Optimization of Entropy Characteristics for Pseudorandom Number Sequences Based on Hybrid Cellular Automata

Abstract

This paper investigates the problem of generating high-entropy pseudorandom number sequences with enhanced statistical properties for systems with limited computational resources, specifically Internet of things devices. It has been established through rigorous testing that classical chaotic Wolfram cellular automata (CA) rules, such as Rules 30, 45, and 86, exhibit significant spectral vulnerabilities. These defects are confirmed by failures in the fast Fourier transform spectral test within the NIST SP 800-22 suite, which identifies hidden deterministic patterns. To address these security gaps, a hybrid method called XOR-MIX is proposed, based on the bitwise mixing of streams from independent CA layers. The mathematical foundation of this approach relies on the Piling-up Lemma, which demonstrates that the bitwise addition of independent sources with distinct statistical profiles exponentially reduces probability bias and masks spectral peaks. Experimental results were obtained through a high-performance implementation in the Rust programming language, utilizing memory-safe mechanisms and look-up table optimization. The analysis demonstrates a significant increase in the NIST statistical test pass rate to a level of 0.99 and the stabilization of Shannon entropy at 7.999998 bits per byte. Furthermore, the system architecture utilizes a "thick client" model with React/Next.js and SHA-256 for deterministic initialization, ensuring data privacy and integrity. The proposed approach provides an optimal balance between cryptographic strength, high throughput, and low computational complexity, making it suitable for hardware-constrained environments and future field-programmable gate array integrations.