Algorithm for Generating Robust S-Boxes Using Adjacency Matrix Parameters

In modern block cipher schemes, the substitution block (S-box) acts as a key nonlinear element that plays an important role in generating entangled entanglement in the creation of the ciphertext. S-boxes with reduced differential uniformity and higher non-linearity are better suited to thwart cryptanalysis attempts. This paper proposes an innovative approach that involves constructing 8 × 8 S-boxes by generating adjacency matrices based on selected graph parameters. After that, the affine transformation is applied. Notably, this process uses any 8-vertex graph and its unique number of edges, resulting in an adjacency matrix. S-boxes are then generated using an affine mapping method using an adjacency matrix structure similar to Rijndael's algorithm. The efficiency and reliability of the resulting S-boxes are carefully evaluated against various cryptographic metrics. The robustness test includes parameters such as non-linearity (NL), strict avalanche criteria (SAC), differential approximation probability (DAP) and linear approximation probability (LAP). This comprehensive evaluation confirms that all structured S-boxes satisfy the vital algebraic properties. In addition, a comparative analysis is carried out comparing the properties of the new S-boxes with the latest analogues found in the existing literature. The results show a significant advantage in terms of resilience to potential exploits by malicious actors. In the end, the outcomes of this research emphasize the significant potential and benefits of the suggested S-box-focused encryption approach, positioning it as a compelling substitute for conventional encryption methods.

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