S-Box Generation Algorithm by Constructing the Non-Singular Adjacency Matrix Using the Genetic Algorithm

In today's applications of block ciphers, the substitution box (S-box) serves as a critical nonlinear component that is essential for generating complex ciphertext. S-boxes that exhibit lower differential uniformity and increased nonlinearity are more adept at resisting cryptanalytic efforts. The paper proposes that the construction of an 8x8 S-box can be accomplished by selecting non-singular adjacency matrices derived from graph parameters generated by a genetic algorithm. This selection is followed by an affine transformation. This method uses any graph with 8 vertices and its edge count, resulting in a non-singular adjacency matrix. The S-box is then generated by an affine mapping technique using the non-singular adjacency matrix, similar to the approach of the Rijndael algorithm. The effectiveness and reliability of the resulting S-box was rigorously tested against various cryptographic standards. The robustness evaluation included factors such as non-linearity, differential approximation probability, linear approximation probability and strict avalanche criteria. A thorough investigation confirmed that the newly created S-box met the required algebraic properties. Furthermore, a comparative analysis was performed to evaluate the performance of this novel S-box against the most recent counterparts in the literature. In terms of defense against potential malicious exploits, the results indicate a significant advantage. Overall, the results of this study underscore the significant promise and advantages of the proposed S-box-centric cryptographic strategy, positioning it as an attractive alternative to conventional encryption techniques.

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