the cover pixel selection (Sect.~\ref{sub:edge}),
the adaptive payload considerations (Sect.~\ref{sub:adaptive}),
and how the distortion has been minimized (Sect.~\ref{sub:stc}).
-The message extraction is finally presented (Sect.\ref{sub:extract}) and a running example ends this section (Sect.~\ref{sub:xpl}).
+The message extraction is finally presented (Sect.~\ref{sub:extract}) and a running example ends this section (Sect.~\ref{sub:xpl}).
The flowcharts given in Fig.~\ref{fig:sch}
\label{fig:sch:ext}
}%\hfill
\end{center}
- \caption{The STABYLO Scheme.}
+ \caption{The STABYLO scheme}
\label{fig:sch}
\end{figure*}
-\subsection{Security Considerations}\label{sub:bbs}
+\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}
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
+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,
this step computes a message $m$, which is the encrypted version of \textit{mess}.
-\subsection{Edge-Based Image Steganography}\label{sub:edge}
+\subsection{Edge-based image steganography}\label{sub:edge}
The edge-based image
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 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.
+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}
+%\JFC{il faudrait comparer les complexites des algo fuzy and canny}
This edge detection is applied on a filtered version of the image given
Let $x$ be the sequence of these bits.
-The next section section presents how our scheme
+The next section presents how our scheme
adapts when the size of $x$ is not sufficient for the message $m$ to embed.
-\subsection{Adaptive Embedding Rate}\label{sub:adaptive}
+\subsection{Adaptive embedding rate}\label{sub:adaptive}
Two strategies have been developed in our scheme,
depending on the embedding rate that is either \emph{adaptive} or \emph{fixed}.
In the former the embedding rate depends on the number of edge pixels.
The higher it is, the larger the message length that can be inserted is.
Practically, a set of edge pixels is computed according to the
-Canny algorithm with an high threshold.
+Canny algorithm with a high threshold.
The message length is thus defined to be less than
half of this set cardinality.
-If $x$ is then to short for $m$, the message is split into sufficient parts
+If $x$ is then too short for $m$, the message is split into sufficient parts
and a new cover image should be used for the remaining part of the message.
-\subsection{Minimizing Distortion with Syndrome-Trellis Codes}\label{sub:stc}
+\subsection{Minimizing distortion with syndrome-trellis codes}\label{sub:stc}
\input{stc}
-\subsection{Data Extraction}\label{sub:extract}
+\subsection{Data extraction}\label{sub:extract}
The message extraction summarized in Fig.~\ref{fig:sch:ext}
follows the data embedding approach
since there exists a reverse function for all its steps.
If the STC approach has been selected in embedding, the STC reverse
algorithm is directly executed to retrieve the encrypted message.
This inverse function takes the $H$ matrix as a parameter.
-Otherwise, \textit{i.e.} if the \emph{sample} strategy is retained,
+Otherwise, \textit{i.e.}, if the \emph{sample} strategy is retained,
the same random bit selection than in the embedding step
is executed with the same seed, given as a key.
Finally, the Blum-Goldwasser decryption function is executed and the original
message is extracted.
-\subsection{Running Example}\label{sub:xpl}
-In this example, the cover image is Lena
+\subsection{Running example}\label{sub:xpl}
+In this example, the cover image is Lena,
which is a $512\times512$ image with 256 grayscale levels.
The message is the poem Ulalume (E. A. Poe), which is constituted by 104 lines, 667
-words, and 3754 characters, \textit{i.e.} 30032 bits.
-Lena and the the first verses are given in Fig.~\ref{fig:lena}.
+words, and 3754 characters, \textit{i.e.}, 30032 bits.
+Lena and the first verses are given in Fig.~\ref{fig:lena}.
\begin{figure}
\begin{center}
\end{figure}
The edge detection returns 18641 and 18455 pixels when $b$ is
-respectively 7 and 6. These edges are represented in Fig.~\ref{fig:edge}
+respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.
\begin{figure}[t]
%\label{fig:sch:ext}
}%\hfill
\end{center}
- \caption{Edge Detection wrt $b$.}
+ \caption{Edge detection wrt $b$}
\label{fig:edge}
\end{figure}
Only 9320 bits (resp. 9227 bits) are available for embedding
in the former configuration where $b$ is 7 (resp. where $b$ is 6).
-In the both case, about the third part of the poem is hidden into the cover.
+In both cases, about the third part of the poem is hidden into the cover.
Results with \emph{adaptive+STC} strategy are presented in
Fig.~\ref{fig:lenastego}.
%\label{fig:sch:ext}
}%\hfill
\end{center}
- \caption{Stego Images wrt $b$.}
+ \caption{Stego images wrt $b$}
\label{fig:lenastego}
\end{figure}
Finally, differences between the original cover and the stego images
-are presented in Fig.~\ref{fig:lenadiff}. For each pixel pair of pixel $X_{ij}$ and $Y_{ij}$ ($X$ and $Y$ being the cover and the stego content respectively),
+are presented in Fig.~\ref{fig:lenadiff}. For each pair of pixel $X_{ij}$ and $Y_{ij}$ ($X$ and $Y$ being the cover and the stego content respectively),
the pixel value $V_{ij}$ of the difference is defined with the following map
$$
V_{ij}= \left\{
\end{array}
\right..
$$
-This function allows to emphasize differences between content.
+This function allows to emphasize differences between contents.
\begin{figure}[t]
\begin{center}
%\label{fig:sch:ext}
}%\hfill
\end{center}
- \caption{Differences with Lena's Cover wrt $b$.}
+ \caption{Differences with Lena's cover wrt $b$}
\label{fig:lenadiff}
\end{figure}
