Design and Performance Evaluation of a Hybrid PRNG: Gold-SA II Optimized LFSR Combined with Discrete Chaotic Maps

Random Number Generators (RNGs) play a critical role in ensuring data security in cryptographic systems. Linear Feedback Shift Registers (LFSRs) are widely used due to their hardware speeds and low costs; however, their linear structures make them vulnerable to algebraic attacks and may yield insufficient results in statistical randomness tests. This study proposes a hybrid architecture based on optimisation and chaos to enhance the cryptographic security of LFSR-based generators. The irreducible polynomials and initial seed values that provide the maximum period length of the LFSR have been optimised using the Modified Golden Sine Algorithm (Gold-SA II). As the raw LFSR outputs failed the NIST SP 800-22 tests, the system was supported by a chaotic final processing layer containing Sine, Chebyshev, Logistic, Tent, and Circle maps. Experimental results demonstrate that the chaotic final processing significantly improves randomness properties and, in particular, that the Sinus map-based structure successfully passes all NIST tests.