A new post-processing approach for improvement of nonlinearity property in substitution boxes

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.