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

Guidong Zhang, Yanhao Zhao, Yanpei Zheng, Yulin Shen and Jun Huang ()
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Guidong Zhang: College of Information Science and Engineering, Lanzhou University, Lanzhou 730030, China
Yanhao Zhao: College of Information Science and Engineering, Lanzhou University, Lanzhou 730030, China
Yanpei Zheng: Gansu Civil Aviation Airport Group Co., Ltd., Lanzhou 730050, China
Yulin Shen: Gansu Computing Center, Lanzhou 730030, China
Jun Huang: College of Information Science and Engineering, Lanzhou University, Lanzhou 730030, China

Mathematics, 2025, vol. 13, issue 9, 1-30

Abstract: 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.

Keywords: image encryption; chaos-based encryption; hyperchaotic system; fast encryption; cyclic shift; security metrics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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