A novel post-processing approach for improving minimum nonlinearity in S-boxes: A case study based on 2D hyper chaotic Schaffer transformation map

Abstract

Substitution boxes (s-boxes), providing nonlinearity in block cipher algorithms, constitute a fundamental security layer against linear and differential cryptanalysis attacks. In this study, an innovative s-box generation method is proposed by integrating a 2D hyper-chaotic Schaffer map (SM) with biomolecular DNA-based encoding techniques. Furthermore, to enhance the security of s-box structures, a novel post-processing algorithm is developed, aiming to simultaneously optimize both the average (NLavg) and minimum (NLmin ) nonlinearity levels by targeting linear components. Unlike traditional meta-heuristic methods, the proposed algorithm avoids random exploration across large search spaces, instead identifying dominant linear components through Walsh spectrum analysis and applying targeted permutation operations to suppress their effects. This strategy not only increases the NLavg value but also balances the contribution of each Boolean function to security, thereby establishing a homogeneous and consistent security structure across all input-output combinations. Comparative experimental analyses with existing methods demonstrate that the proposed approach outperforms prior techniques in terms of both cryptographic security metrics and computational efficiency. In this respect, the study presents an advanced s-box design framework, characterized by high nonlinearity and a balanced spectral distribution, suitable for integration into modern block cipher systems.