+
+\subsection{Security considerations}\label{sub:bbs}
+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 $x_{i-1}$ 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 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.
+
+%\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.
+
+
+
+
+
+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.
