**1. Introduction**

Developments in Industry 4.0, the Internet of Things (IoT) and artificial intelligence have changed our lives significantly. Although these changes make our lives easier in many ways, guaranteeing the security of the huge quantities information called big data is a serious problem. Strong cryptographic protocols are needed to address this problem. However, cryptology is a complex discipline. It is not enough to demonstrate that only certain security requirements are met. New methods and countermeasures should be constantly researched as new attack techniques are developed [1,2]. Application attacks are an important cryptanalysis technique that threatens existing encryption protocols [3]. One of the attack techniques, called side-channel analysis, is based on the principle of obtaining the secret key of the algorithm with the help of measurements such as sound, heat, light and power consumption after the encryption protocol is implemented on hardware such as a computer, mobile phones or FPGA cards.

Recent studies have shown that chaos-based encryption protocols may be more resistant to side-channel attacks than encryption protocols based on mathematical techniques. In the analysis carried out in [4], first, a side-channel analysis of the AES block encryption algorithm was performed. In the second stage of the analysis, a side-channel analysis of the AES block encryption algorithm was performed using chaotic substitution box (s-box) structures instead of the s-box structure based on mathematical methods proposed by Nyberg [5,6]. The second design is more resistant to side-channel attacks than the standard AES algorithm. In other words, chaos-based s-box structures are more

resistant to side-channel attacks than the AES s-box structure, which has the best-known s-box design criteria. However, when a literature review was undertaken, it was shown that even chaos-based designs with the best s-box performance criteria were worse than the Nyberg s-box structure. For example, for nonlinearity measurements, which play an important role in confusion and diffusion requirements, the best achievable value in chaos-based designs is 106.75, while in the Nyberg s-box structure, that value is 112, which is the upper bound value that can be reached [7].

It is therefore possible for chaos-based designs to be more resistant to side-channel attacks than mathematical designs. However, the poor performance criteria for these designs are an important problem. This study seeks to address this problem. Various studies have been published showing that the performance criteria can be improved with the help of optimization algorithms. However, in these approaches, there is another design problem, i.e., the additional processing cost of optimization algorithms. In this study, it has been shown that s-box performance criteria can be improved by applying various postprocessing techniques to chaos-based s-box designs. The practical applicability of the proposed method, its simple structure, and the speed of producing results have been evaluated as the advantages of the proposed method. This also raised a new research question regarding how s-box structures with better performance criteria can be obtained by using different postprocessing techniques in the future.

The rest of the study is organized as follows. In Section 2, the general design principle of chaos-based s-box structures and the basic milestones related to the literature are explained. In Section 3, the details of the proposed postprocessing technique are presented to improve the s-box performance criteria. In Section 4, the success of the proposed method is tested by providing various analysis results. The obtained results are interpreted and a road map for future studies is presented in Section 5.
