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- MakaleAçık Erişim2025Scopus SJRQ1A novel post-processing approach for improving minimum nonlinearity in S-boxes: A case study based on 2D hyper chaotic Schaffer transformation map
Aydın, Yılmaz; Garipcan, Ali Murat; Özkaynak, Fatih
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.
AtıfScopus12WoS13OpenAlex13
İncele - MakaleYayıncıda açık erişim2024Scopus SJRQ2A new post-processing approach for improvement of nonlinearity property in substitution boxes
Artuğer, Fırat; Özkaynak, Fatih
The main reason that makes chaos theory attractive for cryptology studies is the unpredictable nature of chaotic systems. However, the fact that the statistical and cryptographical properties of cryptographic primitives based on the values obtained as a result of the electronic circuit implementation of a chaotic system are not as good as the designs based on mathematical transformations has occupied the agenda of researchers. One of the most striking examples of this problem in practical applications is substitution-box (s-box) structures. While the nonlinearity value is 112 for s-box designs based on mathematical transformations, this value is in the range of 103–106.75 for s-box designs based on random (chaotic) transformations. Thanks to the post-processing algorithm proposed in this study, it has been shown that this problem can be resolved and the nonlinearity values of chaos-based s-box structures can be improved up to 111.5. It is thought that the proposed post-processing algorithm may have various potential contributions not only to improve the nonlinearity criterion of s-box structures but also to other information security applications such as cryptographic random number generators in future studies.
AtıfScopus19WoS13OpenAlex16İncele