-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})
+This section first presents the embedding scheme through its
+four main steps: the data encryption (Sect.~\ref{sub:bbs}),
+the cover pixel selection (Sect.~\ref{sub:edge}),
+the adaptive payload considerations (Sect.~\ref{sub:adaptive}),
+and how the distortion has been minimized (Sect.~\ref{sub:stc}).
+The message extraction is then presented (Sect.~\ref{sub:extract}) and a running example ends this section (Sect.~\ref{sub:xpl}).
+
+
+The flowcharts given in Fig.~\ref{fig:sch}
+summarize our steganography scheme denoted by
+STABYLO, which stands for STeganography with
+Adaptive, Bbs, binarY embedding at LOw cost.
+What follows are successively some details of the inner steps and the flows both inside
+ the embedding stage (Fig.~\ref{fig:sch:emb})
and inside the extraction one (Fig.~\ref{fig:sch:ext}).
+Let us first focus on the data embedding.
-
-\begin{figure*}[t]
+\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=0.45]{emb.ps}
\end{center}
\end{minipage}
\label{fig:sch:emb}
- }%\hfill
+ }
+
\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=0.45]{rec.ps}
\end{center}
\end{minipage}
\label{fig:sch:ext}
}%\hfill
\end{center}
- \caption{The STABYLO Scheme.}
+ \caption{The STABYLO scheme}
\label{fig:sch}
\end{figure*}
-\subsection{Data Embedding}
-This section describes the main three steps of the STABYLO data embedding
-scheme.
-\subsubsection{Edge Based Image Steganography}
+
+\subsection{Security considerations}\label{sub:bbs}
+Among methods of the 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 $x_{i-1}$ or $x_{i+L}$ 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.
+
+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}\label{sub:edge}
+
+
+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 far 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 fast, well known, has been studied in depth, and is implementable
+on many kinds of architectures like FPGAs, smartphones, desktop machines, and
+GPUs, we have chosen this edge detector for illustrative purpose.
+
+%\JFC{il faudrait comparer les complexites des algo fuzy and canny}
+
+
+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.
+
+
-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 :-)}
+Let $x$ be the sequence of these bits.
+The next section presents how our scheme
+adapts when the size of $x$ is not sufficient for the message $m$ to embed.
+
+
+
+
+
+
+
+\subsection{Adaptive embedding rate}\label{sub:adaptive}
+Two strategies have been developed in our scheme,
+depending on the embedding rate that is either \emph{adaptive} or \emph{fixed}.
+In the former the embedding rate depends on the number of edge pixels.
+The higher it is, the larger the message length that can be inserted is.
+Practically, a set of edge pixels is computed according to the
+Canny algorithm with a high threshold.
+The message length is thus defined to be less than
+half of this set cardinality.
+If $x$ is then too short for $m$, the message is split into sufficient parts
+and a new cover image should be used for the remaining part of the message.
+
+
+In the latter, the embedding rate is defined as a percentage between the
+number of modified pixels and the length of the bit message.
+This is the classical approach adopted in steganography.
+Practically, the Canny algorithm generates
+a set of edge pixels related to a threshold that is decreasing
+until its cardinality
+is sufficient. Even in this situation, our scheme is adapting
+its algorithm to met all the user requirements.
+
+
+Once the map of possibly modified pixels is computed,
+two methods may further be applied to extract bits that
+are really modified.
+The first one randomly chooses the subset of pixels to modify by
+applying the BBS PRNG again. This method is further denoted as a \emph{sample}.
+Once this set is selected, a classical LSB replacement is applied to embed the
+stego content.
+The second method is a direct application of the
+STC algorithm~\cite{DBLP:journals/tifs/FillerJF11}.
+It is further referred to as \emph{STC} and is detailed in the next section.
-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.
-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).
% 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.
+
+
+
+
+
+
+\subsection{Minimizing distortion with syndrome-trellis codes}\label{sub:stc}
+\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.
+\subsection{Data extraction}\label{sub:extract}
+The message extraction summarized in Fig.~\ref{fig:sch:ext}
+follows the data embedding approach
+since there exists a reverse function for all its steps.
+More precisely, the same edge detection is applied on the $b$ first bits to
+produce the sequence $y$ of LSBs.
+If the STC approach has been selected in embedding, the STC reverse
+algorithm is directly executed to retrieve the encrypted message.
+This inverse function takes the $H$ matrix as a parameter.
+Otherwise, \textit{i.e.}, if the \emph{sample} strategy is retained,
+the same random bit selection than in the embedding step
+is executed with the same seed, given as a key.
+Finally, the Blum-Goldwasser decryption function is executed and the original
+message is extracted.
+
+
+\subsection{Running example}\label{sub:xpl}
+In this example, the cover image is Lena,
+which is a $512\times512$ image with 256 grayscale levels.
+The message is the poem Ulalume (E. A. Poe), which is constituted by 104 lines, 667
+words, and 3,754 characters, \textit{i.e.}, 30,032 bits.
+Lena and the first verses are given in Fig.~\ref{fig:lena}.
+
+\begin{figure}
+\begin{center}
+\begin{minipage}{0.49\linewidth}
+\begin{center}
+\includegraphics[scale=0.20]{Lena.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{0.49\linewidth}
+\begin{flushleft}
+\begin{scriptsize}
+The skies they were ashen and sober;\linebreak
+$~$ The leaves they were crisped and sere—\linebreak
+$~$ The leaves they were withering and sere;\linebreak
+It was night in the lonesome October\linebreak
+$~$ Of my most immemorial year;\linebreak
+It was hard by the dim lake of Auber,\linebreak
+$~$ In the misty mid region of Weir—\linebreak
+It was down by the dank tarn of Auber,\linebreak
+$~$ In the ghoul-haunted woodland of Weir.
+\end{scriptsize}
+\end{flushleft}
+\end{minipage}
+\end{center}
+\caption{Cover and message examples} \label{fig:lena}
+\end{figure}
+
+The edge detection returns 18,641 and 18,455 pixels when $b$ is
+respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.
+
+
+\begin{figure}[t]
+ \begin{center}
+ \subfloat[$b$ is 7.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{emb.pdf}
+ \includegraphics[scale=0.20]{edge7.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:emb}
+ }%\hfill
+ \subfloat[$b$ is 6.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{rec.pdf}
+ \includegraphics[scale=0.20]{edge6.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:ext}
+ }%\hfill
+ \end{center}
+ \caption{Edge detection wrt $b$}
+ \label{fig:edge}
+\end{figure}
+
+
+
+Only 9,320 bits (resp. 9,227 bits) are available for embedding
+in the former configuration where $b$ is 7 (resp. where $b$ is 6).
+In both cases, about the third part of the poem is hidden into the cover.
+Results with \emph{adaptive+STC} strategy are presented in
+Fig.~\ref{fig:lenastego}.
+
+\begin{figure}[t]
+ \begin{center}
+ \subfloat[$b$ is 7.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{emb.pdf}
+ \includegraphics[scale=0.20]{lena7.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:emb}
+ }%\hfill
+ \subfloat[$b$ is 6.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{rec.pdf}
+ \includegraphics[scale=0.20]{lena6.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:ext}
+ }%\hfill
+ \end{center}
+ \caption{Stego images wrt $b$}
+ \label{fig:lenastego}
+\end{figure}
+
+
+Finally, differences between the original cover and the stego images
+are presented in Fig.~\ref{fig:lenadiff}. For each pair of pixel $X_{ij}$ and $Y_{ij}$ ($X$ and $Y$ being the cover and the stego content respectively),
+the pixel value $V_{ij}$ of the difference is defined with the following map
+$$
+V_{ij}= \left\{
+\begin{array}{rcl}
+0 & \textrm{if} & X_{ij} = Y_{ij} \\
+75 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 1 \\
+150 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 2 \\
+225 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 3
+\end{array}
+\right..
+$$
+This function allows to emphasize differences between contents.
+
+\begin{figure}[t]
+ \begin{center}
+ \subfloat[$b$ is 7.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{emb.pdf}
+ \includegraphics[scale=0.20]{diff7.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:emb}
+ }%\hfill
+ \subfloat[$b$ is 6.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{rec.pdf}
+ \includegraphics[scale=0.20]{diff6.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:ext}
+ }%\hfill
+ \end{center}
+ \caption{Differences with Lena's cover wrt $b$}
+ \label{fig:lenadiff}
+\end{figure}
-\subsubsection{Minimizing Distortion with Syndrome-Treillis Codes}
-\input{stc}
-\subsection{Data Extraction}
-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,
-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
-message is extracted.
