
diff -r f0e51ffd2965 -r 2185acdb43bb slides/slides05.tex
--- a/slides/slides05.tex	Mon Oct 28 11:53:07 2013 +0000
+++ b/slides/slides05.tex	Tue Oct 29 10:33:21 2013 +0000
@@ -1,8 +1,8 @@
 \documentclass[dvipsnames,14pt,t]{beamer}
 \usepackage{proof}
-\usepackage{beamerthemeplainculight}
-\usepackage[T1]{fontenc}
-\usepackage[latin1]{inputenc}
+\usepackage{beamerthemeplaincu}
+%\usepackage[T1]{fontenc}
+%\usepackage[latin1]{inputenc}
 \usepackage{mathpartir}
 \usepackage{isabelle}
 \usepackage{isabellesym}
@@ -89,7 +89,7 @@
 	showstringspaces=false}
 
 % beamer stuff 
-\renewcommand{\slidecaption}{APP 05, King's College London, 23 October 2012}
+\renewcommand{\slidecaption}{APP 05, King's College London, 29 October 2013}
 
 \newcommand{\bl}[1]{\textcolor{blue}{#1}}
 \begin{document}
@@ -112,7 +112,7 @@
   \begin{center}
   \begin{tabular}{ll}
   Email:  & christian.urban at kcl.ac.uk\\
-  Of$\!$fice: & S1.27 (1st floor Strand Building)\\
+  Office: & S1.27 (1st floor Strand Building)\\
   Slides: & KEATS (also homework is there)\\
   \end{tabular}
   \end{center}
@@ -122,52 +122,39 @@
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{Satan's Computer}
-
-Ross Anderson and Roger Needham wrote:\bigskip
-
-\begin{quote}
-In effect, our task is to program a computer which gives 
-answers which are subtly and maliciously wrong at the most 
-inconvenient possible moment\ldots{} we hope that the lessons 
-learned from programming Satan's computer may be helpful 
-in tackling the more common problem of programming Murphy's.
-\end{quote}
-
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+  \mode<presentation>{
+  \begin{frame}[t]
+  \frametitle{Last Week}
+ 
+\mbox{} 
+  
+\begin{tabular}{l}
+{\Large \bl{$A\;\rightarrow\; B : \ldots$}}\\
+\onslide<1->{\Large \bl{$B\;\rightarrow\; A : \ldots$}}\\
+\onslide<1->{\Large \;\;\;\;\;\bl{$:$}}\bigskip
+\end{tabular}  
+  
+ \begin{itemize}
+ \item by convention \bl{$A$}, \bl{$B$} are named principals \bl{Alice\ldots}\\
+ but most likely they are programs
+\item indicates one ``protocol run'', or session,  which specifies an 
+order in the communication
+\item there can be several sessions in parallel (think of wifi routers) 
+\item nonces (randomly generated numbers) used only once 
+\end{itemize} 
+  
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+  
 
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
-\frametitle{Protocol Specifications}
-
-The Needham-Schroeder Protocol:
-
-\begin{center}
-\begin{tabular}{@ {\hspace{-7mm}}l@{\hspace{2mm}}r@ {\hspace{1mm}}l}
-Message 1 & \bl{$A \rightarrow S :$} & \bl{$A, B, N_A$}\\
-Message 2 & \bl{$S \rightarrow A :$} & \bl{$\{N_A, B, K_{AB},\{K_{AB}, A\}_{K_{BS}} \}_{K_{AS}}$}\\
-Message 3 & \bl{$A \rightarrow B :$} & \bl{$\{K_{AB}, A\}_{K_{BS}} $}\\
-Message 4 & \bl{$B \rightarrow A :$} & \bl{$\{N_B\}_{K_{AB}}$}\\
-Message 5 & \bl{$A \rightarrow B :$} & \bl{$\{N_B-1\}_{K_{AB}}$}\\
-\end{tabular}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
 \frametitle{Cryptographic Protocol Failures}
 
-Again Ross Anderson and Roger Needham wrote:\bigskip
+Ross Anderson and Roger Needham wrote:\bigskip
 
 \begin{quote}
 \textcolor{gray}{
@@ -180,36 +167,367 @@
 
 
 \end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Protocols}
+
+Examples where ``over-the-air'' protocols are used
+
+\begin{itemize}
+\item wifi
+\item card readers (you cannot trust the terminals)
+\item RFI (passports)
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+\begin{center}
+\includegraphics[scale=0.5]{pics/dogs.jpg}
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Chip-and-PIN\end{tabular}}
+
+
+\begin{itemize}
+\item A ``tamperesitant'' terminal playing Tetris on 
+\textcolor{blue}{\href{http://www.youtube.com/watch?v=wWTzkD9M0sU}{youtube}}.\\
+\textcolor{lightgray}{\footnotesize(\url{http://www.youtube.com/watch?v=wWTzkD9M0sU})}
+\end{itemize}
+ 
+  
+\includegraphics[scale=0.2]{pics/tetris.jpg}
+  
+  
+\end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1-3>[c]
+  \frametitle{Oyster Cards}
 
+  \includegraphics[scale=0.4]{pics/oysterc.jpg}
+
+  \begin{itemize}
+  \item good example of a bad protocol\\ (security by obscurity)\bigskip
+  \item<3->  ``Breaching security on Oyster cards should not 
+  allow unauthorised use for more than a day, as TfL promises to turn 
+  off any cloned cards within 24 hours\ldots''
+  \end{itemize}
+
+  \only<2>{
+  \begin{textblock}{12}(0.5,0.5)
+  \begin{tikzpicture}
+  \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
+  {\color{darkgray}
+  \begin{minipage}{11cm}\raggedright\footnotesize
+  {\bf Wirelessly Pickpocketing a Mifare Classic Card}\medskip
+
+  The Mifare Classic is the most widely used contactless smartcard on the
+  market. The stream cipher CRYPTO1 used by the Classic has recently been
+  reverse engineered and serious attacks have been proposed. The most serious
+  of them retrieves a secret key in under a second. In order to clone a card,
+  previously proposed attacks require that the adversary either has access to
+  an eavesdropped communication session or executes a message-by-message
+  man-in-the-middle attack between the victim and a legitimate
+  reader. Although this is already disastrous from a cryptographic point of
+  view, system integrators maintain that these attacks cannot be performed
+  undetected.\smallskip
+
+  This paper proposes four attacks that can be executed by an adversary having
+  only wireless access to just a card (and not to a legitimate reader). The
+  most serious of them recovers a secret key in less than a second on ordinary
+  hardware. Besides the cryptographic weaknesses, we exploit other weaknesses
+  in the protocol stack. A vulnerability in the computation of parity bits
+  allows an adversary to establish a side channel. Another vulnerability
+  regarding nested authentications provides enough plaintext for a speedy
+  known-plaintext attack.
+  \end{minipage}};
+  \end{tikzpicture}
+  \end{textblock}}
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1->[t]
+  \frametitle{Another Example}
+
+In an email from Ross Anderson\bigskip\small	
+
+\begin{tabular}{l}
+From: Ross Anderson <Ross.Anderson@cl.cam.ac.uk>\\
+Sender: cl-security-research-bounces@lists.cam.ac.uk\\
+To: cl-security-research@lists.cam.ac.uk\\
+Subject: Birmingham case\\
+Date: Tue, 13 Aug 2013 15:13:17 +0100\\
+\end{tabular}
+
+
+  \only<2>{
+  \begin{textblock}{12}(0.5,0.5)
+  \begin{tikzpicture}
+  \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
+  {\color{darkgray}
+  \begin{minipage}{11cm}\raggedright\footnotesize
+As you may know, Volkswagen got an injunction against the University of
+Birmingham suppressing the publication of the design of a weak cipher
+used in the remote key entry systems in its recent-model cars. The paper
+is being given today at Usenix, minus the cipher design.\medskip
+
+I've been contacted by Birmingham University's lawyers who seek to prove
+that the cipher can be easily obtained anyway. They are looking for a
+student who will download the firmware from any newish VW, disassemble
+it and look for the cipher. They'd prefer this to be done by a student
+rather than by a professor to emphasise how easy it is.\medskip
+
+Volkswagen's argument was that the Birmingham people had reversed a
+locksmithing tool produced by a company in Vietnam, and since their key
+fob chip is claimed to be tamper-resistant, this must have involved a
+corrupt insider at VW or at its supplier Thales. Birmingham's argument
+is that this is nonsense as the cipher is easy to get hold of. Their
+lawyers feel this argument would come better from an independent
+outsider.\medskip
+
+Let me know if you're interested in having a go, and I'll put you in
+touch
+
+Ross
+  \end{minipage}};
+  \end{tikzpicture}
+  \end{textblock}}
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Authentication Protocols}
+
+
+Alice (\bl{$A$}) and Bob (\bl{$B$}) share a secret key \bl{$K_{AB}$}\bigskip
+
+Passwords:
+
+\begin{center}
+\bl{$B \rightarrow A: K_{AB}$} 
+\end{center}\pause\bigskip
+
+Problems: Eavesdropper can capture the secret and replay it; \bl{$A$} cannot confirm the
+identity of \bl{$B$}  
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
-\frametitle{The Access Control Problem}
+\frametitle{Authentication Protocols}
+
+Alice (\bl{$A$}) and Bob (\bl{$B$}) share a secret key \bl{$K_{AB}$}\bigskip
+
+Simple Challenge Response:
+
+\begin{center}
+\begin{tabular}{ll}
+\bl{$A \rightarrow B:$} & \bl{$N$}\\
+\bl{$B \rightarrow A:$} & \bl{$\{N\}_{K_{AB}}$}\\
+\end{tabular} 
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Authentication Protocols}
+
+Alice (\bl{$A$}) and Bob (\bl{$B$}) share a secret key \bl{$K_{AB}$}\bigskip
+
+Mutual Challenge Response:
+
+\begin{center}
+\begin{tabular}{ll}
+\bl{$A \rightarrow B:$} & \bl{$N_A$}\\
+\bl{$B \rightarrow A:$} & \bl{$\{N_A, N_B\}_{K_{AB}}$}\\
+\bl{$A \rightarrow B:$} & \bl{$N_B$}\\
+\end{tabular} 
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{One Time Passwords}
 
 \begin{center}
-  \begin{tikzpicture}[scale=1]
-  
-  \draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
-  \draw (-2.7,1) node {\begin{tabular}{l}access\\request\end{tabular}};
-  \draw (4.2,1) node {\begin{tabular}{l}granted/\\not granted\end{tabular}};
-  \draw (0.6,1.2) node {\footnotesize \begin{tabular}{l}Access\\Control\\Checker\end{tabular}};
- 
-  \draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1); 
-  \draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1);
-  \draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2); 
-  
-  \draw (0.6,4) node {\begin{tabular}{l}\large some rules\\(access policy)\end{tabular}};
+\bl{$B \rightarrow A: C, C_{K_{AB}}$} 
+\end{center}\bigskip
+
+A counter \bl{$C$} increases with each transmission; \bl{$A$} will not accept a 
+\bl{$C$}  which has already been accepted (used in car key fob).
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Person-in-the-Middle}
+
+``Normal'' protocol run:\bigskip
+
+\begin{itemize}
+\item \bl{$A$} sends public key  to \bl{$B$}
+\item \bl{$B$} sends public key  to \bl{$A$}
+\item \bl{$A$} sends message encrypted with \bl{$B$}'s public key, \bl{$B$} decrypts it
+with its private key
+\item \bl{$B$} sends message encrypted with \bl{$A$}'s public key, \bl{$A$} decrypts it
+with its private key
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Person-in-the-Middle}
+
+Attack:
+
+\begin{itemize}
+\item \bl{$A$} sends public key  to \bl{$B$}  --- \bl{$C$} intercepts this message and send his own public key
+\item \bl{$B$} sends public key  to \bl{$A$} --- \bl{$C$} intercepts this message and send his own public key
+\item \bl{$A$} sends message encrypted with \bl{$C$}'s public key, \bl{$C$} decrypts it
+with its private key, re-encrypts with \bl{$B$}'s public key 
+\item similar
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Person-in-the-Middle}
+
+Prevention:
+
+\begin{itemize}
+\item \bl{$A$} sends public key  to \bl{$B$}
+\item \bl{$B$} sends public key  to \bl{$A$}
+\item \bl{$A$} encrypts message with \bl{$B$}'s public key, send's {\bf half} of the message
+\item \bl{$B$} encrypts message with \bl{$A$}'s public key, send's {\bf half} of the message
+\item \bl{$A$} sends other half, \bl{$B$} can now decrypt entire message
+\item \bl{$B$} sends other half, \bl{$A$} can now decrypt entire message
+\end{itemize}\pause
 
-  \end{tikzpicture}
+\bl{$C$} would have to invent a totally new message
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Motivation}
+
+The ISO/IEC 9798 specifies authentication mechanisms which use security 
+techniques. These mechanisms are used to corroborate that an entity is the one 
+that is claimed. An entity to be authenticated proves its identity by showing its 
+knowledge of a secret. The mechanisms are defined as exchanges of information 
+between entities and, where required, exchanges with a trusted third party.
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Motivation}
+
+But\ldots\bigskip 
+
+The ISO/IEC 9798 standard neither specifies a threat model nor defines the security properties that the protocols should satisfy.\pause\bigskip 
+
Unfortunately, there are no general precise definitions for the goals of protocols.
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Best Practices}
+
+{\bf Principle 1:} Every message should say what it means: the interpretation of 
+a message should not depend on the context.\bigskip\pause
+
+{\bf Principle 2:} If the identity of a principal is essential to the meaning of a message, it is prudent 
+to mention the principal’s name explicitly in the message (though difficult).\bigskip
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Best Practices}
+
+{\bf Principle 3:} Be clear about why encryption is being done. Encryption is not wholly cheap, and not asking precisely why it is being done can lead to redundancy. Encryption is not synonymous with security.
+
+\begin{center}
+Possible Uses of Encryption
+
+\begin{itemize}
+\item Preservation of confidentiality: \bl{$\{X\}_K$} only those that have \bl{$K$} may recover \bl{$X$}.
\item Guarantee authenticity: The partner is indeed some particular principal.
\item Guarantee confidentiality and authenticity: binds two parts of a message --- 
+\bl{$\{X,Y\}_K$} is not the same as \bl{$\{X\}_K$} and \bl{$\{Y\}_K$}.
+\end{itemize}
 \end{center}
 
+
+
 \end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{Best Practices}
+
+{\bf Principle 4:} The protocol designer should know which trust relations his protocol depends on, and why the dependence is necessary. The reasons for particular trust relations being acceptable should be explicit though they will be founded on judgment and policy rather than on logic.\bigskip
 
+
Example Certification Authorities: CAs are trusted to certify a key only after proper steps 
+have been taken to identify the principal that owns it.
+
+
+
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
@@ -228,1064 +546,6 @@
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-
-\begin{center}
-  \begin{tikzpicture}[scale=1]
-  
-  \draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
-  \draw (-2.7,1) node {\begin{tabular}{l}access\\request\end{tabular}};
-  \draw (4.2,1) node {\begin{tabular}{l}granted/\\not granted\end{tabular}};
-  \draw (0.6,1.2) node {\footnotesize \begin{tabular}{l}Access\\Control\\Checker\end{tabular}};
- 
-  \draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1); 
-  \draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1);
-  \draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2); 
-  
-  \draw (0.6,3.7) node {\begin{tabular}{l}access policy\end{tabular}};
-
-  \end{tikzpicture}
-\end{center}
-
-Assuming one file on my computer contains a virus.\smallskip\\
-\only<1>{Q: Given my access policy, can this file ``infect'' my whole computer?}%
-\only<2>{Q: Can my access policy prevent that my whole computer gets infected.}
-
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \small
-  \begin{center}
-  \mbox{
-  \inferrule{\mbox{\begin{tabular}{l}
-         \ldots\\
-         is\_at\_library (Christian)\\ 
-         is\_student (a) $\wedge$ is\_at\_library (a) $\Rightarrow$ may\_obtain\_email (a)\\
-         is\_staff (a) $\wedge$ is\_at\_library (a) $\Rightarrow$ may\_obtain\_email (a)\medskip\\
-         \onslide<2->{HoD says is\_staff (a) $\Rightarrow$ is\_staff (a)}\\
-         \onslide<2->{HoD says is\_staff (Christian)}\medskip\\
-         \onslide<3->{may\_obtain\_email (a) $\wedge$ sending\_spam (a) $\Rightarrow$\\}
-         \onslide<3->{\hspace{6cm}$\neg$ may\_obtain\_email (a)}
-       \end{tabular}
-        }}
-        {\mbox{? may\_obtain\_email (Christian)}}}
-  \end{center}
-  \end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{}
-
-  There are two ways for tackling such problems:\medskip
-
-  \begin{itemize}
-  \item either you make up our own language in which you can describe
-  the problem,\medskip
-
-  \item or you use an existing language and represent the problem in
-  this language.
-  \end{itemize}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{\Large\begin{tabular}{@ {}c@ {}}Logic(s)\end{tabular}}
-
-  \begin{itemize}
-  \item Formulas
-
-  \begin{center}\color{blue}
-  \begin{tabular}{rcl@ {\hspace{10mm}}l}
-  \isa{F} & \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}} & \isa{true} \\
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \isa{false} \\
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \isa{F\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F} \\
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \isa{F\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F} \\
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \isa{F\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}       & \textcolor{black}{implies}\\
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ F}       & \textcolor{black}{negation}\\
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \isa{p\ {\isaliteral{28}{\isacharparenleft}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}} & \textcolor{black}{predicates}\\
-   & \onslide<2->{\isa{{\isaliteral{7C}{\isacharbar}}}} & \onslide<2->{\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ F}} & 
-        \onslide<2->{\textcolor{black}{forall quantification}}\\
-   & \onslide<2->{\isa{{\isaliteral{7C}{\isacharbar}}}} & \onslide<2->{\isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ F}} & 
-        \onslide<2->{\textcolor{black}{exists quantification}}\\[-7mm]
-  \end{tabular}
-  \end{center}
-
-  \end{itemize}
-
-  \begin{textblock}{12}(1,14)
-  Terms \textcolor{blue}{\isa{t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{7C}{\isacharbar}}\ c\ {\isaliteral{5C3C646F74733E}{\isasymdots}}}}
-  \end{textblock}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-
-{\lstset{language=Scala}\fontsize{10}{12}\selectfont
-\texttt{\lstinputlisting{programs/formulas.scala}}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{Judgements}
-
-  \begin{center}
-  \LARGE
-  \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}
-  \end{center}
-
-  \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}} is a collection of formulas, called the \alert{assumptions}\bigskip\pause
-
-  \begin{itemize}
-  \item Example\mbox{}\\[-8mm]
-
-  \only<2>{\begin{center}\tiny
-  \textcolor{blue}{
-  \begin{tabular}{l}
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
-  \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
-  \end{tabular}\isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
-  \end{center}}
-  \only<3>{\small
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
-  {\mbox{\begin{tabular}{@ {}l@ {}}
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
-  \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
-  \end{tabular}}
-  }
-  }
-  \end{center}
-  }}
-  \only<4>{\small
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}}}
-  {\mbox{\begin{tabular}{@ {}l@ {}}
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}\\
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
-  \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
-  \end{tabular}}
-  }
-  }
-  \end{center}
-  }}
-
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-
-{\lstset{language=Scala}\fontsize{10}{12}\selectfont
-\texttt{\lstinputlisting{programs/judgement.scala}}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{Inference Rules}
-
-  \textcolor{blue}{
-  \begin{center}
-  \Large
-  \mbox{
-  \infer{\mbox{\isa{conclusion}}}
-        {\mbox{\isa{premise\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} & \mbox{\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}} & \mbox{\isa{premise\isaliteral{5C3C5E697375623E}{}\isactrlisub n}}}}
-  \end{center}}
-
-  The conlusion and premises are judgements\bigskip\pause
-
-  \begin{itemize}
-  \item Examples
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
-  \end{center}}\pause
-
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
-  \hspace{10mm}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
-  \end{center}}
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{Implication}
-  \Large
-
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{2C}{\isacharcomma}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
-  \end{center}}
-
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
-  \end{center}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{Universal Quantification}
-  \Large
-
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F{\isaliteral{5B}{\isacharbrackleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{5D}{\isacharbrackright}}}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ F}}}}
-  \end{center}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{Start Rules / Axioms}
-
-  \normalsize
-  \alert{if \textcolor{blue}{\isa{F\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}}}
-  
-  \textcolor{blue}{\Large
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}{}}
-  \end{center}}\bigskip\pause
-
-  \normalsize
-  Also written as:
-  \textcolor{blue}{\Large
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{2C}{\isacharcomma}}\ F\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}{}}
-  \end{center}}\pause
-
-  \textcolor{blue}{\Large
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ true}}}{}}
-  \end{center}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{}
- 
- \begin{minipage}{1.1\textwidth}
-  Let \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\footnotesize\begin{tabular}{l}
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
-  \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
-  \end{tabular}}
-  \end{minipage}
-
-  \only<2>{
-  \begin{textblock}{12}(4,3)\footnotesize
-  \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}\hspace{10mm}
-  \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
-  \end{textblock}}
-
-  \only<3->{
-  \begin{textblock}{12}(4,3)\footnotesize
-  \mbox{\textcolor{blue}{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
-  {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}} &\hspace{10mm}
-   \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
-  }}
-  \end{textblock}}
-
-  \only<4>{
-  \begin{textblock}{14}(0.5,6)\footnotesize
-  \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}}
-  \end{textblock}}
-
-  \only<5->{
-  \begin{textblock}{14}(0.5,6)\footnotesize
-  \textcolor{blue}{
-  \infer{\mbox{\begin{tabular}{l}\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\ 
-           \hspace{40mm}\isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\end{tabular}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}}}}
-  \end{textblock}}
-
-  \only<6->{
-  \begin{textblock}{14}(5,10)\footnotesize
-  \textcolor{blue}{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
-        {\vdots & \hspace{30mm} \vdots}}
-  \end{textblock}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{Access Control}
-  \Large
-
-  \textcolor{blue}{
-  \begin{center}
-  \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}
-  \end{center}}\bigskip
-
-  \normalsize
-  \begin{itemize}
-  \item If there is a proof \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} yes (granted)
-  \item If there isn't \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} no (denied)
-  \end{itemize}\bigskip\pause
-
-\begin{minipage}{1.1\textwidth}	
-  \small
-  \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
-  \isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
-  \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
-  \end{tabular}}\medskip
-  
-  \textcolor{blue}{
-  \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} $\not\vdash$ \isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}}}
-\end{minipage}
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{The Access Control Problem}
-
-
-\begin{center}
-  \begin{tikzpicture}[scale=1]
-  
-  \draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
-  \draw (-2.7,1) node {\begin{tabular}{l}access\\request\\ (\bl{$F$})\end{tabular}};
-  \draw (4.2,1) node {\begin{tabular}{l}granted/\\not granted\end{tabular}};
-  \draw (0.6,1.2) node {\footnotesize \begin{tabular}{l}Access\\Control\\Checker\end{tabular}};
- 
-  \draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1); 
-  \draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1);
-  \draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2); 
-  
-  \draw (0.6,4) node {\begin{tabular}{l}\large Access Policy (\bl{$\Gamma$})\end{tabular}};
-
-  \end{tikzpicture}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Bad News}
-  
-  \begin{itemize}
-  \item We introduced (roughly) first-order logic. \bigskip\pause
-
-  \item Judgements
-  \begin{center}
-  \textcolor{blue}
-  {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
-  \end{center}
-
-  are in general \alert{undecidable}.\pause\medskip\\ 
- 
-  The problem is \alert{semi-decidable}.
- 
-  \end{itemize}
-
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{\Large\begin{tabular}{@ {}c@ {}}Access Control Logic\end{tabular}}
-  
-  \begin{itemize}
-  \item[]
-  
-  \begin{center}\color{blue}
-  \begin{tabular}[t]{rcl@ {\hspace{10mm}}l}
-  \isa{F} & \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}} & \isa{true} \\
-            & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{false} \\
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \isa{F\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F} \\
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \isa{F\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F} \\
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \isa{F\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}\\
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \isa{p\ {\isaliteral{28}{\isacharparenleft}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}} \\  
-            & \isa{{\isaliteral{7C}{\isacharbar}}}   & \alert{\isa{P\ says\ F}} & \textcolor{black}{``saying predicate''}\\ 
-  \end{tabular}
-  \end{center}
-
-  where \textcolor{blue}{\isa{P\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ Alice{\isaliteral{2C}{\isacharcomma}}\ Bob{\isaliteral{2C}{\isacharcomma}}\ Christian{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}}} (principals)\bigskip\pause
-  
-  \item \textcolor{blue}{\isa{HoD\ says\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
-  \end{itemize}
-  
-
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-
-{\lstset{language=Scala}\fontsize{10}{12}\selectfont
-\texttt{\lstinputlisting{programs/formulas1.scala}}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{Rules about Says}
-
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}}
-  \end{center}}
-
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ {\isaliteral{28}{\isacharparenleft}}F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}}} & \hspace{10mm}\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
-  \end{center}}
-
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}}}}}
-  \end{center}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{}
-
-  Consider the following scenario:
-
-  \begin{itemize}
-  \item If \textcolor{blue}{Admin} says that \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} 
-  should be deleted, then this file must be deleted.
-  \item \textcolor{blue}{Admin} trusts \textcolor{blue}{Bob} to decide whether 
-  \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} should be deleted.
-  \item \textcolor{blue}{Bob} wants to delete \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}.
-  \end{itemize}\bigskip\pause
-
-  \small
-  \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
-  \isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}},\\
-  \isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}},\\
-  \isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}\\
-  \end{tabular}}\medskip\pause
-
-  \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{}
-
-  \textcolor{blue}{
-  \begin{center}
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}}\\\bigskip
-  \mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ {\isaliteral{28}{\isacharparenleft}}F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}}} & \hspace{5mm}\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
-  \end{center}}\bigskip
-
-  \small
-  \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
-  \isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}},\\
-  \isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}},\\
-  \isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}\\
-  \end{tabular}}\medskip
-
-  \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{}
-  \small
-
-  \textcolor{blue}{
-  \begin{center}
-  \only<1>{$ \underbrace{
-  \mbox{\infer{\Gamma \vdash \mbox{Admin says (Bob says del\_file)}}
-  {\infer{\Gamma \vdash \mbox{Bob says del\_file}}{}}}}_{X}$}
-  \end{center}}
-
-  \textcolor{blue}{
-  \begin{center}
-  \only<1>{
-  $ \underbrace{
-  \mbox{\infer{\Gamma \vdash \mbox{Admin says del\_file}}
-  {\infer{\Gamma \vdash \mbox{Admin says (Bob says del\_file \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} del\_file)}}{}
-   &
-   \deduce[$\vdots$]{X}{}
-  }}}_{Y}$}
-  \end{center}}
-
-  \textcolor{blue}{
-  \begin{center}
-  \only<1>{\mbox{\infer{\Gamma \vdash \mbox{del\_file}}
-  {\infer{\Gamma \vdash \mbox{(Admin says del\_file) \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} del\_file}}{}
-   &
-   \deduce[$\vdots$]{Y}{}
-  }}}
-  \end{center}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Controls}
-  \small
-  
-  \begin{itemize}
-  \item \bl{\isa{P\ controls\ F\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}}
-
-  \item its meaning ``\bl{P} is entitled to do \bl{F}''
-  \item if \bl{P controls F} and \bl{P says F} then \bl{F}\pause
-
-  \begin{center}
-  \bl{\mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
-  }}
-  \end{center}\pause
-
-  \begin{center}
-  \bl{\mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
-  }}
-  \end{center}
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Speaks For}
-  \small
-  
-  \begin{itemize}
-  \item \bl{\isa{P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}F{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Q\ says\ F{\isaliteral{29}{\isacharparenright}}}}
-
-  \item its meaning ``\bl{P} speaks for \bl{Q}''
-  
-
-  \begin{center}
-  \bl{\mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ says\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
-  }}
-  \end{center}\pause
-
-  \begin{center}
-  \bl{\mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ controls\ F}}}
-  }}
-  \end{center}
-
-  \begin{center}
-  \bl{\mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ R}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ R}}}
-  }}
-  \end{center}
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Tickets}
-  
-  \begin{itemize}
-  \item Tickets control access to restricted objects.\bigskip
-  \end{itemize}
-  \small
-
-  Example: \bl{Permitted (Bob, enter\_flight)} ? \bigskip
-  
-  \begin{minipage}{1.1\textwidth}
-  \begin{itemize}
-  \item \bl{Bob says Permitted (Bob, enter\_flight)}\\ (access request)
-  \item \bl{Ticket says (Bob controls Permitted (Bob, enter\_flight))}
-  \item \bl{Airline controls (Bob controls Permitted (Bob, enter\_flight))} (access policy)\pause
-  \item \bl{\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Airline}}\\ 
-  (trust assumption)
-  \end{itemize}
-  \end{minipage}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Tickets}
-  \small
-
-  \begin{minipage}{1.1\textwidth}
-  \begin{enumerate}
-  \item \bl{Bob says Permitted (Bob, enter\_flight)}
-  \item \bl{Ticket says (Bob controls Permitted (Bob, enter\_flight))}
-  \item \bl{Airline controls (Bob controls Permitted (Bob, enter\_flight))}
-  \item \bl{\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Airline}}
-  \end{enumerate}
-  \end{minipage}\bigskip\bigskip
-
-  Is  \bl{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Permitted\ {\isaliteral{28}{\isacharparenleft}}Bob{\isaliteral{2C}{\isacharcomma}}\ enter{\isaliteral{5F}{\isacharunderscore}}flight{\isaliteral{29}{\isacharparenright}}}} derivable ? \bigskip
-
-
-  \small
-  \begin{minipage}{1.1\textwidth}
-  \begin{center}
-  \bl{\mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
-  }}
-  \bl{\mbox{\hspace{6mm}
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ says\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
-  }}
-  \end{center}
-  \end{minipage}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Tickets}
-  \small
-  
-  \begin{minipage}{1.1\textwidth}
-  \begin{itemize}
-  \item Access Request:
-  \begin{center}
-  \bl{Person says Object}
-  \end{center}
-
-  \item Ticket:
-  \begin{center}
-  \bl{Ticket says (Person controls Object)}
-  \end{center}
-
-  \item Access policy:
-  \begin{center}
-  \bl{Authority controls (Person controls Object)}
-  \end{center}
-
-  \item Trust assumption:
-  \begin{center}
-  \bl{\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Authority}}
-  \end{center}
-  \end{itemize}
-  \end{minipage}
-
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{\LARGE Derived Rule for Tickets}
-  \small
-  \mbox{}\\[2cm]
-  
-  \begin{center}
-  \bl{\mbox{\infer{\mbox{F}}
-     {\mbox{\begin{tabular}{l}
-      Authority controls (Person controls F)\\
-      Ticket says (Person controls F)\\
-      \isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Authority}\\
-      Person says F
-      \end{tabular}}
-     }}}
-  \end{center}
-  \mbox{}\\[1cm]
-
- 
-  \small
-  \begin{minipage}{1.1\textwidth}
-  \begin{center}
-  \bl{\mbox{
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
-  }}
-  \bl{\mbox{\hspace{6mm}
-  \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ says\ F}}}
-        {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
-  }}
-  \end{center}
-  \end{minipage}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Security Levels}
-  \small
-
-  \begin{itemize}
-  \item Top secret (\bl{$T\!S$})
-  \item Secret (\bl{$S$})
-  \item Public (\bl{$P$})
-  \end{itemize}
-
-  \begin{center}
-  \bl{$slev(P) < slev(S) < slev(T\!S)$}\pause
-  \end{center}
-
-  \begin{itemize}
-  \item Bob has a clearance for ``secret''
-  \item Bob can read documents that are public or sectret, but not top secret
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Reading a File}
-
-  \bl{\begin{center}
-  \begin{tabular}{c}
-  \begin{tabular}{@ {}l@ {}}
-  \only<2->{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$}}\\ 
-  \only<2->{\hspace{3cm}}Bob controls Permitted $($File, read$)$\\
-  Bob says Permitted $($File, read$)$\only<2->{\\}
-  \only<2>{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$}}%
-  \only<3>{\textcolor{red}{$slev($File$)$ $=$ $P$}\\}%
-  \only<3>{\textcolor{red}{$slev($Bob$)$ $=$ $S$}\\}%
-  \only<3>{\textcolor{red}{$slev(P)$ $<$ $slev(S)$}\\}%
-  \end{tabular}\\
-  \hline
-  Permitted $($File, read$)$
-  \end{tabular}
-  \end{center}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Substitution Rule}
-  \small
-  
-  \bl{\begin{center}
-  \begin{tabular}{c}
-  $\Gamma \vdash slev(P) = l_1$ \hspace{4mm} $\Gamma \vdash slev(Q) = l_2$
-  \hspace{4mm} $\Gamma \vdash l_1 < l_2$\\\hline
-  $\Gamma \vdash slev(P) < slev(Q)$
-  \end{tabular}
-  \end{center}}\bigskip\pause
-
-  \begin{itemize}
-  \item \bl{$slev($Bob$)$ $=$ $S$}
-  \item \bl{$slev($File$)$ $=$ $P$}
-  \item \bl{$slev(P) < slev(S)$}
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Reading a File}
-
-  \bl{\begin{center}
-  \begin{tabular}{c}
-  \begin{tabular}{@ {}l@ {}}
-  $slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$\\ 
-  \hspace{3cm}Bob controls Permitted $($File, read$)$\\
-  Bob says Permitted $($File, read$)$\\
-  $slev($File$)$ $=$ $P$\\
-  $slev($Bob$)$ $=$ $T\!S$\\
-  \only<1>{\textcolor{red}{$?$}}%
-  \only<2>{\textcolor{red}{$slev(P) < slev(S)$}\\}%
-  \only<2>{\textcolor{red}{$slev(S) < slev(T\!S)$}}%
-  \end{tabular}\\
-  \hline
-  Permitted $($File, read$)$
-  \end{tabular}
-  \end{center}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Transitivity Rule}
-  \small
-  
-  \bl{\begin{center}
-  \begin{tabular}{c}
-  $\Gamma \vdash l_1 < l_2$ 
-  \hspace{4mm} $\Gamma \vdash l_2 < l_3$\\\hline
-  $\Gamma \vdash l_1 < l_3$
-  \end{tabular}
-  \end{center}}\bigskip
-
-  \begin{itemize}
-  \item \bl{$slev(P) < slev (S)$}
-  \item \bl{$slev(S) < slev (T\!S)$}
-  \item[] \bl{$slev(P) < slev (T\!S)$}
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Reading Files}
-
-  \begin{itemize}
-  \item Access policy for reading
-  \end{itemize}
-
-  \bl{\begin{center}
-  \begin{tabular}{c}
-  \begin{tabular}{@ {}l@ {}}
-  $\forall f.\;slev(f)$ \only<1>{$<$}\only<2>{\textcolor{red}{$\le$}} $slev($Bob$)$ $\Rightarrow$\\ 
-  \hspace{3cm}Bob controls Permitted $(f$, read$)$\\
-  Bob says Permitted $($File, read$)$\\
-  $slev($File$)$ $=$ \only<1>{$P$}\only<2>{\textcolor{red}{$T\!S$}}\\
-  $slev($Bob$)$ $=$ $T\!S$\\
-  $slev(P) < slev(S)$\\
-  $slev(S) < slev(T\!S)$
-  \end{tabular}\\
-  \hline
-  Permitted $($File, read$)$
-  \end{tabular}
-  \end{center}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Writing Files}
-
-  \begin{itemize}
-  \item Access policy for \underline{writing}
-  \end{itemize}
-
-  \bl{\begin{center}
-  \begin{tabular}{c}
-  \begin{tabular}{@ {}l@ {}}
-  $\forall f.\;slev($Bob$)$ $\le$ $slev(f)$ $\Rightarrow$\\ 
-  \hspace{3cm}Bob controls Permitted $(f$, write$)$\\
-  Bob says Permitted $($File, write$)$\\
-  $slev($File$)$ $=$ $T\!S$\\
-  $slev($Bob$)$ $=$ $S$\\
-  $slev(P) < slev(S)$\\
-  $slev(S) < slev(T\!S)$
-  \end{tabular}\\
-  \hline
-  Permitted $($File, write$)$
-  \end{tabular}
-  \end{center}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Bell-LaPadula}
-  \small
-  
-  \begin{itemize}
-  \item \alert{Read Rule}: A principal \bl{$P$} can read an object \bl{$O$} if and only if
-  \bl{$P$}'s security level is at least as high as \bl{$O$}'s.
-  \item \alert{Write Rule}: A principal \bl{$P$} can write an object \bl{$O$} if and only if
-  \bl{$O$}'s security level is at least as high as \bl{$P$}'s.\medskip
-
-  \item Meta-Rule: All principals in a system should have a sufficiently high security level
-  in order to access an object.
-  \end{itemize}\bigskip
-
-  This restricts information flow $\Rightarrow$ military\bigskip\bigskip\pause
-
-  Bell-LaPadula: {\bf `no read up'} - {\bf `no write down'}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{\begin{tabular}{c}Principle of\\[-2mm] Least Privilege\end{tabular}}
-  
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\normalsize\color{darkgray}
-  \begin{minipage}{10cm}\raggedright
-  A principal should have as few privileges as possible to access a resource.
-  \end{minipage}};
-  \end{tikzpicture}\bigskip\bigskip
-  \small
-
-  \begin{itemize}
-  \item Bob ($T\!S$) and Alice ($S$) want to communicate
-  \item[] $\Rightarrow$ Bob should lower his security level
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Biba Policy}
-  \small
-  
-  Data Integrity (rather than data confidentiality)
-
-  \begin{itemize}
-  \item Biba: {\bf `no read down'} - {\bf `no write up'}
-  \item \alert{Read Rule}: A principal \bl{$P$} can read an object \bl{$O$} if and only if
-  \bl{$P$}'s security level is lower or equal than \bl{$O$}'s.
-  \item \alert{Write Rule}: A principal \bl{$P$} can write an object \bl{$O$} if and only if
-  \bl{$O$}'s security level is lower or equal than \bl{$P$}'s.
-  \end{itemize}\bigskip\bigskip\pause
-
-  E.g.~Generals write orders to officers; officers write oders to solidiers\\
-  Firewall: you can read from inside the firewall, but not from outside\\
-  Phishing: you can look at an approved PDF, but not one from a random email\\
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{Point to Take Home}
-
-\begin{itemize}
-\item Formal methods can be an excellent way of finding 
-bugs as they force the designer 
-to make everything explicit and thus confront dif$\!$ficult design 
-choices that might otherwise be fudged. 
-\end{itemize}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-
 
 \end{document}
 




