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The SIJ Transactions on Computer Networks & Communication Engineering (CNCE), Vol. 1, No. 3, July-August 2013
An Improved Algorithm for Designing
Secure Point-to-Point Wireless
Environment
Jagpreet Singh*, Vivek Thapar** & Anshu Aneja***
*Application Support Specialist, Service Support Desk, Accenture, Gurgaon, Haryana, INDIA. E-Mail: jagpreetsingh1987@gmail.com
**Assistant Professor, Department of Computer Science and Engineering, Guru Nanak Dev Engineering College, Ludhiana, Punjab, INDIA.
E-Mail: vivek_thapar_engg@yahoo.com
***Assistant Professor, Department of Information Technology, Guru Nanak Dev Engineering College, Ludhiana, Punjab, INDIA.
E-Mail: anshuaneja@yahoo.co.in
Abstract—The goal of this paper is to be an easy to follow guide for configuring and securing a wireless
network in a windows environment. Security has been one of the most important issues in wireless
communication. Encryption of messages into cipher text is one of the techniques to provide security up to
some extent but, it also causes another problem, i.e., how to safely and confidentially encrypt and deliver
security keys so that hackers have to spend a very long time before they can decrypt the cipher text. In this
paper our main aim is to devise a secure point-to-point encryption method for a wireless communication
environment. Novel Diffie-Hellman-based Public Key Distribution System has been implemented, which
adopts a stream cipher technique to encode plaintext with a pseudo random number sequence. We have
verified the proposed method and simulation results show that the performance of this method can meet users’
communication needs. Also it’s a system with high complexity and unpredictability from the consecutive
creation of increasingly positive real value sequences to the final output of random numbers. 98 % of the
random numbers produced passed 60,000 tests determined by Federal Information processing Standards
Publication.
Keywords—Encryption; Diffe-Hellman; Pseudo Random Number Sequence; Secure Point to Point; Sequence
Ladder; Stream Cipher Technique; Wireless Security.
Abbreviations—Public Key Distribution System (PKDS); Pseudo Random Number Generator (PRNG); Ron
Rivest, Adi Shamir and Leonard Adleman (RSA); WiFi Protected Access (WPA); Wireless Encryption Privacy
(WEP).
I.
A
INTRODUCTION
S technology advances in society the need for wired
and wireless networking has become essential. Each
of these types of networking has their advantages and
disadvantages according to security. Wired networking has
different hardware requirements and the range and benefits
are different. Wireless networking takes into consideration
the range, mobility, and the several types of hardware
components needed to establish a wireless network [Joshua
Muscatello & Joshua Martin, 2005]. The wireless network is
fundamentally different from wired network. The biggest
difference between these two types of networks is one uses
network cables and one uses radio frequencies. A wired
network allows for a faster and more secure connection and
can only be used for shorter distances. A wireless network is
a lot less secure and transmissions speeds can suffer from
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outside interference. Wired networks are more reliable and
predictable than wireless ones. In addition wireless links have
high bit error rate, but they are more dynamic i.e. their
characteristics can change in short periods of time. There is
also another additional difference between them; wired links
are unicast links, while majority of wireless links are
broadcast links. Thus, transmissions over a wired network do
not interfere with each other, which is quite common for the
wireless networks. There are also issues related with mobility
and portability in wireless networks which in contrast are not
present in wired networks. In general, network design based
on a wired realm does not utilize the characteristic of wireless
environments effectively.
Wireless communication is by a measure, the fastest
growing segment of communication industry. As such, it has
captured the attention of media and the imagination of the
public. Due to rapid hardware cost reduction and providing
© 2013 | Published by The Standard International Journals (The SIJ)
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The SIJ Transactions on Computer Networks & Communication Engineering (CNCE), Vol. 1, No. 3, July-August 2013
its devices the portability, it has become one of the most
important communication methods in our everyday life.
Many people communicate with others through wireless
almost everyday. The explosive growth of wireless system
coupled with the proliferation of laptop and palmtop
computers indicate a bright future for wireless networks, both
as stand alone systems and as a part of larger networking
infrastructure. Wireless network provides the ability to enter
a network while being mobile. However, wireless networking
is prone to some security issues [Barbeau, 2005].
Crackers have found wireless networks relatively easy to
break into, and even use wireless technology to crack into
wired networks. The risks to users of wireless technology
have increased as the service has become more popular.
Therefore many technical challenges remain in designing a
robust and secure wireless network that delivers the
performance necessary to support emerging applications
[Safdar et al., 2006]. Security threats are eminent due to the
open nature of communication. The two main security issues
related with the wireless network are authentication and
privacy [Andrea Golsmith, 2004]. As a result, it's very
important that enterprises define effective wireless security
policies that guard against unauthorized access to important
resources. From privacy viewpoint, wireless security is a
crucial work since messages are delivered to their
destinations through the air so hackers can maliciously
intercept the massages and decrypt the messages. Although
wireless networks provide convenience they do open the
organization up to security and privacy risks. There are a
great number of security risks associated with the current
wireless protocols and encryption methods, and in the
carelessness and ignorance that exists at the user and
corporate IT level. Cracking methods have become much
more sophisticated and innovative with wireless.
II.
STRUCTURE OF THE PAPER
This paper reports preliminary research undertaken to answer
the various questions related with the secure communication
of wireless systems. Section 3 introduces the various other
types of existing approaches to provide security. Section 4
then shows the related work done to provide the secure
communication between two end systems in wireless
environment by implementing various authentication
protocols and methods. Section 5 explains the new proposed
approach so as to implement a secure wireless system.
III.
EXISTING SCHEMES
3.1. Diffie and Hellman Public Key Distribution
Diffie and Hellman [Diffie & Hellman, 1976] proposed the
concept of a public key distribution system (PKDS) which is
a public key cryptosystem, and with which two users could
individually generate the same secret key by mutually
exchanging their public keys through public network
channels without directly delivering the private key.
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A single key encryption method can prevent an
unauthorized person being able to access the contents of
message. However once the key has been decrypted by the
hackers, the hackers will realize what information is
conveyed on the message. Stream cipher techniques [Xiao et
al., 2009] have been proved that they can provide cipher text
with higher security levels than those provided by using only
one single key since they encrypt a message with a stream. It
is more difficult for hackers to solve a steam than to solve a
key.In 1978, Rivest, Shamir and Adleman (RSA) [Diffie &
Hellman, 1976], proposed an exponential function as a oneway Trapdoor Function based on factorization. Currently, the
RSA is one of the most popular and famous asymmetric
encryption/decryption systems, with which site A publicizes
its public keys (eA;NA). The other side such as site B,
encrypts its key K with (eA;NA), as RSA En(K;eA) that will
be sent to A. Only A with its own private key (dA;NA) can
decrypt RSA En(K;eA). Therefore, even though RSA
En(K;eA) is delivered through a wireless channel, K can be
safely sent to A.
Diffie–Hellman key exchange (D-H) is a specific method
of exchanging cryptographic keys. It is one of the earliest
practical examples of key exchange implemented within the
field of cryptography. The Diffie–Hellman key exchange
method allows two parties that have no prior knowledge of
each other to jointly establish a shared secret key over an
insecure communications channel. This key can then be used
to encrypt subsequent communications using a symmetric
key cipher. The scheme was first published by Whitfield
Diffie and Martin Hellman in 1976, although it had been
separately invented a few years earlier within GCHQ, the
British signals intelligence agency, by Malcolm J.
Williamson, but was kept classified. In 2002, Hellman
suggested the algorithm be called Diffie–Hellman–Merkle
key exchange in recognition of Ralph Merkle's contribution
to the invention of public-key cryptography (Hellman, 2002).
Although Diffie–Hellman key agreement itself is an
anonymous (non-authenticated) key-agreement protocol, it
provides the basis for a variety of authenticated protocols,
and is used to provide perfect forward secrecy in Transport
Layer Security's ephemeral modes (referred to as EDH or
DHE depending on the cipher suite).The method was
followed shortly afterwards by RSA, an implementation of
public key cryptography using asymmetric algorithms.
Diffie–Hellman establishes a shared secret that can be used
for secret communications by exchanging data over a public
network. The following diagram illustrates the general idea of
the key exchange by using colors instead of a very large
number. The key part of the process is that Alice and Bob
exchange their secret colors in a mix only. Finally this
generates an identical key that is mathematically difficult
(impossible for modern supercomputers to do in a reasonable
amount of time) to reverse for another party that might have
been listening in on them.
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The SIJ Transactions on Computer Networks & Communication Engineering (CNCE), Vol. 1, No. 3, July-August 2013
3.2. RSA System
RSA is an algorithm for public-key cryptography that is
based on the presumed difficulty of factoring large integers,
the factoring problem. RSA stands for Ron Rivest, Adi
Shamir and Leonard Adleman, who first publicly described
the algorithm [Rivest et al., 1978]. Clifford Cocks, an English
mathematician, had developed an equivalent system in 1973,
but it was classified until 1997. A user of RSA creates and
then publishes the product of two large prime numbers, along
with an auxiliary value, as their public key. The prime factors
must be kept secret. Anyone can use the public key to encrypt
a message, but with currently published methods, if the
public key is large enough, only someone with knowledge of
the prime factors can feasibly decode the message. Whether
breaking RSA encryption is as hard as factoring is an open
question known as the RSA problem.
IV.
LITERATURE SURVEY
Unreliable wireless media, host mobility and lack of
infrastructure present a big challenge to the provision of
secure communications in wireless networks. The contents of
the communication must be encrypted and mutual
authentication conducted between the communicating nodes
in order to provide adequate security. Authentication
protocols and key management techniques are utilized to
provide security in many distributed systems. Much research
has been conducted into the development of key management
techniques and authentication protocols for WLAN and
traditional
wireless
networks.
Several
encryption
mechanisms, e.g., Wireless Encryption Privacy (WEP) [Shin
et al., 2006], WiFi Protected Access (WPA) [Shin et al.,
2006] and Privacy Key Management Version 1 (PKMv1)
[IEEE, 2004] have been proposed for wireless network. WEP
as a part of the IEEE 802.11 standard uses RC4, one of the
stream cipher algorithms, to encrypt messages. This
mechanism encrypting data with a key of 64 bits was secure
enough to resist hackers’ attacks. But, its initialization vector
is no longer long enough to protect wireless messages since
now the traffic key 24 bits in length can be cracked easily.
WPA, which also uses RC4 as its encryption algorithm, was
adopted by the WiFi Alliance consortium to substitute WEP.
WPA uses two techniques to exchange keys. First, it employs
a 48-bit IV, rather than a 24-bit IV, as its traffic key; second,
it adopts Temporal Key Integrity Protocol to dynamically
change the traffic key. This mechanism has a problem in that
the management frames can be easily spoofed by malicious
hackers since all sessions between end users and central
control equipments are not robust and safe. The DiHam [Leu
et al., 2010; Huang et al., 2011] was developed based on the
PKMv1 by improving the key exchange flow and providing
different data security levels. Basically, its key exchange
process consists of two phases, the authentication phase and
TEK exchange phase. In the authentication phase, the AK is
individually generated by the BS and MS after the delivery of
the Authentication-Request message and Authentication-
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Reply message. In the TEK exchange phase, three security
levels of TEK generation processes are proposed to meet
different user security requirements. This phase starts when
MS sends a TEK-Exchange. Steven Galbr & Ruprai (2009)
have presented an improvement to the algorithm given by
Gaudry and Schost for solving the 2-dimensional DLP as
well as extending the algorithm to the multidimensional DLP.
They have also given further depth to the analysis given by
Gaudry and Schost specifically for the cases where d > 2. In
Section 6 we have seen just a smattering of applications of
this low-memory algorithm. An open problem is to
investigate how best to exploit the algorithm when the search
space is not an orthotropic but a multidimensional
`arrowhead' which arises in the case of point counting on
curves of genus 2 and higher. Elgamal (1985) described a
public key cryptosystem and a signature scheme based on the
difficulty of computing discrete logarithms over finite fields.
The systems are only described in GF(p). The public key
system can be easily extended to any GF(pm), but recent
progress in computing discrete logarithms over GF(pm)
where m is large makes the key size required very large for
the system to be secure. The sub exponential time algorithm
has been extended to GF(p²) and it appears that it can be
extended to all finite fields, but the estimates for the running
time for the fields GF(pm) with a small m seem better at the
present time. Hence, it seems that it is better to use GF(pm)
with m = 3 or 4 for implementing a cryptographic system.
The estimates for the running time of computing discrete
logarithms and for factoring integers are the best known so
far, and if the estimates remain the same, then, for the same
security level, the size of the public key file and the size of
cipher text will be double the size of those for the RSA
system.
V.
PROPOSED SCHEME
In propose system we presented a secure point-to-point
encryption method (SePem for short) for a wireless
communication environment. The SePem integrates the
Diffie-Hellman PKDS (DH-PKDS for short) and a stream
cipher technique without increasing required information
exchange frequencies and burdens. It uses a seed as input to
trigger a pseudo random number generator (PRNG for short)
which invokes the increasing-doubling able sequence ladder
algorithm we developed to generate a pseudorandom number
sequence (PRNS).
The SePem integrates the DH-PKDS and a stream cipher
technique. Generally, applying multiple variables to a random
number generation algorithm can effectively improve
randomness quality of generated random numbers and then
the security level of the yielded cipher text since hackers have
to calculate values for the variables one by one before they
can decrypt the cipher text. A larger number of unpredictable
factors embedded in each PRNS can also raise randomness
quality of the PRNS which can in turn generate a higher
security-level message.
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The SIJ Transactions on Computer Networks & Communication Engineering (CNCE), Vol. 1, No. 3, July-August 2013
In cryptography, a stream cipher is a symmetric key
cipher where plaintext digits are combined with a
pseudorandom cipher digit stream (key stream). A
stream cipher is a method of encrypting text (to
produce cipher text) in which a cryptographic key
and algorithm are applied to each binary digit in a data
stream, one bit at a time. This method is not much used in
modern cryptography. The main alternative method is
the block cipher in which a key and algorithm are applied to
blocks of data rather than individual bits in a stream. The
pseudorandom key stream is typically generated serially from
a random seed value using digital shift registers. The seed
value serves as the cryptographic key for decrypting the
cipher text stream.
Plaintext Stream
5.1. Stream Cipher Encryption
Pseudo-Random Stream 1 0 0 1 1 0 1 0 1 1 0 1 0 0
Stream ciphers as shown in Fig. 1 represent a different
approach to symmetric encryption from block ciphers [Rivest
et al., 1978]. Block ciphers operate on large blocks of digits
with a fixed, unvarying transformation. This distinction is not
always clear-cut: in some modes of operation, a block cipher
primitive is used in such a way that it acts effectively as a
stream cipher. Stream ciphers typically execute at a higher
speed than block ciphers and have lower hardware
complexity. However, stream ciphers can be susceptible to
serious security problems if used incorrectly: see stream
cipher attacks — in particular, the same starting state (seed)
must never be used twice. A stream cipher is a symmetric
key cipher where plaintext digits are combined with
a pseudorandom cipher digit stream (key stream). In a stream
cipher each plaintext digit is encrypted one at a time with the
corresponding digit of the key stream, to give a digit of the
cipher text stream. An alternative name is a state cipher, as
the encryption of each digit is dependent on the current state.
In practice, a digit is typically a bit and the combining
operation an exclusive-or (xor).
Small
Random
Key
Small
Random
Key
Stream Cipher
Stream Cipher
KeyStream
(pseudorandom
KeyStream
(pseudorandom
string)
string)
Plaintext
Plaintext
Cipher Text
+
+
Key
Pseudo-Random
Sequence Generator
PlainText Bitstream
+
Ciphertext Stream
Cipher text
Bit stream
11111111000000
0 1100101110100
Figure 2: Stream Cipher Principal
5.2. Pseudorandom Number Generator
A pseudorandom number generator (PRNG), also known as a
deterministic random bit generator (DRBG) as shown in Fig.
2, is an algorithm for generating a sequence of numbers that
approximates the properties of random numbers [Huang et
al., 2009]. The sequence is not truly random in that it is
completely determined by a relatively small set of initial
values, called the PRNG's state, which includes a truly
random seed. Although sequences that are closer to truly
random can be generated using hardware random number
generators, pseudorandom numbers are important in practice
for their speed in number generation and their reproducibility,
and they are thus central in applications such as simulations
(e.g., of physical systems with the Monte Carlo method), in
cryptography, and in procedural generation. Good statistical
properties are a central requirement for the output of a
PRNG, and common classes of suitable algorithms include
linear congruent generators, lagged Fibonacci generators, and
linear feedback shift registers. Cryptographic applications
require the output to also be unpredictable, and more
elaborate designs, which do not inherit the linearity of
simpler solutions, are needed. More recent instances of
PRNGs with strong randomness guarantees are based on
computational hardness assumptions, and include the Blum
Blum Shub, Fortuna, and Mersenne Twister algorithms.
In general, careful mathematical analysis is required to
have any confidence that a PRNG generates numbers that are
sufficiently ―random‖ to suit the intended use. John von
Neumann cautioned about the misinterpretation of a PRNG as
a truly random generator, and joked that ―Anyone who
considers arithmetical methods of producing random digits is,
of course, in a state of sin.‖ Robert R. Coveyou of Oak Ridge
National Laboratory once titled an article, ―The generation of
random numbers is too important to be left to chance.‖
Figure 1: Stream Cipher Structure
+
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+
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The SIJ Transactions on Computer Networks & Communication Engineering (CNCE), Vol. 1, No. 3, July-August 2013
5.3. Sequence Ladder
A binary sequence (BS) is a sequence of N bits,
𝑎𝑗 for 𝑗 = 0,1, . . . , 𝑁 − 1,
i.e. 𝑚 ones and 𝑁 − 𝑚 zeros. A BS is pseudo-random
(PRBS) if its autocorrelation function:
𝑁−1
𝑐 𝑣 =
𝑎𝑗 𝑎𝑗 + 𝑣
𝑗 =0
has only two value
𝑐 𝑣 =
𝑚, 𝑖𝑓 𝑣 ≡ 0 (𝑚𝑜𝑑 𝑁)
𝑚𝑐 ′ , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
party B will generate a seed value and further the appropriate
value for the index and number of elements will be chosen. In
the third step a PNRS number will be generated automatically
and the party b will be capable to send a cipher text to other
side. Thus the party A will receive the encrypted text sent by
party B. The received cipher text can be decrypted and read
by party A. Thus the system will be capable to send the
secure key, generate PNRS number and finally provide the
encryption of the text and decryption of cipher text on other
side as shown below.
where,
𝑚−1
𝑁−1
is called the duty cycle of the PRBS.
A PRBS is random in a sense that the value of an aj
element is independent of the values of any of the other
elements, similar to real random sequences.
It is 'pseudo' because it is deterministic and after N
elements it starts to repeat itself, unlike real random
sequences, such as sequences generated by radioactive decay
or by white noise. The PRBS is more general than the nsequence, which is a special pseudo-random binary sequence
of n bits generated as the output of a linear shift register [Jong
Seon et al., 1998]. An n-sequence always has a 1/2 duty cycle
and its number of elements N = 2k − 1. PRBS's are used in
telecommunication, encryption, simulation, correlation
technique and time-of-flight spectroscopy.
𝑐=
VI.
SIMULATION ENVIRONMENT AND
DISCUSSION
6.1. Simulation Model
The simulations were performed in a client-server
environment. With our proposed scheme the plain text is
encrypted and sent to the server via three different wireless
channels. We measured the timing of key delivery in three
different wireless environments including 802.11b without
encryption methods, High Speed Download Packet Access
(3.5) and WiMax. The proposed system is implemented with
the above described approach and a secure communication
between two wireless end systems is demonstrated by
considering two parties such as side A application and side B
application as shown below from Fig. 3 to Fig. 12.The two
applications can run independently on two computer systems
equipped with wireless network adapter cards and using any
of the above mentioned wireless communication channel. The
communication process starts from either end such as party A
application or party B application where both of the sides
need to use the details related with the IP address and port no
of the respective application. After entering the appropriate
details of IP address and port number on each point, both the
parties get ready for communication with each other. At the
very first step one party such as party A will generate and
send the DH key to the other side and that too will be
received by other party such as party B. In second step the
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Figure 3: Party A Ready to Send Data after Entering and Saving the
Details of Party B
Figure 4: Party B Ready to Receive the Data from Side A after
Entering and Saving Details of Party A
© 2013 | Published by The Standard International Journals (The SIJ)
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The SIJ Transactions on Computer Networks & Communication Engineering (CNCE), Vol. 1, No. 3, July-August 2013
Figure 5: Party A Generating and Sending the DH key(K) to Party B
Figure 7: Generation of Text and Seed on Party B
Figure 6: Party B Receiving the key(K) from Party A
Figure 8: Choosing the Right Number of value for Parameters such
as Number of Elements and Index on Party B
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The SIJ Transactions on Computer Networks & Communication Engineering (CNCE), Vol. 1, No. 3, July-August 2013
Figure 9: Generation of PRNS Number on Party B
Figure 11: Receiving the Cipher Text on Party A Sent by Party B
Figure 10: Generating and Sending Cipher Text on Party B
Figure 12: The Decryption of Cipher Text Received by Party A
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The SIJ Transactions on Computer Networks & Communication Engineering (CNCE), Vol. 1, No. 3, July-August 2013
6.2. Simulation Analysis
To analyze the system we can create a simulated environment
for a wireless communication and can run the system in using
various channels to generate the cipher text from a plain text
which can be of 512 bits or 1024 bits length. We run the
above proposed system in a simulated system which can be
implemented in java script or any other supporting platform
that provide different environments to run the system for
wireless communication between two parties. Within the
simulator we can run the system in three environments such
as 802.11, High Speed Download Packet Access (3.5) and
WiMax, which are basically acting as three different channels
in wireless communication. The timing of generating and
delivering the key is measured in each environment. Results
found in running the system in each environment are
measured and are shown in Table 1. We found that the time
required in each step or environment to generate the cipher
text is very short. Here we choose the 802.11b which is the
worst one among the three test environments as an example.
The cost spend in steps 1-3 is 0.34 sec, 0.12 sec, 0.34 sec
respectively as shown in table 1.
Table 1: Time Required to Generate the Cipher Text in Different
Environments
Step
1
2
3
4
Env
(sec)
(sec)
(sec)
(sec)
802.11b
0.34
0.12
0.34
54
HSDPA
1.7
5.55
0.19
19
WiMax
2.5
0.29
1.28
20
The above results are showing time required to encode
the plain text of some length into cipher text in different
environments in a wireless networks which are very short as
compared to other techniques used in same wireless networks
to encode plain text of same length into cipher text. Thus we
can conclude that the propose system has many benefits. First
the system can be adapted to any wireless networks using
different channels and that originally need to deliver
encrypted keys. Second it spends very less time to generate
cipher text on each key exchange step. At last the proposed
system is very secure since both the keys K and K’ and the
PNRS are generated by parties A and B.
VII.
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The most significant benefits of wireless communication are
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adapted to any wireless network and it takes very short time
to generate cipher text on each key exchange. It is very
suitable mechanism for implementing key management and
delivery in wireless environment. It is very difficult and time
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© 2013 | Published by The Standard International Journals (The SIJ)
65
The SIJ Transactions on Computer Networks & Communication Engineering (CNCE), Vol. 1, No. 3, July-August 2013
Jagpreet Singh did his Graduation from
Punjab Technical University, Kapurthala in
2009 and perusing his M.Tech in Information
Technology at Guru Nanak Dev Engineering
College, Ludhaiana , India from Punjab
Technical University, Kapurthala. He is
associated with MNC Accenture as
Application Support Specialist. His job
profile is Incident Management and deal with
Desktop, Application, Server, and Network related issues. His
research interest is in the fields of Network Security, Wan and Lan
Technologies. He has presented many papers in different seminars
and conferences His research papers have been published in various
national and international journals.
Anshu Aneja did his Graduation from
Punjab Technical University, Kapurthala
in 2003 and has completed his M.Tech in
Information Technology at Guru Nanak
Dev Engineering College, Ludhaiana ,
India from Punjab Technical University,
Kapurthala. His research interest is in the
fields of Network Security, Wan
Technologies, Internetworking, and Routing Protocols. He
has presented many papers in different seminars and
conferences His research papers have been published in
various national and international journals.
Vivek Thapar did his graduation from
Punjab Technical University, Kapurthala
and Post Graduation from Punjabi
University with 72%. He is involved in
research since last four years. His
research paper has been published in
many national and internationals
journals. He has presented many papers
in different seminars and conferences. Currently he is
involved in developing novel software for different statistical
methods and presently working as Asst. Prof in Computer
Science and Engineering at Guru Nanak Dev Engineering
College, Ludhiana, India. His area of Specialization is
Network Security and Web Technologies. He is currently
doing PhD from Punjab Technical University.
ISSN: 2321 – 2403
© 2013 | Published by The Standard International Journals (The SIJ)
66
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