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 then presented (Sect.~\ref{sub:extract}) while a running example ends this section (Sect.~\ref{sub:xpl}).
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}).
+STABYLO, which stands for STe\-ga\-no\-gra\-phy with
+Adaptive, Bbs, binarY embedding at LOw cost.
+What follows are successively some details of the inner steps and the flows both inside
+ the embedding stage (Fig.~\ref{fig:sch:emb})
+and inside the extraction one (Fig.~\ref{fig:sch:ext}).
Let us first focus on the data embedding.
-\begin{figure*}[t]
+\begin{figure*}%[t]
\begin{center}
- \subfloat[Data Embedding.]{
+ \subfloat[Data Embedding]{
\begin{minipage}{0.49\textwidth}
\begin{center}
%\includegraphics[width=5cm]{emb.pdf}
\end{center}
\end{minipage}
\label{fig:sch:emb}
- }%\hfill
- \subfloat[Data Extraction.]{
+ }
+
+ \subfloat[Data Extraction]{
\begin{minipage}{0.49\textwidth}
\begin{center}
%\includegraphics[width=5cm]{rec.pdf}
\subsection{Security considerations}\label{sub:bbs}
-Among methods of message encryption/decryption
+Among the 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
+It has been 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
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,
+In first order methods like Sobel, Canny~\cite{Canny:1986:CAE:11274.11275}, and so on,
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
+As the Canny algorithm is fast, well known, has been studied in depth, and is implementable
+on many kinds of architectures like FPGAs, smart phones, desktop machines, and
GPUs, we have chosen this edge detector for illustrative purpose.
%\JFC{il faudrait comparer les complexites des algo fuzy and canny}
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.
+and the LSBs 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.
+The next section presents how to adapt our scheme
+ when the size of $x$ is not sufficient for the message $m$ to embed.
\subsection{Adaptive embedding rate}\label{sub:adaptive}
-Two strategies have been developed in our scheme,
+Two strategies have been developed in our approach,
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.
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 too short for $m$, the message is split into sufficient parts
+If $x$ is 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.
Practically, the Canny algorithm generates
a set of edge pixels related to a threshold that is decreasing
until its cardinality
-is sufficient.
+is sufficient. Even in this situation, our scheme is adapting
+its algorithm to meet all the user's requirements.
-
-Two methods may further be applied to select bits that
-will be modified.
+Once the map of possibly modified pixels is computed,
+two methods may further be applied to extract bits that
+are really modified.
The first one randomly chooses the subset of pixels to modify by
-applying the BBS PRNG again. This method is further denoted as to \emph{sample}.
+applying the BBS PRNG again. This method is further denoted as a \emph{sample}.
Once this set is selected, a classical LSB replacement is applied to embed the
stego content.
-The second method is a direct application of the
-STC algorithm~\cite{DBLP:journals/tifs/FillerJF11}.
+The second method considers the last significant bits of all the pixels
+inside the previous map. It next directly applies the STC
+algorithm~\cite{DBLP:journals/tifs/FillerJF11}.
It is further referred to as \emph{STC} and is detailed in the next section.
-% 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.
-
-
-
-
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.
+words, and 3,754 characters, \textit{i.e.}, 30,032 bits.
Lena and the first verses are given in Fig.~\ref{fig:lena}.
\begin{figure}
\begin{center}
-\begin{minipage}{0.4\linewidth}
-\includegraphics[width=3cm]{Lena.eps}
+\begin{minipage}{0.49\linewidth}
+\begin{center}
+\includegraphics[scale=0.20]{Lena.eps}
+\end{center}
\end{minipage}
-\begin{minipage}{0.59\linewidth}
+\begin{minipage}{0.49\linewidth}
\begin{flushleft}
\begin{scriptsize}
The skies they were ashen and sober;\linebreak
-$~$ The leaves they were crisped and sere—\linebreak
-$~$ The leaves they were withering and sere;\linebreak
+$\qquad$ The leaves they were crisped and sere—\linebreak
+$\qquad$ The leaves they were withering and sere;\linebreak
It was night in the lonesome October\linebreak
-$~$ Of my most immemorial year;\linebreak
+$\qquad$ Of my most immemorial year;\linebreak
It was hard by the dim lake of Auber,\linebreak
-$~$ In the misty mid region of Weir—\linebreak
+$\qquad$ In the misty mid region of Weir—\linebreak
It was down by the dank tarn of Auber,\linebreak
-$~$ In the ghoul-haunted woodland of Weir.
+$\qquad$ In the ghoul-haunted woodland of Weir.
\end{scriptsize}
\end{flushleft}
\end{minipage}
\caption{Cover and message examples} \label{fig:lena}
\end{figure}
-The edge detection returns 18641 and 18455 pixels when $b$ is
+The edge detection returns 18,641 and 18,455 pixels when $b$ is
respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.
-
+When $b$ is 7, it remains one bit per pixel to build the cover vector.
+This configuration leads to a cover vector of size 18,641 if b is 7
+and 36,910 if $b$ is 6.
\begin{figure}[t]
\begin{center}
\begin{minipage}{0.49\linewidth}
\begin{center}
%\includegraphics[width=5cm]{emb.pdf}
- \includegraphics[scale=0.15]{edge7.eps}
+ \includegraphics[scale=0.20]{edge7.eps}
\end{center}
\end{minipage}
%\label{fig:sch:emb}
\begin{minipage}{0.49\linewidth}
\begin{center}
%\includegraphics[width=5cm]{rec.pdf}
- \includegraphics[scale=0.15]{edge6.eps}
+ \includegraphics[scale=0.20]{edge6.eps}
\end{center}
\end{minipage}
%\label{fig:sch:ext}
-Only 9320 bits (resp. 9227 bits) are available for embedding
-in the former configuration where $b$ is 7 (resp. where $b$ is 6).
-In both cases, about the third part of the poem is hidden into the cover.
+The STC algorithm is optimized when the rate between message length and
+cover vector length is lower than 1/2.
+So, only 9,320 bits are available for embedding
+in the configuration where $b$ is 7.
+
+When $b$ is 6, we could have considered 18,455 bits for the message.
+However, first experiments have shown that modifying this number of bits is too
+easily detectable.
+So, we choose to modify the same amount of bits (9,320) and keep STC optimizing
+which bits to change among the 36,910 ones.
+
+In the two 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}.
\begin{minipage}{0.49\linewidth}
\begin{center}
%\includegraphics[width=5cm]{emb.pdf}
- \includegraphics[scale=0.15]{lena7.eps}
+ \includegraphics[scale=0.20]{lena7.eps}
\end{center}
\end{minipage}
%\label{fig:sch:emb}
\begin{minipage}{0.49\linewidth}
\begin{center}
%\includegraphics[width=5cm]{rec.pdf}
- \includegraphics[scale=0.15]{lena6.eps}
+ \includegraphics[scale=0.20]{lena6.eps}
\end{center}
\end{minipage}
%\label{fig:sch:ext}
V_{ij}= \left\{
\begin{array}{rcl}
0 & \textrm{if} & X_{ij} = Y_{ij} \\
-75 & \textrm{if} & \abs{ X_{ij} - Y_{ij}} = 1 \\
-150 & \textrm{if} & \abs{ X_{ij} - Y_{ij}} = 2 \\
-225 & \textrm{if} & \abs{ X_{ij} - Y_{ij}} = 3
+75 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 1 \\
+150 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 2 \\
+225 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 3
\end{array}
\right..
$$
\begin{minipage}{0.49\linewidth}
\begin{center}
%\includegraphics[width=5cm]{emb.pdf}
- \includegraphics[scale=0.15]{diff7.eps}
+ \includegraphics[scale=0.20]{diff7.eps}
\end{center}
\end{minipage}
%\label{fig:sch:emb}
\begin{minipage}{0.49\linewidth}
\begin{center}
%\includegraphics[width=5cm]{rec.pdf}
- \includegraphics[scale=0.15]{diff6.eps}
+ \includegraphics[scale=0.20]{diff6.eps}
\end{center}
\end{minipage}
%\label{fig:sch:ext}
\caption{Differences with Lena's cover wrt $b$}
\label{fig:lenadiff}
\end{figure}
+
+
