
diff -r be35ff24cccc -r d1d07f05325a slides06.tex
--- a/slides06.tex	Sun Dec 09 13:00:33 2012 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,636 +0,0 @@
-\documentclass[dvipsnames,14pt,t]{beamer}
-\usepackage{proof}
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-
-% beamer stuff 
-\renewcommand{\slidecaption}{APP 06, King's College London, 29 October 2012}
-
-\newcommand{\bl}[1]{\textcolor{blue}{#1}}
-\begin{document}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}<1>[t]
-\frametitle{%
-  \begin{tabular}{@ {}c@ {}}
-  \\
-  \LARGE Access Control and \\[-3mm] 
-  \LARGE Privacy Policies (6)\\[-6mm] 
-  \end{tabular}}\bigskip\bigskip\bigskip
-
-  %\begin{center}
-  %\includegraphics[scale=1.3]{pics/barrier.jpg}
-  %\end{center}
-
-\normalsize
-  \begin{center}
-  \begin{tabular}{ll}
-  Email:  & christian.urban at kcl.ac.uk\\
-  Of$\!$fice: & S1.27 (1st floor Strand Building)\\
-  Slides: & KEATS (also homework is there)\\
-  \end{tabular}
-  \end{center}
-
-
-\end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{1st Week}
-
-\begin{itemize}
-\item What are hashes and salts?\bigskip\pause
-\item \ldots can be use to store securely data on a client, but
-you cannot make your protocol dependent on the
-presence of the data\bigskip\pause
-\item \ldots can be used to store and verify passwords
-
-\end{itemize}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{2nd Week}
-
-\begin{itemize}
-\item Buffer overflows\bigskip
-\item choice of programming language can mitigate or even eliminate this problem
-\end{itemize}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{3rd Week}
-
-\begin{itemize}
-\item defence in depth\bigskip
-\item privilege separation afforded by the OS
-\end{itemize}
-
-\begin{center}
-\begin{tikzpicture}[scale=1]
-  
-  \draw[line width=1mm] (0, 1.1) rectangle (1.2,2);
-  \draw (4.7,1) node {Internet};
-  \draw (0.6,1.7) node {\footnotesize Slave};
-  \draw[line width=1mm] (0, 0) rectangle (1.2,0.9);
-  \draw (0.6,1.7) node {\footnotesize Slave};
-  \draw (0.6,0.6) node {\footnotesize Slave};
-  \draw (0.6,-0.5) node {\footnotesize \begin{tabular}{c}unprivileged\\[-1mm] processes\end{tabular}};
-  \draw (-2.7,-0.4) node {\footnotesize \begin{tabular}{c}privileged\\[-1mm] process\end{tabular}};
-  
-  \draw[line width=1mm] (-1.8, 0) rectangle (-3.6,2);
-  \draw (-2.9,1.7) node {\footnotesize Monitor};
-
-  \draw[white] (1.7,1) node (X) {};
-  \draw[white] (3.7,1) node (Y) {};
-  \draw[red, <->, line width = 2mm] (X) -- (Y);
- 
-  \draw[red, <->, line width = 1mm] (-0.4,1.4) -- (-1.4,1.1);
-  \draw[red, <->, line width = 1mm] (-0.4,0.6) -- (-1.4,0.9);
-
-  \end{tikzpicture}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{4th Week}
-
-\begin{itemize}
-\item voting\ldots has security requirements that are in tension with each other
-\begin{center}
-integrity vs ballot secrecy\\
-authentication vs enfranchisment 
-\end{center}\bigskip
-
-\item electronic voting makes `whole sale' fraud easier as opposed to `retail attacks' 
-\end{itemize}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{5th Week}
-
-\begin{itemize}
-\item access control logic\bigskip
-
-\item formulas
-\item judgements
-\item inference rules
-\end{itemize}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[t]
-  \frametitle{\Large\begin{tabular}{@ {}c@ {}}Access Control Logic\end{tabular}}
-  
-  Formulas
-  
-  \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}
-  
-  \end{itemize}
-  
-Judgements
-
-\begin{itemize}
-\item[] \mbox{\hspace{9mm}}\bl{$\Gamma \vdash \text{F}$}
-\end{itemize}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{Inference Rules}
-
-\begin{center}
-\bl{\infer{\Gamma, F\vdash F}{}}\bigskip\\
-
-\bl{\infer{\Gamma \vdash F_2}{\Gamma \vdash F_1 \Rightarrow F_2 \quad \Gamma \vdash F_1}}
-\qquad
-\bl{\infer{\Gamma \vdash F_1 \Rightarrow F_2}{F_1, \Gamma \vdash F_2}}\bigskip\\
-
-\bl{\infer{\Gamma \vdash P\,\text{says}\, F}{\Gamma \vdash F}}\medskip\\
-
-\bl{\infer{\Gamma \vdash P \,\text{says}\, F_2}
-              {\Gamma \vdash P \,\text{says}\, (F_1\Rightarrow F_2) \quad 
-               \Gamma \vdash P \,\text{says}\, F_1}}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{Proofs}
-
-\begin{center}
-\bl{
-\infer{\Gamma \vdash F}
-         {\infer{\hspace{1cm}:\hspace{1cm}}
-             {\infer{\hspace{1cm}:\hspace{1cm}}{:}
-               &
-              \infer{\hspace{1cm}:\hspace{1cm}}{:\quad :}
-           }}
-}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{The Access Control Problem}
-
-
-\begin{center}
-  \begin{tikzpicture}[scale=1]
-  
-  \draw[line width=1mm] (-.3, -0.5) 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}provable/\\not provable\end{tabular}};
-  \draw (0.6,0.8) node {\footnotesize \begin{tabular}{l}AC-\\ Checker:\\ applies\\ inference\\ rules\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{}
-
-  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]
-
-How to prove \bl{$\Gamma \vdash F$}?\bigskip\bigskip
-
-\begin{center}
-\Large \bl{\infer{\Gamma, F\vdash F}{}}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-
-\begin{center}
-\Large 
-\bl{\infer{\Gamma \vdash F_1 \Rightarrow F_2}{F_1, \Gamma \vdash F_2}}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-
-\begin{center}
-\Large 
-\bl{\infer{\Gamma \vdash P \,\text{says}\, F}{\Gamma \vdash F}}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-
-\begin{center}
-\Large 
-\bl{\infer{\Gamma \vdash F_1 \vee F_2}{\Gamma \vdash F_1}}\qquad
-\bl{\infer{\Gamma \vdash F_1 \vee F_2}{\Gamma \vdash F_2}}\
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-
-\begin{center}
-\Large 
-\bl{\infer{\Gamma \vdash F_1 \wedge F_2}{\Gamma \vdash F_1 \quad \Gamma \vdash F_2}}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-
-I want to prove \bl{$\Gamma \vdash \text{Pred}$}\bigskip\bigskip\pause
-
-\begin{enumerate}
-\item I found that \bl{$\Gamma$} contains the assumption \bl{$F_1 \Rightarrow F_2$}\bigskip\pause
-\item If I can prove \bl{$\Gamma \vdash F_1$},\pause{} then I can prove
-\begin{center}
-\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
-\bl{$F_2$}.\bigskip
-\begin{center}
-\bl{$F_2, \Gamma \vdash \text{Pred}$}
-\end{center}
-\end{enumerate}
-
-\only<4>{
-\begin{textblock}{11}(1,10.5)
-\bl{\infer{\Gamma\vdash F_2}{\Gamma\vdash F_1\Rightarrow F_2 & \Gamma\vdash F_1}}
-\end{textblock}}
-
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-
-\begin{itemize}
-\item \bl{$P$} is entitled to do \bl{$F$}\smallskip\\ 
-\bl{$P \,\text{controls}\, F \,\dn\, (P\,\text{says}\, F) \Rightarrow F$}\medskip
-
-\begin{center}
-\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}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\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}}$}\\
-\end{tabular}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{Trusted Third Party}
-
-Simple protocol for establishing a secure connection via a mutually
-trusted 3rd party (server):
-
-\begin{center}
-\begin{tabular}{@ {\hspace{-7mm}}l@{\hspace{2mm}}r@ {\hspace{1mm}}l}
-Message 1 & \bl{$A \rightarrow S :$} & \bl{$A, B$}\\
-Message 2 & \bl{$S \rightarrow A :$} & \bl{$\{K_{AB}\}_{K_{AS}}$} and \bl{$\{\{K_{AB}\}_{K_{BS}} \}_{K_{AS}}$}\\
-Message 3 & \bl{$A \rightarrow B :$} & \bl{$\{K_{AB}\}_{K_{BS}} $}\\
-Message 4 & \bl{$A \rightarrow B :$} & \bl{$\{m\}_{K_{AB}}$}\\
-\end{tabular}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Sending Messages}
-
-  \begin{itemize}
-  \item Alice sends a message \bl{$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>{
-  \begin{frame}[c]
-  \frametitle{Encryption}
-
-  \begin{itemize}
-  \item Encryption of a message\smallskip
-  \begin{center}
-  \bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_K}
-              {\Gamma \vdash \text{Alice}\;\text{says}\;m & \Gamma \vdash \text{Alice}\,\text{says}\,K}}}
-  \end{center}
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-  
-   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Public/Private Keys}
-
-  \begin{itemize}
-  \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_{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{Trusted Third Party}
-
-  \begin{itemize}
-  \item Alice calls Sam for a key to communicate with Bob
-  \item Sam responds with a key that Alice can read and a key Bob can read (pre-shared)
-  \item Alice sends the message encrypted with the key and the second key it recieved
-  \end{itemize}\bigskip
-
-  \begin{center}
-  \bl{\begin{tabular}{lcl}
-  $A$ sends $S$ &:& $\textit{Connect}(A,B)$\\
-  $S$ sends $A$ &:& $\{K_{AB}\}_{K_{AS}}$ \textcolor{black}{and} $\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}}$\\
-  $A$ sends $B$ &:& $\{K_{AB}\}_{K_{BS}}$\\
-  $A$ sends $B$ &:& $\{m\}_{K_{AB}}$
-  \end{tabular}}
-  \end{center}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%      
-  
-   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[c]
-  \frametitle{Sending Rule}
-
-  \bl{\begin{center}
-  \mbox{\infer{\Gamma \vdash Q \;\textit{says}\; F}
-              {\Gamma \vdash P \;\textit{says}\; F & \Gamma \vdash P \;\textit{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{Trusted Third Party}
-
-  \begin{center}
-  \bl{\begin{tabular}{l}
-  $A$ sends $S$ : $\textit{Connect}(A,B)$\\  
-  \bl{$S \,\text{says}\, (\textit{Connect}(A,B) \Rightarrow$}\\ 
-  \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}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%      
-\end{document}
-
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-%%% mode: latex
-%%% TeX-master: t
-%%% End: 
-




