main.tex

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  84
  85
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  87
  88
  89 \title{Random Walk in a N-cube Without Hamiltonian Cycle
  90   to Chaotic Pseudorandom Number Generation: Theoretical and Practical
  91   Considerations}
  92
  93 \begin{document}
  94
  95 \author{Jean-François Couchot, Christophe Guyeux, Pierre-Cyrille Heam}
  96 \address{FEMTO-ST Institute, University of Franche-Comté, Belfort, France}
  97
  98 \keywords{Pseudorandom Number Generator, Theory of Chaos, Markov Matrice, Hamiltonian Path, Mixing Time, Stopping Time, Statistical Test}
  99
 100 \subjclass{34C28, 37A25,11K45}
 101
 102 \begin{abstract}
 103 This paper is dedicated to the design of chaotic random generators
 104 and extends previous works proposed by some of the authors.
 105 We propose a theoretical framework proving both the chaotic properties and
 106 that the limit distribution is uniform.
 107 A theoretical bound on the stationary time is given and
 108 practical experiments show that the generators successfully pass
 109 the classical statistical tests.
 110 \end{abstract}
 111
 112 \maketitle
 113
 114 \section{Introduction}
 115 \input{intro}
 116
 117  \section{\uppercase{Preliminaries}}\label{sec:preliminaries}
 118 \input{preliminaries}
 119
 120 \section{Proof Of Chaos}\label{sec:proofOfChaos}
 121 \input{chaos}
 122
 123 \section{Functions with Strongly Connected $\Gamma_{\{b\}}(f)$}\label{sec:SCCfunc}
 124 \input{generating}
 125
 126 \section{Stopping Time}\label{sec:hypercube}
 127 \input{stopping}
 128
 129 \section{Experiments}\label{sec:prng}
 130 \input{prng}
 131
 132
 133
 134 \section{Conclusion}
 135 \input{conclusion}
 136
 137 %\acknowledgements{...}
 138
 139 \bibliographystyle{alpha}
 140 \bibliography{biblio}
 141
 142 \end{document}