Constructing keyed strong S-Box with optimized nonlinearity using nondegenerate 2D hyper chaotic map

Abstract In the realm of information security, the nonlinearity of an S-Box is a pivotal attribute for ensuring its effectiveness. S-Boxes randomly generated with chaotic maps, however, often exhibit insufficient nonlinearity. To construct a robust S-Box with enhanced nonlinearity, we have developed a nondegenerate two-dimensional hyper chaotic map (2D-NDHCM). We rigorously evaluated its dynamic properties through bifurcation and phase diagrams, Lyapunov exponents, Kolmogorov entropy, correlation dimension, and randomness tests to assess the map’s resilience. Subsequently, we employed the 2D-NDHCM to devise a novel algorithm for constructing and optimizing a keyed strong S-Box, leveraging simulated annealing technique to achieve superior nonlinearity. Finally, We conducted performance analyses of the optimized S-Box using the classic six criteria, and the results confirmed the algorithm’s practicality and effectiveness.