\section{Quality Studies of an Invisible Chaos-Based Watermarking Scheme with Message Extraction~\cite{bcfg+13:ip}}

In this article published in IIHMSP'13, 9th Int. Conf. on Intelligent Information Hiding and Multimedia Signal Processing,
the steganographic scheme formerly denoted by SCISMM and published in Secrypt 11~\cite{fgb11:ip}
(see Section~\ref{sec:secrypt11}) is evaluated regarding its robustness. 
Following the new name provided in~\cite{bcfg+13:ip}, we will now call it $\mathcal{CI}$
to be coherent with the article we summarize here.

\subsection{Practical considerations regarding the $\mathcal{CI}$ steganographic scheme}
\label{section:process-ci2}
%\input{rcl}

To study the robustness of the $\mathcal{CI}$ algorithm necessitates first 
to discuss about the practical issues of its implementation. We have
firstly emphasizes that the following requirements have to be
satisfied~\cite{bcfg+13:ip}:
\begin{enumerate}
\item The number $l$ of iterations is sufficiently large (see details
below).
\item \label{itm2:Sc} Let  $\Im(S_p)$ be the set 
  $ \{S^1_p, S^2_p, \ldots,  S^l_p\}$ of cardinality $k$, $k \leq l$  (repetitions are removed in a
set).  
  This set contains all the elements of $x$ that have been modified 
  along the iteration process.
  Let us consider $\Im(S_c)_{|D}$ defined by 
  $\{S^{d_1}_c, S^{d_2}_c, \ldots,  S^{d_k}_c\}$
  where 
  $d_i$ is the last iteration that has modified the element $i \in \Im(S_p)$.   
  We require that this set is equal
  to $\llbracket 0 ;\mathsf{P} -1 \rrbracket$.
\end{enumerate}



