author | paulson |
Thu, 05 Feb 1998 10:38:34 +0100 | |
changeset 4598 | 649bf14debe7 |
parent 4537 | 4e835bd9fada |
child 4831 | dae4d63a1318 |
permissions | -rw-r--r-- |
1941 | 1 |
(* Title: HOL/Auth/OtwayRees |
2 |
ID: $Id$ |
|
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
|
4 |
Copyright 1996 University of Cambridge |
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5 |
||
6 |
Inductive relation "otway" for the Otway-Rees protocol. |
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7 |
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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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14 |
||
15 |
open OtwayRees; |
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||
4449 | 17 |
set proof_timing; |
1941 | 18 |
HOL_quantifiers := false; |
19 |
||
4470 | 20 |
AddEs spies_partsEs; |
21 |
AddDs [impOfSubs analz_subset_parts]; |
|
22 |
AddDs [impOfSubs Fake_parts_insert]; |
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23 |
||
1996
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Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
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24 |
|
2328 | 25 |
(*A "possibility property": there are traces that reach the end*) |
1996
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goal thy |
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"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
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\ ==> EX K. EX NA. EX evs: otway. \ |
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\ Says B A {|Nonce NA, Crypt (shrK A) {|Nonce NA, Key K|}|} \ |
3465 | 30 |
\ : set evs"; |
1996
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31 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
2032 | 32 |
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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result(); |
1996
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Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
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35 |
|
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36 |
|
1941 | 37 |
(**** Inductive proofs about otway ****) |
38 |
||
39 |
(*Nobody sends themselves messages*) |
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goal thy "!!evs. evs : otway ==> ALL A X. Says A A X ~: set evs"; |
2032 | 41 |
by (etac otway.induct 1); |
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by Auto_tac; |
1941 | 43 |
qed_spec_mp "not_Says_to_self"; |
44 |
Addsimps [not_Says_to_self]; |
|
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AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
|
46 |
||
47 |
||
48 |
(** For reasoning about the encrypted portion of messages **) |
|
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||
3465 | 50 |
goal thy "!!evs. Says A' B {|N, Agent A, Agent B, X|} : set evs \ |
3683 | 51 |
\ ==> X : analz (spies evs)"; |
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52 |
by (dtac (Says_imp_spies RS analz.Inj) 1); |
4470 | 53 |
by (Blast_tac 1); |
3683 | 54 |
qed "OR2_analz_spies"; |
1941 | 55 |
|
3465 | 56 |
goal thy "!!evs. Says S' B {|N, X, Crypt (shrK B) X'|} : set evs \ |
3683 | 57 |
\ ==> X : analz (spies evs)"; |
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by (dtac (Says_imp_spies RS analz.Inj) 1); |
4470 | 59 |
by (Blast_tac 1); |
3683 | 60 |
qed "OR4_analz_spies"; |
1941 | 61 |
|
3465 | 62 |
goal thy "!!evs. Says Server B {|NA, X, Crypt K' {|NB,K|}|} : set evs \ |
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\ ==> K : parts (spies evs)"; |
4470 | 64 |
by (Blast_tac 1); |
3683 | 65 |
qed "Oops_parts_spies"; |
1941 | 66 |
|
3683 | 67 |
bind_thm ("OR2_parts_spies", |
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OR2_analz_spies RS (impOfSubs analz_subset_parts)); |
|
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bind_thm ("OR4_parts_spies", |
|
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OR4_analz_spies RS (impOfSubs analz_subset_parts)); |
|
2032 | 71 |
|
3683 | 72 |
(*For proving the easier theorems about X ~: parts (spies evs).*) |
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73 |
fun parts_induct_tac i = |
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74 |
etac otway.induct i THEN |
3683 | 75 |
forward_tac [Oops_parts_spies] (i+6) THEN |
76 |
forward_tac [OR4_parts_spies] (i+5) THEN |
|
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forward_tac [OR2_parts_spies] (i+3) THEN |
|
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78 |
prove_simple_subgoals_tac i; |
1941 | 79 |
|
80 |
||
3683 | 81 |
(** Theorems of the form X ~: parts (spies evs) imply that NOBODY |
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82 |
sends messages containing X! **) |
1941 | 83 |
|
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84 |
(*Spy never sees a good agent's shared key!*) |
1941 | 85 |
goal thy |
3683 | 86 |
"!!evs. evs : otway ==> (Key (shrK A) : parts (spies evs)) = (A : bad)"; |
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87 |
by (parts_induct_tac 1); |
3961 | 88 |
by (ALLGOALS Blast_tac); |
2135 | 89 |
qed "Spy_see_shrK"; |
90 |
Addsimps [Spy_see_shrK]; |
|
1941 | 91 |
|
2135 | 92 |
goal thy |
3683 | 93 |
"!!evs. evs : otway ==> (Key (shrK A) : analz (spies evs)) = (A : bad)"; |
4091 | 94 |
by (auto_tac(claset() addDs [impOfSubs analz_subset_parts], simpset())); |
2135 | 95 |
qed "Spy_analz_shrK"; |
96 |
Addsimps [Spy_analz_shrK]; |
|
1941 | 97 |
|
4470 | 98 |
AddSDs [Spy_see_shrK RSN (2, rev_iffD1), |
99 |
Spy_analz_shrK RSN (2, rev_iffD1)]; |
|
1941 | 100 |
|
101 |
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102 |
(*Nobody can have used non-existent keys!*) |
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103 |
goal thy "!!evs. evs : otway ==> \ |
3683 | 104 |
\ Key K ~: used evs --> K ~: keysFor (parts (spies evs))"; |
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105 |
by (parts_induct_tac 1); |
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106 |
(*Fake*) |
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107 |
by (blast_tac (claset() addSDs [keysFor_parts_insert]) 1); |
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108 |
(*OR2, OR3*) |
3102 | 109 |
by (ALLGOALS Blast_tac); |
2160 | 110 |
qed_spec_mp "new_keys_not_used"; |
1941 | 111 |
|
112 |
bind_thm ("new_keys_not_analzd", |
|
2032 | 113 |
[analz_subset_parts RS keysFor_mono, |
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new_keys_not_used] MRS contra_subsetD); |
|
1941 | 115 |
|
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Addsimps [new_keys_not_used, new_keys_not_analzd]; |
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117 |
||
118 |
||
2064 | 119 |
|
120 |
(*** Proofs involving analz ***) |
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121 |
||
2135 | 122 |
(*Describes the form of K and NA when the Server sends this message. Also |
123 |
for Oops case.*) |
|
2064 | 124 |
goal thy |
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125 |
"!!evs. [| Says Server B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
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126 |
\ evs : otway |] \ |
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127 |
\ ==> K ~: range shrK & (EX i. NA = Nonce i) & (EX j. NB = Nonce j)"; |
2135 | 128 |
by (etac rev_mp 1); |
129 |
by (etac otway.induct 1); |
|
3102 | 130 |
by (ALLGOALS Simp_tac); |
131 |
by (ALLGOALS Blast_tac); |
|
2135 | 132 |
qed "Says_Server_message_form"; |
2064 | 133 |
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134 |
||
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135 |
(*For proofs involving analz.*) |
3683 | 136 |
val analz_spies_tac = |
137 |
dtac OR2_analz_spies 4 THEN |
|
138 |
dtac OR4_analz_spies 6 THEN |
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139 |
forward_tac [Says_Server_message_form] 7 THEN assume_tac 7 THEN |
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140 |
REPEAT ((eresolve_tac [exE, conjE] ORELSE' hyp_subst_tac) 7); |
1941 | 141 |
|
142 |
||
143 |
(**** |
|
144 |
The following is to prove theorems of the form |
|
145 |
||
3683 | 146 |
Key K : analz (insert (Key KAB) (spies evs)) ==> |
147 |
Key K : analz (spies evs) |
|
1941 | 148 |
|
149 |
A more general formula must be proved inductively. |
|
150 |
****) |
|
151 |
||
152 |
||
153 |
(** Session keys are not used to encrypt other session keys **) |
|
154 |
||
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155 |
(*The equality makes the induction hypothesis easier to apply*) |
1941 | 156 |
goal thy |
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157 |
"!!evs. evs : otway ==> \ |
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158 |
\ ALL K KK. KK <= Compl (range shrK) --> \ |
3683 | 159 |
\ (Key K : analz (Key``KK Un (spies evs))) = \ |
160 |
\ (K : KK | Key K : analz (spies evs))"; |
|
2032 | 161 |
by (etac otway.induct 1); |
3683 | 162 |
by analz_spies_tac; |
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163 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
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164 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
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|
165 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
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166 |
(*Fake*) |
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167 |
by (spy_analz_tac 1); |
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168 |
qed_spec_mp "analz_image_freshK"; |
1941 | 169 |
|
170 |
||
171 |
goal thy |
|
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172 |
"!!evs. [| evs : otway; KAB ~: range shrK |] ==> \ |
3683 | 173 |
\ Key K : analz (insert (Key KAB) (spies evs)) = \ |
174 |
\ (K = KAB | Key K : analz (spies evs))"; |
|
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|
175 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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176 |
qed "analz_insert_freshK"; |
1941 | 177 |
|
178 |
||
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179 |
(*** The Key K uniquely identifies the Server's message. **) |
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180 |
|
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181 |
goal thy |
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182 |
"!!evs. evs : otway ==> \ |
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183 |
\ EX B' NA' NB' X'. ALL B NA NB X. \ |
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|
184 |
\ Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set evs --> \ |
2135 | 185 |
\ B=B' & NA=NA' & NB=NB' & X=X'"; |
2032 | 186 |
by (etac otway.induct 1); |
4091 | 187 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
3730 | 188 |
by (ALLGOALS Clarify_tac); |
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189 |
(*Remaining cases: OR3 and OR4*) |
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190 |
by (ex_strip_tac 2); |
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191 |
by (Best_tac 2); (*Blast_tac's too slow (in reconstruction)*) |
2064 | 192 |
by (expand_case_tac "K = ?y" 1); |
193 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
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194 |
(*...we assume X is a recent message, and handle this case by contradiction*) |
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|
195 |
by (blast_tac (claset() addSEs spies_partsEs) 1); |
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196 |
val lemma = result(); |
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197 |
|
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198 |
goal thy |
3543 | 199 |
"!!evs. [| Says Server B {|NA, X, Crypt (shrK B) {|NB, K|}|} : set evs; \ |
200 |
\ Says Server B' {|NA',X',Crypt (shrK B') {|NB',K|}|} : set evs; \ |
|
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201 |
\ evs : otway |] ==> X=X' & B=B' & NA=NA' & NB=NB'"; |
2417 | 202 |
by (prove_unique_tac lemma 1); |
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203 |
qed "unique_session_keys"; |
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204 |
|
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205 |
|
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206 |
|
2048 | 207 |
(**** Authenticity properties relating to NA ****) |
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208 |
|
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209 |
(*Only OR1 can have caused such a part of a message to appear.*) |
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210 |
goal thy |
3683 | 211 |
"!!evs. [| A ~: bad; evs : otway |] \ |
212 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (spies evs) --> \ |
|
2064 | 213 |
\ Says A B {|NA, Agent A, Agent B, \ |
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|
214 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
3465 | 215 |
\ : set evs"; |
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|
216 |
by (parts_induct_tac 1); |
4470 | 217 |
by (Blast_tac 1); |
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|
218 |
qed_spec_mp "Crypt_imp_OR1"; |
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|
219 |
|
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|
220 |
|
2064 | 221 |
(** The Nonce NA uniquely identifies A's message. **) |
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|
222 |
|
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|
223 |
goal thy |
3683 | 224 |
"!!evs. [| evs : otway; A ~: bad |] \ |
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|
225 |
\ ==> EX B'. ALL B. \ |
3683 | 226 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (spies evs) \ |
2048 | 227 |
\ --> B = B'"; |
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|
228 |
by (parts_induct_tac 1); |
4470 | 229 |
by (Blast_tac 1); |
4091 | 230 |
by (simp_tac (simpset() addsimps [all_conj_distrib]) 1); |
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|
231 |
(*OR1: creation of new Nonce. Move assertion into global context*) |
2064 | 232 |
by (expand_case_tac "NA = ?y" 1); |
4470 | 233 |
by (Blast_tac 1); |
2014
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|
234 |
val lemma = result(); |
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|
235 |
|
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|
236 |
goal thy |
3683 | 237 |
"!!evs.[| Crypt (shrK A) {|NA, Agent A, Agent B|}: parts (spies evs); \ |
238 |
\ Crypt (shrK A) {|NA, Agent A, Agent C|}: parts (spies evs); \ |
|
239 |
\ evs : otway; A ~: bad |] \ |
|
2014
5be4c8ca7b25
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|
240 |
\ ==> B = C"; |
2417 | 241 |
by (prove_unique_tac lemma 1); |
2048 | 242 |
qed "unique_NA"; |
2014
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|
243 |
|
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changeset
|
244 |
|
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diff
changeset
|
245 |
(*It is impossible to re-use a nonce in both OR1 and OR2. This holds because |
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diff
changeset
|
246 |
OR2 encrypts Nonce NB. It prevents the attack that can occur in the |
5be4c8ca7b25
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diff
changeset
|
247 |
over-simplified version of this protocol: see OtwayRees_Bad.*) |
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diff
changeset
|
248 |
goal thy |
3683 | 249 |
"!!evs. [| A ~: bad; evs : otway |] \ |
250 |
\ ==> Crypt (shrK A) {|NA, Agent A, Agent B|} : parts (spies evs) --> \ |
|
3519
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|
251 |
\ Crypt (shrK A) {|NA', NA, Agent A', Agent A|} \ |
3683 | 252 |
\ ~: parts (spies evs)"; |
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Changing "lost" from a parameter of protocol definitions to a constant.
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|
253 |
by (parts_induct_tac 1); |
4470 | 254 |
by (ALLGOALS Blast_tac); |
2014
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Correction of protocol; addition of Reveal message; proofs of
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parents:
1999
diff
changeset
|
255 |
qed_spec_mp"no_nonce_OR1_OR2"; |
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Correction of protocol; addition of Reveal message; proofs of
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parents:
1999
diff
changeset
|
256 |
|
4470 | 257 |
val nonce_OR1_OR2_E = no_nonce_OR1_OR2 RSN (2, rev_notE); |
2014
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parents:
1999
diff
changeset
|
258 |
|
2053 | 259 |
(*Crucial property: If the encrypted message appears, and A has used NA |
260 |
to start a run, then it originated with the Server!*) |
|
2014
5be4c8ca7b25
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1999
diff
changeset
|
261 |
goal thy |
4598
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paulson
parents:
4537
diff
changeset
|
262 |
"!!evs. [| A ~: bad; evs : otway |] \ |
3683 | 263 |
\ ==> Crypt (shrK A) {|NA, Key K|} : parts (spies evs) \ |
2048 | 264 |
\ --> Says A B {|NA, Agent A, Agent B, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
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2264
diff
changeset
|
265 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
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3465
diff
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|
266 |
\ : set evs --> \ |
2048 | 267 |
\ (EX NB. Says Server B \ |
268 |
\ {|NA, \ |
|
2284
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|
269 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
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diff
changeset
|
270 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 271 |
\ : set evs)"; |
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
paulson
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diff
changeset
|
272 |
by (parts_induct_tac 1); |
4470 | 273 |
by (Blast_tac 1); |
2014
5be4c8ca7b25
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paulson
parents:
1999
diff
changeset
|
274 |
(*OR1: it cannot be a new Nonce, contradiction.*) |
4470 | 275 |
by (Blast_tac 1); |
3730 | 276 |
(*OR3 and OR4*) |
4091 | 277 |
by (asm_simp_tac (simpset() addsimps [ex_disj_distrib]) 1); |
3730 | 278 |
by (rtac conjI 1); |
279 |
by (ALLGOALS Clarify_tac); |
|
280 |
(*OR4*) |
|
4470 | 281 |
by (blast_tac (claset() addSIs [Crypt_imp_OR1]) 3); |
282 |
(*OR3, two cases*) (** LEVEL 7 **) |
|
283 |
by (blast_tac (claset() addSEs [nonce_OR1_OR2_E] |
|
284 |
delrules [conjI] (*stop split-up into 4 subgoals*)) 2); |
|
285 |
by (blast_tac (claset() addIs [unique_NA]) 1); |
|
2048 | 286 |
qed_spec_mp "NA_Crypt_imp_Server_msg"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
287 |
|
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paulson
parents:
1999
diff
changeset
|
288 |
|
2053 | 289 |
(*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
|
290 |
then the key really did come from the Server! CANNOT prove this of the |
2048 | 291 |
bad form of this protocol, even though we can prove |
2032 | 292 |
Spy_not_see_encrypted_key*) |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
293 |
goal thy |
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
294 |
"!!evs. [| Says A B {|NA, Agent A, Agent B, \ |
3683 | 295 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \ |
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
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diff
changeset
|
296 |
\ Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} : set evs; \ |
649bf14debe7
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changeset
|
297 |
\ A ~: bad; evs : otway |] \ |
2053 | 298 |
\ ==> EX NB. Says Server B \ |
2048 | 299 |
\ {|NA, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
300 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
301 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 302 |
\ : set evs"; |
4470 | 303 |
by (blast_tac (claset() addSIs [NA_Crypt_imp_Server_msg]) 1); |
2328 | 304 |
qed "A_trusts_OR4"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
305 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
306 |
|
2048 | 307 |
(** Crucial secrecy property: Spy does not see the keys sent in msg OR3 |
308 |
Does not in itself guarantee security: an attack could violate |
|
309 |
the premises, e.g. by having A=Spy **) |
|
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
310 |
|
1941 | 311 |
goal thy |
4537
4e835bd9fada
Expressed most Oops rules using Notes instead of Says, and other tidying
paulson
parents:
4509
diff
changeset
|
312 |
"!!evs. [| A ~: bad; B ~: bad; evs : otway |] \ |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
313 |
\ ==> Says Server B \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
314 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
315 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs --> \ |
4537
4e835bd9fada
Expressed most Oops rules using Notes instead of Says, and other tidying
paulson
parents:
4509
diff
changeset
|
316 |
\ Notes Spy {|NA, NB, Key K|} ~: set evs --> \ |
3683 | 317 |
\ Key K ~: analz (spies evs)"; |
2032 | 318 |
by (etac otway.induct 1); |
3683 | 319 |
by analz_spies_tac; |
1964 | 320 |
by (ALLGOALS |
4091 | 321 |
(asm_simp_tac (simpset() addcongs [conj_cong] |
4509
828148415197
Making proofs faster, especially using keysFor_parts_insert
paulson
parents:
4477
diff
changeset
|
322 |
addsimps [analz_insert_eq, analz_insert_freshK] |
828148415197
Making proofs faster, especially using keysFor_parts_insert
paulson
parents:
4477
diff
changeset
|
323 |
addsimps (pushes@expand_ifs)))); |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
324 |
(*Oops*) |
4091 | 325 |
by (blast_tac (claset() addSDs [unique_session_keys]) 4); |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
326 |
(*OR4*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
327 |
by (Blast_tac 3); |
1941 | 328 |
(*OR3*) |
4470 | 329 |
by (Blast_tac 2); |
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
330 |
(*Fake*) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3207
diff
changeset
|
331 |
by (spy_analz_tac 1); |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
332 |
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
|
333 |
|
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
334 |
goal thy |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
335 |
"!!evs. [| Says Server B \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
336 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
337 |
\ Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
4537
4e835bd9fada
Expressed most Oops rules using Notes instead of Says, and other tidying
paulson
parents:
4509
diff
changeset
|
338 |
\ Notes Spy {|NA, NB, Key K|} ~: set evs; \ |
4e835bd9fada
Expressed most Oops rules using Notes instead of Says, and other tidying
paulson
parents:
4509
diff
changeset
|
339 |
\ A ~: bad; B ~: bad; evs : otway |] \ |
3683 | 340 |
\ ==> Key K ~: analz (spies evs)"; |
2014
5be4c8ca7b25
Correction of protocol; addition of Reveal message; proofs of
paulson
parents:
1999
diff
changeset
|
341 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
4091 | 342 |
by (blast_tac (claset() addSEs [lemma]) 1); |
2032 | 343 |
qed "Spy_not_see_encrypted_key"; |
344 |
||
1945 | 345 |
|
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
346 |
(*A's guarantee. The Oops premise quantifies over NB because A cannot know |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
347 |
what it is.*) |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
348 |
goal thy |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
349 |
"!!evs. [| Says A B {|NA, Agent A, Agent B, \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
350 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
351 |
\ Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} : set evs; \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
352 |
\ ALL NB. Notes Spy {|NA, NB, Key K|} ~: set evs; \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
353 |
\ A ~: bad; B ~: bad; evs : otway |] \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
354 |
\ ==> Key K ~: analz (spies evs)"; |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
355 |
by (blast_tac (claset() addSDs [A_trusts_OR4, Spy_not_see_encrypted_key]) 1); |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
356 |
qed "A_gets_good_key"; |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
357 |
|
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
358 |
|
2048 | 359 |
(**** Authenticity properties relating to NB ****) |
360 |
||
361 |
(*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
|
362 |
know anything about X: it does NOT have to have the right form.*) |
2048 | 363 |
goal thy |
3683 | 364 |
"!!evs. [| B ~: bad; evs : otway |] \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
365 |
\ ==> Crypt (shrK B) {|NA, NB, Agent A, Agent B|} \ |
3683 | 366 |
\ : parts (spies evs) --> \ |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
367 |
\ (EX X. Says B Server \ |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
368 |
\ {|NA, Agent A, Agent B, X, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
369 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|}|} \ |
3465 | 370 |
\ : set evs)"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
371 |
by (parts_induct_tac 1); |
3102 | 372 |
by (ALLGOALS Blast_tac); |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
373 |
bind_thm ("Crypt_imp_OR2", result() RSN (2,rev_mp) RS exE); |
2048 | 374 |
|
375 |
||
376 |
(** The Nonce NB uniquely identifies B's message. **) |
|
377 |
||
378 |
goal thy |
|
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
379 |
"!!evs. [| evs : otway; B ~: bad |] \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
380 |
\ ==> EX NA' A'. ALL NA A. \ |
3683 | 381 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} : parts(spies evs) \ |
2048 | 382 |
\ --> NA = NA' & A = A'"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
383 |
by (parts_induct_tac 1); |
4470 | 384 |
by (Blast_tac 1); |
4091 | 385 |
by (simp_tac (simpset() addsimps [all_conj_distrib]) 1); |
2048 | 386 |
(*OR2: creation of new Nonce. Move assertion into global context*) |
2064 | 387 |
by (expand_case_tac "NB = ?y" 1); |
4470 | 388 |
by (Blast_tac 1); |
2048 | 389 |
val lemma = result(); |
390 |
||
391 |
goal thy |
|
3683 | 392 |
"!!evs.[| Crypt (shrK B) {|NA, NB, Agent A, Agent B|} : parts(spies evs); \ |
393 |
\ Crypt (shrK B) {|NC, NB, Agent C, Agent B|} : parts(spies evs); \ |
|
394 |
\ evs : otway; B ~: bad |] \ |
|
2048 | 395 |
\ ==> NC = NA & C = A"; |
2417 | 396 |
by (prove_unique_tac lemma 1); |
2048 | 397 |
qed "unique_NB"; |
398 |
||
399 |
||
400 |
(*If the encrypted message appears, and B has used Nonce NB, |
|
401 |
then it originated with the Server!*) |
|
402 |
goal thy |
|
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
403 |
"!!evs. [| B ~: bad; evs : otway |] \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
404 |
\ ==> Crypt (shrK B) {|NB, Key K|} : parts (spies evs) \ |
2048 | 405 |
\ --> (ALL X'. Says B Server \ |
406 |
\ {|NA, Agent A, Agent B, X', \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
407 |
\ 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
|
408 |
\ : set evs \ |
2048 | 409 |
\ --> Says Server B \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
410 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
411 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 412 |
\ : set evs)"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
413 |
by (parts_induct_tac 1); |
4470 | 414 |
by (Blast_tac 1); |
2048 | 415 |
(*OR1: it cannot be a new Nonce, contradiction.*) |
4470 | 416 |
by (Blast_tac 1); |
2048 | 417 |
(*OR4*) |
4470 | 418 |
by (blast_tac (claset() addSEs [Crypt_imp_OR2]) 2); |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
419 |
(*OR3*) |
4470 | 420 |
(*Provable in 38s by the single command |
421 |
by (blast_tac (claset() addDs [unique_NB] addEs[nonce_OR1_OR2_E]) 1); |
|
422 |
*) |
|
4091 | 423 |
by (safe_tac (claset() delrules [disjCI, impCE])); |
4470 | 424 |
by (Blast_tac 3); |
425 |
by (blast_tac (claset() addDs [unique_NB]) 2); |
|
426 |
by (blast_tac (claset() addSEs [nonce_OR1_OR2_E] |
|
427 |
delrules [conjI] (*stop split-up*)) 1); |
|
2048 | 428 |
qed_spec_mp "NB_Crypt_imp_Server_msg"; |
429 |
||
430 |
||
431 |
(*Guarantee for B: if it gets a message with matching NB then the Server |
|
432 |
has sent the correct message.*) |
|
433 |
goal thy |
|
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
434 |
"!!evs. [| 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
|
435 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \ |
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
436 |
\ : set evs; \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
437 |
\ Says S' B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
438 |
\ B ~: bad; evs : otway |] \ |
2048 | 439 |
\ ==> Says Server B \ |
440 |
\ {|NA, \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
441 |
\ Crypt (shrK A) {|NA, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
442 |
\ Crypt (shrK B) {|NB, Key K|}|} \ |
3465 | 443 |
\ : set evs"; |
4470 | 444 |
by (blast_tac (claset() addSIs [NB_Crypt_imp_Server_msg]) 1); |
2328 | 445 |
qed "B_trusts_OR3"; |
2048 | 446 |
|
447 |
||
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
448 |
(*The obvious combination of B_trusts_OR3 with Spy_not_see_encrypted_key*) |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
449 |
goal thy |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
450 |
"!!evs. [| Says B Server {|NA, Agent A, Agent B, X', \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
451 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
452 |
\ : set evs; \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
453 |
\ Says S' B {|NA, X, Crypt (shrK B) {|NB, Key K|}|} : set evs; \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
454 |
\ Notes Spy {|NA, NB, Key K|} ~: set evs; \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
455 |
\ A ~: bad; B ~: bad; evs : otway |] \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
456 |
\ ==> Key K ~: analz (spies evs)"; |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
457 |
by (blast_tac (claset() addSDs [B_trusts_OR3, Spy_not_see_encrypted_key]) 1); |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
458 |
qed "B_gets_good_key"; |
2048 | 459 |
|
460 |
||
1945 | 461 |
goal thy |
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
462 |
"!!evs. [| B ~: bad; evs : otway |] \ |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
463 |
\ ==> Says Server B \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
464 |
\ {|NA, Crypt (shrK A) {|NA, Key K|}, \ |
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
465 |
\ 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
|
466 |
\ (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
|
467 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |} \ |
3465 | 468 |
\ : set evs)"; |
2032 | 469 |
by (etac otway.induct 1); |
3102 | 470 |
by (ALLGOALS Asm_simp_tac); |
4470 | 471 |
by (blast_tac (claset() addSEs [Crypt_imp_OR2]) 3); |
3102 | 472 |
by (ALLGOALS Blast_tac); |
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
473 |
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
|
474 |
|
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
475 |
|
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
476 |
(*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
|
477 |
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
|
478 |
strictly necessary for authentication.*) |
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
479 |
goal thy |
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
480 |
"!!evs. [| Says B' A {|NA, Crypt (shrK A) {|NA, Key K|}|} : set evs; \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
481 |
\ Says A B {|NA, Agent A, Agent B, \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
482 |
\ Crypt (shrK A) {|NA, Agent A, Agent B|}|} : set evs; \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
483 |
\ A ~: bad; B ~: bad; evs : otway |] \ |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
484 |
\ ==> 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
|
485 |
\ Crypt (shrK B) {|NA, NB, Agent A, Agent B|} |}\ |
3465 | 486 |
\ : set evs"; |
4470 | 487 |
by (blast_tac (claset() addSDs [A_trusts_OR4] |
488 |
addSEs [OR3_imp_OR2]) 1); |
|
2194
63a68a3a8a76
Removal of an obsolete result, and authentication of
paulson
parents:
2171
diff
changeset
|
489 |
qed "A_auths_B"; |