X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/963b0c034c8a7c7f1fb77fc6b06e3ba6744c1dbd..30a1c774eb33c1344a68625e8958dbbd8b996280:/ourapproach.tex?ds=inline

diff --git a/ourapproach.tex b/ourapproach.tex
index 02d8735..2378139 100644
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -1,48 +1,81 @@
-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}).
+This section first presents the embedding scheme through its 
+four main steps: the data encryption (Sect.~\ref{sub:bbs}),
+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 then presented  (Sect.~\ref{sub:extract}) and a running example ends this section (Sect.~\ref{sub:xpl}). 
 
 
-\begin{figure*}[t]
+The flowcharts given in Fig.~\ref{fig:sch}
+summarize our steganography scheme denoted by
+STABYLO, which stands for STeganography 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{center}
     \subfloat[Data Embedding.]{
       \begin{minipage}{0.49\textwidth}
         \begin{center}
-          \includegraphics[width=5cm]{emb.pdf}
-          %\includegraphics[width=5cm]{emb.ps}
+          %\includegraphics[width=5cm]{emb.pdf}
+          \includegraphics[scale=0.45]{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}
+          %\includegraphics[width=5cm]{rec.pdf}
+          \includegraphics[scale=0.45]{rec.ps}
         \end{center}
       \end{minipage}
       \label{fig:sch:ext}
     }%\hfill
   \end{center}
-  \caption{The STABYLO Scheme.}
+  \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}
 
+\subsection{Security considerations}\label{sub:bbs}
+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 
+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 $x_{i-1}$ 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,
+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}.
 
-The edge-based image steganography schemes 
+
+\subsection{Edge-based image steganography}\label{sub:edge}
+
+
+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.
@@ -55,32 +88,85 @@ how they modify them.
 
 Many techniques have been proposed in the literature to  detect 
 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 in the second hand~\cite{KF11}.
-In first order methods like Sobel,
+They can be separated into 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, 
 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.
-For fuzzy edge methods, 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 Canny algorithm is well known and studied, fast, and implementable
+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 fast, well known, has been studied in depth, and is 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
-merit 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)''.
+%\JFC{il faudrait comparer les complexites des algo fuzy and canny}
+
+
+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. 
+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}
+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 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
+and a new cover image should be used for the remaining part of the message. 
+
+ 
+In the latter, the embedding rate is defined as a percentage between the 
+number of modified pixels and the length of the bit message.
+This is the classical approach adopted in steganography.
+Practically, the Canny algorithm generates  
+a set of edge pixels related to a threshold that is decreasing 
+until its cardinality
+is sufficient. Even in this situation, our scheme is adapting 
+its algorithm to meet all the user's requirements. 
+
+
+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 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}. 
+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},
@@ -92,11 +178,17 @@ In order to be able to compute the same set of edge pixels, we suggest to consid
 % 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.
+
+
+
+
+
+
+
+\subsection{Minimizing distortion with syndrome-trellis codes}\label{sub:stc}
+\input{stc}
+
+
 
 % Edge Based Image Steganography schemes 
 % already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ 
@@ -121,56 +213,175 @@ as the size of the embedded message.
 % 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 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. 
 
 
 
+\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.
+
+More precisely, the same edge detection is applied on the $b$ first bits  to 
+produce the sequence $y$ of LSBs. 
+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,
+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, 
+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 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}{0.49\linewidth}
+\begin{center}
+\includegraphics[scale=0.20]{Lena.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{0.49\linewidth}
+\begin{flushleft}
+\begin{scriptsize}
+The skies they were ashen and sober;\linebreak
+$\qquad$ The leaves they were crisped and sereâ\linebreak
+$\qquad$ The leaves they were withering and sere;\linebreak
+It was night in the lonesome October\linebreak
+$\qquad$ Of my most immemorial year;\linebreak
+It was hard by the dim lake of Auber,\linebreak
+$\qquad$ In the misty mid region of Weirâ\linebreak
+It was down by the dank tarn of Auber,\linebreak
+$\qquad$ In the ghoul-haunted woodland of Weir.
+\end{scriptsize}
+\end{flushleft}
+\end{minipage}
+\end{center}
+\caption{Cover and message examples} \label{fig:lena}
+\end{figure}
+
+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.
+in this configuration, this 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}
+    \subfloat[$b$ is 7.]{
+      \begin{minipage}{0.49\linewidth}
+        \begin{center}
+          %\includegraphics[width=5cm]{emb.pdf}
+          \includegraphics[scale=0.20]{edge7.eps}
+        \end{center}
+      \end{minipage}
+      %\label{fig:sch:emb}
+    }%\hfill
+    \subfloat[$b$ is 6.]{
+      \begin{minipage}{0.49\linewidth}
+        \begin{center}
+          %\includegraphics[width=5cm]{rec.pdf}
+          \includegraphics[scale=0.20]{edge6.eps}
+        \end{center}
+      \end{minipage}
+      %\label{fig:sch:ext}
+    }%\hfill
+  \end{center}
+  \caption{Edge detection wrt $b$}
+  \label{fig:edge}
+\end{figure}
+
+
+
+The STC algorithm is optimized when the rate between message length and 
+cover vector length is less 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 bits.
+
+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{figure}[t]
+  \begin{center}
+    \subfloat[$b$ is 7.]{
+      \begin{minipage}{0.49\linewidth}
+        \begin{center}
+          %\includegraphics[width=5cm]{emb.pdf}
+          \includegraphics[scale=0.20]{lena7.eps}
+        \end{center}
+      \end{minipage}
+      %\label{fig:sch:emb}
+    }%\hfill
+    \subfloat[$b$ is 6.]{
+      \begin{minipage}{0.49\linewidth}
+        \begin{center}
+          %\includegraphics[width=5cm]{rec.pdf}
+          \includegraphics[scale=0.20]{lena6.eps}
+        \end{center}
+      \end{minipage}
+      %\label{fig:sch:ext}
+    }%\hfill
+  \end{center}
+  \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 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
+$$
+V_{ij}= \left\{
+\begin{array}{rcl}
+0 & \textrm{if} &  X_{ij} = Y_{ij} \\
+75 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 1 \\
+150 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 2 \\
+225 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 3 
+\end{array}
+\right..
+$$
+This function allows to emphasize differences between contents.
+
+\begin{figure}[t]
+  \begin{center}
+    \subfloat[$b$ is 7.]{
+      \begin{minipage}{0.49\linewidth}
+        \begin{center}
+          %\includegraphics[width=5cm]{emb.pdf}
+          \includegraphics[scale=0.20]{diff7.eps}
+        \end{center}
+      \end{minipage}
+      %\label{fig:sch:emb}
+    }%\hfill
+    \subfloat[$b$ is 6.]{
+      \begin{minipage}{0.49\linewidth}
+        \begin{center}
+          %\includegraphics[width=5cm]{rec.pdf}
+          \includegraphics[scale=0.20]{diff6.eps}
+        \end{center}
+      \end{minipage}
+      %\label{fig:sch:ext}
+    }%\hfill
+  \end{center}
+  \caption{Differences  with Lena's cover  wrt $b$}
+  \label{fig:lenadiff}
+\end{figure}
 
-\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.
