International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 8, August 2013
ISSN 2319 - 4847
Study and Analysis of Steganography with Pixel
Factor Mapping (PFM) Method
Indradip Banerjee1, Souvik Bhattacharyya2 and Gautam Sanyal3
1
Department of CSE, National Institute of Technology, Durgapur, West Bengal, India.
Department of CSE, University Institute of Technology, Burdwan, West Bengal,India.
3
Department of CSE, National Institute of Technology, Durgapur, West Bengal, India.
2
Abstract
Internet expertise’s are now carrying a imperative responsibility in our habitual living. It has the advantages along with the
disadvantages; it can generate the requirements of information hiding technology for maintaining the secrecy of the secret
information. Steganography is most fashionable information hiding technique in modern day situation, which comes from a
Greek word “στεγανό-ς, γραφ-ειν” means “covered or hidden writing”. Extensive capacity of effort has been carried out by
different researchers in this ground. In this contribution, a novel special domain image Steganography method has been proposed
which has been design based on prime factor calculation on pixel intensity.
Keywords: Steganography, Cover Image, Stego Image, Pixel Factor Mapping (PFM) method.
1. INTRODUCTION
Security of information is the beautiful aspect of information technology and communication system. Computer, Laptop,
Mobile, Internet etc. are most important communication media that join different parts of the world. In contradiction,
safety and security of communication system creates an issue. Consequently, the concept of “Information Hiding” [1] has
been proposed. Then theory of Cryptography [2] and watermarking [3] has been developed. But in the present days,
thanks to the rising computational supremacy, regular cryptographic and watermarking algorithms have been established
to be evidence for weak point against mathematical and statistical methods. The word “Security” is not the same like ten
years back, because the research in reverse engineering techniques has been increased the processing power, most
important race between researches in cryptanalysis [4] and watermarking detection [5]. To solve the problems the
concepts of Steganography [6] has been developed by the researchers. Steganography diverge from cryptography.
Cryptography is a secure communications which changes the data into a specific form and for that reason an
eavesdropper cannot understand it. Steganography techniques attempt to hide the existence of the message itself, so that
an observer or eavesdropper does not know that the information is
even there or not.
Steganography gives the authentication over the data using some tag
or labeling on some objects like text, audio, video, image. Hide the
presence of a message and create a covert channel is the aim of the
Steganography. The message is hidden in another object as a result
the transmitted object will be identical looking to every individual’s
eye. Steganalysis is the art of detecting any hidden message on the
Figure 1: Types of Steganography
communication channel. Steganography is crushed when the
existence of the hidden message is exposed.
The Text Steganography have basic three categories which are as follows [7]: Format-based methods: Hide the
steganographic text in the existing cover text by changing formatting like insertion of spaces or non-displayed characters,
careful errors tinny throughout the text and resizing of fonts. Random and statistical generation method: Generating the
cover text by their own method with the help of known plaintext and make comparison with them. Linguistic methods:
With some documented information in society and some linguistic analysis creates the hiding techniques. In audio
Steganography[8], messages are embedded into digitized audio signal which result slight alteration of binary sequence of
the corresponding audio file. Low-bit Encoding: Binary form of message is used to embed in the LSB (Least Significant
Bit) of the cover audio file. Phase Coding: Embed in the phase components of sound which are not audible to the human
ear. Several new approaches are studied in video data steganography literature [8]. The approaches are: Application of
BPCS Steganography to WAVELET Compressed Video, An Optical Video Cryptosystem with Adaptive Steganography,
A Secure Covert Communication Model based on VIDEO Steganography, Lossless Steganography on AVI File using
Swapping Algorithm, A New Invertible Data Hiding in Compressed Videos or Images etc. In image Steganography there
are various ways have been used by the researchers, which are as follows [9]: Substitution technique in Spatial Domain:
In this case the least significant bits of the cover item are replaced in the cover image without modifying. Transform
domain technique: Discrete Cosine Transform (DCT), Discrete Wavelet Trans- form (DWT) and Fast Fourier Transform
(FFT) are used in this domain to embed information in transform coefficients of the cover images. Spread spectrum
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 8, August 2013
ISSN 2319 - 4847
technique: Wide frequency bandwidths are used to embed the data bit than the minimum required bandwidth. Statistical
technique: Here the information is encoded by changing various numerical properties of cover image and the message bits
are hidden in the block of cover image. Distortion technique: Information is stored by signal distortion. Pixel Mapping
Method (PMM) [10]: Embedding positions are selected by some function and depends on the pixel intensity value of the
seed pixel and its 8 neighbors. The process of embedding is done through mapping of each two or four bits of the secret
message in each of the neighbor pixel based on pixel features.
In this paper author proposed a novel approach of PFM method for embedding four bits of secret message per pixel. The
four bits are combined together and embed using new method i.e. Pixel Factor Mapping (PFM) Method. The pixel
selection technique is also a unique mathematical function used here for better security. Another part of the paper has
been organized as following sections: Section 2 describes some related works on image steganography. Section 3 deals
with proposed method along with the algorithms. In section 4 experimental results are discussed and analyzed. This
Section has discussed various attacks applied and their results on the proposed system. Section 5 draws the conclusion.
2. RELATED WORK
The image steganography can be possible in two domains, one is Spatial and another is frequency domain. There are
various techniques and modules developed by different researchers. Some of them are discussed below:
One of the common techniques is to manipulate the least-significant-bit (LSB) [13], [16], [18] and [32] planes by
straightforwardly replacing the LSBs of the cover-image with the message bits. LSB methods have high capacity but the
LSB insertion is vulnerable in case of cropping and compression of image. The pixel-value differencing (PVD) method
proposed by Wu and Tsai [33] can successfully provide both high embedding capacity and outstanding imperceptibility
for the stego-image. The pixel-value differencing (PVD) method can segment the cover image into some blocks which are
not overlapped. The blocks are containing two connecting pixels and method for embedding is to modify the pixel
difference in each pair. Greater modification has the same opinion in case of larger difference in the original pixel values.
In the extraction phase, the original range table is necessary. It is used to partition the stego-image by the same method as
used to the cover image. Based on PVD method, various approaches have also been proposed. Among them Chang et al.
[19] proposes a new method using tri way pixel value differencing which can improve embedding capacity and PSNR
value than original PVD method. In 2004, Potdar et al. [20] proposes GLM (Gray level modification) technique can
modify Gray level of the image pixels by mapping technique. Gray level modification Steganography is to map data by
modifying the pixels Gray level values. The mapping concept of odd and even numbers within an image is used in GLM.
It is a one-to-one mapping between the binary data and the selected pixels in an image. Wien Hong and Tung-Shou
Chen[11] introduced a new method based on pixel pair matching (PPM). In PPM use the values of pixel pair as a
reference coordinate and search a coordinate in the neighborhood set of this pixel pair according to a given message digit.
Exploiting modification direction (EMD) and diamond encoding (DE) are two data-hiding methods also proposed based
on PPM. Che-Wei Lee and Wen-Hsiang [12] introduced blind an authentication method based on the secret sharing
technique. They used the computed values which are mapped into a range of alpha channel values, whose values are near
their maximum value of 255. Shunquan Tan and Bin Li [14], identify that the readjusting phase of edge adaptive image
steganography based on LSB matching revisited introduces a pulse distortion to the long exponential tail of the histogram
of the absolute difference of the pixel pairs. A targeted steganalytic method based on B-Spline fitting is proposed in their
method. Sian-Jheng Lin and Wei-Ho Chung [15], initiate the idea of Reversible information-embedding (RIE) in their
paper. In this way transform both host signals & message into the stego-signals, and the stego-signals reversed losslessly
to the host signals and the message. G.Karthigai Seivi, Leon Mariadhasan, K. L. Shunmuganathan [17], worked on most
common and easiest method for embedding messages in an image i.e. least-significant bit (LSB) insertion method which
can effectively resist image steganalysis based on statistical analysis. Ching-Nung Yang, Chih-Cheng Wu, Yi-Chin Lin
and Cheonshik Kim [21], proposed an efficient matrix based secret image sharing (MSIS) scheme based on simple binary
matrix operations. Bhattacharyya and Sanyal‘s Transformation: Bhattacharyya and Sanyal proposed a new image
transformation technique in [10] known as Pixel Mapping Method (PMM), this method used for information hiding
within the spatial domain of any gray scale image. Embedding pixels are selected by some mathematical function which
can depends upon the pixel intensity value of the seed pixel and its 8 neighbors are selected in anti clockwise direction.
Data can embed by mapping each two or four bits of the secret message in each of the neighbor pixel based on some
features of that pixel. At the receiver side same reverse operations has been used to get back the original information.
3. PROPOSED WORK
Author present a novel Pixel Factor Mapping (PFM) method which is based on special domain with the help of Gray
scale images (512x512). We have used more than 1000 images in our work, which have been collected from image
databases and also those images are used by most of the researchers. The input message can be adopt as digital character
format and cope with bit stream. Four bit pair has used for embedding in a separate pixel and the selection of embedding
pixel also depends upon mathematical member function. The selection technique is based on pixel intensity value and
pixel position on image. Mapping of four bit from the secret message is used for embedding in a pixel, which is based on
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the maximum prime factor value of image pixel intensity value. In Figure 2 the PFM table shows the mapping of
maximum prime factor value. The existing methods can embeds one bit per pixel where as author’s proposed method can
embed four bit per pixel. Embedding four bit per pixels can extend the embedding capacity four times than other previous
methods and this is the novelty in this contribution. At the receiver side reverse operation has been carried out to get back
the original information.
Binary Form
10100011011101010…
Input Message
Divide 4 bit pair
1010 0011 0111 0101 0…
Cover Image
198
196
197
187
181
174
180
176
170
182
185
191
192
193
188
181
175
179
172
172
172
182
181
195
197
188
181
179
175
169
166
172
176
174
195
195
186
180
179
175
171
171
172
178
181
192
191
180
183
180
181
176
168
170
172
188
191
191
180
183
182
180
169
162
165
169
Select pixel values
77
65
65
66
74
83
86
92
102
101
87
Calculate Prime
Factors
196(2, 2, 7, 7)
188(2, 2, 47)
180(2, 2, 3, 3, 5)
Find out
correspond
ing PFV
Calculate expected Number of
Nearest matching maximum PVF
&
Update image pixel intensity
Stego Image
Calculate Prime Factors of Pixel
Intensity
&
Find out corresponding embedding
4 Bit against PFV
Extract 4 bit pair
1010 0011 0111 0101 0…
PFM Table
Prime Factor
Value (PFV)
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
Embedding
4 Bit
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
Output Message
Figure 2: Proposed Work
3.1 Algorithms:
3.1.1 Embedding Algorithm:
1) Select Message four bit pair form.
2) Select the Pixel for embedding by the help of pixel selection algorithm.
3) Pick the intensity value of embedding position.
4) Mapping the PFM Table with message bit.
5) Find out the corresponding PFV (Prime Factor Value) for each 4 Bit message.
6) Calculate the expected nearest number which matched with PFV and the maximum prime factor value of that expected
number. Expected nearest number may be greater or less than original intensity.
7) Update the Pixel intensity value with expected nearest number.
8) Generate the Stego Image.
3.1.2 Extracting Algorithm:
1) Select the Pixel with the help of pixel selection algorithm.
2) Pick the intensity value of embedding position.
3) Mapping the PFM Table with pixel intensity.
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4) Find out the corresponding 4 Bit message for each PFV (Prime Factor Value).
5) Generate the message.
3.1.3 Pixel Selection Algorithm:
1) Select the pixel intensity µ(x,y) value and pixel position x and y.
2) Calculate the membership function for pixel δ(p)=p/63 for 0 ≤ p ≤ 63; δ(p)=(p-64)/63 for 64 ≤ p ≤ 127; δ(p)=(p128)/63 for 128 ≤ p ≤ 191; δ(p)=(p-192)/63 for 192 ≤ p ≤ 255.
3) Put it to a mathematical function
a. if (δ(p) > 0 AND δ(p) ≤ 0.4) THEN λ=1
b. if (δ(p) > 0.4 AND δ(p) ≤ 0.7) THEN λ=2
c. if (δ(p) > 0.7) THEN λ = 0
d. ∞ = (x + 1) + λ
e. if (∞ ≥ 512) THEN η =1 ; χ = (y + 1) + λ
1. if (χ ≥ 512) THEN χ = 1;
f. else η = (x + 1) + λ; χ = y;
4) Get some parameters including η, χ.
5) Using the parameters value generates the row and column position of the next search pixel.
6) Process continues until full message embedding done.
4. RESULTS & ANALYSIS
The authors explain the experimental results of the method based on some techniques to evaluate the hiding performance
in this section. Capacity of hiding data and Imperceptibility of the stego image, these two techniques is used here for
performance metric. Imperceptibility of the image is called the quality of image. The quality of stego image produced by
the proposed method and the stego image has been tested thorough some image similarity metrics like MSE, PSNR,
Correlations, RMSE, SSIM, KL divergence, Entropy. Figure 3 to 9 shows the graphical representation of calculated value
of various similarity metrics for cover and stego images. Various Techniques used to manage the difference between
pixels. The techniques are described below:
Mean Square Error (MSE) [22]: It is computed by averaging the squared intensity of the cover and stego image pixels.
The equation (1) shows the MSE.
M 1 N 1
1
NM
MSE 
 em, n  ..............................(1)
2
m 0 n  0
Where NM is the image size (N x M) and e(m,n) is the reconstructed imag.
Peak Signal-to-Noise Ratio (PSNR) [22]: A mathematical measure of image quality is Signal–to-noise ratio (SNR), which
is based on the pixel difference between two images [23]. The SNR measure the estimate of Stego image and cover image.
PSNR shows in equation (2).
PSNR  10 log 10
S
2
MSE
.......... .......... .......... (2)
Where, S stands for maximum possible pixel value of the image. If the PSNR is greater than 36 DB then the visibility
looks same in between cover and stego image, so HVS not identified the changes.
Correlations [24]: Pearson’s correlation coefficient is widely used in statistical analysis as well as image processing. Here
apply it in Cover and Stego images to see the difference between these two images. The Correlation shows in equation
(3).
n
r

i 1
( xi  x )  ( yi  y )
n
n
..............................(3)
( xi  x ) 2  i 1 ( yi  y ) 2
i 1

The Xi and Yi are the cover image and bar of X and Y are stego image positions.
Root Mean Square Error (RMSE) [25]: RMSE is a frequently used measure of the difference between Cover Image and
Stego Image values. These individual differences called residuals and the RMSE aggregate them into a single measure of
predictive power. The RMSE shows in equation (4).
n
RMSE 

i1
( X obs,i  X mo del,i )2
n
..............................(4)
Xobsi and Xmodeli are two image vectors i.e. cover and stego.
Structural Similarity Index (SSIM) [22]: Wang et. al[26], proposed Structural Similarity Index concept between original
and distorted image. The Stego and Cover images are divided into blocks of 8 x 8 and converted into vectors. Then two
means and two standard derivations and one covariance value are computed. After that the luminance, contrast and
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structure comparisons based on statistical values are computed. Then The SSIM computed between Cover and Stego
images. SSIM shows in equation (5).
SSIM 
2 
x

2
x
y
 C1 2 xy  C2 

  2y  C1  x2   2y  C2
..............................(5)
KL divergence [27]: With the help of probability density function (PDF) for each Image (cover and stego) we estimate the
Kullback-Leibler Divergence. KL divergence shows in equation (6)
D p || q  x pxlog
px
..............................(6)
qx
Entropy [28]: Entropy is a measure of the uncertainty associated with a random variable. Here, a 'message' means a
specific realization of the random variable. The equation (7) shows it.
S  .
dQrev
.............................(7)
T
Where, S is the entropy and T is the uniform thermodynamic temperature of a closed system divided into an incremental
reversible transfer of heat into that system (dQ)
Figure 3: Performance Metrics (MSE)
Figure 5: Performance Metrics (Correlation)
Figure 7: Performance Metrics (SSIM)
Figure 9: Performance Metrics (Entropy)
Volume 2, Issue 8, August 2013
Figure 4: Performance Metrics (PSNR)
Figure 6: Performance Metrics (RMSE)
Figure 8: Performance Metrics (KL divergence)
Figure 10: RS Analysis of “Lena.bmp” size 512x512
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Figure 11: Chi Square Probability Distribution
of Cover and Stego Images
Figure 12: Chi Square Statistics Distribution
of Cover and Stego Images
Fridrich et al. [30] introduced a powerful steganalytic method which is used for accurately estimate the length of the
embedded message from an image, for several LSB steganographic method is RS Analysis. Let I be the image to be
analyzed having width W and height H pixels. Each pixel has been denoted as P i.e. for a Gray Scale Image (8 bits per
pixel image), value of P = 0, 1,. . . 255. Next step is for divide I into G disjoint groups of n adjacent pixels. For instance n
can be 4. Next define a discriminate function f which is responsible to give a real number f(x1 ,….., xn) ε R for each group
of pixels G = (x1 ,….., xn). The objective is to capture the smoothness of G using f. Let the discrimination function be
n 1
f ( x1 ,..., xn )   xi1  xi .............................(8)
i 1
Furthermore, let F1 be a flipping invertible function F1: 0  1, 2  3, . . . , 254  255, and F-1 be a shifting function
denoted as F-1 : -1  0, 1  2, . . . , 255  256 over P. For completeness, let F0 be the identity function such as F0(x) = x
for all x ε P: Define a mask M that represents which function to apply to each element of a group G. The mask M is an ntuple with values in -1, 0, 1. The value -1 stands for the application of the function F-1, 1 stands for the function F1 and 0
stands for the identity function F0. Similarly, define -M as M’s compliment. Next step is to apply the discriminate
function f with the functions F-1,0,1 defined through a mask M over all G groups to classify them into three categories
Regular (R), Singular (S) and Unchanged (U) - depending on how the flipping changes the value of the discrimination
function.
Re gularGroups : G R  f (F (G))  f (G).............................(9)
E
M
SingularGroups: GE S M  f (F (G)) /  f (G).............................(10)
UnusableGroups: GEU M  f (F (G))  f (G).............................(11)
In similar manner R-M, S-M and U-M can be defined for -M such that (RM +SM)/2 ≤ T and (R-M +S-M)/2 ≤ T, where T is the
total number of G groups. The conclusion of RS Analysis method describes that, for typical images RM ≈ R-M and SM ≈ SM and no change in R and S value for embedding character of various sizes.
Chi-square test[35] is a statistical test. This is used for testing independence and goodness of fit. Testing independence is
determines, whether two or more observations across two populations are dependent on each other, i.e. whether one
variable helps to estimate the other. Testing for goodness of fit determines if an observed frequency distribution matches a
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theoretical frequency distribution. In both cases the equation is used for calculate the chi-square statistic.
2 
(O  E)
E
2
.............................(12)
O equals the observed frequency and E is the expected frequency. The results of a chi-square test, along with the degrees
of freedom, are used with a previously calculated table of chi-square distributions to find a p-value. The p-value can then
be used to determine the significance of the test.
Here the attack is very necessary in case of Steganography algorithm so we have tested through some steganalysis
technique. First exact detector of LSB replacement was the heuristic RS analysis [29] [30] published in 2001. Then
Sample Pairs (SP) analysis was analyzed and reformulated by Dumitrescu et al. [31] in 2002. In this work all the stego
image has been generated with the help of our algorithm and tested through steganalysis attack algorithm i.e. RS
analysis. Figure 10 shows the Analysis of attack of Gray scale image (Lena used here) as cover and stego image after
embedding 100-30000 characters. With the help of RS Analysis, we observe that, a typical images RCOVER ≈ RSTEGO and
SCOVER ≈ SSTEGO and so no changes found in R and S value for embedding characters of different sizes. The steganalysis
tool was developed by Guillermito to implement the chi-square analysis for performing statistical attack and detect any
type of hidden messages [34]. In this work Chi Square Probability Distribution and Statistics Distribution graph (Figure
11 and 12) shows no difference in between cover and stego images. Here the entire attack algorithms are working on
embedding one bit per LSB where as our technique is embedding four bits per pixel. This technique is not depending
upon LSB and for that reason the attack is not performing their profession in this PFM method.
The PFM method is compared with LSB [13,16,18,32], PVD [33,19], GLM [20] and PMM [10] method which is shown
in tabular form in Figure 13.
LSB[13,16,18,32], PVD[33,19], GLM[20]
1. Data can be easily tractable in various
image steganography attacks.
2. Evaluating performance only MSE and
PSNR has been incorporated.
Proposed Pixel Factor Mapping (PFM) Method
1. Tested through some steganography attack like RS
analysis, SP analysis and Chi-square analysis etc.
2. Performance measured using various performance
metric like MSE, PSNR, SSIM, Correlation, RMSE,
KL Divergence, Entropy etc.
3. Security tested and measured high.
3. Security of the hidden data has not tested
properly.
4. LSB method directly replacing the LSBs,
4. Use mapping technique with the help of maximum
PVD requires range table. GML map
prime factor value of pixel intensity and pixel
image data by modifying the Gray level.
selection method.
5. These methods can embed one bit per
5. This method can embed four bits per pixel.
pixel.
Figure 13: Comparison between Previous and Proposed Work
5. CONCLUSION
This work catch with the techniques for steganography in 4 bit PFM (Pixel Factor Mapping) method related to image
Steganography. A well-organized unmarked steganographic method for embedding secret messages into images without
producing any key changes has been projected in this paper with the help of various performances metric. This method is
a robust method which can also avoid some image attacks after noise addition. From the security aspects the attack
technique is very low between the cover image and stego image which surrender a very high security value of the hidden
data. The hidden message also stays undetected after application of some well known steganalysis method on it. This
method can extract the secret message without the use of cover image. This method can improve and maximize the
embedding capacity then previous developed image Steganography systems. In future we have planned to improve the
embedding capacity as well as develop the same technique in frequency domain and also check with some other
steganalysis attack like WS Analysis etc.
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AUTHOR
Indradip Banerjee is a Research Scholar at National Institute of Technology, Durgapur, West Bengal, India.
He received his MCA degree from IGNOU in 2009, PGDCA from IGNOU in 2008, MMM from Annamalai
University in 2005 and BCA (Hons.) from The University of Burdwan in 2003. He is registered and pursuing
his PhD. in Engineering at Computer Science and Engineering Department, National Institute of Technology,
Durgapur, West Bengal, India. His areas of interest are Steganography, Cryptography, Text Steganography, Image
Steganography, Quantum Steganography and Steganalysis. He has published 17 research papers in International and
National Journals / Conferences.
Souvik Bhattacharyya received his B.E. degree in Computer Science and Technology from B.E. College,
Shibpur, India and M.Tech degree in Computer Science and Engineering from National Institute of
Technology, Durgapur, India. He has received Ph.D (Engg.) from National Institute of Technology, Durgapur,
India. Currently he is working as an Assistant Professor and In-Charge in Computer Science and Engineering
Department at University Institute of Technology, The University of Burdwan. His areas of interest are Natural Language
Processing, Network Security and Image Processing. He has published nearly 65 papers in International and National
Journals / Conferences.
Gautam Sanyal has received his B.E and M.Tech degree National Institute of Technology (NIT), Durgapur,
India. He has received Ph.D (Engg.) from Jadavpur University, Kolkata, India, in the area of Robot Vision. He
possesses an experience of more than 25 years in the field of teaching and research. He has published nearly
150 papers in International and National Journals / Conferences. Two Ph.Ds (Engg) have already been
awarded under his guidance. At present he is guiding six Ph.Ds scholars in the field of Steganography, Cellular Network,
High Performance Computing and Computer Vision. He has guided over 10 PG and 100 UG thesis. His research interests
include Natural Language Processing, Stochastic modeling of network traffic, High Performance Computing, Computer
Vision. He is presently working as a Professor in the department of Computer Science and Engineering and also holding
the post of Dean (Students’ Welfare) at National Institute of Technology, Durgapur, India.
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