-The flowcharts given in Fig.~\ref{fig:sch} summarize our steganography scheme denoted by
+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 are successively details of the inner steps and flows inside
both the embedding stage (Fig.~\ref{fig:sch:emb})
and the extraction one (Fig.~\ref{fig:sch:ext}).
-
+Let us first focus on the data embedding.
\begin{figure*}[t]
\begin{center}
\begin{minipage}{0.49\textwidth}
\begin{center}
%\includegraphics[width=5cm]{emb.pdf}
- \includegraphics[width=5cm]{emb.ps}
+ \includegraphics[scale=0.5]{emb.ps}
\end{center}
\end{minipage}
\label{fig:sch:emb}
\begin{minipage}{0.49\textwidth}
\begin{center}
%\includegraphics[width=5cm]{rec.pdf}
- \includegraphics[width=5cm]{rec.ps}
+ \includegraphics[scale=0.5]{rec.ps}
\end{center}
\end{minipage}
\label{fig:sch:ext}
-\subsection{Data Embedding}
-This section describes the main three steps of the STABYLO data embedding
-scheme.
-\subsubsection{Edge-Based Image Steganography}
+
+\subsection{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) 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 $x_{i-1}$ and $x_{i+L}$ 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}
-The edge-based image steganography schemes
+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.
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,
+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 for as fuzzy edge methods are concerned, they are obviously based on fuzzy logic to highlight
-edges.
+As for 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.
-%%
-%
-%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 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.
-Of course, other detectors like the fuzzy edge methods
-deserve 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)''.
+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.
+
+\JFC{il faudrait comparer les complexites des algo fuzy and canny}
+
+
% 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 large
-as the size of the embedded message.
+
+
+
+
+
+
+As argue in the introduction section, we do not adapt the parameters of the
+the edge detection as in~\cite{Luo:2010:EAI:1824719.1824720} but we modify
+the size of the embedding message. Practically, the lenght of $x$
+has to be at least twice as large
+as the size of the embedded encrypted message.
+Otherwise, a new image is used to hide the remaning part of the message.
+
+\subsection{Minimizing Distortion with Syndrome-Treillis Codes}
+\input{stc}
+
+
% Edge Based Image Steganography schemes
% already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ
% 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 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 $x_{i-1}$ and $x_{i+L}$ 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.
-
%%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}
The message extraction summarized in Fig.~\ref{fig:sch:ext} follows data embedding
since there exists a reverse function for all its steps.
