=Paper=
{{Paper
|id=Vol-2577/paper23
|storemode=property
|title=Mathematical Model of Threats Resistance in the Critical Information Resources Protection System
|pdfUrl=https://ceur-ws.org/Vol-2577/paper23.pdf
|volume=Vol-2577
|authors=Bogdan Korniyenko,Liliya Galata,Lesya Ladieva
|dblpUrl=https://dblp.org/rec/conf/its2/KorniyenkoGL19
}}
==Mathematical Model of Threats Resistance in the Critical Information Resources Protection System==
https://ceur-ws.org/Vol-2577/paper23.pdf
281
Mathematical Model of Threats Resistance in the Critical
Information Resources Protection System
© Bogdan Korniyenko1, © Liliya Galata2, © Lesya Ladieva1
1 National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv,
Ukraine
2 National Aviation University, Kyiv, Ukraine
bogdanko@gmx.net, galataliliya@gmail.com,
lrynus@yahoo.com
Abstract. The main problems of information security of critical information re-
sources and causes of their occurrence are considered. The main threats to secu-
rity systems of critical information resources are analyzed. Mathematical model
of counteraction of internal and external threats to the system of protection of
critical information resources of mineral fertilizers production is developed.
The process of building a mathematical model of countering the threats in the
system of protection of critical information resources with the help of Markov
chain. The methodology of finding current threats to data security during their
processing is offered. The software module is developed in the Piton program-
ming language. These examples calculate the probability of mathematical mod-
el of information system in one of four states (the threat did not come; the threat
came but was not implemented; the threat has been implemented; the threat
came, but it was reflected protection system). Examples of numerical results
analysis using proposed techniques clearly show that their use helps to define
threats that are relevant to the system being investigated and can be used in
practice. The disadvantage of proposed methodology is the need to consider the
system behaviour when it comes to each type of threat, individually and inabil-
ity to define behaviour on the simultaneous action of several threats. Studying
the influence of each threat separately allows to study each of its types in more
detail and to determine the probability of which is the greatest occurrence. As a
result of exploitation of critical information resources protection systems and
substantial changes in composition and quality of modern threats, it is necessary
to project and implement information security of the systems taking into ac-
count tendencies of cyber threats development.
Keywords: Mathematical Model; Threat; System of Protection; Critical Infor-
mation Resources.
1 Introduction
In today's world, automated control systems are used more and more often. The
need for information security in automated control systems is increasing every year
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
282
by increasing the number of attacks by intruders and leakage of confidential infor-
mation. But the most susceptible to security is the most automated control systems of
technological processes, as when attackers attack, it can happen not only leakage of
secret information, but also interference into the technological process itself, which,
when malfunctions, can lead to environmental catastrophe.
Control of technological processes in enterprises of small, medium and large size
is impossible without computer equipment and modern means of automation, without
highly effective of automated control systems of technological processes (ACS TP).
ACS is a comprehensive system of hardware and software, which is designed for
remote centralized monitoring of processes and system as a whole, as well as for au-
tomated control of engineering and technical subsystems.
Information Security (IS) is becoming more and more topical issue with the de-
velopment of computing equipment and the increasing penetration of such systems
into the daily lives of people. This is discussed in almost every event on the security
of the IS, and the analysis of reliability and safety of the systems already commis-
sioned is one of the mandatory conditions of State and international certification. One
of the biggest problems of the security is that the majority of ACS of small and medi-
um complexity are projected by small organizations under conditions of strict finan-
cial limitation, which eliminates or complicates the security issue.
Experts believe that the provision of IS is different from the provision of corporate
information systems. Even the term "information security" is very rarely used in rela-
tion to ACS TP. The reason for this is that it is necessary to pay attention not so much
the confidentiality of information, but ensuring the continuity and integrity of the
technological process. Although at the same time a significant amount of attention is
given to the problems of ensuring confidentiality of information, because, according
to many experts, the solution of this problem leads to the automatic solution of the
problem of integrity and availability of information.
Modern ACS in many cases manage difficult and dangerous technological pro-
cesses, failure of which could potentially lead to accidents in production or, in the
worst case, to technogenic disasters. This significantly increases the price of risk due
to violations of the IS, because threats can theoretically cause damage to people, the
environment, and also leads to the financial and reputational losses.
In modern times, the priority in providing the IS ACS TP is to ensure the availa-
bility and integrity of the management and configuration information on the parame-
ters of the technological process. Particular attention should be paid to preventing
unauthorized access to the system to preserve the stable functioning of ACS TP [1-5].
Despite the large number of accidents with catastrophic consequences, the problem of
critical information resources protection at industrial enterprises in the chemical and
energy industries has never been so acute as in recent years.
The general interest to the security of industrial systems occurred only after the in-
cidents with the computer viruses Stuxnet, Duqu, Flame, which attacked Iranian nu-
clear facilities, government agencies and industrial facilities in India, China and other
countries. Separately, attacks to enterprises in the Ukraine’s energy sector and the
banking sector should be highlighted. Before these incidents advent, it was considered
that the protection system of critical information resources was been very difficult to
283
compromise. Such representations were based on the following postulates: the soft-
ware of each protection system for critical information resources is unique and closed;
penetration into the system is associated with high costs of intellectual resources, and
the monetary reward for the attacker is not obvious; the local network of the critical
information resources protection system solves access restriction problems.
A study of software and hardware structure, that used in the protection systems of
critical information resources, has shown that there have been big changes in recent
years. Almost everywhere, widely known software is used, such as Windows OS,
TCP/IP protocols, etc., which, together with their advantages in standardization, sim-
plicity, and quality of use, have also brought disadvantages - vulnerabilities. Comput-
ers connected to the Internet appear in the local network, and they also present a large
number of potential threats to the system [6-10].
2 Formulation of the problem
In industrial systems of critical infrastructure there are the same vulnerabilities as in
most conventional IT systems. In addition, the peculiarity of industrial systems is the
existence of unique vulnerabilities, which include:
Human factor. Operation Industrial and corporate systems are usually involved in
various divisions and specialists. In turn, the personnel of industrial systems, as a rule,
are not far from the issues of providing information security, in its composition there
are no security specialists, and the recommendations of the IT staff are not distributed.
The solution of technological problems arising during the operation of the system,
ensuring its reliability and availability, efficiency and minimization of overhead
should be one of the main tasks of specialists.
OS vulnerabilities. The vulnerabilities of OS (operating systems) are inherent for
both industrial and enterprise systems, but software installations are not normally
implemented in industrial systems. Uninterrupted operation of such system is the
responsibility of the administrator. The establishment of pre-approved software cor-
rections can contribute to serious problems, and there is no time or money on full
testing.
Authentication. Common passwords are usually used for industrial systems. The
two-factor authentication system is rarely used, and sensitive information is often
transmitted in an open form.
Remote access. To control the industrial systems often used remote access by dial-
up channels or by VPN channels via the Internet. If not controlled use, this may cause
serious security problems.
External network connections. Lack of appropriate regulatory framework and us-
age is aimed more at convenience rather than security, sometimes lead to the fact that
network connections are created between industrial and corporate networks. There are
even recommendations for using "composite" networks that allow you to simplify
administration. This can adversely affect the security of both industrial and corporate
284
systems.
Means of protection and monitoring. Unlike enterprise systems, use IDS. Systems,
etc. In the industrial system is not a common practice, the analysis of security audit
logs is also not rarely bypassed.
Wireless networks. In industrial systems, various types of wireless communication
are often used, including 802.11 protocols, which are known to not provide sufficient
capabilities to protect the information.
Remote processors. Some remote processor classes have known vulnerabilities.
Performance of these processors does not always allow to implement security func-
tions. In addition, after installation, they try not to touch for years, during which they
remain vulnerable.
Software. The software of the industrial systems usually does not have enough se-
curity functions. In addition, in most cases, it is not devoid of architectural weakness-
es.
Disclosures. The owners of industrial systems are often deliberately publish in-
formation about their architecture. Consultants and developers often share experienc-
es and reveal useful information about employees.
Physical security. Remote processors and industrial systems equipment can be
outside the controlled area. In such conditions they physically cannot be controlled by
the personnel, and the only mechanism of their physical protection is the use of metal
doors and locks. Such measures are not a serious obstacle to intruders.
In this way, we can conclude that there is a significant number of vulnerabilities
that are both common to any information systems and specific to industrial systems.
These vulnerabilities cause specific security requirements and special operating re-
gimes for such systems [11-15].
Also, the new term “cyberwarfare” has recently appeared, which is often mentioned
in the media, because there is a problem in critical information resource system pro-
tection at infrastructure facilities and hazardous industries. Thus, the widespread use
of computer equipment in the management of industrial enterprises creates the need to
pay more and more attention to the problems of information security of such systems.
The main problems of information security of critical information resources, ac-
cording to experts, appear because there are:
- low protection against unauthorized access (passwords);
- undeclared SCADA capabilities;
- lack of control in management actions;
- using of wireless communications (crypto persistent Wi-Fi encryption);
- lack of clear boundaries between different network segments;
- untimely or incorrect software updates;
- rejection from even minimal security tools (often for convenience or perfor-
mance, companies refuse to install not only, for example, anti-virus protection, but
also password protection for critical assets);
- the distribution of Windows as an operating system for workstations and even
285
servers;
- development for trusted environment of closed industrial networks;
- creating systems without taking into account the best practices in safe code de-
velopment;
- human factor, poor staff discipline.
Here is an example of the main threats to critical information resource systems
found after analyzing these incidents:
- attacks to SCADA;
- attacks to PLC, PLC vulnerabilities (standard password, unauthorized access to
original software);
- attacks to the infrastructure and the operating system (viruses, trojans, worms,
DoS and DDoS attacks, ARP spoofing);
- attacks to protocols, protocol vulnerabilities (unauthorized access, SQL injec-
tion);
- attacks such as Buffer Overflow, Information Disclose, Denial of Access, Ma-
nipulation of View.
Among all types of vulnerable components of critical information resources pro-
tection systems, the next one prevails: SCADA - 87%, systems providing human-
machine interfaces - 49%, programmable controllers - 20%, protocols - 1%.
The vulnerabilities by type was divided as follows: buffer overflow - 36%, authen-
tication / key management - 22.86%, Web application vulnerabilities - server -
10.86%, client - 9.14%, remote code execution - 13.14% [16-18].
As a result of the operation of protection systems for critical information resources
and a significant change in the composition and quality of modern threats, it is neces-
sary to design and implement information security systems taking into account trends
in cyber threats development. On the other hand, it is necessary to carry out regular
work to neutralize emerging or potential threats on working systems. At this level, the
following information security services are implemented: access control, integrity,
secure network connections, antivirus protection, security analysis, intrusion detec-
tion, information security system management (continuous state monitoring, incident
detection, reaction).
3 Analysis of recent research and publications
The protection system of critical information resources of mineral fertilizers produc-
tion was chosen as the object of research [19-21]. The basis of information security
models are the following theories: formal-heuristic approach; probability theory and
random processes; evolutionary modeling; theory of graphs, automata, and Petri nets;
game theory and conflict; catastrophe theory; theory of fuzzy sets; entropy approach.
The differences between the majority of models are which parameters they use as
input and which parameters are given as output after calculations. In addition, recent-
ly, modeling methods based on the informal theory of systems are widely used: struc-
286
turing methods, estimation methods, and methods for finding optimal solutions [22-
24].
Structuring methods is the development of a formal description, applies to organ-
izational and technical systems. Using these methods allows us to present the archi-
tecture and process of complex system functioning in the form that satisfies the fol-
lowing conditions: completeness of main parts display and their relationships; sim-
plicity of elements organization and their relationships; flexibility - simplicity of mak-
ing changes to the structure, etc. Evaluation methods allow you to determine the val-
ues of system characteristics, that cannot be measured or obtained using analytical
expressions, or in the statistical analysis process, such as the probability of threats, the
effectiveness of the protection system element, etc. The basis of such methods is ex-
pert assessment - an approach of attracting specialists in relevant fields to obtain some
characteristics values.
Methods for finding optimal solutions is a generalization of a large number of in-
dependent, mostly mathematical, theories, in order to solve optimization problems. In
the general case, this group includes methods for informally reducing a complex prob-
lem to a formal description, followed by formal approaches. Combining of methods
for these three groups allows you to expand the possibilities of applying formal theo-
ries to do a complete simulation of protection systems.
The purpose of the article is the development and research of a mathematical
model of threats resistance in the critical information resources protection system,
obtaining transitional characteristics for system states.
4 Main research material
The mathematical model of influence resistance of internal and external threats on the
protection system of critical information resources of the mineral fertilizers produc-
tion is proposed. The process of constructing a mathematical model for threats re-
sistance in the critical information resources protection system by using the Markov
chain [25-27] is described in stages. The methodology for finding relevant threats to
data security during their processing is proposed. The examples of calculating the
probabilities of finding a mathematical model of an information system in one of four
states is shown (the threat has not occurred; the threat occurred, but has not been
implemented; the threat occurred, and has been implemented; the threat occurred, but
has been reflected by the security system).
The system can be interpreted as a queuing system, which receives threats. First,
consider the situation when threats of the same type come to the system input, assum-
ing that the threat cannot be realized and come several times in the same time period.
If these conditions are met, then the system can be in one of four states (see Fig. 1):
1. the threat has not been occurred and, accordingly, was not implemented;
2. the threat occurred, but has not been implemented;
3. the threat occurred, but has been implemented;
4. the threat occurred, but has been reflected by the security system.
287
Fig.1. The graph of system states.
The system under consideration is a system with recovery, this system can go
from any state to the initial one. We will consider a system with continuous time. The
transition from state to state occurs according to a directed graph (see Fig. 1). To de-
scribe the transition from state to state, we will construct a transition intensity matrix:
𝜆 𝜆 𝜆 0
𝜆 𝜆 𝜆 𝜆
𝑝 (1)
𝜆 𝜆 𝜆 𝜆
𝜆 𝜆 𝜆 𝜆
From prior approvals, as a result, the elements of this matrix have the following
properties:
𝜆 𝜆 𝜆
𝜆 𝜆 𝜆 𝜆
(2)
𝜆 𝜆 𝜆 𝜆
𝜆 𝜆 𝜆 𝜆
To determine the probabilities of being the system in the states x0, x1, x2, x3, we
construct a system of differential equations:
𝑑𝑝 𝑡
⎧ 𝑝 𝑡 𝜆 𝑝 𝑡 𝜆 𝑝 𝑡 𝜆 𝑝 𝑡 𝜆
⎪ 𝑑𝑡
⎪𝑑𝑝 𝑡
⎪ 𝑝 𝑡 𝜆 𝑝 𝑡 𝜆 𝑝 𝑡 𝜆 𝑝 𝑡 𝜆
𝑑𝑡 (3)
⎨𝑑𝑝 𝑡
𝑝 𝑡 𝜆 𝑝 𝑡 𝜆 𝑝 𝑡 𝜆 𝑝 𝑡 𝜆
⎪ 𝑑𝑡
⎪
⎪ 𝑑𝑝 𝑡
⎩ 𝑝 𝑡 𝜆 𝑝 𝑡 𝜆 𝑝 𝑡 𝜆
𝑑𝑡
As
𝑝 0 1,0,0,0 (4)
is set, so vector of absolute probabilities
288
𝑝 𝑛 𝑝 𝑛 ,𝑝 𝑛 ,𝑝 𝑛 ,𝑝 𝑛 (5)
defines by the ratio:
𝑝 𝑛 𝑝 0 𝑝 𝑛 (6)
After research on the simulation model, two results of finding the coefficients 𝜆
were determined, which will be given below [28-30].
Option 1. Let the transition intensity matrix 𝜆 be as follows:
0.040 0.015 0.010 0.015
0.225 0.250 0.025 0.050
(7)
0.625 0.160 0.855 0.390
0.000 0.075 0.200 0.275
We get the solution of the equations system by the fourth-order Runge-Kutta
method for the time t = 50 s. To implement the solution, a software module has been
developed by Python. As a result of the calculations, the probability values of being
the system in each of the states were found (see Fig. 2).
Fig.2. The probability of being the system in each state.
Option 2. We will make the calculation similar to Option 1 with the values of the
transition intensity matrix 𝜆 :
0.040 0.015 0.010 0.015
0.225 0.250 0.025 0.050
(8)
0.575 0.200 0.875 0.500
0.125 0.145 0.180 0.200
As a result, we will get the following graph (see Fig. 3):
289
Fig.3. The probability of being the system in each state.
5 Conclusions
Based on the obtained results, it can be said that in Option 2, the system is more prob-
able to be in a threatened state, although there is a high probability that the security
system will successfully reflect the threat.
The mathematical model of threats resistance in the protection system of critical
information resources of the mineral fertilizers production is proposed. A methodolo-
gy for identifying actual security threats on the basis of this model has also been de-
veloped and displayed.
Examples of the numerical results analysis using the proposed methodology clear-
ly demonstrate that their use helps to identify threats that are relevant to the research
system and can be used in practice. The disadvantage of the proposed methodology is
the need to consider the behavior of the system when each type of threat is exposed to
it separately and the inability to determine the behavior of the system when simulta-
neous action of several threats is exposed to it. But on the other hand, research of the
influence of each threat separately allows you more detailed study each of its types
and identify those with the highest probability of occurrence.
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