fin reprise preuve chaos

[rairo15.git] / main.tex

diff --git a/main.tex b/main.tex
index 5fa40f49c90e3753b0ccb7a792e66d38ea9cb201..bc8524b5951330394e500461650e708f68be85c5 100644 (file)
--- a/main.tex
+++ b/main.tex
@@ -1,15 +1,18 @@
 \documentclass{ita}
 \usepackage{graphicx}
 \documentclass{ita}
 \usepackage{graphicx}

+\usepackage{caption}
+\usepackage{subcaption}
+

 \usepackage{dsfont}
 \usepackage{stmaryrd}
 \usepackage{dsfont}
 \usepackage{stmaryrd}

-\usepackage[font=footnotesize]{subfig}
+%\usepackage[font=footnotesize]{subfig}

 \usepackage{ifthen}
 \usepackage{color}
 \usepackage{algorithm2e}
 \usepackage{epstopdf}
 \usepackage{ifthen}
 \usepackage{color}
 \usepackage{algorithm2e}
 \usepackage{epstopdf}

+%\usepackage{ntheorem}

 
 

-
-\usepackage[latin1]{inputenc}
+\usepackage[utf8]{inputenc}

 \usepackage[T1]{fontenc} 
 \usepackage[english]{babel}
 \usepackage{amsmath,amssymb,latexsym,eufrak,euscript}
 \usepackage[T1]{fontenc} 
 \usepackage[english]{babel}
 \usepackage{amsmath,amssymb,latexsym,eufrak,euscript}


@@ -28,7 +31,7 @@
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

-% Définitions personnelles
+% Définitions personnelles

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \definecolor{bleuclair}{rgb}{0.75,0.75,1.0}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \definecolor{bleuclair}{rgb}{0.75,0.75,1.0}


@@ -55,23 +58,13 @@
 \def \ts {\tau_{\rm stop}}
 
 
 \def \ts {\tau_{\rm stop}}
 
 

-% \theoremstyle{plain}
-% \theoremheaderfont{\normalfont\bfseries\sc}
-% \theorembodyfont{\slshape}
-% \theoremsymbol{\ensuremath{\diamondsuit}}
-% \theoremprework{\bigskip}
-% \theoremseparator{.}
-\newtheorem{Def}{\underline{Definition}}
-\newtheorem{Lemma}{\underline{Lemma}}
-\newtheorem{Theo}{\underline{Theorem}}
-% \theoremheaderfont{\sc}
-% \theorembodyfont{\upshape}
-% \theoremstyle{nonumberplain}
-% \theoremseparator{}
-% \theoremsymbol{\rule{1ex}{1ex}}
-\newtheorem{Proof}{Proof}
+\newtheorem{Def}{Definition}
+%\newtheorem{Lemma}{\underline{Lemma}}
+\newtheorem{Theo}{Theorem}
+\newtheorem{Corollary}{Corollary}
+\newtheorem{Lemma}{Lemma}

 \newtheorem{proposition}{Proposition}
 \newtheorem{proposition}{Proposition}

-\newtheorem{xpl}{Running Example}
+\newtheorem*{xpl}{Running Example}

 
 \newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}}
 %\newcommand{\ie}{\textit{i.e.}}
 
 \newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}}
 %\newcommand{\ie}{\textit{i.e.}}


@@ -97,17 +90,15 @@
 
 \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-Cyrile Heam}
+\address{Institut FEMTO-ST, Université de Franche-Comté, Belfort, France}

 
 

-%\author{Sylvain Contassot-Vivier}
-%\address{Loria - UMR 7503, Université de Lorraine, Nancy, France}

 
 

-\date{...}

 
 \begin{abstract}
 
 \begin{abstract}

-This   paper  extends   the  results   presented  in~\cite{bcgr11ip}
-and~\cite{chgw14oip} by using the \emph{chaotic} updating mode, in the sense
+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.
 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.


@@ -116,6 +107,8 @@ may be  updated at each iteration.   At the theoretical level,  we show that
     reduced mixing time.
 \end{abstract}
 
     reduced mixing time.
 \end{abstract}
 

+\maketitle
+

 \section{Introduction}
 %\input{intro}
 
 \section{Introduction}
 %\input{intro}
 


@@ -127,27 +120,27 @@ may be  updated at each iteration.   At the theoretical level,  we show that
 \input{chaos}
 
 \section{Generating....}
 \input{chaos}
 
 \section{Generating....}

-\JFC{Reprendre Mons en synthétisant... conclusion: n-cube moins hamitonien.
-question efficacité d'un tel algo}
+\JFC{Reprendre Mons en synthétisant... conclusion: n-cube moins hamitonien.
+question efficacité d'un tel algo}

 %\input{chaos}
 
 \section{Random walk on the modified Hypercube}
 \input{stopping}
 
 % Donner la borne du stopping time quand on marche dedans (nouveau). 
 %\input{chaos}
 
 \section{Random walk on the modified Hypercube}
 \input{stopping}
 
 % Donner la borne du stopping time quand on marche dedans (nouveau). 

-% Énoncer le problème de la taille de cette borne
+% Énoncer le problème de la taille de cette borne

 % (elle est certes finie, mais grande). 
 
 
 
 
 %\section{Quality study of the strategy}
 % (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)
+%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}
 \input{prng}
 
 
 \section{Application to Pseudorandom Number Generation}
 \input{prng}

-\JFC{ajouter ici les expérimentations}
+\JFC{ajouter ici les expérimentations}

 
 
 \section{Conclusion}
 
 
 \section{Conclusion}