From: couchot Date: Sun, 27 Oct 2013 20:54:43 +0000 (+0100) Subject: abstract X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/HindawiJournalOfChaos.git/commitdiff_plain/7d215ac81cb51343a34242683ce9b162170cb852?ds=inline abstract --- diff --git a/article.aux b/article.aux index 808524b..e2ec2a7 100644 --- a/article.aux +++ b/article.aux @@ -1,126 +1,133 @@ \relax +\citation{Cayre2008} +\citation{Cayre2008} +\citation{guyeux13:bc} +\citation{guyeux13:bc} +\citation{bg10b:ip} +\citation{gfb10:ip} +\citation{Guyeux2012} +\citation{Guyeux2012} \citation{1411349,Xie09:BASecurity} \citation{Cayre2008} \citation{Cayre2008} \citation{guyeux13:bc} \citation{guyeux13:bc} \citation{bg10b:ip} -\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}} -\newlabel{sec:introduction}{{1}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}} +\newlabel{sec:introduction}{{1}{2}} \citation{gfb10:ip} \citation{Guyeux2012} \citation{Guyeux2012} 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(etexcmds) That can mean that you are not using pdfTeX 1.50 or @@ -616,30 +615,30 @@ Package grfext Info: Graphics extension search list: G,.JBIG2,.JB2,.eps] (grfext) \AppendGraphicsExtensions on input line 452. -(/usr/share/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv e )) LaTeX Font Info: Try loading font information for OT1+lmr on input line 33. -(/usr/share/texmf-dist/tex/latex/lm/ot1lmr.fd +(/usr/share/texmf/tex/latex/lm/ot1lmr.fd File: ot1lmr.fd 2009/10/30 v1.6 Font defs for Latin Modern ) LaTeX Font Info: Try loading font information for OML+lmm on input line 33. -(/usr/share/texmf-dist/tex/latex/lm/omllmm.fd +(/usr/share/texmf/tex/latex/lm/omllmm.fd File: omllmm.fd 2009/10/30 v1.6 Font defs for Latin Modern ) LaTeX Font Info: Try loading font information for OMS+lmsy on input line 33. -(/usr/share/texmf-dist/tex/latex/lm/omslmsy.fd +(/usr/share/texmf/tex/latex/lm/omslmsy.fd File: omslmsy.fd 2009/10/30 v1.6 Font defs for Latin Modern ) LaTeX Font Info: Try loading font information for OMX+lmex on input line 33. -(/usr/share/texmf-dist/tex/latex/lm/omxlmex.fd +(/usr/share/texmf/tex/latex/lm/omxlmex.fd File: omxlmex.fd 2009/10/30 v1.6 Font defs for Latin Modern ) LaTeX Font Info: External font `lmex10' loaded for size @@ -650,45 +649,50 @@ LaTeX Font Info: External font `lmex10' loaded for size (Font) <6> on input line 33. 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LaTeX Font Info: External font `lmex10' loaded for size (Font) <7> on input line 51. -LaTeX Font Info: External font `lmex10' loaded for size -(Font) <5> on input line 51. ) -(./IH/notations.tex [2] +(./IH/notations.tex [3] LaTeX Font Info: Try loading font information for U+dsrom on input line 49. - (/usr/share/texmf-dist/tex/latex/doublestroke/Udsrom.fd + +(/usr/share/texlive/texmf-dist/tex/latex/doublestroke/Udsrom.fd File: Udsrom.fd 1995/08/01 v0.1 Double stroke roman font definitions ) LaTeX Font Info: Try loading font information for OT1+lmss on input line 100 . - (/usr/share/texmf-dist/tex/latex/lm/ot1lmss.fd + +(/usr/share/texmf/tex/latex/lm/ot1lmss.fd File: ot1lmss.fd 2009/10/30 v1.6 Font defs for Latin Modern -) [3] +) [4] LaTeX Font Info: Try loading font information for OMS+lmr on input line 166. -(/usr/share/texmf-dist/tex/latex/lm/omslmr.fd +(/usr/share/texmf/tex/latex/lm/omslmr.fd File: omslmr.fd 2009/10/30 v1.6 Font defs for Latin Modern ) LaTeX Font Info: Font shape `OMS/lmr/m/n' in size <10> not available @@ -701,7 +705,7 @@ Overfull \hbox (5.15031pt too wide) in paragraph at lines 2--2 []\T1/lmr/bx/n/14.4 The $[][]$ Chaotic It-er-a-tion based Wa-ter-mark- [] -[4] +[5] Overfull \hbox (7.38942pt too wide) in paragraph at lines 51--62 []\T1/lmr/m/it/10 Let us con-sider a set of grayscale im-ages stored into porta ble graymap @@ -709,40 +713,39 @@ ble graymap LaTeX Font Info: Font shape `OMS/lmr/m/it' in size <10> not available (Font) Font shape `OMS/lmsy/m/n' tried instead on input line 69. - +[6] File: IH/img/lena512.pdf Graphic file (type pdf) Package pdftex.def Info: IH/img/lena512.pdf used on input line 95. 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Package epstopdf Info: Output file is already uptodate. - + File: IH/Medias/lena512-eps-converted-to.pdf Graphic file (type pdf) @@ -750,7 +753,7 @@ Package pdftex.def Info: IH/Medias/lena512-eps-converted-to.pdf used on input l ine 142. (pdftex.def) Requested size: 113.81102pt x 113.81pt. - + File: IH/iihmsp13/exp/invader.png Graphic file (type png) @@ -767,18 +770,18 @@ Underfull \hbox (badness 10000) in paragraph at lines 143--143 [] Package epstopdf Info: Source file: -(epstopdf) date: 2011-02-14 11:10:36 +(epstopdf) date: 2013-10-27 21:33:40 (epstopdf) size: 330550 bytes (epstopdf) Output file: -(epstopdf) date: 2013-09-16 16:03:09 +(epstopdf) date: 2013-10-27 21:33:40 (epstopdf) size: 61881 bytes (epstopdf) Command: (epstopdf) \includegraphics on input line 144. Package epstopdf Info: Output file is already uptodate. - File: IH/Medias/lena512marqueDWT-eps-converted-to.pdf Graphic file (type pdf) @@ -789,75 +792,76 @@ n input line 144. 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PDF statistics: - 427 PDF objects out of 1000 (max. 8388607) - 215 compressed objects within 3 object streams + 450 PDF objects out of 1000 (max. 8388607) + 233 compressed objects within 3 object streams 0 named destinations out of 1000 (max. 500000) 86 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/article.pdf b/article.pdf index 2585a90..db2663a 100644 Binary files a/article.pdf and b/article.pdf differ diff --git a/article.synctex.gz b/article.synctex.gz deleted file mode 100644 index a578869..0000000 Binary files a/article.synctex.gz and /dev/null differ diff --git a/article.tex b/article.tex index af63053..7a1c93c 100644 --- a/article.tex +++ b/article.tex @@ -34,68 +34,16 @@ \begin{abstract} -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. - +Steganographic Information Hiding (IH) schemes +are in competition with Artificial Intelligence based +Steganalysers. +However, such kind of latter approaches suffer for dealing with +unpredictable behaviors. +The open problem is how defective they can be +proven against IH schemes based on mathematical chaos, +since this framework is theoretically and practically unpredictable. +This article addresses this problem and presents a review of IH schemes +based on Devaney's mathematical chaos. \end{abstract} \input{IH/intro} diff --git a/article.thm b/article.thm index 3a61f1b..3ba9dbf 100644 --- a/article.thm +++ b/article.thm @@ -1,48 +1,48 @@ -\contentsline {Def}{{Definition}{1}{}}{3} -\contentsline {Def}{{Definition}{2}{}}{3} -\contentsline {Def}{{Definition}{3}{}}{3} -\contentsline {Def}{{Definition}{4}{Devaney's chaos}}{3} -\contentsline {Def}{{Definition}{5}{}}{3} -\contentsline {Def}{{Definition}{6}{}}{3} -\contentsline {Th}{{Theorem}{1}{}}{4} -\contentsline {Def}{{Definition}{7}{}}{5} -\contentsline {Ex}{{Example}{1}{}}{5} -\contentsline {Def}{{Definition}{8}{}}{5} -\contentsline {Def}{{Definition}{9}{PLCM}}{7} -\contentsline {Def}{{Definition}{10}{Security~\cite {Kalker2001}}}{8} -\contentsline {Def}{{Definition}{11}{Robustness~\cite {Kalker2001}}}{8} -\contentsline {Def}{{Definition}{12}{}}{8} -\contentsline {Def}{{Definition}{13}{}}{8} -\contentsline {Def}{{Definition}{14}{}}{8} -\contentsline {Def}{{Definition}{15}{}}{8} -\contentsline {Def}{{Definition}{16}{Stego-Security~\cite {Cayre2008}}}{9} -\contentsline {Prop}{{Proposition}{1}{}}{9} -\contentsline {Def}{{Definition}{17}{}}{10} -\contentsline {Prop}{{Proposition}{2}{}}{10} -\contentsline {Def}{{Definition}{18}{}}{11} -\contentsline {Def}{{Definition}{19}{}}{11} -\contentsline {Def}{{Definition}{20}{}}{11} -\contentsline {Prop}{{Proposition}{3}{}}{12} -\contentsline {Pre}{{Proof}{1}{}}{12} -\contentsline {Prop}{{Proposition}{4}{}}{13} -\contentsline {Prop}{{Proposition}{5}{}}{13} -\contentsline {Th}{{Theorem}{2}{}}{13} -\contentsline {Prop}{{Proposition}{6}{}}{14} -\contentsline {Def}{{Definition}{21}{}}{18} -\contentsline {Def}{{Definition}{22}{}}{18} -\contentsline {Def}{{Definition}{23}{}}{19} -\contentsline {Def}{{Definition}{24}{}}{19} -\contentsline {Def}{{Definition}{25}{}}{20} -\contentsline {Prop}{{Proposition}{7}{}}{20} -\contentsline {Th}{{Theorem}{3}{}}{20} -\contentsline {Prop}{{Proposition}{8}{}}{21} -\contentsline {Th}{{Theorem}{4}{}}{21} -\contentsline {Th}{{Theorem}{5}{}}{21} -\contentsline {Th}{{Theorem}{6}{}}{22} -\contentsline {Rem}{{Rem}{1}{}}{22} -\contentsline {Def}{{Definition}{26}{}}{23} -\contentsline {Def}{{Definition}{27}{}}{23} -\contentsline {Rem}{{Rem}{2}{}}{23} -\contentsline {Def}{{Definition}{28}{$\mathcal {DI}_3$ Data hiding scheme}}{23} -\contentsline {Prop}{{Proposition}{9}{}}{23} -\contentsline {Rem}{{Rem}{3}{}}{25} +\contentsline {Def}{{Definition}{1}{}}{4} +\contentsline {Def}{{Definition}{2}{}}{4} +\contentsline {Def}{{Definition}{3}{}}{4} +\contentsline {Def}{{Definition}{4}{Devaney's chaos}}{4} +\contentsline {Def}{{Definition}{5}{}}{4} +\contentsline {Def}{{Definition}{6}{}}{5} +\contentsline {Th}{{Theorem}{1}{}}{5} +\contentsline {Def}{{Definition}{7}{}}{6} +\contentsline {Ex}{{Example}{1}{}}{6} +\contentsline {Def}{{Definition}{8}{}}{6} +\contentsline {Def}{{Definition}{9}{PLCM}}{8} +\contentsline {Def}{{Definition}{10}{Security~\cite {Kalker2001}}}{9} +\contentsline {Def}{{Definition}{11}{Robustness~\cite {Kalker2001}}}{9} +\contentsline {Def}{{Definition}{12}{}}{9} +\contentsline {Def}{{Definition}{13}{}}{10} +\contentsline {Def}{{Definition}{14}{}}{10} +\contentsline {Def}{{Definition}{15}{}}{10} +\contentsline {Def}{{Definition}{16}{Stego-Security~\cite {Cayre2008}}}{10} +\contentsline {Prop}{{Proposition}{1}{}}{11} +\contentsline {Def}{{Definition}{17}{}}{11} +\contentsline {Prop}{{Proposition}{2}{}}{11} +\contentsline {Def}{{Definition}{18}{}}{12} +\contentsline {Def}{{Definition}{19}{}}{13} +\contentsline {Def}{{Definition}{20}{}}{13} +\contentsline {Prop}{{Proposition}{3}{}}{13} +\contentsline {Pre}{{Proof}{1}{}}{13} +\contentsline {Prop}{{Proposition}{4}{}}{14} +\contentsline {Prop}{{Proposition}{5}{}}{14} +\contentsline {Th}{{Theorem}{2}{}}{14} +\contentsline {Prop}{{Proposition}{6}{}}{15} +\contentsline {Def}{{Definition}{21}{}}{19} +\contentsline {Def}{{Definition}{22}{}}{19} +\contentsline {Def}{{Definition}{23}{}}{20} +\contentsline {Def}{{Definition}{24}{}}{20} +\contentsline {Def}{{Definition}{25}{}}{21} +\contentsline {Prop}{{Proposition}{7}{}}{21} +\contentsline {Th}{{Theorem}{3}{}}{21} +\contentsline {Prop}{{Proposition}{8}{}}{22} +\contentsline {Th}{{Theorem}{4}{}}{22} +\contentsline {Th}{{Theorem}{5}{}}{22} +\contentsline {Th}{{Theorem}{6}{}}{23} +\contentsline {Rem}{{Rem}{1}{}}{23} +\contentsline {Def}{{Definition}{26}{}}{24} +\contentsline {Def}{{Definition}{27}{}}{24} +\contentsline {Rem}{{Rem}{2}{}}{24} +\contentsline {Def}{{Definition}{28}{$\mathcal {DI}_3$ Data hiding scheme}}{24} +\contentsline {Prop}{{Proposition}{9}{}}{25} +\contentsline {Rem}{{Rem}{3}{}}{26}