The development of the modern world community is closely related to advances in computing resources and cyberspace. The formation and expansion of the range of services is based on the achievements of mankind in the field of high technologies. However, the rapid growth of computing resources, the emergence of a full-scale quantum computer tightens the requirements for security systems not only for information and communication systems, but also for cyber-physical systems and technologies. The methodological foundations of building security systems for critical infrastructure facilities based on modeling the processes of behavior of antagonistic agents in security systems are discussed in the first chapter. The concept of information security in social networks, based on mathematical models of data protection, taking into account the influence of specific parameters of the social network, the effects on the network are proposed in second chapter. The nonlinear relationships of the parameters of the defense system, attacks, social networks, as well as the influence of individual characteristics of users and the nature of the relationships between them, takes into account. In the third section, practical aspects of the methodology for constructing post-quantum algorithms for asymmetric McEliece and Niederreiter cryptosystems on algebraic codes (elliptic and modified elliptic codes), their mathematical models and practical algorithms are considered. Hybrid crypto-code constructions of McEliece and Niederreiter on defective codes are proposed. They can significantly reduce the energy costs for implementation, while ensuring the required level of cryptographic strength of the system as a whole. The concept of security of corporate information and educational systems based on the construction of an adaptive information security system is proposed.

Due to the widespread use of sensors and sensor networks in the tasks of territory coverage, the relevant criteria are maximizing coverage and minimizing energy consumption. At the same time, the compliance of the network with these criteria is an urgent problem in the modern technological world. A modification of the method for constructing energy-efficient sensor networks is proposed by introducing an additional criterion for minimizing the number of sensors and limiting the number of sensors used, which allows reducing the energy consumption of sensor networks by 19 %. In the resulting optimization problem, the optimality criteria are the functions of minimizing the area of uncovered territory, the value of energy consumption, and the number of sensors. The optimum solution is formed by pairs of values of the coverage radius and the level of intersection of the coverage areas, which provide maximum coverage while minimizing energy consumption and the number of sensors used. To solve the problem, the parameter convolution method and the genetic algorithm were used. In the case of dynamic sensors, the problem is to find such a trajectory of the sensor that provides the maximum flyby of the territory with a minimum length. A grid algorithm is proposed to find the necessary trajectory. The presented algorithm consists in dividing the territory into nodes and estimating the value of the covered territory by the sensor in this node. After the formation of estimates, the search for a Hamiltonian path was used. The case of a multiply connected territory with the possibility of turning it into a simply connected one is considered. A scheme for finding the parameters of energy-efficient coverage of the territory using static and dynamic sensors is proposed.

The rapid growth of geographic information technologies in the field of processing and analysis of spatial data has led to a significant increase in the role of geographic information systems in various fields of human activity. However, solving complex problems requires the use of large amounts of spatial data, efficient storage of data on on-board recording media and their transmission via communication channels. This leads to the need to create new effective methods of compression and data transmission of remote sensing of the Earth. The possibility of using fractal functions for image processing, which were transmitted via the satellite radio channel of a spacecraft, is considered. The information obtained by such a system is presented in the form of aerospace images that need to be processed and analyzed in order to obtain information about the objects that are displayed. An algorithm for constructing image encoding–decoding using a class of continuous functions that depend on a finite set of parameters and have fractal properties is investigated. The mathematical model used in fractal image compression is called a system of iterative functions. The encoding process is time consuming because it performs a large number of transformations and mathematical calculations. However, due to this, a high degree of image compression is achieved. This class of functions has an interesting property—knowing the initial sets of numbers, we can easily calculate the value of the function, but when the values of the function are known, it is very difficult to return the initial set of values, because there are a huge number of such combinations. Therefore, in order to de-encode the image, it is necessary to know fractal codes that will help to restore the raster image.

The article analyzes the parameters of social networks. The analysis is performed to identify critical threats. Threats may lead to leakage or damage to personal data. The complexity of this issue lies in the ever-increasing volume of data. Analysts note that the main causes of incidents in Internet resources are related to the action of the human factor, the mass hacking of IoT devices and cloud services. This problem is especially exacerbated by the strengthening of the digital humanistic nature of education, the growing role of social networks in human life in general. Therefore, the issue of personal information protection is constantly growing. To address this issue, let’s propose a method of assessing the dependence of personal data protection on the amount of information in the system and trust in social networks. The method is based on a mathematical model to determine the protection of personal data from trust in social networks. Based on the results of the proposed model, modeling was performed for different types of changes in confidence parameters and the amount of information in the system. As a result of mathematical modeling in the MatLab environment, graphical materials were obtained, which showed that the protection of personal data increases with increasing factors of trust in information. The dependence of personal data protection on trust is proportional to other data protection parameters. The protection of personal data is growing from growing factors of trust in information. Mathematical modeling of the proposed models of dependence of personal data protection on trust confirmed the reliability of the developed model and proved that the protection of personal data is proportional to reliability and trust

The development of technologies and computing resources has not only expanded the range of digital services in all spheres of human activity, but also determined the range of targeted cyber attacks. Targeted attacks are aimed at destroying not only the business structure, but also its individual components that determine critical business processes. The continuity of such business processes is a critical component of any company, organization or enterprise of any form of ownership, which has a critical impact on making a profit or organizing production processes. The proposed concept of determining the security level of critical business processes is based on the need to use multiloop information security systems. This makes it possible to ensure the continuity of critical business processes through a timely objective assessment of the level of security and the timely formation of preventive measures. This approach is based on the proposed rules for determining the reach of a given security level, based on assessments of the integrity, availability and confidentiality of information arrays, as well as computer equipment for different points of the organization's business processes. The issues of applying situational management methods to ensure the safe functioning of objects of socio-cyberphysical systems, logical and transformational rules that form the foundation for building a situational type cybersecurity management system are considered. One of the main tasks of systems of this type is described – the task of replenishing the description of the situation. The use of pseudophysical logics, various types of pseudophysical logics, the method of their construction and their interconnection are proposed. Particular attention is paid to causal pseudophysical logic, as the least developed for the purposes of ensuring cybersecurity. The formation of smart technologies, as a rule, uses the wireless standards of communication channels IEEE 802.11X, IEEE 802.15.4, IEEE 802.16, which use only authentication protocols and privacy mechanisms that are formed on the basis of symmetric algorithms. In the conditions of the post-quantum period (the appearance of a full-scale quantum computer), the stability of such algorithms is questioned. Such systems, as a rule, are formed on the basis of the synthesis of socio-cyber-physical systems and cloud technologies, which simplifies the implementation of Advanced Persistent Threat attacks, both on the internal loop of control systems and on the external one. The proposed creation of multi-circuit information protection systems allows for an objective assessment of the flow state of the system as a whole and the formation of preventive measures against cyber threats. In the thied chapter, models of probable threats and information protection in public networks are proposed. The most general model of the formal description of the protection system is the model of the security system with full overlap, in which a complete list of protection objects and threats to information is determined, and means of ensuring security are determined from the point of view of their effectiveness and contribution to ensuring the security of the entire telecommunications system. It is also shown that the combination of four models (M1, M2, M3, M4) in various variants provides wide opportunities for modeling various known types of threats and their implementation. However, in connection with the continuity of the process of developing new and improving existing methods and means of implementing threats, it is necessary to use such approaches to ensuring information protection that allow detecting and preventing threats of unknown types and carrying out dynamic correction of protection behavior, adapting it to specific application conditions. The M5 basic model is described, which enables continuous refinement of threat classes and response measures, and continuous training of the adaptive component of the CSI, which, in turn, detects and prevents threats of unknown types. The M6 basic model is introduced with the aim of obtaining higher security due to the presence of a special module of internal diagnostics that diagnoses the entire protection system, decides on the correction of the SHI behavior algorithm, and makes it possible to achieve SHI fault tolerance; a special module that diagnoses the communication channel with subsequent changes in the level of protection, allows to achieve the adaptability of the SHI. The fourth chapter is deal with the development of cryptographic primitives based on cellular automata. The definition of a cellular automaton is given and the elementary rules of intercellular interaction are described. A number of generators of pseudorandom binary sequences have been developed based on a combination of elementary rules of intercellular interaction, as well as cell interaction according to a rule of our own development. In the “cryptographic sponge” architecture, a cryptographic hashing function with a shuffling function based on cellular automata was developed and its statistical characteristics and avalanche effect were investigated. A block cipher in the SP-network architecture is constructed, in which cellular automata are used to deploy the key, and the encryption process is based on elementary procedures of replacement and permutation. Substitution blocks are used from the well-known AES cipher, a description of a stream cipher is given, where a personal computer keyboard and mouse are used as the initial entropy. Random data received from the specified devices is processed by a proprietary hashing function based on a "cryptographic sponge". All developed cryptographic functions and primitives demonstrated good statistical characteristics and avalanche properties. The fifth chapter proposes a methodology for analyzing the quality of the mechanism for validating the identified vulnerabilities of a corporate network,...

One of the leading areas of cybersecurity of communication networks is considered – the introduction of preventive mechanisms, among which the most promising are the methods of active security analysis. These methods allow, in addition to timely detection of vulnerabilities of the target system (analyzed system), to confirm the possibility of their implementation, that is, to validate vulnerabilities by simulating the real actions of a potential attacker. The urgent need to validate vulnerabilities out of the many identified is caused by the fact that some of them can only be theoretical, while others are exploited using malicious scripts (exploits). At the same time, the process of validating vulnerabilities is practically not studied. That is why the work carried out an experimental study of the functioning of modern tools for exploiting vulnerabilities. Based on the observations, general quantitative characteristics of the vulnerability validation process were identified. A mathematical model for the analysis of the above characteristics based on Bernstein polynomials has been developed. It is the polynomial representation of the procedure for confirming the possibility of implementing the identified vulnerabilities that makes it possible to describe the dynamics of this process, taking into account the complex and volatile nature of the environment. Analytical dependencies are obtained for the number of cases of successful and negative confirmation of vulnerabilities. In particular, negative validation cases include simply failed attempts to validate vulnerabilities, as well as attempts that resulted in critical errors on the target system during the rational cycle of validating the identified vulnerabilities. The proposed dependencies make it possible to construct the probability distribution laws for the above characteristics of the vulnerability testing process. Рассмотрено одно из ведущих направлений кибербезопасности коммуникационных сетей – внедрение превентивных механизмов, среди которых наиболее перспективны являются методы активного анализа безопасности. Эти методы позволяют кроме своевременного выявления уязвимостей целевой системы (анализируемой системы), подтверждать возможность их реализации, то есть валидировать уязвимости путем имитирования реальных действий потенциального злоумышленника. Острая необходимость в валидации уязвимостей из множества выявленных вызвана тем фактом, что некоторые из них могут быть только теоретическими, другие эксплуатируются с использованием вредоносных скриптов (эксплойтов). В то же время, процесс валидации уязвимостей практически не исследован. Именно поэтому в работе проведено экспериментальное исследование функционирования современного инструментария эксплуатации уязвимостей. На основе наблюдений были выделены общие количественные характеристики процесса валидации уязвимостей. Разработана математическая модель анализа вышеупомянутых характеристик на основе полиномов Бернштейна. Именно полиномиальное представление процедуры подтверждения возможности реализации выявленных уязвимостей позволяет описать динамику данного процесса, учитывая сложную и изменчивую природу среды. Получены аналитические зависимости для количества случаев успешного и отрицательного подтверждения уязвимостей. В частности, к отрицательным случаям подтверждения относятся просто неудачные попытки валидации уязвимостей, а также попытки, повлекшие критические ошибки на целевой системе во время рационального цикла валидации выявленных уязвимостей. Предлагаемые зависимости позволяют построить законы распределения вероятностей указанных выше характеристик процесса проверки уязвимостей Розглянуто один із провідних напрямків кібербезпеки комунікаційних мереж – впровадження превентивних механізмів, серед яких найбільш перспективними є методи активного аналізу безпеки. Ці методи дозволяють окрім своєчасного виявлення вразливостей цільової системи (системи, що аналізується), підтверджувати можливість їх реалізації, тобто валідувати вразливості шляхом імітування реальних дій потенційного...