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Документ Analysis and comparative research of the main approaches to the mathematical formalization of the penetration testing process(ФОП Петров В. В., 2021) Liqiang, Zhang; Weiling, Cao; Davydov, Viacheslav; Brechko, VeronikaIn dynamic models, threats (vulnerabilities) can be viewed as a flow of temporary events. If the intervals of real-ized cyber threats are recorded, then a continuous log-list of events related to software security can be formed. In some cases and models, only the number of realized cyber threats for an arbitrary time interval can be recorded. In this case, the software response to threats can be represented only at discrete points. In static models, the implementation of cyber threats is not related to time, but the dependence of the number of errors or the number of implemented test cases (models by error area) on the characteristics of the input data (models by data area) is taken into account. The article analyzes the methods of mathematical formalization of the software penetration testing process. This software testing method is one of many approaches to testing the security of computer systems. The article substantiates the importance of the processes of preliminary prototyping and mathematical formalization. The classification is carried out and the advantages and disadvantages of the main approaches of mathematical modeling are highlighted. The list and main characteristics of dynamic and static models are presented. One of the negative factors of formalization is indicated - the neglect of the factors of a priori uncertainty in the safety parameters in static models.Документ Automated penetration testing method using deep machine learning technology(Національний технічний університет "Харківський політехнічний інститут", 2021) Semenov, S. S.; Weilin, Cao; Liqiang, Zhang; Bulba, S. S.The article developed a method for automated penetration testing using deep machine learning technology. The main purpose of the development is to improve the security of computer systems. To achieve this goal, the analysis of existing penetration testing methods was carried out and their main disadvantages were identified. They are mainly related to the subjectivity of assessments in the case of manual testing. In cases of automated testing, most authors confirm the fact that there is no unified effective solution for the procedures used. This contradiction is resolved using intelligent methods of analysis. It is proposed that the developed method be based on deep reinforcement learning technology. To achieve the main goal, a study was carried out of the Shadov system's ability to collect factual data for designing attack trees, as well as the Mulval platform for generating attack trees. A method for forming a matrix of cyber intrusions using the Mulval tool has been developed. The Deep Q - Lerning Network method has been improved for analyzing the cyber intrusion matrix and finding the optimal attack trajectory. In the study, according to the deep reinforcement learning method, the reward scores assigned to each node, according to the CVSS rating, were used. This made it possible to shrink the attack trees and identify an attack with a greater likelihood of occurring. A comparative study of the automated penetration testing method was carried out. The practical possibility of using the developed method to improve the security of a computer system has been revealed.