author | paulson |
Tue, 27 Feb 2001 16:13:23 +0100 | |
changeset 11185 | 1b737b4c2108 |
parent 11150 | 67387142225e |
child 11204 | bb01189f0565 |
permissions | -rw-r--r-- |
1995 | 1 |
(* Title: HOL/Auth/Yahalom |
1985
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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3432 | 6 |
Inductive relation "yahalom" for the Yahalom protocol. |
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|
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From page 257 of |
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Burrows, Abadi and Needham. A Logic of Authentication. |
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Proc. Royal Soc. 426 (1989) |
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*) |
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|
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Pretty.setdepth 25; |
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|
1995 | 15 |
|
2322 | 16 |
(*A "possibility property": there are traces that reach the end*) |
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Goal "A \\<noteq> Server \ |
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\ ==> \\<exists>X NB K. \\<exists>evs \\<in> yahalom. \ |
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\ Says A B {|X, Crypt K (Nonce NB)|} \\<in> set evs"; |
1995 | 20 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
6335 | 21 |
by (rtac (yahalom.Nil RS |
22 |
yahalom.YM1 RS yahalom.Reception RS |
|
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yahalom.YM2 RS yahalom.Reception RS |
|
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yahalom.YM3 RS yahalom.Reception RS yahalom.YM4) 2); |
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by possibility_tac; |
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result(); |
1995 | 27 |
|
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Goal "[| Gets B X \\<in> set evs; evs \\<in> yahalom |] ==> \\<exists>A. Says A B X \\<in> set evs"; |
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by (etac rev_mp 1); |
30 |
by (etac yahalom.induct 1); |
|
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by Auto_tac; |
|
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qed "Gets_imp_Says"; |
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||
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(*Must be proved separately for each protocol*) |
|
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Goal "[| Gets B X \\<in> set evs; evs \\<in> yahalom |] ==> X \\<in> 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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||
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|
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(**** Inductive proofs about yahalom ****) |
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|
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|
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(** For reasoning about the encrypted portion of messages **) |
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(*Lets us treat YM4 using a similar argument as for the Fake case.*) |
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Goal "[| Gets A {|Crypt (shrK A) Y, X|} \\<in> set evs; evs \\<in> yahalom |] \ |
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\ ==> X \\<in> analz (knows Spy evs)"; |
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by (blast_tac (claset() addSDs [Gets_imp_knows_Spy RS analz.Inj]) 1); |
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qed "YM4_analz_knows_Spy"; |
|
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bind_thm ("YM4_parts_knows_Spy", |
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YM4_analz_knows_Spy RS (impOfSubs analz_subset_parts)); |
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|
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(*For Oops*) |
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Goal "Says Server A {|Crypt (shrK A) {|B,K,NA,NB|}, X|} \\<in> set evs \ |
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\ ==> K \\<in> parts (knows Spy evs)"; |
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by (blast_tac (claset() addSDs [parts.Body, |
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Says_imp_knows_Spy RS parts.Inj]) 1); |
|
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qed "YM4_Key_parts_knows_Spy"; |
2110 | 61 |
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(*For proving the easier theorems about X \\<notin> parts (knows Spy evs).*) |
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fun parts_knows_Spy_tac i = |
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EVERY |
|
7499 | 65 |
[ftac YM4_Key_parts_knows_Spy (i+7), |
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ftac YM4_parts_knows_Spy (i+6), assume_tac (i+6), |
|
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prove_simple_subgoals_tac i]; |
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(*Induction for regularity theorems. If induction formula has the form |
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X \\<notin> analz (knows Spy evs) --> ... then it shortens the proof by discarding |
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needless information about analz (insert X (knows Spy evs)) *) |
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fun parts_induct_tac i = |
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etac yahalom.induct i |
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THEN |
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REPEAT (FIRSTGOAL analz_mono_contra_tac) |
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THEN parts_knows_Spy_tac i; |
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(** Theorems of the form X \\<notin> parts (knows Spy evs) imply that NOBODY |
2013 | 80 |
sends messages containing X! **) |
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(*Spy never sees another agent's shared key! (unless it's bad at start)*) |
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Goal "evs \\<in> yahalom ==> (Key (shrK A) \\<in> parts (knows Spy evs)) = (A \\<in> bad)"; |
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by (parts_induct_tac 1); |
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by (Fake_parts_insert_tac 1); |
3961 | 86 |
by (ALLGOALS Blast_tac); |
2133 | 87 |
qed "Spy_see_shrK"; |
88 |
Addsimps [Spy_see_shrK]; |
|
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|
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Goal "evs \\<in> yahalom ==> (Key (shrK A) \\<in> analz (knows Spy evs)) = (A \\<in> bad)"; |
4091 | 91 |
by (auto_tac(claset() addDs [impOfSubs analz_subset_parts], simpset())); |
2133 | 92 |
qed "Spy_analz_shrK"; |
93 |
Addsimps [Spy_analz_shrK]; |
|
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4471 | 95 |
AddSDs [Spy_see_shrK RSN (2, rev_iffD1), |
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Spy_analz_shrK RSN (2, rev_iffD1)]; |
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(*Nobody can have used non-existent keys! Needed to apply analz_insert_Key*) |
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Goal "evs \\<in> yahalom ==> \ |
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\ Key K \\<notin> used evs --> K \\<notin> 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); |
3961 | 105 |
(*YM2-4: Because Key K is not fresh, etc.*) |
6335 | 106 |
by (REPEAT (blast_tac (claset() addSEs knows_Spy_partsEs) 1)); |
2160 | 107 |
qed_spec_mp "new_keys_not_used"; |
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Addsimps [new_keys_not_used]; |
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|
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(*Earlier, \\<forall>protocol proofs declared this theorem. |
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But Yahalom and Kerberos IV are the only ones that need it!*) |
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112 |
bind_thm ("new_keys_not_analzd", |
2032 | 113 |
[analz_subset_parts RS keysFor_mono, |
114 |
new_keys_not_used] MRS contra_subsetD); |
|
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|
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|
2133 | 117 |
(*Describes the form of K when the Server sends this message. Useful for |
118 |
Oops as well as main secrecy property.*) |
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119 |
Goal "[| Says Server A {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, X|} \ |
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\ \\<in> set evs; evs \\<in> yahalom |] \ |
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\ ==> K \\<notin> range shrK"; |
2133 | 122 |
by (etac rev_mp 1); |
123 |
by (etac yahalom.induct 1); |
|
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by (ALLGOALS Asm_simp_tac); |
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125 |
by (Blast_tac 1); |
5073 | 126 |
qed "Says_Server_not_range"; |
127 |
||
128 |
Addsimps [Says_Server_not_range]; |
|
2110 | 129 |
|
130 |
||
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131 |
(*For proofs involving analz.*) |
6335 | 132 |
val analz_knows_Spy_tac = |
7499 | 133 |
ftac YM4_analz_knows_Spy 7 THEN assume_tac 7; |
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|
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(**** |
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The following is to prove theorems of the form |
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|
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Key K \\<in> analz (insert (Key KAB) (knows Spy evs)) ==> |
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Key K \\<in> analz (knows Spy evs) |
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|
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A more general formula must be proved inductively. |
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****) |
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|
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(** Session keys are not used to encrypt other session keys **) |
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|
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Goal "evs \\<in> yahalom ==> \ |
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\ \\<forall>K KK. KK <= - (range shrK) --> \ |
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148 |
\ (Key K \\<in> analz (Key`KK Un (knows Spy evs))) = \ |
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149 |
\ (K \\<in> KK | Key K \\<in> analz (knows Spy evs))"; |
2032 | 150 |
by (etac yahalom.induct 1); |
6335 | 151 |
by analz_knows_Spy_tac; |
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152 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
3679 | 153 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma)); |
5073 | 154 |
by (ALLGOALS (asm_simp_tac |
155 |
(analz_image_freshK_ss addsimps [Says_Server_not_range]))); |
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156 |
(*Fake*) |
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157 |
by (spy_analz_tac 1); |
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158 |
qed_spec_mp "analz_image_freshK"; |
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|
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160 |
Goal "[| evs \\<in> yahalom; KAB \\<notin> range shrK |] \ |
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161 |
\ ==> Key K \\<in> analz (insert (Key KAB) (knows Spy evs)) = \ |
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162 |
\ (K = KAB | Key K \\<in> analz (knows Spy evs))"; |
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163 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
4d68fbe6378b
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164 |
qed "analz_insert_freshK"; |
1985
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|
165 |
|
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166 |
|
2110 | 167 |
(*** The Key K uniquely identifies the Server's message. **) |
168 |
||
169 |
||
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170 |
Goal "[| Says Server A \ |
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171 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, X|} \\<in> set evs; \ |
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172 |
\ Says Server A' \ |
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|
173 |
\ {|Crypt (shrK A') {|Agent B', Key K, na', nb'|}, X'|} \\<in> set evs; \ |
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174 |
\ evs \\<in> yahalom |] \ |
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|
175 |
\ ==> A=A' & B=B' & na=na' & nb=nb'"; |
11104 | 176 |
by (etac rev_mp 1); |
177 |
by (etac rev_mp 1); |
|
178 |
by (etac yahalom.induct 1); |
|
179 |
by (ALLGOALS Asm_simp_tac); |
|
180 |
(*YM4*) |
|
181 |
by (Blast_tac 2); |
|
182 |
(*YM3, by freshness*) |
|
183 |
by (blast_tac (claset() addSEs knows_Spy_partsEs) 1); |
|
2110 | 184 |
qed "unique_session_keys"; |
185 |
||
186 |
||
187 |
(** Crucial secrecy property: Spy does not see the keys sent in msg YM3 **) |
|
2013 | 188 |
|
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189 |
Goal "[| A \\<notin> bad; B \\<notin> bad; evs \\<in> yahalom |] \ |
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190 |
\ ==> Says Server A \ |
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191 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, \ |
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192 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
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193 |
\ \\<in> set evs --> \ |
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194 |
\ Notes Spy {|na, nb, Key K|} \\<notin> set evs --> \ |
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195 |
\ Key K \\<notin> analz (knows Spy evs)"; |
2032 | 196 |
by (etac yahalom.induct 1); |
6335 | 197 |
by analz_knows_Spy_tac; |
2013 | 198 |
by (ALLGOALS |
199 |
(asm_simp_tac |
|
5535 | 200 |
(simpset() addsimps split_ifs @ pushes @ |
201 |
[analz_insert_eq, analz_insert_freshK]))); |
|
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202 |
(*Oops*) |
4091 | 203 |
by (blast_tac (claset() addDs [unique_session_keys]) 3); |
2013 | 204 |
(*YM3*) |
4091 | 205 |
by (blast_tac (claset() delrules [impCE] |
6335 | 206 |
addSEs knows_Spy_partsEs |
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|
207 |
addIs [impOfSubs analz_subset_parts]) 2); |
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208 |
(*Fake*) |
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|
209 |
by (spy_analz_tac 1); |
2110 | 210 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
2013 | 211 |
|
212 |
||
3432 | 213 |
(*Final version*) |
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214 |
Goal "[| Says Server A \ |
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215 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, \ |
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216 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
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217 |
\ \\<in> set evs; \ |
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218 |
\ Notes Spy {|na, nb, Key K|} \\<notin> set evs; \ |
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219 |
\ A \\<notin> bad; B \\<notin> bad; evs \\<in> yahalom |] \ |
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|
220 |
\ ==> Key K \\<notin> analz (knows Spy evs)"; |
4091 | 221 |
by (blast_tac (claset() addSEs [lemma]) 1); |
2032 | 222 |
qed "Spy_not_see_encrypted_key"; |
2001 | 223 |
|
224 |
||
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225 |
(** Security Guarantee for A upon receiving YM3 **) |
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|
226 |
|
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227 |
(*If the encrypted message appears then it originated with the Server*) |
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228 |
Goal "[| Crypt (shrK A) {|Agent B, Key K, na, nb|} \\<in> parts (knows Spy evs); \ |
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229 |
\ A \\<notin> bad; evs \\<in> yahalom |] \ |
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230 |
\ ==> Says Server A \ |
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231 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, \ |
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|
232 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
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|
233 |
\ \\<in> set evs"; |
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|
234 |
by (etac rev_mp 1); |
3519
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|
235 |
by (parts_induct_tac 1); |
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|
236 |
by (Fake_parts_insert_tac 1); |
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|
237 |
qed "A_trusts_YM3"; |
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|
238 |
|
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|
239 |
(*The obvious combination of A_trusts_YM3 with Spy_not_see_encrypted_key*) |
11185
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|
240 |
Goal "[| Crypt (shrK A) {|Agent B, Key K, na, nb|} \\<in> parts (knows Spy evs); \ |
1b737b4c2108
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|
241 |
\ Notes Spy {|na, nb, Key K|} \\<notin> set evs; \ |
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|
242 |
\ A \\<notin> bad; B \\<notin> bad; evs \\<in> yahalom |] \ |
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|
243 |
\ ==> Key K \\<notin> analz (knows Spy evs)"; |
4598
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Added some more explicit guarantees of key secrecy for agents
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|
244 |
by (blast_tac (claset() addSDs [A_trusts_YM3, Spy_not_see_encrypted_key]) 1); |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
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|
245 |
qed "A_gets_good_key"; |
3444
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|
246 |
|
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|
247 |
(** Security Guarantees for B upon receiving YM4 **) |
2013 | 248 |
|
2110 | 249 |
(*B knows, by the first part of A's message, that the Server distributed |
250 |
the key for A and B. But this part says nothing about nonces.*) |
|
11185
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|
251 |
Goal "[| Crypt (shrK B) {|Agent A, Key K|} \\<in> parts (knows Spy evs); \ |
1b737b4c2108
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|
252 |
\ B \\<notin> bad; evs \\<in> yahalom |] \ |
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|
253 |
\ ==> \\<exists>NA NB. Says Server A \ |
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|
254 |
\ {|Crypt (shrK A) {|Agent B, Key K, \ |
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|
255 |
\ Nonce NA, Nonce NB|}, \ |
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|
256 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
11185
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|
257 |
\ \\<in> set evs"; |
2032 | 258 |
by (etac rev_mp 1); |
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
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|
259 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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|
260 |
by (Fake_parts_insert_tac 1); |
2110 | 261 |
(*YM3*) |
3121
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Conversion to use blast_tac (with other improvements)
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|
262 |
by (Blast_tac 1); |
2110 | 263 |
qed "B_trusts_YM4_shrK"; |
264 |
||
3444
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|
265 |
(*B knows, by the second part of A's message, that the Server distributed |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
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|
266 |
the key quoting nonce NB. This part says nothing about agent names. |
11185
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|
267 |
Secrecy of NB is crucial. Note that Nonce NB \\<notin> analz(knows Spy evs) must |
5065 | 268 |
be the FIRST antecedent of the induction formula.*) |
11185
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|
269 |
Goal "evs \\<in> yahalom \ |
1b737b4c2108
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|
270 |
\ ==> Nonce NB \\<notin> analz (knows Spy evs) --> \ |
1b737b4c2108
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|
271 |
\ Crypt K (Nonce NB) \\<in> parts (knows Spy evs) --> \ |
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|
272 |
\ (\\<exists>A B NA. Says Server A \ |
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|
273 |
\ {|Crypt (shrK A) {|Agent B, Key K, \ |
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|
274 |
\ Nonce NA, Nonce NB|}, \ |
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|
275 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
11185
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|
276 |
\ \\<in> set evs)"; |
3519
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Changing "lost" from a parameter of protocol definitions to a constant.
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|
277 |
by (parts_induct_tac 1); |
3708 | 278 |
by (ALLGOALS Clarify_tac); |
3444
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|
279 |
(*YM3 & Fake*) |
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|
280 |
by (Blast_tac 2); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
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|
281 |
by (Fake_parts_insert_tac 1); |
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|
282 |
(*YM4*) |
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|
283 |
(*A is uncompromised because NB is secure; |
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|
284 |
A's certificate guarantees the existence of the Server message*) |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
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|
285 |
by (blast_tac (claset() addSDs [Gets_imp_Says, Crypt_Spy_analz_bad] |
1b737b4c2108
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|
286 |
addDs [Says_imp_spies, analz.Inj, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
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|
287 |
parts.Inj RS parts.Fst RS A_trusts_YM3]) 1); |
3464
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Trivial changes in connection with the Yahalom paper.
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|
288 |
bind_thm ("B_trusts_YM4_newK", result() RS mp RSN (2, rev_mp)); |
2133 | 289 |
|
3444
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|
290 |
|
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Streamlined proofs of the secrecy of NB and added authentication of A and B
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|
291 |
(**** Towards proving secrecy of Nonce NB ****) |
919de2cb3487
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|
292 |
|
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|
293 |
(** Lemmas about the predicate KeyWithNonce **) |
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Streamlined proofs of the secrecy of NB and added authentication of A and B
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|
294 |
|
5076 | 295 |
Goalw [KeyWithNonce_def] |
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|
296 |
"Says Server A \ |
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|
297 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB|}, X|} \ |
11185
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|
298 |
\ \\<in> set evs ==> KeyWithNonce K NB evs"; |
3444
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|
299 |
by (Blast_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
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|
300 |
qed "KeyWithNonceI"; |
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|
301 |
|
5076 | 302 |
Goalw [KeyWithNonce_def] |
3444
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|
303 |
"KeyWithNonce K NB (Says S A X # evs) = \ |
5114
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|
304 |
\ (Server = S & \ |
11185
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|
305 |
\ (\\<exists>B n X'. X = {|Crypt (shrK A) {|Agent B, Key K, n, Nonce NB|}, X'|}) \ |
5114
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|
306 |
\ | KeyWithNonce K NB evs)"; |
3444
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Streamlined proofs of the secrecy of NB and added authentication of A and B
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|
307 |
by (Simp_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
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|
308 |
by (Blast_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
309 |
qed "KeyWithNonce_Says"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
310 |
Addsimps [KeyWithNonce_Says]; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
311 |
|
5076 | 312 |
Goalw [KeyWithNonce_def] |
4537
4e835bd9fada
Expressed most Oops rules using Notes instead of Says, and other tidying
paulson
parents:
4509
diff
changeset
|
313 |
"KeyWithNonce K NB (Notes A X # evs) = KeyWithNonce K NB evs"; |
4e835bd9fada
Expressed most Oops rules using Notes instead of Says, and other tidying
paulson
parents:
4509
diff
changeset
|
314 |
by (Simp_tac 1); |
4e835bd9fada
Expressed most Oops rules using Notes instead of Says, and other tidying
paulson
parents:
4509
diff
changeset
|
315 |
qed "KeyWithNonce_Notes"; |
4e835bd9fada
Expressed most Oops rules using Notes instead of Says, and other tidying
paulson
parents:
4509
diff
changeset
|
316 |
Addsimps [KeyWithNonce_Notes]; |
4e835bd9fada
Expressed most Oops rules using Notes instead of Says, and other tidying
paulson
parents:
4509
diff
changeset
|
317 |
|
6335 | 318 |
Goalw [KeyWithNonce_def] |
319 |
"KeyWithNonce K NB (Gets A X # evs) = KeyWithNonce K NB evs"; |
|
320 |
by (Simp_tac 1); |
|
321 |
qed "KeyWithNonce_Gets"; |
|
322 |
Addsimps [KeyWithNonce_Gets]; |
|
323 |
||
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
324 |
(*A fresh key cannot be associated with any nonce |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
325 |
(with respect to a given trace). *) |
5076 | 326 |
Goalw [KeyWithNonce_def] |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
327 |
"Key K \\<notin> used evs ==> ~ KeyWithNonce K NB evs"; |
6335 | 328 |
by (blast_tac (claset() addSEs knows_Spy_partsEs) 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
329 |
qed "fresh_not_KeyWithNonce"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
330 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
331 |
(*The Server message associates K with NB' and therefore not with any |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
332 |
other nonce NB.*) |
5076 | 333 |
Goalw [KeyWithNonce_def] |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
334 |
"[| Says Server A \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
335 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB'|}, X|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
336 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
337 |
\ NB \\<noteq> NB'; evs \\<in> yahalom |] \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
338 |
\ ==> ~ KeyWithNonce K NB evs"; |
4091 | 339 |
by (blast_tac (claset() addDs [unique_session_keys]) 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
340 |
qed "Says_Server_KeyWithNonce"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
341 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
342 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
343 |
(*The only nonces that can be found with the help of session keys are |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
344 |
those distributed as nonce NB by the Server. The form of the theorem |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
345 |
recalls analz_image_freshK, but it is much more complicated.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
346 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
347 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
348 |
(*As with analz_image_freshK, we take some pains to express the property |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
349 |
as a logical equivalence so that the simplifier can apply it.*) |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
350 |
Goal "P --> (X \\<in> analz (G Un H)) --> (X \\<in> analz H) ==> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
351 |
\ P --> (X \\<in> analz (G Un H)) = (X \\<in> analz H)"; |
4091 | 352 |
by (blast_tac (claset() addIs [impOfSubs analz_mono]) 1); |
3961 | 353 |
val Nonce_secrecy_lemma = result(); |
2133 | 354 |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
355 |
Goal "evs \\<in> yahalom ==> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
356 |
\ (\\<forall>KK. KK <= - (range shrK) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
357 |
\ (\\<forall>K \\<in> KK. ~ KeyWithNonce K NB evs) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
358 |
\ (Nonce NB \\<in> analz (Key`KK Un (knows Spy evs))) = \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
359 |
\ (Nonce NB \\<in> analz (knows Spy evs)))"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
360 |
by (etac yahalom.induct 1); |
6335 | 361 |
by analz_knows_Spy_tac; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
362 |
by (REPEAT_FIRST (resolve_tac [impI RS allI])); |
3961 | 363 |
by (REPEAT_FIRST (rtac Nonce_secrecy_lemma)); |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
364 |
(*For Oops, simplification proves NBa\\<noteq>NB. By Says_Server_KeyWithNonce, |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
365 |
we get (~ KeyWithNonce K NB evs); then simplification can apply the |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
366 |
induction hypothesis with KK = {K}.*) |
5073 | 367 |
by (ALLGOALS (*4 seconds*) |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
368 |
(asm_simp_tac |
3961 | 369 |
(analz_image_freshK_ss |
4831 | 370 |
addsimps split_ifs |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
371 |
addsimps [all_conj_distrib, ball_conj_distrib, analz_image_freshK, |
6335 | 372 |
KeyWithNonce_Says, KeyWithNonce_Notes, KeyWithNonce_Gets, |
5073 | 373 |
fresh_not_KeyWithNonce, Says_Server_not_range, |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
374 |
imp_disj_not1, (*Moves NBa\\<noteq>NB to the front*) |
3961 | 375 |
Says_Server_KeyWithNonce]))); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
376 |
(*Fake*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
377 |
by (spy_analz_tac 1); |
4422
21238c9d363e
Simplified proofs using rewrites for f``A where f is injective
paulson
parents:
4238
diff
changeset
|
378 |
(*YM4*) (** LEVEL 6 **) |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
379 |
by (thin_tac "\\<forall>KK. ?P KK" 1); |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
380 |
by (Clarify_tac 1); |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
381 |
(*If A:bad then NBa is known, therefore NBa \\<noteq> NB. Previous two steps make |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
382 |
the next step faster.*) |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
383 |
by (blast_tac (claset() addSDs [Gets_imp_Says, Says_imp_spies, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
384 |
Crypt_Spy_analz_bad] |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
385 |
addDs [analz.Inj, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
386 |
parts.Inj RS parts.Fst RS A_trusts_YM3 RS KeyWithNonceI]) 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
387 |
qed_spec_mp "Nonce_secrecy"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
388 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
389 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
390 |
(*Version required below: if NB can be decrypted using a session key then it |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
391 |
was distributed with that key. The more general form above is required |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
392 |
for the induction to carry through.*) |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
393 |
Goal "[| Says Server A \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
394 |
\ {|Crypt (shrK A) {|Agent B, Key KAB, na, Nonce NB'|}, X|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
395 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
396 |
\ NB \\<noteq> NB'; KAB \\<notin> range shrK; evs \\<in> yahalom |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
397 |
\ ==> (Nonce NB \\<in> analz (insert (Key KAB) (knows Spy evs))) = \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
398 |
\ (Nonce NB \\<in> analz (knows Spy evs))"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
399 |
by (asm_simp_tac (analz_image_freshK_ss addsimps |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
400 |
[Nonce_secrecy, Says_Server_KeyWithNonce]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
401 |
qed "single_Nonce_secrecy"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
402 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
403 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
404 |
(*** The Nonce NB uniquely identifies B's message. ***) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
405 |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
406 |
Goal "[| Crypt (shrK B) {|Agent A, Nonce NA, nb|} \\<in> parts (knows Spy evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
407 |
\ Crypt (shrK B') {|Agent A', Nonce NA', nb|} \\<in> parts (knows Spy evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
408 |
\ evs \\<in> yahalom; B \\<notin> bad; B' \\<notin> bad |] \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
409 |
\ ==> NA' = NA & A' = A & B' = B"; |
11104 | 410 |
by (etac rev_mp 1); |
411 |
by (etac rev_mp 1); |
|
412 |
by (parts_induct_tac 1); |
|
413 |
by (Fake_parts_insert_tac 1); |
|
414 |
(*YM2, by freshness*) |
|
415 |
by (blast_tac (claset() addSEs knows_Spy_partsEs) 1); |
|
2133 | 416 |
qed "unique_NB"; |
417 |
||
418 |
||
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
419 |
(*Variant useful for proving secrecy of NB. Because nb is assumed to be |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
420 |
secret, we no longer must assume B, B' not bad.*) |
6335 | 421 |
Goal "[| Says C S {|X, Crypt (shrK B) {|Agent A, Nonce NA, nb|}|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
422 |
\ \\<in> set evs; \ |
6335 | 423 |
\ Gets S' {|X', Crypt (shrK B') {|Agent A', Nonce NA', nb|}|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
424 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
425 |
\ nb \\<notin> analz (knows Spy evs); evs \\<in> yahalom |] \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
426 |
\ ==> NA' = NA & A' = A & B' = B"; |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
427 |
by (blast_tac (claset() addSDs [Gets_imp_Says, Crypt_Spy_analz_bad] |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
428 |
addDs [Says_imp_spies, unique_NB, parts.Inj, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
429 |
analz.Inj]) 1); |
2133 | 430 |
qed "Says_unique_NB"; |
431 |
||
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
432 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
433 |
(** A nonce value is never used both as NA and as NB **) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
434 |
|
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
435 |
Goal "evs \\<in> yahalom \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
436 |
\ ==> Nonce NB \\<notin> analz (knows Spy evs) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
437 |
\ Crypt (shrK B') {|Agent A', Nonce NB, nb'|} \\<in> parts(knows Spy evs) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
438 |
\ Crypt (shrK B) {|Agent A, na, Nonce NB|} \\<notin> parts(knows Spy evs)"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
439 |
by (parts_induct_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
440 |
by (Fake_parts_insert_tac 1); |
6335 | 441 |
by (blast_tac (claset() addDs [Gets_imp_knows_Spy RS analz.Inj] |
4238
679a233fb206
Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents:
4091
diff
changeset
|
442 |
addSIs [parts_insertI] |
11150 | 443 |
addSDs [parts.Body]) 1); |
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
444 |
bind_thm ("no_nonce_YM1_YM2", result() RS mp RSN (2,rev_mp) RSN (2,rev_notE)); |
2133 | 445 |
|
5065 | 446 |
(*more readable version cited in Yahalom paper*) |
447 |
standard (result() RS mp RSN (2,rev_mp)); |
|
448 |
||
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
449 |
(*The Server sends YM3 only in response to YM2.*) |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
450 |
Goal "[| Says Server A \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
451 |
\ {|Crypt (shrK A) {|Agent B, k, na, nb|}, X|} \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
452 |
\ evs \\<in> yahalom |] \ |
6335 | 453 |
\ ==> Gets Server {| Agent B, Crypt (shrK B) {|Agent A, na, nb|} |} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
454 |
\ \\<in> set evs"; |
2133 | 455 |
by (etac rev_mp 1); |
456 |
by (etac yahalom.induct 1); |
|
5932 | 457 |
by Auto_tac; |
2133 | 458 |
qed "Says_Server_imp_YM2"; |
459 |
||
460 |
||
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
461 |
(*A vital theorem for B, that nonce NB remains secure from the Spy.*) |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
462 |
Goal "[| A \\<notin> bad; B \\<notin> bad; evs \\<in> yahalom |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
463 |
\ ==> (\\<forall>k. Notes Spy {|Nonce NA, Nonce NB, k|} \\<notin> set evs) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
464 |
\ Says B Server \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
465 |
\ {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
466 |
\ \\<in> set evs --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
467 |
\ Nonce NB \\<notin> analz (knows Spy evs)"; |
2133 | 468 |
by (etac yahalom.induct 1); |
6335 | 469 |
by analz_knows_Spy_tac; |
2133 | 470 |
by (ALLGOALS |
471 |
(asm_simp_tac |
|
5535 | 472 |
(simpset() addsimps split_ifs @ pushes @ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
473 |
[new_keys_not_analzd, analz_insert_eq, analz_insert_freshK]))); |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
474 |
(*Prove YM3 by showing that no NB can also be an NA*) |
6335 | 475 |
by (blast_tac (claset() addDs [Says_imp_knows_Spy RS parts.Inj] |
9166 | 476 |
addSEs [no_nonce_YM1_YM2, MPair_parts] |
477 |
addDs [Gets_imp_Says, Says_unique_NB]) 4); |
|
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
478 |
(*YM2: similar freshness reasoning*) |
11150 | 479 |
by (blast_tac (claset() addSDs [parts.Body] |
6335 | 480 |
addDs [Gets_imp_Says, |
481 |
Says_imp_knows_Spy RS analz.Inj, |
|
4238
679a233fb206
Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents:
4091
diff
changeset
|
482 |
impOfSubs analz_subset_parts]) 3); |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
483 |
(*YM1: NB=NA is impossible anyway, but NA is secret because it is fresh!*) |
4091 | 484 |
by (blast_tac (claset() addSIs [parts_insertI] |
6335 | 485 |
addSEs knows_Spy_partsEs) 2); |
2377 | 486 |
(*Fake*) |
487 |
by (spy_analz_tac 1); |
|
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
488 |
(** LEVEL 7: YM4 and Oops remain **) |
5932 | 489 |
by (ALLGOALS (Clarify_tac THEN' |
490 |
full_simp_tac (simpset() addsimps [all_conj_distrib]))); |
|
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
491 |
(*YM4: key K is visible to Spy, contradicting session key secrecy theorem*) |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
492 |
(*Case analysis on Aa:bad; PROOF FAILED problems; |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
493 |
use Says_unique_NB to identify message components: Aa=A, Ba=B*) |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
494 |
by (blast_tac (claset() addSDs [Says_unique_NB, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
495 |
parts.Inj RS parts.Fst RS A_trusts_YM3] |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
496 |
addDs [Gets_imp_knows_Spy RS analz.Inj, Gets_imp_Says, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
497 |
Says_imp_spies, Says_Server_imp_YM2, |
6335 | 498 |
Spy_not_see_encrypted_key]) 1); |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
499 |
(** LEVEL 9 **) |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
500 |
(*Oops case: if the nonce is betrayed now, show that the Oops event is |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
501 |
covered by the quantified Oops assumption.*) |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
502 |
by (ftac Says_Server_imp_YM2 1 THEN assume_tac 1); |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
503 |
by (case_tac "NB = NBa" 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
504 |
(*If NB=NBa then all other components of the Oops message agree*) |
5932 | 505 |
by (blast_tac (claset() addDs [Says_unique_NB]) 1); |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
506 |
(*case NB \\<noteq> NBa*) |
4091 | 507 |
by (asm_simp_tac (simpset() addsimps [single_Nonce_secrecy]) 1); |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
508 |
by (blast_tac (claset() addSEs [no_nonce_YM1_YM2] (*to prove NB\\<noteq>NAa*) |
9166 | 509 |
addDs [Says_imp_knows_Spy RS parts.Inj]) 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
510 |
bind_thm ("Spy_not_see_NB", result() RSN(2,rev_mp) RSN(2,rev_mp)); |
2133 | 511 |
|
2001 | 512 |
|
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
513 |
(*B's session key guarantee from YM4. The two certificates contribute to a |
4537
4e835bd9fada
Expressed most Oops rules using Notes instead of Says, and other tidying
paulson
parents:
4509
diff
changeset
|
514 |
single conclusion about the Server's message. Note that the "Notes Spy" |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
515 |
assumption must quantify over \\<forall>POSSIBLE keys instead of our particular K. |
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
516 |
If this run is broken and the spy substitutes a certificate containing an |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
517 |
old key, B has no means of telling.*) |
6335 | 518 |
Goal "[| Gets B {|Crypt (shrK B) {|Agent A, Key K|}, \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
519 |
\ Crypt K (Nonce NB)|} \\<in> set evs; \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
520 |
\ Says B Server \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
521 |
\ {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
522 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
523 |
\ \\<forall>k. Notes Spy {|Nonce NA, Nonce NB, k|} \\<notin> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
524 |
\ A \\<notin> bad; B \\<notin> bad; evs \\<in> yahalom |] \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
525 |
\ ==> Says Server A \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
526 |
\ {|Crypt (shrK A) {|Agent B, Key K, \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
527 |
\ Nonce NA, Nonce NB|}, \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
528 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
529 |
\ \\<in> set evs"; |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
530 |
by (blast_tac (claset() addDs [Spy_not_see_NB, Says_unique_NB, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
531 |
Says_Server_imp_YM2, B_trusts_YM4_newK]) 1); |
2322 | 532 |
qed "B_trusts_YM4"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
533 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
534 |
|
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
535 |
(*The obvious combination of B_trusts_YM4 with Spy_not_see_encrypted_key*) |
6335 | 536 |
Goal "[| Gets B {|Crypt (shrK B) {|Agent A, Key K|}, \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
537 |
\ Crypt K (Nonce NB)|} \\<in> set evs; \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
538 |
\ Says B Server \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
539 |
\ {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
540 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
541 |
\ \\<forall>k. Notes Spy {|Nonce NA, Nonce NB, k|} \\<notin> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
542 |
\ A \\<notin> bad; B \\<notin> bad; evs \\<in> yahalom |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
543 |
\ ==> Key K \\<notin> analz (knows Spy evs)"; |
4598
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
544 |
by (blast_tac (claset() addSDs [B_trusts_YM4, Spy_not_see_encrypted_key]) 1); |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
545 |
qed "B_gets_good_key"; |
649bf14debe7
Added some more explicit guarantees of key secrecy for agents
paulson
parents:
4537
diff
changeset
|
546 |
|
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
547 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
548 |
(*** Authenticating B to A ***) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
549 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
550 |
(*The encryption in message YM2 tells us it cannot be faked.*) |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
551 |
Goal "evs \\<in> yahalom \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
552 |
\ ==> Crypt (shrK B) {|Agent A, Nonce NA, nb|} \\<in> parts (knows Spy evs) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
553 |
\ B \\<notin> bad --> \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
554 |
\ Says B Server {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, nb|}|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
555 |
\ \\<in> set evs"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
556 |
by (parts_induct_tac 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
557 |
by (Fake_parts_insert_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
558 |
bind_thm ("B_Said_YM2", result() RSN (2, rev_mp) RS mp); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
559 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
560 |
(*If the server sends YM3 then B sent YM2*) |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
561 |
Goal "evs \\<in> yahalom \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
562 |
\ ==> Says Server A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, nb|}, X|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
563 |
\ \\<in> set evs --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
564 |
\ B \\<notin> bad --> \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
565 |
\ Says B Server {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, nb|}|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
566 |
\ \\<in> set evs"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
567 |
by (etac yahalom.induct 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
568 |
by (ALLGOALS Asm_simp_tac); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
569 |
(*YM4*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
570 |
by (Blast_tac 2); |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
571 |
(*YM3*) |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
572 |
by (blast_tac (claset() addSDs [B_Said_YM2, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
573 |
Says_imp_knows_Spy RS parts.Inj]) 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
574 |
val lemma = result() RSN (2, rev_mp) RS mp |> standard; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
575 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
576 |
(*If A receives YM3 then B has used nonce NA (and therefore is alive)*) |
6335 | 577 |
Goal "[| Gets A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, nb|}, X|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
578 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
579 |
\ A \\<notin> bad; B \\<notin> bad; evs \\<in> yahalom |] \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
580 |
\==> Says B Server {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, nb|}|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
581 |
\ \\<in> set evs"; |
4091 | 582 |
by (blast_tac (claset() addSDs [A_trusts_YM3, lemma] |
6335 | 583 |
addEs knows_Spy_partsEs) 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
584 |
qed "YM3_auth_B_to_A"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
585 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
586 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
587 |
(*** Authenticating A to B using the certificate Crypt K (Nonce NB) ***) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
588 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
589 |
(*Assuming the session key is secure, if both certificates are present then |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
590 |
A has said NB. We can't be sure about the rest of A's message, but only |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
591 |
NB matters for freshness.*) |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
592 |
Goal "evs \\<in> yahalom \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
593 |
\ ==> Key K \\<notin> analz (knows Spy evs) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
594 |
\ Crypt K (Nonce NB) \\<in> parts (knows Spy evs) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
595 |
\ Crypt (shrK B) {|Agent A, Key K|} \\<in> parts (knows Spy evs) --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
596 |
\ B \\<notin> bad --> \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
597 |
\ (\\<exists>X. Says A B {|X, Crypt K (Nonce NB)|} \\<in> set evs)"; |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3516
diff
changeset
|
598 |
by (parts_induct_tac 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
599 |
(*Fake*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
600 |
by (Fake_parts_insert_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
601 |
(*YM3: by new_keys_not_used we note that Crypt K (Nonce NB) could not exist*) |
4238
679a233fb206
Crypt_imp_keysFor: version of Crypt_imp_invKey_keysFor for shared keys
paulson
parents:
4091
diff
changeset
|
602 |
by (fast_tac (claset() addSDs [Crypt_imp_keysFor] addss (simpset())) 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
603 |
(*YM4: was Crypt K (Nonce NB) the very last message? If not, use ind. hyp.*) |
4091 | 604 |
by (asm_simp_tac (simpset() addsimps [ex_disj_distrib]) 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
605 |
(*yes: apply unicity of session keys*) |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
606 |
by (blast_tac (claset() addSDs [Gets_imp_Says, A_trusts_YM3, B_trusts_YM4_shrK, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
607 |
Crypt_Spy_analz_bad] |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
608 |
addDs [Says_imp_knows_Spy RS parts.Inj, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
609 |
Says_imp_spies RS analz.Inj, unique_session_keys]) 1); |
6335 | 610 |
qed_spec_mp "A_Said_YM3_lemma"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
611 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
612 |
(*If B receives YM4 then A has used nonce NB (and therefore is alive). |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
613 |
Moreover, A associates K with NB (thus is talking about the same run). |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
614 |
Other premises guarantee secrecy of K.*) |
6335 | 615 |
Goal "[| Gets B {|Crypt (shrK B) {|Agent A, Key K|}, \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
616 |
\ Crypt K (Nonce NB)|} \\<in> set evs; \ |
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
617 |
\ Says B Server \ |
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset
|
618 |
\ {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|} \ |
11185
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
619 |
\ \\<in> set evs; \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
620 |
\ (\\<forall>NA k. Notes Spy {|Nonce NA, Nonce NB, k|} \\<notin> set evs); \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
621 |
\ A \\<notin> bad; B \\<notin> bad; evs \\<in> yahalom |] \ |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
622 |
\ ==> \\<exists>X. Says A B {|X, Crypt K (Nonce NB)|} \\<in> set evs"; |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
623 |
by (blast_tac (claset() addSIs [A_Said_YM3_lemma] |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
624 |
addDs [Spy_not_see_encrypted_key, B_trusts_YM4, |
1b737b4c2108
Some X-symbols for <notin>, <noteq>, <forall>, <exists>
paulson
parents:
11150
diff
changeset
|
625 |
Gets_imp_Says, Says_imp_knows_Spy RS parts.Inj]) 1); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
626 |
qed_spec_mp "YM4_imp_A_Said_YM3"; |