Hongyan Zang, Kai Li and Xinyuan Wei. A quartic polynomial chaotic map with its application in S-box generation. Dynamic Systems and Applications 29 (2020) No. 8, 2601 – 2618

https://doi.org/10.46719/dsa20202985

ABSTRACT.
At present, for quartic polynomial chaotic maps, the distribution density of the quartic Chebyshev polynomial has been provided, but the distribution density of other forms of the quartic polynomial chaotic maps is rarely reported. This paper constructs a piecewise linear chaotic map with uniform distribution, and provides the sufficient conditions of topological conjugation of the piecewise linear chaotic map and the general quartic polynomial map. Based on topological conjugation of these two systems, this paper proves the quartic polynomial chaotic maps satisfying the above conditions have four and only four unstable fixed points, and further induces the distribution density of the quartic polynomial chaotic maps. Using the above two chaotic systems that are topologically conjugate, this paper designs a S-box generation algorithm, and the S-boxes generated by the two were compared and tested. The comparison results show that the S-box generated by the homogenized sequence has better properties.

Keywords: S-box, Topological conjugation, chaotic map, keyword four, keyword five.