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\documentclass { beamer}
\usetheme { default}
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\graphicspath { .}
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\setbeamertemplate { frametitle} [default][center]
\title { "Risk" in an untrusted setting}
\author { Jude Southworth}
\begin { document}
\begin { frame} [plain]
\maketitle
\end { frame}
\begin { frame} { Risk}
\begin { itemize}
\item \textit { Risk} is a popular strategy board game.
\item It is played on a single board, depicting a world map, partitioned into regions.
\item A player owns a region of the map by stationing troops within the region.
\item Players fight for regions by gambling some of their troops against the troops in the other player's region.
\end { itemize}
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\begin { center}
\includegraphics [width=6cm] { Risk_ game_ board}
\end { center}
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\end { frame}
\begin { frame} { Risk}
\begin { itemize}
\item \textit { Risk} has a variant called "fog of war".
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\item In this variant, players can only see the number of troops stationed within regions they neighbour.
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\item This variant is therefore only played online, in a \textbf { trusted setup} .
\end { itemize}
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\begin { center}
\includegraphics [width=6cm] { fog-of-war}
\end { center}
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\end { frame}
\begin { frame} { Proposition}
\begin { itemize}
\item Play fog-of-war Risk in an untrusted setup.
\item In the untrusted setup, the same guarantees should be made as the trusted setup, but on a peer-to-peer network.
\end { itemize}
\end { frame}
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\begin { frame} { Rationale}
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\begin { itemize}
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\item \textbf { Decentralised} \begin { itemize}
\item Longer lifespans than centralised platforms.
\item More resistant to censorship and can help promote anonymity and privacy.
\item Encourages user freedom.
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\end { itemize}
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\item \textbf { Security} \begin { itemize}
\item Constantly looking for ways to secure against threats specific to federated and decentralised infrastructures.
\item Security issues can be devastating even to decentralised infrastructures.
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\end { itemize}
\end { itemize}
\end { frame}
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\begin { frame} { State of the art}
\begin { itemize}
\item Private key encryption.
\item Signatures.
\item Additive homomorphic encryption.
\item \textbf { Monero, Zcash} . Decentralised ledgers respectively using the \textit { Bulletproof} and \textit { ZK-SNARK} zero-knowledge proof systems.
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\item \textbf { Web platform} .
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\end { itemize}
\end { frame}
\begin { frame} { Results}
Emulated P2P environment using WebSockets.
\end { frame}
\begin { frame} { Results}
Produce shared random values without beacons using commitment schemes.
\end { frame}
\begin { frame} { Results}
Generating large primes using ECMAScript \texttt { BigInt} and Rabin-Miller.
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\begin { tabular} { cc}
\includegraphics [width=5cm] { random2048} & \includegraphics [width=5cm] { carbon} \\
\multicolumn { 2} { c} { \includegraphics [width=65mm] { miller-rabin} }
\end { tabular}
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\end { frame}
\begin { frame} { Results}
Implementation of the Paillier additive homomorphic cryptosystem.
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\begin { center}
\includegraphics [width=11cm] { paillier}
\end { center}
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\end { frame}
\begin { frame} { Results}
Implementation of Risk.
\end { frame}
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\begin { frame} { Citations}
\textit { Image} Risk game board by CMG Lee, the asterisk denoting the missing link in the 40th Anniversary Collector's Edition, based on shapes from http://commons.wikimedia.org/wiki/File:Risk\_ board.svg. 11 November 2008. CC-BY-SA 4.0
\end { frame}
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\end { document}