Browsing by Author "Olevskyi, V. I."

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Application of Two-Dimensional Padé-Type Approximations for Image Processing
(National University «Zaporizhzhia Polytechnic», Zaporizhzhia, 2023) Olevskyi, V. I.; Hnatushenko, Volodymyr V.; Korotenko, G. M.; Olevska, Yu. B.; Obydennyi, Ye. O.
ENG: Context. The Gibbs phenomenon introduces significant distortions for most popular 2D graphics standards because they use a finite sum of harmonics when image processing by expansion of the signal into a two-dimensional Fourier series is used in order to reduce the size of the graphical file. Thus, the reduction of this phenomenon is a very important problem. Objective. The aim of the current work is the application of two-dimensional Padé-type approximations with the aim of elimination of the Gibbs phenomenon in image processing and reduction of the size of the resulting image file. Method. We use the two-dimensional Padé-type approximants method which we have developed earlier to reduce the Gibbs phenomenon for the harmonic two-dimensional Fourier series. A definition of a Padé-type functional is proposed. For this purpose, we use the generalized two-dimensional Padé approximation proposed by Chisholm when the range of the frequency values on the integer grid is selected according to the Vavilov method. The proposed scheme makes it possible to determine a set of series coefficients necessary and sufficient for construction of a Padé-type approximation with a given structure of the numerator and denominator. We consider some examples of Padé approximants application to simple discontinuous template functions for both formulaic and discrete representation. Results. The study gives us an opportunity to make some conclusions about practical usage of the Padé-type approximation and about its advantages. They demonstrate effective elimination of distortions inherent to Gibbs phenomena for the Padé-type approximant. It is well seen that Padé-type approximant is significantly more visually appropriate than Fourier one. Application of the Padé-type approximation also leads to sufficient decrease of approximants’ parameter number without the loss of precision. Conclusions. The applicability of the technique and the possibility of its application to improve the accuracy of calculations are demonstrated. The study gives us an opportunity to make conclusions about the advantages of the Padé-type approximation practical usage.
Raster image processing using 2D Padé-type approximations
(IOP Publishing, 2023) Olevskyi, V. I.; Olevska, Yu. B.; Olevskyi, O. V.; Hnatushenko, Volodymyr V.
ENG: We have developed a method called the two-dimensional Padé-type approximants method, which can be used to reduce the Gibbs phenomenon in the harmonic two-dimensional Fourier series. This method can be applied to both monochrome and color raster images. To do this, we implement the generalized two-dimensional Padé approximation proposed by Chisholm. In this approach, we select the range of frequency values on the integer grid according to the Vavilov method. We propose a definition of a Padé-type functional and provide examples of its application to simple discontinuous templates represented as raster images. Through this study, we are able to draw conclusions about the practical usage and advantages of the Padé-type approximation. We demonstrate that the Padé-type approximant effectively eliminates distortions associated with the Gibbs phenomenon, and it is visually more appropriate than the Fourier approximant. Additionally, the application of the Padé-type approximation reduces the number of parameters without sacrificing precision.
Simulation-Driven Assessment of Cryptographic Algorithms for Resource-Constrained Infocommunication Networks
(Dnipro University of Technology, Dnipro, 2025) Laktionov, I. S.; Hnatushenko, Volodymyr V.; Udovyk, Iryna M.; Olevskyi, V. I.
ENG: Purpose. To conduct a multi-criteria evaluation and analysis of the performance of encryption algorithms that may be potentially resistant to contemporary cyberattacks, including quantum attacks. The evaluation takes into account the ability of the algorithms to be deployed on devices with limited computational resources within the infocommunication networks during the transmission of information messages. Methodology. Software implementation, testing and validation of selected cryptographic algorithms based on Python, considering the impact of limited resources and destabilising factors, such as signal noise components, based on computer experiments were applied. The performance of the studied cryptographic algorithms was analysed using statistical data processing methods and a multi-criteria evaluation approach. Findings. The symmetric algorithms AES-256-GCM and ChaCha20-Poly1305 demonstrated the highest accuracy in signal recovery following encryption and decryption (MSE ranges from 1.95 · 10-6 to 5.12 · 10-5). The time taken to encrypt and decrypt I/Q signals using symmetric algorithms was found to be around 2.5 times faster than that required by the Kyber family. Computer experiments confirmed the existence of a trade-off between processing speed and security level. Symmetric algorithms are optimal for scenarios with critical processing speed requirements. However, Kyber provides greater protection reliability, albeit at the cost of additional resources. The correctness of the proposed computer model, which enables the computational and information-functional characteristics of cryptographic algorithms to be evaluated, has been proven. Originality. Patterns of the destabilising influence of signal-to-noise ratio indicators and signal length on the accuracy of digital signal recovery after encryption have been established for different cryptographic algorithms (AES, ChaCha20 and the Kyber) in the context of their use in resource-constrained infocommunication systems. Practical value. Implementing the computer model proved its suitability for studying cryptographic algorithms in resource-constrained environments, as well as its potential for improving information security protocols and selecting optimal algorithms based on processing speed requirements and desired security levels.