Development of High-Quality Cryptographic Constructions Based on Many-Valued Logic Affine Transformations

• DOI: 10.3390/electronics14102094
• Publication Date: 2025-05-21T17:59:43Z
• Authors: Mikolaj Karpinski; Artem Sokolov; Aizhan Tokkuliyeva; Volodymyr Radush; Nadiia Kazakova; Aigul Shaikhanova; Nataliya Zagorodna; Anna Korchenko

The S-box is a key component of modern ciphers, determining the quality and performance cryptographic algorithms in which it applied. Many constructions for synthesizing high-quality S-boxes have been established, those based on Galois fields theory—for example, Nyberg construction applied AES algorithm—are particularly important. An integral affine transformation, used to improve avalanche correlation properties S-box. In this paper, new approach adopted transformations quaternary matrices over field GF(4). We describe four basic structures that serve as foundation complete class 648 transformation order n = 3 7776 4 introduce recurrent structure facilitate synthesis higher orders. Using these combination with construction, possible construct bijective outperform original many other known terms strict criterion (SAC) bit independence (BIC SAC) values, while maintaining maximal level nonlinearity good properties. also propose modified GF(4) can be specialized already satisfy SAC both Boolean 4-functions, well minimal between input output, allowing us enhance their value Nf 96. integrate synthesized into algorithm evaluate practical performance. encryption outputs successfully pass NIST statistical test suite 96 out 100 cases, outperforming reference constructions, confirming strength proposed method.