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Commit 4846432e authored by Philipp Muth's avatar Philipp Muth
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\section{General Access Structures and Secret Sharing Schemes}
\begin{frame}
\end{frame}
\section{Actively Secure Key Exchange}
\begin{frame}
\end{frame}
...@@ -20,9 +20,17 @@ ...@@ -20,9 +20,17 @@
\begin{document} \begin{document}
\maketitle \maketitle
\section{Motivation} \input{motivation}
\begin{frame}
\end{frame} \input{key_exchange}
\input{signatures}
\input{generalsss}
\section{References}
\begin{frame}[allowframebreaks]
\bibliographystyle{amsalpha}
\bibliography{pqc}
\end{frame}
\end{document} \end{document}
\section{Motivation}
\begin{frame}
\frametitle{Where are we?}
\begin{block}{Hard Homogeneous Spaces}
A hard homogeneous space \(\left(\mathcal E,\mathcal G\right)\) is
\begin{itemize}
\item a set \(\mathcal E\),
\item a group \(\left(\mathcal G,\odot\right)\) and
\item an action \(\ast: \mathcal G\times \mathcal E \to \mathcal E\)
\end{itemize}
\end{block}
\pause
\begin{block}{Properties of \(\ast\)}
\begin{itemize}
\item Compatibility: \(\forall g,g' \in \mathcal G ~\forall E \in \mathcal E \colon g \ast \left(g'\ast E\right) = \left(g\odot g'\right) E\)
\item Identity: \(\forall E \in \mathcal E \colon i \ast E = E \Leftrightarrow i\) is the neutral element in \(\mathcal G\)
\item Transitivity: \(\forall E,E'\in \mathcal E ~\exists ! g \in \mathcal G \colon g \ast E = E'\)
\end{itemize}
\end{block}
\end{frame}
\begin{frame}
\frametitle{Key Exchange Mechanisms}
\begin{center}
\begin{tikzpicture}
\begin{scope}[minimum size = .7cm]
\node [alice] (alice) at (-3,0){Alice};
\node [bob] (bob) at (3,0){Bob};
\end{scope}
\pause
\node [left = .5 of alice] (pair) {$\left(\sk,\pk\right)$};
%\node [above = 3 of alice] (pk) {$\pk$};
%\draw [->] (alice) -- (pk);
\pause
\node [above = 2.5 of bob] (encaps) {$\encaps \paren* \pk$};
\node [above = 0.5 of bob] (keybob) {$\key$};
\node [above = 2.5 of alice] (cipher) {$c$};
\draw [->] (encaps) -- (cipher);
\draw [->] (encaps) -- (keybob);
\pause
\node [above = 1.5 of alice] (decaps) {$\decaps\paren *{\sk,c}$};
\draw [->] (cipher) -- (decaps);
\node [above = 0.5 of alice] (keyalice) {$\key$};
\draw [->] (decaps) -- (keyalice);
\pause
\node [draw, red, inner sep = -.1em, shape = rectangle, fit=(decaps)] {};
\end{tikzpicture}
\end{center}
\end{frame}
\begin{frame}
\frametitle{A Decapsulation Protocol with Shared Secret Key \cite{FeoM20}}
\begin{center}
\begin{tikzpicture}
\def\radius{2.5cm}
\begin{scope}[minimum size = .7cm]
\node [charlie] (sh1) at (40:3cm) {$s_1$};
\node [dave](sh2) at (140:3cm){$s_2$};
\node [maninblack] (sh3) at (220:3cm){$s_3$};
\node [physician] (sh4) at (320:3cm){$s_4$};
\node (sk) at (0,0) {$\sk$};
\draw [help lines] (sk) edge (sh1) edge (sh2) edge (sh3) edge (sh4);
\pause
\node [right=of sh1] (cipher) {$c$};
\coordinate [left = of sh2] (bla) ;
\draw [->] (cipher) -- (sh1);
\end{scope}
\end{tikzpicture}
\end{center}
\end{frame}
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...@@ -11,7 +11,7 @@ ...@@ -11,7 +11,7 @@
\newcommand\assignTo[2]{#1 \leftarrow #2} \newcommand\assignTo[2]{#1 \leftarrow #2}
%\usepackage{todonotes} %remove for submission %\usepackage{todonotes} %remove for submission
%\let\labelindent\relax %\let\labelindent\relax
\usepackage{enumitem} %\usepackage{enumitem}
\usepackage[english]{babel} \usepackage[english]{babel}
\usepackage[utf8]{inputenc} \usepackage[utf8]{inputenc}
\usepackage{amsmath} \usepackage{amsmath}
...@@ -43,7 +43,8 @@ ...@@ -43,7 +43,8 @@
\usepackage{hyphenat} \usepackage{hyphenat}
\usepackage{tikz} \usepackage{tikz}
\usetikzlibrary{calc,arrows,intersections, through,positioning, matrix} \usetikzlibrary{arrows,calc,fit, matrix,intersections,positioning, through}
\usepackage{tikzpeople}
\usepackage{tcolorbox} \usepackage{tcolorbox}
%\usepackage{titlesec} %\usepackage{titlesec}
......
\section{Deriving a Signature Scheme}
\begin{frame}
\end{frame}
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