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A Color Image Encryption Using a 4D Variable-Order Fractional Hyperchaotic System and Chess-Gameplay-Inspired Dynamic
Xiaomeng Cui1, Xiaoqiang Zhang2, Jiaqi Ji1
1School of Mathematics and Computer Science, Hebei Minzu Normal University, Chengde 067000, China.
Entropy (Basel, Switzerland)
|July 28, 2026
Summary
This study introduces a novel image encryption method using a four-dimensional variable-order fractional hyperchaotic system (4D-VOFHS) and chess-inspired dynamics. The robust scheme enhances security and efficiency for digital image privacy protection.
Area of Science:
- Cryptography and Information Security
- Applied Mathematics and Chaos Theory
- Computer Science and Digital Imaging
Background:
- Increasing digital image transmission and storage necessitates advanced privacy protection.
- Existing constant-order systems are vulnerable to parameter identification attacks, particularly those using deep learning.
- There is a need for more secure and efficient image encryption techniques.
Purpose of the Study:
- To propose a robust image encryption scheme combining a novel chaotic system with a dynamic mechanism.
- To enhance nonlinear dynamics and overcome limitations of constant-order systems.
- To improve security, confusion, diffusion, and computational throughput for image encryption.
Main Methods:
- Construction of a four-dimensional variable-order fractional hyperchaotic system (4D-VOFHS) with time-varying orders and high-dimensional coupling.
- Design of a synchronous encryption framework with a tightly coupled permutation-diffusion mechanism inspired by chess.
- Implementation of a block-based collaborative scrambling strategy with dynamically updated rules based on 4D-VOFHS state evolution.
Main Results:
- The proposed 4D-VOFHS enriches nonlinear dynamics, offering resistance to parameter identification attacks.
- The encryption framework demonstrates enhanced nonlinear complexity, confusion, and diffusion.
- Achieved outstanding performance metrics: average NPCR of 99.6%, UACI of 33.4%, and information entropy of 7.9993.
- Parallel synchronous processing capability improves computational throughput.
Conclusions:
- The developed encryption scheme exhibits strong cryptographic robustness and practical applicability.
- The combination of 4D-VOFHS and chess-inspired dynamics provides a secure and efficient solution for color image encryption.
- The scheme holds significant potential for real-world deployment in digital image privacy protection.
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