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Securing Password For Wireless Device Using Training Functions of MATLAB Dr Menal Dept. of Computer Science Maharaja Surajmal Institute (GGSIPU) Janakpuri, Delhi, India E-mail: [email protected] Dr Sumeet Gill Dept. of Mathematics Maharshi Dayanand University Rohtak, Haryana, India E-mail: [email protected] AbstractTraditional methods of authentication in wireless networking use various approaches like storing the passwords in encrypted form, salting the password, etc... All these simple approaches are not adequate for the proper functioning of any organization. Wireless security needs advanced technologies for protecting data and valuable information. Only cryptographic methods are not sufficient, wireless community requires more attention. Artificial Neural Network has the ability to deal with these types of problems. We propose an authentication mechanism for wireless equipments used in wireless communication. Techniques of Artificial Intelligence and Neural Network have been widely used for solving the problems. This chapter describes the role of different training functions of the algorithm in the memorization of the network parameters and Back propagation algorithm is applied to the collected data. The proposed method uses neural network concepts for storing the passwords and authentication process. KeywordsAuthentication; Artificial Neural Network; Back propagation Algorithm; Wireless Communication; Wireless Security. I. INTRODUCTION This Earlier computer networks were only used by the university researchers, corporate employees for sending office information through e-mail or by sharing peripheral devices among the employees in the military and in government operations. At that time no one realized the security of data, because the use of data was limited and by limited persons in a given amount of time. So, security did not get a lot of attention that time. But for the last few decades, the existence of computer network spread widely. Daily, millions of ordinary people use the network facilities for their convenience such as for banking, shopping, ticket booking, watching movies online, chatting, sending emails and for the use of social networking like Face book, twitter etc. Usage of wireless devices like mobile phones, smart phones, PDA, Laptops increases day by day in every field of life. Mobile phones, smart phones and laptops transfer information and use mobile data over the wireless networks [1]. Wireless devices have become the soul of technology and heart of the growing market. They overcome the market of IT sector and plays a major role in communication. People use each and every facility of internet without knowing the security aspects. The key element for all the organizations or for any system in the networking is the security of the resources, data and sensitive information. Public can access the data from anywhere, anytime by making hotspots without knowing the security measures. The intruders easily attack on such type of users and misuse their sensitive information very often. Due to the proliferation of the technologies of wireless networking, around 80% of the society uses the facility of wireless networking. The rapid advent of the internet and the emergence of various World Wide Web applications across the world, organizations generate a large amount of data on a daily basis. Different types of information and sensitive data is shared between the organizations on a regular basis. Data security is the utmost critical issue in transmission over Wireless Network. Network security issues are also important as layman moving towards digital information age. Network security is comprised of both public and private networks that include businesses, government agencies and individuals. In other words, Computer security is a vast topic and it includes data security and network security [2]. Before the widespread use of the internet, the security of information or data for an organization was provided to the managers or other reliable post and administrative means. Gradually, rapid advancement in the computer world requires automated devices to protect data and important information collected and put aside in the system turn into an evident basically in sharing systems. The general name given by the researchers to a set of tools that safeguard from hackers called computer security [3]. Security covers vast subject matter which includes data security and network security. Security International Journal of Pure and Applied Mathematics Volume 118 No. 7 2018, 9-19 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu 9

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Securing Password For Wireless Device Using

Training Functions of MATLAB

Dr Menal

Dept. of Computer Science

Maharaja Surajmal Institute (GGSIPU)

Janakpuri, Delhi, India

E-mail: [email protected]

Dr Sumeet Gill

Dept. of Mathematics

Maharshi Dayanand University

Rohtak, Haryana, India

E-mail: [email protected]

Abstract— Traditional methods of authentication in wireless

networking use various approaches like storing the passwords in

encrypted form, salting the password, etc... All these simple

approaches are not adequate for the proper functioning of any

organization. Wireless security needs advanced technologies for

protecting data and valuable information. Only cryptographic

methods are not sufficient, wireless community requires more

attention. Artificial Neural Network has the ability to deal with

these types of problems. We propose an authentication

mechanism for wireless equipments used in wireless

communication. Techniques of Artificial Intelligence and Neural

Network have been widely used for solving the problems. This

chapter describes the role of different training functions of the

algorithm in the memorization of the network parameters and

Back propagation algorithm is applied to the collected data. The

proposed method uses neural network concepts for storing the

passwords and authentication process.

Keywords—Authentication; Artificial Neural Network; Back

propagation Algorithm; Wireless Communication; Wireless

Security.

I. INTRODUCTION

This Earlier computer networks were only used by the

university researchers, corporate employees for sending office

information through e-mail or by sharing peripheral devices

among the employees in the military and in government

operations. At that time no one realized the security of data,

because the use of data was limited and by limited persons in a

given amount of time. So, security did not get a lot of attention

that time. But for the last few decades, the existence of

computer network spread widely. Daily, millions of ordinary

people use the network facilities for their convenience such as

for banking, shopping, ticket booking, watching movies

online, chatting, sending emails and for the use of social

networking like Face book, twitter etc. Usage of wireless

devices like mobile phones, smart phones, PDA, Laptops

increases day by day in every field of life. Mobile phones,

smart phones and laptops transfer information and use mobile

data over the wireless networks [1]. Wireless devices have

become the soul of technology and heart of the growing

market. They overcome the market of IT sector and plays a

major role in communication. People use each and every

facility of internet without knowing the security aspects.

The key element for all the organizations or for any system

in the networking is the security of the resources, data and

sensitive information. Public can access the data from

anywhere, anytime by making hotspots without knowing the

security measures. The intruders easily attack on such type of

users and misuse their sensitive information very often. Due to

the proliferation of the technologies of wireless networking,

around 80% of the society uses the facility of wireless

networking. The rapid advent of the internet and the

emergence of various World Wide Web applications across

the world, organizations generate a large amount of data on a

daily basis. Different types of information and sensitive data is

shared between the organizations on a regular basis. Data

security is the utmost critical issue in transmission over

Wireless Network. Network security issues are also important

as layman moving towards digital information age. Network

security is comprised of both public and private networks that

include businesses, government agencies and individuals. In

other words, Computer security is a vast topic and it includes

data security and network security [2].

Before the widespread use of the internet, the security of

information or data for an organization was provided to the

managers or other reliable post and administrative means.

Gradually, rapid advancement in the computer world requires

automated devices to protect data and important information

collected and put aside in the system turn into an evident

basically in sharing systems. The general name given by the

researchers to a set of tools that safeguard from hackers called

computer security [3]. Security covers vast subject matter

which includes data security and network security. Security

International Journal of Pure and Applied MathematicsVolume 118 No. 7 2018, 9-19ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

9

more bothered to ensure that unwanted user don’t access or

alter the message destined for specific receivers and

unauthorized people are not trying to access the services [4].

Network security is a concept to protect data transmission over

a wired or wireless network. The easiest approach to safeguard

a network device from unauthorized access is to assign him a

different user id with a matching password [5]. Network

security is the main pillar in information security as it is

responsible for the whole information passes through the

network that includes hardware and software security

functions, access control, features and operating procedures,

etc... Cryptography is a technology that is introduced to

protect the network from threats [6]. Business Houses and

companies started protecting their useful systems and

networks using cryptographic techniques as a result of prompt

advancement in the global use of computerized data

collection, advancement in communications and

eavesdropping technologies. Earlier, the cryptographic

techniques used exclusively by the military and government

communities. Later on, it is necessary to use some

cryptographic methods or some other means of protection to

enhance the security. Computer systems and networks which are stored,

processing and communicating sensitive or valuable information require protection against such unauthorized access [7]. The usage of the technology and advancement in the technology is directly related to the ascending graph of the wireless networking. However, side by side intruders and unauthorized persons will also try to breach the security measures. This leads an increasing need for taking extra security measures in wireless technology. There are many solutions and methods that provide security to the wireless communication [8]. Network security considers authorization of access of data in a network. Password authentication is one of them. Every user assigns an Id and corresponding password that allows them to access information without any problem. This Id is the identity of its authorized usage

II. AUTHENTICATION MECHANISM

Authentication is a two way process in which user

confirms his or her identity to the computer system [9].

Authentication schemes are mostly based on passwords, smart

cards and biometrics. Authentication ensures that the services

and system resources are used by the authentic person.

Authentication is of two types- message authentication and

user authentication. In message authentication, when the

sender sends the message, it is not necessary that the receiver

is online. On the other hand, in user authentication both, the

receiver and the sender must be present in real time

communication. User authentication involves two important

entities claimant and the verifier [10]. The user whose

distinction requisites to be established is called claimant and a

verifier, who attempt to establish the distinction of the

claimant. In user authentication, always claimant proves his

identity to the verifier.

A. Authentication Methods

There are different methods for verifying the identity, such as- some are we known as a pin, password, keys and some we possess as Identification card, smart card, etc. or some are inherent as fingerprint, handwriting, etc... Currently authentication methods are categorized into [11].

The Biometric is a study of methods that distinguish uniquely between physical characteristics and personal traits of an individual [12]. For example face recognition, iris recognition, handwriting and voice, etc... Two methods applied to authenticate users in biometric authentication are human physiological and behavioral characteristics. Biometric features are not temporary and are not manipulative easily. There is no chance of biometric objects lost, stolen, forgotten or any other mishappening. This is an advantageous feature of biometrics for clients as well as for the organization. Having these advantages, there is disadvantages too [13]. Biometric method is still in improving state as the performance of biometric systems is not ideal. People who are not physically fit or having some problem with their body parts are not suitable for biometric authentication systems. Although, biometric systems are not perfect they also show errors sometimes. As in the case of fingerprint authentication, there are chances of an authorized individual can be denied access [14]. The high cost of hardware and software installation is the major fall in the use of this system. The physical characteristics of an individual changes when he/she aged or affected by some physical injuries. Besides all the drawbacks biometric systems are very desirable also, the most attractive feature is data can’t land up like missing, taken or forgotten as other authentication mechanism.

This mechanism includes password and PIN methods. Password authentication is the most popular method, as it is the old one, but since many of us are interacting with our systems through this method. A user account and the corresponding password are assigned to the account [15]. Whenever the user enters the correct password, the system verifies the user’s authentication from a database that stores all the information regarding the account holders and their password. PIN’s are also working in the same manner and popularly used in smart cards, ATM cards, etc... They use strong security mechanisms like cryptography, recognition, etc. [16].

This technique contain both text based and image based passwords. Most of the researchers used knowledge based authentication techniques with token based methods for increasing the security level of the user and the system [17].

B. Password Based Authentication Scheme

Different authentication mechanisms have their own

disadvantages and advantages regarding security, reliability

and support to the system. Password based authentication is

the simplest and oldest method of authentication [18]. Keeping

International Journal of Pure and Applied Mathematics Special Issue

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passwords are very convenient for users, they are easy to

implement, popular and inexpensive. Other authentication

schemes are also available like smart card and biometrics, but

password authentication is widely used by the public. In

password based authentication, the user is the claimant and

password is something that he knows [19]. Password is

necessary when he tries to access a system to use the services

provided by the system. Password based authentication uses

various schemes like:

First Password Based Authentication Scheme where a file is stored in the system in which user identification and respective passwords are sorted [20]. Whenever a user wants to access the system resources or any service he or she sends his or her user identification and password in plain text. The system, who acts as verifier uses user identification for searching the password in the file. If the sent password matches with the password has already stored in the file, access is granted otherwise rejected.

Second Password based authentication scheme where

system uses more secure approach to store the

password. The passwords that are sent by the users in

plain text are easy to hack by the intruders, so the file

become insecure. In this approach the hash function is

applied to the password, which is almost impossible to

guess the value of the password. Hash functions are

one way encryption methods [21, 22]. It acts like a

summary of a message and used for data integrity

purpose i.e. the message which has been sent by the

sender is received by the receiver without any

modification in the message, contents remains same

throughout the transmission. These are various

algorithms to create hash of a message such as MD5 or

SHA-1. Message digests for the same original data

should always be same. The important property of the

message digest is that it should not work in the

opposite direction and the message digest of two

different messages must be different [23]. In the first

approach, the user password is stored as it is in a

password file without any encryption. But the second

approach is different from the previous one, where user

password is stored in the encrypted form or in the value

that is derived from the password using different

algorithms. That derived value is stored as a password

in the database. When a user needs to be authenticated,

he or she must login to the system by its user Id and

password. After this, a system derived message digest

from the received password and sends both user id and

derived password to the server for authentication

purpose [24]. When the server receives the pair of user

id and corresponding password, the user authentication

program checks it and validates the combination

against the combination that is already stored in the

database and returns as acknowledgement according to

the result. If the combination of user id and derived

password matches than it grants access to the user and

sends positive acknowledgement otherwise it denied

the access. In this scheme, using hash functions in

password completely safe and secure because of the

process of derivation of the value of hashed password

from the original password must not provide idea about

the original password conditions, Identical hash value

is derived by the algorithm every time for the same

password, It should not be feasible for an intruder to

guess the password and obtain the correct derived

password [25].

Salting Approach is another password based

authentication scheme, in which hash function is again

used, but after a random string called salt. This random

string attached to the password, and then the salted

password is hashed. In first approach only user id and

password is stored in the database. In the second

approach, user id and hashed password are stored in the

database. Now in third approach, the user id, the salt

and the hashed password are then stored in the database

file. Now when a person wish to access the properties

of the device, then the system extracts the salt,

concatenates it with the received password and then

derived hash function of the result and compares it with

the hash value stored in the file [26]. If the values

matches, then system resources are accessed but the

user otherwise it is not an authorized person for the

system. These entire password based authentication

schemes are good, but not secure at all. As

authentication schemes increasing the level of security,

parallel hackers also take out the solution of breaching

the security of an organization or system. Attacks on

first approach is Eavesdropping, Stealing a password,

Accessing a password file, Password stored in plain

text, Password travel in plain text from system to

server, Guessing and attack on second approach is

Dictionary attack [27, 28, 29].

III. ARTIFICIAL NEURAL NETWORK

Back-Propagation Network (BPN) is an eminent

subdivision of Artificial Neural Network. The basic system

architecture is a multilayer feed forward network using back

propagation model. The proposed and achieved values of the

neural network are defined as ix as well as hs for ith

neurons

in the input layer along with hth

neuron in the output layer,

including ihw is the weight that link the input of ith

neuron to

the output of hth

neuron [30].

The achieved results are likely by the connection,

h

h yfs 1

Where hy1 are the activation vectors of any layer j and likely

as:

I

j

iih

h xwy1

1

The error formulation initiated for a single perceptron is

normalized to accommodate all squared errors of the achieved

International Journal of Pure and Applied Mathematics Special Issue

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results j=1, 2… J for a particular design p=1, 2, 3… p that is at

the input as well as comes across the output error.

2

12

1

J

j

jj

p ydE

In which, d is the wished output vector t

Jdddd ]..............[ 321

Weights adopted as below:

hj

p

hjw

Ew

Where, stands for Back Propagation learning rate

Formulation adopted as below:

h

hh

j

h

jj

h

j

Ph

hh

j

p

hj

h

h

j

p

hj

p

ysy

ys

ys

Eys

y

E

w

y

y

E

w

E

...

1

1

1

Since

h

j

h

ij

y

yS

= )(

.h

jj yS

Therefore, weight adaptation is presently designated as below:

h

jh

h

jj

J

j

jj

h

jh

h

jjh

jj

P

ih ysySydysySys

Ew ).(.).(.

.

1

.

The final adjusted weight is given by:

h

jh

h

jj

J

j

jjhjhj ysySydtwtw ).(.)()1(.

1

N

j

j

i

j

hhhj

p

jjjih xySwyydw1

.

).(..

For accessing the resources user login the system with

password. The password can enjoy a sundry kind of statistic

such as series, characters and some alphanumeric data. There

are three main components of the authentication process: input

parameters, authentication algorithm and output values. In

figure 1, we show the simplest authentication method that uses

the password as an input and any encryption algorithm that

encrypts the password and store it and further compare it when

someone login the system. In password-based authentication

approach, the passwords are encrypted by one-way hash

functions or encryption algorithms and then are stored as some

patterns [31, 32]. Nevertheless, mentioned approach has few

drawbacks. An attacker still capable of linking up a forged

pattern or replace someone’s encrypted password. There is other technique for above schemes which usages

neural network to overcome the security problem. This technique stores encrypted passwords by training the network with the help of Back Propagation Algorithms. Here, the system keeps the trained weights and when a system memorizes these weights and stores it in the form of encrypted files. We eliminate this encrypted file through which security of the network improves. However, it provides greater security as to prior mechanisms in figure 2.

Fig. 1. Simple Authentication Method.

Fig. 1. Proposed Authentication Method.

IV. EXPERIMENTAL SETUP

For authentication system, we use the information of a

wireless device, i.e. a mobile phone. The user chooses the

password which can be either in characters, in numeric or in

both. Here, the training model (BPNN) is a supervised

learning model. The model made up of input, hidden and

output layers. Training set of the experiment is shown in table

1. Password is consisting of eight characters and for doing

simulation, it transformed into 8-bit binary code. Therefore,

the BPN architecture has sixty four input nodes in the input

layer, 32 processing neurons in the hidden layer and sixty four

output units in the output layer. The coupling strength of the network is increased by

training of the neural network with a password. Password is taken as an input to the network and when training is completed up to the minimized error values, and then obtained output is the final mapped value of the password.

TABLE I. WIRELESS DEVICE AND ITS PASSWORDS

Wireless

Device

Password Hashed password

Mobile Phone

india47i

2e9effee94253981a7e57ae1bdad069c /

01101001011011100110010001101001

01100001001101000011011101101001

International Journal of Pure and Applied Mathematics Special Issue

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A. Training Algorithms

There are different methods of Back Propagation Neural

Network that are used to train the network and are applied on

this experiment such as the Gradient Descent Algorithm,

Conjugate Gradient Algorithm and Quasi-Newton Algorithm.

Along with algorithm there are supported training functions

also in the Feed Forward Neural Network that are as follows:

Trainbr (Bayesian Regularization), Traingdx (Gradient

Descent with adaptive learning rate BP), Traingdm (Gradient

Descent with momentum BP), Trainlm (Levenberg-Marquardt

BP), Trainscg (Scaled Conjugate Gradient BP), Traincgf

(Fletcher-Powell Conjugate Gradient BP), Traincgp (Polak-

Ribiere Conjugate Gradient BP), Trainbfg (BFGS Quasi-

Newton BP), Traingd (Gradient Descent BP), Trainrp

(Resilient Back Propagation) [33].

V. TRAINING USING NEURAL NETWORK FUNCTIONS

A. Training Using Trainlm

TABLE II. THE PARAMETERS USED FOR TRAINING BY NETWORK USING

THE BACK PROPAGATION MODEL.

Parameter Value

Neurons in Input Layer 64

Number of Hidden Layers 1

Neurons in Hidden Layer 32

Neurons in Output Layer 64

Training Function Trainlm

Time 2 Sec

Minimum Error Exist in the Network 0.001

Error Percentage 0

Initial Weights and Biased Term Value

Values between 0 to 1

0.090 0.028 0.025 -0.07 0.015 0.030 0.024 0.031

0.053

0.035 0.055 -0.06 0.033 -0.03 -0.09 0.021

0.909

0.016 -0.05 0.003 0.045 -0.07 -0.03 0.042

0.001

-0.04 -0.09 -0.05 0.005 0.030 -0.06 0.967

Weights between Layer 1 to Input Layer

0.090 -0.08 0.025 -0.91 0.909 0.003 0.036 0.006

0.003

-0.05 -0.02 -0.06 0.033 -0.03 -0.02 0.031

0.008

0.018 0.995 0.903 0.009 -0.98 -0.01 0.082

0.001

-0.04 0.079 -0.04 0.065 0.006 -0.90 0.903

Weights between Hidden Layer to Output Layer

GRAPH 1. PERFORMANCE PLOT OF NETWORK WITH FUNCTION TRAINLM.

B. Training Using Traincgp

TABLE III. THE PARAMETERS USED FOR TRAINING BY NETWORK USING

THE BACK PROPAGATION MODEL.

Parameter Value

Neurons in Input Layer 64

Number of Hidden Layers 1

Neurons in Hidden Layer 32

Neurons in Output Layer 64

Training Function Traincgp

Time 1 Sec

Minimum Error Exist in the Network 0.001

Error Percentage 0

Initial Weights and Biased Term

Value

Values between 0 to 1

0.003 -0.03 0.065 -0.07 0.019 0.034 0.074 0.054

0.904

0.912 0.075 -0.06 -0.03 -0.93 -0.99 0.921

0.008

-0.06 -0.08 0.977 0.007 -0.97 -0.93 0.942

0.034

-0.08 -0.09 -0.02 -0.05 0.055 -0.04 0.067

Weights between Layer 1 to Input Layer

0.044 -0.08 0.005 -0.91 0.900 0.006 0.038 0.907

0.954

-0.05 -0.02 -0.06 0.073 -0.05 -0.02 0.933

0.006

0.013 -0.95 0.973 0.001 -0.07 -0.07 0.988

0.009

-0.04 -0.09 -0.09 0.035 0.004 -0.96 0.088

Weights between Hidden Layer to Output Layer

International Journal of Pure and Applied Mathematics Special Issue

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GRAPH 2. PERFORMANCE PLOT OF NETWORK WITH FUNCTION TRAINCGP.

C. Training Using Traingdm

TABLE IV. THE PARAMETERS USED FOR TRAINING BY NETWORK USING

THE BACK PROPAGATION MODEL.

Parameter Value

Neurons in Input Layer 64

Number of Hidden Layers 1

Neurons in Hidden Layer 32

Neurons in Output Layer 64

Training Function Traingdm

Time 17 Sec

Minimum Error Exist in the Network 0.001

Error Percentage 0

Initial Weight and Bias Term Value Values between 0 to 1

0.070

0.013 0.006 0.031 0.042 0.916 0.002 0.063

0.921

0.045 -0.07 -0.01 0.973 -0.08 0.987 0.921

0.038

0.950 0.034 -0.03 0.033 0.028 0.005 -0.01

0.025

0.005 0.914 -0.02 0.026 0.988 0.002 0.942

Weights between Layer 1 to Input Layer

0.003

0.991 0.023 0.092 0.052 0.942 0.962 0.934

0.982

0.962 0.972 -0.02 -0.02 0.972 -0.02 0.085

-0.08

0.075 -0.02 0.982 0.932 0.942 -0.04 0.031

-0.06

0.945 -0.06 0.032 0.982 0.989 0.074 0.073

Weights between Hidden Layer to Output Layer

GRAPH 3. PERFORMANCE PLOT OF NETWORK WITH FUNCTION TRAINGDM.

D. Training Using Trainscg

TABLE V. THE PARAMETERS USED FOR TRAINING BY NETWORK USING

THE BACK PROPAGATION MODEL.

Parameter Value

Neurons in Input Layer 64

Number of Hidden Layers 1

Neurons in Hidden Layer 32

Neurons in Output Layer 64

Training Function Trainscg

Time 2 Sec

Minimum Error Exist in the Network 0.001

Error Percentage 0

Initial Weight and Bias Term Value Values between 0 to 1

0.991

-0.03 0.057 0.986 0.001 0.079 0.018 0.931

0.931

-0.05 -0.05 0.028 0.086 0.037 0.045 0.921

0.021

0.023 0.946 -0.09 -0.01 0.002 -0.05 0.021

0.028

0.003 0.079 0.026 0.994 0.976 0.043 0.913

Weights between Layer 1 to Input Layer

0.993

-0.02 0.068 0.068 0.932 0.032 -0.08 0.090

0.092

0.002 0.902 0.031 -0.03 -0.07 0.932 0.004

0.922

-0.05 0.042 -0.92 0.021 0.976 -0.01 0.023

0.045

-0.06 0.055 0.949 0.045 -0.05 0.945 0.987

Weights between Hidden Layer to Output Layer

International Journal of Pure and Applied Mathematics Special Issue

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GRAPH 4. PERFORMANCE PLOT OF NETWORK WITH FUNCTION TRAINSCG.

E. Training Using Trainsrp

TABLE VI. THE PARAMETERS USED FOR TRAINING BY NETWORK USING

THE BACK PROPAGATION MODEL.

Parameter Value

Neurons in Input Layer 64

Number of Hidden Layers 1

Neurons in Hidden Layer 32

Neurons in Output Layer 64

Training Function Trainrp

Time 1 Sec

Minimum Error Exist in the Network 0.001

Error Percentage 0

Initial Weight and Bias Term Value Values between 0 to 1

0.010

-0.07 0.061 -0.02 0.088 0.965 0.077 0.090

-0.04

0.970 0.029 -0.01 0.083 0.051 -0.04 -0.05

-0.01

0.935 0.925 -0.04 0.048 -0.02 0.053 0.909

0.934

0.047 0.091 0.989 0.080 -0.07 -0.03 0.055

Weights between Layer 1 to Input Layer

0.993

-0.03 -0.08 0.048 0.032 0.902 -0.06 0.006

0.992

-0.02 0.902 0.031 -0.03 -0.07 0.932 -0.05

0.022

-0.92 0.042 0.002 0.921 0.976 -0.01 0.999

0.045

-0.95 0.055 0.949 -0.04 -0.05 0.945 0.045

Weights between Hidden Layer to Output Layer

GRAPH 5. PERFORMANCE PLOT OF NETWORK WITH FUNCTION TRAINRP.

F. Training Using Trainbfg

TABLE VII. THE PARAMETERS USED FOR TRAINING BY NETWORK USING

THE BACK PROPAGATION MODEL.

Parameter Value

Neurons in Input Layer 64

Number of Hidden Layers 1

Neurons in Hidden Layer 32

Neurons in Output Layer 64

Training Function Trainbfg

Time 0 Sec

Minimum Error Exist in the Network 0.001

Error Percentage 0

Initial Weight and Bias Term Value Values between 0 to 1

0.002

0.977 0.917 -0.01 -0.06 0.008 0.082 0.084

0.001

0.083 0.025 0.032 -0.02 0.994 0.934 0.014

0.037

-0.07 0.985 -0.05 -0.02 -0.03 0.055 0.021

0.944

-0.03 0.064 0.986 0.025 -0.07 0.948 0.913

Weights between Layer 1 to Input Layer

0.025

-0.90 0.909 0.005 -0.91 0.900 0.048 0.032

-0.03

-0.06 -0.03 -0.02 -0.06 -0.07 -0.03 -0.02

-0.99

0.93 0.009 -0.95 0.973 0.001 -0.04 0.921

-0.07

0.040 -0.05 -0.09 -0.09 -0.03 0.949 0.045

Weights between Hidden Layer to Output Layer

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GRAPH 6. PERFORMANCE PLOT OF NETWORK WITH FUNCTION TRAINBFG.

VI. RESULT AND DISCUSSION

Multiple experiments were performed on a feed forward

Neural Network by taking different training functions.

Different training functions have different properties, which

work accordingly for the topology of the network and give

results. Graph 1 to graph 6, depicts the network performance

by various training functions. Training parameters that were

used in the process of training a network are summarized in

tables from table 2 to table 7.

For performing an experiment, we used topology of {64-

32-64} indicates 64 input neurons, 32 hidden neurons and 64

output neurons [34, 35]. Also, six back propagation methods

that are Levenberg-Marquardt (LM), Scaled Conjugate

Gradient (SCG), Gradient Descent with Momentum (GDM),

Conjugate Gradient Back propagation with Polak-Riebre

Updates (CGP), Resilient Back propagation (RP) and Quasi-

Newton (BFGS). If we compare the performance of different

networks, according to the training functions then the results

are:

A. On The Basis of Epochs

TABLE VIII. COMPARISON OF DIFFERENT TRAINING FUNCTION BASED ON

EPOCHS.

S.No. Training Function No. Of Epochs

1 Trainlm 8

2 Trainbfg 6

3 Traingdm 1000

4 Trainscg 14

5 Traincgp 5

6 Trainrp 59

The above summary of training functions with their

corresponding epochs in table 8 indicates that trainlm, trainbfg

and trainrp show equivalent results. Originally epoch is set to

1000. Training function, traingdm takes 1000 iterations to the

network with a given topology while another gradient descent

method takes 59 epochs. Trainscg and traincgp functions train

the network in less number of epochs as compared to gradient

descent methods while trainlm and trainbfg shows better

results.

Multiple experiments were performed on a feed forward

Neural Network by taking different training functions.

Different training functions have different properties, which

work accordingly for the topology of the network and give

results. Graph 1 to graph 6, depicts the network performance

by various training functions. Training parameters that were

used in the process of training a network are summarized in

tables from table 2 to table 7.

B. On The Basis of Epochs

TABLE IX. COMPARISON OF DIFFERENT TRAINING FUNCTION BASED ON

MSE.

S.No. Training Function MSE

1 Trainlm 0.785

2 Trainbfg 0.480

3 Traingdm 0.216

4 Trainscg 0.790

5 Traincgp 2.860

6 Trainrp 4.690

The Mean Square Error (MSE) values in table 9 refer to

the state where it terminates the training of all the Back

Propagation Algorithms. The maximum error is shown by

trainrp function and traincgp function. Trainscg and trainlm

shows the neckline difference on the other hand, training

functions trainbfg and traingdm shows better performance.

C. On The Basis of Time

TABLE X. COMPARISON OF DIFFERENT TRAINING FUNCTION BASED ON

TIME.

S.No. Training Function Time

1 Trainlm 2sec

2 Trainbfg 0 sec

3 Traingdm 17sec

4 Trainscg 2sec

5 Traincgp 1sec

6 Trainrp 1sec

Comparison of different training functions on the basis of

time in table 4.10 shows that traingdm takes much time to

train the network as compare to other training functions.

Trainlm, trainscg, traincgp and trainrp train the network in few

seconds while trainbfg takes negligible time.

The above computations and evaluations describes that

each training function has its own performance criteria. Some

trains the network in time, but take much iteration and

performance is not up to the mark while some training

functions takes time and train the network fully.

VII. CONCLUSION

From the above computed results and discussion of all the

points, we conclude that for the authentication of any wireless

International Journal of Pure and Applied Mathematics Special Issue

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equipment in the networking training functions plays an

important role. Database administrators or system analysts

apply any training function for memorizing the pattern sets in

the memory. The performances of different training functions

according to different aspects summarizes in the previous

section. We can apply one of the functions of the back

propagation algorithm for getting better result. Techniques of

Artificial Intelligent and Neural Network have been used

broadly for solving the problems related to pattern recognition

and classification, signal processing and optimization, etc.

Authentication is mainly focused on the use of passwords,

smart cards and biometrics. Password based authentication is

very common, but due to some limitations like dictionary

attacks and long searching process, researchers have been

working continuously to find out the solution. R.C. Merkle

proposed the scheme of encryption of password by using hash

function and then stored in the table. Later on, verification

table is utilized to replace password tables. Chien et al.

proposed password authentication scheme using smart cards

and prevent the reflection attack and insider attack. Today in

every field, Neural Network has been used to overcome the

traditional approaches. Involvement of Neural Network in the

intrusion detection field becomes apparent when one views the

intrusion detection problem as a pattern classification

problem. Hwang et al. proposed method that produces hashed

password according to input file and replace the password

table using back propagation algorithm. Another engineer

Reyhani et al. proposed a method in which they train a neural

network to store encrypted passwords using RBP algorithm.

Here, in this chapter, we implement back propagation

algorithm on the user’s passwords. We train the passwords

and store it in the form of network parameters by using

different training functions. These functions affect the speed,

convergence rate, space and time of the system. Back

propagation method of neural network is a supervised feed

forward learning algorithm which is applied in the experiment.

Different training functions were applied to the network

architecture. We applied two methods from each of the three

algorithms for performing the simulation. Newton’s method

gives better and faster optimization results as compared to

gradient descent and conjugate gradient descent algorithms.

Both methods of Newton’s algorithm converge the network at

a faster rate and produces good results according to different

criteria such as mean square error, number of epochs and time

of training. Our proposed system is applicable in an open

environment and helps in intrusion detection.

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