X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/51df4be4d70fabf22f3abc0fe92b515086f74021..f96233fc65ad1523ba849069ed5b7daa8f5ef9b1:/ourapproach.tex?ds=sidebyside

diff --git a/ourapproach.tex b/ourapproach.tex
index 5389d35..2378139 100644
--- 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
-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}).
@@ -48,7 +49,7 @@ Let us first focus on the data embedding.
 
 
 \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} 
@@ -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). 
-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 
@@ -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
-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 
@@ -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
-$~$ 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}
@@ -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}.
-
+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}
@@ -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}.
 
@@ -337,9 +350,9 @@ $$
 V_{ij}= \left\{
 \begin{array}{rcl}
 0 & \textrm{if} &  X_{ij} = Y_{ij} \\
-75 & \textrm{if} &  \abs{ X_{ij} - Y_{ij}} = 1 \\
-150 & \textrm{if} &  \abs{ X_{ij} - Y_{ij}} = 2 \\
-225 & \textrm{if} &  \abs{ X_{ij} - Y_{ij}} = 3 
+75 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 1 \\
+150 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 2 \\
+225 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 3 
 \end{array}
 \right..
 $$
@@ -369,3 +382,6 @@ This function allows to emphasize differences between contents.
   \caption{Differences  with Lena's cover  wrt $b$}
   \label{fig:lenadiff}
 \end{figure}
+
+
+