Theory Guard_Yahalom

(*  Title:      HOL/Auth/Guard/Guard_Yahalom.thy
    Author:     Frederic Blanqui, University of Cambridge Computer Laboratory
    Copyright   2002  University of Cambridge
*)

sectionYahalom Protocol

theory Guard_Yahalom imports "../Shared" Guard_Shared begin

subsectionmessages used in the protocol

abbreviation (input)
  ya1 :: "agent => agent => nat => event" where
  "ya1 A B NA == Says A B Agent A, Nonce NA"

abbreviation (input)
  ya1' :: "agent => agent => agent => nat => event" where
  "ya1' A' A B NA == Says A' B Agent A, Nonce NA"

abbreviation (input)
  ya2 :: "agent => agent => nat => nat => event" where
  "ya2 A B NA NB == Says B Server Agent B, Ciph B Agent A, Nonce NA, Nonce NB"

abbreviation (input)
  ya2' :: "agent => agent => agent => nat => nat => event" where
  "ya2' B' A B NA NB == Says B' Server Agent B, Ciph B Agent A, Nonce NA, Nonce NB"

abbreviation (input)
  ya3 :: "agent => agent => nat => nat => key => event" where
  "ya3 A B NA NB K ==
    Says Server A Ciph A Agent B, Key K, Nonce NA, Nonce NB,
                    Ciph B Agent A, Key K"

abbreviation (input)
  ya3':: "agent => msg => agent => agent => nat => nat => key => event" where
  "ya3' S Y A B NA NB K ==
    Says S A Ciph A Agent B, Key K, Nonce NA, Nonce NB, Y"

abbreviation (input)
  ya4 :: "agent => agent => nat => nat => msg => event" where
  "ya4 A B K NB Y == Says A B Y, Crypt K (Nonce NB)"

abbreviation (input)
  ya4' :: "agent => agent => nat => nat => msg => event" where
  "ya4' A' B K NB Y == Says A' B Y, Crypt K (Nonce NB)"


subsectiondefinition of the protocol

inductive_set ya :: "event list set"
where

  Nil: "[]  ya"

| Fake: "[| evs  ya; X  synth (analz (spies evs)) |] ==> Says Spy B X # evs  ya"

| YA1: "[| evs1  ya; Nonce NA  used evs1 |] ==> ya1 A B NA # evs1  ya"

| YA2: "[| evs2  ya; ya1' A' A B NA  set evs2; Nonce NB  used evs2 |]
  ==> ya2 A B NA NB # evs2  ya"

| YA3: "[| evs3  ya; ya2' B' A B NA NB  set evs3; Key K  used evs3 |]
  ==> ya3 A B NA NB K # evs3  ya"

| YA4: "[| evs4  ya; ya1 A B NA  set evs4; ya3' S Y A B NA NB K  set evs4 |]
  ==> ya4 A B K NB Y # evs4  ya"

subsectiondeclarations for tactics

declare knows_Spy_partsEs [elim]
declare Fake_parts_insert [THEN subsetD, dest]
declare initState.simps [simp del]

subsectiongeneral properties of ya

lemma ya_has_no_Gets: "evs  ya  A X. Gets A X  set evs"
by (erule ya.induct, auto)

lemma ya_is_Gets_correct [iff]: "Gets_correct ya"
by (auto simp: Gets_correct_def dest: ya_has_no_Gets)

lemma ya_is_one_step [iff]: "one_step ya"
by (unfold one_step_def, clarify, ind_cases "ev#evs  ya" for ev evs, auto)

lemma ya_has_only_Says' [rule_format]: "evs  ya 
ev  set evs  (A B X. ev=Says A B X)"
by (erule ya.induct, auto)

lemma ya_has_only_Says [iff]: "has_only_Says ya"
by (auto simp: has_only_Says_def dest: ya_has_only_Says')

lemma ya_is_regular [iff]: "regular ya"
apply (simp only: regular_def, clarify)
apply (erule ya.induct, simp_all add: initState.simps knows.simps)
by (auto dest: parts_sub)

subsectionguardedness of KAB

lemma Guard_KAB [rule_format]: "[| evs  ya; A  bad; B  bad |] ==>
ya3 A B NA NB K  set evs  GuardK K {shrK A,shrK B} (spies evs)" 
apply (erule ya.induct)
(* Nil *)
apply simp_all
(* Fake *)
apply (clarify, erule in_synth_GuardK, erule GuardK_analz, simp)
(* YA1 *)
(* YA2 *)
apply safe
apply (blast dest: Says_imp_spies)
(* YA3 *)
apply blast
apply (drule_tac A=Server in Key_neq, simp+, rule No_Key, simp)
apply (drule_tac A=Server in Key_neq, simp+, rule No_Key, simp)
(* YA4 *)
apply (blast dest: Says_imp_spies in_GuardK_kparts)
by blast

subsectionsession keys are not symmetric keys

lemma KAB_isnt_shrK [rule_format]: "evs  ya 
ya3 A B NA NB K  set evs  K  range shrK"
by (erule ya.induct, auto)

lemma ya3_shrK: "evs  ya  ya3 A B NA NB (shrK C)  set evs"
by (blast dest: KAB_isnt_shrK)

subsectionya2' implies ya1'

lemma ya2'_parts_imp_ya1'_parts [rule_format]:
     "[| evs  ya; B  bad |] ==>
      Ciph B Agent A, Nonce NA, Nonce NB  parts (spies evs) 
      Agent A, Nonce NA  spies evs"
by (erule ya.induct, auto dest: Says_imp_spies intro: parts_parts)

lemma ya2'_imp_ya1'_parts: "[| ya2' B' A B NA NB  set evs; evs  ya; B  bad |]
==> Agent A, Nonce NA  spies evs"
by (blast dest: Says_imp_spies ya2'_parts_imp_ya1'_parts)

subsectionuniqueness of NB

lemma NB_is_uniq_in_ya2'_parts [rule_format]: "[| evs  ya; B  bad; B'  bad |] ==>
Ciph B Agent A, Nonce NA, Nonce NB  parts (spies evs) 
Ciph B' Agent A', Nonce NA', Nonce NB  parts (spies evs) 
A=A'  B=B'  NA=NA'"
apply (erule ya.induct, simp_all, clarify)
apply (drule Crypt_synth_insert, simp+)
apply (drule Crypt_synth_insert, simp+, safe)
apply (drule not_used_parts_false, simp+)+
by (drule Says_not_parts, simp+)+

lemma NB_is_uniq_in_ya2': "[| ya2' C A B NA NB  set evs;
ya2' C' A' B' NA' NB  set evs; evs  ya; B  bad; B'  bad |]
==> A=A'  B=B'  NA=NA'"
by (drule NB_is_uniq_in_ya2'_parts, auto dest: Says_imp_spies)

subsectionya3' implies ya2'

lemma ya3'_parts_imp_ya2'_parts [rule_format]: "[| evs  ya; A  bad |] ==>
Ciph A Agent B, Key K, Nonce NA, Nonce NB  parts (spies evs)
 Ciph B Agent A, Nonce NA, Nonce NB  parts (spies evs)"
apply (erule ya.induct, simp_all)
apply (clarify, drule Crypt_synth_insert, simp+)
apply (blast intro: parts_sub, blast)
by (auto dest: Says_imp_spies parts_parts)

lemma ya3'_parts_imp_ya2' [rule_format]: "[| evs  ya; A  bad |] ==>
Ciph A Agent B, Key K, Nonce NA, Nonce NB  parts (spies evs)
 (B'. ya2' B' A B NA NB  set evs)"
apply (erule ya.induct, simp_all, safe)
apply (drule Crypt_synth_insert, simp+)
apply (drule Crypt_synth_insert, simp+, blast)
apply blast
apply blast
by (auto dest: Says_imp_spies2 parts_parts)

lemma ya3'_imp_ya2': "[| ya3' S Y A B NA NB K  set evs; evs  ya; A  bad |]
==> (B'. ya2' B' A B NA NB  set evs)"
by (drule ya3'_parts_imp_ya2', auto dest: Says_imp_spies)

subsectionya3' implies ya3

lemma ya3'_parts_imp_ya3 [rule_format]: "[| evs  ya; A  bad |] ==>
Ciph A Agent B, Key K, Nonce NA, Nonce NB  parts(spies evs)
 ya3 A B NA NB K  set evs"
apply (erule ya.induct, simp_all, safe)
apply (drule Crypt_synth_insert, simp+)
by (blast dest: Says_imp_spies2 parts_parts)

lemma ya3'_imp_ya3: "[| ya3' S Y A B NA NB K  set evs; evs  ya; A  bad |]
==> ya3 A B NA NB K  set evs"
by (blast dest: Says_imp_spies ya3'_parts_imp_ya3)

subsectionguardedness of NB

definition ya_keys :: "agent  agent  nat  nat  event list  key set" where
"ya_keys A B NA NB evs  {shrK A,shrK B}  {K. ya3 A B NA NB K  set evs}"

lemma Guard_NB [rule_format]: "[| evs  ya; A  bad; B  bad |] ==>
ya2 A B NA NB  set evs  Guard NB (ya_keys A B NA NB evs) (spies evs)"
apply (erule ya.induct)
(* Nil *)
apply (simp_all add: ya_keys_def)
(* Fake *)
apply safe
apply (erule in_synth_Guard, erule Guard_analz, simp, clarify)
apply (frule_tac B=B in Guard_KAB, simp+)
apply (drule_tac p=ya in GuardK_Key_analz, simp+)
apply (blast dest: KAB_isnt_shrK, simp)
(* YA1 *)
apply (drule_tac n=NB in Nonce_neq, simp+, rule No_Nonce, simp)
(* YA2 *)
apply blast
apply (drule Says_imp_spies)
apply (drule_tac n=NB in Nonce_neq, simp+)
apply (drule_tac n'=NAa in in_Guard_kparts_neq, simp+)
apply (rule No_Nonce, simp)
(* YA3 *)
apply (rule Guard_extand, simp, blast)
apply (case_tac "NAa=NB", clarify)
apply (frule Says_imp_spies)
apply (frule in_Guard_kparts_Crypt, simp+)
apply (frule_tac A=A and B=B and NA=NA and NB=NB and C=Ba in ya3_shrK, simp)
apply (drule ya2'_imp_ya1'_parts, simp, blast, blast)
apply (case_tac "NBa=NB", clarify)
apply (frule Says_imp_spies)
apply (frule in_Guard_kparts_Crypt, simp+)
apply (frule_tac A=A and B=B and NA=NA and NB=NB and C=Ba in ya3_shrK, simp)
apply (drule NB_is_uniq_in_ya2', simp+, blast, simp+)
apply (simp add: No_Nonce, blast)
(* YA4 *)
apply (blast dest: Says_imp_spies)
apply (case_tac "NBa=NB", clarify)
apply (frule_tac A=S in Says_imp_spies)
apply (frule in_Guard_kparts_Crypt, simp+)
apply (blast dest: Says_imp_spies)
apply (case_tac "NBa=NB", clarify)
apply (frule_tac A=S in Says_imp_spies)
apply (frule in_Guard_kparts_Crypt, simp+, blast, simp+)
apply (frule_tac A=A and B=B and NA=NA and NB=NB and C=Aa in ya3_shrK, simp)
apply (frule ya3'_imp_ya2', simp+, blast, clarify)
apply (frule_tac A=B' in Says_imp_spies)
apply (rotate_tac -1, frule in_Guard_kparts_Crypt, simp+)
apply (frule_tac A=A and B=B and NA=NA and NB=NB and C=Ba in ya3_shrK, simp)
apply (drule NB_is_uniq_in_ya2', simp+, blast, clarify)
apply (drule ya3'_imp_ya3, simp+)
apply (simp add: Guard_Nonce)
apply (simp add: No_Nonce)
done

end