A 4D Trigonometric-Based Memristor Hyperchaotic Map to Ultra-Fast PRNG

Abstract

Extensive research has demonstrated that memristors or trigonometric functions can enhance the complexity of discrete chaotic maps. This article introduces a four-dimensional trigonometric-based memristor hyperchaotic map (4D-TBMHM). By combining discrete memristors, sine, and cosine, the 4D-TBMHM exhibits complex dynamical behaviors. Bifurcation and multistability phenomena are demonstrated using numerical methods. The 4D-TBMHM demonstrates symmetric or attractor self-growth based on iteration length for various system control parameters and initial states, and its complicated complex fractal structure and exemplary performance metrics are also highlighted. Furthermore, an attractor hybrid control, capable of arbitrary positioning and shaping, is proposed. An field-programmable gate array (FPGA)-based hardware prototype is developed, and the attractors are experimentally captured. Moreover, by combining 4D-TBMHM with an arrayed linear feedback shift register, an ultra-fast pseudorandom number generator (UFPRNG) with a throughput of 195.2 Gbps is achieved on an FPGA, surpassing contemporary techniques. Last, the generated UFPRNG is employed for 2.8 Gbps signal generation with noise, and experimental results illustrate its remarkable real-time capability and the PRNG's inherent randomness, facilitating signal generation with any signal-to-noise ratios.