Generating highly nonlinear S-boxes using a hybrid approach with particle swarm optimization

Abstract

A substitution box (S-box) is a fundamental component in cryptographic algorithms that enhance data security by providing a complex mapping between input and output values. S-box strengthens the encryption and decryption process by introducing nonlinearity and protecting the encrypted data against various differential and linear cryptanalytic attacks. The problem of generating an S-box with optimal properties is challenging and falls under the category of NP-Hard problems. This study proposes a hybrid approach combining the Particle Swarm optimization algorithm (PSO) and the Booster algorithm to construct a highly nonlinear S-box with low computational efforts. The PSO algorithm, assisted by the Transfer function and Random Key (RK), is utilized to navigate the large permutation search space to find an S-box with acceptable cryptographic properties. The Booster algorithm works based on random applications of local operators for shuffling the elements of the S-box with each other and transforming the elements' arrangement, resulting in a modified S-box with increased nonlinearity.