author | wenzelm |
Mon, 28 Dec 2015 23:13:33 +0100 | |
changeset 61956 | 38b73f7940af |
parent 61830 | 4f5ab843cf5b |
child 67613 | ce654b0e6d69 |
permissions | -rw-r--r-- |
41775 | 1 |
(* Title: HOL/Auth/Guard/Guard_NS_Public.thy |
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Author: Frederic Blanqui, University of Cambridge Computer Laboratory |
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Copyright 2002 University of Cambridge |
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Incorporating Lowe's fix (inclusion of B's identity in round 2). |
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*) |
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section\<open>Needham-Schroeder-Lowe Public-Key Protocol\<close> |
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theory Guard_NS_Public imports Guard_Public begin |
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subsection\<open>messages used in the protocol\<close> |
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abbreviation (input) |
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ns1 :: "agent => agent => nat => event" where |
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"ns1 A B NA == Says A B (Crypt (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>)" |
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abbreviation (input) |
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ns1' :: "agent => agent => agent => nat => event" where |
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"ns1' A' A B NA == Says A' B (Crypt (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>)" |
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abbreviation (input) |
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ns2 :: "agent => agent => nat => nat => event" where |
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"ns2 B A NA NB == Says B A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB, Agent B\<rbrace>)" |
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abbreviation (input) |
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ns2' :: "agent => agent => agent => nat => nat => event" where |
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"ns2' B' B A NA NB == Says B' A (Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB, Agent B\<rbrace>)" |
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abbreviation (input) |
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ns3 :: "agent => agent => nat => event" where |
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"ns3 A B NB == Says A B (Crypt (pubK B) (Nonce NB))" |
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subsection\<open>definition of the protocol\<close> |
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inductive_set nsp :: "event list set" |
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where |
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Nil: "[]:nsp" |
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| Fake: "[| evs:nsp; X:synth (analz (spies evs)) |] ==> Says Spy B X # evs : nsp" |
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| NS1: "[| evs1:nsp; Nonce NA ~:used evs1 |] ==> ns1 A B NA # evs1 : nsp" |
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| NS2: "[| evs2:nsp; Nonce NB ~:used evs2; ns1' A' A B NA:set evs2 |] ==> |
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ns2 B A NA NB # evs2:nsp" |
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| NS3: "!!A B B' NA NB evs3. [| evs3:nsp; ns1 A B NA:set evs3; ns2' B' B A NA NB:set evs3 |] ==> |
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ns3 A B NB # evs3:nsp" |
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subsection\<open>declarations for tactics\<close> |
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declare knows_Spy_partsEs [elim] |
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declare Fake_parts_insert [THEN subsetD, dest] |
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declare initState.simps [simp del] |
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subsection\<open>general properties of nsp\<close> |
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lemma nsp_has_no_Gets: "evs:nsp ==> ALL A X. Gets A X ~:set evs" |
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by (erule nsp.induct, auto) |
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lemma nsp_is_Gets_correct [iff]: "Gets_correct nsp" |
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by (auto simp: Gets_correct_def dest: nsp_has_no_Gets) |
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lemma nsp_is_one_step [iff]: "one_step nsp" |
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by (unfold one_step_def, clarify, ind_cases "ev#evs:nsp" for ev evs, auto) |
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lemma nsp_has_only_Says' [rule_format]: "evs:nsp ==> |
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ev:set evs --> (EX A B X. ev=Says A B X)" |
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by (erule nsp.induct, auto) |
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lemma nsp_has_only_Says [iff]: "has_only_Says nsp" |
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by (auto simp: has_only_Says_def dest: nsp_has_only_Says') |
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lemma nsp_is_regular [iff]: "regular nsp" |
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apply (simp only: regular_def, clarify) |
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by (erule nsp.induct, auto simp: initState.simps knows.simps) |
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subsection\<open>nonce are used only once\<close> |
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lemma NA_is_uniq [rule_format]: "evs:nsp ==> |
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Crypt (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>:parts (spies evs) |
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--> Crypt (pubK B') \<lbrace>Nonce NA, Agent A'\<rbrace>:parts (spies evs) |
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--> Nonce NA ~:analz (spies evs) --> A=A' & B=B'" |
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apply (erule nsp.induct, simp_all) |
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by (blast intro: analz_insertI)+ |
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lemma no_Nonce_NS1_NS2 [rule_format]: "evs:nsp ==> |
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Crypt (pubK B') \<lbrace>Nonce NA', Nonce NA, Agent A'\<rbrace>:parts (spies evs) |
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--> Crypt (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>:parts (spies evs) |
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--> Nonce NA:analz (spies evs)" |
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apply (erule nsp.induct, simp_all) |
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by (blast intro: analz_insertI)+ |
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lemma no_Nonce_NS1_NS2' [rule_format]: |
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"[| Crypt (pubK B') \<lbrace>Nonce NA', Nonce NA, Agent A'\<rbrace>:parts (spies evs); |
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Crypt (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>:parts (spies evs); evs:nsp |] |
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==> Nonce NA:analz (spies evs)" |
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by (rule no_Nonce_NS1_NS2, auto) |
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lemma NB_is_uniq [rule_format]: "evs:nsp ==> |
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Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB, Agent B\<rbrace>:parts (spies evs) |
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--> Crypt (pubK A') \<lbrace>Nonce NA', Nonce NB, Agent B'\<rbrace>:parts (spies evs) |
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--> Nonce NB ~:analz (spies evs) --> A=A' & B=B' & NA=NA'" |
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apply (erule nsp.induct, simp_all) |
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by (blast intro: analz_insertI)+ |
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subsection\<open>guardedness of NA\<close> |
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110 |
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lemma ns1_imp_Guard [rule_format]: "[| evs:nsp; A ~:bad; B ~:bad |] ==> |
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ns1 A B NA:set evs --> Guard NA {priK A,priK B} (spies evs)" |
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apply (erule nsp.induct) |
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(* Nil *) |
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apply simp_all |
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(* Fake *) |
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apply safe |
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apply (erule in_synth_Guard, erule Guard_analz, simp) |
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119 |
(* NS1 *) |
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apply blast |
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121 |
apply blast |
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122 |
apply blast |
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123 |
apply (drule Nonce_neq, simp+, rule No_Nonce, simp) |
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124 |
(* NS2 *) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
125 |
apply (frule_tac A=A in Nonce_neq, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
126 |
apply (case_tac "NAa=NA") |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
127 |
apply (drule Guard_Nonce_analz, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
128 |
apply (drule Says_imp_knows_Spy)+ |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
129 |
apply (drule_tac B=B and A'=Aa in NA_is_uniq, auto) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
130 |
(* NS3 *) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
131 |
apply (case_tac "NB=NA", clarify) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
132 |
apply (drule Guard_Nonce_analz, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
133 |
apply (drule Says_imp_knows_Spy)+ |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
134 |
by (drule no_Nonce_NS1_NS2, auto) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
135 |
|
61830 | 136 |
subsection\<open>guardedness of NB\<close> |
17394
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
137 |
|
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
138 |
lemma ns2_imp_Guard [rule_format]: "[| evs:nsp; A ~:bad; B ~:bad |] ==> |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
139 |
ns2 B A NA NB:set evs --> Guard NB {priK A,priK B} (spies evs)" |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
140 |
apply (erule nsp.induct) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
141 |
(* Nil *) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
142 |
apply simp_all |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
143 |
(* Fake *) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
144 |
apply safe |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
145 |
apply (erule in_synth_Guard, erule Guard_analz, simp) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
146 |
(* NS1 *) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
147 |
apply (frule Nonce_neq, simp+, blast, rule No_Nonce, simp) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
148 |
(* NS2 *) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
149 |
apply blast |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
150 |
apply blast |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
151 |
apply blast |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
152 |
apply (frule_tac A=B and n=NB in Nonce_neq, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
153 |
apply (case_tac "NAa=NB") |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
154 |
apply (drule Guard_Nonce_analz, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
155 |
apply (drule Says_imp_knows_Spy)+ |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
156 |
apply (drule no_Nonce_NS1_NS2, auto) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
157 |
(* NS3 *) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
158 |
apply (case_tac "NBa=NB", clarify) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
159 |
apply (drule Guard_Nonce_analz, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
160 |
apply (drule Says_imp_knows_Spy)+ |
48261 | 161 |
apply (drule_tac A=Aa and A'=A in NB_is_uniq) |
162 |
apply auto[1] |
|
163 |
apply (auto simp add: guard.No_Nonce) |
|
164 |
done |
|
17394
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
165 |
|
61830 | 166 |
subsection\<open>Agents' Authentication\<close> |
17394
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
167 |
|
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
168 |
lemma B_trusts_NS1: "[| evs:nsp; A ~:bad; B ~:bad |] ==> |
61956 | 169 |
Crypt (pubK B) \<lbrace>Nonce NA, Agent A\<rbrace>:parts (spies evs) |
17394
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
170 |
--> Nonce NA ~:analz (spies evs) --> ns1 A B NA:set evs" |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
171 |
apply (erule nsp.induct, simp_all) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
172 |
by (blast intro: analz_insertI)+ |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
173 |
|
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
174 |
lemma A_trusts_NS2: "[| evs:nsp; A ~:bad; B ~:bad |] ==> ns1 A B NA:set evs |
61956 | 175 |
--> Crypt (pubK A) \<lbrace>Nonce NA, Nonce NB, Agent B\<rbrace>:parts (spies evs) |
17394
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
176 |
--> ns2 B A NA NB:set evs" |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
177 |
apply (erule nsp.induct, simp_all, safe) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
178 |
apply (frule_tac B=B in ns1_imp_Guard, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
179 |
apply (drule Guard_Nonce_analz, simp+, blast) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
180 |
apply (frule_tac B=B in ns1_imp_Guard, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
181 |
apply (drule Guard_Nonce_analz, simp+, blast) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
182 |
apply (frule_tac B=B in ns1_imp_Guard, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
183 |
by (drule Guard_Nonce_analz, simp+, blast+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
184 |
|
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
185 |
lemma B_trusts_NS3: "[| evs:nsp; A ~:bad; B ~:bad |] ==> ns2 B A NA NB:set evs |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
186 |
--> Crypt (pubK B) (Nonce NB):parts (spies evs) --> ns3 A B NB:set evs" |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
187 |
apply (erule nsp.induct, simp_all, safe) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
188 |
apply (frule_tac B=B in ns2_imp_Guard, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
189 |
apply (drule Guard_Nonce_analz, simp+, blast) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
190 |
apply (frule_tac B=B in ns2_imp_Guard, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
191 |
apply (drule Guard_Nonce_analz, simp+, blast) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
192 |
apply (frule_tac B=B in ns2_imp_Guard, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
193 |
apply (drule Guard_Nonce_analz, simp+, blast, blast) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
194 |
apply (frule_tac B=B in ns2_imp_Guard, simp+) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
195 |
by (drule Guard_Nonce_analz, auto dest: Says_imp_knows_Spy NB_is_uniq) |
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
196 |
|
a8c9ed3f9818
renamed Guard/NS_Public, Guard/OtwayRees, Guard/Yahalom.thy to avoid clash with plain Auth versions;
wenzelm
parents:
diff
changeset
|
197 |
end |