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 
both the embedding stage (Fig.~\ref{fig:sch:emb}) 
and the extraction one (Fig.~\ref{fig:sch:ext}).


\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}
        \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}
        \end{center}
      \end{minipage}
      \label{fig:sch:ext}
    }%\hfill
  \end{center}
  \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}


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. 
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
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.

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.
% 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 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 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 
% 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}
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) 
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. 





\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.
