Design and FPGA Implementation of a Pseudorandom Number Generator Based on a Four-Wing Memristive Hyperchaotic System and Bernoulli Map

Random numbers are widely used in the fields of computer, digital signature, secure communication and information security. Especially in recent years, with the large-scale application of smart card and the demand of information security, the demand for high-quality random number generator is increasingly urgent. With the development of the theory of non-linear systems, the design of pseudorandom number generator (PRNG) for chaotic behavior of non-linear systems provides a new theoretical basis and implementation method. This paper presents a PRNG based on a no-equilibrium four-wing memristive hyperchaotic system (FWMHS) and its implementation on Field Programmable Gate Array (FPGA) board. In order to increase the output throughput and the statistical quality of the generated bit sequences, we propose the PRNG design which uses a dual entropy sources architecture with FWMHS and Bernoulli map. Simulation and experimental results verifying the feasibility of the FWMHS are also given. Then, the proposed PRNG system is modeled and simulated on the Vivado 2018.3 platform, and implemented on the Xilinx ZYNQ-XC7Z020 FPGA evaluation board. The maximum operating frequency has been achieved as 135.04 MHz with a speed of 62.5 Mbit/s. Finally, we have experimentally verified that the binary data obtained by this dual entropy sources architecture pass the tests of NIST 800.22, ENT and AIS.31 statistical test suites with XOR function post-processing for a high throughput speed. The security analysis is carried out by means of dynamical degradation, key space, key sensitivity, correlation and information entropy. Statistical tests and security analysis show that it has good pseudorandom characteristics and can be used in chaos-based cryptographic applications at hardware or software implementation.