Design and Analysis of a Pseudo-Random Number Generator (PRNG) Using 2D Chaotic Mapping for Enhanced Randomness

This paper introduces a novel two-dimensional chaotic mapping and leverages its properties to design an efficient Pseudo-Random Number Generator (PRNG). Chaotic mappings find widespread applications in cryptography, simulation, and random algorithms, playing a crucial role in enhancing randomness and ensuring data security. The proposed two-dimensional chaotic mapping combines two independent chaotic equations, achieving a more complex and diversified generation of random sequences. The paper provides a detailed description of the mathematical model of this mapping and analyzes its performance and statistical characteristics. Building upon the two-dimensional chaotic mapping, we design and implement a high-quality PRNG. This PRNG demonstrates significant improvements in randomness, uniformity, and periodicity compared to traditional PRNGs. We conduct thorough performance evaluations, including tests for randomness, distribution analysis, and periodicity detection. Experimental results indicate superior performance across various metrics compared to conventional PRNGs. We also discuss potential application areas for the proposed PRNG, such as encrypted communication, simulation experiments, and Monte Carlo simulations. Our research offers new insights into enhancing the quality and security of PRNGs, contributing significantly to the application of chaos theory in information security and computing.