Design of S-box multi-objective optimization algorithm based on combined chaotic system

Abstract S-box is the only nonlinear cryptographic component that determines the security of the block cipher. The higher the security of the S-box, the higher the security of the block cipher. Therefore, this paper proposes an S-box multi-objective optimization algorithm based on the combined chaotic system. Firstly, designing an integrated chaotic system based on a fractional index and its dynamic behavior is studied; it shows incredibly high-performance stability and chaotic parameter range coverage in the entire parameter space. A novel chaotic S-box construction algorithm is proposed based on the combined chaotic system. It introduces a linear congruential pseudo-random number generator to extend the sequence period and scramble the chaotic S-box through Henon mapping to improve the nonlinearity of the s-box. Finally, introducing a teaching and learning multi-objective optimization model and the performance evaluation criteria of the S-box are incorporated into the design of the objective function; this design enables the resulting S-box to perform well under multiple performance indicators, and then the approximate optimal S-box in the population is obtained. Through the performance test of the approximate optimal S-box, the comparative analysis shows that the S-box has good cryptographic performance, can resist linear analysis and differential analysis, and has a good application prospect in lightweight cipher.