Two-dimensional complex exponential remainder chaotic map with provable chaotic dynamics and secure communication applications

Due to the existence of complex parameters and variables, complex chaotic systems can possess high chaos complexity and abundant dynamical behaviors. However, most existing chaotic maps are still constructed in the real domain, and many reported complex chaotic maps lack sufficient theoretical guarantees. In light of this, this paper presents a two-dimensional complex exponential remainder map, termed the 2D-CER map. The 2D-CER map integrates an exponential nonlinear function with a remainder operation in the complex domain, which strengthens nonlinear coupling and keeps the state evolution bounded. Theoretical analysis proves the chaotic behaviors of the 2D-CER map in terms of Lyapunov exponent. Numerical evaluations show that the proposed map exhibits rich dynamics and high chaos complexity. An STM32 hardware platform is developed to verify the practical feasibility of the 2D-CER map, and hardware comparisons demonstrate its competitive implementation efficiency. In addition, a pseudorandom number generator is designed based on the proposed map and successfully passes TestU01 and NIST SP 800-22 tests under different finite-precision settings. The 2D-CER map is further applied to a complex singular vector precoded OFDM-DCSK communication scheme. Simulation results demonstrate improved BER and image transmission performance over representative schemes under different fading channels.