Suggested S-Box DP table.

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 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.

代换盒（Substitution Box，S-Box）向来是各类密码系统的核心组成部分。本文提出一种全新的S-Box设计方案，将八边形几何与混沌动力学相融合，以提升密码系统的安全性能。具体而言，所提方法借助八边形的几何特性与混沌映射的不可预测性，构建出一款安全特性更优的新型S-Box。本设计中的混淆操作由八边形这一数学构造完成，这些八边形的中心假设生成于数值矩阵的边界范围内，且各八边形拥有不同的半径、位置，以及其边界上的数值需要执行顺时针或逆时针循环移位的幅度，以此实现混淆效果。若八边形的部分区域超出矩阵边界，则其边界上的数值将被循环包裹处理。上述过程经多次迭代后，可得到可靠且安全的S-Box。全面的安全分析验证表明，所提S-Box具备优异的安全性能，能够有效抵御各类密码分析威胁。其非线性度与差分概率分别为105.625与0.0391，这一结果彰显了该代换盒所具备的固有鲁棒性。