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 successively details all the inner steps and flows inside
+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}).
\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[width=5cm]{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[width=5cm]{rec.ps}
\end{center}
\end{minipage}
\label{fig:sch:ext}
-\subsubsection{Edge Based Image Steganography}
+\subsubsection{Edge-Based Image Steganography}
-The edge based image steganography schemes
-already presented (\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10}) differ
+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 :-)}
+%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.
-The most common ones are filter
-edge detection methods such as Sobel or Canny filters, low order methods such as
-first order and second order ones. 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 that depend on the
-motivations behind that edges detection. 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
+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,
+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.
+%%
+%
+%Of course, all the algorithms have advantages and drawbacks that depend on the
+%motivations behind that edges detection. 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
+As the Canny algorithm is well known and studied, fast, and implementable
on many kinds of architectures like FPGAs, smartphones, desktop machines, and
-GPUs. And of course, we do not pretend that this is the best solution.
+GPUs, we have chosen this edge detector for illustrative purpose.
+Of course, other detectors like the fuzzy edge methods
+deserve much further attention, which is why we intend
+to investigate systematically all of these detectors in our next work.
+%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)''.
+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. Thus, 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.
% Let then $M$ and $N$ be the dimension of the original image.
% According to~\cite{Hu:2007:HPE:1282866.1282944},
that is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} pseudorandom 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, $x_{i+L-1}$,
+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 $1/2$.
-Thus, even if the encrypted message would be extracted,
-it would thus be not possible to retrieve the original one in a
+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.
\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
