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-\author{
- Jean-Fran\c cois Couchot, Christophe Guyeux, and
- Jacques M. Bahi,~\IEEEmembership{Senior Member,~IEEE}\\
- FEMTO-ST Institute, UMR 6174 CNRS\\
- DISC Department, University of Franche-Comt\'{e}\\
- Belfort, France\\
- \{jean-francois.couchot, christophe.guyeux, jacques.bahi\}@femto-st.fr\\
-}
-
-
-\input{macroE}
-
-
-\title{Mathematical topology: a new practicable framework for
-studying information-hiding security.
-Application to Spread-Spectrum schemes.}
-
-
-
-
-\begin{document}
-\maketitle
-
-\newcommand{\ie}{\textit{i.e.}}
-%\newcommand{\Nats}[0]{\ensuremath{\mathds{N}}}
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-
-
-
-\begin{abstract}
-Information hiding security is often expressed as a probability problem.
-However, various classes of attacks cannot currently be addressed,
-due to strong hypotheses not compatible with a probabilistic approach.
-In this work, a complementary theoretical framework is presented to
-improve security. Contrary to existing ones, it is not based
-on probability theory, but on mathematical topology.
-It addresses thus security issues in classes of
-attacks that are not currently studied.
-It can also be used to reinforce the
-confidence in a new scheme.
-In this paper, first the theoretical framework of the study is presented,
-then some concrete examples are detailed in order to show how our approach
-can be applied.
-\end{abstract}
-
-
-
-\begin{IEEEkeywords}
-Information Hiding Security,
- Mathematical Theory of Chaos,
-Spread-Spectrum, Discrete Dynamical Systems,
-Chaotic Iterations
-\end{IEEEkeywords}
-
-
-
-
-
-
-
-
-\section{Introduction}
-\input{intro}
-
-
-
-
-\section{Related Work and Contributions}
-\label{Refs}
-\input{refs}
-
-
-
-
-
-%\JFC{
-%Reprendre les contributions.}
-%\input{contribs}
-
-
-
-\section{Chaos for Data Hiding Security}
-\label{section:Chaos}
-
-This section starts with a state of the art in chaos-based information hiding
-(Sec.~\ref{subsection:ChaosInComputerScience}).
-It reminds the readers of the theory of chaos as introduced by Devaney
-(Sec.~\ref{subsection:Devaney}).
-Other qualitative and quantitative properties are next introduced
-(Sec.~\ref{subsection:properties}).
-Their application to information hiding concludes this section (Sec.~\ref{subsection:links}).
-
-\subsection{State of the Art}
-\label{subsection:ChaosInComputerScience}
-\input{art.tex}
-
-\subsection{Devaney's Chaotic Dynamical Systems}
-\label{subsection:Devaney}
-\input{devaney}
-
-\subsection{Qualitative and Quantitative
-Properties of Discrete Dynamical Systems}
-\label{subsection:properties}
-\input{properties}
-
-\subsection{Chaos Properties and Information Hiding Security}
-\label{subsection:links}
-\input{relations}
-
-
-\section{Chaos-Security of two Data Hiding Schemes}
-\label{CS}
-
-To check whether an existing data hiding scheme is chaos-secure, we
-first write it as an iterate process $X^{n+1}=f(X^n)$
-defined on the set $\mathcal{X}$, with $X^0$ as the initial
-configuration of the machine.
-Let then $\mathcal{T}(S)$ be the iterative process of a data hiding scheme $S$
-and $\tau$ be a topology on the topological space $\mathcal{X}$.
-If $\mathcal{T}(S)$ has a chaotic behavior on $\mathcal{X}$,
-as defined by Devaney, $S$ is said
-to be \emph{chaos-secure} on $(\mathcal{X},\tau)$.
-
-This section studies two classes of
-data hiding schemes in the perspective
-of chaos theory.
-
-
-
-
-\subsection{Spread-Spectrum Data Hiding Schemes}
-\label{SS}
-\input{spreadspectrum}
-
-
-\subsection{dhCI: Chaos-based Expansive Data Hiding Schemes}
-\label{sec:Algo}
-\input{dhci}
-
-
-
-\section{Discussion and Future Work}
-\input{conclusion}
-
-
-%\bibliographystyle{compj}
-\bibliographystyle{IEEEtran}
-\bibliography{forensicsVer4}
-
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-
-
-\end{document}
