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\begin{document}
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\mode<presentation>{
\begin{frame}<1>[t]
\frametitle{%
\begin{tabular}{@ {}c@ {}}
\\
\LARGE Access Control and \\[-3mm]
\LARGE Privacy Policies (5)\\[-6mm]
\end{tabular}}\bigskip\bigskip\bigskip
%\begin{center}
%\includegraphics[scale=1.3]{pics/barrier.jpg}
%\end{center}
\normalsize
\begin{center}
\begin{tabular}{ll}
Email: & christian.urban at kcl.ac.uk\\
Of$\!$fice: & S1.27 (1st floor Strand Building)\\
Slides: & KEATS (also homework is there)\\
\end{tabular}
\end{center}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\frametitle{Satan's Computer}
Ross Anderson and Roger Needham wrote:\bigskip
\begin{quote}
In effect, our task is to program a computer which gives
answers which are subtly and maliciously wrong at the most
inconvenient possible moment\ldots{} we hope that the lessons
learned from programming Satan's computer may be helpful
in tackling the more common problem of programming Murphy's.
\end{quote}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\frametitle{Protocol Specifications}
The Needham-Schroeder Protocol:
\begin{center}
\begin{tabular}{@ {\hspace{-7mm}}l@{\hspace{2mm}}r@ {\hspace{1mm}}l}
Message 1 & \bl{$A \rightarrow S :$} & \bl{$A, B, N_A$}\\
Message 2 & \bl{$S \rightarrow A :$} & \bl{$\{N_A, B, K_{AB},\{K_{AB}, A\}_{K_{BS}} \}_{K_{AS}}$}\\
Message 3 & \bl{$A \rightarrow B :$} & \bl{$\{K_{AB}, A\}_{K_{BS}} $}\\
Message 4 & \bl{$B \rightarrow A :$} & \bl{$\{N_B\}_{K_{AB}}$}\\
Message 5 & \bl{$A \rightarrow B :$} & \bl{$\{N_B-1\}_{K_{AB}}$}\\
\end{tabular}
\end{center}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\frametitle{Cryptographic Protocol Failures}
Again Ross Anderson and Roger Needham wrote:\bigskip
\begin{quote}
\textcolor{gray}{
A lot of the recorded frauds were the result of this kind of blunder, or from
management negligence pure and simple.} However, there have been a
significant number of cases where the designers protected the right things,
used cryptographic algorithms which were not broken, and yet found that their
systems were still successfully attacked.
\end{quote}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\frametitle{The Access Control Problem}
\begin{center}
\begin{tikzpicture}[scale=1]
\draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
\draw (-2.7,1) node {\begin{tabular}{l}access\\request\end{tabular}};
\draw (4.2,1) node {\begin{tabular}{l}granted/\\not granted\end{tabular}};
\draw (0.6,1.2) node {\footnotesize \begin{tabular}{l}Access\\Control\\Checker\end{tabular}};
\draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1);
\draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1);
\draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2);
\draw (0.6,4) node {\begin{tabular}{l}\large some rules\\(access policy)\end{tabular}};
\end{tikzpicture}
\end{center}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\frametitle{Access Control Logic}
Ross Anderson about the use of Logic:\bigskip
\begin{quote}
Formal methods can be an excellent way of finding
bugs in security protocol designs as they force the designer
to make everything explicit and thus confront dif$\!$ficult design
choices that might otherwise be fudged.
\end{quote}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\begin{center}
\begin{tikzpicture}[scale=1]
\draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
\draw (-2.7,1) node {\begin{tabular}{l}access\\request\end{tabular}};
\draw (4.2,1) node {\begin{tabular}{l}granted/\\not granted\end{tabular}};
\draw (0.6,1.2) node {\footnotesize \begin{tabular}{l}Access\\Control\\Checker\end{tabular}};
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\draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2);
\draw (0.6,3.7) node {\begin{tabular}{l}access policy\end{tabular}};
\end{tikzpicture}
\end{center}
Assuming one file on my computer contains a virus.\smallskip\\
\only<1>{Q: Given my access policy, can this file ``infect'' my whole computer?}%
\only<2>{Q: Can my access policy prevent that my whole computer gets infected.}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\small
\begin{center}
\mbox{
\inferrule{\mbox{\begin{tabular}{l}
\ldots\\
is\_at\_library (Christian)\\
is\_student (a) $\wedge$ is\_at\_library (a) $\Rightarrow$ may\_obtain\_email (a)\\
is\_staff (a) $\wedge$ is\_at\_library (a) $\Rightarrow$ may\_obtain\_email (a)\medskip\\
\onslide<2->{HoD says is\_staff (a) $\Rightarrow$ is\_staff (a)}\\
\onslide<2->{HoD says is\_staff (Christian)}\medskip\\
\onslide<3->{may\_obtain\_email (a) $\wedge$ sending\_spam (a) $\Rightarrow$\\}
\onslide<3->{\hspace{6cm}$\neg$ may\_obtain\_email (a)}
\end{tabular}
}}
{\mbox{? may\_obtain\_email (Christian)}}}
\end{center}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\frametitle{}
There are two ways for tackling such problems:\medskip
\begin{itemize}
\item either you make up our own language in which you can describe
the problem,\medskip
\item or you use an existing language and represent the problem in
this language.
\end{itemize}
\end{frame}}
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\mode<presentation>{
\begin{frame}[t]
\frametitle{\Large\begin{tabular}{@ {}c@ {}}Logic(s)\end{tabular}}
\begin{itemize}
\item Formulas
\begin{center}\color{blue}
\begin{tabular}{rcl@ {\hspace{10mm}}l}
\isa{F} & \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}} & \isa{true} \\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{false} \\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F} \\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F} \\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F} & \textcolor{black}{implies}\\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ F} & \textcolor{black}{negation}\\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{p\ {\isaliteral{28}{\isacharparenleft}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}} & \textcolor{black}{predicates}\\
& \onslide<2->{\isa{{\isaliteral{7C}{\isacharbar}}}} & \onslide<2->{\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ F}} &
\onslide<2->{\textcolor{black}{forall quantification}}\\
& \onslide<2->{\isa{{\isaliteral{7C}{\isacharbar}}}} & \onslide<2->{\isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ F}} &
\onslide<2->{\textcolor{black}{exists quantification}}\\[-7mm]
\end{tabular}
\end{center}
\end{itemize}
\begin{textblock}{12}(1,14)
Terms \textcolor{blue}{\isa{t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{7C}{\isacharbar}}\ c\ {\isaliteral{5C3C646F74733E}{\isasymdots}}}}
\end{textblock}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[c]
{\lstset{language=Scala}\fontsize{10}{12}\selectfont
\texttt{\lstinputlisting{programs/formulas.scala}}}
\end{frame}}
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\mode<presentation>{
\begin{frame}[t]
\frametitle{Judgements}
\begin{center}
\LARGE
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}
\end{center}
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}} is a collection of formulas, called the \alert{assumptions}\bigskip\pause
\begin{itemize}
\item Example\mbox{}\\[-8mm]
\only<2>{\begin{center}\tiny
\textcolor{blue}{
\begin{tabular}{l}
\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
\isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
\end{tabular}\isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
\end{center}}
\only<3>{\small
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
{\mbox{\begin{tabular}{@ {}l@ {}}
\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
\isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
\end{tabular}}
}
}
\end{center}
}}
\only<4>{\small
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}}}
{\mbox{\begin{tabular}{@ {}l@ {}}
\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}\\
\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
\isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
\end{tabular}}
}
}
\end{center}
}}
\end{itemize}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
{\lstset{language=Scala}\fontsize{10}{12}\selectfont
\texttt{\lstinputlisting{programs/judgement.scala}}}
\end{frame}}
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\mode<presentation>{
\begin{frame}[t]
\frametitle{Inference Rules}
\textcolor{blue}{
\begin{center}
\Large
\mbox{
\infer{\mbox{\isa{conclusion}}}
{\mbox{\isa{premise\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} & \mbox{\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}} & \mbox{\isa{premise\isaliteral{5C3C5E697375623E}{}\isactrlisub n}}}}
\end{center}}
The conlusion and premises are judgements\bigskip\pause
\begin{itemize}
\item Examples
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
\end{center}}\pause
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
\hspace{10mm}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
\end{center}}
\end{itemize}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[t]
\frametitle{Implication}
\Large
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{2C}{\isacharcomma}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
\end{center}}
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
\end{center}}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[t]
\frametitle{Universal Quantification}
\Large
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F{\isaliteral{5B}{\isacharbrackleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{5D}{\isacharbrackright}}}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ F}}}}
\end{center}}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[t]
\frametitle{Start Rules / Axioms}
\normalsize
\alert{if \textcolor{blue}{\isa{F\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}}}
\textcolor{blue}{\Large
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}{}}
\end{center}}\bigskip\pause
\normalsize
Also written as:
\textcolor{blue}{\Large
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{2C}{\isacharcomma}}\ F\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}{}}
\end{center}}\pause
\textcolor{blue}{\Large
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ true}}}{}}
\end{center}}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[t]
\frametitle{}
\begin{minipage}{1.1\textwidth}
Let \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\footnotesize\begin{tabular}{l}
\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
\isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
\end{tabular}}
\end{minipage}
\only<2>{
\begin{textblock}{12}(4,3)\footnotesize
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}\hspace{10mm}
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
\end{textblock}}
\only<3->{
\begin{textblock}{12}(4,3)\footnotesize
\mbox{\textcolor{blue}{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}} &\hspace{10mm}
\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
}}
\end{textblock}}
\only<4>{
\begin{textblock}{14}(0.5,6)\footnotesize
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}}
\end{textblock}}
\only<5->{
\begin{textblock}{14}(0.5,6)\footnotesize
\textcolor{blue}{
\infer{\mbox{\begin{tabular}{l}\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
\hspace{40mm}\isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\end{tabular}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}}}}
\end{textblock}}
\only<6->{
\begin{textblock}{14}(5,10)\footnotesize
\textcolor{blue}{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
{\vdots & \hspace{30mm} \vdots}}
\end{textblock}}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[t]
\frametitle{Access Control}
\Large
\textcolor{blue}{
\begin{center}
\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}
\end{center}}\bigskip
\normalsize
\begin{itemize}
\item If there is a proof \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} yes (granted)
\item If there isn't \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} no (denied)
\end{itemize}\bigskip\pause
\begin{minipage}{1.1\textwidth}
\small
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
\isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
\isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
\end{tabular}}\medskip
\textcolor{blue}{
\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} $\not\vdash$ \isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}}}
\end{minipage}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[c]
\frametitle{The Access Control Problem}
\begin{center}
\begin{tikzpicture}[scale=1]
\draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
\draw (-2.7,1) node {\begin{tabular}{l}access\\request\\ (\bl{$F$})\end{tabular}};
\draw (4.2,1) node {\begin{tabular}{l}granted/\\not granted\end{tabular}};
\draw (0.6,1.2) node {\footnotesize \begin{tabular}{l}Access\\Control\\Checker\end{tabular}};
\draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1);
\draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1);
\draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2);
\draw (0.6,4) node {\begin{tabular}{l}\large Access Policy (\bl{$\Gamma$})\end{tabular}};
\end{tikzpicture}
\end{center}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\frametitle{Bad News}
\begin{itemize}
\item We introduced (roughly) first-order logic. \bigskip\pause
\item Judgements
\begin{center}
\textcolor{blue}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
\end{center}
are in general \alert{undecidable}.\pause\medskip\\
The problem is \alert{semi-decidable}.
\end{itemize}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[t]
\frametitle{\Large\begin{tabular}{@ {}c@ {}}Access Control Logic\end{tabular}}
\begin{itemize}
\item[]
\begin{center}\color{blue}
\begin{tabular}[t]{rcl@ {\hspace{10mm}}l}
\isa{F} & \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}} & \isa{true} \\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{false} \\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F} \\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F} \\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}\\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{p\ {\isaliteral{28}{\isacharparenleft}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}} \\
& \isa{{\isaliteral{7C}{\isacharbar}}} & \alert{\isa{P\ says\ F}} & \textcolor{black}{``saying predicate''}\\
\end{tabular}
\end{center}
where \textcolor{blue}{\isa{P\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ Alice{\isaliteral{2C}{\isacharcomma}}\ Bob{\isaliteral{2C}{\isacharcomma}}\ Christian{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}}} (principals)\bigskip\pause
\item \textcolor{blue}{\isa{HoD\ says\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
\end{itemize}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[c]
{\lstset{language=Scala}\fontsize{10}{12}\selectfont
\texttt{\lstinputlisting{programs/formulas1.scala}}}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
\begin{frame}[t]
\frametitle{Rules about Says}
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}}
\end{center}}
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ {\isaliteral{28}{\isacharparenleft}}F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}}} & \hspace{10mm}\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
\end{center}}
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}}}}}
\end{center}}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[c]
\frametitle{}
Consider the following scenario:
\begin{itemize}
\item If \textcolor{blue}{Admin} says that \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
should be deleted, then this file must be deleted.
\item \textcolor{blue}{Admin} trusts \textcolor{blue}{Bob} to decide whether
\textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} should be deleted.
\item \textcolor{blue}{Bob} wants to delete \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}.
\end{itemize}\bigskip\pause
\small
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
\isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}},\\
\isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}},\\
\isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}\\
\end{tabular}}\medskip\pause
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
\end{frame}}
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%
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\mode<presentation>{
\begin{frame}[c]
\frametitle{}
\textcolor{blue}{
\begin{center}
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}}\\\bigskip
\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ {\isaliteral{28}{\isacharparenleft}}F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}}} & \hspace{5mm}\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
\end{center}}\bigskip
\small
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
\isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}},\\
\isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}},\\
\isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}\\
\end{tabular}}\medskip
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{}
\small
\textcolor{blue}{
\begin{center}
\only<1>{$ \underbrace{
\mbox{\infer{\Gamma \vdash \mbox{Admin says (Bob says del\_file)}}
{\infer{\Gamma \vdash \mbox{Bob says del\_file}}{}}}}_{X}$}
\end{center}}
\textcolor{blue}{
\begin{center}
\only<1>{
$ \underbrace{
\mbox{\infer{\Gamma \vdash \mbox{Admin says del\_file}}
{\infer{\Gamma \vdash \mbox{Admin says (Bob says del\_file \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} del\_file)}}{}
&
\deduce[$\vdots$]{X}{}
}}}_{Y}$}
\end{center}}
\textcolor{blue}{
\begin{center}
\only<1>{\mbox{\infer{\Gamma \vdash \mbox{del\_file}}
{\infer{\Gamma \vdash \mbox{(Admin says del\_file) \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} del\_file}}{}
&
\deduce[$\vdots$]{Y}{}
}}}
\end{center}}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Controls}
\small
\begin{itemize}
\item \bl{\isa{P\ controls\ F\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}}
\item its meaning ``\bl{P} is entitled to do \bl{F}''
\item if \bl{P controls F} and \bl{P says F} then \bl{F}\pause
\begin{center}
\bl{\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
}}
\end{center}\pause
\begin{center}
\bl{\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
}}
\end{center}
\end{itemize}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
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\mode<presentation>{
\begin{frame}[c]
\frametitle{Speaks For}
\small
\begin{itemize}
\item \bl{\isa{P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}F{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Q\ says\ F{\isaliteral{29}{\isacharparenright}}}}
\item its meaning ``\bl{P} speaks for \bl{Q}''
\begin{center}
\bl{\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ says\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
}}
\end{center}\pause
\begin{center}
\bl{\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ controls\ F}}}
}}
\end{center}
\begin{center}
\bl{\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ R}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ R}}}
}}
\end{center}
\end{itemize}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Tickets}
\begin{itemize}
\item Tickets control access to restricted objects.\bigskip
\end{itemize}
\small
Example: \bl{Permitted (Bob, enter\_flight)} ? \bigskip
\begin{minipage}{1.1\textwidth}
\begin{itemize}
\item \bl{Bob says Permitted (Bob, enter\_flight)}\\ (access request)
\item \bl{Ticket says (Bob controls Permitted (Bob, enter\_flight))}
\item \bl{Airline controls (Bob controls Permitted (Bob, enter\_flight))} (access policy)\pause
\item \bl{\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Airline}}\\
(trust assumption)
\end{itemize}
\end{minipage}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Tickets}
\small
\begin{minipage}{1.1\textwidth}
\begin{enumerate}
\item \bl{Bob says Permitted (Bob, enter\_flight)}
\item \bl{Ticket says (Bob controls Permitted (Bob, enter\_flight))}
\item \bl{Airline controls (Bob controls Permitted (Bob, enter\_flight))}
\item \bl{\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Airline}}
\end{enumerate}
\end{minipage}\bigskip\bigskip
Is \bl{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Permitted\ {\isaliteral{28}{\isacharparenleft}}Bob{\isaliteral{2C}{\isacharcomma}}\ enter{\isaliteral{5F}{\isacharunderscore}}flight{\isaliteral{29}{\isacharparenright}}}} derivable ? \bigskip
\small
\begin{minipage}{1.1\textwidth}
\begin{center}
\bl{\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
}}
\bl{\mbox{\hspace{6mm}
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ says\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
}}
\end{center}
\end{minipage}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Tickets}
\small
\begin{minipage}{1.1\textwidth}
\begin{itemize}
\item Access Request:
\begin{center}
\bl{Person says Object}
\end{center}
\item Ticket:
\begin{center}
\bl{Ticket says (Person controls Object)}
\end{center}
\item Access policy:
\begin{center}
\bl{Authority controls (Person controls Object)}
\end{center}
\item Trust assumption:
\begin{center}
\bl{\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Authority}}
\end{center}
\end{itemize}
\end{minipage}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\LARGE Derived Rule for Tickets}
\small
\mbox{}\\[2cm]
\begin{center}
\bl{\mbox{\infer{\mbox{F}}
{\mbox{\begin{tabular}{l}
Authority controls (Person controls F)\\
Ticket says (Person controls F)\\
\isa{Ticket\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Authority}\\
Person says F
\end{tabular}}
}}}
\end{center}
\mbox{}\\[1cm]
\small
\begin{minipage}{1.1\textwidth}
\begin{center}
\bl{\mbox{
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
}}
\bl{\mbox{\hspace{6mm}
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ says\ F}}}
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
}}
\end{center}
\end{minipage}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Security Levels}
\small
\begin{itemize}
\item Top secret (\bl{$T\!S$})
\item Secret (\bl{$S$})
\item Public (\bl{$P$})
\end{itemize}
\begin{center}
\bl{$slev(P) < slev(S) < slev(T\!S)$}\pause
\end{center}
\begin{itemize}
\item Bob has a clearance for ``secret''
\item Bob can read documents that are public or sectret, but not top secret
\end{itemize}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Reading a File}
\bl{\begin{center}
\begin{tabular}{c}
\begin{tabular}{@ {}l@ {}}
\only<2->{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$}}\\
\only<2->{\hspace{3cm}}Bob controls Permitted $($File, read$)$\\
Bob says Permitted $($File, read$)$\only<2->{\\}
\only<2>{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$}}%
\only<3>{\textcolor{red}{$slev($File$)$ $=$ $P$}\\}%
\only<3>{\textcolor{red}{$slev($Bob$)$ $=$ $S$}\\}%
\only<3>{\textcolor{red}{$slev(P)$ $<$ $slev(S)$}\\}%
\end{tabular}\\
\hline
Permitted $($File, read$)$
\end{tabular}
\end{center}}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Substitution Rule}
\small
\bl{\begin{center}
\begin{tabular}{c}
$\Gamma \vdash slev(P) = l_1$ \hspace{4mm} $\Gamma \vdash slev(Q) = l_2$
\hspace{4mm} $\Gamma \vdash l_1 < l_2$\\\hline
$\Gamma \vdash slev(P) < slev(Q)$
\end{tabular}
\end{center}}\bigskip\pause
\begin{itemize}
\item \bl{$slev($Bob$)$ $=$ $S$}
\item \bl{$slev($File$)$ $=$ $P$}
\item \bl{$slev(P) < slev(S)$}
\end{itemize}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Reading a File}
\bl{\begin{center}
\begin{tabular}{c}
\begin{tabular}{@ {}l@ {}}
$slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$\\
\hspace{3cm}Bob controls Permitted $($File, read$)$\\
Bob says Permitted $($File, read$)$\\
$slev($File$)$ $=$ $P$\\
$slev($Bob$)$ $=$ $T\!S$\\
\only<1>{\textcolor{red}{$?$}}%
\only<2>{\textcolor{red}{$slev(P) < slev(S)$}\\}%
\only<2>{\textcolor{red}{$slev(S) < slev(T\!S)$}}%
\end{tabular}\\
\hline
Permitted $($File, read$)$
\end{tabular}
\end{center}}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Transitivity Rule}
\small
\bl{\begin{center}
\begin{tabular}{c}
$\Gamma \vdash l_1 < l_2$
\hspace{4mm} $\Gamma \vdash l_2 < l_3$\\\hline
$\Gamma \vdash l_1 < l_3$
\end{tabular}
\end{center}}\bigskip
\begin{itemize}
\item \bl{$slev(P) < slev (S)$}
\item \bl{$slev(S) < slev (T\!S)$}
\item[] \bl{$slev(P) < slev (T\!S)$}
\end{itemize}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Reading Files}
\begin{itemize}
\item Access policy for reading
\end{itemize}
\bl{\begin{center}
\begin{tabular}{c}
\begin{tabular}{@ {}l@ {}}
$\forall f.\;slev(f)$ \only<1>{$<$}\only<2>{\textcolor{red}{$\le$}} $slev($Bob$)$ $\Rightarrow$\\
\hspace{3cm}Bob controls Permitted $(f$, read$)$\\
Bob says Permitted $($File, read$)$\\
$slev($File$)$ $=$ \only<1>{$P$}\only<2>{\textcolor{red}{$T\!S$}}\\
$slev($Bob$)$ $=$ $T\!S$\\
$slev(P) < slev(S)$\\
$slev(S) < slev(T\!S)$
\end{tabular}\\
\hline
Permitted $($File, read$)$
\end{tabular}
\end{center}}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Writing Files}
\begin{itemize}
\item Access policy for \underline{writing}
\end{itemize}
\bl{\begin{center}
\begin{tabular}{c}
\begin{tabular}{@ {}l@ {}}
$\forall f.\;slev($Bob$)$ $\le$ $slev(f)$ $\Rightarrow$\\
\hspace{3cm}Bob controls Permitted $(f$, write$)$\\
Bob says Permitted $($File, write$)$\\
$slev($File$)$ $=$ $T\!S$\\
$slev($Bob$)$ $=$ $S$\\
$slev(P) < slev(S)$\\
$slev(S) < slev(T\!S)$
\end{tabular}\\
\hline
Permitted $($File, write$)$
\end{tabular}
\end{center}}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Bell-LaPadula}
\small
\begin{itemize}
\item \alert{Read Rule}: A principal \bl{$P$} can read an object \bl{$O$} if and only if
\bl{$P$}'s security level is at least as high as \bl{$O$}'s.
\item \alert{Write Rule}: A principal \bl{$P$} can write an object \bl{$O$} if and only if
\bl{$O$}'s security level is at least as high as \bl{$P$}'s.\medskip
\item Meta-Rule: All principals in a system should have a sufficiently high security level
in order to access an object.
\end{itemize}\bigskip
This restricts information flow $\Rightarrow$ military\bigskip\bigskip\pause
Bell-LaPadula: {\bf `no read up'} - {\bf `no write down'}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{\begin{tabular}{c}Principle of\\[-2mm] Least Privilege\end{tabular}}
\begin{tikzpicture}
\draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
{\normalsize\color{darkgray}
\begin{minipage}{10cm}\raggedright
A principal should have as few privileges as possible to access a resource.
\end{minipage}};
\end{tikzpicture}\bigskip\bigskip
\small
\begin{itemize}
\item Bob ($T\!S$) and Alice ($S$) want to communicate
\item[] $\Rightarrow$ Bob should lower his security level
\end{itemize}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Biba Policy}
\small
Data Integrity (rather than data confidentiality)
\begin{itemize}
\item Biba: {\bf `no read down'} - {\bf `no write up'}
\item \alert{Read Rule}: A principal \bl{$P$} can read an object \bl{$O$} if and only if
\bl{$P$}'s security level is lower or equal than \bl{$O$}'s.
\item \alert{Write Rule}: A principal \bl{$P$} can write an object \bl{$O$} if and only if
\bl{$O$}'s security level is lower or equal than \bl{$P$}'s.
\end{itemize}\bigskip\bigskip\pause
E.g.~Generals write orders to officers; officers write oders to solidiers\\
Firewall: you can read from inside the firewall, but not from outside\\
Phishing: you can look at an approved PDF, but not one from a random email\\
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{Point to Take Home}
\begin{itemize}
\item Formal methods can be an excellent way of finding
bugs as they force the designer
to make everything explicit and thus confront dif$\!$ficult design
choices that might otherwise be fudged.
\end{itemize}
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
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