Random Number Generator Design Based on an Incommensurate Fractional-Order Chaotic System with Exponential Function

Abstract

This research proposes an approach to design random number generator (RNG) by harnessing the inherent unpredictability of chaotic systems with an incommensurate fractional-order structure, coupled with the dynamic properties of exponential functions. The inclusion of incommensurate fractional-order structure introduces an additional layer of nonlinearity, enhancing the entropy and randomness of the generated sequences. The research begins by providing mathematical foundations of incommensurate fractional-order chaotic system with exponential function. The proposed RNG architecture is then detailed, outlining the integration of these elements to achieve an unpredictable random number sequence. The study employs rigorous mathematical analyses, simulations, and statistical tests to validate the effectiveness of the proposed RNG in producing sequences with desirable randomness properties. The performance of the RNG is tested with NIST-800-22, highlighting its strengths in terms of statistical properties, computational efficiency, and suitability for cryptographic applications. The findings of this research contribute to the advancement of random number generation techniques, offering a promising avenue for enhancing the security and reliability of applications reliant on high-quality random sequences. The unique combination of incommensurate fractional-order chaotic systems with exponential function provides a versatile and innovative approach to RNG design, with implications for diverse domains requiring unpredictable randomization.