Construction algorithm of non-degenerate complex domain chaotic system with application on PRNG

Based on the theorem of eigenvalue estimation, this paper proposes a construction algorithm for an N-dimensional discrete non-degenerate complex domain chaotic system (ND-NCCS). Through theoretical analysis, it is demonstrated that the chaotic system constructed by this algorithm not only exhibits non-degenerate properties in the complex domain but also maintains non-degeneracy in its real and imaginary components. To verify the effectiveness and feasibility, we construct a three-dimensional discrete complex domain chaotic system as an example. The dynamic behaviors and properties of this system are thoroughly analyzed, including the chaotic generation mechanism, Lyapunov exponents (LEs), chaotic phase diagram and sequence statistical characteristics. The algorithm adjusts the relative positions between the Gerschgorin disks of system’s coefficient matrix and the unit circle, ensuring all eigenvalues fall within the desired range. Based on the relationship between the eigenvalues of the coefficient matrix and the Lyapunov exponents, a non-degenerate chaotic system is constructed where all LEs are positive. Additionally, the algorithm is applied to a pseudo-random number generator based on confusion and diffusion mechanism (PRNG-CD). Under limited precision conditions, various experimental tests are conducted on the generated binary sequences, including distribution histogram, \(\chi ^2\) ${\chi }^2$ distribution, and NIST SP800-22 standard test. The experimental results show that the CD-PRNG exhibits excellent pseudo-randomness and uniform distribution characteristics. Finally, the constructed PRNG is implemented on Xilinx’s Artix-7 series xc7a35tfgg484-2 chip to verify its practical effectiveness. With a calculation precision set to 32 bits, the results show that the PRNG-CD consumes only \(18.75\%\) $18.75\%$ of the total resources, while achieving a bit throughput of up to 16 Gbps.