{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T18:17:10Z","timestamp":1777918630508,"version":"3.51.4"},"reference-count":17,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,13]],"date-time":"2023-08-13T00:00:00Z","timestamp":1691884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61872408"],"award-info":[{"award-number":["61872408"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2020JJ4238"],"award-info":[{"award-number":["2020JJ4238"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["19YBA098"],"award-info":[{"award-number":["19YBA098"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Hunan Province","award":["61872408"],"award-info":[{"award-number":["61872408"]}]},{"name":"Natural Science Foundation of Hunan Province","award":["2020JJ4238"],"award-info":[{"award-number":["2020JJ4238"]}]},{"name":"Natural Science Foundation of Hunan Province","award":["19YBA098"],"award-info":[{"award-number":["19YBA098"]}]},{"name":"Social Science Foundation of Hunan Province","award":["61872408"],"award-info":[{"award-number":["61872408"]}]},{"name":"Social Science Foundation of Hunan Province","award":["2020JJ4238"],"award-info":[{"award-number":["2020JJ4238"]}]},{"name":"Social Science Foundation of Hunan Province","award":["19YBA098"],"award-info":[{"award-number":["19YBA098"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>To improve the randomness of the Chebyshev chaotic sequences by coupling the Logistic map and the Chebyshev map, a new one-dimensional Logistic\u2013Chebyshev chaotic map (LCCM) is first presented in this paper. Several tests, including the bifurcation diagram, Lyapunov exponents, and information entropy, are employed to analyze the dynamics of the LCCM. The proposed LCCM has better ergodicity and unpredictability than the traditional Chebyshev map. Next, a new image encryption algorithm based on the LCCM and multi-level manipulation is proposed. The LCCM is used to control the pixel permutation, bit-level shuffling, and subsequent pixel diffusion based on the modulo and XOR operation. Extensive experiments, including histogram analysis, information entropy, adjacent pixel correlation, and key sensitivity, show that the image encryption algorithm has high security and can effectively resist malicious attacks.<\/jats:p>","DOI":"10.3390\/info14080456","type":"journal-article","created":{"date-parts":[[2023,8,14]],"date-time":"2023-08-14T10:40:31Z","timestamp":1692009631000},"page":"456","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Image Encryption Algorithm Using Multi-Level Permutation and Improved Logistic\u2013Chebyshev Coupled Map"],"prefix":"10.3390","volume":"14","author":[{"given":"Mingfang","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Computer Science, Hunan First Normal University, Changsha 410205, China"},{"name":"Hunan Provincial Key Laboratory of Informationization for Basic Education, Hunan First Normal University, Changsha 410205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hengfu","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer Science, Hunan First Normal University, Changsha 410205, China"},{"name":"Hunan Provincial Key Laboratory of Informationization for Basic Education, Hunan First Normal University, Changsha 410205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1142\/S021812749800098X","article-title":"Symmetric ciphers based on two-dimensional chaotic maps","volume":"8","author":"Fridrich","year":"1998","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Sabery, M.K., and Yaghoobi, M. (2008, January 20\u201322). A new approach for image encryption using chaotic Logistic map. Proceedings of the 2008 International Conference on Advanced Computer Theory and Engineering, Phuket, Thailand.","DOI":"10.1109\/ICACTE.2008.177"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ai-hong, Z., and Lian, L. (2010, January 17\u201318). Improving for chaotic image encryption algorithm based on logistic map. Proceedings of the 2010 the 2nd Conference on Environmental Science and Information Application Technology, Wuhan, China.","DOI":"10.1109\/ESIAT.2010.5568374"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hazarika, N., and Saikia, M. (2014, January 20\u201321). A novel partial image encryption using chaotic logistic map. 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Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Qi, F., Huang, S., Li, T., Yang, H., and Kang, X. (2019, January 10\u201312). 2D Henon-Chebyshev Chaotic map for image encryption. Proceedings of the 2019 IEEE 21st International Conference on High Performance Computing and Communications; IEEE 17th International Conference on Smart City; IEEE 5th International Conference on Data Science and Systems (HPCC\/SmartCity\/DSS), Zhangjiajie, China.","DOI":"10.1109\/HPCC\/SmartCity\/DSS.2019.00114"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106162","DOI":"10.1016\/j.asoc.2020.106162","article-title":"A novel image encryption scheme using both pixel level and bit level permutation with chaotic map","volume":"90","author":"Shahna","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Dai, Y., and Wang, X. (2012, January 6\u20138). 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