\subsubsection{Edge Based Image Steganography}
+
Edge Based Image Steganography schemes
already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} 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.
+
+
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},
one is practically enlarged untill its size is at least twice as many larger
than the size of embedded message.
+Edge Based Image Steganography schemes
+already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ
+how they select edge pixels, and
+how they modify these ones.
+
+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},
+even if the fuzzy logic based edge detection methods~\cite{Tyan1993}
+have promising results, its complexity is in $C_3 \times O(M \times N)$
+whereas the complexity on the Canny method~\cite{Canny:1986:CAE:11274.11275}
+is in $C_1 \times O(M \times N)$ where $C_1 < C_3$.
+\JFC{Verifier ceci...}
+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 canny parameters to get a sufficiently large set of edge bits: this
+one is practically enlarged untill its size is at least twice as many larger
+than the size of embedded message.
\subsubsection{Security Considerations}
polynomial time.
+\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.
