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\documentclass[dvipsnames,14pt,t]{beamer}
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\usepackage{proof}
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\usepackage{beamerthemeplainculight}
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\usepackage[T1]{fontenc}
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\usepackage[latin1]{inputenc}
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\usepackage{mathpartir}
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\usepackage{isabelle}
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\usepackage{isabellesym}
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\usepackage[absolute,overlay]{textpos}
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\usepackage{ifthen}
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\usepackage{tikz}
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\usepackage{courier}
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\usepackage{listings}
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\usetikzlibrary{arrows}
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\usetikzlibrary{positioning}
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\usetikzlibrary{calc}
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\usepackage{graphicx}
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\isabellestyle{rm}
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\renewcommand{\isastyle}{\rm}%
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\renewcommand{\isastyleminor}{\rm}%
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\renewcommand{\isastylescript}{\footnotesize\rm\slshape}%
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\renewcommand{\isatagproof}{}
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\renewcommand{\endisatagproof}{}
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\renewcommand{\isamarkupcmt}[1]{#1}
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% Isabelle characters
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\renewcommand{\isacharunderscore}{\_}
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\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc
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\lstset{language=Java,
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basicstyle=\ttfamily,
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keywordstyle=\color{javapurple}\bfseries,
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stringstyle=\color{javagreen},
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commentstyle=\color{javagreen},
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morecomment=[s][\color{javadocblue}]{/**}{*/},
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numbers=left,
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numberstyle=\tiny\color{black},
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showspaces=false,
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showstringspaces=false}
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\lstdefinelanguage{scala}{
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morekeywords={abstract,case,catch,class,def,%
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do,else,extends,false,final,finally,%
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for,if,implicit,import,match,mixin,%
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new,null,object,override,package,%
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private,protected,requires,return,sealed,%
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super,this,throw,trait,true,try,%
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type,val,var,while,with,yield},
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otherkeywords={=>,<-,<\%,<:,>:,\#,@},
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sensitive=true,
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morestring=[b]",
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morestring=[b]',
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morestring=[b]"""
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}
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\lstset{language=Scala,
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basicstyle=\ttfamily,
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keywordstyle=\color{javapurple}\bfseries,
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commentstyle=\color{javagreen},
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morecomment=[s][\color{javadocblue}]{/**}{*/},
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showstringspaces=false}
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% beamer stuff
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\renewcommand{\slidecaption}{APP 05, King's College London, 23 October 2012}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1>[t]
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\
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\LARGE Access Control and \\[-3mm]
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\LARGE Privacy Policies (5)\\[-6mm]
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\end{tabular}}\bigskip\bigskip\bigskip
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%\begin{center}
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%\includegraphics[scale=1.3]{pics/barrier.jpg}
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%\end{center}
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\normalsize
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\begin{center}
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\begin{tabular}{ll}
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Email: & christian.urban at kcl.ac.uk\\
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Of$\!$fice: & S1.27 (1st floor Strand Building)\\
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Slides: & KEATS (also homework is there)\\
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\end{tabular}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Satan's Computer}
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Ross Anderson and Roger Needham wrote:\bigskip
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\begin{quote}
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In effect, our task is to program a computer which gives
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answers which are subtly and maliciously wrong at the most
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inconvenient possible moment\ldots{} we hope that the lessons
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learned from programming Satan's computer may be helpful
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in tackling the more common problem of programming Murphy's.
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\end{quote}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Protocol Specifications}
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The Needham-Schroeder Protocol:
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\begin{center}
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\begin{tabular}{@ {\hspace{-7mm}}l@{\hspace{2mm}}r@ {\hspace{1mm}}l}
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Message 1 & \bl{$A \rightarrow S :$} & \bl{$A, B, N_A$}\\
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Message 2 & \bl{$S \rightarrow A :$} & \bl{$\{N_A, B, K_{AB},\{K_{AB}, A\}_{K_{BS}} \}_{K_{AS}}$}\\
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Message 3 & \bl{$A \rightarrow B :$} & \bl{$\{K_{AB}, A\}_{K_{BS}} $}\\
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Message 4 & \bl{$B \rightarrow A :$} & \bl{$\{N_B\}_{K_{AB}}$}\\
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Message 5 & \bl{$A \rightarrow B :$} & \bl{$\{N_B-1\}_{K_{AB}}$}\\
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\end{tabular}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Cryptographic Protocol Failures}
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Again Ross Anderson and Roger Needham wrote:\bigskip
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\begin{quote}
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\textcolor{gray}{
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A lot of the recorded frauds were the result of this kind of blunder, or from
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management negligence pure and simple.} However, there have been a
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significant number of cases where the designers protected the right things,
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used cryptographic algorithms which were not broken, and yet found that their
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systems were still successfully attacked.
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\end{quote}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{The Access Control Problem}
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\begin{center}
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\begin{tikzpicture}[scale=1]
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\draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
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\draw (-2.7,1) node {\begin{tabular}{l}access\\request\end{tabular}};
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\draw (4.2,1) node {\begin{tabular}{l}granted/\\not granted\end{tabular}};
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\draw (0.6,1.2) node {\footnotesize \begin{tabular}{l}Access\\Control\\Checker\end{tabular}};
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\draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1);
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\draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1);
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\draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2);
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\draw (0.6,4) node {\begin{tabular}{l}\large some rules\\(access policy)\end{tabular}};
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\end{tikzpicture}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Access Control Logic}
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Ross Anderson about the use of Logic:\bigskip
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\begin{quote}
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Formal methods can be an excellent way of finding
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bugs in security protocol designs as they force the designer
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to make everything explicit and thus confront dif$\!$ficult design
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choices that might otherwise be fudged.
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\end{quote}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\begin{center}
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\begin{tikzpicture}[scale=1]
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\draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
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\draw (-2.7,1) node {\begin{tabular}{l}access\\request\end{tabular}};
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\draw (4.2,1) node {\begin{tabular}{l}granted/\\not granted\end{tabular}};
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\draw (0.6,1.2) node {\footnotesize \begin{tabular}{l}Access\\Control\\Checker\end{tabular}};
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\draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1);
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\draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1);
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\draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2);
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\draw (0.6,3.7) node {\begin{tabular}{l}access policy\end{tabular}};
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\end{tikzpicture}
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\end{center}
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Assuming one file on my computer contains a virus.\smallskip\\
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\only<1>{Q: Given my access policy, can this file ``infect'' my whole computer?}%
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\only<2>{Q: Can my access policy prevent that my whole computer gets infected.}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\small
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\begin{center}
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\mbox{
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\inferrule{\mbox{\begin{tabular}{l}
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\ldots\\
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is\_at\_library (Christian)\\
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is\_student (a) $\wedge$ is\_at\_library (a) $\Rightarrow$ may\_obtain\_email (a)\\
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is\_staff (a) $\wedge$ is\_at\_library (a) $\Rightarrow$ may\_obtain\_email (a)\medskip\\
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\onslide<2->{HoD says is\_staff (a) $\Rightarrow$ is\_staff (a)}\\
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\onslide<2->{HoD says is\_staff (Christian)}\medskip\\
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\onslide<3->{may\_obtain\_email (a) $\wedge$ sending\_spam (a) $\Rightarrow$\\}
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\onslide<3->{\hspace{6cm}$\neg$ may\_obtain\_email (a)}
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\end{tabular}
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}}
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{\mbox{? may\_obtain\_email (Christian)}}}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{}
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There are two ways for tackling such problems:\medskip
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\begin{itemize}
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\item either you make up our own language in which you can describe
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the problem,\medskip
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\item or you use an existing language and represent the problem in
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this language.
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\end{itemize}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[t]
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\frametitle{\Large\begin{tabular}{@ {}c@ {}}Logic(s)\end{tabular}}
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\begin{itemize}
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\item Formulas
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\begin{center}\color{blue}
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\begin{tabular}{rcl@ {\hspace{10mm}}l}
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\isa{F} & \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}} & \isa{true} \\
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& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{false} \\
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& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F} \\
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& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F} \\
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& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F} & \textcolor{black}{implies}\\
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& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ F} & \textcolor{black}{negation}\\
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& \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}\\
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& \onslide<2->{\isa{{\isaliteral{7C}{\isacharbar}}}} & \onslide<2->{\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ F}} &
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\onslide<2->{\textcolor{black}{forall quantification}}\\
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& \onslide<2->{\isa{{\isaliteral{7C}{\isacharbar}}}} & \onslide<2->{\isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ F}} &
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\onslide<2->{\textcolor{black}{exists quantification}}\\[-7mm]
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\end{tabular}
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\end{center}
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\end{itemize}
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\begin{textblock}{12}(1,14)
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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}}}}
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\end{textblock}
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\end{frame}}
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%
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\mode<presentation>{
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\begin{frame}[c]
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{\lstset{language=Scala}\fontsize{10}{12}\selectfont
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\texttt{\lstinputlisting{programs/formulas.scala}}}
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\end{frame}}
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\mode<presentation>{
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\begin{frame}[t]
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\frametitle{Judgements}
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\begin{center}
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\LARGE
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\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}
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\end{center}
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\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}} is a collection of formulas, called the \alert{assumptions}\bigskip\pause
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\begin{itemize}
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\item Example\mbox{}\\[-8mm]
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\only<2>{\begin{center}\tiny
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\textcolor{blue}{
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\begin{tabular}{l}
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\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
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\isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
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\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}}}\\
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\end{tabular}\isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
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\end{center}}
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\only<3>{\small
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\textcolor{blue}{
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\begin{center}
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\mbox{
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\infer{\mbox{\isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
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{\mbox{\begin{tabular}{@ {}l@ {}}
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\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
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\isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
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\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}}}\\
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\end{tabular}}
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}
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}
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\end{center}
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}}
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\only<4>{\small
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\textcolor{blue}{
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\begin{center}
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\mbox{
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\infer{\mbox{\isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}}}
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{\mbox{\begin{tabular}{@ {}l@ {}}
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\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}\\
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\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
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\isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
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\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}}}\\
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\end{tabular}}
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}
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}
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\end{center}
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}}
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\end{itemize}
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\end{frame}}
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\mode<presentation>{
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\begin{frame}[c]
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{\lstset{language=Scala}\fontsize{10}{12}\selectfont
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\texttt{\lstinputlisting{programs/judgement.scala}}}
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\end{frame}}
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\mode<presentation>{
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\begin{frame}[t]
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\frametitle{Inference Rules}
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\textcolor{blue}{
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\begin{center}
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\Large
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420 |
\mbox{
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\infer{\mbox{\isa{conclusion}}}
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{\mbox{\isa{premise\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} & \mbox{\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}} & \mbox{\isa{premise\isaliteral{5C3C5E697375623E}{}\isactrlisub n}}}}
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\end{center}}
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The conlusion and premises are judgements\bigskip\pause
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\begin{itemize}
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\item Examples
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\textcolor{blue}{
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430 |
\begin{center}
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431 |
\mbox{
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432 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
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433 |
{\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}}}}}}
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\end{center}}\pause
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435 |
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436 |
\textcolor{blue}{
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437 |
\begin{center}
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438 |
\mbox{
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439 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
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440 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
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\hspace{10mm}
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\mbox{
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443 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
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{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
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\end{center}}
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\end{itemize}
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\end{frame}}
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%
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\mode<presentation>{
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\begin{frame}[t]
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\frametitle{Implication}
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\Large
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\textcolor{blue}{
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\begin{center}
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\mbox{
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\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
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{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{2C}{\isacharcomma}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
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\end{center}}
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\textcolor{blue}{
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\begin{center}
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\mbox{
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\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
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468 |
{\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}}}}}}
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\end{center}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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476 |
\begin{frame}[t]
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\frametitle{Universal Quantification}
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\Large
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479 |
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\textcolor{blue}{
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\begin{center}
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\mbox{
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483 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F{\isaliteral{5B}{\isacharbrackleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{5D}{\isacharbrackright}}}}}
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484 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ F}}}}
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485 |
\end{center}}
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486 |
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487 |
\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[t]
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\frametitle{Start Rules / Axioms}
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495 |
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496 |
\normalsize
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497 |
\alert{if \textcolor{blue}{\isa{F\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}}}
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498 |
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\textcolor{blue}{\Large
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500 |
\begin{center}
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501 |
\mbox{
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502 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}{}}
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503 |
\end{center}}\bigskip\pause
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504 |
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505 |
\normalsize
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506 |
Also written as:
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507 |
\textcolor{blue}{\Large
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|
508 |
\begin{center}
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|
509 |
\mbox{
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|
510 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{2C}{\isacharcomma}}\ F\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}{}}
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511 |
\end{center}}\pause
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512 |
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513 |
\textcolor{blue}{\Large
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514 |
\begin{center}
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515 |
\mbox{
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516 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ true}}}{}}
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517 |
\end{center}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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523 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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524 |
\mode<presentation>{
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525 |
\begin{frame}[t]
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526 |
\frametitle{}
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54
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527 |
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528 |
\begin{minipage}{1.1\textwidth}
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529 |
Let \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\footnotesize\begin{tabular}{l}
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|
52
|
530 |
\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
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|
531 |
\isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
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532 |
\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}}}\\
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533 |
\end{tabular}}
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54
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534 |
\end{minipage}
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52
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535 |
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536 |
\only<2>{
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537 |
\begin{textblock}{12}(4,3)\footnotesize
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538 |
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}\hspace{10mm}
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539 |
\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}}}}
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540 |
\end{textblock}}
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541 |
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542 |
\only<3->{
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543 |
\begin{textblock}{12}(4,3)\footnotesize
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544 |
\mbox{\textcolor{blue}{
|
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545 |
\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}}}}}
|
|
|
546 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}} &\hspace{10mm}
|
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|
547 |
\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
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548 |
}}
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549 |
\end{textblock}}
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550 |
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551 |
\only<4>{
|
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552 |
\begin{textblock}{14}(0.5,6)\footnotesize
|
|
|
553 |
\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}}}}
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554 |
\end{textblock}}
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555 |
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556 |
\only<5->{
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557 |
\begin{textblock}{14}(0.5,6)\footnotesize
|
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558 |
\textcolor{blue}{
|
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|
559 |
\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}}}\\
|
|
|
560 |
\hspace{40mm}\isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\end{tabular}}}
|
|
|
561 |
{\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}}}}}}
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562 |
\end{textblock}}
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563 |
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564 |
\only<6->{
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|
565 |
\begin{textblock}{14}(5,10)\footnotesize
|
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566 |
\textcolor{blue}{
|
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|
567 |
\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}}}}}
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568 |
{\vdots & \hspace{30mm} \vdots}}
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569 |
\end{textblock}}
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570 |
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571 |
\end{frame}}
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572 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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573 |
%
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574 |
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575 |
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576 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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577 |
\mode<presentation>{
|
|
|
578 |
\begin{frame}[t]
|
|
|
579 |
\frametitle{Access Control}
|
|
|
580 |
\Large
|
|
|
581 |
|
|
|
582 |
\textcolor{blue}{
|
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|
583 |
\begin{center}
|
|
|
584 |
\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}
|
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|
585 |
\end{center}}\bigskip
|
|
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586 |
|
|
|
587 |
\normalsize
|
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|
588 |
\begin{itemize}
|
|
|
589 |
\item If there is a proof \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} yes (granted)
|
|
|
590 |
\item If there isn't \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} no (denied)
|
|
|
591 |
\end{itemize}\bigskip\pause
|
|
|
592 |
|
|
54
|
593 |
\begin{minipage}{1.1\textwidth}
|
|
52
|
594 |
\small
|
|
54
|
595 |
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
|
|
52
|
596 |
\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
|
|
|
597 |
\isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
|
|
|
598 |
\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}}}\\
|
|
|
599 |
\end{tabular}}\medskip
|
|
|
600 |
|
|
|
601 |
\textcolor{blue}{
|
|
|
602 |
\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} $\not\vdash$ \isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}}}
|
|
54
|
603 |
\end{minipage}
|
|
52
|
604 |
\end{frame}}
|
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605 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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606 |
%
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607 |
|
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608 |
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609 |
|
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610 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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|
611 |
\mode<presentation>{
|
|
|
612 |
\begin{frame}[c]
|
|
|
613 |
\frametitle{The Access Control Problem}
|
|
|
614 |
|
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|
615 |
|
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|
616 |
\begin{center}
|
|
|
617 |
\begin{tikzpicture}[scale=1]
|
|
|
618 |
|
|
|
619 |
\draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
|
|
|
620 |
\draw (-2.7,1) node {\begin{tabular}{l}access\\request\\ (\bl{$F$})\end{tabular}};
|
|
|
621 |
\draw (4.2,1) node {\begin{tabular}{l}granted/\\not granted\end{tabular}};
|
|
|
622 |
\draw (0.6,1.2) node {\footnotesize \begin{tabular}{l}Access\\Control\\Checker\end{tabular}};
|
|
|
623 |
|
|
|
624 |
\draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1);
|
|
|
625 |
\draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1);
|
|
|
626 |
\draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2);
|
|
|
627 |
|
|
|
628 |
\draw (0.6,4) node {\begin{tabular}{l}\large Access Policy (\bl{$\Gamma$})\end{tabular}};
|
|
|
629 |
|
|
|
630 |
\end{tikzpicture}
|
|
|
631 |
\end{center}
|
|
|
632 |
|
|
|
633 |
\end{frame}}
|
|
|
634 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
635 |
|
|
|
636 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
637 |
\mode<presentation>{
|
|
|
638 |
\begin{frame}[c]
|
|
|
639 |
\frametitle{Bad News}
|
|
|
640 |
|
|
|
641 |
\begin{itemize}
|
|
|
642 |
\item We introduced (roughly) first-order logic. \bigskip\pause
|
|
|
643 |
|
|
|
644 |
\item Judgements
|
|
|
645 |
\begin{center}
|
|
|
646 |
\textcolor{blue}
|
|
|
647 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
|
|
|
648 |
\end{center}
|
|
|
649 |
|
|
|
650 |
are in general \alert{undecidable}.\pause\medskip\\
|
|
|
651 |
|
|
|
652 |
The problem is \alert{semi-decidable}.
|
|
|
653 |
|
|
|
654 |
\end{itemize}
|
|
|
655 |
|
|
|
656 |
|
|
|
657 |
\end{frame}}
|
|
|
658 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
659 |
%
|
|
|
660 |
|
|
|
661 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
662 |
\mode<presentation>{
|
|
|
663 |
\begin{frame}[t]
|
|
|
664 |
\frametitle{\Large\begin{tabular}{@ {}c@ {}}Access Control Logic\end{tabular}}
|
|
|
665 |
|
|
|
666 |
\begin{itemize}
|
|
|
667 |
\item[]
|
|
|
668 |
|
|
|
669 |
\begin{center}\color{blue}
|
|
|
670 |
\begin{tabular}[t]{rcl@ {\hspace{10mm}}l}
|
|
|
671 |
\isa{F} & \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}} & \isa{true} \\
|
|
|
672 |
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{false} \\
|
|
|
673 |
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F} \\
|
|
|
674 |
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F} \\
|
|
|
675 |
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}\\
|
|
|
676 |
& \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}}} \\
|
|
|
677 |
& \isa{{\isaliteral{7C}{\isacharbar}}} & \alert{\isa{P\ says\ F}} & \textcolor{black}{``saying predicate''}\\
|
|
|
678 |
\end{tabular}
|
|
|
679 |
\end{center}
|
|
|
680 |
|
|
|
681 |
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
|
|
|
682 |
|
|
|
683 |
\item \textcolor{blue}{\isa{HoD\ says\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
|
|
|
684 |
\end{itemize}
|
|
|
685 |
|
|
|
686 |
|
|
|
687 |
|
|
|
688 |
\end{frame}}
|
|
|
689 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
690 |
%
|
|
|
691 |
|
|
|
692 |
|
|
|
693 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
694 |
\mode<presentation>{
|
|
55
|
695 |
\begin{frame}[c]
|
|
|
696 |
|
|
|
697 |
{\lstset{language=Scala}\fontsize{10}{12}\selectfont
|
|
|
698 |
\texttt{\lstinputlisting{programs/formulas1.scala}}}
|
|
|
699 |
|
|
|
700 |
\end{frame}}
|
|
|
701 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
702 |
|
|
|
703 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
704 |
\mode<presentation>{
|
|
52
|
705 |
\begin{frame}[t]
|
|
|
706 |
\frametitle{Rules about Says}
|
|
|
707 |
|
|
|
708 |
\textcolor{blue}{
|
|
|
709 |
\begin{center}
|
|
|
710 |
\mbox{
|
|
|
711 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
|
|
|
712 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}}
|
|
|
713 |
\end{center}}
|
|
|
714 |
|
|
|
715 |
\textcolor{blue}{
|
|
|
716 |
\begin{center}
|
|
|
717 |
\mbox{
|
|
|
718 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
|
|
|
719 |
{\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}}}}}}
|
|
|
720 |
\end{center}}
|
|
|
721 |
|
|
|
722 |
\textcolor{blue}{
|
|
|
723 |
\begin{center}
|
|
|
724 |
\mbox{
|
|
|
725 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
|
|
|
726 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}}}}}
|
|
|
727 |
\end{center}}
|
|
|
728 |
|
|
|
729 |
\end{frame}}
|
|
|
730 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
731 |
%
|
|
|
732 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
733 |
\mode<presentation>{
|
|
|
734 |
\begin{frame}[c]
|
|
|
735 |
\frametitle{}
|
|
|
736 |
|
|
|
737 |
Consider the following scenario:
|
|
|
738 |
|
|
|
739 |
\begin{itemize}
|
|
|
740 |
\item If \textcolor{blue}{Admin} says that \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
|
|
|
741 |
should be deleted, then this file must be deleted.
|
|
|
742 |
\item \textcolor{blue}{Admin} trusts \textcolor{blue}{Bob} to decide whether
|
|
|
743 |
\textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} should be deleted.
|
|
|
744 |
\item \textcolor{blue}{Bob} wants to delete \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}.
|
|
|
745 |
\end{itemize}\bigskip\pause
|
|
|
746 |
|
|
|
747 |
\small
|
|
|
748 |
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
|
|
|
749 |
\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}}},\\
|
|
|
750 |
\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}}},\\
|
|
|
751 |
\isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}\\
|
|
|
752 |
\end{tabular}}\medskip\pause
|
|
|
753 |
|
|
|
754 |
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
|
|
|
755 |
\end{frame}}
|
|
|
756 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
757 |
%
|
|
|
758 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
759 |
\mode<presentation>{
|
|
|
760 |
\begin{frame}[c]
|
|
|
761 |
\frametitle{}
|
|
|
762 |
|
|
|
763 |
\textcolor{blue}{
|
|
|
764 |
\begin{center}
|
|
|
765 |
\mbox{
|
|
|
766 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
|
|
|
767 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}}\\\bigskip
|
|
|
768 |
\mbox{
|
|
|
769 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
|
|
|
770 |
{\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}}}}}}
|
|
|
771 |
\end{center}}\bigskip
|
|
|
772 |
|
|
|
773 |
\small
|
|
|
774 |
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
|
|
|
775 |
\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}}},\\
|
|
|
776 |
\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}}},\\
|
|
|
777 |
\isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}\\
|
|
|
778 |
\end{tabular}}\medskip
|
|
|
779 |
|
|
|
780 |
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
|
|
|
781 |
\end{frame}}
|
|
|
782 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
783 |
%
|
|
|
784 |
|
|
|
785 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
786 |
\mode<presentation>{
|
|
|
787 |
\begin{frame}[t]
|
|
|
788 |
\frametitle{}
|
|
|
789 |
\small
|
|
|
790 |
|
|
|
791 |
\textcolor{blue}{
|
|
|
792 |
\begin{center}
|
|
|
793 |
\only<1>{$ \underbrace{
|
|
|
794 |
\mbox{\infer{\Gamma \vdash \mbox{Admin says (Bob says del\_file)}}
|
|
|
795 |
{\infer{\Gamma \vdash \mbox{Bob says del\_file}}{}}}}_{X}$}
|
|
|
796 |
\end{center}}
|
|
|
797 |
|
|
|
798 |
\textcolor{blue}{
|
|
|
799 |
\begin{center}
|
|
|
800 |
\only<1>{
|
|
|
801 |
$ \underbrace{
|
|
|
802 |
\mbox{\infer{\Gamma \vdash \mbox{Admin says del\_file}}
|
|
|
803 |
{\infer{\Gamma \vdash \mbox{Admin says (Bob says del\_file \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} del\_file)}}{}
|
|
|
804 |
&
|
|
|
805 |
\deduce[$\vdots$]{X}{}
|
|
|
806 |
}}}_{Y}$}
|
|
|
807 |
\end{center}}
|
|
|
808 |
|
|
|
809 |
\textcolor{blue}{
|
|
|
810 |
\begin{center}
|
|
|
811 |
\only<1>{\mbox{\infer{\Gamma \vdash \mbox{del\_file}}
|
|
|
812 |
{\infer{\Gamma \vdash \mbox{(Admin says del\_file) \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} del\_file}}{}
|
|
|
813 |
&
|
|
|
814 |
\deduce[$\vdots$]{Y}{}
|
|
|
815 |
}}}
|
|
|
816 |
\end{center}}
|
|
|
817 |
|
|
|
818 |
\end{frame}}
|
|
|
819 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
820 |
%
|
|
|
821 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
822 |
\mode<presentation>{
|
|
|
823 |
\begin{frame}[c]
|
|
|
824 |
\frametitle{Controls}
|
|
|
825 |
\small
|
|
|
826 |
|
|
|
827 |
\begin{itemize}
|
|
|
828 |
\item \bl{\isa{P\ controls\ F\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}}
|
|
|
829 |
|
|
|
830 |
\item its meaning ``\bl{P} is entitled to do \bl{F}''
|
|
|
831 |
\item if \bl{P controls F} and \bl{P says F} then \bl{F}\pause
|
|
|
832 |
|
|
|
833 |
\begin{center}
|
|
|
834 |
\bl{\mbox{
|
|
|
835 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
|
|
|
836 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
|
|
|
837 |
}}
|
|
|
838 |
\end{center}\pause
|
|
|
839 |
|
|
|
840 |
\begin{center}
|
|
|
841 |
\bl{\mbox{
|
|
|
842 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
|
|
|
843 |
{\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}}}
|
|
|
844 |
}}
|
|
|
845 |
\end{center}
|
|
|
846 |
\end{itemize}
|
|
|
847 |
|
|
|
848 |
\end{frame}}
|
|
|
849 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
850 |
%
|
|
|
851 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
852 |
\mode<presentation>{
|
|
|
853 |
\begin{frame}[c]
|
|
|
854 |
\frametitle{Speaks For}
|
|
|
855 |
\small
|
|
|
856 |
|
|
|
857 |
\begin{itemize}
|
|
|
858 |
\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}}}}
|
|
|
859 |
|
|
|
860 |
\item its meaning ``\bl{P} speaks for \bl{Q}''
|
|
|
861 |
|
|
|
862 |
|
|
|
863 |
\begin{center}
|
|
|
864 |
\bl{\mbox{
|
|
|
865 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ says\ F}}}
|
|
|
866 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
|
|
|
867 |
}}
|
|
|
868 |
\end{center}\pause
|
|
|
869 |
|
|
|
870 |
\begin{center}
|
|
|
871 |
\bl{\mbox{
|
|
|
872 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}}}
|
|
|
873 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ controls\ F}}}
|
|
|
874 |
}}
|
|
|
875 |
\end{center}
|
|
|
876 |
|
|
|
877 |
\begin{center}
|
|
|
878 |
\bl{\mbox{
|
|
|
879 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ R}}}
|
|
|
880 |
{\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}}}
|
|
|
881 |
}}
|
|
|
882 |
\end{center}
|
|
|
883 |
\end{itemize}
|
|
|
884 |
|
|
|
885 |
\end{frame}}
|
|
|
886 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
887 |
%
|
|
|
888 |
|
|
|
889 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
890 |
\mode<presentation>{
|
|
|
891 |
\begin{frame}[c]
|
|
|
892 |
\frametitle{Tickets}
|
|
|
893 |
|
|
|
894 |
\begin{itemize}
|
|
|
895 |
\item Tickets control access to restricted objects.\bigskip
|
|
|
896 |
\end{itemize}
|
|
|
897 |
\small
|
|
|
898 |
|
|
|
899 |
Example: \bl{Permitted (Bob, enter\_flight)} ? \bigskip
|
|
|
900 |
|
|
|
901 |
\begin{minipage}{1.1\textwidth}
|
|
|
902 |
\begin{itemize}
|
|
|
903 |
\item \bl{Bob says Permitted (Bob, enter\_flight)}\\ (access request)
|
|
|
904 |
\item \bl{Ticket says (Bob controls Permitted (Bob, enter\_flight))}
|
|
|
905 |
\item \bl{Airline controls (Bob controls Permitted (Bob, enter\_flight))} (access policy)\pause
|
|
|
906 |
\item \bl{\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Airline}}\\
|
|
|
907 |
(trust assumption)
|
|
|
908 |
\end{itemize}
|
|
|
909 |
\end{minipage}
|
|
|
910 |
|
|
|
911 |
\end{frame}}
|
|
|
912 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
913 |
%
|
|
|
914 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
915 |
\mode<presentation>{
|
|
|
916 |
\begin{frame}[c]
|
|
|
917 |
\frametitle{Tickets}
|
|
|
918 |
\small
|
|
|
919 |
|
|
|
920 |
\begin{minipage}{1.1\textwidth}
|
|
|
921 |
\begin{enumerate}
|
|
|
922 |
\item \bl{Bob says Permitted (Bob, enter\_flight)}
|
|
|
923 |
\item \bl{Ticket says (Bob controls Permitted (Bob, enter\_flight))}
|
|
|
924 |
\item \bl{Airline controls (Bob controls Permitted (Bob, enter\_flight))}
|
|
|
925 |
\item \bl{\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Airline}}
|
|
|
926 |
\end{enumerate}
|
|
|
927 |
\end{minipage}\bigskip\bigskip
|
|
|
928 |
|
|
|
929 |
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
|
|
|
930 |
|
|
|
931 |
|
|
55
|
932 |
\small
|
|
|
933 |
\begin{minipage}{1.1\textwidth}
|
|
52
|
934 |
\begin{center}
|
|
|
935 |
\bl{\mbox{
|
|
|
936 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
|
|
|
937 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
|
|
|
938 |
}}
|
|
55
|
939 |
\bl{\mbox{\hspace{6mm}
|
|
52
|
940 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ says\ F}}}
|
|
|
941 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
|
|
|
942 |
}}
|
|
|
943 |
\end{center}
|
|
55
|
944 |
\end{minipage}
|
|
52
|
945 |
|
|
|
946 |
\end{frame}}
|
|
|
947 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
948 |
%
|
|
|
949 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
950 |
\mode<presentation>{
|
|
|
951 |
\begin{frame}[c]
|
|
|
952 |
\frametitle{Tickets}
|
|
|
953 |
\small
|
|
|
954 |
|
|
|
955 |
\begin{minipage}{1.1\textwidth}
|
|
|
956 |
\begin{itemize}
|
|
|
957 |
\item Access Request:
|
|
|
958 |
\begin{center}
|
|
|
959 |
\bl{Person says Object}
|
|
|
960 |
\end{center}
|
|
|
961 |
|
|
|
962 |
\item Ticket:
|
|
|
963 |
\begin{center}
|
|
|
964 |
\bl{Ticket says (Person controls Object)}
|
|
|
965 |
\end{center}
|
|
|
966 |
|
|
|
967 |
\item Access policy:
|
|
|
968 |
\begin{center}
|
|
|
969 |
\bl{Authority controls (Person controls Object)}
|
|
|
970 |
\end{center}
|
|
|
971 |
|
|
|
972 |
\item Trust assumption:
|
|
|
973 |
\begin{center}
|
|
|
974 |
\bl{\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Authority}}
|
|
|
975 |
\end{center}
|
|
|
976 |
\end{itemize}
|
|
|
977 |
\end{minipage}
|
|
|
978 |
|
|
|
979 |
|
|
|
980 |
\end{frame}}
|
|
|
981 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
982 |
%
|
|
|
983 |
|
|
|
984 |
|
|
|
985 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
986 |
\mode<presentation>{
|
|
|
987 |
\begin{frame}[t]
|
|
|
988 |
\frametitle{\LARGE Derived Rule for Tickets}
|
|
|
989 |
\small
|
|
|
990 |
\mbox{}\\[2cm]
|
|
|
991 |
|
|
|
992 |
\begin{center}
|
|
|
993 |
\bl{\mbox{\infer{\mbox{F}}
|
|
|
994 |
{\mbox{\begin{tabular}{l}
|
|
|
995 |
Authority controls (Person controls F)\\
|
|
|
996 |
Ticket says (Person controls F)\\
|
|
|
997 |
\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Authority}\\
|
|
|
998 |
Person says F
|
|
|
999 |
\end{tabular}}
|
|
|
1000 |
}}}
|
|
|
1001 |
\end{center}
|
|
|
1002 |
\mbox{}\\[1cm]
|
|
|
1003 |
|
|
55
|
1004 |
|
|
|
1005 |
\small
|
|
|
1006 |
\begin{minipage}{1.1\textwidth}
|
|
52
|
1007 |
\begin{center}
|
|
|
1008 |
\bl{\mbox{
|
|
|
1009 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
|
|
|
1010 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
|
|
|
1011 |
}}
|
|
55
|
1012 |
\bl{\mbox{\hspace{6mm}
|
|
52
|
1013 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ says\ F}}}
|
|
|
1014 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
|
|
|
1015 |
}}
|
|
|
1016 |
\end{center}
|
|
55
|
1017 |
\end{minipage}
|
|
52
|
1018 |
|
|
|
1019 |
\end{frame}}
|
|
|
1020 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1021 |
%
|
|
|
1022 |
\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
|
|
|
1023 |
|
|
|
1024 |
|
|
|
1025 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1026 |
\mode<presentation>{
|
|
|
1027 |
\begin{frame}[c]
|
|
|
1028 |
\frametitle{Security Levels}
|
|
|
1029 |
\small
|
|
|
1030 |
|
|
|
1031 |
\begin{itemize}
|
|
|
1032 |
\item Top secret (\bl{$T\!S$})
|
|
|
1033 |
\item Secret (\bl{$S$})
|
|
|
1034 |
\item Public (\bl{$P$})
|
|
|
1035 |
\end{itemize}
|
|
|
1036 |
|
|
|
1037 |
\begin{center}
|
|
|
1038 |
\bl{$slev(P) < slev(S) < slev(T\!S)$}\pause
|
|
|
1039 |
\end{center}
|
|
|
1040 |
|
|
|
1041 |
\begin{itemize}
|
|
|
1042 |
\item Bob has a clearance for ``secret''
|
|
|
1043 |
\item Bob can read documents that are public or sectret, but not top secret
|
|
|
1044 |
\end{itemize}
|
|
|
1045 |
|
|
|
1046 |
\end{frame}}
|
|
|
1047 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1048 |
%
|
|
|
1049 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1050 |
\mode<presentation>{
|
|
|
1051 |
\begin{frame}[c]
|
|
|
1052 |
\frametitle{Reading a File}
|
|
|
1053 |
|
|
|
1054 |
\bl{\begin{center}
|
|
|
1055 |
\begin{tabular}{c}
|
|
|
1056 |
\begin{tabular}{@ {}l@ {}}
|
|
|
1057 |
\only<2->{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$}}\\
|
|
|
1058 |
\only<2->{\hspace{3cm}}Bob controls Permitted $($File, read$)$\\
|
|
|
1059 |
Bob says Permitted $($File, read$)$\only<2->{\\}
|
|
|
1060 |
\only<2>{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$}}%
|
|
|
1061 |
\only<3>{\textcolor{red}{$slev($File$)$ $=$ $P$}\\}%
|
|
|
1062 |
\only<3>{\textcolor{red}{$slev($Bob$)$ $=$ $S$}\\}%
|
|
|
1063 |
\only<3>{\textcolor{red}{$slev(P)$ $<$ $slev(S)$}\\}%
|
|
|
1064 |
\end{tabular}\\
|
|
|
1065 |
\hline
|
|
|
1066 |
Permitted $($File, read$)$
|
|
|
1067 |
\end{tabular}
|
|
|
1068 |
\end{center}}
|
|
|
1069 |
|
|
|
1070 |
\end{frame}}
|
|
|
1071 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1072 |
%
|
|
|
1073 |
|
|
|
1074 |
|
|
|
1075 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1076 |
\mode<presentation>{
|
|
|
1077 |
\begin{frame}[c]
|
|
|
1078 |
\frametitle{Substitution Rule}
|
|
|
1079 |
\small
|
|
|
1080 |
|
|
|
1081 |
\bl{\begin{center}
|
|
|
1082 |
\begin{tabular}{c}
|
|
|
1083 |
$\Gamma \vdash slev(P) = l_1$ \hspace{4mm} $\Gamma \vdash slev(Q) = l_2$
|
|
|
1084 |
\hspace{4mm} $\Gamma \vdash l_1 < l_2$\\\hline
|
|
|
1085 |
$\Gamma \vdash slev(P) < slev(Q)$
|
|
|
1086 |
\end{tabular}
|
|
|
1087 |
\end{center}}\bigskip\pause
|
|
|
1088 |
|
|
|
1089 |
\begin{itemize}
|
|
|
1090 |
\item \bl{$slev($Bob$)$ $=$ $S$}
|
|
|
1091 |
\item \bl{$slev($File$)$ $=$ $P$}
|
|
|
1092 |
\item \bl{$slev(P) < slev(S)$}
|
|
|
1093 |
\end{itemize}
|
|
|
1094 |
|
|
|
1095 |
\end{frame}}
|
|
|
1096 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1097 |
%
|
|
|
1098 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1099 |
\mode<presentation>{
|
|
|
1100 |
\begin{frame}[c]
|
|
|
1101 |
\frametitle{Reading a File}
|
|
|
1102 |
|
|
|
1103 |
\bl{\begin{center}
|
|
|
1104 |
\begin{tabular}{c}
|
|
|
1105 |
\begin{tabular}{@ {}l@ {}}
|
|
|
1106 |
$slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$\\
|
|
|
1107 |
\hspace{3cm}Bob controls Permitted $($File, read$)$\\
|
|
|
1108 |
Bob says Permitted $($File, read$)$\\
|
|
|
1109 |
$slev($File$)$ $=$ $P$\\
|
|
|
1110 |
$slev($Bob$)$ $=$ $T\!S$\\
|
|
|
1111 |
\only<1>{\textcolor{red}{$?$}}%
|
|
|
1112 |
\only<2>{\textcolor{red}{$slev(P) < slev(S)$}\\}%
|
|
|
1113 |
\only<2>{\textcolor{red}{$slev(S) < slev(T\!S)$}}%
|
|
|
1114 |
\end{tabular}\\
|
|
|
1115 |
\hline
|
|
|
1116 |
Permitted $($File, read$)$
|
|
|
1117 |
\end{tabular}
|
|
|
1118 |
\end{center}}
|
|
|
1119 |
|
|
|
1120 |
\end{frame}}
|
|
|
1121 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1122 |
%
|
|
|
1123 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1124 |
\mode<presentation>{
|
|
|
1125 |
\begin{frame}[c]
|
|
|
1126 |
\frametitle{Transitivity Rule}
|
|
|
1127 |
\small
|
|
|
1128 |
|
|
|
1129 |
\bl{\begin{center}
|
|
|
1130 |
\begin{tabular}{c}
|
|
|
1131 |
$\Gamma \vdash l_1 < l_2$
|
|
|
1132 |
\hspace{4mm} $\Gamma \vdash l_2 < l_3$\\\hline
|
|
|
1133 |
$\Gamma \vdash l_1 < l_3$
|
|
|
1134 |
\end{tabular}
|
|
|
1135 |
\end{center}}\bigskip
|
|
|
1136 |
|
|
|
1137 |
\begin{itemize}
|
|
|
1138 |
\item \bl{$slev(P) < slev (S)$}
|
|
|
1139 |
\item \bl{$slev(S) < slev (T\!S)$}
|
|
|
1140 |
\item[] \bl{$slev(P) < slev (T\!S)$}
|
|
|
1141 |
\end{itemize}
|
|
|
1142 |
|
|
|
1143 |
\end{frame}}
|
|
|
1144 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1145 |
%
|
|
|
1146 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1147 |
\mode<presentation>{
|
|
|
1148 |
\begin{frame}[c]
|
|
|
1149 |
\frametitle{Reading Files}
|
|
|
1150 |
|
|
|
1151 |
\begin{itemize}
|
|
|
1152 |
\item Access policy for reading
|
|
|
1153 |
\end{itemize}
|
|
|
1154 |
|
|
|
1155 |
\bl{\begin{center}
|
|
|
1156 |
\begin{tabular}{c}
|
|
|
1157 |
\begin{tabular}{@ {}l@ {}}
|
|
|
1158 |
$\forall f.\;slev(f)$ \only<1>{$<$}\only<2>{\textcolor{red}{$\le$}} $slev($Bob$)$ $\Rightarrow$\\
|
|
|
1159 |
\hspace{3cm}Bob controls Permitted $(f$, read$)$\\
|
|
|
1160 |
Bob says Permitted $($File, read$)$\\
|
|
|
1161 |
$slev($File$)$ $=$ \only<1>{$P$}\only<2>{\textcolor{red}{$T\!S$}}\\
|
|
|
1162 |
$slev($Bob$)$ $=$ $T\!S$\\
|
|
|
1163 |
$slev(P) < slev(S)$\\
|
|
|
1164 |
$slev(S) < slev(T\!S)$
|
|
|
1165 |
\end{tabular}\\
|
|
|
1166 |
\hline
|
|
|
1167 |
Permitted $($File, read$)$
|
|
|
1168 |
\end{tabular}
|
|
|
1169 |
\end{center}}
|
|
|
1170 |
|
|
|
1171 |
\end{frame}}
|
|
|
1172 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1173 |
%
|
|
|
1174 |
|
|
|
1175 |
|
|
|
1176 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1177 |
\mode<presentation>{
|
|
|
1178 |
\begin{frame}[c]
|
|
|
1179 |
\frametitle{Writing Files}
|
|
|
1180 |
|
|
|
1181 |
\begin{itemize}
|
|
|
1182 |
\item Access policy for \underline{writing}
|
|
|
1183 |
\end{itemize}
|
|
|
1184 |
|
|
|
1185 |
\bl{\begin{center}
|
|
|
1186 |
\begin{tabular}{c}
|
|
|
1187 |
\begin{tabular}{@ {}l@ {}}
|
|
|
1188 |
$\forall f.\;slev($Bob$)$ $\le$ $slev(f)$ $\Rightarrow$\\
|
|
|
1189 |
\hspace{3cm}Bob controls Permitted $(f$, write$)$\\
|
|
|
1190 |
Bob says Permitted $($File, write$)$\\
|
|
|
1191 |
$slev($File$)$ $=$ $T\!S$\\
|
|
|
1192 |
$slev($Bob$)$ $=$ $S$\\
|
|
|
1193 |
$slev(P) < slev(S)$\\
|
|
|
1194 |
$slev(S) < slev(T\!S)$
|
|
|
1195 |
\end{tabular}\\
|
|
|
1196 |
\hline
|
|
|
1197 |
Permitted $($File, write$)$
|
|
|
1198 |
\end{tabular}
|
|
|
1199 |
\end{center}}
|
|
|
1200 |
|
|
|
1201 |
\end{frame}}
|
|
|
1202 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1203 |
%
|
|
|
1204 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1205 |
\mode<presentation>{
|
|
|
1206 |
\begin{frame}[c]
|
|
|
1207 |
\frametitle{Bell-LaPadula}
|
|
|
1208 |
\small
|
|
|
1209 |
|
|
|
1210 |
\begin{itemize}
|
|
|
1211 |
\item \alert{Read Rule}: A principal \bl{$P$} can read an object \bl{$O$} if and only if
|
|
|
1212 |
\bl{$P$}'s security level is at least as high as \bl{$O$}'s.
|
|
|
1213 |
\item \alert{Write Rule}: A principal \bl{$P$} can write an object \bl{$O$} if and only if
|
|
|
1214 |
\bl{$O$}'s security level is at least as high as \bl{$P$}'s.\medskip
|
|
|
1215 |
|
|
|
1216 |
\item Meta-Rule: All principals in a system should have a sufficiently high security level
|
|
|
1217 |
in order to access an object.
|
|
|
1218 |
\end{itemize}\bigskip
|
|
|
1219 |
|
|
|
1220 |
This restricts information flow $\Rightarrow$ military\bigskip\bigskip\pause
|
|
|
1221 |
|
|
|
1222 |
Bell-LaPadula: {\bf `no read up'} - {\bf `no write down'}
|
|
|
1223 |
|
|
|
1224 |
\end{frame}}
|
|
|
1225 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1226 |
%
|
|
|
1227 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1228 |
\mode<presentation>{
|
|
|
1229 |
\begin{frame}[c]
|
|
|
1230 |
\frametitle{\begin{tabular}{c}Principle of\\[-2mm] Least Privilege\end{tabular}}
|
|
|
1231 |
|
|
|
1232 |
\begin{tikzpicture}
|
|
|
1233 |
\draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
|
1234 |
{\normalsize\color{darkgray}
|
|
|
1235 |
\begin{minipage}{10cm}\raggedright
|
|
|
1236 |
A principal should have as few privileges as possible to access a resource.
|
|
|
1237 |
\end{minipage}};
|
|
|
1238 |
\end{tikzpicture}\bigskip\bigskip
|
|
|
1239 |
\small
|
|
|
1240 |
|
|
|
1241 |
\begin{itemize}
|
|
|
1242 |
\item Bob ($T\!S$) and Alice ($S$) want to communicate
|
|
|
1243 |
\item[] $\Rightarrow$ Bob should lower his security level
|
|
|
1244 |
\end{itemize}
|
|
|
1245 |
|
|
|
1246 |
\end{frame}}
|
|
|
1247 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1248 |
%
|
|
|
1249 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1250 |
\mode<presentation>{
|
|
|
1251 |
\begin{frame}[c]
|
|
|
1252 |
\frametitle{Biba Policy}
|
|
|
1253 |
\small
|
|
|
1254 |
|
|
|
1255 |
Data Integrity (rather than data confidentiality)
|
|
|
1256 |
|
|
|
1257 |
\begin{itemize}
|
|
|
1258 |
\item Biba: {\bf `no read down'} - {\bf `no write up'}
|
|
|
1259 |
\item \alert{Read Rule}: A principal \bl{$P$} can read an object \bl{$O$} if and only if
|
|
|
1260 |
\bl{$P$}'s security level is lower or equal than \bl{$O$}'s.
|
|
|
1261 |
\item \alert{Write Rule}: A principal \bl{$P$} can write an object \bl{$O$} if and only if
|
|
|
1262 |
\bl{$O$}'s security level is lower or equal than \bl{$P$}'s.
|
|
|
1263 |
\end{itemize}\bigskip\bigskip\pause
|
|
|
1264 |
|
|
|
1265 |
E.g.~Generals write orders to officers; officers write oders to solidiers\\
|
|
|
1266 |
Firewall: you can read from inside the firewall, but not from outside\\
|
|
|
1267 |
Phishing: you can look at an approved PDF, but not one from a random email\\
|
|
|
1268 |
|
|
|
1269 |
\end{frame}}
|
|
|
1270 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1271 |
%
|
|
|
1272 |
|
|
53
|
1273 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1274 |
\mode<presentation>{
|
|
|
1275 |
\begin{frame}[c]
|
|
|
1276 |
\frametitle{Point to Take Home}
|
|
|
1277 |
|
|
|
1278 |
\begin{itemize}
|
|
|
1279 |
\item Formal methods can be an excellent way of finding
|
|
|
1280 |
bugs as they force the designer
|
|
|
1281 |
to make everything explicit and thus confront dif$\!$ficult design
|
|
|
1282 |
choices that might otherwise be fudged.
|
|
|
1283 |
\end{itemize}
|
|
|
1284 |
|
|
|
1285 |
\end{frame}}
|
|
|
1286 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1287 |
|
|
52
|
1288 |
|
|
|
1289 |
|
|
|
1290 |
\end{document}
|
|
|
1291 |
|
|
|
1292 |
%%% Local Variables:
|
|
|
1293 |
%%% mode: latex
|
|
|
1294 |
%%% TeX-master: t
|
|
|
1295 |
%%% End:
|
|
|
1296 |
|