Hybrid Cuckoo Search–Bees Algorithm with Memristive Chaotic Initialization for Cryptographically Strong S-Box Generation

One of the essential parts of contemporary cryptographic systems is s-boxes (Substitution Boxes), which give encryption algorithms more complexity and resilience due to their nonlinear structure. In this study, we propose CSBA (Cuckoo Search-Bees Algorithm), a hybrid evolutionary method that combines the strengths of Cuckoo Search and Bees algorithms, to generate s-box structures with strong cryptographic properties. The initial population is generated with a high-diversity four-dimensional Memristive Lu chaotic map, taking advantage of the random yet deterministic nature of chaotic systems. This proposed method was designed with inspiration from biological systems. It was developed based on the foraging strategies of bees and the reproductive strategies of cuckoos. This nature-inspired structure enables an efficient scanning of the solution space. The resultant s-boxes' fitness was assessed using the nonlinearity value. These s-boxes were then optimized using the hybrid CSBA algorithm suggested in this paper as well as the Bees algorithm. The performance of the proposed approaches was measured using SAC, nonlinearity, BIC-SAC, BIC-NL, maximum difference distribution, and linear uniformity (LU) metrics. Compared to other studies in the literature that used metaheuristic algorithms to generate s-boxes, the proposed approach demonstrates good performance. In particular, the average value of 109.75 obtained for the nonlinearity metric demonstrates high success. Therefore, this study demonstrates that robust and reliable s-boxes can be generated for symmetric encryption algorithms using the developed metaheuristic algorithms.