Two-Dimensional Multivalued Chaotic Map With a Zynq-Based Parallel PRNG Design

Designing multivalued chaotic map with rich dynamical behaviors in the complex domain is both interesting and challenging. However, most existing chaotic maps remain confined to the real domain and exhibit only single-valued dynamics. In light of this, we propose a two-dimensional multivalued chaotic (2D-MVC) map by coupling multivalued radical functions with a componentwise modular operation. Theoretical analysis demonstrates that the proposed 2D-MVC map exhibits chaotic behavior in the sense of the Lyapunov exponent. Property analysis reveals that the 2D-MVC map possesses rich dynamical characteristics, particularly multivalued chaotic behaviors. Extensive experiments show that the 2D-MVC map achieves high performance across multiple chaos complexity indicators and outperforms several representative chaotic systems. A Zynq-based hardware platform is implemented to capture the principal-valued and multivalued attractors of the proposed map. Leveraging the multivalued property, a multisequence pseudorandom number generator is implemented on this hardware platform. Statistical testing confirms that the generated sequences exhibit high randomness, highlighting the practicality and general applicability of the proposed 2D-MVC map.