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Article

A New Chaotic Image Encryption Algorithm Based on Transversals in a Latin Square

1
School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
2
Department of Mathematics and Computer Science, Hengshui University, Hengshui 053000, China
3
Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2022, 24(11), 1574; https://doi.org/10.3390/e24111574
Submission received: 5 October 2022 / Revised: 23 October 2022 / Accepted: 27 October 2022 / Published: 31 October 2022
(This article belongs to the Special Issue Applications of Information Theory in Economics)

Abstract

In this paper, a new combinatorial structure is introduced for image encryption, which has an excellent encryption effect on security and efficiency. An n-transversal in a Latin square has the function of classifying all the matrix’s positions, and it can provide a pair of orthogonal Latin squares. Employing an n-transversal of a Latin square, we can permutate all the pixels of an image group by group for the first time, then use two Latin squares for auxiliary diffusion based on a chaotic sequence, and finally, make use of a pair of orthogonal Latin squares to perform the second scrambling. The whole encryption process is “scrambling–diffusion–scrambling”. The experimental results indicated that this algorithm passed various tests and achieved a secure and fast encryption effect, which outperformed many of the latest papers. The final information entropy was very close to 8, and the correlation coefficient was approximately 0. All these tests verified the robustness and practicability of the proposed algorithm.
Keywords: image encryption; chaotic; Latin square; transversals; n-transversal image encryption; chaotic; Latin square; transversals; n-transversal

Share and Cite

MDPI and ACS Style

Shen, H.; Shan, X.; Xu, M.; Tian, Z. A New Chaotic Image Encryption Algorithm Based on Transversals in a Latin Square. Entropy 2022, 24, 1574. https://doi.org/10.3390/e24111574

AMA Style

Shen H, Shan X, Xu M, Tian Z. A New Chaotic Image Encryption Algorithm Based on Transversals in a Latin Square. Entropy. 2022; 24(11):1574. https://doi.org/10.3390/e24111574

Chicago/Turabian Style

Shen, Honglian, Xiuling Shan, Ming Xu, and Zihong Tian. 2022. "A New Chaotic Image Encryption Algorithm Based on Transversals in a Latin Square" Entropy 24, no. 11: 1574. https://doi.org/10.3390/e24111574

APA Style

Shen, H., Shan, X., Xu, M., & Tian, Z. (2022). A New Chaotic Image Encryption Algorithm Based on Transversals in a Latin Square. Entropy, 24(11), 1574. https://doi.org/10.3390/e24111574

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