X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/HindawiJournalOfChaos.git/blobdiff_plain/361c59391688b55ec2afbb15ab479d17986b42f5..7d215ac81cb51343a34242683ce9b162170cb852:/article.aux

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}
 \citation{Devaney}
-\@writefile{toc}{\contentsline {section}{\numberline {2}Notations and Terminologies}{2}}
-\newlabel{not}{{2}{2}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}The mathematical theory of chaos}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Notations and Terminologies}{3}}
+\newlabel{not}{{2}{3}}
 \citation{Banks92}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}The mathematical theory of chaos}{4}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{1}{}}{4}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{2}{}}{4}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{3}{}}{4}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{4}{Devaney's chaos}}{4}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{5}{}}{4}}
+\newlabel{sensitivity}{{5}{4}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Chaotic iterations and watermarking scheme}{4}}
+\newlabel{sec:chaotic iterations}{{2.2}{4}}
 \citation{guyeux10}
-\@writefile{thm}{\contentsline {Def}{{Definition}{1}{}}{3}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{2}{}}{3}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{3}{}}{3}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{4}{Devaney's chaos}}{3}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{5}{}}{3}}
-\newlabel{sensitivity}{{5}{3}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Chaotic iterations and watermarking scheme}{3}}
-\newlabel{sec:chaotic iterations}{{2.2}{3}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{6}{}}{3}}
-\newlabel{Def:chaotic iterations}{{6}{3}}
 \citation{Devaney}
 \citation{guyeux10}
 \citation{guyeux10}
 \citation{gfb10:ip,bcg11b:ip}
+\@writefile{thm}{\contentsline {Def}{{Definition}{6}{}}{5}}
+\newlabel{Def:chaotic iterations}{{6}{5}}
+\newlabel{Gf}{{1}{5}}
+\@writefile{thm}{\contentsline {Th}{{Theorem}{1}{}}{5}}
 \citation{gfb10:ip,bcg11b:ip}
-\newlabel{Gf}{{1}{4}}
-\@writefile{thm}{\contentsline {Th}{{Theorem}{1}{}}{4}}
-\@writefile{toc}{\contentsline {section}{\numberline {3}The $\mathcal  {CIW}_1$ Chaotic Iteration based Watermarking Process}{4}}
-\newlabel{sec:ciw1}{{3}{4}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Using chaotic iterations as information hiding schemes}{4}}
-\newlabel{sec:data-hiding-algo-chaotic iterations}{{3.1}{4}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.1}Presentation of the dhCI process}{4}}
 \citation{guyeux10ter}
 \citation{Guyeux2012}
 \citation{gfb10:ip}
+\@writefile{toc}{\contentsline {section}{\numberline {3}The $\mathcal  {CIW}_1$ Chaotic Iteration based Watermarking Process}{6}}
+\newlabel{sec:ciw1}{{3}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Using chaotic iterations as information hiding schemes}{6}}
+\newlabel{sec:data-hiding-algo-chaotic iterations}{{3.1}{6}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.1}Presentation of the dhCI process}{6}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.2}Most and least significant coefficients}{6}}
+\newlabel{sec:msc-lsc}{{3.1.2}{6}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{7}{}}{6}}
+\@writefile{thm}{\contentsline {Ex}{{Example}{1}{}}{6}}
+\newlabel{Exemple LSC}{{1}{6}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{8}{}}{6}}
+\newlabel{def:msc,lsc}{{8}{6}}
 \citation{guyeux10ter}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.2}Most and least significant coefficients}{5}}
-\newlabel{sec:msc-lsc}{{3.1.2}{5}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{7}{}}{5}}
-\@writefile{thm}{\contentsline {Ex}{{Example}{1}{}}{5}}
-\newlabel{Exemple LSC}{{1}{5}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{8}{}}{5}}
-\newlabel{def:msc,lsc}{{8}{5}}
 \citation{gfb10:ip}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Most and least significant coefficients of Lena.}}{7}}
+\newlabel{fig:MSCLSC}{{1}{7}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.3}Presentation of the $\mathcal  {CIW}_1$ dhCI scheme}{7}}
+\newlabel{trucMachin}{{3.1.3}{7}}
 \citation{Shujun1}
-\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Most and least significant coefficients of Lena.}}{6}}
-\newlabel{fig:MSCLSC}{{1}{6}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.3}Presentation of the $\mathcal  {CIW}_1$ dhCI scheme}{6}}
-\newlabel{trucMachin}{{3.1.3}{6}}
 \citation{Shujun1}
 \citation{Shujun1}
+\newlabel{invad}{{2(b)}{8}}
+\newlabel{sub@invad}{{(b)}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Data hiding with chaotic iterations}}{8}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Original Lena.}}}{8}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Watermark.}}}{8}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(c)}{\ignorespaces {Watermarked Lena.}}}{8}}
+\newlabel{fig:DWT}{{2}{8}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.4}Examples of strategies}{8}}
+\newlabel{sec:ciis-cids-example}{{3.1.4}{8}}
+\@writefile{toc}{\contentsline {paragraph}{CIIS strategy}{8}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{9}{PLCM}}{8}}
+\newlabel{Def:PLCM}{{9}{8}}
+\newlabel{eq:PLCM-for-strategy}{{3.1.4}{8}}
 \citation{gfb10:ip}
-\newlabel{invad}{{2(b)}{7}}
-\newlabel{sub@invad}{{(b)}{7}}
-\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Data hiding with chaotic iterations}}{7}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Original Lena.}}}{7}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Watermark.}}}{7}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(c)}{\ignorespaces {Watermarked Lena.}}}{7}}
-\newlabel{fig:DWT}{{2}{7}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.4}Examples of strategies}{7}}
-\newlabel{sec:ciis-cids-example}{{3.1.4}{7}}
-\@writefile{toc}{\contentsline {paragraph}{CIIS strategy}{7}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{9}{PLCM}}{7}}
-\newlabel{Def:PLCM}{{9}{7}}
-\newlabel{eq:PLCM-for-strategy}{{3.1.4}{7}}
-\newlabel{sec:cids-example}{{3.1.4}{7}}
-\@writefile{toc}{\contentsline {paragraph}{CIDS strategy}{7}}
 \citation{Perez-Freire06}
 \citation{Kalker2001,ComesanaPP05bis}
 \citation{Kalker2001}
 \citation{Kalker2001}
 \citation{Kalker2001}
 \citation{Cayre2008}
+\newlabel{sec:cids-example}{{3.1.4}{9}}
+\@writefile{toc}{\contentsline {paragraph}{CIDS strategy}{9}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Security versus robustness}{9}}
+\newlabel{sec:chaotic iterations-security-level}{{3.2}{9}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.1}Presentation}{9}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{10}{Security~\cite {Kalker2001}}}{9}}
+\newlabel{def:security}{{10}{9}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{11}{Robustness~\cite {Kalker2001}}}{9}}
+\newlabel{def:robustness}{{11}{9}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.2}Classification of attacks}{9}}
+\newlabel{sec:attack-classes}{{3.2.2}{9}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{12}{}}{9}}
 \citation{Kalker2001}
 \citation{Simmons83}
-\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Security versus robustness}{8}}
-\newlabel{sec:chaotic iterations-security-level}{{3.2}{8}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.1}Presentation}{8}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{10}{Security~\cite {Kalker2001}}}{8}}
-\newlabel{def:security}{{10}{8}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{11}{Robustness~\cite {Kalker2001}}}{8}}
-\newlabel{def:robustness}{{11}{8}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.2}Classification of attacks}{8}}
-\newlabel{sec:attack-classes}{{3.2.2}{8}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{12}{}}{8}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{13}{}}{8}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{14}{}}{8}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{15}{}}{8}}
 \citation{Cayre2008}
 \citation{Cayre2008}
 \citation{Cachin2004}
 \citation{gfb10:ip}
+\@writefile{thm}{\contentsline {Def}{{Definition}{13}{}}{10}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{14}{}}{10}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{15}{}}{10}}
+\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Watermarking attacks classification in context of\nobreakspace  {}\cite  {Kalker2001}}}{10}}
+\newlabel{table:attack-classification}{{1}{10}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.3}Definition of stego-security}{10}}
+\newlabel{sec:stego-security-definition}{{3.2.3}{10}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{16}{Stego-Security~\cite {Cayre2008}}}{10}}
+\newlabel{Def:Stego-security}{{16}{10}}
 \citation{gfb10:ip}
-\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Watermarking attacks classification in context of\nobreakspace  {}\cite  {Kalker2001}}}{9}}
-\newlabel{table:attack-classification}{{1}{9}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.3}Definition of stego-security}{9}}
-\newlabel{sec:stego-security-definition}{{3.2.3}{9}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{16}{Stego-Security~\cite {Cayre2008}}}{9}}
-\newlabel{Def:Stego-security}{{16}{9}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Security evaluation}{9}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.1}Evaluation of the stego-security}{9}}
-\newlabel{sec:stego-security-proof}{{3.3.1}{9}}
-\@writefile{thm}{\contentsline {Prop}{{Proposition}{1}{}}{9}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.2}Evaluation of the topological security}{9}}
-\newlabel{sec:topological security-evaluation}{{3.3.2}{9}}
 \citation{gfb10:ip}
 \citation{gfb10:ip}
 \citation{gfb10:ip}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Security evaluation}{11}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.1}Evaluation of the stego-security}{11}}
+\newlabel{sec:stego-security-proof}{{3.3.1}{11}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{1}{}}{11}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.2}Evaluation of the topological security}{11}}
+\newlabel{sec:topological security-evaluation}{{3.3.2}{11}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{17}{}}{11}}
+\newlabel{Def:topological security-definition}{{17}{11}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{2}{}}{11}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Comparison between spread-spectrum and chaotic iterations}{11}}
+\newlabel{sec:comparison-application-context}{{3.4}{11}}
 \citation{bfg12:ip}
-\@writefile{thm}{\contentsline {Def}{{Definition}{17}{}}{10}}
-\newlabel{Def:topological security-definition}{{17}{10}}
-\@writefile{thm}{\contentsline {Prop}{{Proposition}{2}{}}{10}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Comparison between spread-spectrum and chaotic iterations}{10}}
-\newlabel{sec:comparison-application-context}{{3.4}{10}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Lyapunov exponent evaluation}{10}}
 \citation{Guyeux2012}
 \citation{gfb10:ip}
 \citation{Cayre2008}
@@ -128,119 +135,120 @@
 \citation{fgb11:ip}
 \citation{gfb10:ip}
 \citation{fgb11:ip}
-\@writefile{toc}{\contentsline {section}{\numberline {4}The $\mathcal  {CIS}_2$ Chaotic Iteration based Steganographic Process}{11}}
-\newlabel{sec:secrypt11}{{4}{11}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}The improved algorithm}{11}}
-\newlabel{section:Algorithm}{{4.1}{11}}
-\newlabel{section:IH based on CIs}{{4.1}{11}}
-\newlabel{sec:topological}{{4.1}{11}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{18}{}}{11}}
-\newlabel{def:strategy-adapter}{{18}{11}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{19}{}}{11}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{20}{}}{11}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Lyapunov exponent evaluation}{12}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}The $\mathcal  {CIS}_2$ Chaotic Iteration based Steganographic Process}{12}}
+\newlabel{sec:secrypt11}{{4}{12}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}The improved algorithm}{12}}
+\newlabel{section:Algorithm}{{4.1}{12}}
+\newlabel{section:IH based on CIs}{{4.1}{12}}
+\newlabel{sec:topological}{{4.1}{12}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{18}{}}{12}}
+\newlabel{def:strategy-adapter}{{18}{12}}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
-\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Security study of the $\mathcal  {CIS}_2$}{12}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.1}Stego-security}{12}}
-\@writefile{thm}{\contentsline {Prop}{{Proposition}{3}{}}{12}}
-\@writefile{thm}{\contentsline {Pre}{{Proof}{1}{}}{12}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.2}Topological security}{12}}
-\@writefile{toc}{\contentsline {paragraph}{Topological model}{12}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{19}{}}{13}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{20}{}}{13}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Security study of the $\mathcal  {CIS}_2$}{13}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.1}Stego-security}{13}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{3}{}}{13}}
+\@writefile{thm}{\contentsline {Pre}{{Proof}{1}{}}{13}}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{bcfg+13:ip}
-\@writefile{thm}{\contentsline {Prop}{{Proposition}{4}{}}{13}}
-\@writefile{toc}{\contentsline {paragraph}{A new distance on $\mathcal  {X}_2$}{13}}
-\@writefile{toc}{\contentsline {paragraph}{Continuity of $\mathcal  {CIS}_2$}{13}}
-\@writefile{thm}{\contentsline {Prop}{{Proposition}{5}{}}{13}}
-\newlabel{section:chaos-security}{{4.2.2}{13}}
-\@writefile{toc}{\contentsline {paragraph}{$\mathcal  {CIS}_2$ is chaotic}{13}}
-\@writefile{thm}{\contentsline {Th}{{Theorem}{2}{}}{13}}
-\newlabel{theo:chaotic}{{2}{13}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Correctness and completeness studies}{13}}
-\newlabel{sub:ci2:discussion}{{4.3}{13}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.2}Topological security}{14}}
+\@writefile{toc}{\contentsline {paragraph}{Topological model}{14}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{4}{}}{14}}
+\@writefile{toc}{\contentsline {paragraph}{A new distance on $\mathcal  {X}_2$}{14}}
+\@writefile{toc}{\contentsline {paragraph}{Continuity of $\mathcal  {CIS}_2$}{14}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{5}{}}{14}}
+\newlabel{section:chaos-security}{{4.2.2}{14}}
+\@writefile{toc}{\contentsline {paragraph}{$\mathcal  {CIS}_2$ is chaotic}{14}}
+\@writefile{thm}{\contentsline {Th}{{Theorem}{2}{}}{14}}
+\newlabel{theo:chaotic}{{2}{14}}
 \citation{bcfg+13:ip}
 \citation{rifq/others03}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Correctness and completeness studies}{15}}
+\newlabel{sub:ci2:discussion}{{4.3}{15}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{6}{}}{15}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Deciding whether a possibly attacked media is watermarked}{15}}
+\newlabel{sub:ci2:distances}{{4.4}{15}}
 \citation{bcfg+13:ip}
 \citation{bcfg+13:ip}
-\@writefile{thm}{\contentsline {Prop}{{Proposition}{6}{}}{14}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Deciding whether a possibly attacked media is watermarked}{14}}
-\newlabel{sub:ci2:distances}{{4.4}{14}}
 \citation{bcfg+13:ip}
 \citation{Boss10}
 \citation{bcfg+13:ip}
 \citation{bcfg+13:ip}
-\@writefile{toc}{\contentsline {subsection}{\numberline {4.5}Robustness study of the process}{15}}
-\newlabel{Fig:atq:dec:curves}{{4.5}{15}}
-\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Cropping Results}}{15}}
-\newlabel{Fig:atck:dec}{{3}{15}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.5}Robustness study of the process}{16}}
+\newlabel{Fig:atq:dec:curves}{{4.5}{16}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Cropping Results}}{16}}
+\newlabel{Fig:atck:dec}{{3}{16}}
 \citation{bcfg+13:ip}
+\newlabel{Fig:atq:jpg:curves}{{4(a)}{17}}
+\newlabel{sub@Fig:atq:jpg:curves}{{(a)}{17}}
+\newlabel{Fig:atq:jp2:curves}{{4(b)}{17}}
+\newlabel{sub@Fig:atq:jp2:curves}{{(b)}{17}}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Compression Results}}{17}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {JPEG Effect}}}{17}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {JPEG 2000 Effect}}}{17}}
+\newlabel{Fig:atck:comp}{{4}{17}}
+\newlabel{Fig:atq:rot:curve}{{4.5}{17}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Rotation Attack Results}}{17}}
+\newlabel{Fig:atq:rot}{{5}{17}}
 \citation{bcfg+13:ip}
-\newlabel{Fig:atq:jpg:curves}{{4(a)}{16}}
-\newlabel{sub@Fig:atq:jpg:curves}{{(a)}{16}}
-\newlabel{Fig:atq:jp2:curves}{{4(b)}{16}}
-\newlabel{sub@Fig:atq:jp2:curves}{{(b)}{16}}
-\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Compression Results}}{16}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {JPEG Effect}}}{16}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {JPEG 2000 Effect}}}{16}}
-\newlabel{Fig:atck:comp}{{4}{16}}
-\newlabel{Fig:atq:rot:curve}{{4.5}{16}}
-\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Rotation Attack Results}}{16}}
-\newlabel{Fig:atq:rot}{{5}{16}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {4.6}Evaluation of the embeddings}{16}}
-\newlabel{sub:roc}{{4.6}{16}}
+\newlabel{Fig:atq:lsb:curve}{{6(a)}{18}}
+\newlabel{sub@Fig:atq:lsb:curve}{{(a)}{18}}
+\newlabel{Fig:atq:ci2:curve}{{6(b)}{18}}
+\newlabel{sub@Fig:atq:ci2:curve}{{(b)}{18}}
+\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces LSB Modifications}}{18}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {LSB erasing effects}}}{18}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Applying algorithm twice}}}{18}}
+\newlabel{Fig:atq:lsb}{{6}{18}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.6}Evaluation of the embeddings}{18}}
+\newlabel{sub:roc}{{4.6}{18}}
+\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces ROC Curves for DWT or DCT Embeddings}}{18}}
+\newlabel{fig:roc:dwt}{{7}{18}}
 \citation{bfg13:ip}
-\newlabel{Fig:atq:lsb:curve}{{6(a)}{17}}
-\newlabel{sub@Fig:atq:lsb:curve}{{(a)}{17}}
-\newlabel{Fig:atq:ci2:curve}{{6(b)}{17}}
-\newlabel{sub@Fig:atq:ci2:curve}{{(b)}{17}}
-\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces LSB Modifications}}{17}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {LSB erasing effects}}}{17}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Applying algorithm twice}}}{17}}
-\newlabel{Fig:atq:lsb}{{6}{17}}
-\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces ROC Curves for DWT or DCT Embeddings}}{17}}
-\newlabel{fig:roc:dwt}{{7}{17}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {4.7}Lyapunov evaluation of $\mathcal  {CIS}_2$}{17}}
-\newlabel{sec:lyapCIS2}{{4.7}{17}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.7.1}A topological semi-conjugacy between $\mathcal  {X}_2$ and $\mathds  {R}$}{18}}
-\newlabel{sec:topological-semiconjugacy}{{4.7.1}{18}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{21}{}}{18}}
-\newlabel{def:psi-function}{{21}{18}}
-\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Some values for $\psi $\nobreakspace  {}(see Definition\nobreakspace  {}21\hbox {}).}}{18}}
-\newlabel{tablePsi}{{2}{18}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{22}{}}{18}}
 \citation{bfg13:ip}
 \citation{bfg13:ip}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.7}Lyapunov evaluation of $\mathcal  {CIS}_2$}{19}}
+\newlabel{sec:lyapCIS2}{{4.7}{19}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.7.1}A topological semi-conjugacy between $\mathcal  {X}_2$ and $\mathds  {R}$}{19}}
+\newlabel{sec:topological-semiconjugacy}{{4.7.1}{19}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{21}{}}{19}}
+\newlabel{def:psi-function}{{21}{19}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{22}{}}{19}}
 \citation{bfg13:ip}
-\@writefile{thm}{\contentsline {Def}{{Definition}{23}{}}{19}}
-\newlabel{def:e et s}{{23}{19}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{24}{}}{19}}
-\newlabel{def:function-g-on-R}{{24}{19}}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Some values for $\psi $\nobreakspace  {}(see Definition\nobreakspace  {}21\hbox {}).}}{20}}
+\newlabel{tablePsi}{{2}{20}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{23}{}}{20}}
+\newlabel{def:e et s}{{23}{20}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{24}{}}{20}}
+\newlabel{def:function-g-on-R}{{24}{20}}
 \citation{bfg13:ip}
 \citation{bfg13:ip}
 \citation{bfg13:ip}
+\@writefile{thm}{\contentsline {Def}{{Definition}{25}{}}{21}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{7}{}}{21}}
+\@writefile{thm}{\contentsline {Th}{{Theorem}{3}{}}{21}}
 \citation{bfg13:ip}
-\@writefile{thm}{\contentsline {Def}{{Definition}{25}{}}{20}}
-\@writefile{thm}{\contentsline {Prop}{{Proposition}{7}{}}{20}}
-\@writefile{thm}{\contentsline {Th}{{Theorem}{3}{}}{20}}
 \citation{Formenti1998}
 \citation{bfg13:ip}
 \citation{bfg13:ip}
 \citation{bfg13:ip}
-\@writefile{thm}{\contentsline {Prop}{{Proposition}{8}{}}{21}}
-\newlabel{Prop:derivabilite-de-g}{{8}{21}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.7.2}Topological security of $\mathcal  {CIS}_2$ on $\mathds  {R}$}{21}}
-\newlabel{section:topo-secu-cis2-R}{{4.7.2}{21}}
-\@writefile{thm}{\contentsline {Th}{{Theorem}{4}{}}{21}}
-\newlabel{theo:chaos-and-fineness}{{4}{21}}
-\@writefile{thm}{\contentsline {Th}{{Theorem}{5}{}}{21}}
-\newlabel{th:cis2-topo-order}{{5}{21}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{8}{}}{22}}
+\newlabel{Prop:derivabilite-de-g}{{8}{22}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.7.2}Topological security of $\mathcal  {CIS}_2$ on $\mathds  {R}$}{22}}
+\newlabel{section:topo-secu-cis2-R}{{4.7.2}{22}}
+\@writefile{thm}{\contentsline {Th}{{Theorem}{4}{}}{22}}
+\newlabel{theo:chaos-and-fineness}{{4}{22}}
+\@writefile{thm}{\contentsline {Th}{{Theorem}{5}{}}{22}}
+\newlabel{th:cis2-topo-order}{{5}{22}}
 \citation{bfg13:ip}
 \citation{gfb10:ip}
 \citation{Cayre2008}
@@ -253,90 +261,90 @@
 \citation{DBLP:conf/mmsec/FridrichPK07}
 \citation{DBLP:conf/ih/KimDR06}
 \citation{DBLP:conf/ih/PevnyFB10}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.7.3}Evaluation of the Lyapunov exponent}{22}}
-\newlabel{section:lyapunov-exponent-evaluation}{{4.7.3}{22}}
-\@writefile{thm}{\contentsline {Th}{{Theorem}{6}{}}{22}}
-\@writefile{thm}{\contentsline {Rem}{{Rem}{1}{}}{22}}
-\@writefile{toc}{\contentsline {section}{\numberline {5}The $\mathcal  {DI}_3$ Steganographic Process}{22}}
-\newlabel{di3sec}{{5}{22}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Mathematical definitions and notations}{22}}
-\newlabel{sec:math-def}{{5.1}{22}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.7.3}Evaluation of the Lyapunov exponent}{23}}
+\newlabel{section:lyapunov-exponent-evaluation}{{4.7.3}{23}}
+\@writefile{thm}{\contentsline {Th}{{Theorem}{6}{}}{23}}
+\@writefile{thm}{\contentsline {Rem}{{Rem}{1}{}}{23}}
+\@writefile{toc}{\contentsline {section}{\numberline {5}The $\mathcal  {DI}_3$ Steganographic Process}{23}}
+\newlabel{di3sec}{{5}{23}}
 \citation{bcfg12a:ip}
 \citation{bcfg12b:ip}
 \citation{bcfg12a:ip}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Mathematical definitions and notations}{24}}
+\newlabel{sec:math-def}{{5.1}{24}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{26}{}}{24}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{27}{}}{24}}
+\newlabel{def:injective-sequence}{{27}{24}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}The new $\mathcal  {DI}_3$ process}{24}}
+\newlabel{sec:new-process-di-1}{{5.2}{24}}
+\@writefile{thm}{\contentsline {Rem}{{Rem}{2}{}}{24}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{28}{$\mathcal {DI}_3$ Data hiding scheme}}{24}}
+\newlabel{def:process-DI-1}{{28}{24}}
 \citation{bcfg12a:ip}
-\@writefile{thm}{\contentsline {Def}{{Definition}{26}{}}{23}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{27}{}}{23}}
-\newlabel{def:injective-sequence}{{27}{23}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}The new $\mathcal  {DI}_3$ process}{23}}
-\newlabel{sec:new-process-di-1}{{5.2}{23}}
-\@writefile{thm}{\contentsline {Rem}{{Rem}{2}{}}{23}}
-\@writefile{thm}{\contentsline {Def}{{Definition}{28}{$\mathcal {DI}_3$ Data hiding scheme}}{23}}
-\newlabel{def:process-DI-1}{{28}{23}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Security study}{23}}
-\@writefile{thm}{\contentsline {Prop}{{Proposition}{9}{}}{23}}
 \citation{junod1999cryptographic}
 \citation{prng-Blum-goldwasser}
 \citation{Jenkins1996}
 \citation{bcfg12a:ip}
 \citation{bcfg12b:ip}
 \citation{bcfg12a:ip}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Security study}{25}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{9}{}}{25}}
 \citation{bcfg12a:ip}
 \citation{bcfg12b:ip}
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Implementing the $\mathcal  {DI}_3$ scheme}{24}}
 \citation{bcfg12a:ip}
 \citation{DBLP:conf/ih/SolankiSM07}
 \citation{DBLP:conf/ih/PevnyFB10}
 \citation{DBLP:conf/mmsec/FridrichPK07}
 \citation{bcfg12a:ip}
-\@writefile{thm}{\contentsline {Rem}{{Rem}{3}{}}{25}}
-\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces $strategy(N,P,\lambda )$}}{25}}
-\newlabel{algo:strategy}{{1}{25}}
 \citation{DBLP:conf/ih/BasFP11}
 \citation{bcfg12a:ip}
 \citation{holmes11,ensemble11}
 \citation{DBLP:conf/ih/BasFP11}
 \citation{bcfg12a:ip}
-\citation{bcfg12a:ip}
-\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces $embed(LSC, M, S, \lambda )$}}{26}}
-\newlabel{algo:embed}{{2}{26}}
-\@writefile{loa}{\contentsline {algocf}{\numberline {3}{\ignorespaces $extract(LSC, S, \lambda ,P)$}}{26}}
-\newlabel{algo:extract}{{3}{26}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Implementing the $\mathcal  {DI}_3$ scheme}{26}}
+\@writefile{thm}{\contentsline {Rem}{{Rem}{3}{}}{26}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {5.5}Evaluation against steganalyzers}{26}}
 \newlabel{section:steganalysis}{{5.5}{26}}
+\citation{bcfg12a:ip}
 \citation{bcfg12b:ip}
 \citation{DBLP:conf/ih/BasFP11}
+\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces $strategy(N,P,\lambda )$}}{27}}
+\newlabel{algo:strategy}{{1}{27}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces $embed(LSC, M, S, \lambda )$}}{27}}
+\newlabel{algo:embed}{{2}{27}}
 \citation{bcfg12b:ip}
 \citation{bcfg12b:ip}
-\@writefile{loa}{\contentsline {algocf}{\numberline {4}{\ignorespaces $significationFunction(H)$}}{27}}
-\newlabel{algo:signification-function}{{4}{27}}
-\newlabel{algo:build-function}{{5}{27}}
-\@writefile{loa}{\contentsline {algocf}{\numberline {5}{\ignorespaces $buildFunction(MSC,PC,LSC)$ )}}{27}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.6}Robustness study}{27}}
-\newlabel{sec:robustness-study}{{5.6}{27}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {3}{\ignorespaces $extract(LSC, S, \lambda ,P)$}}{28}}
+\newlabel{algo:extract}{{3}{28}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {4}{\ignorespaces $significationFunction(H)$}}{28}}
+\newlabel{algo:signification-function}{{4}{28}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.6}Robustness study}{28}}
+\newlabel{sec:robustness-study}{{5.6}{28}}
 \citation{Fridrich:2009:SDM:1721894}
 \citation{DBLP:conf/ih/SolankiSM07}
 \citation{SSM09}
-\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Steganalysis results of HugoBreakers steganalyser applied on steganographic scheme}}{28}}
-\newlabel{table:holme}{{3}{28}}
-\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion}{28}}
-\@writefile{toc}{\contentsline {section}{\numberline {7}Appendix}{28}}
-\newlabel{AppendixIH}{{7}{28}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}YASS}{28}}
+\newlabel{algo:build-function}{{5}{29}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {5}{\ignorespaces $buildFunction(MSC,PC,LSC)$ )}}{29}}
+\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Steganalysis results of HugoBreakers steganalyser applied on steganographic scheme}}{29}}
+\newlabel{table:holme}{{3}{29}}
+\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion}{29}}
+\@writefile{toc}{\contentsline {section}{\numberline {7}Appendix}{29}}
+\newlabel{AppendixIH}{{7}{29}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}YASS}{29}}
 \citation{DBLP:conf/mmsec/FridrichPK07}
 \citation{DBLP:conf/ih/Westfeld01}
-\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Robustness of $\mathcal  {DI}_3$ scheme facing several attacks (50 images from the BOSS repository)}}{29}}
-\newlabel{fig:robustness-results}{{8}{29}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}nsF5}{29}}
+\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Robustness of $\mathcal  {DI}_3$ scheme facing several attacks (50 images from the BOSS repository)}}{30}}
+\newlabel{fig:robustness-results}{{8}{30}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}nsF5}{31}}
 \citation{DBLP:conf/ih/KimDR06}
 \citation{DBLP:conf/ih/KimDR06}
 \citation{DBLP:conf/ih/PevnyFB10}
 \citation{DBLP:journals/tifs/PevnyBF10}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}MMx}{32}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.4}HUGO}{32}}
 \bibstyle{plain}
 \bibdata{mabase}
 \bibcite{bcfg12a:ip}{1}
-\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}MMx}{31}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {7.4}HUGO}{31}}
 \bibcite{bcfg12b:ip}{2}
 \bibcite{bcfg+13:ip}{3}
 \bibcite{bcg11b:ip}{4}