\contentsline {section}{\numberline {1}Introduction}{2}
\contentsline {section}{\numberline {2}The $\mathcal {CIW}_1$ Chaotic Iteration based Watermarking Process}{3}
\contentsline {subsection}{\numberline {2.1}Using chaotic iterations as information hiding schemes}{3}
\contentsline {subsubsection}{\numberline {2.1.1}Presentation of the dhCI process}{3}
\contentsline {subsubsection}{\numberline {2.1.2}Most and least significant coefficients}{4}
\contentsline {subsubsection}{\numberline {2.1.3}Presentation of the $\mathcal {CIW}_1$ dhCI scheme}{4}
\contentsline {subsubsection}{\numberline {2.1.4}Examples of strategies}{6}
\contentsline {paragraph}{CIIS strategy}{6}
\contentsline {paragraph}{CIDS strategy}{6}
\contentsline {subsection}{\numberline {2.2}Security versus robustness}{7}
\contentsline {subsubsection}{\numberline {2.2.1}Presentation}{7}
\contentsline {subsubsection}{\numberline {2.2.2}Classification of attacks}{7}
\contentsline {subsubsection}{\numberline {2.2.3}Definition of stego-security}{8}
\contentsline {subsection}{\numberline {2.3}Security evaluation}{8}
\contentsline {subsubsection}{\numberline {2.3.1}Evaluation of the stego-security}{8}
\contentsline {subsubsection}{\numberline {2.3.2}Evaluation of the topological security}{9}
\contentsline {subsection}{\numberline {2.4}Comparison between spread-spectrum and chaotic iterations}{9}
\contentsline {subsection}{\numberline {2.5}Lyapunov exponent evaluation}{10}
\contentsline {section}{\numberline {3}The $\mathcal {CIS}_2$ Chaotic Iteration based Steganographic Process}{10}
\contentsline {subsection}{\numberline {3.1}The improved algorithm}{10}
\contentsline {subsection}{\numberline {3.2}Security study of the $\mathcal {CIS}_2$}{11}
\contentsline {subsubsection}{\numberline {3.2.1}Stego-security}{11}
\contentsline {subsubsection}{\numberline {3.2.2}Topological security}{12}
\contentsline {paragraph}{Topological model}{12}
\contentsline {paragraph}{A new distance on $\mathcal {X}_2$}{12}
\contentsline {paragraph}{Continuity of $\mathcal {CIS}_2$}{12}
\contentsline {paragraph}{$\mathcal {CIS}_2$ is chaotic}{12}
\contentsline {subsection}{\numberline {3.3}Correctness and completeness studies}{13}
\contentsline {subsection}{\numberline {3.4}Deciding whether a possibly attacked media is watermarked}{13}
\contentsline {subsection}{\numberline {3.5}Robustness study of the process}{14}
\contentsline {subsection}{\numberline {3.6}Evaluation of the embeddings}{16}
\contentsline {subsection}{\numberline {3.7}Lyapunov evaluation of $\mathcal {CIS}_2$}{17}
\contentsline {subsubsection}{\numberline {3.7.1}A topological semi-conjugacy between $\mathcal {X}_2$ and $\mathds {R}$}{17}
\contentsline {subsubsection}{\numberline {3.7.2}Topological security of $\mathcal {CIS}_2$ on $\mathds {R}$}{20}
\contentsline {subsubsection}{\numberline {3.7.3}Evaluation of the Lyapunov exponent}{21}
\contentsline {section}{\numberline {4}The $\mathcal {DI}_3$ Steganographic Process}{21}
\contentsline {subsection}{\numberline {4.1}Mathematical definitions and notations}{22}
\contentsline {subsection}{\numberline {4.2}The new $\mathcal {DI}_3$ process}{22}
\contentsline {subsection}{\numberline {4.3}Security study}{23}
\contentsline {subsection}{\numberline {4.4}Implementing the $\mathcal {DI}_3$ scheme}{24}
\contentsline {subsection}{\numberline {4.5}Evaluation against steganalyzers}{24}
\contentsline {subsection}{\numberline {4.6}Robustness study}{26}
\contentsline {section}{\numberline {5}Further Investigations of the dhCI Class}{27}
\contentsline {subsection}{\numberline {5.1}Introduction}{28}
\contentsline {subsection}{\numberline {5.2}Formalization of steganographic methods}{29}
\contentsline {subsection}{\numberline {5.3}Security analysis}{32}
\contentsline {subsection}{\numberline {5.4}Discovering another relevant mode}{32}
\contentsline {subsection}{\numberline {5.5}dhCI in frequency domains}{33}
\contentsline {subsubsection}{\numberline {5.5.1}DWT embedding}{33}
\contentsline {subsubsection}{\numberline {5.5.2}DCT embedding}{34}
\contentsline {subsection}{\numberline {5.6}Image quality}{36}
\contentsline {subsection}{\numberline {5.7}Robustness}{36}
\contentsline {subsubsection}{\numberline {5.7.1}Robustness against cropping}{37}
\contentsline {subsubsection}{\numberline {5.7.2}Robustness against compression}{37}
\contentsline {subsubsection}{\numberline {5.7.3}Robustness against contrast and sharpness}{38}
\contentsline {subsubsection}{\numberline {5.7.4}Robustness against geometric transformations}{38}
\contentsline {subsection}{\numberline {5.8}Evaluation of the Embedding}{39}
\contentsline {section}{\numberline {6}A Cryptographic Approach for Steganography}{40}
\contentsline {subsection}{\numberline {6.1}Drawbacks of the stego-security notion}{41}
\contentsline {subsection}{\numberline {6.2}Toward a cryptographically secure hiding}{41}
\contentsline {subsubsection}{\numberline {6.2.1}Definition of a stegosystem}{42}
\contentsline {subsubsection}{\numberline {6.2.2}Heading notions}{42}
\contentsline {subsubsection}{\numberline {6.2.3}A cryptographically secure information hiding scheme}{42}