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\title{Random Walk in a N-cube Without Hamiltonian Cycle 
  to Chaotic Pseudorandom Number Generation: Theoretical and Practical 
  Considerations}

\begin{document}

\author{Jean-François Couchot, Christophe Guyeux, Pierre-Cyrille Heam}
\address{FEMTO-ST Institute, University of Franche-Comté, Belfort, France}

\keywords{Pseudorandom Number Generator, Theory of Chaos, Markov Matrice, Hamiltonian Path, Mixing Time, Stopping Time, Statistical Test}

\subjclass{34C28, 37A25,11K45}

\begin{abstract}
This paper is dedicated to the design of chaotic random generators
and extends previous works proposed by some of the authors.
We propose a theoretical framework proving both the chaotic properties and
that the limit distribution is uniform.
A theoretical bound on the stationary time is given and
practical experiments show that the generators successfully pass
the classical statistical tests.
\end{abstract}

\maketitle

\section{Introduction}
\input{intro}

\section{Preliminaries}\label{sec:preliminaries}
\input{preliminaries}

\section{Proof Of Chaos}\label{sec:proofOfChaos}
\input{chaos}

\section{Functions with Strongly Connected $\Gamma_{\{b\}}(f)$}\label{sec:SCCfunc}
\input{generating}

\section{(Locally) Balanced Hamiltonian Cycle}\label{sec:hamilton}
\input{hamilton}


\section{Stopping Time}\label{sec:hypercube}
\input{stopping}

\section{Experiments}\label{sec:prng}
\input{prng}



\section{Conclusion}
\input{conclusion}

%\acknowledgements{...}

\bibliographystyle{alpha}
\bibliography{biblio}

\end{document}
