From Deterministic Chaos to Machine Learning: A Comparative Review of Pseudo-Random Number Generators for Modern Computing and Cryptography

Abstract

Pseudo-random number generators are central to simulation, cryptography, embedded systems, privacy-preserving computation, and machine-learning workflows. This review compares traditional, chaos-based, hybrid, residue-number-system-based, and machine-learning-assisted approaches using computational efficiency, period length, entropy, autocorrelation, statistical-test performance, scalability, and cryptographic suitability. Traditional generators such as linear congruential generators, linear feedback shift registers, Xorshift, and the Mersenne Twister remain attractive for high-throughput simulation because they are simple, reproducible, and fast. Their linearity and recoverable internal states, however, limit their suitability for security-sensitive applications. Chaos-based generators improve nonlinearity, sensitivity to initial conditions, and entropy, but their performance depends strongly on parameter tuning and finite-precision implementation. Hybrid and residue-number-system designs offer a promising middle ground by combining modular arithmetic, nonlinear dynamics, and parallel residue computation. Machine-learning techniques further expand generator evaluation and design by detecting hidden bias, learning complex output patterns, and supporting adaptive generation, although they introduce training costs, reproducibility concerns, and hardware requirements. Future research should prioritize secure hybrid architectures, precision-aware chaotic maps, adaptive reseeding, hardware acceleration, and standardized testing frameworks for nonlinear and data-driven random-number generation systems.