-\title{XXX}
+\title{Random Walk in a N-cube Without Hamiltonian Cycle
+ to Chaotic Pseudorandom Number Generation: Theoretical and Practical
+ Considerations}
\begin{document}
\begin{abstract}
-This paper extends the results presented in~\cite{bcgr11:ip}
-and~\cite{DBLP:conf/secrypt/CouchotHGWB14}
-by using the \emph{chaotic} updating mode, in the sense
-of F. Robert~\cite{Robert}. In this mode, several components of the system
-may be updated at each iteration. At the theoretical level, we show that
- the properties of chaos and uniformity of the obtained PRNG are preserved.
- At the practical level, we show that the algorithm that builds strongly
- connected iteration graphs, with doubly stochastic Markov matrix, has a
- reduced mixing time.
+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 passe
+the classical statsitcal tests.
\end{abstract}
\maketitle
\section{Introduction}
-%\input{intro}
+\input{intro}
\section{\uppercase{Preliminaries}}\label{sec:preliminaries}
\input{preliminaries}
-\section{Proof Of Chaos}
-\JFC{Enlever les refs aux PRNGs, harmoniser l'exemple}
+\section{Proof Of Chaos}\label{sec:proofOfChaos}
\input{chaos}
-\section{Generating....}
-\JFC{Reprendre Mons en synthétisant... conclusion: n-cube moins hamitonien.
-question efficacité d'un tel algo}
-%\input{chaos}
+\section{Functions with Strongly Connected $\Gamma_{\{b\}}(f)$}\label{sec:SCCfunc}
+\input{generating}
-\section{Random walk on the modified Hypercube}
+\section{Random walk on the modified Hypercube}\label{sec:hypercube}
\input{stopping}
% Donner la borne du stopping time quand on marche dedans (nouveau).
%6) Se pose alors la question de comment générer une stratégie de "bonne qualité". Par exemple, combien de générateurs aléatoires embarquer ? (nouveau)
-\section{Application to Pseudorandom Number Generation}
+\section{Application to Pseudorandom Number Generation}\label{sec:prng}
\input{prng}
\JFC{ajouter ici les expérimentations}
