Autonomous Boolean network and physical random number generator based on XOR gate

Abstract

As a controllable nonlinear system, autonomous Boolean network which is easy to generate chaotic signals has become a hot research topic. We realize an 18-node autonomous Boolean network circuit which can generate high entropy chaos by using the nonlinear characteristics of two-input XOR gate, and establish an improved mathematical model for the circuit by introducing the filter coefficient. Through numerical simulation and circuit comparison experiment, we study the influence of filter coefficient and delay parameters on network dynamic characteristics of this model. The numerical simulation results are basically consistent with those of the experimental phenomena. When the transmission delay between nodes is not equal, the filter coefficient has a modulation effect on the generation of chaos, which well indicates that the introduction of the filter coefficient makes the improved mathematical model more objective to describe the physical phenomena in the circuit. In addition, using bifurcation diagram, Lyapunov exponent and permutation entropy, we further analyze the nonlinear characteristics and randomness of the autonomous Boolean network. The output chaotic sequence of the network has the characteristics of high bandwidth, high entropy and strong robustness, which is used to generate high speed physical random sequences and has passed the NIST SP 800-22 randomness tests of National Institute of Standards and Technology of America.