{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:43:04Z","timestamp":1785404584091,"version":"3.56.0"},"reference-count":26,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T00:00:00Z","timestamp":1784678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Open Project of the Key Laboratory of Intelligent Control Technology for Wuling-Mountain Ecological Agriculture in Hunan Province, China","award":["ZNKZD2024-9"],"award-info":[{"award-number":["ZNKZD2024-9"]}]},{"name":"Key Scientific Research Project of the Education Department of Hunan Province, China","award":["25A0578"],"award-info":[{"award-number":["25A0578"]}]},{"award":["25A0578"],"award-info":[{"award-number":["25A0578"]}],"id":[{"id":"https:\/\/ror.org\/05ckg3w11","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we propose a novel image encryption algorithm that integrates a six-dimensional hyperchaotic system with the forward diffusion process of denoising diffusion probabilistic models (DDPMs). The proposed framework synergistically combines the hyperchaotic system\u2019s high sensitivity to initial conditions with the DDPM\u2019s Markov chain-based skipping-step diffusion mechanism, thereby enabling dual-level confusion-diffusion operations at both the pixel and bit levels. This dual-strategy approach significantly enhances plaintext sensitivity and ciphertext randomness. Comprehensive simulations demonstrate that the algorithm achieves superior performance in key space expansion, histogram uniformity, adjacent pixel correlation reduction, information entropy optimization, and resistance to differential attacks. The algorithm exhibits strong resilience against various attack vectors, including brute-force attacks, statistical analysis, chosen-plaintext attacks and common image degradation factors (e.g., noise contamination and cropping). These characteristics establish the proposed method as a highly secure and practical solution for image data protection in cloud-IoT environments.<\/jats:p>","DOI":"10.3390\/e28070831","type":"journal-article","created":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T01:01:28Z","timestamp":1784768488000},"page":"831","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Image Encryption via DDPM Skipping-Step Diffusion Based on a Six-Dimensional Hyperchaotic System with Feedback Control"],"prefix":"10.3390","volume":"28","author":[{"given":"Songran","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Computational Sciences, Huaihua University, Huaihua 418000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hanqing","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Hubei Minzu University, Enshi 445000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"He","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computational Sciences, Huaihua University, Huaihua 418000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Hubei Minzu University, Enshi 445000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiben","family":"Zhuang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computational Sciences, Huaihua University, Huaihua 418000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianfu","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Hubei Minzu University, Enshi 445000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiacheng","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Hubei Minzu University, Enshi 445000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,22]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Research on the new development of image encryption algorithms","volume":"34","author":"Zhang","year":"2012","journal-title":"Comput. 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