Mathematical Model for Collecting and Evaluating Complex Security Factors and Ensuring the Prevention of Threats to Individuals and Society in Cyberspace

This a rticle i s de voted to the de velopment of a model a nd e laboration of t he s tructure of t he mathematical formalism for the assessment of the state of comprehensive security in order to prevent threats to the individual and society in cyberspace. The types and objects of information threats are examined, the main properties, which are indicators and parameters we should possess, are revealed and the key stages of status assessment of comprehensive security in state entities, municipalities and organizations are identified.


Introduction
The s ystem o f co mprehensive s ecurity o f each s tate is a set of bodies and institutions that function in the areas of regulation, pr evention a nd elimination o f the consequences of v arious t hreats ( political, economic, biological, chemical, environmental, etc.). In Russia there is a s ystem o f e nsuring na tional s ecurity, c onsisting of state a nd n on-state s ubsystems. T he s tate s ystem i s formed b y legislative, executive, a nd j udicial state institutions t hat t ake part i n t he process of m aking decisions and im plementing p olitical, legal, organizational, e conomic, m ilitary, and other m easures aimed at ensuring the security o f the individual, society, and t he s tate. The no n-state system consists o f p ublic associations, w hich i nclude t he m edia a nd individuals who c an influence t he formation and implementation of national s ecurity p olicies. The concept o f s ecurity i s a multi-vector a nd m ultidimensional concept, w hich includes a whole set of structural components. [1,2] The i ntegrated security s ystem o f each S tate consists of t he bodies and i nstitutions t hat operate t o r egulate, prevent and r espond to va rious threats ( political, economic, b iological, chemical, ec ological and o thers). The R ussian F ederation h as a n ational s ecurity s ystem consisting of S tate and no n-State s ubsystems. T he S tate system shall form legislative, executive and judicial State institutions th at ta ke part i n t he process of f ormulating decisions and implementing measures of a political, legal, organizational, economic, military or other nature; aimed at e nsuring th e s ecurity o f i ndividuals, s ociety a nd th e State. T he non-State s ystem c onsists of v oluntary associations, w hich i nclude t he m edia a nd private individuals w ho c an influence t he f ormulation a nd implementation of national security policies. The concept of s ecurity is a m ultidimensional a nd m ultifaceted one that incorporates a variety of structural components.
Assessing t he s tate of c omprehensive s ecurity t o prevent threats to the person and society in cyberspace is one of t he m ost i mportant tasks t hat t he s tate s olves. Currently, t here a re n o a pproved m ethods or recommendations f or as sessing t he s tate o f comprehensive s ecurity t o prevent threats t o t he person and society in cyberspace, and the existing international recommendations do not t ake into account the s pecifics of the Russian F ederation. T he types and o bjects o f threats in cyberspace are shown in table 1. [3,4]

Theoretical basis
The theoretical basis of t his work was t he na tional scientific w orks of R ussian a nd f oreign s cientists on development information management and its subjects, as well as

Discussion
In t he m ethodology p resented b elow, t he assessment o f the state of comprehensive security to prevent threats to the individual and s ociety i n c yberspace (hereinafter referred to as the comprehensive security) is expressed by an in tegral d imensionless in dicator, d etermined in the range from 0 to 1 and showing the probability with which the in tegrated s ecurity o f th e object of assessment is ready t o pe rform t asks on de stination. I n t his article, the object o f a ssessment means a federal executive b ody, a constituent entity o f th e R ussian F ederation, a municipality or an organization. The co nsidered i ntegral i ndicator of t he s tate of complex s ecurity i s t he u pper l evel o f t he h ierarchy shown in Figure 1, and is determined based on the values of indicators of the state of complex security. These indicators should have the following properties: • reliability -the indicator s hould characterize progress in a chieving a g oal or s olving a pr oblem a nd cover the maximum number of aspects of achieving the goal or solving complex security problems; • objectivity -it is n ecessary t o u se in dicators that reflect the real state of affairs; • unambiguity -the definition o f th e in dicator should provide the same understanding of the essence of the measured c haracteristic, e xclude the po ssibility of double interpretation or understanding; • cost-effectiveness -reporting d ata s hould be obtained a t the lowest p ossible c ost, a nd t he i ndicators used s hould be based a s m uch a s possible on e xisting procedures for collecting information in th e field of comprehensive security; • reliability -the method o f collecting a nd processing th e in itial in formation s hould allow th e possibility of verifying the accuracy of the data obtained; • timeliness a nd r egularity -to be us ed f or monitoring purposes, reporting data should be updated at least once a year. [5] Taking into a ccount t he a bove pr operties, t he following in dicators o f the state of integrated s afety are established ( depending o n the o bject o f assessment, indicators can be supplemented or reduced): • protection of the individual (society, state); • readiness o f t he m anagement s ystem o f s ecurity agencies; • the readiness of the security forces; • stability of functioning of economic objects.
The values o f the groups o f indicators are calculated by a ggregating t he c orresponding m arks of t he s tate of integrated s ecurity, w hich a re c ollected w ithin th e framework of information exchange.
Mathematically, s uch a h ierarchy ( Figure 1) c an be written as: Among the ba sic principles underlying the t heory o f management, the central place belongs to the hierarchical subordination in th e activities of v arious s ystems a t various levels. [6,7] If, as an i ntegral indicator o f as sessing t he s tate of comprehensive s ecurity, t he probability o f developing instability in society is taken, th en v arious s cales can be used to as sess the s tate of c omprehensive s ecurity: "unstable" -from 0 to 0.7; " Satisfactory" -from 0 .7 t o 0.8; "Stable" -from 0.8 to 1.
In t he f ollowing methodological approach t o assessing t he s tate of c omprehensive s ecurity, t he Harrington desirability s cale is u sed: " Very ba d" 0.00 -0.20; " Bad" 0 .20 -0.37; " Satisfactory" 0. 37 -0.63; "Good" 0.63 -0.80; "Very good" 0.80 -1.00. The choice of marks 0.37 and 0.63 on the desirability scale is explained b y t he c onvenience of c alculations, s ince t he desirability function is exponential: Let's gi ve a n e xample: t he r eadiness of comprehensive security in a border state entity of 0,6 can be es timated as "not ready", w hile t he s ame r eadiness value for another entity can correspond to the assessment "limited ready".
Thus, t he t ranslation of t he va lues of t he groups of indicators M into the conditional scale M ' is carried out in order to evaluate various objects of assessment on the same scale. Dependencies for coding: for s tate e ntities, m unicipalities th at a re n ot assigned to civil defense gr oups, a nd or ganizations t hat a re n ot assigned to civil defense categories by (3): for s tate e ntities, municipalities a ssigned to c ivil defense groups, a nd o rganizations a ssigned to civil d efense categories by (4): An explanation of the f orm of e quations (3) a nd (4) and the values of the corresponding coefficients is given below.
On s ub-stage 3.2 by ( 5), p articular v alues o f desirability of g roups of i ndicators are calculated b y (5): It is as sumed t hat t he relationship between t he indicator value and its encoded value is linear, so: The co ded v alue of ′ is e xpressed f rom ( 5) by double logarithm: Substituting the value of ′ in (6), we obtain: For t he m inimum a nd m aximum de sirable v alue of the group of indicators and , respectively, it is possible to create a system of equations (8) The c oefficients a 1 and a 0 used in ( 3) and ( 4) where: -the rank of the group of indicators.
The β values for ranks 1 to 9 are shown in Table 2. After determining th e v alues of a ll g roups o f indicators, a n in tegral assessment o f th e s tate of comprehensive safety is determined at stage 4.
The calculation sequence for its definition is the same as stage 3 and can be presented in three sub-stages: 4  In th e R ussian Federation, this strategy has been adopted at the federal level and supplemented by acts of the constituent entities.

Results and Discussion
The concept o f comprehensive state security is aimed at creating a s ystem o f t ools (authorities, s ervices, et c.) which, t aken t ogether, a re c apable o f preventing and resolving all kinds of threats to the rights and freedoms of the individual, society and the State. [9,10] In conclusion, it should be noted that the advantage of using t he de scribed m ethodological a pproach i s t he possibility o f us ing different ranges w hen a ssessing t he state of integrated safety of various objects of assessment without making changes to the mathematical formalism. In a ddition, t he desirability f unction ha s s uch us eful properties a s c ontinuity, m onotony a nd s moothness, i s not s ensitive at ex treme v alues, an d reflects w ell the estimate in the middle zone.
The p roposed mathematical model f or collecting a nd evaluating co mplex s ecurity factors a nd e nsuring t he prevention o f th reats t o in dividuals and s ociety in cyberspace may be of interest to specialists in the field of information threats to qualitatively assess the problems of the state of an object.