-The flowcharts given in Fig.~\ref{fig:sch} summarize our steganography scheme denoted as to
-STABYLO for STeganography with Canny, Bbs, binarY embedding at LOw cost.
-What follows successively details all the inner steps and flow inside
-the embedding stage (Fig.\ref{fig:sch:emb})
-and inside the extraction one (Fig.~\ref{fig:sch:ext}).
-
+The flowcharts given in Fig.~\ref{fig:sch}
+summarize our steganography scheme denoted by
+STABYLO, which stands for STeganography with cAnny, Bbs, binarY embedding at LOw cost.
+What follows are successively details of the inner steps and flows inside
+both the embedding stage (Fig.~\ref{fig:sch:emb})
+and the extraction one (Fig.~\ref{fig:sch:ext}).
+Let us first focus on the data embedding.
\begin{figure*}[t]
\begin{center}
\subfloat[Data Embedding.]{
\begin{minipage}{0.49\textwidth}
\begin{center}
- \includegraphics[width=5cm]{emb.pdf}
- %\includegraphics[width=5cm]{emb.ps}
+ %\includegraphics[width=5cm]{emb.pdf}
+ \includegraphics[scale=0.5]{emb.ps}
\end{center}
\end{minipage}
\label{fig:sch:emb}
\subfloat[Data Extraction.]{
\begin{minipage}{0.49\textwidth}
\begin{center}
- \includegraphics[width=5cm]{rec.pdf}
- %\includegraphics[width=5cm]{rec.ps}
+ %\includegraphics[width=5cm]{rec.pdf}
+ \includegraphics[scale=0.5]{rec.ps}
\end{center}
\end{minipage}
\label{fig:sch:ext}
-\subsection{Data Embedding}
-This section describes the main three steps of the STABYLO data embedding
-scheme.
-
-
-
-\subsubsection{Edge Based Image Steganography}
-
-Edge Based Image Steganography schemes
-already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10} differ
-how they select edge pixels, and
-how they modify these ones.
-Image Quality: Edge Image Steganography
-\JFC{Raphael, les fuzzy edge detection sont souvent utilisés.
- il faudrait comparer les approches en terme de nombre de bits retournés,
- en terme de complexité. } \cite{KF11}
-\RC{Ben, à voir car on peut choisir le nombre de pixel avec Canny. Supposons que les fuzzy edge soient retourne un peu plus de points, on sera probablement plus détectable... Finalement on devrait surement vendre notre truc en : on a choisi cet algo car il est performant en vitesse/qualité. Mais on peut aussi en utilisé d'autres :-)}
-There are many techniques to detect edges in images. Main methods are filter
-edge detection methods such as Sobel or Canny filter, low order methods such as
-first order and second order methods, these methods are based on gradient or
-Laplace operators and fuzzy edge methods, which are based on fuzzy logic to
-highlight edges.
-Of course, all the algorithms have advantages and drawbacks which depend on the
-motivation to highlight edges. Unfortunately unless testing most of the
-algorithms, which would require many times, it is quite difficult to have an
-accurate idea on what would produce such algorithm compared to another. That is
-why we have chosen Canny algorithm which is well known, fast and implementable
-on many kinds of architecture, such as FPGA, smartphone, desktop machines and
-GPU. And of course, we do not pretend that this is the best solution.
+\subsection{Security Considerations}
+Among methods of message encryption/decryption
+(see~\cite{DBLP:journals/ejisec/FontaineG07} for a survey)
+we implement the Blum-Goldwasser cryptosystem~\cite{Blum:1985:EPP:19478.19501}
+that is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82}
+pseudorandom number generator (PRNG) and the
+XOR binary function.
+It has been indeed proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG
+has the property of cryptographical security, \textit{i.e.},
+for any sequence of $L$ output bits $x_i$, $x_{i+1}$, \ldots, $x_{i+L-1}$,
+there is no algorithm, whose time complexity is polynomial in $L$, and
+which allows to find $x_{i-1}$ and $x_{i+L}$ with a probability greater
+than $1/2$.
+Equivalent formulations of such a property can
+be found. They all lead to the fact that,
+even if the encrypted message is extracted,
+it is impossible to retrieve the original one in
+polynomial time.
-In order to be able to compute the same set of edge pixels, we suggest to consider all the bits of the image (cover or stego) without the LSB. With an 8 bits image, only the 7 first bits are considered. In our flowcharts, this is represented by LSB(7 bits Edge Detection).
+Starting thus with a key $k$ and the message \textit{mess} to hide,
+this step computes a message $m$, which is the encrypted version of \textit{mess}.
+
+
+\subsection{Edge-Based Image Steganography}
+
+
+The edge-based image
+steganography schemes
+already presented \cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10} differ
+in how carefully they select edge pixels, and
+how they modify them.
+
+%Image Quality: Edge Image Steganography
+%\JFC{Raphael, les fuzzy edge detection sont souvent utilisés.
+% il faudrait comparer les approches en terme de nombre de bits retournés,
+% en terme de complexité. } \cite{KF11}
+%\RC{Ben, à voir car on peut choisir le nombre de pixel avec Canny. Supposons que les fuzzy edge soient retourne un peu plus de points, on sera probablement plus détectable... Finalement on devrait surement vendre notre truc en : on a choisi cet algo car il est performant en vitesse/qualité. Mais on peut aussi en utilisé d'autres :-)}
+
+Many techniques have been proposed in the literature to detect
+edges in images (whose noise has been initially reduced).
+They can be separated in two categories: first and second order detection
+methods on the one hand, and fuzzy detectors on the other hand~\cite{KF11}.
+In first order methods like Sobel, Canny~\cite{Canny:1986:CAE:11274.11275}, \ldots,
+a first-order derivative (gradient magnitude, etc.) is computed
+to search for local maxima, whereas in second order ones, zero crossings in a second-order derivative, like the Laplacian computed from the image,
+are searched in order to find edges.
+As for as fuzzy edge methods are concerned, they are obviously based on fuzzy logic to highlight edges.
+
+Canny filters, on their parts, are an old family of algorithms still remaining a state-of-the-art edge detector. They can be well approximated by first-order derivatives of Gaussians.
+As the Canny algorithm is well known and studied, fast, and implementable
+on many kinds of architectures like FPGAs, smartphones, desktop machines, and
+GPUs, we have chosen this edge detector for illustrative purpose.
+
+This edge detection is applied on a filtered version of the image given
+as input.
+More precisely, only $b$ most
+significant bits are concerned by this step, where
+the parameter $b$ is practically set with $6$ or $7$.
+If set with the same value $b$, the edge detection returns thus the same
+set of pixels for both the cover and the stego image.
+In our flowcharts, this is represented by ``edgeDetection(b bits)''.
+Then only the 2 LSBs of pixels in the set of edges are returned if $b$ is 6,
+and the LSB of pixels if $b$ is 7.
+Let $x$ be the sequence of these bits.
+
+\JFC{il faudrait comparer les complexites des algo fuzy and canny}
% First of all, let us discuss about compexity of edge detetction methods.
% but the whole approach can be updated to consider
% the fuzzy logic edge detector.
-Next, following~\cite{Luo:2010:EAI:1824719.1824720}, our scheme automatically
-modifies the Canny algorithm
-parameters to get a sufficiently large set of edge bits: this
-one is practically enlarged until its size is at least twice as many larger
-than the size of embedded message.
+
+
+
+
+
+As argue in the introduction section, we do not adapt the parameters of the
+the edge detection as in~\cite{Luo:2010:EAI:1824719.1824720} but we modify
+the size of the embedding message. Practically, the lenght of $x$
+has to be at least twice as large
+as the size of the embedded encrypted message.
+Otherwise, a new image is used to hide the remaning part of the message.
+
+\subsection{Minimizing Distortion with Syndrome-Treillis Codes}
+\input{stc}
+
+
% Edge Based Image Steganography schemes
% already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ
% than the size of embedded message.
-\subsubsection{Security Considerations}
-Among methods of message encryption/decryption
-(see~\cite{DBLP:journals/ejisec/FontaineG07} for a survey)
-we implement the Blum-Goldwasser cryptosystem~\cite{Blum:1985:EPP:19478.19501}
-which is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} Pseudo Random Number Generator (PRNG)
-for security reasons.
-It has been indeed proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG
-has the cryptographically security property, \textit{i.e.},
-for any sequence $L$ of output bits $x_i$, $x_{i+1}$, \ldots, $x_{i+L-1}$,
-there is no algorithm, whose time complexity is polynomial in $L$, and
-which allows to find $x_{i-1}$ and $x_{i+L}$ with a probability greater
-than $1/2$.
-Thus, even if the encrypted message would be extracted,
-it would thus be not possible to retrieve the original one in a
-polynomial time.
-
%%RAPH: paragraphe en double :-)
-%% \subsubsection{Security Considerations}
-%% Among methods of message encryption/decryption
-%% (see~\cite{DBLP:journals/ejisec/FontaineG07} for a survey)
-%% we implement the Blum-Goldwasser cryptosystem~\cite{Blum:1985:EPP:19478.19501}
-%% which is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} Pseudo Random Number Generator (PRNG)
-%% for security reasons.
-%% It has been indeed proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG
-%% has the cryptographically security property, \textit{i.e.},
-%% for any sequence $L$ of output bits $x_i$, $x_{i+1}$, \ldots, $x_{i+L-1}$,
-%% there is no algorithm, whose time complexity is polynomial in $L$, and
-%% which allows to find $x_{i-1}$ and $x_{i+L}$ with a probability greater
-%% than $1/2$.
-%% Thus, even if the encrypted message would be extracted,
-%% it would thus be not possible to retrieve the original one in a
-%% polynomial time.
-
-
-\subsubsection{Minimizing Distortion with Syndrome-Treillis Codes}
-\input{stc}
-
-
\subsection{Data Extraction}
-Message extraction summarized in Fig.~\ref{fig:sch:ext} follows data embedding
+The message extraction summarized in Fig.~\ref{fig:sch:ext} follows data embedding
since there exists a reverse function for all its steps.
-First of all, the same edge detection is applied (on the 7 first bits) to get set,
+First of all, the same edge detection is applied (on the 7 first bits) to
+get the set of LSBs,
which is sufficiently large with respect to the message size given as a key.
Then the STC reverse algorithm is applied to retrieve the encrypted message.
Finally, the Blum-Goldwasser decryption function is executed and the original
