X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/HindawiJournalOfChaos.git/blobdiff_plain/361c59391688b55ec2afbb15ab479d17986b42f5..f5dfadd98093d3fb12f61c1b56c7e2c0b56a2a25:/article.tex

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 \begin{abstract}
-\begin{color}{red}TODO\end{color}
+Information hiding schemes are studied 
+Spread-spectrum data-hiding techniques have been widely studied in recent years
+under the scope of security. These techniques encompass several schemes, such as 
+Improved Spread Spectrum~(ISS), Circular Watermarking~(CW), and Natural 
+Watermarking~(NW). Some of these schemes have revealed various 
+security issues. On the contrary, it has
+been proven in~\cite{Cayre2008} that the Natural Watermarking technique is 
+stego-secure. This stego-security is one of the security classes defined 
+in~\cite{Cayre2008}, where probabilistic models are used to 
+categorize the security of data hiding algorithms in the Watermark Only 
+Attack~(WOA) framework.
+
+We have explained in our previous research works~\cite{guyeux13:bc}
+that any algorithm can be rewritten as an iterative
+process, leading to the possibility to study its
+topological behavior. As a concrete example, 
+we have shown that the security level of some information hiding algorithms 
+(of the spread-spectrum kind) can be studied into a 
+novel framework based on unpredictability, as it is understood in the mathematical
+theory of chaos~\cite{guyeux13:bc}. 
+The key idea motivating our research works is that: \emph{if artificial intelligence (AI)
+tools seem to have difficulties to deal with chaos, then steganalyzers (software based 
+on AI that try to separate original from stego-contents) may
+be proven defective against chaotic information hiding schemes}. Our work
+has thus constituted in showing theoretically that such chaotic schemes can be constructed. 
+We are not looking to struggle with best available information hiding techniques and
+we do not focus on effective and operational aspects, as
+our questioning are more locating in a conceptual domain. Among other things, we do
+not specify how to chose embedding coefficients, but the way to insert the hidden
+message in a selection of these ``least significant coefficient'' in an unpredictable
+manner. To say this another
+way, our intention is not to realize an hidden channel that does not appear as sleazy
+to a steganalyzer, but to construct an information hiding scheme whose behavior cannot
+be predicted: supposing that the adversary has anything (algorithm, possible embedding 
+coefficient, etc.) but the secret key, we want to determine if he can predict which coefficients
+will be finally used, and in which order. To do so, a new class of security has been 
+introduced in~\cite{bg10b:ip}, namely the topological security. This new class can be used to study 
+some categories of attacks that are difficult to investigate in the existing 
+security approach. It also enriches the variety of qualitative and quantitative 
+tools that evaluate how strong the security is, thus reinforcing the confidence 
+that can be added in a given scheme. 
+
+In addition of being stego-secure, we have proven in~\cite{gfb10:ip} that 
+Natural Watermarking (NW) technique is topologically secure. Moreover, this technique 
+possesses additional properties of unpredictability, namely, strong transitivity,
+topological mixing, and a constant of sensitivity equal to $\frac{N}{2}$~\cite{Guyeux2012}.
+However NW are not expansive, which is in our opinion problematic in the Constant-Message 
+Attack (CMA) and Known Message Attack (KMA) setups, when we
+consider that the attacker has all but the embedding key~\cite{Guyeux2012}. 
+Since these initial investigations, our research works in that information hiding field have
+thus consisted in searching more secure schemes than NW, regarding the 
+concerns presented in the first paragraph of this introduction. The objective
+of this review paper is to list the results obtained by following such an approach.
+
+This article is organized as follows. Notations and terminologies are firstly recalled in 
+the next section. Then the formerly published $\mathcal{CIW}_1$ chaotic iteration based one-bit watermarking 
+process is recalled in detail in Section~\ref{sec:ciw1}. Its steganographic version $\mathcal{CIS}_2$ 
+is then explained in Section~\ref{sec:secrypt11}, while Section~\ref{di3sec} presents the
+$\mathcal{DI}_3$ process, whose aims is to merge the two previous approaches.
+This review article of chaotic iterations based information hiding algorithms 
+ends by a conclusion section containing intended future works.
+
 \end{abstract}
 
 \input{IH/intro}