Atıcı Turan, Gülcan

This study introduces a flexible framework for analyzing how sequences of numbers approach a limit, even when traditional convergence criteria fail. By incorporating modulus function mathematical tools that quantify growth rates, this research extends the concept of statistical convergence to handle sequences with irregular or sparse behavior. Key results establish connections between this generalized convergence theory and related properties, like boundedness, providing a unified approach to understanding sequence dynamics. The findings enhance our ability to model and analyze complex data patterns in mathematics and beyond.

AtıfScopus1·WoS2·OpenAlex3

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Artuğer, Firat; Özkaynak, Fatih

Symmetry plays an important role in nonlinear system theory. In particular, it offers several methods by which to understand and model the chaotic behavior of mathematical, physical and biological systems. This study examines chaotic behavior in the field of information security. A novel method is proposed to improve the performance of chaos-based substitution box structures. Substitution box structures have a special role in block cipher algorithms, since they are the only nonlinear components in substitution permutation network architectures. However, the substitution box structures used in modern block encryption algorithms contain various vulnerabilities to side-channel attacks. Recent studies have shown that chaos-based designs can offer a variety of opportunities to prevent side-channel attacks. However, the problem of chaos-based designs is that substitution box performance criteria are worse than designs based on mathematical transformation. In this study, a postprocessing algorithm is proposed to improve the performance of chaos-based designs. The analysis results show that the proposed method can improve the performance criteria. The importance of these results is that chaos-based designs may offer opportunities for other practical applications in addition to the prevention of side-channel attacks.

AtıfScopus55·WoS44·OpenAlex56

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