A 4D hyperchaotic image encryption scheme using Circular Radius–Angle Transformation and bit-level permutation

Abstract

With the rapid growth of digital data transmission, secure image encryption has become a critical requirement for protecting visual information against unauthorized access and cryptanalytic attacks. Existing chaotic-based encryption schemes often suffer from limited resistance to statistical and differential attacks due to weak key dependence, low-dimensional chaotic behavior, or the partial use of image features during encryption. To overcome these limitations, this study proposes a novel four-dimensional (4D) hyperchaotic image encryption mechanism that is independent of image statistical features and semantic information, thereby making cryptanalysis highly infeasible. The proposed algorithm utilizes a 4D Lorenz hyperchaotic system to generate the primary pseudo-random key sequences, which are then processed using mathematical and modular operations to produce dynamic subkeys for each encryption stage. The encryption process consists of three structured phases: (1) initial pixel sorting based on the first and second keys; (2) Circular Radius–Angle Transformation (CRAT) using the third and fourth keys to remap pixel positions in a nonlinear circular coordinate space; and (3) a final diffusion phase using the fifth key to perform XOR-based confusion. Experimental evaluations confirm that the proposed approach achieves high key sensitivity, a vast key space, and strong resistance to statistical, differential, and chosen-plaintext attacks. Furthermore, the encrypted images demonstrate uniform histograms, minimal pixel correlation, high information entropy, and excellent computational efficiency, highlighting the algorithm’s robustness and applicability for secure image transmission in real-world scenarios.