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A multi-image hierarchical scrambling encryption algorithm based on 2D McCormick map
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DOI：10.1140/epjs/s11734-025-02062-4.png)
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Abstract
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Chaotic systems find extensive applications in fields, such as communication, cryptography, and biomedical engineering. However, existing chaos systems suffer from limitations, such as a limited key space and a low complexity. This paper introduces a novel two-dimensional hyper-chaotic system, the 2D McCormick map, designed for scenarios requiring high complexity. Inspired by the McCormick function, the hyper-chaotic system is evaluated using rigorous chaos indicators, including the maximum Lyapunov exponent, bifurcation diagram, sample entropy, correlation dimension, and Kolmogorov entropy. The superiority of the proposed chaos system is verified through a comparison with the existing systems. Additionally, a new scrambling algorithm is presented, which is capable of encrypting at the pixel block, the pixel, and the bit levels. Based on the spiral scrambling algorithm, the improved version expands the scrambling patterns to 16 types. The integration of the 2D McCormick hyper-chaotic system with this algorithm is applied to image encryption. Experimental results demonstrate that the proposed encryption algorithm exhibits excellent security properties. https://doi.org/10.5281/zenodo.17482002
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