An Efficient Image Encryption Scheme Based on DNA Mutations and Compression Sensing

Qiu, Jianhua; Zhu, Shenli; Liu, Yu; Luo, Xize; Liu, Dongxin; Zhou, Hui; Zhu, Congxu; Qin, Zheng

doi:10.3390/math14010005

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Open AccessArticle

An Efficient Image Encryption Scheme Based on DNA Mutations and Compression Sensing

by

Jianhua Qiu

¹,

Shenli Zhu

^1,*

,

Yu Liu

¹,

Xize Luo

¹,

Dongxin Liu

¹,

Hui Zhou

¹,

Congxu Zhu

² and

Zheng Qin

^1,*

¹

College of Information Science and Engineering, Hunan University, Changsha 410082, China

²

School of Computer Science and Engineering, Central South University, Changsha 410083, China

^*

Authors to whom correspondence should be addressed.

Mathematics 2026, 14(1), 5; https://doi.org/10.3390/math14010005

Submission received: 14 November 2025 / Revised: 4 December 2025 / Accepted: 16 December 2025 / Published: 19 December 2025

(This article belongs to the Special Issue Chaotic Systems and Their Applications, 2nd Edition)

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Abstract

In communication environments with limited computing resources, securely and efficiently transmitting image data has become a challenging problem. However, most existing image data protection schemes are based on high-dimensional chaotic systems as key generators, which suffer from issues such as high algorithmic complexity and large computational overhead. To address this, this paper presents new designs for a 1D Sine Fractional Chaotic Map (1D-SFCM) as a random sequence generator and provides mathematical proofs related to the boundedness and fixed points of this model. Furthermore, this paper improves the traditional 2D compressive sensing (2DCS) algorithm by using the newly designed 1D-SFCM map to generate a chaotic measurement matrix, which can effectively enhance the quality of image recovery and reconstruction. Moreover, referring to the principle of gene mutation in biogenetics, this paper designs an image encryption algorithm based on DNA base substitution. Finally, the security of the proposed encryption scheme and the quality of image compression and reconstruction are verified through indicators such as key space, information entropy, and Number of Pixel Change Rate (NPCR).

Keywords: image encryption; chaotic map; DNA mutation; compression sensing

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MDPI and ACS Style

Qiu, J.; Zhu, S.; Liu, Y.; Luo, X.; Liu, D.; Zhou, H.; Zhu, C.; Qin, Z. An Efficient Image Encryption Scheme Based on DNA Mutations and Compression Sensing. Mathematics 2026, 14, 5. https://doi.org/10.3390/math14010005

AMA Style

Qiu J, Zhu S, Liu Y, Luo X, Liu D, Zhou H, Zhu C, Qin Z. An Efficient Image Encryption Scheme Based on DNA Mutations and Compression Sensing. Mathematics. 2026; 14(1):5. https://doi.org/10.3390/math14010005

Chicago/Turabian Style

Qiu, Jianhua, Shenli Zhu, Yu Liu, Xize Luo, Dongxin Liu, Hui Zhou, Congxu Zhu, and Zheng Qin. 2026. "An Efficient Image Encryption Scheme Based on DNA Mutations and Compression Sensing" Mathematics 14, no. 1: 5. https://doi.org/10.3390/math14010005

APA Style

Qiu, J., Zhu, S., Liu, Y., Luo, X., Liu, D., Zhou, H., Zhu, C., & Qin, Z. (2026). An Efficient Image Encryption Scheme Based on DNA Mutations and Compression Sensing. Mathematics, 14(1), 5. https://doi.org/10.3390/math14010005

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An Efficient Image Encryption Scheme Based on DNA Mutations and Compression Sensing

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