author | paulson |
Fri, 22 Oct 1999 18:26:46 +0200 | |
changeset 7913 | 86be2946bb0b |
parent 7499 | 23e090051cb8 |
child 10833 | c0844a30ea4e |
permissions | -rw-r--r-- |
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1 |
(* Title: HOL/Auth/OtwayRees_AN |
2090 | 2 |
ID: $Id$ |
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
|
4 |
Copyright 1996 University of Cambridge |
|
5 |
||
6 |
Inductive relation "otway" for the Otway-Rees protocol. |
|
7 |
||
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Abadi-Needham version: minimal encryption, explicit messages |
2090 | 9 |
|
10 |
From page 11 of |
|
11 |
Abadi and Needham. Prudent Engineering Practice for Cryptographic Protocols. |
|
12 |
IEEE Trans. SE 22 (1), 1996 |
|
13 |
*) |
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14 |
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AddEs knows_Spy_partsEs; |
4470 | 16 |
AddDs [impOfSubs analz_subset_parts]; |
17 |
AddDs [impOfSubs Fake_parts_insert]; |
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18 |
||
2090 | 19 |
|
2331 | 20 |
(*A "possibility property": there are traces that reach the end*) |
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Goal "[| B ~= Server |] \ |
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\ ==> EX K. EX NA. EX evs: otway. \ |
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\ Says B A (Crypt (shrK A) {|Nonce NA, Agent A, Agent B, Key K|}) \ |
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\ : set evs"; |
2090 | 25 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
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26 |
by (rtac (otway.Nil RS |
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27 |
otway.OR1 RS otway.Reception RS |
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otway.OR2 RS otway.Reception RS |
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otway.OR3 RS otway.Reception RS otway.OR4) 2); |
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30 |
by possibility_tac; |
2090 | 31 |
result(); |
32 |
||
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Goal "[| Gets B X : set evs; evs : otway |] ==> EX A. Says A B X : set evs"; |
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34 |
by (etac rev_mp 1); |
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by (etac otway.induct 1); |
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by Auto_tac; |
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qed"Gets_imp_Says"; |
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38 |
|
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(*Must be proved separately for each protocol*) |
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Goal "[| Gets B X : set evs; evs : otway |] ==> X : knows Spy evs"; |
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by (blast_tac (claset() addSDs [Gets_imp_Says, Says_imp_knows_Spy]) 1); |
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qed"Gets_imp_knows_Spy"; |
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AddDs [Gets_imp_knows_Spy RS parts.Inj]; |
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2090 | 45 |
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(**** Inductive proofs about otway ****) |
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47 |
||
48 |
(** For reasoning about the encrypted portion of messages **) |
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49 |
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Goal "[| Gets B {|X, Crypt(shrK B) X'|} : set evs; evs : otway |] ==> \ |
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51 |
\ X : analz (knows Spy evs)"; |
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52 |
by (blast_tac (claset() addSDs [Gets_imp_knows_Spy RS analz.Inj]) 1); |
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qed "OR4_analz_knows_Spy"; |
2090 | 54 |
|
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Goal "Says Server B {|X, Crypt K' {|NB, a, Agent B, K|}|} : set evs \ |
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56 |
\ ==> K : parts (knows Spy evs)"; |
4470 | 57 |
by (Blast_tac 1); |
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58 |
qed "Oops_parts_knows_Spy"; |
2090 | 59 |
|
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bind_thm ("OR4_parts_knows_Spy", |
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61 |
OR4_analz_knows_Spy RS (impOfSubs analz_subset_parts)); |
2090 | 62 |
|
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63 |
(*For proving the easier theorems about X ~: parts (knows Spy evs).*) |
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64 |
fun parts_induct_tac i = |
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65 |
etac otway.induct i THEN |
7499 | 66 |
ftac Oops_parts_knows_Spy (i+7) THEN |
67 |
ftac OR4_parts_knows_Spy (i+6) THEN |
|
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prove_simple_subgoals_tac i; |
2090 | 69 |
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70 |
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71 |
(** Theorems of the form X ~: parts (knows Spy evs) imply that NOBODY |
2090 | 72 |
sends messages containing X! **) |
73 |
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(*Spy never sees a good agent's shared key!*) |
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75 |
Goal "evs : otway ==> (Key (shrK A) : parts (knows Spy evs)) = (A : bad)"; |
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76 |
by (parts_induct_tac 1); |
3961 | 77 |
by (ALLGOALS Blast_tac); |
2131 | 78 |
qed "Spy_see_shrK"; |
79 |
Addsimps [Spy_see_shrK]; |
|
2090 | 80 |
|
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81 |
Goal "evs : otway ==> (Key (shrK A) : analz (knows Spy evs)) = (A : bad)"; |
4091 | 82 |
by (auto_tac(claset() addDs [impOfSubs analz_subset_parts], simpset())); |
2131 | 83 |
qed "Spy_analz_shrK"; |
84 |
Addsimps [Spy_analz_shrK]; |
|
2090 | 85 |
|
4470 | 86 |
AddSDs [Spy_see_shrK RSN (2, rev_iffD1), |
87 |
Spy_analz_shrK RSN (2, rev_iffD1)]; |
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2090 | 88 |
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89 |
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(*Nobody can have used non-existent keys!*) |
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Goal "evs : otway ==> Key K ~: used evs --> K ~: keysFor (parts (knows Spy evs))"; |
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by (parts_induct_tac 1); |
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(*Fake*) |
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by (blast_tac (claset() addSDs [keysFor_parts_insert]) 1); |
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95 |
(*OR3*) |
3102 | 96 |
by (Blast_tac 1); |
2160 | 97 |
qed_spec_mp "new_keys_not_used"; |
2090 | 98 |
|
99 |
bind_thm ("new_keys_not_analzd", |
|
100 |
[analz_subset_parts RS keysFor_mono, |
|
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new_keys_not_used] MRS contra_subsetD); |
|
102 |
||
103 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
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104 |
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105 |
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106 |
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107 |
(*** Proofs involving analz ***) |
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108 |
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2131 | 109 |
(*Describes the form of K and NA when the Server sends this message.*) |
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110 |
Goal "[| Says Server B \ |
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\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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112 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
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113 |
\ : set evs; \ |
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\ evs : otway |] \ |
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\ ==> K ~: range shrK & (EX i. NA = Nonce i) & (EX j. NB = Nonce j)"; |
2131 | 116 |
by (etac rev_mp 1); |
117 |
by (etac otway.induct 1); |
|
3102 | 118 |
by (ALLGOALS Asm_simp_tac); |
119 |
by (Blast_tac 1); |
|
2131 | 120 |
qed "Says_Server_message_form"; |
2090 | 121 |
|
122 |
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123 |
(*For proofs involving analz.*) |
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124 |
val analz_knows_Spy_tac = |
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125 |
dtac OR4_analz_knows_Spy 7 THEN assume_tac 7 THEN |
7499 | 126 |
ftac Says_Server_message_form 8 THEN assume_tac 8 THEN |
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127 |
REPEAT ((eresolve_tac [exE, conjE] ORELSE' hyp_subst_tac) 8); |
2090 | 128 |
|
129 |
||
130 |
(**** |
|
131 |
The following is to prove theorems of the form |
|
132 |
||
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Key K : analz (insert (Key KAB) (knows Spy evs)) ==> |
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134 |
Key K : analz (knows Spy evs) |
2090 | 135 |
|
136 |
A more general formula must be proved inductively. |
|
137 |
****) |
|
138 |
||
139 |
||
140 |
(** Session keys are not used to encrypt other session keys **) |
|
141 |
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142 |
(*The equality makes the induction hypothesis easier to apply*) |
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143 |
Goal "evs : otway ==> \ |
5492 | 144 |
\ ALL K KK. KK <= -(range shrK) --> \ |
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145 |
\ (Key K : analz (Key``KK Un (knows Spy evs))) = \ |
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146 |
\ (K : KK | Key K : analz (knows Spy evs))"; |
2090 | 147 |
by (etac otway.induct 1); |
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148 |
by analz_knows_Spy_tac; |
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by (REPEAT_FIRST (resolve_tac [allI, impI])); |
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150 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
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151 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
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152 |
(*Fake*) |
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153 |
by (spy_analz_tac 1); |
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154 |
qed_spec_mp "analz_image_freshK"; |
2090 | 155 |
|
156 |
||
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157 |
Goal "[| evs : otway; KAB ~: range shrK |] ==> \ |
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158 |
\ Key K : analz (insert (Key KAB) (knows Spy evs)) = \ |
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159 |
\ (K = KAB | Key K : analz (knows Spy evs))"; |
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160 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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161 |
qed "analz_insert_freshK"; |
2090 | 162 |
|
163 |
||
4155 | 164 |
(*** The Key K uniquely identifies the Server's message. **) |
2090 | 165 |
|
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166 |
Goal "evs : otway ==> \ |
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167 |
\ EX A' B' NA' NB'. ALL A B NA NB. \ |
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168 |
\ Says Server B \ |
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169 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, K|}, \ |
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170 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, K|}|} : set evs \ |
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171 |
\ --> A=A' & B=B' & NA=NA' & NB=NB'"; |
2090 | 172 |
by (etac otway.induct 1); |
4091 | 173 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
3730 | 174 |
by (ALLGOALS Clarify_tac); |
2090 | 175 |
(*Remaining cases: OR3 and OR4*) |
176 |
by (ex_strip_tac 2); |
|
3102 | 177 |
by (Blast_tac 2); |
2090 | 178 |
by (expand_case_tac "K = ?y" 1); |
179 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
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180 |
(*...we assume X is a recent message and handle this case by contradiction*) |
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181 |
by (blast_tac (claset() addSEs knows_Spy_partsEs) 1); |
2090 | 182 |
val lemma = result(); |
183 |
||
184 |
||
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185 |
Goal "[| Says Server B \ |
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186 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, K|}, \ |
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187 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, K|}|} \ |
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188 |
\ : set evs; \ |
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189 |
\ Says Server B' \ |
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190 |
\ {|Crypt (shrK A') {|NA', Agent A', Agent B', K|}, \ |
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191 |
\ Crypt (shrK B') {|NB', Agent A', Agent B', K|}|} \ |
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192 |
\ : set evs; \ |
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193 |
\ evs : otway |] \ |
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194 |
\ ==> A=A' & B=B' & NA=NA' & NB=NB'"; |
2417 | 195 |
by (prove_unique_tac lemma 1); |
2090 | 196 |
qed "unique_session_keys"; |
197 |
||
198 |
||
199 |
||
200 |
(**** Authenticity properties relating to NA ****) |
|
201 |
||
202 |
(*If the encrypted message appears then it originated with the Server!*) |
|
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203 |
Goal "[| A ~: bad; A ~= B; evs : otway |] \ |
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204 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B, Key K|} : parts (knows Spy evs) \ |
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205 |
\ --> (EX NB. Says Server B \ |
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206 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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207 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
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208 |
\ : set evs)"; |
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209 |
by (parts_induct_tac 1); |
4470 | 210 |
by (Blast_tac 1); |
4091 | 211 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [ex_disj_distrib]))); |
2090 | 212 |
(*OR3*) |
3102 | 213 |
by (Blast_tac 1); |
2090 | 214 |
qed_spec_mp "NA_Crypt_imp_Server_msg"; |
215 |
||
216 |
||
2454 | 217 |
(*Corollary: if A receives B's OR4 message then it originated with the Server. |
218 |
Freshness may be inferred from nonce NA.*) |
|
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219 |
Goal "[| Gets A (Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}) \ |
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220 |
\ : set evs; \ |
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221 |
\ A ~: bad; A ~= B; evs : otway |] \ |
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222 |
\ ==> EX NB. Says Server B \ |
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223 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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224 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
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225 |
\ : set evs"; |
4470 | 226 |
by (blast_tac (claset() addSIs [NA_Crypt_imp_Server_msg]) 1); |
2331 | 227 |
qed "A_trusts_OR4"; |
2090 | 228 |
|
229 |
||
230 |
(** Crucial secrecy property: Spy does not see the keys sent in msg OR3 |
|
231 |
Does not in itself guarantee security: an attack could violate |
|
232 |
the premises, e.g. by having A=Spy **) |
|
233 |
||
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234 |
Goal "[| A ~: bad; B ~: bad; evs : otway |] \ |
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235 |
\ ==> Says Server B \ |
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236 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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237 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
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238 |
\ : set evs --> \ |
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239 |
\ Notes Spy {|NA, NB, Key K|} ~: set evs --> \ |
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240 |
\ Key K ~: analz (knows Spy evs)"; |
2090 | 241 |
by (etac otway.induct 1); |
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242 |
by analz_knows_Spy_tac; |
2090 | 243 |
by (ALLGOALS |
6915 | 244 |
(asm_simp_tac (simpset() addcongs [conj_cong] |
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245 |
addsimps [analz_insert_eq, analz_insert_freshK] |
5535 | 246 |
@ pushes @ split_ifs))); |
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247 |
(*Oops*) |
4091 | 248 |
by (blast_tac (claset() addSDs [unique_session_keys]) 4); |
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249 |
(*OR4*) |
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250 |
by (Blast_tac 3); |
2090 | 251 |
(*OR3*) |
4470 | 252 |
by (Blast_tac 2); |
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253 |
(*Fake*) |
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254 |
by (spy_analz_tac 1); |
2090 | 255 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
256 |
||
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257 |
Goal "[| Says Server B \ |
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258 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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259 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
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260 |
\ : set evs; \ |
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261 |
\ Notes Spy {|NA, NB, Key K|} ~: set evs; \ |
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262 |
\ A ~: bad; B ~: bad; evs : otway |] \ |
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|
263 |
\ ==> Key K ~: analz (knows Spy evs)"; |
7499 | 264 |
by (ftac Says_Server_message_form 1 THEN assume_tac 1); |
4091 | 265 |
by (blast_tac (claset() addSEs [lemma]) 1); |
2090 | 266 |
qed "Spy_not_see_encrypted_key"; |
267 |
||
268 |
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269 |
(*A's guarantee. The Oops premise quantifies over NB because A cannot know |
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|
270 |
what it is.*) |
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|
271 |
Goal "[| Gets A (Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}) \ |
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272 |
\ : set evs; \ |
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273 |
\ ALL NB. Notes Spy {|NA, NB, Key K|} ~: set evs; \ |
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|
274 |
\ A ~: bad; B ~: bad; A ~= B; evs : otway |] \ |
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|
275 |
\ ==> Key K ~: analz (knows Spy evs)"; |
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|
276 |
by (blast_tac (claset() addSDs [A_trusts_OR4, Spy_not_see_encrypted_key]) 1); |
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|
277 |
qed "A_gets_good_key"; |
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|
278 |
|
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279 |
|
2090 | 280 |
(**** Authenticity properties relating to NB ****) |
281 |
||
282 |
(*If the encrypted message appears then it originated with the Server!*) |
|
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283 |
Goal "[| B ~: bad; A ~= B; evs : otway |] \ |
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|
284 |
\ ==> Crypt (shrK B) {|NB, Agent A, Agent B, Key K|} : parts (knows Spy evs) \ |
5114
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285 |
\ --> (EX NA. Says Server B \ |
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|
286 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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|
287 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
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|
288 |
\ : set evs)"; |
3519
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|
289 |
by (parts_induct_tac 1); |
4470 | 290 |
by (Blast_tac 1); |
4091 | 291 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [ex_disj_distrib]))); |
2090 | 292 |
(*OR3*) |
3102 | 293 |
by (Blast_tac 1); |
2090 | 294 |
qed_spec_mp "NB_Crypt_imp_Server_msg"; |
295 |
||
296 |
||
2454 | 297 |
(*Guarantee for B: if it gets a well-formed certificate then the Server |
298 |
has sent the correct message in round 3.*) |
|
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|
299 |
Goal "[| Gets B {|X, Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
5114
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|
300 |
\ : set evs; \ |
5434
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|
301 |
\ B ~: bad; A ~= B; evs : otway |] \ |
5114
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|
302 |
\ ==> EX NA. Says Server B \ |
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|
303 |
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \ |
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|
304 |
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
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|
305 |
\ : set evs"; |
4470 | 306 |
by (blast_tac (claset() addSIs [NB_Crypt_imp_Server_msg]) 1); |
2331 | 307 |
qed "B_trusts_OR3"; |
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|
308 |
|
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|
309 |
|
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|
310 |
(*The obvious combination of B_trusts_OR3 with Spy_not_see_encrypted_key*) |
6308
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|
311 |
Goal "[| Gets B {|X, Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \ |
5434
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|
312 |
\ : set evs; \ |
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|
313 |
\ ALL NA. Notes Spy {|NA, NB, Key K|} ~: set evs; \ |
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|
314 |
\ A ~: bad; B ~: bad; A ~= B; evs : otway |] \ |
6308
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Added Bella's "Gets" model for Otway_Rees. Also affects some other theories.
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|
315 |
\ ==> Key K ~: analz (knows Spy evs)"; |
4598
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Added some more explicit guarantees of key secrecy for agents
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|
316 |
by (blast_tac (claset() addDs [B_trusts_OR3, Spy_not_see_encrypted_key]) 1); |
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Added some more explicit guarantees of key secrecy for agents
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|
317 |
qed "B_gets_good_key"; |