Characteristics of 3D coupled map lattice and its application in pseudo-random number generator

Coupled map lattice (CML), as a classical model of the higher-dimensional chaotic system, possesses outstanding chaotic dynamic behavior both at time and space. Compared with one-dimensional CML and two-dimensional CML, three-dimensional (3D) CML has more complicated chaotic behavior, and it is pretty suitable for designing chaos-based cryptographic schemes. In this paper, foremost, theoretical mathematical expressions of Lyapunov exponent (LE) and synchronization stability in the 3D CML model are deeply and comprehensively obtained, which guide the parameters setting to keep the model in the fully chaotic state and avoid synchronization state. Also, other chaotic behaviors such as bifurcation, ergodicity, and probability density distribution are analyzed, and all of those demonstrate the 3D CML model has complex chaotic performance. Furthermore, according to the 3D CML model and theoretical results, a novel pseudo-random number generator (PRNG) has been proposed with safety assurance via the simple interception operation. Finally, large amounts of simulations verify the theoretical results are correct and our proposed PRNG scheme possesses outstanding performance. Finally, the 3D CML model is extended into the ND CML one, LE expression is also derived. Above all, our research can provide some theoretical guidance for using the CML model (i.e. 3D CML and ND CML) as a core component to construct chaos-based cryptographic schemes, and it owns well potential application.