Open Access

ARTICLE

Brownian-Perturbed Hénon Map for Image Encryption: Application in Biomedical Images

Walaa Alayed¹, Asad Ur Rehman², M.Awais Ehsan³, Waqar Ul Hassan⁴, Ahmed Zeeshan^5,6,*

1 Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
2 Department of Mathematics, Capital University of Science & Technology (CUST), Islamabad, Pakistan
3 School of Natural Sciences, National University of Science and Technology, Islamabad, Pakistan
4 Department of Mathematics, Government College University, Lahore, Pakistan
5 Department of Mathematics & Statistics, Faculty of Science, International Islamic University Islamabad, H-10, Islamabad, Pakistan
6 Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, Republic of Korea

* Corresponding Author: Ahmed Zeeshan. Email:

(This article belongs to the Special Issue: Advances in Secure Computing: Post-Quantum Security, Multimedia Encryption, and Intelligent Threat Defence)

Computers, Materials & Continua 2026, 88(1), 29 https://doi.org/10.32604/cmc.2026.078078

Received 23 December 2025; Accepted 26 February 2026; Issue published 08 May 2026

Abstract

The rapid growth in the field of data and cloud computing has made it essential to ensure information security. Encryption consists of multiple layers, among which a critical component is the Substitution box (S-box). The S-box provides nonlinearity and confusion between the original and cipher forms, and its performance directly determines the security of the cipher against cryptanalysis. Chaotic systems have been widely used for image encryption, however, they suffer from well known limitations such as deterministic periodicity and reduced unpredictability in finite field digital environments. To address these issues, we propose a new S-box generation scheme based on an improved chaotic map, which combines the Hénon chaotic map with Brownian motion, concept in thermodynamics. In the proposed method, the initial keys used in the permutation and diffusion stages interact with each other, thereby enhancing the complexity of the system. We leverage the sensitivity and periodicity of the Hénon map and inject a zigzag Brownian motion sequence into its iteration process to overcome limitations of standalone chaotic maps. The extended scheme is implemented, and a comprehensive security analysis is performed on various cipher images obtained through the modified design. The results of the analysis demonstrate strong security properties, while the running time of the proposed scheme is comparatively better. The proposed scheme is both novel and adaptable, making it suitable for enhancing resistance against differential and algebraic attacks. Hénon-map S-box with Brownian perturbation secures biomedical images (MRI/CT, ultrasound and Xrays) and biofluid sequences (micro-PIV/microfluidics). High unpredictability enables real-time encryption which preserves privacy of patient data/IP.

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Keywords

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