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\documentclass[dvipsnames,14pt,t]{beamer}
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\usepackage{proof}
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\usepackage{beamerthemeplaincu}
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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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\usetikzlibrary{shapes}
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\usepackage{graphicx}
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\setmonofont[Scale=MatchLowercase]{Consolas}
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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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\renewcommand{\isacharbar}{\isamath{\mid}}
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\renewcommand{\isasymiota}{}
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\renewcommand{\isacharbraceleft}{\{}
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\renewcommand{\isacharbraceright}{\}}
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\renewcommand{\isacharless}{$\langle$}
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\renewcommand{\isachargreater}{$\rangle$}
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\renewcommand{\isasymsharp}{\isamath{\#}}
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\renewcommand{\isasymdots}{\isamath{...}}
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\renewcommand{\isasymbullet}{\act}
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\newcommand{\isaliteral}[1]{}
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\newcommand{\isactrlisub}[1]{\emph{\isascriptstyle${}\sb{#1}$}}
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\definecolor{javared}{rgb}{0.6,0,0} % for strings
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\definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments
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\definecolor{javapurple}{rgb}{0.5,0,0.35} % keywords
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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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stepnumber=1,
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numbersep=10pt,
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tabsize=2,
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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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morecomment=[l]{//},
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morecomment=[n]{/*}{*/},
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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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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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stepnumber=1,
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numbersep=10pt,
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tabsize=2,
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showspaces=false,
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showstringspaces=false}
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%sudoku
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\newcounter{row}
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\newcounter{col}
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\newcommand\setrow[9]{
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\setcounter{col}{1}
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\foreach \n in {#1, #2, #3, #4, #5, #6, #7, #8, #9} {
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\edef\x{\value{col} - 0.5}
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\edef\y{9.5 - \value{row}}
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\node[anchor=center] at (\x, \y) {\n};
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\stepcounter{col}
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}
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\stepcounter{row}
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
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% beamer stuff
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\renewcommand{\slidecaption}{APP 06, King's College London, 12 November 2013}
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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 (6)\\[-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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Office: & N7.07 (North Wing, Bush House)\\
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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}[t]
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\frametitle{\Large\begin{tabular}{@ {}c@ {}}Access Control Logic\end{tabular}}
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Formulas
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\begin{itemize}
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\item[]
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\begin{center}\color{blue}
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\begin{tabular}[t]{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}\\
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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}}} \\
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& \isa{{\isaliteral{7C}{\isacharbar}}} & \alert{\isa{P\ says\ F}} & \textcolor{black}{``saying predicate''}\\
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\end{tabular}
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\end{center}
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\end{itemize}
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Judgements
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\begin{itemize}
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\item[] \mbox{\hspace{9mm}}\bl{$\Gamma \vdash \text{F}$}
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\end{itemize}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\frametitle{Judgements}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{tikzpicture}[scale=1]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (0.0,0.0) node {\LARGE \bl{$\Gamma \vdash F$}};
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\onslide<2->{
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\draw (-1,-0.3) node (X) {};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (-2.0,-2.0) node (Y) {};
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\draw (0.7,-3) node {\begin{tabular}{l}Gamma\\stands for a collection of formulas\\(``assumptions'')\end{tabular}};
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\draw[red, ->, line width = 2mm] (Y) -- (X);
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\draw (1.2,-0.1) node (X1) {};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (2.8,-0.1) node (Y1) {};
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\draw (4.5,-0.1) node {\begin{tabular}{l}a single formula\end{tabular}};
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\draw[red, ->, line width = 2mm] (Y1) -- (X1);
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\draw (-0.1,0.1) node (X2) {};
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\draw (0.5,1.5) node (Y2) {};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (1,1.8) node {\begin{tabular}{l}entails sign\end{tabular}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw[red, ->, line width = 2mm] (Y2) -- (X2);}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{frame}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\frametitle{Inference Rules}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{tikzpicture}[scale=1]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (0.0,0.0) node
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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{\Large\bl{\infer{\Gamma \vdash F_1 \wedge F_2}{\Gamma \vdash F_1 & \Gamma \vdash F_2}}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (-0.1,-0.7) node (X) {};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (-0.1,-1.9) node (Y) {};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (-0.2,-2) node {\begin{tabular}{l}conclusion\end{tabular}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw[red, ->, line width = 2mm] (Y) -- (X);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (-1,0.6) node (X2) {};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (0.0,1.6) node (Y2) {};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (0,1.8) node {\begin{tabular}{l}premisses\end{tabular}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw[red, ->, line width = 2mm] (Y2) -- (X2);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (1,0.6) node (X3) {};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (0.0,1.6) node (Y3) {};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw[red, ->, line width = 2mm] (Y3) -- (X3);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\only<2>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{textblock}{11}(1,13)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\small
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\bl{$P \,\text{says}\, F \vdash Q\,\text{says}\, F\wedge P \,\text{says}\, G $}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{textblock}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\only<3>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{textblock}{11}(1,13)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\small
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\bl{$\underbrace{P \,\text{says}\, F}_{\Gamma} \vdash \underbrace{Q\,\text{says}\, F}_{F_1} \,\wedge
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\underbrace{P \,\text{says}\, G}_{F_2} $}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{textblock}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{frame}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Inference Rules}
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\begin{center}
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\bl{\infer{\Gamma, F\vdash F}{}}\bigskip\\
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\bl{\infer{\Gamma \vdash F_2}{\Gamma \vdash F_1 \Rightarrow F_2 \quad \Gamma \vdash F_1}}
|
59
|
261 |
\qquad
|
|
262 |
\bl{\infer{\Gamma \vdash F_1 \Rightarrow F_2}{F_1, \Gamma \vdash F_2}}\bigskip\\
|
|
263 |
|
|
264 |
\bl{\infer{\Gamma \vdash P\,\text{says}\, F}{\Gamma \vdash F}}\medskip\\
|
|
265 |
|
|
266 |
\bl{\infer{\Gamma \vdash P \,\text{says}\, F_2}
|
|
267 |
{\Gamma \vdash P \,\text{says}\, (F_1\Rightarrow F_2) \quad
|
|
268 |
\Gamma \vdash P \,\text{says}\, F_1}}
|
|
269 |
\end{center}
|
|
270 |
|
|
271 |
\end{frame}}
|
|
272 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
273 |
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
274 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
275 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
276 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
277 |
\frametitle{Sending Messages}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
278 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
279 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
280 |
\item Alice sends a message \bl{$m$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
281 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
282 |
\bl{Alice says $m$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
283 |
\end{center}\medskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
284 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
285 |
\item Alice sends an encrypted message \bl{$m$} with key \bl{$K$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
286 |
(\bl{$\{m\}_K \dn K \Rightarrow m$})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
287 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
288 |
\bl{Alice says $\{m\}_K$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
289 |
\end{center}\medskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
290 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
291 |
\item Decryption of Alice's message\smallskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
292 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
293 |
\bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;m}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
294 |
{\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_K & \Gamma \vdash \text{Alice}\,\text{says}\,K}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
295 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
296 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
297 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
298 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
299 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
300 |
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
301 |
|
59
|
302 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
303 |
\mode<presentation>{
|
|
304 |
\begin{frame}[c]
|
|
305 |
\frametitle{Proofs}
|
|
306 |
|
60
|
307 |
\begin{center}
|
|
308 |
\bl{
|
|
309 |
\infer{\Gamma \vdash F}
|
|
310 |
{\infer{\hspace{1cm}:\hspace{1cm}}
|
|
311 |
{\infer{\hspace{1cm}:\hspace{1cm}}{:}
|
|
312 |
&
|
|
313 |
\infer{\hspace{1cm}:\hspace{1cm}}{:\quad :}
|
|
314 |
}}
|
|
315 |
}
|
|
316 |
\end{center}
|
59
|
317 |
|
|
318 |
\end{frame}}
|
|
319 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
320 |
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
321 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
322 |
|
59
|
323 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
324 |
\mode<presentation>{
|
|
325 |
\begin{frame}[c]
|
|
326 |
\frametitle{The Access Control Problem}
|
|
327 |
|
|
328 |
|
|
329 |
\begin{center}
|
|
330 |
\begin{tikzpicture}[scale=1]
|
|
331 |
|
|
332 |
\draw[line width=1mm] (-.3, -0.5) rectangle (1.5,2);
|
|
333 |
\draw (-2.7,1) node {\begin{tabular}{l}access\\request\\ (\bl{$F$})\end{tabular}};
|
|
334 |
\draw (4.2,1) node {\begin{tabular}{l}provable/\\not provable\end{tabular}};
|
|
335 |
\draw (0.6,0.8) node {\footnotesize \begin{tabular}{l}AC-\\ Checker:\\ applies\\ inference\\ rules\end{tabular}};
|
|
336 |
|
|
337 |
\draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1);
|
|
338 |
\draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1);
|
|
339 |
\draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2);
|
|
340 |
|
|
341 |
\draw (0.6,4) node {\begin{tabular}{l}\large Access Policy (\bl{$\Gamma$})\end{tabular}};
|
|
342 |
|
|
343 |
\end{tikzpicture}
|
|
344 |
\end{center}
|
|
345 |
|
|
346 |
\end{frame}}
|
|
347 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
348 |
|
|
349 |
|
|
350 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
351 |
\mode<presentation>{
|
|
352 |
\begin{frame}[c]
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
353 |
\frametitle{Proofs}
|
59
|
354 |
|
|
355 |
\begin{center}
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
356 |
\includegraphics[scale=0.4]{pics/river-stones.jpg}
|
59
|
357 |
\end{center}
|
|
358 |
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
359 |
\begin{textblock}{5}(11.7,5)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
360 |
goal
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
361 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
362 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
363 |
\begin{textblock}{5}(11.7,14)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
364 |
start
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
365 |
\end{textblock}
|
59
|
366 |
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
367 |
\begin{textblock}{5}(0,7)
|
59
|
368 |
\begin{center}
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
369 |
\bl{\infer[\small\textcolor{black}{\text{axiom}}]{\quad\vdash\quad}{}}\\[8mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
370 |
\bl{\infer{\vdash}{\quad\vdash\quad}}\\[8mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
371 |
\bl{\infer{\vdash}{\quad\vdash\qquad\vdash\quad}}
|
59
|
372 |
\end{center}
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
373 |
\end{textblock}
|
59
|
374 |
|
|
375 |
\end{frame}}
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
376 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
59
|
377 |
|
60
|
378 |
|
|
379 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
380 |
\mode<presentation>{
|
|
381 |
\begin{frame}[c]
|
126
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
382 |
\frametitle{Sudoku}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
383 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
384 |
\begin{tikzpicture}[scale=.5]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
385 |
\begin{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
386 |
\draw (0, 0) grid (9, 9);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
387 |
\draw[very thick, scale=3] (0, 0) grid (3, 3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
388 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
389 |
\setcounter{row}{1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
390 |
\setrow { }{2}{ } {5}{ }{1} { }{9}{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
391 |
\setrow {8}{ }{ } {2}{ }{3} { }{ }{6}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
392 |
\setrow { }{3}{ } { }{6}{ } { }{7}{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
393 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
394 |
\setrow { }{ }{1} { }{ }{ } {6}{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
395 |
\setrow {5}{4}{ } { }{ }{ } { }{1}{9}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
396 |
\setrow { }{ }{2} { }{ }{ } {7}{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
397 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
398 |
\setrow { }{9}{ } { }{3}{ } { }{8}{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
399 |
\setrow {2}{ }{ } {8}{ }{4} { }{ }{7}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
400 |
\setrow { }{1}{ } {9}{ }{7} { }{6}{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
401 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
402 |
\fill[red, fill opacity=0.4] (4,0) rectangle (5,9);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
403 |
\fill[red, fill opacity=0.4] (0,5) rectangle (9,6);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
404 |
\fill[red!50, fill opacity=0.4] (3,3) rectangle (4,5);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
405 |
\fill[red!50, fill opacity=0.4] (5,3) rectangle (6,5);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
406 |
\node[gray, anchor=center] at (4.5, -0.5) {columns};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
407 |
\node[gray, rotate=90, anchor=center] at (-0.6, 4.5, -0.5) {rows};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
408 |
\node[gray, anchor=center] at (4.5, 4.5) {box};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
409 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
410 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
411 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
412 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
413 |
\begin{textblock}{7}(9,3)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
414 |
\begin{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
415 |
\item {\bf Row-Column:} each cell, must contain exactly one number
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
416 |
\item {\bf Row-Number:} each row must contain each number exactly once
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
417 |
\item {\bf Column-Number:} each column must contain each number exactly once
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
418 |
\item {\bf Box-Number:} each box must contain each number exactly once
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
419 |
\end{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
420 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
421 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
422 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
423 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
424 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
425 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
426 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
427 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
428 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
429 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
430 |
\frametitle{Solving Sudokus}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
431 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
432 |
\begin{tikzpicture}[scale=.5]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
433 |
\begin{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
434 |
\draw (0, 0) grid (9, 9);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
435 |
\draw[very thick, scale=3] (0, 0) grid (3, 3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
436 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
437 |
\setcounter{row}{1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
438 |
\setrow { }{ }{ } {7}{ }{ } { }{5}{8}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
439 |
\setrow {}{5}{6} {2}{1}{8} {7}{9}{3}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
440 |
\setrow { }{ }{ } { }{ }{ } {1}{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
441 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
442 |
\setrow { }{ }{ } { }{ }{ } { }{8}{1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
443 |
\setrow { }{ }{ } {3}{7}{6} { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
444 |
\setrow {9}{6}{ } { }{ }{ } { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
445 |
|
133
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
446 |
\setrow { }{ }{5} { }{ }{ } { }{ }{ }
|
126
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
447 |
\setrow { }{ }{4} { }{2}{1} {8}{3}{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
448 |
\setrow {8}{7}{ } { }{ }{3} { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
449 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
450 |
\fill[red, fill opacity=0.4] (0,7) rectangle (1,8);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
451 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
452 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
453 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
454 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
455 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
456 |
\begin{textblock}{6}(9,6)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
457 |
{\bf single position rules}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
458 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
459 |
\bl{\infer{4\;\text{in empty position}}{\{1..9\} - \{4\}\;\text{in one row}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
460 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
461 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
462 |
\onslide<2->{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
463 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
464 |
\bl{\infer{x\;\text{in empty position}}{\{1..9\} - \{x\}\;\text{in one column}}}\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
465 |
\bl{\infer{x\;\text{in empty position}}{\{1..9\} - \{x\}\;\text{in one box}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
466 |
\end{center}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
467 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
468 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
469 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
470 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
471 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
472 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
473 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
474 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
475 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
476 |
\frametitle{Solving Sudokus}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
477 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
478 |
\begin{tikzpicture}[scale=.5]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
479 |
\begin{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
480 |
\draw (0, 0) grid (9, 9);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
481 |
\draw[very thick, scale=3] (0, 0) grid (3, 3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
482 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
483 |
\setcounter{row}{1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
484 |
\setrow { }{ }{ } {7}{ }{ } {\alert{\footnotesize 2}}{5}{8}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
485 |
\setrow {}{5}{6} {2}{1}{8} {7}{9}{3}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
486 |
\setrow { }{ }{ } { }{ }{ } {1}{\alert{\footnotesize 2}}{\alert{\footnotesize 2}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
487 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
488 |
\setrow { }{ }{ } { }{ }{ } { }{8}{1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
489 |
\setrow { }{ }{ } {3}{7}{6} { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
490 |
\setrow {9}{6}{ } { }{ }{ } { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
491 |
|
133
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
492 |
\setrow { }{ }{5} { }{ }{ } { }{ }{ }
|
126
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
493 |
\setrow { }{ }{4} { }{2}{1} {8}{3}{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
494 |
\setrow {8}{7}{ } { }{ }{3} { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
495 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
496 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
497 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
498 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
499 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
500 |
\begin{textblock}{6}(7.5,6)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
501 |
{\bf candidate rules}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
502 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
503 |
\bl{\infer{x\;\text{candidate in empty positions}}{X - \{x\}\;\text{in one box} & X \subseteq \{1..9\}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
504 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
505 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
506 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
507 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
508 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
509 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
510 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
511 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
512 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
513 |
\frametitle{Solving Sudokus}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
514 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
515 |
\begin{tikzpicture}[scale=.5]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
516 |
\begin{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
517 |
\draw (0, 0) grid (9, 9);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
518 |
\draw[very thick, scale=3] (0, 0) grid (3, 3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
519 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
520 |
\setcounter{row}{1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
521 |
\setrow { }{ }{ } {7}{ }{ } {\alert{\footnotesize 2}}{5}{8}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
522 |
\setrow {\alert{4}}{5}{6} {2}{1}{8} {7}{9}{3}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
523 |
\setrow { }{ }{ } { }{ }{ } {1}{\alert{\footnotesize 2}}{\alert{\footnotesize 2}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
524 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
525 |
\setrow { }{ }{ } { }{ }{ } { }{8}{1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
526 |
\setrow { }{ }{ } {3}{7}{6} { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
527 |
\setrow {9}{6}{ } { }{ }{ } { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
528 |
|
133
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
529 |
\setrow { }{ }{5} { }{ }{ } { }{ }{ }
|
126
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
530 |
\setrow { }{ }{4} { }{2}{1} {8}{3}{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
531 |
\setrow {8}{7}{ } { }{ }{3} { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
532 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
533 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
534 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
535 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
536 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
537 |
\begin{textblock}{6}(7.5,6)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
538 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
539 |
\bl{\infer{4\;\text{in empty position}}{\{1..9\} - \{4\}\;\text{in one row}}}\bigskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
540 |
\bl{\infer{2\;\text{candidate in empty positions}}{X - \{2\}\;\text{in one box} & X \subseteq \{1..9\}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
541 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
542 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
543 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
544 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
545 |
\begin{textblock}{3}(13.5,6.8)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
546 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
547 |
\onslide<1>{\node at (0,0) [single arrow, shape border rotate=270, fill=red,text=white]{\mbox{\alert{a}}};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
548 |
\onslide<2>{\node at (0,0) [single arrow, shape border rotate=90, fill=red,text=white]{\mbox{\alert{a}}};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
549 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
550 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
551 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
552 |
\begin{textblock}{3}(14.5,9.3)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
553 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
554 |
\onslide<1>{\node at (0,0) [single arrow, shape border rotate=270, fill=red,text=white]{\mbox{\alert{a}}};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
555 |
\onslide<2>{\node at (0,0) [single arrow, shape border rotate=90, fill=red,text=white]{\mbox{\alert{a}}};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
556 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
557 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
558 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
559 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
560 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
561 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
562 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
563 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
564 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
565 |
\frametitle{Solving Sudokus}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
566 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
567 |
\begin{tikzpicture}[scale=.5]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
568 |
\begin{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
569 |
\draw (0, 0) grid (9, 9);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
570 |
\draw[very thick, scale=3] (0, 0) grid (3, 3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
571 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
572 |
\setcounter{row}{1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
573 |
\setrow { }{ }{ } {7}{ }{ } { }{5}{8}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
574 |
\setrow { }{5}{6} {2}{1}{8} {7}{9}{3}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
575 |
\setrow { }{ }{ } { }{ }{ } {1}{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
576 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
577 |
\setrow { }{ }{ } { }{ }{ } { }{8}{1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
578 |
\setrow { }{ }{ } {3}{7}{6} { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
579 |
\setrow {9}{6}{ } { }{ }{ } { }{ }{ \alert{2}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
580 |
|
133
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
581 |
\setrow { }{ }{5} { }{ }{ } { }{ }{ }
|
126
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
582 |
\setrow { }{ }{4} { }{2}{1} {8}{3}{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
583 |
\setrow {8}{7}{ } { }{ }{3} { }{ }{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
584 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
585 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
586 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
587 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
588 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
589 |
\begin{textblock}{6}(7.5,6)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
590 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
591 |
\bl{\infer{2\;\text{candidate}}{X - \{2\}\;\text{in one box} & X \subseteq \{1..9\}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
592 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
593 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
594 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
595 |
\begin{textblock}{3}(14.5,8.3)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
596 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
597 |
\onslide<1>{\node at (0,0) [single arrow, shape border rotate=90, fill=red,text=white]{\mbox{\alert{a}}};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
598 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
599 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
600 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
601 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
602 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
603 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
604 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
605 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
606 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
607 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
608 |
\begin{frame}[c]
|
131
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
609 |
\frametitle{BTW}
|
126
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
610 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
611 |
Are there sudokus that cannot be solved?\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
612 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
613 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
614 |
\begin{tikzpicture}[scale=.5]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
615 |
\begin{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
616 |
\draw (0, 0) grid (9, 9);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
617 |
\draw[very thick, scale=3] (0, 0) grid (3, 3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
618 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
619 |
\setcounter{row}{1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
620 |
\setrow {1}{2}{3} {4}{5}{6} {7}{8}{ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
621 |
\setrow { }{ }{ } { }{ }{ } { }{ }{2}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
622 |
\setrow { }{ }{ } { }{ }{ } { }{ }{3}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
623 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
624 |
\setrow { }{ }{ } { }{ }{ } { }{ }{4}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
625 |
\setrow { }{ }{ } { }{ }{ } { }{ }{5}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
626 |
\setrow { }{ }{ } { }{ }{ } { }{ }{6}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
627 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
628 |
\setrow { }{ }{ } { }{ }{ } { }{ }{7}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
629 |
\setrow { }{ }{ } { }{ }{ } { }{ }{8}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
630 |
\setrow { }{ }{ } { }{ }{ } { }{ }{9}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
631 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
632 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
633 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
634 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
635 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
636 |
Sometimes no rules apply at all....unsolvable sudoku.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
637 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
638 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
639 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
640 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
641 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
642 |
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
643 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
644 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
645 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
646 |
\frametitle{Example Proof}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
647 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
648 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
649 |
\bl{\infer{P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash Q\;\text{says}\;F_2 \wedge P\;\text{says}\;F_1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
650 |
{\raisebox{2mm}{\text{\LARGE $?$}}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
651 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
652 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
653 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
654 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
655 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
656 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
657 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
658 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
659 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
660 |
\frametitle{Example Proof}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
661 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
662 |
\begin{tabular}{@{\hspace{-6mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
663 |
\begin{minipage}{1.1\textwidth}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
664 |
We have (by axiom)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
665 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
666 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
667 |
\begin{tabular}{@{}ll@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
668 |
(1) & \bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
669 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
670 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
671 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
672 |
From (1) we get
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
673 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
674 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
675 |
\begin{tabular}{@{}ll@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
676 |
(2) & \bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash P\;\text{says}\;F_1$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
677 |
(3) & \bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash Q\;\text{says}\;F_2$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
678 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
679 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
680 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
681 |
From (3) and (2) we get
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
682 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
683 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
684 |
\begin{tabular}{@{}ll@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
685 |
\bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash Q\;\text{says}\;F_2 \wedge P\;\text{says}\;F_1$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
686 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
687 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
688 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
689 |
Done.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
690 |
\end{minipage}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
691 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
692 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
693 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
694 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
695 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
696 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
697 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
698 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
699 |
\frametitle{Other Direction}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
700 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
701 |
\begin{tabular}{@{\hspace{-6mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
702 |
\begin{minipage}{1.1\textwidth}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
703 |
We want to prove
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
704 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
705 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
706 |
\begin{tabular}{@{}ll@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
707 |
\bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash Q\;\text{says}\;F_2 \wedge P\;\text{says}\;F_1$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
708 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
709 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
710 |
|
129
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
711 |
We better be able to prove:
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
712 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
713 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
714 |
\begin{tabular}{@{}ll@{}}
|
129
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
715 |
(1) & \bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash Q\;\text{says}\;F_2$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
716 |
(2) & \bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash P\;\text{says}\;F_1$}\\
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
717 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
718 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
719 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
720 |
For (1): If we can prove
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
721 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
722 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
723 |
\begin{tabular}{@{}ll@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
724 |
\bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash Q\;\text{says}\;F_2 \wedge P\;\text{says}\;F_1$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
725 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
726 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
727 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
728 |
then (1) is fine. Similarly for (2).
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
729 |
\end{minipage}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
730 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
731 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
732 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
733 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
734 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
735 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
129
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
736 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
737 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
738 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
739 |
I want to prove
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
740 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
741 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
742 |
\bl{$\Gamma \vdash \text{del\_file}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
743 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
744 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
745 |
There is an inference rule
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
746 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
747 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
748 |
\bl{\infer{\Gamma \vdash P \,\text{says}\, F}{\Gamma \vdash F}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
749 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
750 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
751 |
So I can derive \bl{$\Gamma \vdash \text{Alice} \,\text{says}\,\text{del\_file}$}.\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
752 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
753 |
\bl{$\Gamma$} contains already \bl{$\text{Alice} \,\text{says}\,\text{del\_file}$}. \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
754 |
So I can use the rule
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
755 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
756 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
757 |
\bl{\infer{\Gamma, F \vdash F}{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
758 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
759 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
760 |
\onslide<5>{\bf\alert{What is wrong with this?}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
761 |
\hfill{\bf Done. Qed.}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
762 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
763 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
764 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
765 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
766 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
767 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
768 |
\begin{frame}[c]
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
769 |
\frametitle{Program}
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
770 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
771 |
How to prove \bl{$\Gamma \vdash F$}?\bigskip\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
772 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
773 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
774 |
\Large \bl{\infer{\Gamma, F\vdash F}{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
775 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
776 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
777 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
778 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
779 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
780 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
781 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
782 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
783 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
784 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
785 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
786 |
\bl{\infer{\Gamma \vdash F_1 \Rightarrow F_2}{F_1, \Gamma \vdash F_2}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
787 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
788 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
789 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
790 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
791 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
792 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
793 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
794 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
795 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
796 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
797 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
798 |
\bl{\infer{\Gamma \vdash P \,\text{says}\, F}{\Gamma \vdash F}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
799 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
800 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
801 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
802 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
803 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
804 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
805 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
806 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
807 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
808 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
809 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
810 |
\bl{\infer{\Gamma \vdash F_1 \vee F_2}{\Gamma \vdash F_1}}\qquad
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
811 |
\bl{\infer{\Gamma \vdash F_1 \vee F_2}{\Gamma \vdash F_2}}\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
812 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
813 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
814 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
815 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
816 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
817 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
818 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
819 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
820 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
821 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
822 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
823 |
\bl{\infer{\Gamma \vdash F_1 \wedge F_2}{\Gamma \vdash F_1 \quad \Gamma \vdash F_2}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
824 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
825 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
826 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
827 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
828 |
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
829 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
830 |
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
831 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
832 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
833 |
\begin{frame}[t]
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
834 |
\frametitle{Program: \texttt{prove2}}
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
835 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
836 |
I want to prove \bl{$\Gamma \vdash \text{Pred}$}\bigskip\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
837 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
838 |
\begin{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
839 |
\item I found that \bl{$\Gamma$} contains the assumption \bl{$F_1 \Rightarrow F_2$}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
840 |
\item If I can prove \bl{$\Gamma \vdash F_1$},\pause{} then I can prove
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
841 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
842 |
\bl{$\Gamma \vdash F_2$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
843 |
\end{center}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
844 |
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
845 |
\item So I am able to try to prove \bl{$\Gamma \vdash \text{Pred}$} with the additional assumption
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
846 |
\bl{$F_2$}.\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
847 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
848 |
\bl{$F_2, \Gamma \vdash \text{Pred}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
849 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
850 |
\end{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
851 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
852 |
\only<4>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
853 |
\begin{textblock}{11}(1,10.5)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
854 |
\bl{\infer{\Gamma\vdash F_2}{\Gamma\vdash F_1\Rightarrow F_2 & \Gamma\vdash F_1}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
855 |
\end{textblock}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
856 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
857 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
858 |
\end{frame}}
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
859 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
860 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
861 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
862 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
863 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
864 |
\frametitle{}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
865 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
866 |
Recall the following scenario:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
867 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
868 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
869 |
\item If \textcolor{blue}{Admin} says that \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{} {}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
870 |
should be deleted, then this file must be deleted.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
871 |
\item \textcolor{blue}{Admin} trusts \textcolor{blue}{Bob} to decide whether
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
872 |
\textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}}} should be deleted.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
873 |
\item \textcolor{blue}{Bob} wants to delete \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}}}.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
874 |
\end{itemize}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
875 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
876 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
877 |
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
878 |
\isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}},\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
879 |
\isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}},\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
880 |
\isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
881 |
\end{tabular}}\medskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
882 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
883 |
\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
884 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
885 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
886 |
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
887 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
888 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
889 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
890 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
891 |
\begin{itemize}
|
135
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
892 |
\item \bl{$P \,\text{says}\, F$} means \bl{$P$} can send a ``signal'' \bl{$F$} through a wire, or
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
893 |
can make a statement \bl{$F$}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
894 |
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
895 |
\item \bl{$P$} is entitled to do \bl{$F$}\smallskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
896 |
\bl{$P \,\text{controls}\, F \,\dn\, (P\,\text{says}\, F) \Rightarrow F$}\medskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
897 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
898 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
899 |
\bl{\infer{\Gamma \vdash F}{\Gamma \vdash P\,\text{controls}\, F & \Gamma \vdash P\,\text{says}\,F}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
900 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
901 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
902 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
903 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
904 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
905 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
906 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
907 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
908 |
|
126
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
909 |
|
60
|
910 |
|
|
911 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
912 |
\mode<presentation>{
|
|
913 |
\begin{frame}[c]
|
|
914 |
\frametitle{Trusted Third Party}
|
|
915 |
|
|
916 |
Simple protocol for establishing a secure connection via a mutually
|
|
917 |
trusted 3rd party (server):
|
|
918 |
|
|
919 |
\begin{center}
|
|
920 |
\begin{tabular}{@ {\hspace{-7mm}}l@{\hspace{2mm}}r@ {\hspace{1mm}}l}
|
|
921 |
Message 1 & \bl{$A \rightarrow S :$} & \bl{$A, B$}\\
|
|
922 |
Message 2 & \bl{$S \rightarrow A :$} & \bl{$\{K_{AB}\}_{K_{AS}}$} and \bl{$\{\{K_{AB}\}_{K_{BS}} \}_{K_{AS}}$}\\
|
|
923 |
Message 3 & \bl{$A \rightarrow B :$} & \bl{$\{K_{AB}\}_{K_{BS}} $}\\
|
|
924 |
Message 4 & \bl{$A \rightarrow B :$} & \bl{$\{m\}_{K_{AB}}$}\\
|
|
925 |
\end{tabular}
|
|
926 |
\end{center}
|
|
927 |
|
|
928 |
\end{frame}}
|
|
929 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
930 |
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
931 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
932 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
933 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
934 |
\frametitle{Sending Rule}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
935 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
936 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
937 |
\mbox{\infer{\Gamma \vdash Q \;\text{says}\; F}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
938 |
{\Gamma \vdash P \;\text{says}\; F & \Gamma \vdash P \;\text{sends}\; Q : F}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
939 |
\end{center}}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
940 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
941 |
\bl{$P \,\text{sends}\, Q : F \dn$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
942 |
\hspace{6mm}\bl{$(P \,\text{says}\, F) \Rightarrow (Q \,\text{says}\, F)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
943 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
944 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
945 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
946 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
947 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
60
|
948 |
\mode<presentation>{
|
|
949 |
\begin{frame}[c]
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
950 |
\frametitle{Trusted Third Party}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
951 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
952 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
953 |
\bl{\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
954 |
$A$ sends $S$ : $\text{Connect}(A,B)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
955 |
\bl{$S \,\text{says}\, (\text{Connect}(A,B) \Rightarrow$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
956 |
\hspace{2.5cm}\bl{$\{K_{AB}\}_{K_{AS}} \wedge
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
957 |
\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}})$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
958 |
$S$ sends $A$ : $\{K_{AB}\}_{K_{AS}}$ \bl{$\wedge$} $\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
959 |
$A$ sends $B$ : $\{K_{AB}\}_{K_{BS}}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
960 |
$A$ sends $B$ : $\{m\}_{K_{AB}}$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
961 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
962 |
\end{center}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
963 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
964 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
965 |
\bl{$\Gamma \vdash B \,\text{says} \, m$}?
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
966 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
967 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
968 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
969 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
970 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
971 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
972 |
\frametitle{Public/Private Keys}
|
60
|
973 |
|
|
974 |
\begin{itemize}
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
975 |
\item Bob has a private and public key: \bl{$K_{Bob}^{pub}$}, \bl{$K_{Bob}^{priv}$}\bigskip
|
60
|
976 |
\begin{center}
|
|
977 |
\bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;m}
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
978 |
{\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_{K_{Bob}^{pub}} &
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
979 |
\Gamma \vdash K_{Bob}^{priv}}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
980 |
\end{center}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
981 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
982 |
\item this is {\bf not} a derived rule!
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
983 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
984 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
985 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
986 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
987 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
988 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
989 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
990 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
991 |
\frametitle{Security Levels}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
992 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
993 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
994 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
995 |
\item Top secret (\bl{$T\!S$})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
996 |
\item Secret (\bl{$S$})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
997 |
\item Public (\bl{$P$})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
998 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
999 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1000 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1001 |
\bl{$slev(P) < slev(S) < slev(T\!S)$}\pause
|
60
|
1002 |
\end{center}
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1003 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1004 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1005 |
\item Bob has a clearance for ``secret''
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1006 |
\item Bob can read documents that are public or sectret, but not top secret
|
60
|
1007 |
\end{itemize}
|
|
1008 |
|
|
1009 |
\end{frame}}
|
130
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1010 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1011 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1012 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1013 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1014 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1015 |
\frametitle{Reading a File}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1016 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1017 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1018 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1019 |
\begin{tabular}{@ {}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1020 |
\only<2->{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$}}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1021 |
\only<2->{\hspace{3cm}}Bob controls Permitted $($File, read$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1022 |
Bob says Permitted $($File, read$)$\only<2->{\\}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1023 |
\only<2>{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$}}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1024 |
\only<3>{\textcolor{red}{$slev($File$)$ $=$ $P$}\\}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1025 |
\only<3>{\textcolor{red}{$slev($Bob$)$ $=$ $S$}\\}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1026 |
\only<3>{\textcolor{red}{$slev(P)$ $<$ $slev(S)$}\\}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1027 |
\end{tabular}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1028 |
\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1029 |
Permitted $($File, read$)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1030 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1031 |
\end{center}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1032 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1033 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1034 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1035 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1036 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1037 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1038 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1039 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1040 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1041 |
\frametitle{Substitution Rule}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1042 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1043 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1044 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1045 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1046 |
$\Gamma \vdash slev(P) = l_1$ \hspace{4mm} $\Gamma \vdash slev(Q) = l_2$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1047 |
\hspace{4mm} $\Gamma \vdash l_1 < l_2$\\\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1048 |
$\Gamma \vdash slev(P) < slev(Q)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1049 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1050 |
\end{center}}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1051 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1052 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1053 |
\item \bl{$slev($Bob$)$ $=$ $S$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1054 |
\item \bl{$slev($File$)$ $=$ $P$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1055 |
\item \bl{$slev(P) < slev(S)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1056 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1057 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1058 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1059 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1060 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1061 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1062 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1063 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1064 |
\frametitle{Reading a File}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1065 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1066 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1067 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1068 |
\begin{tabular}{@ {}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1069 |
$slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1070 |
\hspace{3cm}Bob controls Permitted $($File, read$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1071 |
Bob says Permitted $($File, read$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1072 |
$slev($File$)$ $=$ $P$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1073 |
$slev($Bob$)$ $=$ $T\!S$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1074 |
\only<1>{\textcolor{red}{$?$}}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1075 |
\only<2>{\textcolor{red}{$slev(P) < slev(S)$}\\}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1076 |
\only<2>{\textcolor{red}{$slev(S) < slev(T\!S)$}}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1077 |
\end{tabular}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1078 |
\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1079 |
Permitted $($File, read$)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1080 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1081 |
\end{center}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1082 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1083 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1084 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1085 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1086 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1087 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1088 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1089 |
\frametitle{Transitivity Rule}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1090 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1091 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1092 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1093 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1094 |
$\Gamma \vdash l_1 < l_2$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1095 |
\hspace{4mm} $\Gamma \vdash l_2 < l_3$\\\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1096 |
$\Gamma \vdash l_1 < l_3$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1097 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1098 |
\end{center}}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1099 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1100 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1101 |
\item \bl{$slev(P) < slev (S)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1102 |
\item \bl{$slev(S) < slev (T\!S)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1103 |
\item[] \bl{$slev(P) < slev (T\!S)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1104 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1105 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1106 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1107 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1108 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1109 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1110 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1111 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1112 |
\frametitle{Reading Files}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1113 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1114 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1115 |
\item Access policy for reading
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1116 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1117 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1118 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1119 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1120 |
\begin{tabular}{@ {}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1121 |
$\forall f.\;slev(f)$ \only<1>{$<$}\only<2>{\textcolor{red}{$\le$}} $slev($Bob$)$ $\Rightarrow$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1122 |
\hspace{3cm}Bob controls Permitted $(f$, read$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1123 |
Bob says Permitted $($File, read$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1124 |
$slev($File$)$ $=$ \only<1>{$P$}\only<2>{\textcolor{red}{$T\!S$}}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1125 |
$slev($Bob$)$ $=$ $T\!S$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1126 |
$slev(P) < slev(S)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1127 |
$slev(S) < slev(T\!S)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1128 |
\end{tabular}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1129 |
\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1130 |
Permitted $($File, read$)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1131 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1132 |
\end{center}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1133 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1134 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1135 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1136 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1137 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1138 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1139 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1140 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1141 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1142 |
\frametitle{Writing Files}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1143 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1144 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1145 |
\item Access policy for \underline{writing}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1146 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1147 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1148 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1149 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1150 |
\begin{tabular}{@ {}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1151 |
$\forall f.\;slev($Bob$)$ $\le$ $slev(f)$ $\Rightarrow$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1152 |
\hspace{3cm}Bob controls Permitted $(f$, write$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1153 |
Bob says Permitted $($File, write$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1154 |
$slev($File$)$ $=$ $T\!S$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1155 |
$slev($Bob$)$ $=$ $S$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1156 |
$slev(P) < slev(S)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1157 |
$slev(S) < slev(T\!S)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1158 |
\end{tabular}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1159 |
\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1160 |
Permitted $($File, write$)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1161 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1162 |
\end{center}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1163 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1164 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1165 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1166 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1167 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1168 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1169 |
\end{document}
|
60
|
1170 |
|
|
1171 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1172 |
\mode<presentation>{
|
|
1173 |
\begin{frame}[c]
|
|
1174 |
\frametitle{Encryption}
|
|
1175 |
|
|
1176 |
\begin{itemize}
|
|
1177 |
\item Encryption of a message\smallskip
|
|
1178 |
\begin{center}
|
|
1179 |
\bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_K}
|
62
|
1180 |
{\Gamma \vdash \text{Alice}\;\text{says}\;m & \Gamma \vdash \text{Alice}\,\text{says}\,K}}}
|
60
|
1181 |
\end{center}
|
|
1182 |
\end{itemize}
|
|
1183 |
|
|
1184 |
\end{frame}}
|
|
1185 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1186 |
|
61
|
1187 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1188 |
\mode<presentation>{
|
|
1189 |
\begin{frame}[c]
|
|
1190 |
\frametitle{Public/Private Keys}
|
|
1191 |
|
|
1192 |
\begin{itemize}
|
|
1193 |
\item Bob has a private and public key: \bl{$K_{Bob}^{pub}$}, \bl{$K_{Bob}^{priv}$}\bigskip
|
|
1194 |
\begin{center}
|
|
1195 |
\bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;m}
|
|
1196 |
{\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_{K_{Bob}^{pub}} &
|
|
1197 |
\Gamma \vdash K_{Bob}^{priv}}}}
|
|
1198 |
\end{center}\bigskip\pause
|
|
1199 |
|
|
1200 |
\item this is {\bf not} a derived rule!
|
|
1201 |
\end{itemize}
|
|
1202 |
|
|
1203 |
\end{frame}}
|
|
1204 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1205 |
|
|
1206 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1207 |
\mode<presentation>{
|
|
1208 |
\begin{frame}[c]
|
|
1209 |
\frametitle{Trusted Third Party}
|
|
1210 |
|
|
1211 |
\begin{itemize}
|
|
1212 |
\item Alice calls Sam for a key to communicate with Bob
|
|
1213 |
\item Sam responds with a key that Alice can read and a key Bob can read (pre-shared)
|
|
1214 |
\item Alice sends the message encrypted with the key and the second key it recieved
|
|
1215 |
\end{itemize}\bigskip
|
|
1216 |
|
|
1217 |
\begin{center}
|
|
1218 |
\bl{\begin{tabular}{lcl}
|
|
1219 |
$A$ sends $S$ &:& $\textit{Connect}(A,B)$\\
|
|
1220 |
$S$ sends $A$ &:& $\{K_{AB}\}_{K_{AS}}$ \textcolor{black}{and} $\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}}$\\
|
|
1221 |
$A$ sends $B$ &:& $\{K_{AB}\}_{K_{BS}}$\\
|
|
1222 |
$A$ sends $B$ &:& $\{m\}_{K_{AB}}$
|
|
1223 |
\end{tabular}}
|
|
1224 |
\end{center}
|
|
1225 |
|
|
1226 |
\end{frame}}
|
|
1227 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1228 |
|
128
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1229 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1230 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1231 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1232 |
\frametitle{Controls}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1233 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1234 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1235 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1236 |
\item \bl{\isa{P\ controls\ F\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1237 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1238 |
\item its meaning ``\bl{P} is entitled to do \bl{F}''
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1239 |
\item if \bl{P controls F} and \bl{P says F} then \bl{F}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1240 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1241 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1242 |
\bl{\mbox{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1243 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1244 |
{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1245 |
}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1246 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1247 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1248 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1249 |
\bl{\mbox{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1250 |
\infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1251 |
{\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}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1252 |
}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1253 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1254 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1255 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1256 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1257 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1258 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1259 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1260 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1261 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1262 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1263 |
\frametitle{Security Levels}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1264 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1265 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1266 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1267 |
\item Top secret (\bl{$T\!S$})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1268 |
\item Secret (\bl{$S$})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1269 |
\item Public (\bl{$P$})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1270 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1271 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1272 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1273 |
\bl{$slev(P) < slev(S) < slev(T\!S)$}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1274 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1275 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1276 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1277 |
\item Bob has a clearance for ``secret''
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1278 |
\item Bob can read documents that are public or sectret, but not top secret
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1279 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1280 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1281 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1282 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1283 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1284 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1285 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1286 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1287 |
\frametitle{Reading a File}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1288 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1289 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1290 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1291 |
\begin{tabular}{@ {}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1292 |
\only<2->{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$}}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1293 |
\only<2->{\hspace{3cm}}Bob controls Permitted $($File, read$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1294 |
Bob says Permitted $($File, read$)$\only<2->{\\}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1295 |
\only<2>{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$}}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1296 |
\only<3>{\textcolor{red}{$slev($File$)$ $=$ $P$}\\}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1297 |
\only<3>{\textcolor{red}{$slev($Bob$)$ $=$ $S$}\\}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1298 |
\only<3>{\textcolor{red}{$slev(P)$ $<$ $slev(S)$}\\}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1299 |
\end{tabular}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1300 |
\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1301 |
Permitted $($File, read$)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1302 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1303 |
\end{center}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1304 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1305 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1306 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1307 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1308 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1309 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1310 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1311 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1312 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1313 |
\frametitle{Substitution Rule}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1314 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1315 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1316 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1317 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1318 |
$\Gamma \vdash slev(P) = l_1$ \hspace{4mm} $\Gamma \vdash slev(Q) = l_2$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1319 |
\hspace{4mm} $\Gamma \vdash l_1 < l_2$\\\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1320 |
$\Gamma \vdash slev(P) < slev(Q)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1321 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1322 |
\end{center}}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1323 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1324 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1325 |
\item \bl{$slev($Bob$)$ $=$ $S$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1326 |
\item \bl{$slev($File$)$ $=$ $P$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1327 |
\item \bl{$slev(P) < slev(S)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1328 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1329 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1330 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1331 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1332 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1333 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1334 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1335 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1336 |
\frametitle{Reading a File}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1337 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1338 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1339 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1340 |
\begin{tabular}{@ {}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1341 |
$slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1342 |
\hspace{3cm}Bob controls Permitted $($File, read$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1343 |
Bob says Permitted $($File, read$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1344 |
$slev($File$)$ $=$ $P$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1345 |
$slev($Bob$)$ $=$ $T\!S$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1346 |
\only<1>{\textcolor{red}{$?$}}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1347 |
\only<2>{\textcolor{red}{$slev(P) < slev(S)$}\\}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1348 |
\only<2>{\textcolor{red}{$slev(S) < slev(T\!S)$}}%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1349 |
\end{tabular}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1350 |
\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1351 |
Permitted $($File, read$)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1352 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1353 |
\end{center}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1354 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1355 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1356 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1357 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1358 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1359 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1360 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1361 |
\frametitle{Transitivity Rule}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1362 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1363 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1364 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1365 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1366 |
$\Gamma \vdash l_1 < l_2$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1367 |
\hspace{4mm} $\Gamma \vdash l_2 < l_3$\\\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1368 |
$\Gamma \vdash l_1 < l_3$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1369 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1370 |
\end{center}}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1371 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1372 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1373 |
\item \bl{$slev(P) < slev (S)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1374 |
\item \bl{$slev(S) < slev (T\!S)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1375 |
\item[] \bl{$slev(P) < slev (T\!S)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1376 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1377 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1378 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1379 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1380 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1381 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1382 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1383 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1384 |
\frametitle{Reading Files}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1385 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1386 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1387 |
\item Access policy for reading
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1388 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1389 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1390 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1391 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1392 |
\begin{tabular}{@ {}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1393 |
$\forall f.\;slev(f)$ \only<1>{$<$}\only<2>{\textcolor{red}{$\le$}} $slev($Bob$)$ $\Rightarrow$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1394 |
\hspace{3cm}Bob controls Permitted $(f$, read$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1395 |
Bob says Permitted $($File, read$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1396 |
$slev($File$)$ $=$ \only<1>{$P$}\only<2>{\textcolor{red}{$T\!S$}}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1397 |
$slev($Bob$)$ $=$ $T\!S$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1398 |
$slev(P) < slev(S)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1399 |
$slev(S) < slev(T\!S)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1400 |
\end{tabular}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1401 |
\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1402 |
Permitted $($File, read$)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1403 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1404 |
\end{center}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1405 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1406 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1407 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1408 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1409 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1410 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1411 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1412 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1413 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1414 |
\frametitle{Writing Files}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1415 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1416 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1417 |
\item Access policy for \underline{writing}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1418 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1419 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1420 |
\bl{\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1421 |
\begin{tabular}{c}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1422 |
\begin{tabular}{@ {}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1423 |
$\forall f.\;slev($Bob$)$ $\le$ $slev(f)$ $\Rightarrow$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1424 |
\hspace{3cm}Bob controls Permitted $(f$, write$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1425 |
Bob says Permitted $($File, write$)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1426 |
$slev($File$)$ $=$ $T\!S$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1427 |
$slev($Bob$)$ $=$ $S$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1428 |
$slev(P) < slev(S)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1429 |
$slev(S) < slev(T\!S)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1430 |
\end{tabular}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1431 |
\hline
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1432 |
Permitted $($File, write$)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1433 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1434 |
\end{center}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1435 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1436 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1437 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1438 |
%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1439 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1440 |
|
61
|
1441 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1442 |
\mode<presentation>{
|
|
1443 |
\begin{frame}[c]
|
|
1444 |
\frametitle{Sending Rule}
|
|
1445 |
|
|
1446 |
\bl{\begin{center}
|
|
1447 |
\mbox{\infer{\Gamma \vdash Q \;\textit{says}\; F}
|
|
1448 |
{\Gamma \vdash P \;\textit{says}\; F & \Gamma \vdash P \;\textit{sends}\; Q : F}}
|
|
1449 |
\end{center}}\bigskip\pause
|
|
1450 |
|
|
1451 |
\bl{$P \,\text{sends}\, Q : F \dn$}\\
|
|
1452 |
\hspace{6mm}\bl{$(P \,\text{says}\, F) \Rightarrow (Q \,\text{says}\, F)$}
|
|
1453 |
|
|
1454 |
\end{frame}}
|
|
1455 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1456 |
|
|
1457 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1458 |
\mode<presentation>{
|
|
1459 |
\begin{frame}[c]
|
|
1460 |
\frametitle{Trusted Third Party}
|
|
1461 |
|
|
1462 |
\begin{center}
|
|
1463 |
\bl{\begin{tabular}{l}
|
|
1464 |
$A$ sends $S$ : $\textit{Connect}(A,B)$\\
|
|
1465 |
\bl{$S \,\text{says}\, (\textit{Connect}(A,B) \Rightarrow$}\\
|
|
1466 |
\hspace{2.5cm}\bl{$\{K_{AB}\}_{K_{AS}} \wedge
|
62
|
1467 |
\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}})$}\\
|
61
|
1468 |
$S$ sends $A$ : $\{K_{AB}\}_{K_{AS}}$ \bl{$\wedge$} $\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}}$\\
|
|
1469 |
$A$ sends $B$ : $\{K_{AB}\}_{K_{BS}}$\\
|
|
1470 |
$A$ sends $B$ : $\{m\}_{K_{AB}}$
|
|
1471 |
\end{tabular}}
|
|
1472 |
\end{center}\bigskip\pause
|
|
1473 |
|
|
1474 |
|
|
1475 |
\bl{$\Gamma \vdash B \,\text{says} \, m$}?
|
|
1476 |
\end{frame}}
|
|
1477 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
59
|
1478 |
\end{document}
|
|
1479 |
|
|
1480 |
%%% Local Variables:
|
|
1481 |
%%% mode: latex
|
|
1482 |
%%% TeX-master: t
|
|
1483 |
%%% End:
|
|
1484 |
|