X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/c6d3dd0e0b8e5c982b6a8d28649ab4079666815d..771c241658964b134e9ee35cba6f6fc35dbc2ea0:/ourapproach.tex?ds=sidebyside

diff --git a/ourapproach.tex b/ourapproach.tex
index 4099700..25defad 100644
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -61,17 +61,15 @@ first order  and second order ones. These methods  are based on  gradient or
 Laplace  operators and  fuzzy edge  methods, which  are based  on fuzzy  logic to
 highlight edges.
 
-Of course, all the algorithms have  advantages and drawbacks which depend on the
-motivation  to  highlight  edges.   Unfortunately  unless testing  most  of  the
+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 Canny algorithm which is well  known, fast and implementable
-on many  kinds of architecture, such  as FPGA, smartphone,  desktop machines and
-GPU. And of course, 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. With an 8 bits image, only the 7 first bits are considered. In our flowcharts, this is represented by LSB(7 bits Edge Detection).
-
+why we have  chosen Canny algorithm, which is well  known, fast, and implementable
+on many  kinds of architectures like FPGAs, smartphones,  desktop machines, and
+GPUs. And of course, 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. With an 8 bits image, only the 7 first bits are considered. In our flowcharts, this is represented by ``LSB(7 bits Edge Detection)''.
 % 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},
@@ -83,12 +81,11 @@ 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 many larger 
-than the size of embedded message.
+one is practically enlarged until its size is at least twice as large 
+as the size of the embedded message.
 
 % Edge Based Image Steganography schemes 
 % already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ 
@@ -117,16 +114,18 @@ than the size of embedded message.
 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) 
+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 $L$ of output bits $x_i$, $x_{i+1}$, \ldots, $x_{i+L-1}$,
+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 $1/2$.
-Thus, even if the encrypted message would be extracted, 
-it would thus be not possible to retrieve the original one in a 
+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.   
 
 
