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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

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.

Given recent events, training during quarantine can only take place remotely. To ensure quality training, communication must be seamless. To do this, the network must function smoothly. The solution to this problem is functionally stable networks that allow uninterrupted transmission of information due to redundancy. An important issue is the definition of redundancy. To solve this problem, the article considers the method of synthesis of the structure of the distance learning system. The method of synthesis of network structure used for providing distance learning by the criterion of maximum functional stability on the basis of the introduction of correcting communication lines is offered. With this method, you can develop tools for self-recovery of distributed software, taking into account the characteristics of disparate computer resources through the use of redundancy. This will allow you to develop functionally stable software systems, significantly reduce the recovery time of such systems after or in the event of possible failures. To increase the efficiency of the developed method, the mathematical model of the hyper network based on two hypergraphs was improved, which allows taking into account different requirements for the quality of the network.

The article investigates the method of calculating the basic parameters of random signals emitted by hidden transmitters. The method is based on a mathematical model of differential signal transformations within the framework of correlation theory. It is proved that under certain initial conditions the expected value of a random signal consists of the sum of all expectations of the differential spectrum. A method for numeric calculating of the variance, which consists of determining the differential spectrum and calculating the variance for each discrete component of the signal, is presented. The approach to determining the correlation function of a random signal is justified. It is shown that on the basis of two differential spectra it consists of the sum of all discrete components of the differential spectrum defined for the correlation function. As a partial case, the conditions for the coincidence of the correlation function with the variance are given. A model of hidden transmitter was built. In order to obtain its characteristics, a simulation of a random signal was made in the MathLab software environment, which modulates digital signal of hidden transmitter. The numerical parameters of the random signal are obtained: expectation and variance. Three-dimensional graphs of the results of random signal modeling have been constructed, which allows to visualize the implementation of the random signal. Graphical results of the signal itself and its expectation and variance were also obtained. Analysis of the statistical characteristics showed that the expectation completely repeats the graphical appearance of the signal. The variance graph repeats the signal at zero but with increasing time. These results confirm the adequacy of the mathematical model of the hidden transmitters based on the theory of differential transformations.

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