{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T05:20:19Z","timestamp":1773120019662,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,18]],"date-time":"2025-08-18T00:00:00Z","timestamp":1755475200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>With the rapid advancement of information technology, as critical information carriers, images are confronted with significant security risks. To ensure the image security, this paper proposes an image encryption algorithm based on a dynamic rhombus transformation and digital tube model. Firstly, a two-dimensional hyper-chaotic system is constructed by combining the Sine map, Cubic map and May map. The analysis results demonstrate that the constructed hybrid chaotic map exhibits superior chaotic characteristics in terms of bifurcation diagrams, Lyapunov exponents, sample entropy, etc. Secondly, a dynamic rhombus transformation is proposed to scramble pixel positions, and chaotic sequences are used to dynamically select transformation centers and traversal orders. Finally, a digital tube model is designed to diffuse pixel values, which utilizes chaotic sequences to dynamically control the bit reversal and circular shift operations, and the exclusive OR operation to diffuse pixel values. The performance analyses show that the information entropy of the cipher image is 7.9993, and the correlation coefficients in horizontal, vertical, and diagonal directions are 0.0008, 0.0001, and 0.0005, respectively. Moreover, the proposed algorithm has strong resistance against noise attacks, cropping attacks, and exhaustive attacks, effectively ensuring the security of images during storage and transmission.<\/jats:p>","DOI":"10.3390\/e27080874","type":"journal-article","created":{"date-parts":[[2025,8,18]],"date-time":"2025-08-18T16:22:33Z","timestamp":1755534153000},"page":"874","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Image Encryption Algorithm Based on Dynamic Rhombus Transformation and Digital Tube Model"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7686-2841","authenticated-orcid":false,"given":"Xiaoqiang","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"}]},{"given":"Yupeng","family":"Song","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"}]},{"given":"Ke","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1088\/2040-8986\/ad3e0d","article-title":"New 4D hyperchaotic system\u2019s application in image encryption","volume":"26","author":"Xu","year":"2024","journal-title":"J. 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