A new chaotic system and its practical applications in substitution box and random number generator

Abstract

AbstractOne of the successful practical applications of chaos theory and nonlinear dynamics is chaos-based cryptology studies. In this study, a new chaotic system is proposed. The proposed chaotic system generator model has a simple algorithmic structure. In addition to, generated chaotic systems have rich dynamics. It has been examined whether this system has potential advantages, especially for information security applications. As a result of the analysis and experimental studies, it is seen that the study makes many contributions to the literature. The simple mathematical generator structure has the potential to reduce computational complexity, which is an important problem for cryptology applications. One of the most comprehensive studies has been realized for chaos-based substitution box designs. 70,000 different substitution box structures have been generated. It has been known that the highest nonlinearity value that can be achieved for designs that transform chaotic system outputs into substitution box structures is 106.75 today. It has been shown that this value may be higher. The new highest nonlinearity value is calculated as 107. Side channel analysis has been examined for substitution box structures with the highest nonlinearity value among the substitution boxes generated in the study. Analysis results show that the proposed new substitution box structures may have an advantage for application-oriented attacks. Among the generated substitution box structures, 289 substitution box structures with a nonlinearity value of 106 and above are presented as a public dataset for researchers to use. In addition, 3 different random sequences with a length of 1 million-bit were produced with the proposed map, and the NIST SP 800–22 test was applied. Test results for all datasets were successful. In this way, the proposed map can also be used as a random number generator.