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