-\documentclass[preprint,review,12pt]{elsarticle}
-
+\documentclass{ws-ijbc}
\usepackage{graphicx}
-\usepackage{caption}
-\usepackage{subcaption}
+%\usepackage{amsthm}
+%\usepackage{subcaption}
+\usepackage{subfigure}
\usepackage{dsfont}
\usepackage{stmaryrd}
%\usepackage[font=footnotesize]{subfig}
\usepackage{ifthen}
\usepackage{color}
+%\usepackage{subfigure}
\usepackage{algorithm2e}
\usepackage{epstopdf}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
-\usepackage{amsmath,amssymb,amsthm,latexsym,eufrak,euscript}
+%\usepackage{amsmath,amssymb,amsthm,latexsym,eufrak,euscript}
\usepackage{pstricks,pst-node,pst-coil}
\def \ts {\tau_{\rm stop}}
-\newtheorem*{xpl}{Running Example}
+%\newtheorem*{xpl}{Running Example}
+\newenvironment{xpl}[1][Running Example]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
-\newtheorem{definition}{Definition}
+%\newtheorem{definition}{Definition}
\newtheorem{prpstn}{Proposition}
\newtheorem{thrm}{Theorem}
\newtheorem{crllr}{Corollary}
% a separate \thanks must be used for each paragraph as LaTeX2e's \thanks
% was not built to handle multiple paragraphs
%
-\author[label1]{Sylvain Contassot-Vivier}
-\author[label2]{Jean-François Couchot}
-\author[label2]{Christophe Guyeux}
-\author[label2]{Pierre-Cyrille Heam}
-\address[label1]{LORIA, Université de Lorraine, Nancy, France}
-\address[label2]{FEMTO-ST Institute, University of Franche-Comté, Belfort, France}
+\author{Sylvain Contassot-Vivier}
+\address{LORIA, Université de Lorraine, Nancy, France\\
+sylvain.contassotvivier@loria.fr}
+
+\author{Jean-François Couchot}
+\address{FEMTO-ST Institute, CNRS, Univ. Bourgogne Franche-Comté (UBFC), France\\
+jean-francois.couchot@univ-fcomte.fr}
+
+\author{Christophe Guyeux}
+\address{FEMTO-ST Institute, CNRS, Univ. Bourgogne Franche-Comté (UBFC), France\\
+christophe.guyeux@univ-fcomte.fr}
+
+\author{Pierre-Cyrille Heam}
+\address{FEMTO-ST Institute, CNRS, Univ. Bourgogne Franche-Comté (UBFC), France\\
+pierre-cyrille.heam@univ-fcomte.fr}
% the classical statistical tests.
% \end{abstract}
-\begin{abstract}
-Designing a pseudorandom number generator (PRNG) is a hard and complex task.
-Many recent works have considered chaotic functions as the basis of built
-PRNGs:
-the quality of the output would be an obvious consequence of some chaos
-properties.
-However, there is no direct reasoning that goes from chaotic functions to
-uniform distribution of the output.
-Moreover, it is not clear that embedding such kind of functions into a PRNG
-allows to get a chaotic output, which could be required for simulating
-some chaotic behaviors.
-
-In a previous work, some of the authors have proposed the idea of walking
-into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle has been
-removed as the basis of a chaotic PRNG. In this article, all the difficult
-issues observed in the previous work have been tackled. The chaotic behavior
-of the whole PRNG is proven. The construction of the balanced Hamiltonian
-cycle is theoretically and practically solved. An upper bound of the
-expected length of the walk to obtain a uniform distribution is calculated.
-Finally practical experiments show that the generators successfully pass the
-classical statistical tests.
-\end{abstract}
-
-
-
% Note that keywords are not normally used for peerreview papers.
% \begin{IEEEkeywords}
% creates the second title. It will be ignored for other modes.
\maketitle
+\begin{abstract}
+ Designing a pseudorandom number generator (PRNG) is a
+difficult and complex task. Many recent works have considered chaotic
+functions as the basis of built PRNGs: the quality of the output would
+indeed
+be an obvious consequence of some chaos properties. However, there is
+no direct reasoning that goes from chaotic functions to uniform
+distribution of the output.
+Moreover,
+embedding such kind of functions into a PRNG does not necessarily
+allow to get a chaotic output,
+which could be required for simulating some chaotic behaviors.
+
+In a previous work, some of the authors have proposed the idea of
+walking into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle
+has been removed as the basis of a chaotic PRNG. In this article, all
+the difficult issues observed in the previous work have been
+tackled. The chaotic behavior of the whole PRNG is proven. The
+construction of the balanced Hamiltonian cycle is theoretically and
+practically solved. An upper bound of the expected length of the walk
+to obtain a uniform distribution is calculated. Finally practical
+experiments show that the generators successfully pass the classical
+statistical tests.
+\end{abstract}
+
+
+\keywords{Pseudorandom Numbers Generator, Chaotic iterations, Random Walk}
+
\section{Introduction}
\input{intro}
\section{Preliminaries}\label{sec:preliminaries}
\input{preliminaries}
-\section{Proof Of Chaos}\label{sec:proofOfChaos}
+\section{Proof of Chaos}\label{sec:proofOfChaos}
\input{chaos}
\section{Functions with Strongly Connected $\Gamma_{\{b\}}(f)$}\label{sec:SCCfunc}
-\bibliographystyle{elsarticle-num}
+\bibliographystyle{ws-ijbc}
\bibliography{biblio}
