X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rairo15.git/blobdiff_plain/07a05f881830e54c344db7060dfbfd74220d0eec..935ffe48008761ee21d78930849f51e32c62fcec:/main.tex

diff --git a/main.tex b/main.tex
index bc8524b..9e544ca 100644
--- a/main.tex
+++ b/main.tex
@@ -86,7 +86,9 @@
 
 
 
-\title{XXX}
+\title{Random Walk in a N-cube Without Hamiltonian Cycle 
+  to Chaotic Pseudorandom Number Generation: Theoretical and Practical 
+  Considerations}
 
 \begin{document}
 
@@ -96,35 +98,30 @@
 
 
 \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). 
@@ -138,13 +135,13 @@ question efficacité d'un tel algo}
 %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}
 
 
 \section{Conclusion}
-%\input{conclusion}
+\input{conclusion}
 
 %\acknowledgements{...}