Substitution Box Construction Using Transfer‐Function Assisted Metaheuristic and Booster Algorithm: A Hybrid Approach

Abstract

S‐box strengthens the encryption and decryption process by introducing nonlinearity and protecting the encrypted data against various differential and linear cryptanalytic attacks. Generating a highly nonlinear S‐box with maximal nonlinearity is computationally impractical due to the expansive search space, classifying it as an NP‐hard problem. This paper proposes the Hawkboost algorithm, a novel hybrid method merging the Harris Hawks optimization algorithm (HHO) and the Booster algorithm for generating highly nonlinear S‐boxes with low computational efforts. The HHO algorithm is utilized to navigate in the large permutation search space to find an S‐box with acceptable cryptographic properties. The HHO algorithm is assisted by the Transfer function and Random Key (RK) method to speed up the S‐box design process. Additionally, the Booster algorithm enhances S‐box nonlinearity by applying random local operators like swap and inversion, effectively reshaping elements of S‐box. This novel combination of methodologies facilitates the efficient generation of S‐boxes that exhibit excellent cryptographic properties while addressing key challenges in S‐box optimization. The performance of the proposed S‐box has been analyzed by comparing various state‐of‐the‐art S‐boxes based on numerous characteristics including average nonlinearity, strict Avalanche criterion (SAC), SAC offset, bit independence criterion (BIC), linear approximation probability (LP), differential approximation probability (DP), fixed points, opposite fixed points, and cycle counts. The results from experiments and analysis based on multiple metrics show that the proposed Hawkboost algorithm satisfies all requirements for safe and reliable S‐boxes without sacrificing any crucial security features.