Use of Entropy Pools Obtained from Optimisation Based Random Number Generators in S-Box Generation and Performance Analysis of Image Encryption

Abstract

This study analyzes how optimization algorithms and random number generators jointly produce random numbers (the entropy pool) used to generate S-boxes for image encryption. As a result of running the Bat Algorithm (BA), Golden Sine Search Algorithm - 2 (GoldSA- 2) and Particle Swarm Optimization (PSO) algorithms together with Linear Feedback Shift Register (LFSR) and Delayed Fibonacci Generators (LFG), initial configurations suitable for generator structures and successfully passing the NIST SP 800-22 test functions, which is our objective function, were determined. Random number sequences that pass 15/15 of the NIST tests accepted in the literature are transferred to the entropy pool. Chi-square and autocorrelation analyses of the random numbers taken from the entropy pool, which are other test methods, are evaluated, and the success of the random numbers obtained with successful results in the areas of S-boxing and image encryption applications is shown. The effectiveness of random numbers in practical applications is investigated by using S-box analysis and image encryption analysis metrics. The findings show that high-quality entropy pools, obtained from optimization-based random number generators, exhibit superior cryptographic properties compared to conventional methods in S-box generation and image encryption applications. The experimental results show that the generated random sequences successfully passed all 15 NIST SP 800-22 statistical tests, achieved chi-square values significantly below critical thresholds (e.g., 9.02 compared to 30.57 at ?=0.01), and produced S-boxes with high nonlinearity (average 105.25) and near-ideal SAC values (~0.50). In image encryption experiments, the algorithm achieved NPCR = 100%, UACI ? 33%, and entropy values of 7.45, confirming both statistical quality and practical security performance.