--- a/slides/slides06.tex Tue Nov 12 09:57:22 2013 +0000
+++ b/slides/slides06.tex Tue Nov 12 10:51:02 2013 +0000
@@ -16,6 +16,7 @@
\usetikzlibrary{calc}
\usetikzlibrary{shapes}
\usepackage{graphicx}
+\setmonofont[Scale=MatchLowercase]{Consolas}
\isabellestyle{rm}
\renewcommand{\isastyle}{\rm}%
@@ -106,6 +107,7 @@
\stepcounter{row}
}
+\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
% beamer stuff
\renewcommand{\slidecaption}{APP 06, King's College London, 12 November 2013}
@@ -246,31 +248,6 @@
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}[c]
- \frametitle{Sending Messages}
-
- \begin{itemize}
- \item Alice sends a message \bl{$m$}
- \begin{center}
- \bl{Alice says $m$}
- \end{center}\medskip\pause
-
- \item Alice sends an encrypted message \bl{$m$}\\ (with key \bl{$K$})
- \begin{center}
- \bl{Alice says $\{m\}_K$}
- \end{center}\medskip\pause
-
- \item Decryption of Alice's message\smallskip
- \begin{center}
- \bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;m}
- {\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_K & \Gamma \vdash \text{Alice}\,\text{says}\,K}}}
- \end{center}
- \end{itemize}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
@@ -294,6 +271,33 @@
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Sending Messages}
+
+ \begin{itemize}
+ \item Alice sends a message \bl{$m$}
+ \begin{center}
+ \bl{Alice says $m$}
+ \end{center}\medskip\pause
+
+ \item Alice sends an encrypted message \bl{$m$} with key \bl{$K$}
+ (\bl{$\{m\}_K \dn K \Rightarrow m$})
+ \begin{center}
+ \bl{Alice says $\{m\}_K$}
+ \end{center}\medskip\pause
+
+ \item Decryption of Alice's message\smallskip
+ \begin{center}
+ \bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;m}
+ {\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_K & \Gamma \vdash \text{Alice}\,\text{says}\,K}}}
+ \end{center}
+ \end{itemize}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
@@ -758,37 +762,11 @@
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}[c]
- \frametitle{}
-
- Recall the following scenario:
-
- \begin{itemize}
- \item If \textcolor{blue}{Admin} says that \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{} {}}}
- 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}{}}} should be deleted.
- \item \textcolor{blue}{Bob} wants to delete \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}}}.
- \end{itemize}\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}{}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}},\\
- \isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}},\\
- \isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}}\\
- \end{tabular}}\medskip
-
- \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}}}
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
+\frametitle{Program}
How to prove \bl{$\Gamma \vdash F$}?\bigskip\bigskip
@@ -848,9 +826,12 @@
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
+\frametitle{Program: \texttt{prove2}}
I want to prove \bl{$\Gamma \vdash \text{Pred}$}\bigskip\bigskip\pause
@@ -861,7 +842,7 @@
\bl{$\Gamma \vdash F_2$}
\end{center}\bigskip\pause
-\item So better I try to prove \bl{$\Gamma \vdash \text{Pred}$} with the additional assumption
+\item So I am able to try to prove \bl{$\Gamma \vdash \text{Pred}$} with the additional assumption
\bl{$F_2$}.\bigskip
\begin{center}
\bl{$F_2, \Gamma \vdash \text{Pred}$}
@@ -875,8 +856,34 @@
\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{}
+
+ Recall the following scenario:
+
+ \begin{itemize}
+ \item If \textcolor{blue}{Admin} says that \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{} {}}}
+ 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}{}}} should be deleted.
+ \item \textcolor{blue}{Bob} wants to delete \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}}}.
+ \end{itemize}\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}{}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}},\\
+ \isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}},\\
+ \isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}}\\
+ \end{tabular}}\medskip
+
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}}}
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
@@ -889,15 +896,7 @@
\bl{\infer{\Gamma \vdash F}{\Gamma \vdash P\,\text{controls}\, F & \Gamma \vdash P\,\text{says}\,F}}
\end{center}
-\item \bl{$P$} speaks for \bl{$Q$}\smallskip\\
-\bl{$P \mapsto Q \,\dn\, \forall F. (P\,\text{says}\, F) \Rightarrow (Q \,\text{says}\,F)$}\medskip
-\begin{center}
-\bl{\infer{\Gamma \vdash Q\,\text{says}\,F}{\Gamma \vdash P\mapsto Q & \Gamma \vdash P\,\text{says}\,F}}
-\medskip\\
-\bl{\infer{\Gamma \vdash P\,\text{controls}\,F}{\Gamma \vdash P\mapsto Q & \Gamma \vdash Q\,\text{controls}\,F}}\\
-
-\end{center}
\end{itemize}
\end{frame}}
@@ -905,25 +904,6 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\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}}$}\\
-\end{tabular}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
@@ -945,31 +925,245 @@
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Sending Rule}
+
+ \bl{\begin{center}
+ \mbox{\infer{\Gamma \vdash Q \;\text{says}\; F}
+ {\Gamma \vdash P \;\text{says}\; F & \Gamma \vdash P \;\text{sends}\; Q : F}}
+ \end{center}}\bigskip\pause
+
+ \bl{$P \,\text{sends}\, Q : F \dn$}\\
+ \hspace{6mm}\bl{$(P \,\text{says}\, F) \Rightarrow (Q \,\text{says}\, F)$}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
- \frametitle{Sending Messages}
+ \frametitle{Trusted Third Party}
+
+ \begin{center}
+ \bl{\begin{tabular}{l}
+ $A$ sends $S$ : $\text{Connect}(A,B)$\\
+ \bl{$S \,\text{says}\, (\text{Connect}(A,B) \Rightarrow$}\\
+ \hspace{2.5cm}\bl{$\{K_{AB}\}_{K_{AS}} \wedge
+ \{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}})$}\\
+ $S$ sends $A$ : $\{K_{AB}\}_{K_{AS}}$ \bl{$\wedge$} $\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}}$\\
+ $A$ sends $B$ : $\{K_{AB}\}_{K_{BS}}$\\
+ $A$ sends $B$ : $\{m\}_{K_{AB}}$
+ \end{tabular}}
+ \end{center}\bigskip\pause
+
+
+ \bl{$\Gamma \vdash B \,\text{says} \, m$}?
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Public/Private Keys}
\begin{itemize}
- \item Alice sends a message \bl{$m$}
- \begin{center}
- \bl{Alice says $m$}
- \end{center}\medskip\pause
-
- \item Alice sends an encrypted message \bl{$m$}\\ (with key \bl{$K$})
- \begin{center}
- \bl{Alice says $\{m\}_K$}
- \end{center}\medskip\pause
-
- \item Decryption of Alice's message\smallskip
+ \item Bob has a private and public key: \bl{$K_{Bob}^{pub}$}, \bl{$K_{Bob}^{priv}$}\bigskip
\begin{center}
\bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;m}
- {\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_K & \Gamma \vdash \text{Alice}\,\text{says}\,K}}}
+ {\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_{K_{Bob}^{pub}} &
+ \Gamma \vdash K_{Bob}^{priv}}}}
+ \end{center}\bigskip\pause
+
+ \item this is {\bf not} a derived rule!
+ \end{itemize}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \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}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+
+\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{