A novel approach to pseudorandom number generation using Hamiltonian conservative chaotic systems

Vinod Patidar ^* Tanu Singh ^*

• University of Petroleum and Energy Studies, Dehradun, India

High-quality random number generators are required for various applications such as cryptography, secure communications, Monte Carlo simulations, and randomized algorithms.Existing pseudo-random number generators (PRNGs) face limitations such as periodic behavior, dependence on high-quality entropy sources, or computational inefficiency. On the other hand, chaotic systems are widely used for pseudo-random sequence generation due to their sensitivity to initial conditions and rich dynamical properties. The dissipative chaotic systems settle into low-dimensional attractors; however, the conservative chaotic systems (CCSs) conserve phasespace volume and exhibit superior ergodicity, making them particularly suitable for chaos-based cryptographic applications. However, challenges remain with existing approaches, such as limited phase space and periodic behavior, necessitating more robust CCS-based solutions for secure and efficient implementations. To address these challenges, in this paper, we propose a pseudorandom number generator based on a Hamiltonian conservative chaotic system (HCCS) constructed using the 4D Euler equations of rigid body rotations. Although the proposed method is described using a specific chaotic system, the approach can be easily extended to other Hamiltonian conservative chaotic systems (HCCSs) following a careful analysis of their behaviour in phase space. We provide a detailed description of the pre-analysis, followed by two methods that utilize the Poincar é sections of HCCS to extract pseudo-random sequences, along with their corresponding pseudo codes. Additionally, we present the results of the performance analysis of the two pseudo-random number generation methods using the NIST randomness test suite, which confirm their robustness and compliance with randomness standards. Our innovative approach demonstrates significant potential to enhance the quality, unpredictability, and efficiency of pseudo-random number generation, making it highly suitable for cryptographic applications.