{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T23:22:44Z","timestamp":1783552964189,"version":"3.55.0"},"reference-count":44,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,6]],"date-time":"2021-10-06T00:00:00Z","timestamp":1633478400000},"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":["51967019"],"award-info":[{"award-number":["51967019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As an essential part of an encryption system, the performance of a chaotic map is critical for system security. However, there are many defects for the existing chaotic maps. The low-dimension (LD) ones are easily predicted and are vulnerable to be attacked, while high-dimension (HD) ones have a low iteration speed. In this paper, a 2D multiple collapse chaotic map (2D-MCCM) was designed, which had a wide chaos interval, a high complexity, and a high iteration speed. Then, a new chaotic S-box was constructed based on 2D-MCCM, and a diffusion method was designed based on the S-box, which improved security and efficiency. Based on these, a new image encryption algorithm was proposed. Performance analysis showed that the encryption algorithm had high security to resist all kinds of attacks easily.<\/jats:p>","DOI":"10.3390\/e23101312","type":"journal-article","created":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T09:24:04Z","timestamp":1633598644000},"page":"1312","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["S-Box Design Based on 2D Multiple Collapse Chaotic Map and Their Application in Image Encryption"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3847-0887","authenticated-orcid":false,"given":"Chao","family":"Yang","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Xinjiang University, Urumqi 830046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xia","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Xinjiang University, Urumqi 830046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Xinjiang University, Urumqi 830046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1016\/j.promfg.2017.09.047","article-title":"Network and information security challenges within Industry 4.0 paradigm","volume":"13","author":"Pereira","year":"2017","journal-title":"Procedia Manuf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8660","DOI":"10.1109\/ACCESS.2018.2890116","article-title":"Image encryption using josephus problem and filtering diffusion","volume":"7","author":"Hua","year":"2019","journal-title":"IEEE Access"},{"key":"ref_3","first-page":"2317","article-title":"A novel image encryption using calligraphy based scan method and random number","volume":"9","author":"Sivakumar","year":"2015","journal-title":"KSII Trans. 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