https://doi.org/10.1140/epjs/s11734-025-02062-4
Regular Article
A multi-image hierarchical scrambling encryption algorithm based on 2D McCormick map
Digital Intelligence Industry College, Inner Mongolia University of Science and Technology, 014000, Baotou, Inner Mongolia, China
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
10
June
2025
Accepted:
3
November
2025
Published online:
14
November
2025
Abstract
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
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
