A Fast Image Encryption Scheme Based on a Four-Dimensional Variable-Parameter Hyperchaotic Map and Cyclic Shift Strategy

Digital images are widely transmitted over untrusted networks, raising severe challenges to the security of confidential and personal data. To address these issues, this paper develops a four-dimensional variable-parameter hyperchaotic system that leverages the advantages of the classical Sine and two-dimensional Logistic chaotic systems. The proposed system not only features a wider parameter range but also exhibits more complex and unpredictable chaotic behavior, as confirmed by multiple rigorous tests. Building upon this system, we design a fast image encryption algorithm that employs a cyclic shift strategy to continuously expand a small-scale random sequence, thereby generating the random numbers required for secure encryption. This approach significantly reduces the overhead associated with random number generation and effectively addresses the challenges posed by large-scale image encryption. Furthermore, to more accurately evaluate the algorithm’s resistance to differential attacks, we introduce improved metrics—namely, BL-NPCR and BL-UACI—which measure the subtle differences between encrypted images at the binary level. Extensive simulation experiments demonstrate that our proposed encryption algorithm outperforms existing methods in both security and efficiency, effectively resisting various attacks and providing a novel technological pathway for efficient image encryption.