Development of a Pseudorandom Number Generation Method Based on the Chen System

Abstract

This paper presents a hybrid pseudorandom number generator (PRNG) based on the Chen chaotic dynamical system combined with cryptographic hashing. The Chen system serves as a continuous chaotic core, discretized using the fourth-order Runge-Kutta method. The resulting real-valued trajectory is quantized into bytes and then processed by the GOST R 34.11-2012 (Stribog) hash function to eliminate residual correlations and improve statistical uniformity. The proposed generator is evaluated through Shannon entropy analysis, byte distribution histograms, the Pearson chi-square test, autocorrelation, and power spectrum estimation. Experimental results demonstrate near-ideal entropy of 7.999821 bits per byte, a chi-square value of 251.35 (below the critical value of 293.25 at a 95% confidence level), and a flat power spectrum characteristic of white noise. The statistical properties are comparable to those of the widely used Mersenne Twister MT19937. The generator exhibits high sensitivity to initial conditions, reproducibility, and suitability for cryptographic and simulation applications.