Beyond Fixed Maps: Robust and Flexible Chaotic PRNGs Applied to Image Encryption

Chaos-based Pseudo-Random Number Generators (PRNGs) have achieved considerable attention due to their inherent randomness and deterministic properties. However, reliance on a single chaotic map may yield insufficient randomness because of intrinsic structural patterns. To mitigate this limitation, a proposed PRNG framework employs multiple state variables from chaotic systems and incorporates an XOR operation to improve bit randomness. This method exhibits high flexibility, permitting integration of any chaotic map contingent upon specific computational resources and application needs. In contrast to conventional chaos-based PRNGs, which are limited by fixed maps, the present approach offers enhanced adaptability. The proposed framework was implemented using four chaotic maps, including the one-dimensional logistic map, the two-dimensional logistic map, the two-dimensional hénon map, and the three-dimensional Lorenz system. Extensive evaluations, including NIST, TestU01, key sensitivity analysis, autocorrelation tests, time complexity assessments, and Monte Carlo \(\pi\) estimation, were conducted to verify the quality of the proposed algorithm. Cryptographic applicability was further evaluated through the implementation of a two-phase image-encryption scheme. Each RGB channel undergoes a PRNG‐driven permutation to disrupt pixel adjacency, followed by multi‐round diffusion based on neighboring intensities and key bits. Uniform histograms, near‐zero pixel correlations, high Number of Pixels Change Rate and Unified Average Changing Intensity values, and perfect decryption verify that our flexible PRNG framework provides robust security and lossless reversibility in image processing. The results confirmed its strong randomness, high sensitivity to initial conditions, and computational efficiency.