From: couchot Date: Tue, 29 Oct 2013 20:26:20 +0000 (+0100) Subject: abstract, conclusion X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/HindawiJournalOfChaos.git/commitdiff_plain abstract, conclusion --- diff --git a/IH/ciw1.tex b/IH/ciw1.tex index 1a07a76..6c9a618 100644 --- a/IH/ciw1.tex +++ b/IH/ciw1.tex @@ -1,6 +1,13 @@ \section{The $\mathcal{CIW}_1$ Chaotic Iteration based Watermarking Process} \label{sec:ciw1} + +This section introduces the $\mathcal{CIW}_1$ watermarking process. +It first recalls its fundations, addresses security issues, +compares it with the Spread Spectrum Scheme, and ends with evaluating +its Lyapunov exponent. + + \subsection{Using chaotic iterations as information hiding schemes} \label{sec:data-hiding-algo-chaotic iterations} @@ -120,7 +127,7 @@ These two definitions are illustrated on Figure~\ref{fig:MSCLSC}, \subsubsection{Presentation of the $\mathcal{CIW}_1$ dhCI scheme} \label{trucMachin} -We have proposed in SECRYPT10~\cite{guyeux10ter} to +We have proposed in~\cite{guyeux10ter} to study a particular instance of the dhCI class, which considers the negation function as iteration mode. The resulting chaotic iterations watermarking\footnote{Watermarking means here that only a binary information, like the presence of a copyright, can be extracted.} process has been denoted by diff --git a/IH/conclusion.tex b/IH/conclusion.tex index 5e87498..e720b40 100644 --- a/IH/conclusion.tex +++ b/IH/conclusion.tex @@ -1 +1,23 @@ \section{Conclusion} +This work has reviewed the evolution of chaos based data hiding schemes. +The whole class of algorithms has been formally presented and implemented. +Two watermarking processes ($\mathcal{CIW}_1$ and $\mathcal{CIS}_2$) have been +recalled; the former is a one-bit approach whereas the latter allows to +embed any message of reasonable size. +The two schemes have been +theoretically evaluated: both are stego-secure and verify the +topological expansiveness property. +These two scheme has been practically evaluated: they have been proven to be +robust against a large class of attacks. +Finally, $\mathcal{DI}_3$ which adapts the $\mathcal{CIS}_2$ scheme to +the steganography field. It capacity to resists to steganalysis has been +evaluated and has shown promissing results. + +To summarize, this works has presented three +chaos based data hiding schemes and has study their security. +In a future work we plan to combine these approaches to other data hiding +schemes to take benefit of their best behaviors: +for instance the pixel selection may be achieved by state of the art +distortion function and modifications may be delayed to chaos +based schemes. + \ No newline at end of file diff --git a/IH/notations.tex b/IH/notations.tex index 6938df2..e04a991 100644 --- a/IH/notations.tex +++ b/IH/notations.tex @@ -7,7 +7,7 @@ $S^{n}$ stands for the $n^{th}$ term of a sequence $S$, $V_{i}$ is for the $i^{th}$ component of a vector $V$, and $\llbracket0;N\rrbracket$ is the integer interval $\{0,1,\hdots,N\}$. -\begin{color}{red} Compléter éventuellement les notations\end{color}. +%\begin{color}{red} Compléter éventuellement les notations\end{color}. % Furthermore, the 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\bibcite{bfg13:ip}{6} \bibcite{bg10b:ip}{7} diff --git a/article.log b/article.log index e364bda..00e6313 100644 --- a/article.log +++ b/article.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2013.10.25) 27 OCT 2013 21:34 +This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2013.10.25) 29 OCT 2013 21:26 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -664,20 +664,17 @@ Overfull \hbox (28.75941pt too wide) in paragraph at lines 33--33 [][] [] -[1 +(./IH/intro.tex [1 {/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] LaTeX Font Info: External font `lmex10' loaded for size -(Font) <9> on input line 82. -LaTeX Font Info: External font `lmex10' loaded for size -(Font) <5> on input line 82. - (./IH/intro.tex [2] -LaTeX Font Info: External font `lmex10' loaded for size (Font) <10> on input line 51. 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PDF statistics: - 450 PDF objects out of 1000 (max. 8388607) - 233 compressed objects within 3 object streams + 430 PDF objects out of 1000 (max. 8388607) + 217 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 db2663a..9434ffd 100644 Binary files a/article.pdf and b/article.pdf differ diff --git a/article.thm b/article.thm index 3ba9dbf..4c75434 100644 --- a/article.thm +++ b/article.thm @@ -1,48 +1,48 @@ -\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}{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}{}}{4} +\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}{}}{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}{13}{}}{9} +\contentsline {Def}{{Definition}{14}{}}{9} +\contentsline {Def}{{Definition}{15}{}}{9} +\contentsline {Def}{{Definition}{16}{Stego-Security~\cite {Cayre2008}}}{9} +\contentsline {Prop}{{Proposition}{1}{}}{10} +\contentsline {Def}{{Definition}{17}{}}{10} +\contentsline {Prop}{{Proposition}{2}{}}{10} \contentsline {Def}{{Definition}{18}{}}{12} -\contentsline {Def}{{Definition}{19}{}}{13} -\contentsline {Def}{{Definition}{20}{}}{13} +\contentsline {Def}{{Definition}{19}{}}{12} +\contentsline {Def}{{Definition}{20}{}}{12} \contentsline {Prop}{{Proposition}{3}{}}{13} \contentsline {Pre}{{Proof}{1}{}}{13} -\contentsline {Prop}{{Proposition}{4}{}}{14} -\contentsline {Prop}{{Proposition}{5}{}}{14} +\contentsline {Prop}{{Proposition}{4}{}}{13} +\contentsline {Prop}{{Proposition}{5}{}}{13} \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} +\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}{}}{24} +\contentsline {Rem}{{Rem}{3}{}}{25}