The flowcharts given in Fig.~\ref{fig:sch} summarize our steganography scheme denoted as to
-STABYLO for STeganography with cAnny, Bbs, binarY embedding at LOw cost.
+STABYLO for STeganography with Canny, Bbs, binarY embedding at LOw cost.
What follows successively details all the inner steps and flow inside
the embedding stage (Fig.\ref{fig:sch:emb})
and inside the extraction one (Fig.~\ref{fig:sch:ext}).
Edge Based Image Steganography schemes
-already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ
+already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10} differ
how they select edge pixels, and
how they modify these ones.
\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 :-)}
+\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
+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
+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).
-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.
+
+% 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
+modifies the Canny algorithm
+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.
+% 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.
+%%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.
+
\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 to get set,
+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
