{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T14:37:32Z","timestamp":1777559852679,"version":"3.51.4"},"reference-count":48,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T00:00:00Z","timestamp":1727654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Laboratory of Target Cognition and Application Technology","award":["2023-CXPT-LC-005"],"award-info":[{"award-number":["2023-CXPT-LC-005"]}]},{"name":"Key Laboratory of Target Cognition and Application Technology","award":["D040404"],"award-info":[{"award-number":["D040404"]}]},{"name":"Civil Aerospace Technology Pre-research Project of China\u2019s 14th Five-Year Plan","award":["2023-CXPT-LC-005"],"award-info":[{"award-number":["2023-CXPT-LC-005"]}]},{"name":"Civil Aerospace Technology Pre-research Project of China\u2019s 14th Five-Year Plan","award":["D040404"],"award-info":[{"award-number":["D040404"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The design of a chaotic system and pseudo-random sequence generation method with excellent performance and its application in image encryption have always been attractive and challenging research fields. In this paper, a new model of parameter-variabled coupled chaotic system (PVCCS) is established by interaction coupling between parameters and states of multiple low-dimensional chaotic systems, and a new way to construct more complex hyperchaotic systems from simple low-dimensional systems is obtained. At the same time, based on this model and dynamical DNA codings and operations, a new pseudo-random sequence generation method (PSGM-3DPVCCS\/DNA) is proposed, and it is verified that the generated pseudo-random sequence of PSGM-3DPVCCS\/DNA has excellent random characteristics. Furthermore, this paper designs a novel pixel chain diffusion image encryption algorithm based on the proposed parameter-variabled coupled chaotic system (PVCCS) in which the hash value of plaintext image is associated with the initial key to participate in the encryption process so that the encryption key is closely associated with plaintext, which improves the security of the algorithm and effectively resists the differential cryptanalysis risk. In addition, an information hiding method is designed to hide the hash value of plaintext image in ciphertext image so that the hash value does not need to be transmitted in each encryption, and the initial key can be reused, which solves the key management problem in application and improves the application efficiency of the encryption algorithm. The experimental analysis shows that the chaotic system constructed in this paper is creative and universal and has more excellent chaotic characteristics than the original low-dimensional system. The sequence generated by the pseudo-random sequence generation method has excellent pseudo-random characteristics and security, and the image encryption algorithm can effectively resist differential cryptanalysis risk, showing advanced encryption performance.<\/jats:p>","DOI":"10.3390\/e26100832","type":"journal-article","created":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T10:00:47Z","timestamp":1727690447000},"page":"832","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Novel Parameter-Variabled and Coupled Chaotic System and Its Application in Image Encryption with Plaintext-Related Key Concealment"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7679-0171","authenticated-orcid":false,"given":"Zuxi","family":"Wang","sequence":"first","affiliation":[{"name":"National Key Laboratory of Multispectral Information Intelligent Processing Technology, Wuhan 430074, China"},{"name":"Key Laboratory of Image Information Processing and Intelligent Control, Ministry of Education of China, Wuhan 430074, China"},{"name":"School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-5567-7609","authenticated-orcid":false,"given":"Siyang","family":"Wang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Multispectral Information Intelligent Processing Technology, Wuhan 430074, China"},{"name":"Key Laboratory of Image Information Processing and Intelligent Control, Ministry of Education of China, Wuhan 430074, China"},{"name":"School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8256-0156","authenticated-orcid":false,"given":"Zhong","family":"Chen","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Multispectral Information Intelligent Processing Technology, Wuhan 430074, China"},{"name":"Key Laboratory of Image Information Processing and Intelligent Control, Ministry of Education of China, Wuhan 430074, China"},{"name":"School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Boyun","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,30]]},"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","first-page":"105","article-title":"An improved image encryption algorithm based on chaotic logistic map","volume":"23","author":"Wang","year":"2012","journal-title":"Int. Symp. Comput. Intell. Des."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"34323","DOI":"10.1007\/s11042-019-08072-4","article-title":"Image encryption based on Henon chaotic system with nonlinear term","volume":"78","author":"Luo","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1007\/s11071-015-2392-7","article-title":"A novel chaos-based image encryption using dna sequence operation and secure hash algorithm sha-2","volume":"83","author":"Guesmi","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_5","unstructured":"Yang, B., Deng, C., Wu, P., Xi, J., and Shi, L. (2014, January 27\u201329). Image encryption algorithm based on two-one-dimension logistic chaotic inter-scrambling systems and m-sequence. Proceedings of the 2014 IEEE 5th International Conference on Software Engineering and Service Science, Beijing, China."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.ins.2014.11.018","article-title":"2D Sine Logistic modulation map for image encryption","volume":"297","author":"Hua","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"065214","DOI":"10.1088\/1402-4896\/ad418d","article-title":"Local bit-level image encryption algorithm based on one dimensional zero excluded chaotic map","volume":"99","author":"Feng","year":"2024","journal-title":"Phys. Scr."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wan, Y., Gu, S., and Du, B. (2020). A New Image Encryption Algorithm Based on Composite Chaos and Hyperchaos Combined with DNA Coding. Entropy, 22.","DOI":"10.3390\/e22020171"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"27785","DOI":"10.1007\/s11042-021-10970-5","article-title":"Novel pseudo random key & cosine transformed chaotic maps based satellite image encryption","volume":"80","author":"Kumar","year":"2021","journal-title":"Multim. Tools Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.asr.2019.09.027","article-title":"An improved image encryption algorithm for satellite applications","volume":"66","author":"Bentoutou","year":"2020","journal-title":"Adv. Sp. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3234","DOI":"10.1007\/s10773-016-2954-6","article-title":"Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations","volume":"55","author":"Gong","year":"2016","journal-title":"Int. J. Theor. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Peng, J., Yang, W., Jin, S., Pang, S., Tang, D., Bai, J., and Zhang, D. (2020, January 9\u201313). Image Encryption Based on Fractional-order Chen Hyperchaotic System. Proceedings of the 15th IEEE Conference on Industrial Electronics and Applications (ICIEA), Kristiansand, Norway.","DOI":"10.1109\/ICIEA48937.2020.9248115"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1240","DOI":"10.1016\/j.compeleceng.2012.02.007","article-title":"A RGB image encryption algorithm based on DNA encoding and Chaos Map","volume":"38","author":"Liu","year":"2012","journal-title":"Comput. Electr. Eng. Des."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"148935","DOI":"10.1109\/ACCESS.2020.3015687","article-title":"A New Fuzzy-DNA Image Encryption and Steganography Technique","volume":"8","author":"Korany","year":"2020","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"65450","DOI":"10.1109\/ACCESS.2019.2917498","article-title":"A Remote-Sensing Image Encryption Scheme Using DNA Bases Probability and Two-Dimensional Logistic Map","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1080\/02564602.2019.1595751","article-title":"Secure, Lossless, and Noise-resistive Image Encryption using Chaos, Hyper-chaos, and DNA Sequence Operation","volume":"37","author":"Patro","year":"2020","journal-title":"Iete Tech. Rev."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3673","DOI":"10.1007\/s11071-021-06761-0","article-title":"An efficient block-level image encryption scheme based on multi-chaotic maps with DNA encoding","volume":"105","author":"Naskar","year":"2021","journal-title":"Nonlinear Dyn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6303","DOI":"10.1007\/s11042-015-2573-x","article-title":"Chaos-based image encryption scheme combining DNA coding and entropy","volume":"75","author":"Zhen","year":"2015","journal-title":"Multimed. Tools Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"21579","DOI":"10.1007\/s11042-020-08880-z","article-title":"A multidimensional chaotic image encryption algorithm based on DNA coding","volume":"79","author":"Liu","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.optlaseng.2016.08.009","article-title":"A novel chaos-based image encryption algorithm using dna sequence operations","volume":"88","author":"Chai","year":"2017","journal-title":"Opt. Lasers Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"012028","DOI":"10.1088\/1742-6596\/974\/1\/012028","article-title":"Implementation of digital image encryption algorithm using logistic function and DNA encoding","volume":"974","author":"Suryadi","year":"2018","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Li, Y., and Xu, J. (2021, January 12\u201314). Image Encryption System Based On Chaotic System And DNA Computing. Proceedings of the 2021 2nd International Conference on Computer Engineering and Intelligent Control (ICCEIC), Chongqing, China.","DOI":"10.1109\/ICCEIC54227.2021.00028"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.asoc.2012.01.016","article-title":"Image encryption using DNA complementary rule and chaotic maps","volume":"12","author":"Liu","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1049\/iet-ipr.2019.0051","article-title":"Chaotic image encryption algorithm using frequency-domain DNA encoding","volume":"13","author":"Guan","year":"2019","journal-title":"Iet Image Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/j.compeleceng.2015.03.011","article-title":"Security analysis on a color image encryption based on dna encoding and chaos map","volume":"46","author":"Wang","year":"2015","journal-title":"Comput. Electr. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Xiao, Y., and Tong, X. (2021, January 20\u201322). An Image Encryption Algorithm Based on Four Dimensional Hyperchaotic System. Proceedings of the 2021 IEEE 12th International Conference on Software Engineering and Service Science (ICSESS), Beijing, China.","DOI":"10.1109\/ICSESS52187.2021.9522277"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"22231","DOI":"10.1007\/s11042-022-13461-3","article-title":"The unified image encryption algorithm based on composite chaotic system","volume":"82","author":"Zheng","year":"2022","journal-title":"Multimed. Tools Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"15977","DOI":"10.1007\/s11042-022-12623-7","article-title":"A secure and robust image encryption algorithm based on compressive sensing and DNA coding","volume":"81","author":"Bao","year":"2022","journal-title":"Multimed. Tools Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"21779","DOI":"10.1007\/s11042-022-12472-4","article-title":"A novel hyperchaotic encryption algorithm for color image utilizing DNA dynamic encoding and self-adapting permutation","volume":"81","author":"Liu","year":"2022","journal-title":"Multimed. Tools Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"29901","DOI":"10.1007\/s11042-020-09454-9","article-title":"An efficient image encryption algorithm based on multi chaotic system and random DAN coding","volume":"79","author":"Zheng","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6645","DOI":"10.1007\/s12652-021-03532-y","article-title":"Evaluation and performance analysis of Chinese remainder theorem and its application to lossless image compression","volume":"14","author":"Vidhya","year":"2021","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Guo, L., Chen, J., and Li, J. (2016, January 16\u201318). Chaos-Based color image encryption and compression scheme using DNA complementary rule and Chinese remainder theorem. Proceedings of the 2016 13th International Computer Conference on Wavelet Active Media Technology and Information Processing (ICCWAMTIP), Chengdu, China.","DOI":"10.1109\/ICCWAMTIP.2016.8079839"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"106408","DOI":"10.1016\/j.neunet.2024.106408","article-title":"Dynamics of heterogeneous Hopfield neural network with adaptive activation function based on memristor","volume":"178","author":"Wang","year":"2024","journal-title":"Neural Netw."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"14463","DOI":"10.1007\/s11071-024-09791-6","article-title":"Symmetric multi-double-scroll attractors in Hopfield neural network under pulse controlled memristor","volume":"112","author":"Li","year":"2024","journal-title":"Nonlinear. Dyn"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"114387","DOI":"10.1016\/j.chaos.2023.114387","article-title":"Memristive Hopfield neural network dynamics with heterogeneous activation functions and its application","volume":"178","author":"Deng","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"7859","DOI":"10.1007\/s11071-023-08230-2","article-title":"3D variable-structure chaotic system and its application in color image encryption with new Rubik\u2019s Cube-like permutation","volume":"111","author":"Xin","year":"2023","journal-title":"Nonlinear Dyn."},{"key":"ref_37","unstructured":"(2002). National Institute of Standards and Technology, Security Requirements for Cryptographic Modules (Standard No. Federal Information Processing Standards Publications (FIPS PUBS) 140-2)."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2797","DOI":"10.1007\/s11071-018-4723-y","article-title":"A fast image encryption algorithm based on non-adjacent dynamically coupled map lattice model","volume":"95","author":"Wang","year":"2019","journal-title":"Nonlinear Dyn."},{"key":"ref_39","unstructured":"Rukhin, A. (2010). A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, NIST Special Publication."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"119076","DOI":"10.1016\/j.eswa.2022.119076","article-title":"2D hyperchaotic system based on Schaffer function for image encryption","volume":"213","author":"Erkan","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1109\/MMUL.2022.3194066","article-title":"3D-BCNN-Based Image Encryption With Finite Computing Precision","volume":"29","author":"Kong","year":"2022","journal-title":"IEEE Multimed."},{"key":"ref_42","unstructured":"Ye, X., and Wang, X. (IEEE Multimed., 2022). Design A Novel Image Encryption Algorithm Based on A PRNG with High Performance, IEEE Multimed., early access."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"122030","DOI":"10.1016\/j.eswa.2023.122030","article-title":"Region of interest-based medical image encryption technique based on chaotic S-boxes","volume":"238","author":"Jamal","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"119923","DOI":"10.1016\/j.eswa.2023.119923","article-title":"A cross-channel color image encryption algorithm using two-dimensional hyperchaotic map","volume":"223","author":"Lai","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1109\/MMUL.2021.3080579","article-title":"Characteristic Analysis of 2D Lag-Complex Logistic Map and Its Application in Image Encryption","volume":"28","author":"Zhang","year":"2021","journal-title":"IEEE Multimed."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1007\/s11071-021-06663-1","article-title":"Color image encryption based on cross 2D hyperchaotic map using combined cycle shift scrambling and selecting diffusion","volume":"105","author":"Teng","year":"2021","journal-title":"Nonlinear Dyn."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2869","DOI":"10.1007\/s11071-022-07756-1","article-title":"A color image encryption algorithm based on hyperchaotic map and Rubik\u2019s Cube scrambling","volume":"110","author":"Qiu","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1007\/s11071-018-4390-z","article-title":"A pseudo-random numbers generator based on a novel 3D chaotic map with an application to color image encryption","volume":"94","author":"Sahari","year":"2018","journal-title":"Nonlinear Dyn."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/10\/832\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:07:50Z","timestamp":1760112470000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/10\/832"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,30]]},"references-count":48,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["e26100832"],"URL":"https:\/\/doi.org\/10.3390\/e26100832","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,30]]}}}