This article leads a research on the development of a method and a program module evaluating the security of information of restricted access (IRA). The assessment of existing security technologies for information of limited access is given. Based on the general method of quantitative assessment of the safety of IRA a private method of quantitative assessment of the safety of IRA has been developed for a continuous ow of threats. The algorithm of the program for assessing the security of restricted access information for a continuous ow of threats has been developed and described.
Information technologies include methods for collecting information, its processing, transformation, storage
and distribution [
The formation of the process of electronic information space is accompanied by the development of methods for ensuring the protection of information circulating in it. So an organization that cares about the protection of restricted access information (IOD) circulating in it, has to implement a whole range of measures to ensure the security of information. The following groups are most pressing problems in the eld of computer security for IRA [2, 5, 6]:IRA integrity violation, IRA con dentiality violation, violation of automatic information systems (AIS) that processes IRA: IRA integrity violation, IRA con dentiality violation, violation of automatic information systems (AIS) that processes IRA.
One of the directions of scienti c research of con dential information security is a natural experiment.The method is based on the fact that at the preparatory stage an absolute copy of the protected information system is created, all interrelations between the system objects (internal and external) are established. Then all sorts of attacking actions of intruders begin to be modeled in order to overcome the organizations security system. The result is statistical data on the modelling.
There are two strategies for natural experiment: active and passive. In the rst case the experimenter has the ability to change the external conditions that determine the state of the object. Second - this is not possible. The advantage of this method the high accuracy of the results of the experiment. The main disadvantage of such research are the complexity and high cost of experimental studies, as is required to put into practice a large number of identical experiments.
Another method to study the safety of restricted information is semi-natural modeling.Semi-natural modeling is a kind of experimental theoretical study in which several nodes investigated system is replaced by their physical counterparts [2]. The method allows the study not to create a complete copy of the studied information system. Due to the fact that some assumptions were made, respectively decreases the accuracy of the study, the error appears. Also, another disadvantage of this method is that the established experimental model will not be enough similar to the real system that was introduced in full-scale experiment, thereby decreasing reliability. However, because of the insu cient development of the mathematical apparatus, an excessively large dimension of the problem, the large number of random factors, this method is often not applicable [2].
To solve the problem of analyzing a security system containing IRA, it is proposed to use a mathematical
modeling apparatus based on Markov random processes. This mathematical model has all the functionality
necessary to simulate the security of a system against accidental and deliberate threats. However, there are
many other methods by which it is possible to analyze the security of information of various in-formation
systems. So, in the article [
Formulation of the problem
The impact of accidental threats to the security elements of IRA system can result in two outcomes [
The probability of the i -this a special situation qi, and the conditional probability of it re ect the e ects of its occurrence ri, and the probability of not re ect the e ects of ri.
Then we de ne the probability qi and piAs automatic information system (AIS) sequence of transitions from
one state to another in a Markov random process with a number of states and continuous time. This process is
conveniently represented as a logical - probabilistic process. [
Fig. 1 shows that there is a threat of IRA exposure to security threats in the AIS. At this time, the system
state may be described by the following conditions [
State <<BY>> and <<P>> are states of a successful outcome when exposed to AIS security risks of IRA and is
expressed by formula [
As a result, it is proposed as a criterion for quantifying IRA security, likely to take a successful outcome from
exposure to threats random system. This probability is de-noted by p, and the probability of the opposite event
is denoted by q. Since the magnitude of the favorable and unfavorable outcome constitute a complete group of
events, then the condition [
State <<P>> is a condition characterized by the occurrence of an event unfavorable outcome, when IRA exposed to security threats and expressed by the formula:
Pbii = pi + qiri
Qbii = qiri
Qbii + Pbii = 1 Likelihood Qbui andPbui form a complete group of events, and thus ful lled the formula:
A ecting AIS IRA security threats can be generated by a one with a certain probability. It is therefore proposed to adopt a base - model of Markov processes with continuous parameter for safety assessment, taking into account the impact on AIS dependent ows threats. The process of mathematical modeling of complex systems based on a Markov random process can be divided into three successive steps - building a mathematical model, developing and modeling an algorithm for building a model based on Markov processes, studying the original system with a model that represents an experiment, processing and interpreting the results. 2.2
Development and research of the method of the software module for quantitative assessment of the security of restricted access information In Markov processes AIS future state depends on the last only through the present.
A random process with respect to the AIS is called Markov if for any time t0 probability of AIS in the future
depends only on its state at the moment t0 and does not depend on when and how AIS came into this state [
Classi cation of Markov random process is performed depending on the continuous or discrete values of the set function X (t) and the parameter t [13, 14].
Let AIS on a nite time acts n just a stream of threats with intensities i. i= 1;n.
Let i{ the intensity of the e ects Parry i-the second threat. Respectively,Ri{ parry, and R^i{ the probability of not parry i-th threat.
Then, i Ri{ the intensity of the parry and i R^i{ the intensity is not parry impacts on the ow of AIS threats.
Assumptions: parry ow and not parry the threat of the simplest, ability to parry the e ects of exposure to AIS i{ second threat is not limited, that is, i i, since these elementary streams, the appearance at the same time two or more threats is impossible event.
To determine the probability of a successful outcome when exposed to the ow of AIS n threats the AIS system is represent as a graph.
Referring to gure 1, the AIS at time may be in one of the following conditions [
failed to appear; state <<1>>, i..., n{ one of the threats was manifested; state <<n+1>> { unfavorable absorbing state in which the threat was realized. According to gure 1 can write intensities transition matrix form: k jkk =
0 uiRi unRn 0 : : : : : : : : : : : : i ui where 0 = 1 + 2 + : : : + n; j = k = 1; 2; : : : ; n + 2.
Matrix (5) has the following properties: the diagonal terms of the matrix are equal to the sum of the remaining elements of the line, taken with the opposite sign; the sum of all elements in each row is equal to zero; the number of zero crossings in the matrix rows correspond to the number of intensities absorbing states; the transition intensity is zero in the absence of the arrow.
To determine the AIS transition probabilities to each possible state of the system Kolmogorov di erential equations are used, in accordance with which one can write: dP0( ) d
Applying to the set of di erential equations (6) the direct the Laplace transform to the reference data P0 (0) = 1. Pi (0) = Pn+1 (0) = 0 and given the fact that R01 P ( ) e Stdt= Pi (0) + SPj (S), the following expression for determining probabilities in accordance with the count states is obtained ( gure 1).
P0(0) + SP0(S) =
n 0P0(S) + X
i=1 Pi(0) + SPi(S) = iP0(S)
n Pn+1(0) + SPn+1(S) = X i=1 iRiPi(S) iPi(S); iR^i(S) wherePi (S) = R01 Pi ( )e Std { the desired image.
For the initial conditions of equations (7) becomes:
n (S + 0)P0(S) = X i=1 iRi(S) = 1 iP0(S) + (S + i)Pi(S) = 0 n X iR^iPi(S) + SPn+1(S) = 0 i=1 According to Cramer's rule the desired image is determined by the ratio:
Pj(S) =
; j = 1; n j(S) (S)
n 0(S) = S Y (S + l)
i=1 (6) (7) (8) (9) (10) (11) where (S) = S[(S + 0) Qin=1 (S + i) Pin=1 i iRi Qin=1 S + l)] { the main determinant of the system; j(S) { partial determinant system, is the main determinant by replacing j-th column coe cients on the right of equations (8). [13, 12].
Private determinants obtained by introducing determinants of induction will be equal to:
In view of the indicated and with the proviso that j(S) = takes the form: jS(S) , (S) =
S(S) the system of equations (8) and the probability of an unfavorable outcome: Finally, with regard to (10) the expressions (11) take the form: where (S) = S2 + Sc1 + c0, c1 = + , c0 = R^.
Applying to the (15) the inverse Laplace transform of taking (13) and (14) the expression for the determination of the desired probability is obtained, namely:
Pbi( ) = P0( ) + P1( )
QBI( ) = Pn+1( ) (12) (13) (14) (15) (16) (17) (18) (19) (20) Based on the method of evaluation of information security limited access, for one continuous ow threats examined input parameters to the algorithm, and the output parameters that the algorithm, which block diagram is shown in Figure 2 must provide the program on the basis of the work, it has been realized.
To implement the safety assessment algorithm IRA was selected Java SE 8, a programming language, because it provides more opportunities for programming Windows and Linux operating system applications. For the development was chosen IntelliJ IDEA development environment that includes a high-performance tool visually build applications based on GUI programming library Swing and AWT [11, 10, 16].
The algorithm of the IOD safety assessment program is developed on the basis of the owchart of the method for quantifying the safety of IOD for one continuous ow of threats, presented in the owchart in Figure 2.
As seen from the block diagram in the block number 1 initialization constants necessary for further operation of the algorithm is carried. Namely TIME RANGE constant is set to 40, which determines the exposure time on stream AIS threats, TIME DELTA to 1, which corresponds to the time sampling rate threats stream impacts on the system.
The block number 2 is the input of the input data: the ow rate of threats , the intensity parry threats , parry R.
In block number 3 input valid data-in is checked, if the data is correct, then control is passed to the block number 4, otherwise, control is transferred to block number 2, to re-enter the input data.
The number 4 unit is cleaned mParryTable component elds of data that it can contain the above [6, 15].
A variable rowCount (rowCount = (TIME RANGE + 1) / TIME DELTA) is determined in the room unit 5 the number of rows of the matrix to be created at step 6.
The resulting empty matrix B, comprising 5 rowCount columns and rows is created in room unit 6. The auxiliary values are initializes the room unit 7:
B0 = ; A0 = 1
B0; B1 = ; A1 =
B1; (21) D = + 2 2 +
2 + 2 + pD (2 +
R 2
1) ; pD s1 = s2 + s2 s1 ;
s2 = In the 8-block is generated by a variable cycle i, sequentially taking values from 0 to rowCount.
In block number 9, the values of matrix B are assigned in accordance with step i. B [i, 0] - the probability of the system in state 0, B [i, 1] - in state 1, B [i, 2] - in state 2, B [i, 3] - the probability of a successful outcome, B [i, 4] - the probability of an unsuccessful outcome. To calculate the probabilities, the values obtained in block 7 of algorithm (21) are used, as well as the following formulas:
B [i; 0] = A0 es1 i + B0 es2 i; B [i; 1] = A1 es1 i + B1 es2 i;
B [i; 2] = A2 + B2
es1 i + C2 es2 i; B [i; 3] = B [i; 0] ; B [i; 4] = 1 As a result of the program, statistics were obtained that are presented on the graph of the dependence of a successful outcome on the time of the impact of the threat ow in Figure 3.
The graph shown in gure 3 can observe the probability of a successful outcome decrease with increasing
exposure time on stream AIS threats [
As a result, conclusions can be drawn: probability Pbi of AIS successful outcome from exposure to the ux IRA threats decreases with increasing exposure time threats stream, the rate of decrease in probabilityPbi depends on the probability of countering the threat, as well as on the intensity of the impact of the ow of threats.
Let us conduct a modelling of a quantitative assessment of the security of the IOD, to study the in uence of the parameters of the intensity of the threat ow and the intensity of the parry, on the probability of a successful outcome. To do this, several di erent sets of input parameters, with di erent indicators of the intensity of the threat ow and the intensity of the parry, and a xed value of the probability of parry.
The value of the probability of parrying by setting the value to 0.6 is xed. The values of the intensity of the ow of threats and the intensity of parry together, from a value of 0.1 to 3 are changed.
Based on the modelling, a graph of the overall modelling results for various intensities of the threat ow and the intensity of parry is built, the results are presented in Figure 4.
Based on Figure 4, it is concluded: the probability of a successful outcome for AIS, from the impact of the ow of threats from the IOD on it, depends on the intensity of the ow of threats and the intensity of parry. The greater the intensity of the threat ow and the intensity of the parry, the faster it decreases, which means that AIS prone to a more intense ow of threats is less secure. 4
As a method and software module for assessing the security of information of limited distribution, a mathematical modeling apparatus based on Markov random processes was analyzed. This mathematical model has all the functionality necessary to simulate the security of a system against accidental and deliberate threats. Its use will allow to accurately determine the ow of the impact of threats on the AIS. 5
The aim of this study was to increase the security of AIS using the method developed information security assessment of restricted access and its software implementation. To achieve this, all the tasks were performed.
In the process, an analysis of existing security restricted information technology, concluded the relevance assessment IRA security.
In the next step the existing methods of assessing the safety of restricted information were studied, namely: a natural experiment, simulation and semi-natural method of expert evaluations. The method of mathematical modeling based on Markov processes was proposed.
A general method of information security assessment on the basis of the limited access of Markov is processed. Based on the general method for quantifying the safety of IOD, a particular method has been developed for quantifying the safety of IOD for a continuous ow of threats. A software module was developed. [13] E. M. Meyers. \Access denied: How students resolve information needs when an "ideal" document is restricted". In: ACM International Conference Proceeding Series (2012).
C. Wang, Z. Zhang, and X. Song. \Research on the information security technology of university campus network". In: Advances in Intelligent and Soft Computing, AISC (VOL. 2) (2012).
H. Wang et al. \The security protection and technology analysis of information system". In: Applied Mechanics and Materials (2013).
C. Tang. \Study of security technology in wireless sensor networks". In: Lecture Notes in Electrical Engineering, 219 LNEE (VOL. 4) (2013).
Karim Lounis. \Stochastic-based Semantics of Attack-defense Trees for Security Assessment". In: Electronic Notes in Theoretical Computer Science 337 (2018).
M. Ge et al. \A framework for automating security analysis of the internet of things". In: Journal of Network and Computer Applications (2017).
D. Lovtsov, D. Makarenko, and A. Fedichev. \Architecture of the national classi cation of legal regimes of restricted access information". In: CEUR Workshop Proceedings (2017).
A. P. Rosenko and E. A. Nekrasova. \Mathematical modelling of the process for impact on automated information system security of threats access to restricted information". In: CEUR Workshop Proceedings (2017).
Vybornova O. N. Azhmukhamedov I.M. \Introduction of metric characteristics for solving the problem of risk assessment and management". In: Caspian Journal: Management and High Technologies (2015).