-\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 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).
-
-
+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 in the second 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.
+For fuzzy edge methods, 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 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.
+Of course, other detectors like the fuzzy edge methods
+merit 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. 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},
% In experiments detailled in this article, the Canny method has been retained
% 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.
+one is practically enlarged until its size is at least twice as large
+as the size of the embedded message.
% Edge Based Image Steganography schemes
% already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ
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)
+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, $x_{i+L-1}$,
+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.
