abstract, conclusion

diff --git a/IH/ciw1.tex b/IH/ciw1.tex
index 1a07a763432cd0f01fff1fce6fc5f1fbd539a2d9..6c9a61889979a092c192fc2226f79c45935bb889 100644 (file)
--- 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 5e874985bdd3f12dbca18f532da6f556be699173..e720b401114d950870e50d9c062b0cc665391c23 100644 (file)
--- 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 6938df26ec11ca7ed19cdadd45ad9b57902a9b37..e04a9919381e6f3f076d8379bc32d370b220c5d7 100644 (file)
--- 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 \r
 $\llbracket0;N\rrbracket$ 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}.
 \r
 % Furthermore, the following definitions will be used in this document.\r
 % \r

diff --git a/article.aux b/article.aux
index e2ec2a79104d5ef4e798c8f23c1925a90c0d55dd..37412ed6d9f16a48059069768b5156b127b1470a 100644 (file)
--- a/article.aux
+++ b/article.aux
@@ -1,83 +1,74 @@
 \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}{2}}
-\newlabel{sec:introduction}{{1}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
+\newlabel{sec:introduction}{{1}{1}}
 \citation{gfb10:ip}
 \citation{Guyeux2012}
 \citation{Guyeux2012}
 \citation{Devaney}
-\@writefile{toc}{\contentsline {section}{\numberline {2}Notations and Terminologies}{3}}
-\newlabel{not}{{2}{3}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Notations and Terminologies}{2}}
+\newlabel{not}{{2}{2}}
 \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}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}The mathematical theory of chaos}{3}}
+\@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}}
 \citation{guyeux10}
 \citation{Devaney}
 \citation{guyeux10}
 \citation{guyeux10}
+\@writefile{thm}{\contentsline {Def}{{Definition}{6}{}}{4}}
+\newlabel{Def:chaotic iterations}{{6}{4}}
+\newlabel{Gf}{{1}{4}}
+\@writefile{thm}{\contentsline {Th}{{Theorem}{1}{}}{4}}
 \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}
 \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}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}The $\mathcal  {CIW}_1$ Chaotic Iteration based Watermarking Process}{5}}
+\newlabel{sec:ciw1}{{3}{5}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Using chaotic iterations as information hiding schemes}{5}}
+\newlabel{sec:data-hiding-algo-chaotic iterations}{{3.1}{5}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.1}Presentation of the dhCI process}{5}}
+\@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{guyeux10ter}
+\@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{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}
 \citation{Shujun1}
+\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}}
 \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}
 \citation{Perez-Freire06}
 \citation{Kalker2001,ComesanaPP05bis}
@@ -85,48 +76,49 @@
 \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}}
+\newlabel{eq:PLCM-for-strategy}{{3.1.4}{8}}
+\newlabel{sec:cids-example}{{3.1.4}{8}}
+\@writefile{toc}{\contentsline {paragraph}{CIDS strategy}{8}}
+\@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}}
 \citation{Kalker2001}
 \citation{Simmons83}
 \citation{Cayre2008}
 \citation{Cayre2008}
 \citation{Cachin2004}
+\@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}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{13}{}}{9}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{14}{}}{9}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{15}{}}{9}}
+\@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}}
 \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}
 \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}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Security evaluation}{10}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.1}Evaluation of the stego-security}{10}}
+\newlabel{sec:stego-security-proof}{{3.3.1}{10}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{1}{}}{10}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.2}Evaluation of the topological security}{10}}
+\newlabel{sec:topological security-evaluation}{{3.3.2}{10}}
+\@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}}
 \citation{bfg12:ip}
 \citation{Guyeux2012}
 \citation{gfb10:ip}
@@ -135,120 +127,120 @@
 \citation{fgb11:ip}
 \citation{gfb10:ip}
 \citation{fgb11:ip}
-\@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 {3.5}Lyapunov exponent evaluation}{11}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}The $\mathcal  {CIS}_2$ Chaotic Iteration based Steganographic Process}{11}}
+\newlabel{sec:secrypt11}{{4}{11}}
+\citation{fgb11:ip}
+\citation{fgb11:ip}
+\citation{fgb11:ip}
 \@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}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{19}{}}{12}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{20}{}}{12}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Security study of the $\mathcal  {CIS}_2$}{12}}
+\citation{fgb11:ip}
+\citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
 \citation{fgb11:ip}
-\@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}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.2}Topological security}{13}}
+\@writefile{toc}{\contentsline {paragraph}{Topological model}{13}}
+\@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}}
 \citation{bcfg+13:ip}
-\@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}}
+\citation{bcfg+13:ip}
+\citation{rifq/others03}
 \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}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Correctness and completeness studies}{14}}
+\newlabel{sub:ci2:discussion}{{4.3}{14}}
+\@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{bcfg+13:ip}
 \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}{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}}
+\@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}}
 \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}}
+\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}}
 \citation{bcfg+13:ip}
-\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}}
+\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{toc}{\contentsline {subsection}{\numberline {4.6}Evaluation of the embeddings}{17}}
+\newlabel{sub:roc}{{4.6}{17}}
+\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces ROC Curves for DWT or DCT Embeddings}}{17}}
+\newlabel{fig:roc:dwt}{{7}{17}}
 \citation{bfg13:ip}
 \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}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.7}Lyapunov evaluation of $\mathcal  {CIS}_2$}{18}}
+\newlabel{sec:lyapCIS2}{{4.7}{18}}
+\@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{thm}{\contentsline {Def}{{Definition}{22}{}}{18}}
 \citation{bfg13:ip}
-\@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}}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Some values for $\psi $\nobreakspace  {}(see Definition\nobreakspace  {}21\hbox {}).}}{19}}
+\newlabel{tablePsi}{{2}{19}}
+\@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}}
 \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}}
+\@writefile{thm}{\contentsline {Def}{{Definition}{25}{}}{20}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{7}{}}{20}}
+\@writefile{thm}{\contentsline {Th}{{Theorem}{3}{}}{20}}
 \citation{bfg13:ip}
 \citation{Formenti1998}
 \citation{bfg13:ip}
 \citation{bfg13:ip}
 \citation{bfg13:ip}
-\@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}}
+\@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}}
 \citation{bfg13:ip}
 \citation{gfb10:ip}
 \citation{Cayre2008}
@@ -261,25 +253,25 @@
 \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}{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}}
+\@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}}
 \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}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Mathematical definitions and notations}{23}}
+\newlabel{sec:math-def}{{5.1}{23}}
+\@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}}
 \citation{bcfg12a:ip}
 \citation{junod1999cryptographic}
 \citation{prng-Blum-goldwasser}
@@ -287,8 +279,8 @@
 \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}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Security study}{24}}
+\@writefile{thm}{\contentsline {Prop}{{Proposition}{9}{}}{24}}
 \citation{bcfg12a:ip}
 \citation{bcfg12b:ip}
 \citation{bcfg12a:ip}
@@ -301,53 +293,53 @@
 \citation{holmes11,ensemble11}
 \citation{DBLP:conf/ih/BasFP11}
 \citation{bcfg12a:ip}
-\@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}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Implementing the $\mathcal  {DI}_3$ scheme}{25}}
+\@writefile{thm}{\contentsline {Rem}{{Rem}{3}{}}{25}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.5}Evaluation against steganalyzers}{25}}
+\newlabel{section:steganalysis}{{5.5}{25}}
 \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}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces $strategy(N,P,\lambda )$}}{26}}
+\newlabel{algo:strategy}{{1}{26}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces $embed(LSC, M, S, \lambda )$}}{26}}
+\newlabel{algo:embed}{{2}{26}}
 \citation{bcfg12b:ip}
 \citation{bcfg12b:ip}
-\@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}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {3}{\ignorespaces $extract(LSC, S, \lambda ,P)$}}{27}}
+\newlabel{algo:extract}{{3}{27}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {4}{\ignorespaces $significationFunction(H)$}}{27}}
+\newlabel{algo:signification-function}{{4}{27}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.6}Robustness study}{27}}
+\newlabel{sec:robustness-study}{{5.6}{27}}
 \citation{Fridrich:2009:SDM:1721894}
+\newlabel{algo:build-function}{{5}{28}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {5}{\ignorespaces $buildFunction(MSC,PC,LSC)$ )}}{28}}
+\@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}}
 \citation{DBLP:conf/ih/SolankiSM07}
 \citation{SSM09}
-\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{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 {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)}}{30}}
-\newlabel{fig:robustness-results}{{8}{30}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}nsF5}{31}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}nsF5}{30}}
 \citation{DBLP:conf/ih/KimDR06}
 \citation{DBLP:conf/ih/KimDR06}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}MMx}{31}}
 \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}
 \bibcite{bcfg12b:ip}{2}
 \bibcite{bcfg+13:ip}{3}
 \bibcite{bcg11b:ip}{4}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.4}HUGO}{32}}
 \bibcite{bfg12:ip}{5}
 \bibcite{bfg13:ip}{6}
 \bibcite{bg10b:ip}{7}

diff --git a/article.log b/article.log
index e364bdac05c7e02faf12f1c00751d0a306bfb5c0..00e631334b7d4ba426eb4a9f364bcc1bc828482e 100644 (file)
--- 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.
 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 [3]
+(./IH/notations.tex [2]
 LaTeX Font Info:    Try loading font information for U+dsrom on input line 49.
 
 (/usr/share/texlive/texmf-dist/tex/latex/doublestroke/Udsrom.fd
@@ -688,7 +685,7 @@ LaTeX Font Info:    Try loading font information for OT1+lmss on input line 100
 
 (/usr/share/texmf/tex/latex/lm/ot1lmss.fd
 File: ot1lmss.fd 2009/10/30 v1.6 Font defs for Latin Modern
-) [4]
+) [3]
 LaTeX Font Info:    Try loading font information for OMS+lmr on input line 166.
 
 
@@ -705,34 +702,34 @@ 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-
  []
 
-[5]
-Overfull \hbox (7.38942pt too wide) in paragraph at lines 51--62
+[4]
+Overfull \hbox (7.38942pt too wide) in paragraph at lines 58--69
 []\T1/lmr/m/it/10 Let us con-sider a set of grayscale im-ages stored into porta
 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] <IH/img/lena512.pdf, id=50, 514.92375pt x 514.92375pt>
+(Font)              Font shape `OMS/lmsy/m/n' tried instead on input line 76.
+[5] <IH/img/lena512.pdf, id=42, 514.92375pt x 514.92375pt>
 File: IH/img/lena512.pdf Graphic file (type pdf)
 
 <use IH/img/lena512.pdf>
-Package pdftex.def Info: IH/img/lena512.pdf used on input line 95.
+Package pdftex.def Info: IH/img/lena512.pdf used on input line 102.
 (pdftex.def)             Requested size: 106.69783pt x 106.69147pt.
 
-<IH/img/lena_msb_678.pdf, id=51, 514.92375pt x 514.92375pt>
+<IH/img/lena_msb_678.pdf, id=43, 514.92375pt x 514.92375pt>
 File: IH/img/lena_msb_678.pdf Graphic file (type pdf)
 
 <use IH/img/lena_msb_678.pdf>
-Package pdftex.def Info: IH/img/lena_msb_678.pdf used on input line 100.
+Package pdftex.def Info: IH/img/lena_msb_678.pdf used on input line 107.
 (pdftex.def)             Requested size: 106.69783pt x 106.69147pt.
 
-<IH/img/lena_lsb_1234_facteur17.pdf, id=52, 514.92375pt x 514.92375pt>
+<IH/img/lena_lsb_1234_facteur17.pdf, id=44, 514.92375pt x 514.92375pt>
 File: IH/img/lena_lsb_1234_facteur17.pdf Graphic file (type pdf)
 
 <use IH/img/lena_lsb_1234_facteur17.pdf>
 Package pdftex.def Info: IH/img/lena_lsb_1234_facteur17.pdf used on input line 
-106.
+113.
 (pdftex.def)             Requested size: 106.69783pt x 106.69147pt.
 Package epstopdf Info: Source file: <IH/Medias/lena512.eps>
 (epstopdf)                    date: 2013-10-27 21:33:40
@@ -742,30 +739,30 @@ Package epstopdf Info: Source file: <IH/Medias/lena512.eps>
 (epstopdf)                    size: 61882 bytes
 (epstopdf)             Command: <repstopdf --outfile=IH/Medias/lena512-eps-conv
 erted-to.pdf IH/Medias/lena512.eps>
-(epstopdf)             \includegraphics on input line 142.
+(epstopdf)             \includegraphics on input line 149.
 Package epstopdf Info: Output file is already uptodate.
 
-<IH/Medias/lena512-eps-converted-to.pdf, id=53, 514.92375pt x 514.92375pt>
+<IH/Medias/lena512-eps-converted-to.pdf, id=45, 514.92375pt x 514.92375pt>
 File: IH/Medias/lena512-eps-converted-to.pdf Graphic file (type pdf)
 
 <use IH/Medias/lena512-eps-converted-to.pdf>
 Package pdftex.def Info: IH/Medias/lena512-eps-converted-to.pdf used on input l
-ine 142.
+ine 149.
 (pdftex.def)             Requested size: 113.81102pt x 113.81pt.
 
-<IH/iihmsp13/exp/invader.png, id=54, 64.24pt x 64.24pt>
+<IH/iihmsp13/exp/invader.png, id=46, 64.24pt x 64.24pt>
 File: IH/iihmsp13/exp/invader.png Graphic file (type png)
 
 <use IH/iihmsp13/exp/invader.png>
-Package pdftex.def Info: IH/iihmsp13/exp/invader.png used on input line 143.
+Package pdftex.def Info: IH/iihmsp13/exp/invader.png used on input line 150.
 (pdftex.def)             Requested size: 28.45274pt x 28.4529pt.
 
-Underfull \hbox (badness 10000) in paragraph at lines 143--143
+Underfull \hbox (badness 10000) in paragraph at lines 150--150
 []\T1/lmr/m/n/8 (b)
  []
 
 
-Underfull \hbox (badness 10000) in paragraph at lines 143--143
+Underfull \hbox (badness 10000) in paragraph at lines 150--150
 \T1/lmr/m/n/8 Wa-ter-
  []
 
@@ -778,85 +775,85 @@ o.pdf>
 (epstopdf)                    size: 61881 bytes
 (epstopdf)             Command: <repstopdf --outfile=IH/Medias/lena512marqueDWT
 -eps-converted-to.pdf IH/Medias/lena512marqueDWT.eps>
-(epstopdf)             \includegraphics on input line 144.
+(epstopdf)             \includegraphics on input line 151.
 Package epstopdf Info: Output file is already uptodate.
 
-<IH/Medias/lena512marqueDWT-eps-converted-to.pdf, id=55, 514.92375pt x 514.9237
+<IH/Medias/lena512marqueDWT-eps-converted-to.pdf, id=47, 514.92375pt x 514.9237
 5pt>
 File: IH/Medias/lena512marqueDWT-eps-converted-to.pdf Graphic file (type pdf)
  <use IH/Medias/lena512marqueDWT-eps-converted-to.pdf>
 Package pdftex.def Info: IH/Medias/lena512marqueDWT-eps-converted-to.pdf used o
-n input line 144.
+n input line 151.
 (pdftex.def)             Requested size: 113.81102pt x 113.81pt.
 
 
 LaTeX Warning: `!h' float specifier changed to `!ht'.
 
-[7 <./IH/img/lena512.pdf> <./IH/img/lena_msb_678.pdf> <./IH/img/lena_lsb_1234_f
+[6 <./IH/img/lena512.pdf> <./IH/img/lena_msb_678.pdf> <./IH/img/lena_lsb_1234_f
 acteur17.pdf>]
-Overfull \hbox (7.57658pt too wide) in paragraph at lines 175--176
+Overfull \hbox (7.57658pt too wide) in paragraph at lines 182--183
  \T1/lmr/bx/n/10 CIIS strat-egy[] \T1/lmr/m/n/10 Let us first in-tro-duce the P
 iece-wise Lin-ear Chaotic Map (PLCM,
  []
 
-[8 <./IH/Medias/lena512-eps-converted-to.pdf> <./IH/iihmsp13/exp/invader.png (P
-NG copy)> <./IH/Medias/lena512marqueDWT-eps-converted-to.pdf>] [9] [10]
-[11]) (./IH/cis2.tex [12]
+[7 <./IH/Medias/lena512-eps-converted-to.pdf> <./IH/iihmsp13/exp/invader.png (P
+NG copy)> <./IH/Medias/lena512marqueDWT-eps-converted-to.pdf>] [8] [9] [10])
+(./IH/cis2.tex [11]
 Overfull \hbox (4.41489pt too wide) in paragraph at lines 87--95
 []\T1/lmr/m/n/10 The in-for-ma-tion hid-ing scheme pub-lished in [20] was for-m
 erly called Steganog-
  []
 
-[13] [14] [15] <IH/iihmsp13/exp/atq-dec.png, id=106, 578.16pt x 433.62pt>
+[12] [13] [14] <IH/iihmsp13/exp/atq-dec.png, id=99, 578.16pt x 433.62pt>
 File: IH/iihmsp13/exp/atq-dec.png Graphic file (type png)
 
 <use IH/iihmsp13/exp/atq-dec.png>
 Package pdftex.def Info: IH/iihmsp13/exp/atq-dec.png used on input line 376.
 (pdftex.def)             Requested size: 172.5pt x 129.37242pt.
 
-<IH/iihmsp13/exp/atq-jpg.png, id=107, 578.16pt x 433.62pt>
+<IH/iihmsp13/exp/atq-jpg.png, id=100, 578.16pt x 433.62pt>
 File: IH/iihmsp13/exp/atq-jpg.png Graphic file (type png)
 
 <use IH/iihmsp13/exp/atq-jpg.png>
 Package pdftex.def Info: IH/iihmsp13/exp/atq-jpg.png used on input line 398.
 (pdftex.def)             Requested size: 155.24895pt x 116.43716pt.
 
-<IH/iihmsp13/exp/atq-jp2.png, id=108, 578.16pt x 433.62pt>
+<IH/iihmsp13/exp/atq-jp2.png, id=101, 578.16pt x 433.62pt>
 File: IH/iihmsp13/exp/atq-jp2.png Graphic file (type png)
 
 <use IH/iihmsp13/exp/atq-jp2.png>
 Package pdftex.def Info: IH/iihmsp13/exp/atq-jp2.png used on input line 400.
 (pdftex.def)             Requested size: 155.24895pt x 116.43716pt.
- [16 <./IH/iihmsp13/exp/atq-dec.png>]
-<IH/iihmsp13/exp/atq-rot.png, id=113, 578.16pt x 433.62pt>
+ [15 <./IH/iihmsp13/exp/atq-dec.png>]
+<IH/iihmsp13/exp/atq-rot.png, id=106, 578.16pt x 433.62pt>
 File: IH/iihmsp13/exp/atq-rot.png Graphic file (type png)
 
 <use IH/iihmsp13/exp/atq-rot.png>
 Package pdftex.def Info: IH/iihmsp13/exp/atq-rot.png used on input line 418.
 (pdftex.def)             Requested size: 172.5pt x 129.37242pt.
- [17 <./IH/iihmsp13/exp/atq-jpg.png> <./IH/iihmsp13/exp/atq-jp2.png> <./IH/iihm
+ [16 <./IH/iihmsp13/exp/atq-jpg.png> <./IH/iihmsp13/exp/atq-jp2.png> <./IH/iihm
 sp13/exp/atq-rot.png>]
-<IH/iihmsp13/exp/atq-lsb.png, id=120, 578.16pt x 433.62pt>
+<IH/iihmsp13/exp/atq-lsb.png, id=113, 578.16pt x 433.62pt>
 File: IH/iihmsp13/exp/atq-lsb.png Graphic file (type png)
 
 <use IH/iihmsp13/exp/atq-lsb.png>
 Package pdftex.def Info: IH/iihmsp13/exp/atq-lsb.png used on input line 444.
 (pdftex.def)             Requested size: 155.24895pt x 116.43716pt.
 
-<IH/iihmsp13/exp/atq-ci2.png, id=121, 578.16pt x 433.62pt>
+<IH/iihmsp13/exp/atq-ci2.png, id=114, 578.16pt x 433.62pt>
 File: IH/iihmsp13/exp/atq-ci2.png Graphic file (type png)
 
 <use IH/iihmsp13/exp/atq-ci2.png>
 Package pdftex.def Info: IH/iihmsp13/exp/atq-ci2.png used on input line 446.
 (pdftex.def)             Requested size: 155.24895pt x 116.43716pt.
 
-<IH/iihmsp13/exp/ROC.png, id=122, 578.16pt x 433.62pt>
+<IH/iihmsp13/exp/ROC.png, id=115, 578.16pt x 433.62pt>
 File: IH/iihmsp13/exp/ROC.png Graphic file (type png)
 
 <use IH/iihmsp13/exp/ROC.png>
 Package pdftex.def Info: IH/iihmsp13/exp/ROC.png used on input line 465.
 (pdftex.def)             Requested size: 172.5pt x 129.37242pt.
- [18 <./IH/iihmsp13/exp/atq-lsb.png> <./IH/iihmsp13/exp/atq-ci2.png> <./IH/iihm
+ [17 <./IH/iihmsp13/exp/atq-lsb.png> <./IH/iihmsp13/exp/atq-ci2.png> <./IH/iihm
 sp13/exp/ROC.png>]
 
 LaTeX Warning: `h' float specifier changed to `ht'.
@@ -873,12 +870,12 @@ equal to: $\OML/lmm/m/it/10 s \OT1/lmr/m/n/10 = 0\OML/lmm/m/it/10 ;   []  []  [
 ]  []  []  [] []$
  []
 
-[19] [20] [21] [22]) (./IH/di3.tex [23]
+[18] [19] [20] [21]) (./IH/di3.tex [22]
 
 LaTeX Font Warning: Font shape `U/stmry/b/n' undefined
 (Font)              using `U/stmry/m/n' instead on input line 75.
 
-[24] [25]
+[23] [24]
 LaTeX Font Info:    Try loading font information for T1+lmtt on input line 226.
 
  (/usr/share/texmf/tex/latex/lm/t1lmtt.fd
@@ -899,51 +896,54 @@ LaTeX Warning: `h' float specifier changed to `ht'.
 
 LaTeX Warning: `h' float specifier changed to `ht'.
 
-[26] [27] <IH/graphs/atq-jpg.pdf, id=162, 578.16pt x 433.62pt>
+[25] [26] <IH/graphs/atq-jpg.pdf, id=155, 578.16pt x 433.62pt>
 File: IH/graphs/atq-jpg.pdf Graphic file (type pdf)
 
 <use IH/graphs/atq-jpg.pdf>
 Package pdftex.def Info: IH/graphs/atq-jpg.pdf used on input line 404.
 (pdftex.def)             Requested size: 199.16928pt x 149.3741pt.
 
-<IH/graphs/atq-jp2.pdf, id=163, 578.16pt x 433.62pt>
+<IH/graphs/atq-jp2.pdf, id=156, 578.16pt x 433.62pt>
 File: IH/graphs/atq-jp2.pdf Graphic file (type pdf)
 
 <use IH/graphs/atq-jp2.pdf>
 Package pdftex.def Info: IH/graphs/atq-jp2.pdf used on input line 410.
 (pdftex.def)             Requested size: 199.16928pt x 149.3741pt.
 
-<IH/graphs/atq-dec.pdf, id=164, 578.16pt x 433.62pt>
+<IH/graphs/atq-dec.pdf, id=157, 578.16pt x 433.62pt>
 File: IH/graphs/atq-dec.pdf Graphic file (type pdf)
 
 <use IH/graphs/atq-dec.pdf>
 Package pdftex.def Info: IH/graphs/atq-dec.pdf used on input line 416.
 (pdftex.def)             Requested size: 199.16928pt x 149.3741pt.
 
-<IH/graphs/atq-rot.pdf, id=165, 578.16pt x 433.62pt>
+<IH/graphs/atq-rot.pdf, id=158, 578.16pt x 433.62pt>
 File: IH/graphs/atq-rot.pdf Graphic file (type pdf)
 
 <use IH/graphs/atq-rot.pdf>
 Package pdftex.def Info: IH/graphs/atq-rot.pdf used on input line 422.
 (pdftex.def)             Requested size: 199.16928pt x 149.3741pt.
- [28]) (./IH/conclusion.tex) (./IH/wellKnown.tex
-[29] [30 <./IH/graphs/atq-jpg.pdf> <./IH/graphs/atq-jp2.pdf> <./IH/graphs/atq-d
-ec.pdf> <./IH/graphs/atq-rot.pdf>] [31] [32]) (./article.bbl [33] [34] [35]
-[36])
+ [27]) (./IH/conclusion.tex) (./IH/wellKnown.tex
+[28] [29 <./IH/graphs/atq-jpg.pdf> <./IH/graphs/atq-jp2.pdf> <./IH/graphs/atq-d
+ec.pdf> <./IH/graphs/atq-rot.pdf>] [30] [31]) (./article.bbl [32] [33] [34]
+[35])
 \tf@thm=\write3
 \openout3 = `article.thm'.
 
- [37] (./article.aux)
+ [36] (./article.aux)
 
 LaTeX Font Warning: Some font shapes were not available, defaults substituted.
 
+
+LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.
+
  ) 
 Here is how much of TeX's memory you used:
- 5767 strings out of 495031
- 77738 string characters out of 6181530
- 156848 words of memory out of 5000000
- 8743 multiletter control sequences out of 15000+600000
- 125203 words of font info for 105 fonts, out of 8000000 for 9000
+ 5753 strings out of 495031
+ 77595 string characters out of 6181530
+ 156845 words of memory out of 5000000
+ 8734 multiletter control sequences out of 15000+600000
+ 116722 words of font info for 98 fonts, out of 8000000 for 9000
  14 hyphenation exceptions out of 8191
  38i,18n,26p,437b,407s stack positions out of 5000i,500n,10000p,200000b,80000s
 {/usr/share/texmf/fonts/enc/dvips/lm/lm-ec.enc}{/usr/share/texmf/fonts/enc/dv
@@ -956,28 +956,26 @@ type1/public/lm/lmbx10.pfb></usr/share/texmf/fonts/type1/public/lm/lmbx12.pfb><
 /usr/share/texmf/fonts/type1/public/lm/lmbx7.pfb></usr/share/texmf/fonts/type1/
 public/lm/lmbx9.pfb></usr/share/texmf/fonts/type1/public/lm/lmex10.pfb></usr/sh
 are/texmf/fonts/type1/public/lm/lmmi10.pfb></usr/share/texmf/fonts/type1/public
-/lm/lmmi5.pfb></usr/share/texmf/fonts/type1/public/lm/lmmi6.pfb></usr/share/tex
-mf/fonts/type1/public/lm/lmmi7.pfb></usr/share/texmf/fonts/type1/public/lm/lmr1
-0.pfb></usr/share/texmf/fonts/type1/public/lm/lmr12.pfb></usr/share/texmf/fonts
-/type1/public/lm/lmr17.pfb></usr/share/texmf/fonts/type1/public/lm/lmr5.pfb></u
-sr/share/texmf/fonts/type1/public/lm/lmr6.pfb></usr/share/texmf/fonts/type1/pub
-lic/lm/lmr7.pfb></usr/share/texmf/fonts/type1/public/lm/lmr8.pfb></usr/share/te
-xmf/fonts/type1/public/lm/lmr9.pfb></usr/share/texmf/fonts/type1/public/lm/lmri
-10.pfb></usr/share/texmf/fonts/type1/public/lm/lmri7.pfb></usr/share/texmf/font
-s/type1/public/lm/lmri9.pfb></usr/share/texmf/fonts/type1/public/lm/lmss10.pfb>
-</usr/share/texmf/fonts/type1/public/lm/lmss8.pfb></usr/share/texmf/fonts/type1
-/public/lm/lmsy10.pfb></usr/share/texmf/fonts/type1/public/lm/lmsy5.pfb></usr/s
-hare/texmf/fonts/type1/public/lm/lmsy7.pfb></usr/share/texmf/fonts/type1/public
-/lm/lmsy9.pfb></usr/share/texmf/fonts/type1/public/lm/lmtt10.pfb></usr/share/te
-xlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb></usr/share/tex
-live/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb></usr/share/texl
-ive/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm7.pfb></usr/share/texliv
-e/texmf-dist/fonts/type1/public/stmaryrd/stmary10.pfb></usr/share/texlive/texmf
--dist/fonts/type1/public/stmaryrd/stmary7.pfb>
-Output written on article.pdf (37 pages, 1170420 bytes).
+/lm/lmmi5.pfb></usr/share/texmf/fonts/type1/public/lm/lmmi7.pfb></usr/share/tex
+mf/fonts/type1/public/lm/lmr10.pfb></usr/share/texmf/fonts/type1/public/lm/lmr1
+2.pfb></usr/share/texmf/fonts/type1/public/lm/lmr17.pfb></usr/share/texmf/fonts
+/type1/public/lm/lmr5.pfb></usr/share/texmf/fonts/type1/public/lm/lmr6.pfb></us
+r/share/texmf/fonts/type1/public/lm/lmr7.pfb></usr/share/texmf/fonts/type1/publ
+ic/lm/lmr8.pfb></usr/share/texmf/fonts/type1/public/lm/lmr9.pfb></usr/share/tex
+mf/fonts/type1/public/lm/lmri10.pfb></usr/share/texmf/fonts/type1/public/lm/lmr
+i7.pfb></usr/share/texmf/fonts/type1/public/lm/lmss10.pfb></usr/share/texmf/fon
+ts/type1/public/lm/lmss8.pfb></usr/share/texmf/fonts/type1/public/lm/lmsy10.pfb
+></usr/share/texmf/fonts/type1/public/lm/lmsy5.pfb></usr/share/texmf/fonts/type
+1/public/lm/lmsy7.pfb></usr/share/texmf/fonts/type1/public/lm/lmtt10.pfb></usr/
+share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb></usr/s
+hare/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb></usr/sh
+are/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm7.pfb></usr/shar
+e/texlive/texmf-dist/fonts/type1/public/stmaryrd/stmary10.pfb></usr/share/texli
+ve/texmf-dist/fonts/type1/public/stmaryrd/stmary7.pfb>
+Output written on article.pdf (36 pages, 1138179 bytes).
 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 db2663a2b25256ac3e567201612bfb08ce2a397a..9434ffd58233d70a29612196209d6161a4afc83f 100644 (file)
Binary files a/article.pdf and b/article.pdf differ

diff --git a/article.thm b/article.thm
index 3ba9dbf1a0d9e1e81db3d21cfe4f2e00daea7b1f..4c754346763ab12b0bedca4ea373a6353a3c0f70 100644 (file)
--- 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}