X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/b04e55fbbcdcbca04098f1bf05ec4473e47b5c51..af81455342fce2b4d7f96ecb4f1194635a5a13a4:/ourapproach.tex diff --git a/ourapproach.tex b/ourapproach.tex index ec73f7d..12b3a32 100644 --- a/ourapproach.tex +++ b/ourapproach.tex @@ -18,20 +18,19 @@ Let us first focus on the data embedding. \begin{figure*}%[t] \begin{center} \subfloat[Data Embedding]{ - \begin{minipage}{0.49\textwidth} + \begin{minipage}{0.4\textwidth} \begin{center} - %\includegraphics[width=5cm]{emb.pdf} - \includegraphics[scale=0.45]{emb} + %\includegraphics[scale=0.45]{emb} + \includegraphics[scale=0.4]{emb} \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[scale=0.45]{rec} + \includegraphics[scale=0.4]{dec} \end{center} \end{minipage} \label{fig:sch:ext} @@ -51,11 +50,13 @@ Let us first focus on the data embedding. \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} +we implement the asymmetric +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 proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG +The main justification of this choice +is that 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 @@ -101,27 +102,30 @@ As the Canny algorithm is fast, well known, has been studied in depth, and is im 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} + 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 $7$. +More precisely, only $b$ most significant bits are concerned by this step, +where the parameter $b$ is practically set with $6$ or $7$. +Notice that 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. 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 LSBs of pixels if $b$ is 7. - - - +Moreover, to provide edge gradient value, +the Canny algorithm computes derivatives +in the two directions with respect to a mask of size $T$. +The higher $T$ is, the coarse the approach is. Practically, +$T$ is set with $3$, $5$, or $7$. +In our flowcharts, this step is represented by ``Edge Detection(b, T, X)''. Let $x$ be the sequence of these bits. The next section presents how to adapt our scheme - when the size of $x$ is not sufficient for the message $m$ to embed. +with respect to the size +of the message $m$ to embed and the size of the cover $x$. + @@ -131,22 +135,21 @@ The next section presents how to adapt our scheme \subsection{Adaptive embedding rate}\label{sub:adaptive} Two strategies have been developed in our approach, -depending on the embedding rate that is either \emph{adaptive} or \emph{fixed}. +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. +Canny algorithm with parameters $b=7$ and $T=3$. The message length is thus defined to be less than half of this set cardinality. 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. - 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 +a set of edge pixels related to increasing values of $T$ and until its cardinality is sufficient. Even in this situation, our scheme is adapting its algorithm to meet all the user's requirements. @@ -171,7 +174,7 @@ It is further referred to as \emph{STC} and is detailed in the next section. -\subsection{Minimizing distortion with syndrome-trellis codes}\label{sub:stc} +\subsection{Minimizing distortion with Syndrome-Trellis Codes}\label{sub:stc} \input{stc} @@ -210,11 +213,13 @@ 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 +More precisely, let $b$ be the most significant bits and +$T$ be the size of the canny mask, both be given as a key. +Thus, the same edge detection is applied on a stego content $Y$ 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. +This inverse function takes the $\hat{H}$ 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. @@ -233,7 +238,7 @@ Lena and the first verses are given in Fig.~\ref{fig:lena}. \begin{center} \begin{minipage}{0.49\linewidth} \begin{center} -\includegraphics[scale=0.20]{Lena.eps} +\includegraphics[scale=0.20]{lena512} \end{center} \end{minipage} \begin{minipage}{0.49\linewidth} @@ -256,7 +261,8 @@ $\qquad$ In the ghoul-haunted woodland of Weir. \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}. +respectively 7 and 6 and $T=3$. +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. @@ -267,7 +273,7 @@ and 36,910 if $b$ is 6. \begin{minipage}{0.49\linewidth} \begin{center} %\includegraphics[width=5cm]{emb.pdf} - \includegraphics[scale=0.20]{edge7.eps} + \includegraphics[scale=0.20]{edge7} \end{center} \end{minipage} %\label{fig:sch:emb} @@ -276,13 +282,13 @@ and 36,910 if $b$ is 6. \begin{minipage}{0.49\linewidth} \begin{center} %\includegraphics[width=5cm]{rec.pdf} - \includegraphics[scale=0.20]{edge6.eps} + \includegraphics[scale=0.20]{edge6} \end{center} \end{minipage} %\label{fig:sch:ext} }%\hfill \end{center} - \caption{Edge detection wrt $b$} + \caption{Edge detection wrt $b$ with $T=3$} \label{fig:edge} \end{figure} @@ -300,7 +306,7 @@ 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 +Results with {Adaptive} and {STC} strategies are presented in Fig.~\ref{fig:lenastego}. \begin{figure}[t] @@ -309,7 +315,7 @@ Fig.~\ref{fig:lenastego}. \begin{minipage}{0.49\linewidth} \begin{center} %\includegraphics[width=5cm]{emb.pdf} - \includegraphics[scale=0.20]{lena7.eps} + \includegraphics[scale=0.20]{lena7} \end{center} \end{minipage} %\label{fig:sch:emb} @@ -318,7 +324,7 @@ Fig.~\ref{fig:lenastego}. \begin{minipage}{0.49\linewidth} \begin{center} %\includegraphics[width=5cm]{rec.pdf} - \includegraphics[scale=0.20]{lena6.eps} + \includegraphics[scale=0.20]{lena6} \end{center} \end{minipage} %\label{fig:sch:ext} @@ -343,6 +349,12 @@ V_{ij}= \left\{ \right.. $$ This function allows to emphasize differences between contents. +Notice that since $b$ is 7 in Fig.~\ref{fig:diff7}, the embedding is binary +and this image only contains 0 and 75 values. +Similarly, if $b$ is 6 as in Fig.~\ref{fig:diff6}, the embedding is ternary +and the image contains all the values in $\{0,75,150,225\}$. + + \begin{figure}[t] \begin{center} @@ -350,19 +362,19 @@ This function allows to emphasize differences between contents. \begin{minipage}{0.49\linewidth} \begin{center} %\includegraphics[width=5cm]{emb.pdf} - \includegraphics[scale=0.20]{diff7.eps} + \includegraphics[scale=0.20]{diff7} \end{center} \end{minipage} - %\label{fig:sch:emb} + \label{fig:diff7} }%\hfill \subfloat[$b$ is 6.]{ \begin{minipage}{0.49\linewidth} \begin{center} %\includegraphics[width=5cm]{rec.pdf} - \includegraphics[scale=0.20]{diff6.eps} + \includegraphics[scale=0.20]{diff6} \end{center} \end{minipage} - %\label{fig:sch:ext} + \label{fig:diff6} }%\hfill \end{center} \caption{Differences with Lena's cover wrt $b$} @@ -370,3 +382,4 @@ This function allows to emphasize differences between contents. \end{figure} +