ajout espace bib

[rairo15.git] / main.tex

diff --git a/main.tex b/main.tex
index bc8524b5951330394e500461650e708f68be85c5..465fbf5a2d179b15236d958a0c98136a958c0de4 100644 (file)
--- a/main.tex
+++ b/main.tex
@@ -58,12 +58,6 @@
 \def \ts {\tau_{\rm stop}}
 
 
 \def \ts {\tau_{\rm stop}}
 
 

-\newtheorem{Def}{Definition}
-%\newtheorem{Lemma}{\underline{Lemma}}
-\newtheorem{Theo}{Theorem}
-\newtheorem{Corollary}{Corollary}
-\newtheorem{Lemma}{Lemma}
-\newtheorem{proposition}{Proposition}

 \newtheorem*{xpl}{Running Example}
 
 \newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}}
 \newtheorem*{xpl}{Running Example}
 
 \newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}}


@@ -86,65 +80,53 @@
 
 
 
 
 
 

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

 
 \begin{document}
 
 
 \begin{document}
 

-\author{Jean-François Couchot, Christophe Guyeux, Pierre-Cyrile Heam}
-\address{Institut FEMTO-ST, Université de Franche-Comté, Belfort, France}
+\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}
 
 \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 pass
+the classical statistical tests.

 \end{abstract}
 
 \maketitle
 
 \section{Introduction}
 \end{abstract}
 
 \maketitle
 
 \section{Introduction}

-%\input{intro}
+\input{intro}

 
  \section{\uppercase{Preliminaries}}\label{sec:preliminaries}
 \input{preliminaries}
 
 
  \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}
 
 \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{Stopping Time}\label{sec:hypercube}

 \input{stopping}
 
 \input{stopping}
 

-% Donner la borne du stopping time quand on marche dedans (nouveau). 
-% Énoncer le problème de la taille de cette borne
-% (elle est certes finie, mais grande). 
-
-
-
-
-%\section{Quality study of the strategy}
-%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{Experiments}\label{sec:prng}

 \input{prng}
 \input{prng}

-\JFC{ajouter ici les expérimentations}
+

 
 
 \section{Conclusion}
 
 
 \section{Conclusion}

-%\input{conclusion}
+\input{conclusion}

 
 %\acknowledgements{...}
 
 
 %\acknowledgements{...}