The transition to the digital economy is not possible without considering the issues of creating a modern information infrastructure, which is confirmed by a number of documents adopted at the level of the President and the Government of the Russian Federation. One of the main problems in the implementation of these documents is associated with the creation of an effective system for managing the information infrastructure of state bodies, state institutions, Russian legal entities and (or) individual entrepreneurs who are subjects of critical information infrastructure (hereinafter - SCII). At the same time, the task facing the heads of the SCII, who in this case bear criminal responsibility for the low level of reliability of the subject, is associated with the creation of an effective management system for the operation of facilities of the CII. The existing regulations of the regulators on the safety of the SCII fix the composition of the factors influencing the facilities of the SCII. Strict regulation in this matter increases the level of error in the complex assessment of information security (hereinafter - SCII) of the subject, therefore, leads to a decrease in the level of requirements already at the stage of categorizing objects. The proposed solution is a synthesis of cognitive and logical-probabilistic approaches, taking into account destructive influences on the infrastructure in dynamics at all stages of the life cycle of a critical information infrastructure (hereinafter - SCII) objects.
The legislation of the Russian Federation [1-5] defines the areas of functioning of enterprises and organizations that affect the quality of life and health of society, in order to ensure their safety. State bodies, government agencies, Russian legal entities and individual entrepreneurs operating in the selected areas, which are subjects of the CII, are responsible for maintaining the stability of the area to which they belong.
One of the guarantors of stability and information security of society and the state as a whole is the reliability and security of SCII. Currently existing methods and models for assessing IS, as applied to SCII, are considered without taking into account the factors of destructive impact on SCII. This leads to significant errors in the analysis of the information security of the SCII, therefore, reduces the effectiveness of the information protection means declared for the facilities of the CII.
In the process of modeling the actions of an attacker, as a basis, for example, descriptive models of networks and attackers [6], structured description based on trees [7], object-oriented discrete event modeling [8], regulatory modeling [9], etc. are considered.
However, when building the SCII protection system, the algorithm of actions prescribed in [1] is used and does not take into account the "strength" of destructive influences as one of the significant indicators of a potential violator. In addition, the assessment of information security is often considered without considering infrastructure changes over time. Thus, the purpose of the study is to build a model for assessing the information security of the SCII through integrative components - models for assessing the reliability and security of the SCII, taking into account the destructive effects on the facilities of the SCII. At the same time, the subject of CII is considered within the framework of this study as a set of objects of CII, which are its structural components.
The "input" research was carried out in the following directions: analysis of models and methods for assessing the reliability of the subject of CII, analysis of ways to increase the reliability of the subject of CII, analysis of existing software systems for assessing the reliability of technical systems, analysis of approaches to model development and assessment of destructive malicious influences.
The considered approaches to the development of a model and the assessment of destructive malicious influences (DMI) [10-15], despite their certain significance, do not fully describe the model of behavior and actions of the offender with any simple and understandable indicator convenient for further use in the assessment or the development of a set of protective measures. The methodology proposed below takes advantage of the strengths of existing algorithms, fills in the gaps and removes a number of assumptions that limit functionality during development, and introduces a reasonable quantitative value that characterizes the level of destructive impact of an intruder on the system.
In the course of analyzing the models and methods for assessing the reliability of the subject of CII, the following were considered: the probabilistic method (the "block - diagram" model), the logical probabilistic method, the logical - probabilistic method. Failure tree model, Markov model. According to the criteria highlighted in the study, the probabilistic method (the “Block-diagram” model) was determined as the most effective.
Based on the results of the analysis of ways to improve the reliability of the functioning of the CII subject, the most effective and appropriate methods of redundancy are loaded and loaded redundancy.
In the study of software systems for assessing the reliability of technical systems, (Automated Calculation of Safety and Technical Risk) (PC ASM SZMA), ASONIKA-K, ASRN (2000, 2002), Isograph (England, USA), RAM Commander (Israel), Windchill Quality Solutions (Relex) (USA) were considered. In the course of the study, the WQS software package was determined as satisfying the largest number of selected criteria. However, to solve the problem, it is necessary to fulfill all the criteria, which leads to the need to develop an appropriate model.
To implement the modeling process, sub-objects are identified - inventory units of the CII subject. The reliability of the CII objects and the CII subject as a whole depends on their reliability of functioning.
In order to reduce the error in the assessment of information security, the life cycle of the subject of CII was determined and analyzed in accordance with GOST 34.601-90 [16]. On the basis of the "Life Cycle of the information security information system of the CII subject", the types of destructive influences leading to the emergence of vulnerabilities in the protection system of CII objects at different stages of the life cycle of the CII subject are identified. Vulnerabilities can be used to implement threats, attacks by cybercriminals on the subject of CII as a whole. Selected types of destructive influences (destructions): Destr 0 - Errors associated with the primary development of the plant's AS; Destr 1 errors at the categorization stage; Destr 2 - Infrastructure Analysis Errors; Destr 3 - Errors in the formation of requirements for the information security of the subject of the CII; Destr 4 - Errors in the development of the concept of information security for a CII subject Destr 5 - Errors in the development of technical specifications at SBCII and PSBCII; Destr 7 - Errors in the technical design; Destr 8 Errors entering SBCII and PSBCII; Destr 9 - Errors while accompanying the CII subject [17].
Vulnerabilities of typical APCS, GIS, ISPDN, KIS are analyzed by the method of constructing vulnerability trees. The relationship between the selected destructs and a number of vulnerabilities has been revealed [14-15]. Destructions Destr 0, Destr 1, Destr 2, Destr 3, Destr 4, Destr 5, Destr 6, Destr 7 are associated with the vulnerability of lack of compliance with information security requirements in the design of information security system solutions. Destruction Destr 8 is associated with a vulnerability in the absence or insufficient level of knowledge in the field of information security among the maintenance personnel. Destr 9 destruct identifies a number of vulnerabilities, such as the problems of delimiting and controlling access for contractors associated with the need to provide temporary access to a limited amount of equipment without the possibility of affecting the rest of the system, as well as the cancellation of such access at the end of work; lack or insufficient level of knowledge in the field of information security among the maintenance personnel; long service life of vulnerable components caused by the complexity of upgrading equipment and systems.
Physical, physicochemical, chemical, biological, operational, and the implementation of threats by intruders are identified as factors affecting the decrease in the reliability of the functioning of the CII subject.
When assessing the reliability of SCII, the indicators of the reliability of recoverable and nonrecoverable objects are assessed. For recoverable ones - mean time between failures, mean time between failures, probability of recovery, mean time to recover, availability factor, coefficient of technical utilization. For non-recoverable ones - the probability of failure, the probability of failure-free operation, the time of failure-free operation, the intensity of failure.
The subject of CII is a complex, multicomponent system [16-30]. It can be viewed from the point of view of different approaches. For example, when conducting a comprehensive assessment of the IS of a CII subject, the assessment of the security of the IS - CII objects, which, in turn, can be considered as economic systems, is taken into account.
Another indicator when analyzing the functioning of a CII subject is reliability. In [21], mathematical support for the analysis of the reliability of network ICs is proposed. This apparatus can also be used in the study of CII objects. As a model of a network IS, a graph representation is used, based on the formalization of the description of the graph by bracketed projections. Based on the resulting combination of projections, obtained as a result of the cutting algorithm implementation, a probabilistic reliability function is constructed.
Comprehensive information security of a CII subject is also an example of a socio-technical system [22] operating under conditions of uncertainty. Thus, taking into account the peculiarities of poorly formalized processes occurring in socio-technical systems, in particular, in the system for assessing the information security of a CII subject, it was decided to use the methods of cognitive and logicalprobabilistic modeling.
To assess the IS SCII, it is proposed to consider the cognitive model for assessing the security of the SCII as a base one, where one of the influencing factors - the reliability of the SCII is the result of the work of the logical-probabilistic model. Positive impact
Negative impact
Model assessment of the reliability of the SCII
The threat of negligent attitude of employees of
CII objects
V8
The threat of changing social
conditions V4 Threat of changing conditions for the country's defense
V6
Threat of changing contractual relations
V11 Threat of changing economic conditions
V1 Assessment of the IB of the subject of the CII
V13
V10
The threat of disruption of the functioning of all performed CII processes
V5
V9 Threat of destructive
impact of infrastructural nature
V12 The threat of an unplanned natural disaster Threat of malicious actions on the CII object
V7
V2
The threat of changing political conditions
V3 The threat of changing the regulatory framework
The main sources of risk factors in the activities of CII subjects for building a cognitive model are presented in accordance with the Decree of the Government of the Russian Federation of February 8, 2018 No. 127 "On approval of the Rules for categorizing objects of critical information infrastructure of the Russian Federation, as well as a list of indicators of criteria for the significance of critical information infrastructure of the Russian Federation. Federation and their meanings (as amended on 13.04.2019). In addition, the target vertex V13 "Information security of the CII subject" has been introduced into the cognitive model, according to the results of the work in which the impact of DMI on the information security of the CII subject will be assessed.
In the course of modeling, a cognitive map is built for assessing the IS of the subject of CII under destructive influences (Figure 1). For a deeper analysis of the model in the form of a weighted digraph, an algorithm is built for the influence of changes in the values of one vertex on the values of other vertices.
This algorithm is based on the idea of an impulse process proposed by F.S. Roberts. Its essence lies in the fact that an external disturbance is introduced into some vertex of the analyzed graph.
The algorithm for the development of the impulse process can be represented by the following matrix formula:
V_((t)) = V_((initial)) + P0*(I+A+A2+⋯+At), where V_((initial)) ‒ initial state vector; P_0 ‒ initial impulse; A – adjacency matrix; I –identity matrix of size n×n.
Evaluation of DMI is implemented in the module for categorizing the attacker in the model of cognitive assessment of information security of the subject of CII under destructive influences (Figure 2). A methodology is proposed to implement this assessment.
Pulse modeling module
PhL: [x]/LogL: [x]/C: [x]/A: [x]/ /M: [x], where [x] ‒ the value of the corresponding parameter.
The proposed mathematical model for assessing the reliability of the subject of critical information infrastructure is represented by the function of the model for assessing the reliability of the subject of CII: where Preli – probability of failure-free operation of CII facilities; P_thr - the likelihood of an IS threat.
Pthr - can take the following values: = ( ℎ , ) ℎ = ∨ where PDestri – the likelihood of the implementation of threats generated by destructions at different stages of the CII life cycle; Pexp – expert assessment of the likelihood of the implementation of threats.
In the model for assessing, the reliability of the subject of CII PDestri is predicted by the least squares extrapolation method based on the existing statistics on the implementation of threats at enterprises and organizations operating in the areas of CII. Wherein = { 2 10 ℎ
≠ {2, 10} , The occurrence of errors, destructions, at different stages of the life cycle of the information security system of the CII subject generates vulnerabilities in the CII protection system, which attackers can exploit to implement threats to the CII subject.
Probability of failure-free operation of CII facilities Preli depends on the probabilities of failure-free operation of CII subobjects and their interconnections: = ( 1, 2, 3, 7, 9 ) where InvU1 – АРМ; InvU2 – server; InvU3 – АСО; InvU7 – channels of connection; InvU9 – CII sub-object, specific for each individual CII subject.
To calculate the assessment of the reliability of the Preli CII facilities, three cases were considered, where pi – probability of failure-free operation of CII subobjects:
Assessment of the reliability of the subject of CII Psubj is calculated similarly to the schemes for assessing the reliability of CII objects: using calculations for parallel and serial connection of CII objects. After assessing the reliability of the CII objects, to assess the reliability of the CII subject, a structural diagram of the interconnection of the CII objects is formed and, based on the probabilities of the failure-free operation of the CII objects and the probability of the implementation of threats, an assessment of the reliability of the CII subject is calculated.
= ∗ (1 − ℎ )
Assessment of the reliability of the CII, when using the methods of redundancy in order to increase the reliability of the subject of the CII, the following methods and calculations are used to reserve the subobjects of the CII, where pi – probability of failure-free operation of CII subobjects: a general redundancy with a multiplicity of k, separate redundancy with a multiplicity of k, subobjects are k + 1).
Here 1 – when using loaded redundancy - for a system with a serial connection of n subobjects with 2 – when using a loaded redundancy - for a system with a serial connection of n objects with a 3 – when using an unloaded redundancy - systems with unloaded redundancy of multiplicity k (all Based on the results of the assessment of the reliability of the CII subject before and after the reservation, the reliability gain coefficient is calculated: where Pbefore – assessment of the reliability of the subject of CII before reservation; Pafter – assessment of the reliability of the CII subject after reservation.
1 − (1 − ) +1 = 1 − (1 − ∏ =1 ( )) +1 , = { ∏ =1(1 − (1 − ( )) +1) , 1 −
1 ∏ ( +1)! =+11(1 − ( )), (1) (2) (3)
● ● nature;
At the first stage, the assessment of the reliability of the CII subjects operating in various industries, including various types of CII objects, was carried out. The problem being solved is to increase the reliability of the CII subject, if the initial assessment of the reliability of the CII subject is less than the permissible one. Experimental studies involved not only assessing the reliability of the CII subject, based on the presented schemes of CII objects, but also, if necessary, the subsequent application of backup methods to the CII sub-objects in order to increase the reliability of the CII subject.
At the second stage, experimental studies were carried out on:
study of the influence of the destructive influences of an intruder with a low potential on the assessment of the IS of the CII subject, consisting of an object - IS with 1 category of significance; study of the influence of destructive influences of an intruder without potential and with high potential on the assessment of IS of a CII subject, consisting of an object - IS with 3 categories of significance and ACS - 2 categories of significance with destructive influences of an infrastructural ● the study of the impact of destructive influences of violators with high, medium and low potentials on the assessment of IS of the subject of CII, consisting of objects: IS of the 2nd category of significance, ITS - 1 category and ACS - 3 categories of significance with destructive influences of an infrastructural nature.
The analysis of the results of the first stage of experimental studies using the example of SCIIHospital is presented in table 1. The results of stage 2 are in table 2.
The use of the developed model made it possible to assess the IS of the subject of CII under destructive influences, taking into account the indicator of the infrastructural component - the reliability of the CII. The synthesis of models made it possible to categorize the attacker, build a cognitive map for assessing the IS of the CII subject, simulate the DMI through various vertices-sources, and provide recommendations for increasing the level of the IS of the CII subject.
The proposed model can become an active assistant for the owners of CII facilities in the process of solving practical problems at all stages of the SCII life cycle. For regulators, the proposed approach to assessing the IS SCII will increase the reliability of the data provided by the owners of the objects of CII facilities at the categorization stage.
The proposed model is related to the use of: ● specifics of the regulatory and legal framework in the field of SCII safety, ● structured detailing of the CII subject, taking into account the specifics of the subject, ● stages of the life cycle of the SCII information protection system, ● highlighted destructive malicious influences of an infrastructural nature, ● the relationships between the selected destructs and a number of vulnerabilities on CII objects, ● factors affecting the decrease in the reliability of the functioning of the CII subject, ● evaluating the reliability indicators of recoverable and non-recoverable objects, backup methods and allows you to perform a comprehensive assessment of the information security of the subject of CII.
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