--- a/slides06.tex	Tue Oct 30 14:27:59 2012 +0000
+++ b/slides06.tex	Tue Oct 30 14:48:13 2012 +0000
@@ -548,6 +548,85 @@
   \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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