| author | Christian Urban <christian dot urban at kcl dot ac dot uk> |
| Tue, 12 Nov 2013 01:53:41 +0000 | |
| changeset 126 | b091e0abb894 |
| parent 90 | d1d07f05325a |
| child 128 | 4e108563716c |
| permissions | -rw-r--r-- |
| 59 | 1 |
\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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\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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% 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: & S1.27 (1st floor Strand Building)\\ |
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Slides: & KEATS (also homework is there)\\ |
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\end{tabular}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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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}}
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\qquad |
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\bl{\infer{\Gamma \vdash F_1 \Rightarrow F_2}{F_1, \Gamma \vdash F_2}}\bigskip\\
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\bl{\infer{\Gamma \vdash P\,\text{says}\, F}{\Gamma \vdash F}}\medskip\\
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\bl{\infer{\Gamma \vdash P \,\text{says}\, F_2}
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{\Gamma \vdash P \,\text{says}\, (F_1\Rightarrow F_2) \quad
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\Gamma \vdash P \,\text{says}\, F_1}}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Proofs}
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\begin{center}
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\bl{
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\infer{\Gamma \vdash F}
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{\infer{\hspace{1cm}:\hspace{1cm}}
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{\infer{\hspace{1cm}:\hspace{1cm}}{:}
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& |
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\infer{\hspace{1cm}:\hspace{1cm}}{:\quad :}
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}} |
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} |
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{The Access Control Problem}
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\begin{center}
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\begin{tikzpicture}[scale=1]
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\draw[line width=1mm] (-.3, -0.5) rectangle (1.5,2); |
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\draw (-2.7,1) node {\begin{tabular}{l}access\\request\\ (\bl{$F$})\end{tabular}};
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\draw (4.2,1) node {\begin{tabular}{l}provable/\\not provable\end{tabular}};
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\draw (0.6,0.8) node {\footnotesize \begin{tabular}{l}AC-\\ Checker:\\ applies\\ inference\\ rules\end{tabular}};
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\draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1); |
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\draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1); |
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\draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2); |
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\draw (0.6,4) node {\begin{tabular}{l}\large Access Policy (\bl{$\Gamma$})\end{tabular}};
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\end{tikzpicture}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{}
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Recall the following scenario: |
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\begin{itemize}
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\item If \textcolor{blue}{Admin} says that \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{} {}}}
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should be deleted, then this file must be deleted. |
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\item \textcolor{blue}{Admin} trusts \textcolor{blue}{Bob} to decide whether
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\textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}}} should be deleted.
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\item \textcolor{blue}{Bob} wants to delete \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}}}.
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\end{itemize}\bigskip
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\small |
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\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
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\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}{}},\\
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\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}}},\\
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\isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}}\\
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\end{tabular}}\medskip
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\textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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How to prove \bl{$\Gamma \vdash F$}?\bigskip\bigskip
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\begin{center}
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\Large \bl{\infer{\Gamma, F\vdash F}{}}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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\begin{center}
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\Large |
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\bl{\infer{\Gamma \vdash F_1 \Rightarrow F_2}{F_1, \Gamma \vdash F_2}}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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\begin{center}
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\Large |
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\bl{\infer{\Gamma \vdash P \,\text{says}\, F}{\Gamma \vdash F}}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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\begin{center}
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\Large |
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\bl{\infer{\Gamma \vdash F_1 \vee F_2}{\Gamma \vdash F_1}}\qquad
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\bl{\infer{\Gamma \vdash F_1 \vee F_2}{\Gamma \vdash F_2}}\
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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\begin{center}
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\Large |
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\bl{\infer{\Gamma \vdash F_1 \wedge F_2}{\Gamma \vdash F_1 \quad \Gamma \vdash F_2}}
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\end{center}
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||
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\end{frame}}
|
|
329 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
330 |
||
331 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
332 |
\mode<presentation>{
|
|
333 |
\begin{frame}[t]
|
|
334 |
||
335 |
I want to prove \bl{$\Gamma \vdash \text{Pred}$}\bigskip\bigskip\pause
|
|
336 |
||
337 |
\begin{enumerate}
|
|
338 |
\item I found that \bl{$\Gamma$} contains the assumption \bl{$F_1 \Rightarrow F_2$}\bigskip\pause
|
|
339 |
\item If I can prove \bl{$\Gamma \vdash F_1$},\pause{} then I can prove
|
|
340 |
\begin{center}
|
|
341 |
\bl{$\Gamma \vdash F_2$}
|
|
342 |
\end{center}\bigskip\pause
|
|
343 |
||
344 |
\item So better I try to prove \bl{$\Gamma \vdash \text{Pred}$} with the additional assumption
|
|
345 |
\bl{$F_2$}.\bigskip
|
|
346 |
\begin{center}
|
|
347 |
\bl{$F_2, \Gamma \vdash \text{Pred}$}
|
|
348 |
\end{center}
|
|
| 60 | 349 |
\end{enumerate}
|
| 59 | 350 |
|
| 60 | 351 |
\only<4>{
|
352 |
\begin{textblock}{11}(1,10.5)
|
|
353 |
\bl{\infer{\Gamma\vdash F_2}{\Gamma\vdash F_1\Rightarrow F_2 & \Gamma\vdash F_1}}
|
|
354 |
\end{textblock}}
|
|
355 |
||
| 59 | 356 |
|
357 |
\end{frame}}
|
|
358 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
| 60 | 359 |
\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
|
360 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
361 |
\mode<presentation>{
|
|
362 |
\begin{frame}[c]
|
|
| 59 | 363 |
|
| 60 | 364 |
\begin{itemize}
|
365 |
\item \bl{$P$} is entitled to do \bl{$F$}\smallskip\\
|
|
366 |
\bl{$P \,\text{controls}\, F \,\dn\, (P\,\text{says}\, F) \Rightarrow F$}\medskip
|
|
367 |
||
368 |
\begin{center}
|
|
369 |
\bl{\infer{\Gamma \vdash F}{\Gamma \vdash P\,\text{controls}\, F & \Gamma \vdash P\,\text{says}\,F}}
|
|
370 |
\end{center}
|
|
371 |
||
372 |
\item \bl{$P$} speaks for \bl{$Q$}\smallskip\\
|
|
373 |
\bl{$P \mapsto Q \,\dn\, \forall F. (P\,\text{says}\, F) \Rightarrow (Q \,\text{says}\,F)$}\medskip
|
|
374 |
||
375 |
\begin{center}
|
|
376 |
\bl{\infer{\Gamma \vdash Q\,\text{says}\,F}{\Gamma \vdash P\mapsto Q & \Gamma \vdash P\,\text{says}\,F}}
|
|
377 |
\medskip\\ |
|
378 |
\bl{\infer{\Gamma \vdash P\,\text{controls}\,F}{\Gamma \vdash P\mapsto Q & \Gamma \vdash Q\,\text{controls}\,F}}\\
|
|
379 |
||
380 |
\end{center}
|
|
381 |
\end{itemize}
|
|
382 |
||
383 |
\end{frame}}
|
|
384 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
385 |
||
386 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
387 |
\mode<presentation>{
|
|
388 |
\begin{frame}[c]
|
|
|
126
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
389 |
\frametitle{Sudoku}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
390 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
391 |
\begin{tikzpicture}[scale=.5]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
392 |
\begin{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
393 |
\draw (0, 0) grid (9, 9); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
394 |
\draw[very thick, scale=3] (0, 0) grid (3, 3); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
395 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
396 |
\setcounter{row}{1}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
397 |
\setrow { }{2}{ } {5}{ }{1} { }{9}{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
398 |
\setrow {8}{ }{ } {2}{ }{3} { }{ }{6}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
399 |
\setrow { }{3}{ } { }{6}{ } { }{7}{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
400 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
401 |
\setrow { }{ }{1} { }{ }{ } {6}{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
402 |
\setrow {5}{4}{ } { }{ }{ } { }{1}{9}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
403 |
\setrow { }{ }{2} { }{ }{ } {7}{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
404 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
405 |
\setrow { }{9}{ } { }{3}{ } { }{8}{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
406 |
\setrow {2}{ }{ } {8}{ }{4} { }{ }{7}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
407 |
\setrow { }{1}{ } {9}{ }{7} { }{6}{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
408 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
409 |
\fill[red, fill opacity=0.4] (4,0) rectangle (5,9); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
410 |
\fill[red, fill opacity=0.4] (0,5) rectangle (9,6); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
411 |
\fill[red!50, fill opacity=0.4] (3,3) rectangle (4,5); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
412 |
\fill[red!50, fill opacity=0.4] (5,3) rectangle (6,5); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
413 |
\node[gray, anchor=center] at (4.5, -0.5) {columns};
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
414 |
\node[gray, rotate=90, anchor=center] at (-0.6, 4.5, -0.5) {rows};
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
415 |
\node[gray, anchor=center] at (4.5, 4.5) {box};
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
416 |
\end{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
417 |
\end{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
418 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
419 |
\small |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
420 |
\begin{textblock}{7}(9,3)
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
421 |
\begin{enumerate}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
422 |
\item {\bf Row-Column:} each cell, must contain exactly one number
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
423 |
\item {\bf Row-Number:} each row must contain each number exactly once
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
424 |
\item {\bf Column-Number:} each column must contain each number exactly once
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
425 |
\item {\bf Box-Number:} each box must contain each number exactly once
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
426 |
\end{enumerate}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
427 |
\end{textblock}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
428 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
429 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
430 |
\end{frame}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
431 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
432 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
433 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
434 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
435 |
\mode<presentation>{
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
436 |
\begin{frame}[c]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
437 |
\frametitle{Solving Sudokus}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
438 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
439 |
\begin{tikzpicture}[scale=.5]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
440 |
\begin{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
441 |
\draw (0, 0) grid (9, 9); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
442 |
\draw[very thick, scale=3] (0, 0) grid (3, 3); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
443 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
444 |
\setcounter{row}{1}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
445 |
\setrow { }{ }{ } {7}{ }{ } { }{5}{8}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
446 |
\setrow {}{5}{6} {2}{1}{8} {7}{9}{3}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
447 |
\setrow { }{ }{ } { }{ }{ } {1}{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
448 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
449 |
\setrow { }{ }{ } { }{ }{ } { }{8}{1}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
450 |
\setrow { }{ }{ } {3}{7}{6} { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
451 |
\setrow {9}{6}{ } { }{ }{ } { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
452 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
453 |
\setrow { }{ }{5} { }{3}{ } { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
454 |
\setrow { }{ }{4} { }{2}{1} {8}{3}{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
455 |
\setrow {8}{7}{ } { }{ }{3} { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
456 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
457 |
\fill[red, fill opacity=0.4] (0,7) rectangle (1,8); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
458 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
459 |
\end{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
460 |
\end{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
461 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
462 |
\small |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
463 |
\begin{textblock}{6}(9,6)
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
464 |
{\bf single position rules}\\
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
465 |
\begin{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
466 |
\bl{\infer{4\;\text{in empty position}}{\{1..9\} - \{4\}\;\text{in one row}}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
467 |
\end{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
468 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
469 |
\onslide<2->{
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
470 |
\begin{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
471 |
\bl{\infer{x\;\text{in empty position}}{\{1..9\} - \{x\}\;\text{in one column}}}\medskip\\
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
472 |
\bl{\infer{x\;\text{in empty position}}{\{1..9\} - \{x\}\;\text{in one box}}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
473 |
\end{center}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
474 |
\end{textblock}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
475 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
476 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
477 |
\end{frame}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
478 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
479 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
480 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
481 |
\mode<presentation>{
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
482 |
\begin{frame}[c]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
483 |
\frametitle{Solving Sudokus}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
484 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
485 |
\begin{tikzpicture}[scale=.5]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
486 |
\begin{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
487 |
\draw (0, 0) grid (9, 9); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
488 |
\draw[very thick, scale=3] (0, 0) grid (3, 3); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
489 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
490 |
\setcounter{row}{1}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
491 |
\setrow { }{ }{ } {7}{ }{ } {\alert{\footnotesize 2}}{5}{8}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
492 |
\setrow {}{5}{6} {2}{1}{8} {7}{9}{3}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
493 |
\setrow { }{ }{ } { }{ }{ } {1}{\alert{\footnotesize 2}}{\alert{\footnotesize 2}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
494 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
495 |
\setrow { }{ }{ } { }{ }{ } { }{8}{1}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
496 |
\setrow { }{ }{ } {3}{7}{6} { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
497 |
\setrow {9}{6}{ } { }{ }{ } { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
498 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
499 |
\setrow { }{ }{5} { }{3}{ } { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
500 |
\setrow { }{ }{4} { }{2}{1} {8}{3}{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
501 |
\setrow {8}{7}{ } { }{ }{3} { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
502 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
503 |
\end{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
504 |
\end{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
505 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
506 |
\small |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
507 |
\begin{textblock}{6}(7.5,6)
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
508 |
{\bf candidate rules}\\
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
509 |
\begin{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
510 |
\bl{\infer{x\;\text{candidate in empty positions}}{X - \{x\}\;\text{in one box} & X \subseteq \{1..9\}}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
511 |
\end{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
512 |
\end{textblock}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
513 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
514 |
\end{frame}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
515 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
516 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
517 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
518 |
\mode<presentation>{
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
519 |
\begin{frame}[c]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
520 |
\frametitle{Solving Sudokus}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
521 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
522 |
\begin{tikzpicture}[scale=.5]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
523 |
\begin{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
524 |
\draw (0, 0) grid (9, 9); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
525 |
\draw[very thick, scale=3] (0, 0) grid (3, 3); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
526 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
527 |
\setcounter{row}{1}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
528 |
\setrow { }{ }{ } {7}{ }{ } {\alert{\footnotesize 2}}{5}{8}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
529 |
\setrow {\alert{4}}{5}{6} {2}{1}{8} {7}{9}{3}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
530 |
\setrow { }{ }{ } { }{ }{ } {1}{\alert{\footnotesize 2}}{\alert{\footnotesize 2}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
531 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
532 |
\setrow { }{ }{ } { }{ }{ } { }{8}{1}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
533 |
\setrow { }{ }{ } {3}{7}{6} { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
534 |
\setrow {9}{6}{ } { }{ }{ } { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
535 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
536 |
\setrow { }{ }{5} { }{3}{ } { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
537 |
\setrow { }{ }{4} { }{2}{1} {8}{3}{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
538 |
\setrow {8}{7}{ } { }{ }{3} { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
539 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
540 |
\end{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
541 |
\end{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
542 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
543 |
\small |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
544 |
\begin{textblock}{6}(7.5,6)
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
545 |
\begin{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
546 |
\bl{\infer{4\;\text{in empty position}}{\{1..9\} - \{4\}\;\text{in one row}}}\bigskip\\
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
547 |
\bl{\infer{2\;\text{candidate in empty positions}}{X - \{2\}\;\text{in one box} & X \subseteq \{1..9\}}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
548 |
\end{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
549 |
\end{textblock}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
550 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
551 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
552 |
\begin{textblock}{3}(13.5,6.8)
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
553 |
\begin{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
554 |
\onslide<1>{\node at (0,0) [single arrow, shape border rotate=270, fill=red,text=white]{\mbox{\alert{a}}};}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
555 |
\onslide<2>{\node at (0,0) [single arrow, shape border rotate=90, fill=red,text=white]{\mbox{\alert{a}}};}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
556 |
\end{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
557 |
\end{textblock}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
558 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
559 |
\begin{textblock}{3}(14.5,9.3)
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
560 |
\begin{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
561 |
\onslide<1>{\node at (0,0) [single arrow, shape border rotate=270, fill=red,text=white]{\mbox{\alert{a}}};}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
562 |
\onslide<2>{\node at (0,0) [single arrow, shape border rotate=90, fill=red,text=white]{\mbox{\alert{a}}};}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
563 |
\end{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
564 |
\end{textblock}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
565 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
566 |
\end{frame}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
567 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
568 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
569 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
570 |
\mode<presentation>{
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
571 |
\begin{frame}[c]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
572 |
\frametitle{Solving Sudokus}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
573 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
574 |
\begin{tikzpicture}[scale=.5]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
575 |
\begin{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
576 |
\draw (0, 0) grid (9, 9); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
577 |
\draw[very thick, scale=3] (0, 0) grid (3, 3); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
578 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
579 |
\setcounter{row}{1}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
580 |
\setrow { }{ }{ } {7}{ }{ } { }{5}{8}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
581 |
\setrow { }{5}{6} {2}{1}{8} {7}{9}{3}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
582 |
\setrow { }{ }{ } { }{ }{ } {1}{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
583 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
584 |
\setrow { }{ }{ } { }{ }{ } { }{8}{1}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
585 |
\setrow { }{ }{ } {3}{7}{6} { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
586 |
\setrow {9}{6}{ } { }{ }{ } { }{ }{ \alert{2}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
587 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
588 |
\setrow { }{ }{5} { }{3}{ } { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
589 |
\setrow { }{ }{4} { }{2}{1} {8}{3}{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
590 |
\setrow {8}{7}{ } { }{ }{3} { }{ }{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
591 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
592 |
\end{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
593 |
\end{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
594 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
595 |
\small |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
596 |
\begin{textblock}{6}(7.5,6)
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
597 |
\begin{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
598 |
\bl{\infer{2\;\text{candidate}}{X - \{2\}\;\text{in one box} & X \subseteq \{1..9\}}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
599 |
\end{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
600 |
\end{textblock}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
601 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
602 |
\begin{textblock}{3}(14.5,8.3)
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
603 |
\begin{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
604 |
\onslide<1>{\node at (0,0) [single arrow, shape border rotate=90, fill=red,text=white]{\mbox{\alert{a}}};}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
605 |
\end{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
606 |
\end{textblock}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
607 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
608 |
\end{frame}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
609 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
610 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
611 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
612 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
613 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
614 |
\mode<presentation>{
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
615 |
\begin{frame}[c]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
616 |
\frametitle{Sudoku}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
617 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
618 |
Are there sudokus that cannot be solved?\pause |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
619 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
620 |
\begin{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
621 |
\begin{tikzpicture}[scale=.5]
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
622 |
\begin{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
623 |
\draw (0, 0) grid (9, 9); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
624 |
\draw[very thick, scale=3] (0, 0) grid (3, 3); |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
625 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
626 |
\setcounter{row}{1}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
627 |
\setrow {1}{2}{3} {4}{5}{6} {7}{8}{ }
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
628 |
\setrow { }{ }{ } { }{ }{ } { }{ }{2}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
629 |
\setrow { }{ }{ } { }{ }{ } { }{ }{3}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
630 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
631 |
\setrow { }{ }{ } { }{ }{ } { }{ }{4}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
632 |
\setrow { }{ }{ } { }{ }{ } { }{ }{5}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
633 |
\setrow { }{ }{ } { }{ }{ } { }{ }{6}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
634 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
635 |
\setrow { }{ }{ } { }{ }{ } { }{ }{7}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
636 |
\setrow { }{ }{ } { }{ }{ } { }{ }{8}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
637 |
\setrow { }{ }{ } { }{ }{ } { }{ }{9}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
638 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
639 |
\end{scope}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
640 |
\end{tikzpicture}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
641 |
\end{center}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
642 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
643 |
Sometimes no rules apply at all....unsolvable sudoku. |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
644 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
645 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
646 |
\end{frame}}
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
647 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
648 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
649 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
650 |
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
651 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
652 |
\mode<presentation>{
|
|
b091e0abb894
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
653 |
\begin{frame}[c]
|
| 60 | 654 |
\frametitle{Protocol Specifications}
|
655 |
||
656 |
The Needham-Schroeder Protocol: |
|
657 |
||
658 |
\begin{center}
|
|
659 |
\begin{tabular}{@ {\hspace{-7mm}}l@{\hspace{2mm}}r@ {\hspace{1mm}}l}
|
|
660 |
Message 1 & \bl{$A \rightarrow S :$} & \bl{$A, B, N_A$}\\
|
|
661 |
Message 2 & \bl{$S \rightarrow A :$} & \bl{$\{N_A, B, K_{AB},\{K_{AB}, A\}_{K_{BS}} \}_{K_{AS}}$}\\
|
|
662 |
Message 3 & \bl{$A \rightarrow B :$} & \bl{$\{K_{AB}, A\}_{K_{BS}} $}\\
|
|
663 |
Message 4 & \bl{$B \rightarrow A :$} & \bl{$\{N_B\}_{K_{AB}}$}\\
|
|
664 |
Message 5 & \bl{$A \rightarrow B :$} & \bl{$\{N_B-1\}_{K_{AB}}$}\\
|
|
665 |
\end{tabular}
|
|
666 |
\end{center}
|
|
667 |
||
668 |
\end{frame}}
|
|
669 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
670 |
||
671 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
672 |
\mode<presentation>{
|
|
673 |
\begin{frame}[c]
|
|
674 |
\frametitle{Trusted Third Party}
|
|
675 |
||
676 |
Simple protocol for establishing a secure connection via a mutually |
|
677 |
trusted 3rd party (server): |
|
678 |
||
679 |
\begin{center}
|
|
680 |
\begin{tabular}{@ {\hspace{-7mm}}l@{\hspace{2mm}}r@ {\hspace{1mm}}l}
|
|
681 |
Message 1 & \bl{$A \rightarrow S :$} & \bl{$A, B$}\\
|
|
682 |
Message 2 & \bl{$S \rightarrow A :$} & \bl{$\{K_{AB}\}_{K_{AS}}$} and \bl{$\{\{K_{AB}\}_{K_{BS}} \}_{K_{AS}}$}\\
|
|
683 |
Message 3 & \bl{$A \rightarrow B :$} & \bl{$\{K_{AB}\}_{K_{BS}} $}\\
|
|
684 |
Message 4 & \bl{$A \rightarrow B :$} & \bl{$\{m\}_{K_{AB}}$}\\
|
|
685 |
\end{tabular}
|
|
686 |
\end{center}
|
|
687 |
||
688 |
\end{frame}}
|
|
689 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
690 |
||
691 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
692 |
\mode<presentation>{
|
|
693 |
\begin{frame}[c]
|
|
694 |
\frametitle{Sending Messages}
|
|
695 |
||
696 |
\begin{itemize}
|
|
697 |
\item Alice sends a message \bl{$m$}
|
|
698 |
\begin{center}
|
|
699 |
\bl{Alice says $m$}
|
|
700 |
\end{center}\medskip\pause
|
|
701 |
||
702 |
\item Alice sends an encrypted message \bl{$m$}\\ (with key \bl{$K$})
|
|
703 |
\begin{center}
|
|
704 |
\bl{Alice says $\{m\}_K$}
|
|
705 |
\end{center}\medskip\pause
|
|
706 |
||
707 |
\item Decryption of Alice's message\smallskip |
|
708 |
\begin{center}
|
|
709 |
\bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;m}
|
|
| 62 | 710 |
{\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_K & \Gamma \vdash \text{Alice}\,\text{says}\,K}}}
|
| 60 | 711 |
\end{center}
|
712 |
\end{itemize}
|
|
713 |
||
714 |
\end{frame}}
|
|
715 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
716 |
||
717 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
718 |
\mode<presentation>{
|
|
719 |
\begin{frame}[c]
|
|
720 |
\frametitle{Encryption}
|
|
721 |
||
722 |
\begin{itemize}
|
|
723 |
\item Encryption of a message\smallskip |
|
724 |
\begin{center}
|
|
725 |
\bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_K}
|
|
| 62 | 726 |
{\Gamma \vdash \text{Alice}\;\text{says}\;m & \Gamma \vdash \text{Alice}\,\text{says}\,K}}}
|
| 60 | 727 |
\end{center}
|
728 |
\end{itemize}
|
|
729 |
||
730 |
\end{frame}}
|
|
731 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
732 |
||
| 61 | 733 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
734 |
\mode<presentation>{
|
|
735 |
\begin{frame}[c]
|
|
736 |
\frametitle{Public/Private Keys}
|
|
737 |
||
738 |
\begin{itemize}
|
|
739 |
\item Bob has a private and public key: \bl{$K_{Bob}^{pub}$}, \bl{$K_{Bob}^{priv}$}\bigskip
|
|
740 |
\begin{center}
|
|
741 |
\bl{\mbox{\infer{\Gamma \vdash \text{Alice}\;\text{says}\;m}
|
|
742 |
{\Gamma \vdash \text{Alice}\;\text{says}\;\{m\}_{K_{Bob}^{pub}} &
|
|
743 |
\Gamma \vdash K_{Bob}^{priv}}}}
|
|
744 |
\end{center}\bigskip\pause
|
|
745 |
||
746 |
\item this is {\bf not} a derived rule!
|
|
747 |
\end{itemize}
|
|
748 |
||
749 |
\end{frame}}
|
|
750 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
751 |
||
752 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
753 |
\mode<presentation>{
|
|
754 |
\begin{frame}[c]
|
|
755 |
\frametitle{Trusted Third Party}
|
|
756 |
||
757 |
\begin{itemize}
|
|
758 |
\item Alice calls Sam for a key to communicate with Bob |
|
759 |
\item Sam responds with a key that Alice can read and a key Bob can read (pre-shared) |
|
760 |
\item Alice sends the message encrypted with the key and the second key it recieved |
|
761 |
\end{itemize}\bigskip
|
|
762 |
||
763 |
\begin{center}
|
|
764 |
\bl{\begin{tabular}{lcl}
|
|
765 |
$A$ sends $S$ &:& $\textit{Connect}(A,B)$\\
|
|
766 |
$S$ sends $A$ &:& $\{K_{AB}\}_{K_{AS}}$ \textcolor{black}{and} $\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}}$\\
|
|
767 |
$A$ sends $B$ &:& $\{K_{AB}\}_{K_{BS}}$\\
|
|
768 |
$A$ sends $B$ &:& $\{m\}_{K_{AB}}$
|
|
769 |
\end{tabular}}
|
|
770 |
\end{center}
|
|
771 |
||
772 |
\end{frame}}
|
|
773 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
774 |
||
775 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
776 |
\mode<presentation>{
|
|
777 |
\begin{frame}[c]
|
|
778 |
\frametitle{Sending Rule}
|
|
779 |
||
780 |
\bl{\begin{center}
|
|
781 |
\mbox{\infer{\Gamma \vdash Q \;\textit{says}\; F}
|
|
782 |
{\Gamma \vdash P \;\textit{says}\; F & \Gamma \vdash P \;\textit{sends}\; Q : F}}
|
|
783 |
\end{center}}\bigskip\pause
|
|
784 |
||
785 |
\bl{$P \,\text{sends}\, Q : F \dn$}\\
|
|
786 |
\hspace{6mm}\bl{$(P \,\text{says}\, F) \Rightarrow (Q \,\text{says}\, F)$}
|
|
787 |
||
788 |
\end{frame}}
|
|
789 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
790 |
||
791 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
792 |
\mode<presentation>{
|
|
793 |
\begin{frame}[c]
|
|
794 |
\frametitle{Trusted Third Party}
|
|
795 |
||
796 |
\begin{center}
|
|
797 |
\bl{\begin{tabular}{l}
|
|
798 |
$A$ sends $S$ : $\textit{Connect}(A,B)$\\
|
|
799 |
\bl{$S \,\text{says}\, (\textit{Connect}(A,B) \Rightarrow$}\\
|
|
800 |
\hspace{2.5cm}\bl{$\{K_{AB}\}_{K_{AS}} \wedge
|
|
| 62 | 801 |
\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}})$}\\
|
| 61 | 802 |
$S$ sends $A$ : $\{K_{AB}\}_{K_{AS}}$ \bl{$\wedge$} $\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}}$\\
|
803 |
$A$ sends $B$ : $\{K_{AB}\}_{K_{BS}}$\\
|
|
804 |
$A$ sends $B$ : $\{m\}_{K_{AB}}$
|
|
805 |
\end{tabular}}
|
|
806 |
\end{center}\bigskip\pause
|
|
807 |
||
808 |
||
809 |
\bl{$\Gamma \vdash B \,\text{says} \, m$}?
|
|
810 |
\end{frame}}
|
|
811 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
| 59 | 812 |
\end{document}
|
813 |
||
814 |
%%% Local Variables: |
|
815 |
%%% mode: latex |
|
816 |
%%% TeX-master: t |
|
817 |
%%% End: |
|
818 |