modif des styles

[canny.git] / ourapproach.tex

diff --git a/ourapproach.tex b/ourapproach.tex
index e87c1486bc31d3942abf9acd70e48c53077c7733..2378139e821b501c86f0f68f2a6d0f632b95427a 100644 (file)
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -8,7 +8,8 @@ The message extraction is then presented  (Sect.~\ref{sub:extract}) and a runnin
 
 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.
+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}).
 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}).


@@ -48,7 +49,7 @@ Let us first focus on the data embedding.
 
 
 \subsection{Security considerations}\label{sub:bbs}
 
 
 \subsection{Security considerations}\label{sub:bbs}

-Among methods of the 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} 
 (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} 


@@ -87,7 +88,7 @@ how they modify them.
 
 Many techniques have been proposed in the literature to  detect 
 edges in  images (whose noise has been initially reduced). 
 
 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
+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 
 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 


@@ -147,12 +148,13 @@ 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
 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 a \emph{sample}.
 Once this set is selected, a classical LSB replacement is applied to embed the 
 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 


@@ -252,14 +254,14 @@ Lena and the first verses are given in Fig.~\ref{fig:lena}.
 \begin{flushleft}
 \begin{scriptsize}
 The skies they were ashen and sober;\linebreak
 \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
 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
 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
 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}
 \end{scriptsize}
 \end{flushleft}
 \end{minipage}


@@ -269,7 +271,9 @@ $~$ In the ghoul-haunted woodland of Weir.
 
 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}.
 
 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}
 
 \begin{figure}[t]
   \begin{center}


@@ -298,9 +302,18 @@ respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.
 
 
 
 
 
 

-Only 9,320 bits (resp. 9,227 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 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}.
 
 Results with \emph{adaptive+STC} strategy are presented in 
 Fig.~\ref{fig:lenastego}.
 


@@ -372,35 +385,3 @@ This function allows to emphasize differences between contents.
 
 
 
 
 
 

-\section{Complexity Analysis}\label{sub:complexity}
-This section aims at justifying the leightweight attribute of our approach.
-To be more precise, we compare the complexity of our schemes to the 
-state of the art steganography, namely HUGO~\cite{DBLP:conf/ih/PevnyFB10}.
-
-
-In what folllows, we consider an $n \times n$ square image. 
-First of all, HUGO starts with computing the second order SPAM Features.
-This steps is in  $O(n^2 + 2.343^2)$ due to the calculation 
-of the difference arrays and next of the 686 features (of size 343).
-Next for each pixel, the distortion measure is calculated by +1/-1 modifying
-its value and computing again the SPAM 
-features. Pixels are thus selected according to their ability to provide
-an image whose SPAM features are close to the original one. 
-The algorithm is thus computing a distance between each Feature, 
-which is at least in $O(343)$ and an overall distance between these 
-metrics which is in $O(686)$. Computing the distance is thus in 
-$O(2\time 343^2)$ and this mdification is thus in $O(2\time 343^2 \time n^2)$.
-Ranking these results may be achieved with a insertion sort which is in $2.n^2 \ln(n)$.
-The overall complexity of the pixel selection is thus 
-$O(n^2 +2.343^2 + 2\time 343^2 \time n^2 + 2.n^2 \ln(n))$, \textit{i.e}
-$O(2.n^2(343^2 + \ln(n)))$.
-
-Our edge selection is based on a Canny  Filter, 
-whose complexity is in $O(2n^2.\ln(n))$ thanks to the convolution step
-which can be implemented with FFT.
-The complexity of Hugo is  at least $343^2/\ln{n}$ times higher than our scheme. 
-
-
-
-
-