International Journal of Scientific & Engineering Research, Volume 6, Issue 1, January-2015 420

ISSN 2229-5518

Modeling and Simulation concept for evaluating the Performance of Computers in a Network

under Cyber Attack

Anil Kumar Mishra, Tarini Charan Panda, Sujata Dash

Abstract— This paper gives an current survey on application of modeling and simulation .We have focused on what we observed as some of the the major mathematical challenges in Cybersecurity.This review paper presents mathematical or statistical modeling for cybersecurity. Different types of modeling concepts are discussed.When systems connected through the internet are attacked how the system survives what is the rate of survival will be calculated.Cyber security models and possible elements of the models are also discussed.We have organized our ideas into modeling large scale networks, performance evaluation and reliability study.

Index Terms— Virus, Worm, Epedemics, Networks, Modeling, Reliability, Hazard function.

——————————  ——————————

1 INTRODUCTION

he rapid growth of attacks and securirt measures de- grades not only information system infrastructure and
to a large system but also the simplification o the system.[9,10]
assurance, but also the performance of comput- ers,networks and wireless devices[1,3,13].Due to the sharing of the resources on the web or network, it becomes easy for at- tackers to attack.Each year more complex malwares such as viruses,worms,botnets and Trojans are launched via inter- net.These malwares are used for attacking on :
Availability: To reduce communications/computation ca- pacity or to prevent the availability of information and com- munication systems.
Confidentiality: To Compromise the confidential infor- mation.

2.1 Classification of different models

Model

100

East

Privacy: To obtain detailed information about individuals
and organizations.
Integrity:To create uncertainnity about information.
Ko-tenko in2005 and stytz et. Al 2010 have discussed about
cyber attackers and its prevention.Modelling and Simulation
Physical Model Mathematical
Model

tools are also available (OM-NeT++, cayiric and Marincic) for
simulating cyber attacks.However, mathematical modeling
plays a major role in Cyber Security .
Cyber attack may create a situation which is very difficult
to face for the decision makers due to lack of information
available to predict attack.The insinuation and consequences
of this phenomenon are serious.Therefore, practical solutions
and procedures against it should be developed, tested and
trained, which requires efficiency in modeling and simulation
techniques[5,10,12].
In this paper we aim to discuss the basics to relate cyberat-
tacks and how to prevent the systems by evaluating their per-
formance of the systems connected through network.
Static
Model

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

Dynamic
Model

(Figure 1)

Static Nu- merical Model
Dynamic
Numerical
Stat- ic/Dynamic Analytical

2 MATHEMATICAL MODELING CONCEPT

Modeling is a mathematical tool to develop a prototype of a proposed system before it is developed or implemented[1].For many scenarios it is not feasible(Technically feasible and eco- nomical feasible) to develop prototype of a systemto study the characterstics of a system. A prototype is not only replacement

Physical Model: These models are based on some methodology of

Electrical, Hydraulic, and Mechanical Systems.

Mathematical Model: Models which can be represented in the form of mathematical equations, example- economics students apply linear algebra for input/output models.
Physical static Model: These models don’t change their behav- ior as time changes.

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ISSN 2229-5518

Physical dynamic model:These models change their behavior as time changes.
Mathematical Static Model:These mathematical models give a mathematical equation when the system is in equilibrium stage.
Mathematical Dynamic Model: In these mathematical models allow change of attributes as the function of time.
Mathematical Static Analytical Model:These are small static mathematical models which can be solved by conventional mathematics.
Mathematical/Dynamic Analytical Model:These are small dynamic mathematical models which can be solved by simula- tion.

2.2 MATHEMATICAL MODELING PRINCIPLE FOR CYBER DEDFENCE SYSTEM

Cyber attacks are major problem of today’s world.To over- come this problem it is necessary to understand the behavior of malicious objects.For this mathematical modeling play an important role. It can help to fix possible parameters of mala- cious objects,those are important to tell how the malicious ob- jects can propagate through internet[3,5,6,14].The reason for cyberdefence is due to various malicious objects like Tro- jan,worm,virus, spam etc.The attacks on internet and internet attached systems have grown more sophisticated while the amount of skill and the knowledge required to mount an at- tack has declined[5,6].The attacks have become more automat- ed and can cause greater amount of damage.

derstood by using modeling.

3 WAYS TO STUDY A CYBER DEFENCE SYSTEM

The figure 1 given below gives a pictorial idea to study cyber defence system by using the mathematical modeling tech- niques[2,8].The mathematical and statistical techniques can be used for evaluating the performance of systems under attack or for the prediction of attack.From the network traffic comes to our system we must know about the existience of malicious objects or data which force our system to behave abnormal- ly.The length of data, source of data, how it affect our system and how we can measure the reliability under the such type of attacks are topics for prediction using mathematical or stasti- cal techniques.
Cyber Defence System
Model, Variable, Parameter
Model Prediction
Verfy and Predict Model?
Failure
Success
Predicted Model Accepted
(Figure 1: Mathematical Modeling Process)
Table 1

Table 1 gives information about different types of attack we came across.For providing security for this type of attacks we must be aware of behavior of malicious objects and it can be un-

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4 THE RELIABILITY, FAILURE DENSITY OF A SYSTEM DUE TO MALACIOUS OBJECTS BY USING THE RELIABILITY, FAILURE DENSITY AND HAZARD FUNCTION

In the current scenarios the internet system are prone to threat from various malicious objects which is discussed in table number 1.The host computer can be infected from the internet and it affects the total immune system of computer e.g. prima- ry memory, secondary memory , the current messaging etc.
The attacks are totally stochastic and it is very difficult to pre- dict the next time of attack[2,4].But we can study the reliability of a system under such situations.We have applied Continuos random variables for doing the study.
Let the random variable X be the life time or the time of failure of the system due to malicious objects or due to virus attack.The probability that the system will sur- vive until some time ‘t’ is called reliability R(t) of the system.

R(t )= P(X>t) = 1-F(t) (1)
Where F is the distribution function of the system life time,

h(t)=f(t)/R(t) (7)
Here ,h(t)∆t represents the conditional probability that a com-
puter will survive in a network to the time ‘t’ fail in the inter-
val (t,t+∆t).
h(t) , Alternatively known as the hazard rate or force mortality
of a computer.
Now, for modeling a cyber defence system one should know
the different components and parameters required.Now, our

proposed model is described below in Figure 2.
Cyber Defense System
System Design Attacks/Viral infections
X.
The Component is assumed to be working properly at time
t=0 [i.e. R(0)=1] and no system will work for ever without fail- ure.Consider a fixed number of identical Systems. The number of systems under test is N0 .After time t, Nf (t) systems or computers have failed in anetwork and Ns (t) computers have survived.

Nf (t) + N s (t) = N0 (2) The Probability of survival of a system P(survival)= Ns (t)/ N0 (3)
When, N0 →∞, The P(survival) approaches to R(t).
Where R(t) is the reliability of the total system(Number sys- tems exsists in a particular network).When Ns (t) gets smaller
and R(t) decreases.
R(t)= Ns (t)/ N0
=(N0 - Nf (t))/ N 0

= 1`- Nf (t)/N0 (4)
As the total number of computer numbers is constant in a network so the failed number of components Nf increases
with time. Taking derivatives of both sides

R’(t)=(-1/N0 )N’f (t) (5)
N’f (t) is the rate at which the computers of the network will fail due to virus attack. As N0 →∞, the very right hand side maybe interpreted as negative of the failure density function, fx (t)
R’(t)= -fx (t) (6)
f(t) ∆t is the unconditional probability that a component will
fail at the interval (t, t+∆t).The component of a system function
upto time ‘t’ and the failure will be different from f(t)∆t.This
causes instantaneous failure.The instantaneous failure rate
h(t) at time ‘t’ due to the virus attack is defined as
Evaluate the Reliability, Failure density, Hazard function
Tune the system based on value
Figure 2

5 CONCLUSION AND FUTURE WORKS

It is very difficult to trace the attacker in cyberdence.All the features of malicious object’s propagation have to be repre- sented in the form of mathematical equations so it will be easy to predict the future behavior.And it is very difficult to calcu- late the actual reliability of the computers due to virus at- tack.In our future scope we are planning to apply the soft computing techniques in Computer Security. Most of the cyber defense Systems, when implemented create overheads like slow down in exsisting system performance, increase in packet length or take time for comparision etc.We have fo- cused an area to do our research i.e IDS(intrusion detection system). We will model the IDS by using the soft computing

International Journal of Scientific & Engineering Research, Volume 6, Issue 1, January-2015 423

ISSN 2229-5518

techniques.
.

• Dr. Anil Kumar Mishra is currently working as an Associate Professor in

Orissa Engineering College ,CSE Department,Bhubaneswar. E-mail: anilmish-

ra.oec@gmail.com

• Dr. Sujata Dash is currently workingas a Reader in the Department of Com-

puter Science and Applications in North Orissa University Baripada.E-mail:

sujata_dash@yahoo.com.

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