Where octagonal geometry meets chaos: A new S-Box for advanced cryptographic systems

Substitution Box (S-Box) has had been a cardinal component of various cryptographic systems. In this paper, we introduce a novel S-Box design that merges octagonal geometry with chaotic dynamics to enhance the security effects of the cryptographic systems. In particular, the proposed method leverages the geometric properties of octagons and the unpredictability of chaotic maps to construct a novel S-Box with improved security features. The mathematical construct octagon carries out the necessary operation of confusion in the proposed S-Box. The centres of these octagons are hypothetically created within the confines of the 16 × 16 matrix of numbers. Further, these octagons have different radii, locations, and the amounts with which the numbers lying on their boundaries have to be circularly shifted clockwise or anti-clockwise to create the confusion effects. In case, a portion of octagon goes past the edges of the matrix, the numbers lying on its boundary have been wrapped out. This process has been repeated numerous times to come up with a reliable and a secured S-Box. The comprehensive security analyses validate that the proposed S-Box is furnished with nice security effects and has the requisite resilience to defy the varied cryptanalytic threats. The results of non-linearity and differential probability are 105.625 and 0.0391 respectively which signals towards the inherent robustness of the suggested S-Box.