otway.induct 1); |
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Correction of protocol; addition of Reveal message; proofs of
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|
199 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
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|
200 |
by (Step_tac 1); |
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|
201 |
(*Remaining cases: OR3 and OR4*) |
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diff
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|
202 |
by (ex_strip_tac 2); |
3102 | 203 |
by (Best_tac 2); |
2064 | 204 |
by (expand_case_tac "K = ?y" 1); |
205 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
206 |
(*...we assume X is a recent message, and handle this case by contradiction*) |
3102 | 207 |
by (blast_tac (!claset addSEs sees_Spy_partsEs |
208 |
delrules [conjI] (*no split-up into 4 subgoals*)) 1); |
|
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|
209 |
val lemma = result(); |
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|
210 |
|
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|
211 |
goal thy |
3543 | 212 |
"!!evs. [| Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set evs; \ |
213 |
\ Says Server B' {|NA',X',Crypt (shrK B') {|NB',K|}|} : set evs; \ |
|
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|
214 |
\ evs : otway |] ==> X=X' & B=B' & NA=NA' & NB=NB'"; |
2417 | 215 |
by (prove_unique_tac lemma 1); |
2014
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|
216 |
qed "unique_session_keys"; |
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|
217 |
|
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|
218 |
|
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|
219 |
|
2048 | 220 |
(**** Authenticity properties relating to NA ****) |
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|
221 |
|
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diff
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|
222 |
(*Only OR1 can have caused such a part of a message to appear.*) |
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diff
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|
223 |
goal thy |
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|
224 |
"!!evs. [| A ~: lost; evs : otway |] \ |
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|
225 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} \ |
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|
226 |
\ : parts (sees Spy evs) --> \ |
2064 | 227 |
\ Says A B {|NA, Agent A, Agent B, \ |
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|
228 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
3465 | 229 |
\ : set evs"; |
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|
230 |
by (parts_induct_tac 1); |
3121
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Conversion to use blast_tac (with other improvements)
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changeset
|
231 |
by (Fake_parts_insert_tac 1); |
2014
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changeset
|
232 |
qed_spec_mp "Crypt_imp_OR1"; |
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changeset
|
233 |
|
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|
234 |
|
2064 | 235 |
(** The Nonce NA uniquely identifies A's message. **) |
2014
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|
236 |
|
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|
237 |
goal thy |
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diff
changeset
|
238 |
"!!evs. [| evs : otway; A ~: lost |] \ |
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Changing "lost" from a parameter of protocol definitions to a constant.
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|
239 |
\ ==> EX B'. ALL B. \ |
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Changing "lost" from a parameter of protocol definitions to a constant.
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|
240 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (sees Spy evs) \ |
2048 | 241 |
\ --> B = B'"; |
3519
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changeset
|
242 |
by (parts_induct_tac 1); |
3121
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Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
243 |
by (Fake_parts_insert_tac 1); |
2064 | 244 |
by (simp_tac (!simpset addsimps [all_conj_distrib]) 1); |
2026
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Last working version prior to introduction of "lost"
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parents:
2014
diff
changeset
|
245 |
(*OR1: creation of new Nonce. Move assertion into global context*) |
2064 | 246 |
by (expand_case_tac "NA = ?y" 1); |
3102 | 247 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
2014
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1999
diff
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|
248 |
val lemma = result(); |
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|
249 |
|
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|
250 |
goal thy |
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parents:
3516
diff
changeset
|
251 |
"!!evs.[| Crypt (shrK A) {|NA, Agent A, Agent B|}: parts (sees Spy evs); \ |
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Changing "lost" from a parameter of protocol definitions to a constant.
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changeset
|
252 |
\ Crypt (shrK A) {|NA, Agent A, Agent C|}: parts (sees Spy evs); \ |
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Changing "lost" from a parameter of protocol definitions to a constant.
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changeset
|
253 |
\ evs : otway; A ~: lost |] \ |
2014
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Correction of protocol; addition of Reveal message; proofs of
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parents:
1999
diff
changeset
|
254 |
\ ==> B = C"; |
2417 | 255 |
by (prove_unique_tac lemma 1); |
2048 | 256 |
qed "unique_NA"; |
2014
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Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
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diff
changeset
|
257 |
|
5be4c8ca7b25
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changeset
|
258 |
|
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Correction of protocol; addition of Reveal message; proofs of
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parents:
1999
diff
changeset
|
259 |
(*It is impossible to re-use a nonce in both OR1 and OR2. This holds because |
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Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
260 |
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
|
261 |
over-simplified version of this protocol: see OtwayRees_Bad.*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
262 |
goal thy |
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
263 |
"!!evs. [| A ~: lost; evs : otway |] \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
264 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
265 |
\ : parts (sees Spy evs) --> \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
266 |
\ Crypt (shrK A) {|NA', NA, Agent A', Agent A|} \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
267 |
\ ~: parts (sees Spy evs)"; |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
268 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
269 |
by (Fake_parts_insert_tac 1); |
3102 | 270 |
by (REPEAT (blast_tac (!claset addSEs sees_Spy_partsEs |
271 |
addSDs [impOfSubs parts_insert_subset_Un]) 1)); |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
272 |
qed_spec_mp"no_nonce_OR1_OR2"; |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
273 |
|
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Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
274 |
|
2053 | 275 |
(*Crucial property: If the encrypted message appears, and A has used NA |
276 |
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
|
277 |
goal thy |
3543 | 278 |
"!!evs. [| A ~: lost; A ~= Spy; evs : otway |] \ |
279 |
\ ==> Crypt (shrK A) {|NA, Key K|} : parts (sees Spy evs) \ |
|
2048 | 280 |
\ --> 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
|
281 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
282 |
\ : set evs --> \ |
2048 | 283 |
\ (EX NB. Says Server B \ |
284 |
\ {|NA, \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
285 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
286 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 287 |
\ : set evs)"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
288 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
289 |
by (Fake_parts_insert_tac 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
290 |
(*OR1: it cannot be a new Nonce, contradiction.*) |
3102 | 291 |
by (blast_tac (!claset addSIs [parts_insertI] addSEs sees_Spy_partsEs) 1); |
2064 | 292 |
(*OR3 and OR4*) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
293 |
(*OR4*) |
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
294 |
by (REPEAT (Safe_step_tac 2)); |
3102 | 295 |
by (REPEAT (blast_tac (!claset addSDs [parts_cut]) 3)); |
3543 | 296 |
by (blast_tac (!claset addSIs [Crypt_imp_OR1] |
297 |
addEs sees_Spy_partsEs) 2); |
|
2064 | 298 |
(*OR3*) (** LEVEL 5 **) |
299 |
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
|
300 |
by (step_tac (!claset delrules [disjCI, impCE]) 1); |
3102 | 301 |
by (blast_tac (!claset addSEs [MPair_parts] |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
302 |
addSDs [Says_imp_sees_Spy RS parts.Inj] |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
303 |
addEs [no_nonce_OR1_OR2 RSN (2, rev_notE)] |
2048 | 304 |
delrules [conjI] (*stop split-up into 4 subgoals*)) 2); |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
305 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy RS parts.Inj] |
2048 | 306 |
addSEs [MPair_parts] |
3102 | 307 |
addIs [unique_NA]) 1); |
2048 | 308 |
qed_spec_mp "NA_Crypt_imp_Server_msg"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
309 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
310 |
|
2053 | 311 |
(*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
|
312 |
then the key really did come from the Server! CANNOT prove this of the |
2048 | 313 |
bad form of this protocol, even though we can prove |
2032 | 314 |
Spy_not_see_encrypted_key*) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
315 |
goal thy |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
316 |
"!!evs. [| Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
317 |
\ : set evs; \ |
2053 | 318 |
\ 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
|
319 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
320 |
\ : set evs; \ |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
321 |
\ A ~: lost; A ~= Spy; evs : otway |] \ |
2053 | 322 |
\ ==> EX NB. Says Server B \ |
2048 | 323 |
\ {|NA, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
324 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
325 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 326 |
\ : set evs"; |
3102 | 327 |
by (blast_tac (!claset addSIs [NA_Crypt_imp_Server_msg] |
328 |
addEs sees_Spy_partsEs) 1); |
|
2328 | 329 |
qed "A_trusts_OR4"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
330 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
331 |
|
2048 | 332 |
(** Crucial secrecy property: Spy does not see the keys sent in msg OR3 |
333 |
Does not in itself guarantee security: an attack could violate |
|
334 |
the premises, e.g. by having A=Spy **) |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
335 |
|
1941 | 336 |
goal thy |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
337 |
"!!evs. [| A ~: lost; B ~: lost; evs : otway |] \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
338 |
\ ==> Says Server B \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
339 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
340 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs --> \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
341 |
\ Says B Spy {|NA, NB, Key K|} ~: set evs --> \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
342 |
\ Key K ~: analz (sees Spy evs)"; |
2032 | 343 |
by (etac otway.induct 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
344 |
by analz_sees_tac; |
1964 | 345 |
by (ALLGOALS |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
346 |
(asm_simp_tac (!simpset addcongs [conj_cong] |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
347 |
addsimps [analz_insert_eq, not_parts_not_analz, |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
348 |
analz_insert_freshK] |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
349 |
setloop split_tac [expand_if]))); |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
350 |
(*Oops*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
351 |
by (blast_tac (!claset addSDs [unique_session_keys]) 4); |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
352 |
(*OR4*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
353 |
by (Blast_tac 3); |
1941 | 354 |
(*OR3*) |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
355 |
by (blast_tac (!claset addSEs sees_Spy_partsEs |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
356 |
addIs [impOfSubs analz_subset_parts]) 2); |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
357 |
(*Fake*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
358 |
by (spy_analz_tac 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
359 |
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
|
360 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
361 |
goal thy |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
362 |
"!!evs. [| Says Server B \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
363 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
364 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
365 |
\ Says B Spy {|NA, NB, Key K|} ~: set evs; \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
366 |
\ A ~: lost; B ~: lost; evs : otway |] \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
367 |
\ ==> Key K ~: analz (sees Spy evs)"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
368 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
3102 | 369 |
by (blast_tac (!claset addSEs [lemma]) 1); |
2032 | 370 |
qed "Spy_not_see_encrypted_key"; |
371 |
||
1945 | 372 |
|
2048 | 373 |
(**** Authenticity properties relating to NB ****) |
374 |
||
375 |
(*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
|
376 |
know anything about X: it does NOT have to have the right form.*) |
2048 | 377 |
goal thy |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
378 |
"!!evs. [| B ~: lost; evs : otway |] \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
379 |
\ ==> Crypt (shrK B) {|NA, NB, Agent A, Agent B|} \ |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
380 |
\ : parts (sees Spy evs) --> \ |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
381 |
\ (EX X. Says B Server \ |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
382 |
\ {|NA, Agent A, Agent B, X, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
383 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|} \ |
3465 | 384 |
\ : set evs)"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
385 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
386 |
by (Fake_parts_insert_tac 1); |
3102 | 387 |
by (ALLGOALS Blast_tac); |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
388 |
bind_thm ("Crypt_imp_OR2", result() RSN (2,rev_mp) RS exE); |
2048 | 389 |
|
390 |
||
391 |
(** The Nonce NB uniquely identifies B's message. **) |
|
392 |
||
393 |
goal thy |
|
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
394 |
"!!evs. [| evs : otway; B ~: lost |] \ |
2064 | 395 |
\ ==> EX NA' A'. ALL NA A. \ |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
396 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} : parts(sees Spy evs) \ |
2048 | 397 |
\ --> NA = NA' & A = A'"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
398 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
399 |
by (Fake_parts_insert_tac 1); |
2064 | 400 |
by (simp_tac (!simpset addsimps [all_conj_distrib]) 1); |
2048 | 401 |
(*OR2: creation of new Nonce. Move assertion into global context*) |
2064 | 402 |
by (expand_case_tac "NB = ?y" 1); |
3102 | 403 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
2048 | 404 |
val lemma = result(); |
405 |
||
406 |
goal thy |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
407 |
"!!evs.[| Crypt (shrK B) {|NA, NB, Agent A, Agent B|} \ |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
408 |
\ : parts(sees Spy evs); \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
409 |
\ Crypt (shrK B) {|NC, NB, Agent C, Agent B|} \ |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
410 |
\ : parts(sees Spy evs); \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
411 |
\ evs : otway; B ~: lost |] \ |
2048 | 412 |
\ ==> NC = NA & C = A"; |
2417 | 413 |
by (prove_unique_tac lemma 1); |
2048 | 414 |
qed "unique_NB"; |
415 |
||
416 |
||
417 |
(*If the encrypted message appears, and B has used Nonce NB, |
|
418 |
then it originated with the Server!*) |
|
419 |
goal thy |
|
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
420 |
"!!evs. [| B ~: lost; B ~= Spy; evs : otway |] \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
421 |
\ ==> Crypt (shrK B) {|NB, Key K|} : parts (sees Spy evs) \ |
2048 | 422 |
\ --> (ALL X'. Says B Server \ |
423 |
\ {|NA, Agent A, Agent B, X', \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
424 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
425 |
\ : set evs \ |
2048 | 426 |
\ --> Says Server B \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
427 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
428 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 429 |
\ : set evs)"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
430 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
3102
diff
changeset
|
431 |
by (Fake_parts_insert_tac 1); |
2048 | 432 |
(*OR1: it cannot be a new Nonce, contradiction.*) |
3102 | 433 |
by (blast_tac (!claset addSIs [parts_insertI] addSEs sees_Spy_partsEs) 1); |
2048 | 434 |
(*OR4*) |
3102 | 435 |
by (blast_tac (!claset addSEs [MPair_parts, Crypt_imp_OR2]) 2); |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
436 |
(*OR3*) |
2048 | 437 |
by (step_tac (!claset delrules [disjCI, impCE]) 1); |
3102 | 438 |
by (blast_tac (!claset delrules [conjI] (*stop split-up*)) 3); |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
439 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy RS parts.Inj] |
3102 | 440 |
addSEs [MPair_parts] |
441 |
addDs [unique_NB]) 2); |
|
442 |
by (blast_tac (!claset addSEs [MPair_parts, no_nonce_OR1_OR2 RSN (2, rev_notE)] |
|
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
443 |
addSDs [Says_imp_sees_Spy RS parts.Inj] |
3102 | 444 |
delrules [conjI, impCE] (*stop split-up*)) 1); |
2048 | 445 |
qed_spec_mp "NB_Crypt_imp_Server_msg"; |
446 |
||
447 |
||
448 |
(*Guarantee for B: if it gets a message with matching NB then the Server |
|
449 |
has sent the correct message.*) |
|
450 |
goal thy |
|
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
451 |
"!!evs. [| B ~: lost; B ~= Spy; evs : otway; \ |
2837
dee1c7f1f576
Trivial renamings (for consistency with CSFW papers)
paulson
parents:
2637
diff
changeset
|
452 |
\ Says S' B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
453 |
\ : set evs; \ |
2048 | 454 |
\ 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
|
455 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
456 |
\ : set evs |] \ |
2048 | 457 |
\ ==> Says Server B \ |
458 |
\ {|NA, \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
459 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
460 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 461 |
\ : set evs"; |
3102 | 462 |
by (blast_tac (!claset addSIs [NB_Crypt_imp_Server_msg] |
463 |
addSEs sees_Spy_partsEs) 1); |
|
2328 | 464 |
qed "B_trusts_OR3"; |
2048 | 465 |
|
466 |
||
2328 | 467 |
B_trusts_OR3 RS Spy_not_see_encrypted_key; |
2048 | 468 |
|
469 |
||
1945 | 470 |
goal thy |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
471 |
"!!evs. [| B ~: lost; evs : otway |] \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
472 |
\ ==> Says Server B \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
473 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
474 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs --> \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
475 |
\ (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
|
476 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \ |
3465 | 477 |
\ : set evs)"; |
2032 | 478 |
by (etac otway.induct 1); |
3102 | 479 |
by (ALLGOALS Asm_simp_tac); |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
480 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy RS parts.Inj] |
3102 | 481 |
addSEs [MPair_parts, Crypt_imp_OR2]) 3); |
482 |
by (ALLGOALS Blast_tac); |
|
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
483 |
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
|
484 |
|
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
485 |
|
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
486 |
(*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
|
487 |
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
|
488 |
strictly necessary for authentication.*) |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
489 |
goal thy |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
490 |
"!!evs. [| Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
491 |
\ Says A B {|NA, Agent A, Agent B, \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
492 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \ |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
493 |
\ A ~: lost; A ~= Spy; B ~: lost; evs : otway |] \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
494 |
\ ==> 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
|
495 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |}\ |
3465 | 496 |
\ : set evs"; |
3102 | 497 |
by (blast_tac (!claset addSDs [A_trusts_OR4] |
498 |
addSEs [OR3_imp_OR2]) 1); |
|
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
499 |
qed "A_auths_B"; |