A Method for Designing Substitution Boxes Based on Chaos with High Nonlinearity

Cryptography aims to design algorithms for the protection of important data transmitted over unsecured networks. These algorithms encrypt the data and render it incomprehensible even if it is captured by enemies. Today’s data encryption standard is the AES algorithm. The most important and nonlinear unit in the AES algorithm is the s-box structure. The S-box provides the mixing process in the algorithm, that is, the confusion. An s-box structure with a high nonlinearity value greatly increases the security against various attacks. Therefore, s-box is of vital importance in an encryption algorithm. When we look at the literature, chaos-based s-box structures are frequently used. However, the nonlinearity value of s-boxes produced with chaos is low. In this article, a new, fast, and very simple method is proposed to increase the nonlinearity value of chaos-based s-box structures. In the proposed method, the nonlinearity value is calculated by changing the places of the elements respectively. When the nonlinearity value increases, the s-box is updated, and the next element is passed. In this way, many iterations are not looked at in vain. This saves a lot of time. As a result of the analysis, it has been proven that the s-box structure obtained by the proposed method is cryptographically strong and has a high nonlinearity value. It is thought that the proposed method will provide many advantages for future cryptography applications.