{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T13:46:04Z","timestamp":1782913564558,"version":"3.54.5"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Provincial Youth Innovation Talent Program for Colleges and Universities","award":["2025KQNCX255"],"award-info":[{"award-number":["2025KQNCX255"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>To address the limitations of existing chaotic systems such as complex structure and potential chaotic degradation, this paper proposes a novel four-dimensional discrete chaotic system (4D-DCS) and an image encryption algorithm based on it. The 4D-DCS is constructed by integrating a feedback controller and modulo operation into a linear discrete-time system, featuring a simple structure without the need for intricate matrix reconstruction or memristor circuits. Mathematical analysis confirms its chaos in the sense of Li\u2013Yorke and numerical simulations including Lyapunov exponent (LE) analysis, 0\u20131 test, and NIST SP 800-22 test demonstrate its hyperchaotic characteristics and excellent pseudorandomness. Based on the 4D-DCS, the proposed encryption algorithm employs SHA-256 to generate initial states for key uniqueness, combines row\u2013column permutation to disrupt pixel correlation, and adopts a reversible neural network for diffusion to enhance confusion capability. Comprehensive security analysis shows that the algorithm achieves an NPCR of \u223c99.61% and a UACI of \u223c33.46%, a key space of 2216, information entropy close to 8, and correlation coefficients of encrypted images near 0. It also exhibits strong robustness against differential, cropping, noise, and chosen-plaintext attacks. Comparative analysis with state-of-the-art algorithms validates the 4D-DCS\u2019s advantages in structural simplicity and stability, and the encryption algorithm\u2019s superiority in security and practicality, making it suitable for security-critical applications such as image encryption.<\/jats:p>","DOI":"10.3390\/e28070753","type":"journal-article","created":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T12:41:38Z","timestamp":1782909698000},"page":"753","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Low-Complexity 4D Discrete Chaotic System for Secure Image Encryption Based on Reversible Neural Network"],"prefix":"10.3390","volume":"28","author":[{"given":"Han","family":"Chen","sequence":"first","affiliation":[{"name":"School of Marine Science and Technology, Shanwei Institute of Technology, Shanwei 516600, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingye","family":"Huang","sequence":"additional","affiliation":[{"name":"Institute of Collaborative Innovation, University of Macau, Macau 999078, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yingjie","family":"Su","sequence":"additional","affiliation":[{"name":"College of Information Science and Technology, Jinan University, Guangzhou 510632, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lezhu","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Shanwei Institute of Technology, Shanwei 516600, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baoyi","family":"Liao","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Shanwei Institute of Technology, Shanwei 516600, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9636-499X","authenticated-orcid":false,"given":"Linqing","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Advanced Manufacturing, Guangdong University of Technology, Jieyang 522000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changwen","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Shanwei Institute of Technology, Shanwei 516600, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18115","DOI":"10.1109\/JIOT.2025.3540097","article-title":"A Parallel Color Image Encryption Algorithm Based on a 2-D Logistic-Rulkov Neuron Map","volume":"12","author":"Gao","year":"2025","journal-title":"IEEE Internet Things J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"115109","DOI":"10.1016\/j.chaos.2024.115109","article-title":"A hidden grid multi-scroll chaotic system coined with two multi-stable memristors","volume":"185","author":"Zhang","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1562","DOI":"10.1109\/TCSVT.2024.3470110","article-title":"Multi-Image Encryption Algorithm Based on Novel Spatiotemporal Chaotic System and Dynamical Chaotic Trajectories","volume":"35","author":"Teng","year":"2025","journal-title":"IEEE Trans. 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