The paper considers the formulation of the problem of ensuring the survivability of the information system in the presence of harmful external influences. The main factors affecting survivability are identified, such as the level of information security and the level of cyber security. The possible structure of the vector criterion of survivability, which is based on indicators of the level of information security according to the security profiles of the information system: integrity, availability, and confidentiality, is analyzed. Considered ways of transition from a multi-criteria optimization problem to a single-criteria one: the method of transformation of criteria into constraints and the method of scalarization of a vector criterion. The method of scalarization of the vector criterion using scalar convolutions was chosen as the main method of transition to a single-criteria optimization problem. It was determined that additive convolution was the most widespread in scalarization problems. For the use in one convolution of criteria that may differ in physical nature, approaches were considered for the normalization of information security level values according to security profiles and the normalization of the corresponding weighting factors. An information security level assessment model based on additive convolution was created for the scenario when all component indicators and weighting factors dynamically change according to periodic laws. The simulation result shows the dynamics of changes in the general level of information security, which directly affects the level of survivability of the information system. It is shown that the obtained result is not trivial and the model is practically useful. The simulation model was created using the MatLab algorithmic language.
Digital technologies permeate all spheres of society. A large number of industries can no longer exist without computer support. Digital systems facilitate and speed up many processes of people’s activities. But digital accessibility, at the same time, facilitates the implementation of harmful effects on information systems. This reduces the survivability of information systems. Survivability is the ability of an information system to maintain its performance in conditions of harmful effects on the information system. One of the most common types of impacts on the survivability of information systems is impacts on information security, in particular its component—cyber security. Ensuring survivability is relevant for information systems at all levels: personal, corporate, state, and global. Ensuring the viability of information systems that process any state and community information [1], public and private sector enterprises [2], scientific and educational information [3, 4], as well as the personal information of citizens of Ukraine and citizens of Ukraine’s partner countries is urgent. This is evidenced by the analysis of the main trends regarding the state of cyber security in the world [5]. This question became especially relevant in the conditions of the full-scale war of the Russian Federation against Ukraine.
Unfortunately, any use of information protection leads to a decrease in performance. That is, the protection systems themselves, in a certain sense, are also a threat to the efficiency, that is, to the survivability of the system. A certain balance is required between the level of protection and the functionality of the information system. For this, it is necessary to optimize information protection according to all information protection profiles: integrity, confidentiality, and availability. That is, it is necessary to solve a multi-criteria problem, according to at least three criteria. Others can be added to these criteria directly related to safety and survivability, for example, minimum time to identify hazards, minimum time to create a security system, minimum costs for security, etc. One of the effective ways to solve multicriteria problems is to reduce them to single 0009-0004-5427-1196 (O. Bakaiev); 0009-0005-3248-3371 (I. Syvachenko); 0000-0002-9457-7454 (V. Shevchenko) © 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). criteria using scalar convolutions, among which additive audit of information infrastructure are presented in [23]. convolutions are the most common. 2. Analysis of existing studies Usually, the costs of information protection correlate with the costs of information technologies that need protection. guarantee capability of automated information systems of critical infrastructure objects are considered. Ensuring the cyber security of critical infrastructure facilities today in the conditions of war in Ukraine is one of the main tasks. In [14], a general analysis of the danger of cybernetic attacks on critical infrastructure is performed. Regulatory aspects of ensuring the information security of critical infrastructure objects are considered in [15]. Approaches to cyber protection of critical infrastructure based on integrated systems at the national level are studied in [16]. The issue of protecting critical infrastructure objects from cyber-attacks by decentralizing telecommunication networks is discussed in [17]. The advantage of works [13– 17] is the systematic study of the issue. The disadvantage is the concentration on the features of critical infrastructure objects only. The situation requires universal approaches that could ensure the survivability of information systems within the framework of Ukraine’s digital transformation.
General approaches to information security and cyber security management are considered in [18, 19]. More specific methodical approaches of NIST standards for assessing and ensuring cyber security in the creation of electronic government are considered in [20]. Targeted management is possible only if there are metrics and methods for evaluating the state of the process. Approaches to assessing the level of information security in distributed wireless systems are considered in [21]. Methods of assessing the level of security of communication systems against cyber-attacks are studied in [22]. Approaches to the
Approaches to assessing information security risks are studied in [24, 25]. Methodical approaches to the creation and implementation of complex cybersecurity programs are presented in [26]. Approaches to assessing information security risks and creating information security systems are presented in [27, 28]. Unfortunately, in works [18–28] we did not receive the appropriate development of the model based on additive convolutions, which reduced the possibilities of numerically taking into account all the necessary representative factors, in particular, and not only safety factors. 3. The purpose of the work
and optimality criteria The purpose of the work is the development of models and methods for optimizing information protection according to many criteria by reducing multi-criteria problems to singlecriteria ones using scalar additive convolutions.
On the way to the set goal, it is necessary to take into account the fact that on the scale of the organization, costs for information technology and costs for information protection exist within the framework of a single budget. The problem arises of its optimal distribution between functionality and protection on two levels: 1. 2.
At the stage of creation of defense systems and information systems in general by establishing the share of defense funding within the general budget. During operation, the computing resource of the information system is between tasks of basic functionality and tasks of information protection. This is done by choosing the mode of operation of the protection system (setting the degree of protection of the information system) by the security scenario of the information system [7].
At the strategic level, certain types of resources can be the governing parameters that determine the level of survivability, in particular, information system protection:
is a resource spent on creating an information system,
is a resource spent on creating an information protection system, is an information resource spent on the main functions of the system, is an information resource spent on information protection.
The main quality criteria, according to which information protection optimization should be performed, are as follows: =
is level of information security, = —the level of ensuring system functionality, = is the level of budget savings in the creation of information technologies, =
is the level of budget savings when using information technologies.
On the one hand, the given list of criteria can be expanded with
other criteria by the situation and clarification of the problem statement. On the other hand, the given criteria can be a collapse of more detailed additional criteria. For example, the information security level criterion may consist of the following subcriteria: =
is ensuring information security according to the integrity profile (Integrity), = is ensuring information security according to the availability profile (Availability), =
is ensuring information security according to the confidentiality profile (Confidentiality).
As you can see, a two-level hierarchy of quality criteria of the optimization process is formed. However, the number of levels of the hierarchy of criteria can be greater. For example, the integrity criterion may contain the following components: =
is the level of ensuring data integrity at the physical level (physical destruction of the information carrier), = is the level of ensuring data integrity at the program level (program erasure of information), =
is data integrity level at the addressing level (destruction of the FAT file location table).
The number of levels of the hierarchy of quality criteria is determined according to the statement of the problem.
As you can see, many of the criteria are contradictory. Most of the criteria cannot be nested in a complementary hierarchy, such as a situation where improving the integrity criterion can simultaneously improve the performance of the availability criterion. In most cases, the situation is different. For example, the minimum time criterion is contradictory to the minimum cost criterion. Because if you need to speed up the execution of the task, then you need to spend more resources on its implementation (more funding, more equipment, more personnel). 4. Transition to a single-criteria problem by the method of replacing criteria with restrictions It is precisely because of the inconsistency of the criteria that multi-criteria optimization problems have great difficulties in solving them. To solve the problem, multicriteria problems are converted to single-criteria problems. The main methods of transition to single-criteria problems are the following: replacing criteria with restrictions and convolution of criteria.
Replacing part of the criteria with restrictions. For example, the minimum time criterion =
→ can be replaced by a limitation—to spend no more than a certain time on execution
= constraint.
Task 2.1. = = ≤ .
→ ≤ . → , ≤ , ≥ . replace with restrictions—spend no more than a given amount of money on the project
Usually, all criteria except one, the most uncertain, the most variable, or the most important, are turned into constraints. After that, a solution to the single-criteria optimization problem is found, taking into account the constraints.
For example, the task of minimizing time, finances and simultaneously maximizing the effect → = ,
= → → can be transformed into one of the following problems with
Task 2.3.
≤ , = → , ≥ . ≤ , ≤ , = →
Unfortunately, it is not always clear which problem 2.1, 2.2, or 2.3 is the most adequate to the primary formulation of problem 1. Secondly, this transformation of the problem is not always adequate in principle. Such a transformation occurs relatively easily if the importance of one criterion is much higher than the importance of others. If all criteria have approximately the same importance or the importance changes over time, then such a transformation of the problem statement may not be sufficiently justified. 5. Transition to a single-criterion problem by the method of scalar convolution In such cases, another approach can be used—criteria convolution (or vector criterion scalarization). At the same time, it is worth remembering that for the criteria to be used together in a single calculation procedure, they must be normalized, that is, brought to a single scale of values. In this case, it will be possible to build a general dependency to determine the assessment of the level of information security of the information system as a whole = ( , ,
). = ( , ,
). =
.
A similar dependency can be used at the next level
An additive convolution can be used as a function [8–10]
(1)
(2)
(
.
Here is the index of constituent elements at the th level of the hierarchy, is the number of constituent elements at the th level of the hierarchy, is the criterion of the lower level of the hierarchy (component of the vector criterion), is the criterion of the upper level of the hierarchy (scalarized criterion).
Additive (or it is also called linear) convolution is the most widespread type of scalar convolution. It is called scalar because it allows us to move from multi-criteria optimization (when we have a multi-dimensional vector of criteria) to single-criteria when the optimization criterion is represented by a scalar value. Additive convolution collapses the set of criteria to one scalar criterion . Next, to simplify the study, we will consider the features of scalar convolutions on the example of a one-level convolution =
.
Here is the serial number of a separate criterion, is the total number of criteria, is the component of the collapsing vector criterion, is a scalar criterion resulting from the convolution.
It is worth noting that the
criteria have different
importance. Therefore, weight coefficients
are usually used,
which determine the importance of the relevant criteria
(7)
(8)
(9)
(
However, this requires a clear mathematical procedure, which is usually simply absent at the initial stages of research. Expert assessment in such a case is a quick decision, which, regardless of its inaccuracy in details, gives a good assessment in general. That is, with the help of expert evaluation, it is possible to determine the value of the weighting coefficients at a level that allows you to adequately find a scalar criterion based on several known constituent criteria. But that’s not all. 6. Normalization of scalar
convolution For various components of quality criteria to work together, they must be normalized. For example, so that they all have values in the same range of values. Most often, the range from 0 to 1 is used as such a range. Then, if the nonnormalized values of individual criteria were equal to , and the maximum possible value of the corresponding , then the normalized value of the criterion is equal to criterion will be equal to = 7. Modeling of assessment of the level of information security With the help of the given formalisms regarding the normalization of weighting factors and quality criteria, we will build a model of the level of information security, which includes components according to the profiles of integrity, availability, and confidentiality. Let’s introduce the notation for the weighting coefficients.
= = = information security according to the Integrity profile. —the weighting
factor —the weighting factor for for normalized weight coefficients ̅ will take the form of the weighting coefficients of the importance of protection , availability and in the weighting coefficients of the importance of protection of weighting coefficients of the importance of protection We will present the information security level model as follows
—weight factor and level of ensuring information security according to the integrity profile,
—weight factor and level of ensuring information security according to the availability profile, , —the weighting factor and the level of ensuring information security according to the confidentiality profile. At the same time, we take into account that all the specified values change over time and depending on the information risk scenario. That is, the refined model takes the form
If the values of the levels of ensuring information security according to the security profiles of integrity, availability, and confidentiality do not change over time and are equal to each other (Fig. 5) then the resulting level of ensuring information security ( ) also does not change over time (Fig. 6) without referring to the significant dynamics of changes in weighting factors (Fig. 1). (20) (21) (22) the profiles of integrity , availability and confidentiality , provided that the specified security levels are equal information security ensuring under the condition of equality of components according to the profiles of integrity , availability and confidentiality A completely different picture is observed if the values of the levels of ensuring information security according to the profiles of integrity , availability and confidentiality
change dynamically over time (Fig. 7). In this case, the resulting level of information security ensuring under the condition of the dynamic change over time of the components according to the profiles of integrity , availability and confidentiality The problem remains to provide the model with representative input data regarding the values of the criteria. Here you can rely on data from objective the case of weighting coefficients, on data from expert assessments.
The creation of an effective information protection system requires determining the correct balance between expenses for protection and the functioning of the system.
Decisions regarding the optimization of protection should be made both for the stage of creating an information system and for the stage of its operation.
Quality criteria for information security should form a certain structure, one of which options is a hierarchical structure.
The study is planned to maximize the level of information protection according to a set of different criteria: integrity, confidentiality, availability, minimum time to detect danger, minimum resources, and minimum time to create an information security system.
Solving a multi-criteria optimization problem is a big problem. To simplify the decision, it was decided to reduce the multi-criteria problem to a single-criteria one.
The scalarization of quality criteria using additive convolution is adopted as the main method of transition to a single-criteria problem.
To simplify the processing of criteria that have different physical nature, individual criteria were normalized and weighting factors were normalized.
The directions of further research are the construction of a complete structure of quality criteria for all security profiles, as well as the approbation of the proposed approach based on simplified data of a real system containing the personal data of users. [1] Y. Dreis, et al., Model to Formation Data Base of Secondary Parameters for Assessing Status of the State Secret Protection, in: Cyber Security and Data Protection, vol. 3800 (2024) 1–11. [2] O. Burov, et al.,
Networks, Advances in Intelligent Systems and Computing (2020) 359–364. doi: 10.1007/978-3-03039512-4_56. [3] V. Buriachok, V. Sokolov, Implementation of Active Learning in the Master’s Program on Cybersecurity, Advances in Computer Science for Engineering and Education II, vol. 938 (2020) 610-624. doi:10.1007/9783-030-16621-2_57. [4] V. Buriachok, et al., Implementation of Active Cybersecurity Education in Ukrainian Higher School, Information Technology for Education, Science, and Technics, vol. 178 (2023) 533–551. doi:10.1007/978-3031-35467-0_32. [5] V. Svanadze, Near Future of Cyber Security and New Trends in Cyberspace, Global Foundation for Cyber
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