2D mixed pseudo-random coupling PS map lattice and its application in S-box generation

Abstract

In this paper, firstly, we investigate a new 1D PWLCM-Sin (PS) map which derived from PWLCM and Sin map by modulo operation. Due to the stronger parameter space, bigger Lyapunov exponents and better ergodicity than simple 1D map, the PS map is more suitable for local map of spatiotemporal dynamics. Secondly, with the novel 2D pseudo-random mixed coupling method we present a spatiotemporal chaos which used PS map as local map f(x). This spatiotemporal chaos named 2D Mixed pseudo-random Coupling PS Map Lattice (2DMCPML). The experimental results of bifurcation diagrams, Kolmogorov–Sinai entropy density and spatiotemporal chaotic diagrams showed that 2DMCPML has advantages of larger parameter space, more complex chaotic behavior and more ergodic output sequence than CML. Therefore, 2DMCPML is more suitable in cryptography than CML. Subsequently, we proposed a chaos-based random S-box design algorithm employed the spatial chaotic character of 2DMCPML to generate a large number of S-boxes. The cryptographic performance indicated that generated S-boxes can resist cryptanalysis attack well. Finally, four criteria bounds are set. The numbers of S-boxes satisfying these bounds generated by 2DMCPML and several 1D chaotic maps is calculated, respectively. The result showed that spatiotemporal chaos can generate more S-boxes with high cryptographic quality than low-dimensional chaos. This new discovery is significant to the development of some cryptographic researches such as dynamic S-box algorithm.