CHAOTIC RANDOM NUMBER GENERATOR WITH FUZZY CONTROL FOR CRYPTOGRAPHIC SYSTEMS WITH DYNAMIC TRUST

DOI: 10.31673/2412-4338.2025.048916

Abstract

The paper proposes a model of a Chaotic Random Number Generator (CRNG) with fuzzy control elements, designed for adaptive adjustment of chaotic map parameters according to the dynamic trust level of the system. This approach combines the cryptographic robustness of chaotic processes with the flexibility of fuzzy regulators, enhancing the entropy and resistance of the generator against state-recovery attacks. A mathematical model based on the second-order Chebyshev map is developed, where the chaoticity coefficient and disturbance are determined by a Mamdani-type fuzzy controller depending on the current trust score. The fuzzification procedure, rule base, and defuzzification process are formalized considering behavioral and contextual parameters. Simulation of the generator demonstrated the system’s ability to autonomously adjust its chaoticity level as trust varies and to maintain high entropy of the output sequence. To confirm the effectiveness, testing was carried out using the NIST SP 800-22 and Dieharder suites, showing over 98% test pass rates and a 2–3% entropy increase compared to classical CSPRNGs. The results confirm the feasibility of applying fuzzy logic for regulating the parameters of chaotic generators in cryptographic systems with dynamic trust, Zero Trust architectures, and multi-factor authentication mechanisms. The findings indicate the potential for further hardware implementation of the model on FPGA and its integration into adaptive security management tools.

Keywords: chaotic random number generator, fuzzy logic, cryptographic strength, dynamic trust, entropy control, cryptographic systems, Zero Trust, adaptive security, Chebyshev map.