find bug: a created proc can be tainted by a message, which cannot remain and maynot be duplicated
theory Dynamic_static
imports Main Flask Static Init_prop Valid_prop Tainted_prop Delete_prop Co2sobj_prop S2ss_prop S2ss_prop2
Temp
begin
context tainting_s begin
fun remove_create_flag :: "t_open_flags \<Rightarrow> t_open_flags"
where
"remove_create_flag (mflag, oflags) = (mflag, oflags - {OF_CREAT})"
fun all_procs :: "t_state \<Rightarrow> t_process set"
where
"all_procs [] = init_procs"
| "all_procs (Clone p p' fds shms # s) = insert p' (all_procs s)"
| "all_procs (e # s) = all_procs s"
definition brandnew_proc :: "t_state \<Rightarrow> t_process"
where
"brandnew_proc s \<equiv> next_nat (all_procs s)"
(*
definition brandnew_proc :: "t_state \<Rightarrow> t_process"
where
"brandnew_proc s \<equiv> next_nat ({p | p s'. p \<in> current_procs s' \<and> s' \<preceq> s})"
another approach:
brandnew_proc = next_nat (all_procs s),
where all_procs is a event-trace listener *)
(*
lemma brandnew_proc_prop1:
"\<lbrakk>s' \<preceq> s; valid s\<rbrakk> \<Longrightarrow> brandnew_proc s \<notin> current_procs s'"
apply (frule vd_preceq, simp)
apply (simp add:brandnew_proc_def)
apply (auto)
sorry
lemma brandnew_proc_prop2:
"\<lbrakk>p \<in> current_procs s'; s' \<preceq> s; valid s\<rbrakk> \<Longrightarrow> brandnew_proc s \<noteq> p"
by (auto dest:brandnew_proc_prop1)
lemma brandnew_proc_prop3:
"\<lbrakk>p \<in> current_procs s; valid (e # s)\<rbrakk> \<Longrightarrow> brandnew_proc (e # s) \<noteq> p"
apply (rule brandnew_proc_prop2, simp)
apply (rule no_juniorI, simp+)
done
*)
(* enrich s target_proc duplicated_pro *)
fun enrich_proc :: "t_state \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> t_state"
where
"enrich_proc [] tp dp = []"
| "enrich_proc (Execve p f fds # s) tp dp = (
if (tp = p)
then Execve dp f (fds \<inter> proc_file_fds s p) # Execve p f fds # (enrich_proc s tp dp)
else Execve p f fds # (enrich_proc s tp dp))"
| "enrich_proc (Clone p p' fds shms # s) tp dp = (
if (tp = p')
then Clone p dp (fds \<inter> proc_file_fds s p) shms # Clone p p' fds shms # s
else Clone p p' fds shms # (enrich_proc s tp dp))"
| "enrich_proc (Open p f flags fd opt # s) tp dp = (
if (tp = p)
then Open dp f (remove_create_flag flags) fd opt # Open p f flags fd opt # (enrich_proc s tp dp)
else Open p f flags fd opt # (enrich_proc s tp dp))"
| "enrich_proc (CloseFd p fd # s) tp dp = (
if (tp = p)
then CloseFd dp fd # CloseFd p fd # (enrich_proc s tp dp)
else CloseFd p fd # (enrich_proc s tp dp))"
| "enrich_proc (Attach p h flag # s) tp dp = (
if (tp = p)
then Attach dp h flag # Attach p h flag # (enrich_proc s tp dp)
else Attach p h flag # (enrich_proc s tp dp))"
| "enrich_proc (Detach p h # s) tp dp = (
if (tp = p)
then Detach dp h # Detach p h # (enrich_proc s tp dp)
else Detach p h # (enrich_proc s tp dp))"
| "enrich_proc (Kill p p' # s) tp dp = (
if (tp = p) then Kill p p' # s
else Kill p p' # (enrich_proc s tp dp))"
| "enrich_proc (Exit p # s) tp dp = (
if (tp = p) then Exit p # s
else Exit p # (enrich_proc s tp dp))"
| "enrich_proc (e # s) tp dp = e # (enrich_proc s tp dp)"
definition is_created_proc:: "t_state \<Rightarrow> t_process \<Rightarrow> bool"
where
"is_created_proc s p \<equiv> p \<in> init_procs \<longrightarrow> deleted (O_proc p) s"
lemma enrich_search_check:
assumes grant: "search_check s (up, rp, tp) f"
and cf2sf: "\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile s' f = cf2sfile s f"
and vd: "valid s" and f_in: "is_file s f" and f_in': "is_file s' f"
and sec: "sectxt_of_obj s' (O_file f) = sectxt_of_obj s (O_file f)"
shows "search_check s' (up, rp, tp) f"
proof (cases f)
case Nil
with f_in vd have "False"
by (auto dest:root_is_dir')
thus ?thesis by simp
next
case (Cons n pf)
from vd f_in obtain sf where sf: "cf2sfile s f = Some sf"
apply (drule_tac is_file_in_current, drule_tac current_file_has_sfile, simp)
apply (erule exE, simp)
done
then obtain psfs where psfs: "get_parentfs_ctxts s pf = Some psfs" using Cons
by (auto simp:cf2sfile_def split:option.splits if_splits)
from sf cf2sf f_in have sf': "cf2sfile s' f = Some sf" by (auto dest:is_file_in_current)
then obtain psfs' where psfs': "get_parentfs_ctxts s' pf = Some psfs'"using Cons
by (auto simp:cf2sfile_def split:option.splits if_splits)
with sf sf' psfs have psfs_eq: "set psfs' = set psfs" using Cons f_in f_in'
apply (simp add:cf2sfile_def split:option.splits)
apply (case_tac sf, simp)
done
show ?thesis using grant f_in f_in' psfs psfs' psfs_eq sec
apply (simp add:Cons split:option.splits)
by (case_tac a, simp)
qed
lemma proc_filefd_has_sfd: "\<lbrakk>fd \<in> proc_file_fds s p; valid s\<rbrakk> \<Longrightarrow> \<exists> sfd. cfd2sfd s p fd = Some sfd"
apply (simp add:proc_file_fds_def)
apply (auto dest: current_filefd_has_sfd)
done
lemma enrich_inherit_fds_check:
assumes grant: "inherit_fds_check s (up, nr, nt) p fds" and vd: "valid s"
and cp2sp: "\<forall> p. p \<in> current_procs s \<longrightarrow> cp2sproc s' p = cp2sproc s p"
and p_in: "p \<in> current_procs s" and p_in': "p \<in> current_procs s'"
and fd_in: "fds \<subseteq> proc_file_fds s p" and fd_in': "fds \<subseteq> proc_file_fds s' p"
shows "inherit_fds_check s' (up, nr, nt) p fds"
proof-
have "\<And> fd. fd \<in> fds \<Longrightarrow> sectxt_of_obj s' (O_fd p fd) = sectxt_of_obj s (O_fd p fd)"
proof-
fix fd
assume fd_in_fds: "fd \<in> fds"
hence fd_in_cfds: "fd \<in> proc_file_fds s p"
and fd_in_cfds': "fd \<in> proc_file_fds s' p"
using fd_in fd_in' by auto
from p_in vd obtain sp where csp: "cp2sproc s p = Some sp"
by (drule_tac current_proc_has_sp, simp, erule_tac exE, simp)
with cp2sp have "cpfd2sfds s p = cpfd2sfds s' p"
apply (erule_tac x = p in allE)
by (auto simp:cp2sproc_def split:option.splits simp:p_in)
hence "cfd2sfd s p fd = cfd2sfd s' p fd" using fd_in_cfds fd_in_cfds'
apply (simp add:cpfd2sfds_def)
apply (frule proc_filefd_has_sfd, simp add:vd, erule exE)
apply (drule_tac x = sfd in eqset_imp_iff, simp)
(*
thm inherit_fds_check_def
thm sectxts_of_fds_def
thm cpfd2sfds_def
apply (
*)sorry
show "sectxt_of_obj s' (O_fd p fd) = sectxt_of_obj s (O_fd p fd)"
sorry
qed
hence "sectxts_of_fds s' p fds = sectxts_of_fds s p fds"
by (simp add:sectxts_of_fds_def)
thus ?thesis using grant
by (simp add:inherit_fds_check_def)
qed
lemma enrich_proc_aux1:
assumes vs': "valid s'"
and os: "os_grant s e" and grant: "grant s e" and vd: "valid s"
and alive: "\<forall> obj. alive s obj \<longrightarrow> alive s' obj"
and cp2sp: "\<forall> p. p \<in> current_procs s \<longrightarrow> cp2sproc s' p = cp2sproc s p"
and cf2sf: "\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile s' f = cf2sfile s f"
shows "valid (e # s')"
sorry (*
proof (cases e)
case (Execve p f fds)
have p_in: "p \<in> current_procs s'" using os alive
apply (erule_tac x = "O_proc p" in allE)
by (auto simp:Execve)
have f_in: "is_file s' f" using os alive
apply (erule_tac x = "O_file f" in allE)
by (auto simp:Execve)
have fd_in: "fds \<subseteq> current_proc_fds s' p" using os alive
apply (auto simp:Execve)
by (erule_tac x = "O_fd p x" in allE, auto)
have "os_grant s' e" using p_in f_in fd_in by (simp add:Execve)
moreover have "grant s' e" apply (simp add:Execve)
proof-
from grant obtain up rp tp uf rf tf
where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)"
by (simp add:Execve split:option.splits, blast)
with grant obtain pu nr nt where p3: "npctxt_execve (up, rp, tp) (uf, rf, tf) = Some (pu, nr, nt)"
by (simp add:Execve split:option.splits del:npctxt_execve.simps, blast)
from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
using os cp2sp
apply (erule_tac x = p in allE)
by (auto simp:Execve co2sobj.simps cp2sproc_def split:option.splits)
from os have f_in': "is_file s f" by (simp add:Execve)
from vd os have "\<exists> sf. cf2sfile s f = Some sf"
by (auto dest!:is_file_in_current current_file_has_sfile simp:Execve)
hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in' p2 cf2sf
apply (erule_tac x = f in allE)
apply (auto dest:is_file_in_current simp:cf2sfile_def split:option.splits)
apply (case_tac f, simp)
apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
done
show ?
proof-
have
*)
lemma enrich_proc_prop:
"\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> valid (enrich_proc s p p') \<and>
(p \<in> current_procs s \<longrightarrow> co2sobj (enrich_proc s p p') (O_proc p') = co2sobj (enrich_proc s p p') (O_proc p)) \<and>
(\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and>
(\<forall> p'. p' \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and>
(\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and>
(Tainted (enrich_proc s p p') = (Tainted s \<union> (if (O_proc p \<in> Tainted s) then {O_proc p'} else {})))"
sorry (*
proof (induct s)
case Nil
thus ?case by (auto simp:is_created_proc_def)
next
case (Cons e s)
hence p1: "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> valid (enrich_proc s p p') \<and>
(p \<in> current_procs s \<longrightarrow> co2sobj (enrich_proc s p p') (O_proc p') = co2sobj (enrich_proc s p p') (O_proc p)) \<and>
(alive s obj \<longrightarrow> alive (enrich_proc s p p') obj \<and> co2sobj (enrich_proc s p p') obj = co2sobj s obj)"
and p2: "valid (e # s)" and p3: "is_created_proc (e # s) p" and p4: "p' \<notin> all_procs (e # s)"
by auto
from p2 have vd: "valid s" and os: "os_grant s e" and grant: "grant s e"
by (auto dest:vd_cons vt_grant vt_grant_os)
from p4 have p4': "p' \<notin> all_procs s" by (case_tac e, auto)
from p1 p4' have a1: "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p')" by (auto simp:vd)
have c1: "valid (enrich_proc (e # s) p p')"
apply (case_tac e)
using a1 os p3
apply (auto simp:is_created_proc_def)
sorry
moreover have c2: "p' \<in> current_procs (enrich_proc (e # s) p p')"
sorry
moreover have c3: "co2sobj (enrich_proc (e # s) p p') (O_proc p') = co2sobj (enrich_proc (e # s) p p') (O_proc p)"
sorry
moreover have c4: "alive (e # s) obj \<longrightarrow>
alive (enrich_proc (e # s) p p') obj \<and> co2sobj (enrich_proc (e # s) p p') obj = co2sobj (e # s) obj"
sorry
ultimately show ?case by auto
qed
*)
lemma "alive s obj \<Longrightarrow> alive (enrich_proc s p p') obj"
apply (induct s, simp)
apply (case_tac a, case_tac[!] obj) sorry (*
apply (auto simp:is_file_def is_dir_def split:option.splits t_inode_tag.splits)
thm is_file_other
*)
lemma enrich_proc_valid:
"\<lbrakk>p \<in> current_procs s; valid s; p \<in> init_procs \<longrightarrow> deleted (O_proc p) s; p' \<notin> current_procs s\<rbrakk> \<Longrightarrow> valid (enrich_proc s p p')" (*
apply (induct s, simp)
apply (frule vd_cons, frule vt_grant, frule vt_grant_os, case_tac a)
apply (auto intro!:valid.intros(2))
prefer 28
end
*)
sorry
(* for any created obj, we can enrich trace with events that create new objs with the same static-properties *)
definition enriched:: "t_state \<Rightarrow> t_object set \<Rightarrow> t_state \<Rightarrow> bool"
where
"enriched s objs s' \<equiv> \<forall> obj \<in> objs. \<exists> obj'. \<not> alive s obj' \<and> obj' \<notin> objs \<and>
alive s' obj' \<and> co2sobj s' obj' = co2sobj s' obj"
definition reserved:: "t_state \<Rightarrow> t_object set \<Rightarrow> t_state \<Rightarrow> bool"
where
"reserved s objs s' \<equiv> \<forall> obj. alive s obj \<longrightarrow> alive s' obj \<and> co2sobj s' obj = co2sobj s obj"
definition enrichable :: "t_state \<Rightarrow> t_object set \<Rightarrow> bool"
where
"enrichable s objs \<equiv> \<exists> s'. valid s' \<and> s2ss s' = s2ss s \<and> enriched s objs s' \<and> reserved s objs s'"
fun is_created :: "t_state \<Rightarrow> t_object \<Rightarrow> bool"
where
"is_created s (O_file f) = (\<forall> f' \<in> same_inode_files s f. init_alive (O_file f') \<longrightarrow> deleted (O_file f') s)"
| "is_created s obj = (init_alive obj \<longrightarrow> deleted obj s)"
definition is_inited :: "t_state \<Rightarrow> t_object \<Rightarrow> bool"
where
"is_inited s obj \<equiv> init_alive obj \<and> \<not> deleted obj s"
(*
lemma is_inited_eq_not_created:
"is_inited s obj = (\<not> is_created s obj)"
by (auto simp:is_created_def is_inited_def)
*)
lemma many_sq_imp_sms:
"\<lbrakk>S_msgq (Create, sec, sms) \<in> ss; ss \<in> static\<rbrakk> \<Longrightarrow> \<forall> sm \<in> (set sms). is_many_smsg sm"
sorry
(* recorded in our static world *)
fun recorded :: "t_object \<Rightarrow> bool"
where
"recorded (O_proc p) = True"
| "recorded (O_file f) = True"
| "recorded (O_dir f) = True"
| "recorded (O_node n) = False" (* cause socket is temperary not considered *)
| "recorded (O_shm h) = True"
| "recorded (O_msgq q) = True"
| "recorded _ = False"
lemma cf2sfile_fi_init_file:
"\<lbrakk>cf2sfile s f = Some (Init f', sec, psec, asecs); is_file s f; valid s\<rbrakk>
\<Longrightarrow> is_init_file f \<and> \<not> deleted (O_file f) s"
apply (simp add:cf2sfile_def sroot_def split:option.splits if_splits)
apply (case_tac f, simp, drule root_is_dir', simp+)
done
lemma root_not_deleted:
"valid s \<Longrightarrow> \<not> deleted (O_dir []) s"
apply (induct s, simp)
apply (frule vd_cons, frule vt_grant_os, case_tac a)
by auto
lemma cf2sfile_fi_init_dir:
"\<lbrakk>cf2sfile s f = Some (Init f', sec, psec, asecs); is_dir s f; valid s\<rbrakk>
\<Longrightarrow> is_init_dir f \<and> \<not> deleted (O_dir f) s"
apply (simp add:cf2sfile_def sroot_def split:option.splits if_splits)
apply (case_tac f, simp add:root_is_init_dir root_not_deleted, simp)
apply (drule file_dir_conflict, simp+)
done
lemma is_created_imp_many:
"\<lbrakk>is_created s obj; co2sobj s obj = Some sobj; alive s obj; valid s\<rbrakk> \<Longrightarrow> is_many sobj"
apply (case_tac obj, auto simp:co2sobj.simps split:option.splits)
apply (case_tac [!] a)
apply (auto simp:cp2sproc_def ch2sshm_def cq2smsgq_def cf2sfiles_def same_inode_files_def
split:option.splits if_splits)
apply (frule cf2sfile_fi_init_file, simp add:is_file_def, simp)
apply (erule_tac x = f' in allE, simp)
apply (frule cf2sfile_fi_init_dir, simp+)+
done
lemma anotherp_imp_manysp:
"\<lbrakk>cp2sproc s p = Some sp; co2sobj s (O_proc p') = co2sobj s (O_proc p); p' \<noteq> p;
p' \<in> current_procs s; p \<in> current_procs s\<rbrakk>
\<Longrightarrow> is_many_sproc sp"
by (case_tac sp, auto simp:cp2sproc_def co2sobj.simps split:option.splits if_splits)
lemma is_file_has_sfs:
"\<lbrakk>is_file s f; valid s; cf2sfile s f = Some sf\<rbrakk>
\<Longrightarrow> \<exists> sfs. co2sobj s (O_file f) = Some (S_file sfs (O_file f \<in> Tainted s)) \<and> sf \<in> sfs"
apply (rule_tac x = "{sf' | f' sf'. cf2sfile s f' = Some sf' \<and> f' \<in> same_inode_files s f}" in exI)
apply (auto simp:co2sobj.simps cf2sfiles_def tainted_eq_Tainted)
apply (rule_tac x = f in exI, simp add:same_inode_files_prop9)
done
declare Product_Type.split_paired_Ex Product_Type.split_paired_All [simp del]
lemma current_proc_in_s2ss:
"\<lbrakk>cp2sproc s p = Some sp; p \<in> current_procs s; valid s\<rbrakk>
\<Longrightarrow> S_proc sp (O_proc p \<in> Tainted s) \<in> s2ss s"
apply (simp add:s2ss_def, rule_tac x = "O_proc p" in exI)
apply (auto simp:co2sobj.simps tainted_eq_Tainted)
done
lemma current_file_in_s2ss:
"\<lbrakk>co2sobj s (O_file f) = Some (S_file sfs tagf); is_file s f; valid s\<rbrakk>
\<Longrightarrow> S_file sfs tagf \<in> s2ss s"
by (simp add:s2ss_def, rule_tac x = "O_file f" in exI, simp)
declare npctxt_execve.simps grant_execve.simps search_check.simps [simp del]
lemma npctxt_execve_eq_sec:
"\<lbrakk>sectxt_of_obj (Execve p f fds # s) (O_proc p) = Some sec'; sectxt_of_obj s (O_proc p) = Some sec;
sectxt_of_obj s (O_file f) = Some fsec; valid (Execve p f fds # s)\<rbrakk>
\<Longrightarrow> npctxt_execve sec fsec = Some sec'"
by (case_tac sec, case_tac fsec, auto simp:npctxt_execve.simps sectxt_of_obj_simps split:option.splits)
lemma npctxt_execve_eq_cp2sproc:
"\<lbrakk>cp2sproc (Execve p f fds # s) p = Some (pi', sec', sfds', shms'); valid (Execve p f fds # s);
cp2sproc s p = Some (pi, sec, sfds, shms); cf2sfile s f = Some (fi, fsec, psec, asecs)\<rbrakk>
\<Longrightarrow> npctxt_execve sec fsec = Some sec'"
apply (frule vt_grant_os, frule vd_cons)
apply (rule npctxt_execve_eq_sec, auto simp:cp2sproc_def cf2sfile_def split:option.splits)
apply (case_tac f, auto dest:root_is_dir')
done
lemma seach_check_eq_static:
"\<lbrakk>cf2sfile s f = Some sf; valid s; is_dir s f \<or> is_file s f\<rbrakk>
\<Longrightarrow> search_check_s sec sf (is_file s f) = search_check s sec f"
apply (case_tac sf)
apply (induct f)
apply (auto simp:search_check_s_def search_check.simps cf2sfile_def sroot_def
root_sec_remains init_sectxt_prop sec_of_root_valid
dest!:root_is_dir' current_has_sec' split:option.splits)
done
lemma grant_execve_intro_execve:
"\<lbrakk>cp2sproc (Execve p f fds # s) p = Some (pi', sec', sfds', shms'); valid (Execve p f fds # s);
cp2sproc s p = Some (pi, sec, sfds, shms); cf2sfile s f = Some (fi, fsec, psec, asecs)\<rbrakk>
\<Longrightarrow> grant_execve sec fsec sec'"
apply (frule vt_grant_os, frule vd_cons, frule vt_grant)
apply (auto split:option.splits dest!:current_has_sec' simp del:grant_execve.simps simp add:cp2sproc_execve)
apply (erule_tac x = aba in allE, erule_tac x = aca in allE, erule_tac x = bb in allE)
apply (auto simp del:grant_execve.simps simp add:cp2sproc_def cf2sfile_def split:option.splits)
apply (case_tac f, simp, drule root_is_dir', simp, simp, simp)
apply (simp add:sectxt_of_obj_simps)
done
lemma search_check_intro_execve:
"\<lbrakk>cp2sproc s p = Some (pi, sec, sfds, shms); valid (Execve p f fds # s)\<rbrakk>
\<Longrightarrow> search_check s sec f"
apply (frule vt_grant_os, frule vd_cons, frule vt_grant)
apply (auto split:option.splits dest!:current_has_sec' simp del:grant_execve.simps simp add:cp2sproc_execve)
apply (erule_tac x = aaa in allE, erule_tac x = ab in allE, erule_tac x = ba in allE)
apply (auto simp add:cp2sproc_def cf2sfile_def split:option.splits)
done
lemma inherit_fds_check_intro_execve:
"\<lbrakk>cp2sproc (Execve p f fds # s) p = Some (pi', sec', sfds', shms'); valid (Execve p f fds # s)\<rbrakk>
\<Longrightarrow> inherit_fds_check s sec' p fds"
apply (frule vt_grant_os, frule vd_cons, frule vt_grant)
apply (auto split:option.splits dest!:current_has_sec' simp add:cp2sproc_execve)
apply (erule_tac x = aba in allE, erule_tac x = aca in allE, erule_tac x = bb in allE)
apply (auto simp add:cp2sproc_def cf2sfile_def split:option.splits)
apply (simp add:sectxt_of_obj_simps)
done
lemma execve_sfds_subset:
"\<lbrakk>cp2sproc (Execve p f fds # s) p = Some (pi', sec', sfds', shms'); valid (Execve p f fds # s);
cp2sproc s p = Some (pi, sec, sfds, shms)\<rbrakk>
\<Longrightarrow> sfds' \<subseteq> sfds"
apply (frule vt_grant_os)
apply (auto simp:cp2sproc_def cpfd2sfds_execve split:option.splits dest!:current_has_sec')
apply (simp add:cpfd2sfds_def)
apply (rule_tac x = fd in bexI, auto simp:proc_file_fds_def)
done
lemma inherit_fds_check_imp_static:
"\<lbrakk>cp2sproc (Execve p f fds # s) p = Some (pi', sec', sfds', shms');
inherit_fds_check s sec' p fds; valid (Execve p f fds # s)\<rbrakk>
\<Longrightarrow> inherit_fds_check_s sec' sfds'"
apply (frule vt_grant_os, frule vd_cons, frule vt_grant)
apply (auto simp:cp2sproc_def cpfd2sfds_execve inherit_fds_check_def inherit_fds_check_s_def split:option.splits)
sorry (*
apply (erule_tac x = "(ad, ae, bc)" in ballE, auto simp:sectxts_of_sfds_def sectxts_of_fds_def)
apply (erule_tac x = fd in ballE, auto simp:cfd2sfd_def split:option.splits)
done *)
lemma d2s_main_execve_grant_aux:
"\<lbrakk>cp2sproc (Execve p f fds # s) p = Some (pi', sec', sfds', shms'); valid (Execve p f fds # s);
cp2sproc s p = Some (pi, sec, sfds, shms); cf2sfile s f = Some (fi, fsec, psec, asecs)\<rbrakk>
\<Longrightarrow> (npctxt_execve sec fsec = Some sec') \<and> grant_execve sec fsec sec' \<and>
search_check_s sec (fi, fsec, psec, asecs) (is_file s f) \<and>
inherit_fds_check_s sec' sfds' \<and> sfds' \<subseteq> sfds"
apply (rule conjI, erule_tac pi = pi and sec = sec and sfds = sfds and
shms = shms and fi = fi and fsec = fsec and psec = psec and
asecs = asecs in npctxt_execve_eq_cp2sproc, simp, simp, simp)
apply (rule conjI, erule_tac pi = pi and sec = sec and sfds = sfds and
shms = shms and fi = fi and fsec = fsec and psec = psec and
asecs = asecs in grant_execve_intro_execve, simp, simp, simp)
apply (rule conjI, drule_tac sec = sec in search_check_intro_execve, simp)
apply (frule vd_cons, frule vt_grant_os)
apply (drule_tac sec = sec in seach_check_eq_static, simp, simp, simp)
apply (rule conjI, rule inherit_fds_check_imp_static, simp)
apply (erule inherit_fds_check_intro_execve, simp, simp)
apply (erule_tac pi = pi and sfds = sfds and shms = shms in execve_sfds_subset, simp+)
done
lemma d2s_main_execve:
"\<lbrakk>valid (Execve p f fds # s); s2ss s \<propto> static\<rbrakk> \<Longrightarrow> s2ss (Execve p f fds # s) \<propto> static"
apply (frule vd_cons, frule vt_grant_os, clarsimp)
apply (frule is_file_has_sfile', simp, erule exE, frule is_file_has_sfs, simp+, erule exE, erule conjE)
apply (auto simp:s2ss_execve split:if_splits option.splits dest:current_proc_has_sp')
apply (clarsimp simp add:init_ss_in_def init_ss_eq_def)
apply (rule_tac x = "update_ss ss' (S_proc (ah, (ai, aj, bd), ak, be) (O_proc p \<in> Tainted s))
(S_proc (ad, (ae, af, bb), ag, bc) (O_proc p \<in> Tainted s \<or> O_file f \<in> Tainted s))" in bexI)
apply (auto simp:update_ss_def elim:Set.subset_insertI2 simp:anotherp_imp_manysp)[1]
apply (case_tac "ah = ad", case_tac "bc = {}", simp)
apply (erule_tac sfs = sfs and fi = a and fsec = "(aa, ab,b)" and pfsec = ac and asecs = ba in s_execve,
auto intro:current_proc_in_s2ss current_file_in_s2ss split:option.splits dest:d2s_main_execve_grant_aux)[1]
apply (simp add:cp2sproc_execve split:option.splits)
apply (simp add:cp2sproc_def split:option.splits if_splits)
apply (clarsimp simp add:init_ss_in_def init_ss_eq_def)
apply (rule_tac x = "update_ss ss' (S_proc (ah, (ai, aj, bd), ak, be) (O_proc p \<in> Tainted s))
(S_proc (ad, (ae, af, bb), ag, bc) (O_proc p \<in> Tainted s \<or> O_file f \<in> Tainted s))" in bexI)
apply (rule conjI, simp add:update_ss_def)
apply (rule conjI, simp add:update_ss_def)
apply (auto)[1]
apply (simp add:update_ss_def)
apply (rule conjI, rule impI)
apply (rule subsetI, clarsimp)
apply (erule impE)
apply (erule set_mp, simp)
apply (case_tac ah, simp+)
apply (rule impI, rule subsetI, clarsimp)
apply (erule set_mp, simp)
apply (case_tac "ah = ad", case_tac "bc = {}", simp)
apply (erule_tac sfs = sfs and fi = a and fsec = "(aa, ab,b)" and pfsec = ac and asecs = ba in s_execve,
auto intro:current_proc_in_s2ss current_file_in_s2ss split:option.splits dest:d2s_main_execve_grant_aux)[1]
apply (simp add:cp2sproc_execve split:option.splits)
apply (simp add:cp2sproc_def split:option.splits if_splits)
done
lemma co2sobj_eq_alive_proc_imp:
"\<lbrakk>co2sobj s obj = co2sobj s (O_proc p); alive s (O_proc p); valid s\<rbrakk>
\<Longrightarrow> \<exists> p'. obj = O_proc p'"
by (auto simp add:co2sobj.simps split:option.splits dest:current_proc_has_sp' intro:co2sobj_sproc_imp)
lemma enrichable_execve:
assumes p1: "\<And> objs. \<forall> obj \<in> objs. alive s obj \<and> is_created s obj \<and> recorded obj
\<Longrightarrow> \<exists> s'. valid s' \<and> s2ss s' = s2ss s \<and> enriched s objs s' \<and> reserved s objs s'"
and p2: "valid (e # s)" and p3: "\<forall>obj\<in>objs. alive (e # s) obj \<and> is_created (e # s) obj \<and> recorded obj"
and p4: "e = Execve p f fds"
shows "enrichable (e # s) objs"
proof-
from p2 have os: "os_grant s e" and se: "grant s e" and vd: "valid s"
by (auto dest:vt_grant_os vd_cons vt_grant)
from p3 have recorded: "\<forall> obj \<in> objs. recorded obj" by auto
from p3 p4 p2 have p1': "\<forall> obj \<in> objs. alive s obj \<and> is_created s obj"
apply clarify
apply (erule_tac x = obj in ballE, simp add:alive_simps)
apply (case_tac obj, auto simp:same_inode_files_simps)
done
then obtain s' where a1: "valid s'" and a2: "s2ss s' = s2ss s" and a3: "enriched s objs s'"
and a4: "reserved s objs s'"
using p1 recorded by metis
show ?thesis
proof (cases "O_proc p \<in> objs")
case True
hence p_in: "p \<in> current_procs s'" using a4 os p4
by (auto simp:reserved_def elim:allE[where x = "O_proc p"])
with a1 a3 True obtain p' where b1: "\<not> alive s (O_proc p')" and b2: "O_proc p' \<notin> objs"
and b3: "alive s' (O_proc p')" and b4: "co2sobj s' (O_proc p') = co2sobj s' (O_proc p)"
apply (simp only:enriched_def)
apply (erule_tac x = "O_proc p" in ballE)
apply (erule exE|erule conjE)+
apply (frule co2sobj_eq_alive_proc_imp, auto)
done
have "valid (Execve p' f fds # e # s')"
sorry
moreover have "s2ss (Execve p' f fds # e # s') = s2ss (e # s)"
sorry
moreover have "enriched (e # s) objs (Execve p' f fds # e # s')"
sorry
moreover have "reserved (e # s) objs (Execve p' f fds # e # s')"
sorry
ultimately show ?thesis
apply (simp add:enrichable_def)
apply (rule_tac x = "Execve p' f fds # e # s'" in exI)
by auto
next
case False
from a4 os p4 have "p \<in> current_procs s'"
apply (simp add:reserved_def)
by (erule_tac x = "O_proc p" in allE, auto)
moreover from a4 os p4 have "is_file s' f"
apply (simp add:reserved_def)
by (erule_tac x = "O_file f" in allE, auto)
moreover from a4 os p4 vd have "fds \<subseteq> proc_file_fds s' p"
apply (rule_tac subsetI, clarsimp simp:reserved_def current_proc_fds.simps)
apply (erule_tac x = "O_fd p x" in allE, erule impE)
sorry
ultimately have "os_grant s' e"
by (simp add:p4)
moreover have "grant s' e"
sorry
ultimately have "valid (e # s')"
using a1 by (erule_tac valid.intros(2), simp+)
thus ?thesis
apply (simp add:enrichable_def)
apply (rule_tac x = "e # s'" in exI)
apply (simp)
sorry
qed
qed
lemma s2d_main_execve:
"\<lbrakk>grant_execve pctxt fsec pctxt'; ss \<in> static; S_proc (pi, pctxt, fds, shms) tagp \<in> ss; S_file sfs tagf \<in> ss;
(fi, fsec, pfsec, asecs) \<in> sfs; npctxt_execve pctxt fsec = Some pctxt';
search_check_s pctxt (fi, fsec, pfsec, asecs) True; inherit_fds_check_s pctxt' fds'; fds' \<subseteq> fds; valid s;
s2ss s = ss\<rbrakk> \<Longrightarrow> \<exists>s. valid s \<and>
s2ss s = update_ss ss (S_proc (pi, pctxt, fds, shms) tagp) (S_proc (pi, pctxt', fds', {}) (tagp \<or> tagf))"
apply (simp add:update_ss_def)
thm update_ss_def
sorry
(*
lemma s2d_main_execve:
"ss \<in> static \<Longrightarrow> \<exists> s. valid s \<and> s2ss s = ss"
apply (erule static.induct)
apply (rule_tac x = "[]" in exI, simp add:s2ss_nil_prop valid.intros)
apply (erule exE|erule conjE)+
apply (rule s2d_main_execve, simp+)
apply (erule exE|erule conjE)+
sorry
*)
(*********************** uppest-level 3 theorems ***********************)
lemma enrichability:
"\<lbrakk>valid s; \<forall> obj \<in> objs. alive s obj \<and> is_created s obj \<and> recorded obj\<rbrakk>
\<Longrightarrow> enrichable s objs" sorry (*
proof (induct s arbitrary:objs)
case Nil
hence "objs = {}"
apply (auto)
apply (erule_tac x = x in ballE)
apply (case_tac x)
apply (auto simp:init_alive_prop)
sorry (* done *)
thus ?case using Nil unfolding enrichable_def enriched_def reserved_def
by (rule_tac x = "[]" in exI, auto)
next
case (Cons e s)
hence p1: "\<And> objs. \<forall> obj \<in> objs. alive s obj \<and> is_created s obj \<and> recorded obj
\<Longrightarrow> \<exists> s'. valid s' \<and> s2ss s' = s2ss s \<and> enriched s objs s' \<and> reserved s objs s'"
and p2: "valid (e # s)" and p3: "\<forall>obj\<in>objs. alive (e # s) obj \<and> is_created (e # s) obj \<and> recorded obj"
and os: "os_grant s e" and se: "grant s e" and vd: "valid s"
by (auto dest:vt_grant_os vd_cons vt_grant simp:enrichable_def)
show ?case
proof (cases e)
case (Execve p f fds)
hence p4: "e = Execve p f fds" by simp
from p3 have p5: "is_inited s (O_proc p) \<Longrightarrow> (O_proc p) \<notin> objs"
by (auto simp:is_created_def is_inited_def p4 elim!:ballE[where x = "O_proc p"])
show "enrichable (e # s) objs"
proof (cases "is_inited s (O_proc p)")
case True
with p5 have a1: "(O_proc p) \<notin> objs" by simp
with p3 p4 p2 have a2: "\<forall> obj \<in> objs. alive s obj \<and> is_created s obj" and a2': "\<forall> obj \<in> objs. recorded obj"
apply (auto simp:is_created_def alive_simps is_inited_def)
apply (erule_tac x = obj in ballE, auto simp:alive_simps split:t_object.splits)
done
then obtain s' where a3: "valid s'" and a4: "s2ss s' = s2ss s"
and a5: "enriched s objs s'" and a6: "reserved s objs s'"
using p1 apply (simp add:enrichable_def) sorry
from a5 p4 p2 a2' have a7: "enriched s objs (e # s')"
apply (clarsimp simp add:enriched_def co2sobj_execve)
apply (erule_tac x = obj in ballE, clarsimp)
apply (rule_tac x = obj' in exI, auto simp:co2sobj_execve alive_simps)
thm enriched_def
obtain s' where p6:"enriched s objs s'"
apply (simp add: alive_simps enrichable_def)
apply auto apply (rule ballI, rule_tac x = obj in exI)
have p6:"enriched (e # s) objs (e # s)"
apply (simp add:enriched_def alive_simps)
apply auto apply (rule ballI, rule_tac x = obj in exI)
have "enrich (e # s) objs (e # s)"
apply (simp add:enrich_def p4)
sorry
moreover have "reserve (e # s) objs (e # s)"
sorry
ultimately show ?thesis using p2
apply (simp add:enrichable_def)
by (rule_tac x = "e # s" in exI, simp)
next
thm enrichable_def
apply (simp add:enrichable_def p4)
apply auto
apply (auto simp:enrichable_def)
apply (induct s)
done
qed
*)
lemma d2s_main:
"valid s \<Longrightarrow> s2ss s \<propto> static"
apply (induct s, simp add:s2ss_nil_prop init_ss_in_def)
apply (rule_tac x = "init_static_state" in bexI, simp, simp add:s_init)
apply (frule vd_cons, frule vt_grant_os, simp)
apply (case_tac a)
apply (clarsimp simp add:s2ss_execve)
apply (rule conjI, rule impI)
sorry
lemma s2d_main:
"ss \<in> static \<Longrightarrow> \<exists> s. valid s \<and> s2ss s = ss"
apply (erule static.induct)
apply (rule_tac x = "[]" in exI, simp add:s2ss_nil_prop valid.intros)
apply (erule exE|erule conjE)+
apply (simp add:update_ss_def)
sorry
lemma s2d_main':
"ss \<in> static \<Longrightarrow> \<exists> s. valid s \<and> s2ss s \<doteq> ss"
apply (erule static.induct)
apply (rule_tac x = "[]" in exI, simp add:s2ss_nil_prop valid.intros)
apply (erule exE|erule conjE)+
apply (simp add:update_ss_def)
sorry
end
end