Modeling and Analysis of Patching Structured
Benign Worms Countering against Worms
Hanxun Zhou Wei Guo Guo dong Zhang
Department of Information Science Department of Computer Science Dept. of Information Science
and Technology and Technology
LiaoNing University Shenyang Aerospace University Shenyang Aerospace University
Shenyang, China Shenyang, China Shenyang, China
26054036@qq.com bensonbb00@163.com zhouhxcool@gmail.com
Abstract —Due to the active defense of benign worms against the
damage imposed by worms, benign worms have been paid
enough attention by network security researchers. This paper
presents patching structured benign worms, and we designed
their deployment and work mechanism. Furthermore, the
process of patching structured benign worms countering against
worms is modeled based on the infectious model. Finally, the
model was simulated. From the simulation, two factors(detection
rate of the sensor and delay time),which affect the process of
patching structured benign worms countering against worms,
were summarized. The model of patching structured benign
worms leads to a better understanding and prediction of the scale
and speed of benign worms countering against the propagation of
worms.
Keywords- network security; malicious code; worm; patching
structured benign worm; worm modeling
I. INTRODUCTION
The Internet has become critically important to the
financial viability of the national and the global economy.
Meanwhile, we are witnessing an upsurge in the incidents of
malicious code in the form of computer viruses and worms.
One class of such malicious code, known as random scanning
worms, spreads itself without human intervention by using a
scanning strategy to find vulnerable hosts to infect. Just like
the Code Red worm
[1-3]
and Slammer worm
[4]
, they can
compromise thousands of hosts in several hours, causing
remarkable disruption to finance, transportation and
government instructions, and precluding any human-based
response.
Since an accurate Internet worm model provides insight
into worm behavior, researchers have modeled the spread of a
virus or worm within a network. S. Staniford etc.
[5]
apply the
simple epidemic model (SEM) to model the spread of worms.
The KM model
[7]
improves the classical simple epidemic
This work is supported by the national natural science
foundation of China under Grant Nos. 61300233, Shenyang
Science and Technology Foundation No. F13-316-1-35 and
the PhD Start-up Fund of National Science Foundation of
Liaoning Province No. 20131086.
model by assuming that some infectious hosts either recover
or die after some time. Zou etc.
[8]
, considering the dynamic
countermeasures and the slowed down worm infection rate,
derive the two-factor model. Besides the epidemiological
model, Chen etc. [9] propose the Analytical Active Worm
Propagation(AAWP) model. There are also some models on
topology worms[10-11]. [12] models the unstructured benign
worm.
This paper presents a mathematical model which
describes the process of patching structure benign worms
countering against worms. Firstly, we analyze the deployment
of patching structured benign worms. Then we derive the
model of patching structured benign worms containing the
spread of worms by the differential equations and simulate the
model. This model of worms can help us understand the
interaction between patching structured benign worms and
worms deeply.
The rest of the paper is organized as follows. Section Ċ
is on related work. Section ċ describes how the patching
structured benign worm contains the spread of worms. We
present the model of patching structured benign worms
countering against worms in section Č . In section č, we
simulate the model with different parameter values and
summarize two important elements. Section Ď concludes the
paper.
II.
RELATED WORK
As mentioned in the section above, deterministic
epidemic models have been used to study worm propagation
[6]. For illustration, consider the two-factor worm model
proposed by Zou et al. [8]:
() ()
()[ () () ()] ()
dI t dR t
t V Rt It Qt It
dt dt
β
=−−− − (1)
where V is the total number of susceptible hosts on the
Internet, and I(t), R(t), Q(t) represent the number of
infectious hosts, the number of removed hosts from the
infectious population, and the number of removed hosts from
the susceptible population at time t, respectively. The
parameter I(t) is the infection rate at time t and reflects the
impact of the Internet traffic on the worm propagation. The
parameters of I(t) and Q(t) reflect the human countermeasures
in patching.
When there is no patching and the infection rate is
2014 International Conference on Virtual Reality and Visualization
978-1-4799-6854-1/14 $31.00 © 2014 IEEE
DOI 10.1109/ICVRV.2014.17
236