src/HOL/Unix/document/root.tex

some refinements in Algebra and Number_Theory

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\begin{document}

\title{Some aspects of Unix file-system security}
\author{Markus Wenzel \\ TU M\"unchen}
\maketitle

\begin{abstract}
  Unix is a simple but powerful system where everything is either a process or
  a file.  Access to system resources works mainly via the file-system,
  including special files and devices.  Most Unix security issues are
  reflected directly within the file-system.  We give a mathematical model of
  the main aspects of the Unix file-system including its security model, but
  ignoring processes.  Within this formal model we discuss some aspects of
  Unix security, including a few odd effects caused by the general
  ``worse-is-better'' approach followed in Unix.
  
  Our formal specifications will be giving in simply-typed classical
  set-theory as provided by Isabelle/HOL.  Formal proofs are expressed in a
  human-readable fashion using the structured proof language of Isabelle/Isar,
  which is a system intended to support intelligible semi-automated reasoning
  over a wide range of application domains.  Thus the present development also
  demonstrates that Isabelle/Isar is sufficiently flexible to cover typical
  abstract verification tasks as well.  So far this has been the classical
  domain of interactive theorem proving systems based on unstructured tactic
  languages.
\end{abstract}

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\section{Introduction}\label{sec:unix-intro}

\subsection{The Unix philosophy}

Over the last 2 or 3 decades the Unix community has collected a certain amount
of folklore wisdom on building systems that actually work, see
\cite{Unix-heritage} for further historical background information.  Here is a
recent account of the philosophical principles behind the Unix way of software
and systems engineering.\footnote{This has appeared on \emph{Slashdot} on
  25-March-2000, see \url{http://slashdot.com}.}

{\small
\begin{verbatim}
The UNIX Philosophy (Score:2, Insightful)
by yebb on Saturday March 25, @11:06AM EST (#69)
(User Info) 

The philosophy is a result of more than twenty years of software
development and has grown from the UNIX community instead of being
enforced upon it. It is a defacto-style of software development. The
nine major tenets of the UNIX Philosophy are:

  1. small is beautiful 
  2. make each program do one thing well 
  3. build a prototype as soon as possible 
  4. choose portability over efficiency 
  5. store numerical data in flat files 
  6. use software leverage to your advantage 
  7. use shell scripts to increase leverage and portability 
  8. avoid captive user interfaces 
  9. make every program a filter 

The Ten Lesser Tenets 

  1. allow the user to tailor the environment 
  2. make operating system kernels small and lightweight 
  3. use lower case and keep it short 
  4. save trees 
  5. silence is golden 
  6. think parallel 
  7. the sum of the parts if greater than the whole 
  8. look for the ninety percent solution 
  9. worse is better 
 10. think hierarchically 
\end{verbatim}
}

The ``worse-is-better'' approach quoted above is particularly interesting.  It
basically means that \emph{relevant} concepts have to be implemented in the
right way, while \emph{irrelevant} issues are simply ignored in order to avoid
unnecessary complication of the design and implementation.  Certainly, the
overall quality of the resulting system heavily depends on the virtue of
distinction between the two categories of ``relevant'' and ``irrelevant''.


\subsection{Unix security}

The main entities of a Unix system are \emph{files} and \emph{processes}
\cite{Tanenbaum:1992}.  Files subsume any persistent ``static'' entity managed
by the system --- ranging from plain files and directories, to more special
ones such device nodes, pipes etc.  On the other hand, processes are
``dynamic'' entities that may perform certain operations while being run by
the system.

The security model of classic Unix systems is centered around the file system.
The operations permitted by a process that is run by a certain user are
determined from information stored within the file system.  This includes any
kind of access control, such as read/write access to some plain file, or
read-only access to a certain global device node etc.  Thus proper arrangement
of the main Unix file-system is very critical for overall
security.\footnote{Incidently, this is why the operation of mounting new
  volumes into the existing file space is usually restricted to the
  super-user.}

\medskip Generally speaking, the Unix security model is a very simplistic one.
The original designers did not have maximum security in mind, but wanted to
get a decent system working for typical multi-user environments.  Contemporary
Unix implementations still follow the basic security model of the original
versions from the early 1970's \cite{Unix-heritage}.  Even back then there
would have been better approaches available, albeit with more complexity
involved both for implementers and users.

On the other hand, even in the 2000's many computer systems are run with
little or no file-system security at all, even though virtually any system is
exposed to the net in one way or the other.  Even ``personal'' computer
systems have long left the comfortable home environment and entered the
wilderness of the open net sphere.

\medskip This treatment of file-system security is a typical example of the
``worse-is-better'' principle introduced above.  The simplistic security model
of Unix got widely accepted within a large user community, while the more
innovative (and cumbersome) ones are only used very reluctantly and even tend
to be disabled by default in order to avoid confusion of beginners.


\subsection{Odd effects}

Simplistic systems usually work very well in typical situations, but tend to
exhibit some odd features in non-typical ones.  As far as Unix file-system
security is concerned, there are many such features that are well-known to
experts, but may surprise naive users.

Subsequently, we consider an example that is not so exotic after all.  As may
be easily experienced on a running Unix system, the following sequence of
commands may put a user's file-system into an uncouth state.  Below we assume
that \texttt{user1} and \texttt{user2} are working within the same directory
(e.g.\ somewhere within the home of \texttt{user1}).

{\small
\begin{verbatim}
  user1> umask 000; mkdir foo; umask 022
  user2> mkdir foo/bar
  user2> touch foo/bar/baz
\end{verbatim}
}
  
That is, \texttt{user1} creates a directory that is writable for everyone, and
\texttt{user2} puts there a non-empty directory without write-access for
others.

In this situation it has become impossible for \texttt{user1} to remove his
very own directory \texttt{foo} without the cooperation of either
\texttt{user2}, since \texttt{foo} contains another non-empty and non-writable
directory, which cannot be removed.

{\small
\begin{verbatim}
  user1> rmdir foo
  rmdir: directory "foo": Directory not empty
  user1> rmdir foo/bar
  rmdir: directory "bar": Directory not empty
  user1> rm foo/bar/baz
  rm not removed: Permission denied
\end{verbatim}
}

Only after \texttt{user2} has cleaned up his directory \texttt{bar}, is
\texttt{user1} enabled to remove both \texttt{foo/bar} and \texttt{foo}.
Alternatively \texttt{user2} could remove \texttt{foo/bar} as well.  In the
unfortunate case that \texttt{user2} does not cooperate or is presently
unavailable, \texttt{user1} would have to find the super user (\texttt{root})
to clean up the situation.  In Unix \texttt{root} may perform any file-system
operation without any access control limitations.\footnote{This is the typical
  Unix way of handling abnormal situations: while it is easy to run into odd
  cases due to simplistic policies it is as well quite easy to get out.  There
  are other well-known systems that make it somewhat harder to get into a fix,
  but almost impossible to get out again!}

\bigskip Is there really no other way out for \texttt{user1} in the above
situation?  Experiments can only show possible ways, but never demonstrate the
absence of other means exhaustively.  This is a typical situation where
(formal) proof may help.  Subsequently, we model the main aspects Unix
file-system security within Isabelle/HOL \cite{Nipkow-et-al:2000:HOL} and
prove that there is indeed no way for \texttt{user1} to get rid of his
directory \texttt{foo} without help by others (see
\secref{sec:unix-main-result} for the main theorem stating this).

\medskip The formal techniques employed in this development are the typical
ones for abstract ``verification'' tasks, namely induction and case analysis
over the structure of file-systems and possible system transitions.
Isabelle/HOL \cite{Nipkow-et-al:2000:HOL} is particularly well-suited for this
kind of application.  By the present development we also demonstrate that the
Isabelle/Isar environment \cite{Wenzel:1999:TPHOL,Wenzel:2002:isar-ref} for
readable formal proofs is sufficiently flexible to cover non-trivial
verification tasks as well.  So far this has been the classical domain of
``interactive'' theorem proving systems based on unstructured tactic
languages.


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