Development of A Method for Checking Vulnerabilities of A Corporate Network Using Bernstein Transformations

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

Applying an Adaptive Method of the Orthogonal Laguerre Filtration of Noise Interference to Increase the Signal/noise Ratio

A relevant task for control systems is to reduce the impact of noise interference in order to increase the signal/noise ratio (SNR). This issue is relevant to other technical systems as well. This work addresses the orthogonal Laguerre filtration of noise processes, which are described by the linear random processes. The proposed method of filtration makes it possible to reduce the influence of noise interference, which is described by the stationary linear random processes, in the operation of correlation systems. The essence of this method implies the use of orthogonal Laguerre filters as the input links of the correlation system.The sequence of the noise processes, which are uncorrelated over a significant time interval of their mutual shift, has been derived on the basis of orthogonal Laguerre filtration of the stationary white noise. Such processes are described by the stationary linear random processes and are the models of a wide range of noise interference, which are explored in the operation of various technical systems, including control, detection, recognition, measurement systems, etc. The application of this method decreases the effect of noise interference with different correlation-spectral characteristics and increases the SNR at the output from the correlation system. Practical tasks on reducing the action of stationary noise interference have been solved within the framework of the proposed adaptive method of orthogonal Laguerre filtration; to this end, the article shows a structural-logical scheme of the correlation system. Using the software, the algorithm of the adaptive filtration based on the complex Laguerre filters has been implemented. The implementation has been carried out for an actual noise interference that belongs to the RLC class of noise, employing the pre-training of the filter. The effectiveness of reducing the impact of the predefined stationary noise interference has been confirmed by the derived efficiency coefficients the size of –6 dB and –16 dB for the set of the interference zeroing point