{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T02:56:31Z","timestamp":1784861791451,"version":"3.55.0"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T00:00:00Z","timestamp":1749168000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Chongqing, China","award":["CSTB2022NSCQ\u2013MSX1520"],"award-info":[{"award-number":["CSTB2022NSCQ\u2013MSX1520"]}]},{"name":"Natural Science Foundation of Chongqing, China","award":["20230201084GX"],"award-info":[{"award-number":["20230201084GX"]}]},{"name":"Jilin Provincial Department of Science and Technology, China","award":["CSTB2022NSCQ\u2013MSX1520"],"award-info":[{"award-number":["CSTB2022NSCQ\u2013MSX1520"]}]},{"name":"Jilin Provincial Department of Science and Technology, China","award":["20230201084GX"],"award-info":[{"award-number":["20230201084GX"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This study presents a novel two-dimensional hyperchaotic map, referred to as the 2D exponent-logarithm-sine chaotic map (2D-ELSCM), which is intricately designed through the interplay of exponential, logarithmic, and sine functions. To comprehensively evaluate the chaotic performance of the 2D-ELSCM, several critical metrics are employed, including the largest Lyapunov exponent (LLE), permutation entropy (PE), sample entropy (SE), Kolmogorov entropy (KE), and the results of the 0\u20131 test, which yield values of 8.3175, 0.9998, 1.9826, 2.1117, and 0.9970, respectively. Furthermore, the 2D-ELSCM successfully passes the NIST randomness tests, collectively confirming its exceptional randomness and complexity. Building upon this robust chaotic map, we develop a distinctive chaotic image encryption scheme that employs an improved Knuth-Durstenfeld shuffle (IKDS) to rearrange pixel positions, effectively disrupting the correlation between adjacent pixels. Complementing this, we introduce a dynamic diffusion mechanism that integrates DNA encoding with the Zigzag transform, thereby promoting global pixel diffusion and enhancing encryption security. The initial conditions of the chaotic map are generated from the SHA-512 hash of the plaintext image in conjunction with an external key, which not only expands the key space but also significantly improves key sensitivity. Simulation results demonstrate that the proposed encryption scheme achieves correlation coefficients approaching 0 in the encrypted test images, with an average NPCR of 99.6090% and UACI of 33.4707%. These findings indicate a strong resistance to various attacks and showcase excellent encryption quality, thereby underscoring the scheme\u2019s potential for secure image transmission and storage.<\/jats:p>","DOI":"10.3390\/e27060606","type":"journal-article","created":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T09:02:03Z","timestamp":1749200523000},"page":"606","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Robust Image Encryption with 2D Hyperchaotic Map and Dynamic DNA-Zigzag Encoding"],"prefix":"10.3390","volume":"27","author":[{"given":"Haijun","family":"Zhang","sequence":"first","affiliation":[{"name":"Chongqing Research Institute, Changchun University of Science and Technology, Chongqing 401135, China"},{"name":"School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaojiao","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0762-3871","authenticated-orcid":false,"given":"Kehan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rigen","family":"Te","sequence":"additional","affiliation":[{"name":"Chang Guang Satellite Technology Co., Ltd., Changchun 130000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8532-1978","authenticated-orcid":false,"given":"Fei","family":"Yan","sequence":"additional","affiliation":[{"name":"Chongqing Research Institute, Changchun University of Science and Technology, Chongqing 401135, China"},{"name":"School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,6]]},"reference":[{"key":"ref_1","first-page":"11","article-title":"Advanced encryption standard (AES) algorithm to encrypt and decrypt data","volume":"16","author":"Abdullah","year":"2017","journal-title":"Cryptogr. 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