X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/fdf9d8855582d89072dcd1339af9f5b74a167ac6..36f33066d192d54e79b234d89f223b3f4016ff12:/ourapproach.tex

diff --git a/ourapproach.tex b/ourapproach.tex
index 4539cf1..f832695 100644
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -85,6 +85,27 @@ modifies canny parameters to get a sufficiently large set of edge bits: this
 one is practically enlarged untill its size is at least twice as many larger 
 than the size of embedded message.
 
+Edge Based Image Steganography schemes 
+already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ 
+how they select edge pixels, and  
+how they modify these ones.
+
+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.   
+
+Next, following~\cite{Luo:2010:EAI:1824719.1824720}, our scheme automatically
+modifies canny parameters to get a sufficiently large set of edge bits: this 
+one is practically enlarged untill its size is at least twice as many larger 
+than the size of embedded message.
 
 
 \subsubsection{Security Considerations}
@@ -104,6 +125,21 @@ it would thus be not possible to retrieve the original one in a
 polynomial time.   
 
 
+\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.   
 
 
 
