{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T15:39:27Z","timestamp":1766504367932,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T00:00:00Z","timestamp":1751328000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basic Scientific Research Operation Fund of Liaoning Provincial Universities in 2024","award":["LJ212410152016"],"award-info":[{"award-number":["LJ212410152016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>A dual watermark and DNA image encryption based on a chaotic map is proposed. Firstly, a new discrete chaotic map is proposed, and the dynamic characteristics are analyzed. Then, the hash value changes initial conditions, and the pseudo-random sequence is generated. The encrypted copyright image is fused with the feature value of the original image and then encrypted again to form zero-watermarking, which is registered with the copyright certification authority. The zero-watermarking is taken as a robust watermark and embedded into the original image based on a chaotic sequence to ensure its invisibility. Finally, a cross-mutation DNA encryption is proposed. The experimental results verify the performance of encryption and dual watermark copyright authentication, and the ability to resist attacks.<\/jats:p>","DOI":"10.3390\/cryptography9030049","type":"journal-article","created":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:45:08Z","timestamp":1751366708000},"page":"49","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Image Encryption with Dual Watermark Based on Chaotic Map"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5760-4903","authenticated-orcid":false,"given":"Ran","family":"Chu","sequence":"first","affiliation":[{"name":"Information Science and Engineering College, Dalian Polytechnic University, Dalian 116034, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7774-2833","authenticated-orcid":false,"given":"Jun","family":"Mou","sequence":"additional","affiliation":[{"name":"Information Science and Engineering College, Dalian Polytechnic University, Dalian 116034, China"}]},{"given":"Yuanhui","family":"Cui","sequence":"additional","affiliation":[{"name":"Information Science and Engineering College, Dalian Polytechnic University, Dalian 116034, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18115","DOI":"10.1109\/JIOT.2025.3540097","article-title":"A Parallel Color Image Encryption Algorithm Based on a 2-D Logistic-Rulkov Neuron Map","volume":"12","author":"Gao","year":"2025","journal-title":"IEEE Internet Things J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102336","DOI":"10.1016\/j.vlsi.2024.102336","article-title":"Image encryption algorithm based on the dynamic RNA computing and a new chaotic map","volume":"101","author":"Zhou","year":"2025","journal-title":"Integration"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"116088","DOI":"10.1016\/j.chaos.2025.116088","article-title":"Novel hyperchaotic system: Implementation to audio encryption","volume":"193","author":"Zhou","year":"2025","journal-title":"Chaos Solitons Fractals"},{"key":"ref_4","first-page":"102","article-title":"Based zero-watermark digital watermarking technology","volume":"Volume 109","author":"Wen","year":"2001","journal-title":"Proceedings of the 3rd National Conference in Information Hiding"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"102804","DOI":"10.1016\/j.jvcir.2020.102804","article-title":"Combining polar harmonic transforms and 2D compound chaotic map for distinguishable and robust color image zero-watermarking algorithm","volume":"70","author":"Kang","year":"2020","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_6","first-page":"160","article-title":"A Zero Watermarking Scheme with Strong Robustness in Spatial Domain","volume":"44","author":"Xiong","year":"2018","journal-title":"Acta Autom. Sin."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7599","DOI":"10.1007\/s11042-019-08459-3","article-title":"A robust zero-watermarking algorithm for color image based on tensor mode expansion","volume":"79","author":"Jiang","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chen, J., Sun, Y., and Yang, M. (2021). Zero-Watermarking Algorithm Based on Modified Singular Value and Chaos Scrambling. International Conference on Intelligent Automation and Soft Computing, Springer.","DOI":"10.1007\/978-3-030-81007-8_125"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Xi, X., Zhang, X., Liang, W., Xin, Q., and Zhang, P. (2019). Dual Zero-Watermarking Scheme for Two-Dimensional Vector Map Based on Delaunay Triangle Mesh and Singular Value Decomposition. Appl. Sci., 9.","DOI":"10.3390\/app9040642"},{"key":"ref_10","first-page":"43","article-title":"Dual-watermarking scheme for copyright and privacy protection in medical image","volume":"46","author":"Shi","year":"2023","journal-title":"Joummal Liaoning Norm. Univ."},{"key":"ref_11","first-page":"0617001","article-title":"Double Watermarking Algorithm for Tamper Detection of Medical Images","volume":"60","author":"Miao","year":"2023","journal-title":"Laser Optoelectron. Prog."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2250186","DOI":"10.1142\/S0218127422501863","article-title":"A chaotic image encryption scheme based on genetic central dogma and kmp method","volume":"32","author":"Sha","year":"2022","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S012918312550010X","article-title":"Constructing a novel n-dimensional chaotic map with application to image encryption","volume":"36","author":"Zhou","year":"2025","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"9082","DOI":"10.1109\/JIOT.2024.3506118","article-title":"Novel n-Dimensional Nondegenerate Discrete Hyperchaotic Map with Any Desired Lyapunov Exponents","volume":"12","author":"Zhou","year":"2025","journal-title":"IEEE Internet Things J."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Gao, S., Iu, H.H.-C., Erkan, U., Simsek, C., Toktas, A., Cao, Y., Wu, R., Mou, J., Li, Q., and Wang, C. (2025). A 3D Memristive Cubic Map with Dual Discrete Memristors: Design, Implementation, and Application in Image Encryption. IEEE Transactions on Circuits and Systems for Video Technology, IEEE.","DOI":"10.1109\/TCSVT.2025.3545868"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2557","DOI":"10.1109\/TIE.2017.2736515","article-title":"Sine-Transform-Based Chaotic System with FPGA Implementation","volume":"65","author":"Hua","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"25711","DOI":"10.1007\/s11042-021-10764-9","article-title":"A flexible image encryption algorithm based on 3D CTBCS and DNA computing","volume":"80","author":"Xu","year":"2021","journal-title":"Multimed. Tools Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjp\/s13360-022-02734-3","article-title":"A new set of hyperchaotic maps based on modulation and coupling","volume":"137","author":"Han","year":"2022","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1007\/s13198-019-00855-0","article-title":"A multipurpose image watermarking scheme for digital image protection","volume":"11","author":"Sinhal","year":"2019","journal-title":"Int. J. Syst. Assur. Eng. Manag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.jss.2011.08.017","article-title":"A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system","volume":"85","author":"Wei","year":"2012","journal-title":"J. Syst. Softw."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Gao, X., Yu, J., Banerjee, S., Yan, H., and Mou, J. (2021). A new image encryption scheme based on fractional-order hyperchaotic system and multiple image fusion. Sci. Rep., 11.","DOI":"10.1038\/s41598-021-94748-7"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"03017","DOI":"10.1051\/matecconf\/202030903017","article-title":"Color image encryption via compressive sensing and chaotic systems","volume":"309","author":"Joo","year":"2020","journal-title":"MATEC Web Conf."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.sigpro.2018.09.029","article-title":"A color image cryptosystem based on dynamic DNA encryption and chaos","volume":"155","author":"Chai","year":"2019","journal-title":"Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"12845","DOI":"10.1007\/s00521-021-05937-4","article-title":"Exploiting 2D compressed sensing and information entropy for secure color image compression and encryption","volume":"33","author":"Gan","year":"2021","journal-title":"Neural Comput. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"106139","DOI":"10.1016\/j.optlaseng.2020.106139","article-title":"Triple color image encryption based on 2D multiple parameter fractional discrete Fourier transform and 3D Arnold transform","volume":"133","author":"Joshi","year":"2020","journal-title":"Opt. Lasers Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"33865","DOI":"10.1007\/s11042-019-08171-2","article-title":"Fast encryption scheme for 3D models based on chaos system","volume":"78","author":"Wang","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1007\/s11042-019-08191-y","article-title":"Robust and secure zero-watermarking algorithm for color images based on majority voting pattern and hyper-chaotic encryption","volume":"79","author":"Kang","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"91209","DOI":"10.1109\/ACCESS.2021.3091614","article-title":"New Color Image Zero-Watermarking Using Orthogonal Multi-Channel Fractional-Order Legendre-Fourier Moments","volume":"9","author":"Hosny","year":"2021","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5669","DOI":"10.1007\/s11042-021-11802-2","article-title":"Image encryption using DNA coding and three-dimensional chaotic systems","volume":"81","author":"Nazir","year":"2022","journal-title":"Multimed. Tools Appl."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhang, D., Chen, L., and Li, T. (2021). Hyper-Chaotic Color Image Encryption Based on Transformed Zigzag Diffusion and RNA Operation. Entropy, 23.","DOI":"10.3390\/e23030361"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s12530-021-09369-2","article-title":"Neural network based CT-Canny edge detector considering watermarking framework","volume":"13","author":"Kazemi","year":"2021","journal-title":"Evol. Syst."},{"key":"ref_32","first-page":"565","article-title":"Robust Multi-Watermarking Algorithm for Medical Images Based on GoogLeNet and Henon Map","volume":"75","author":"Zhang","year":"2023","journal-title":"Comput. Mater. Contin."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4863","DOI":"10.1007\/s11042-016-3862-8","article-title":"A proposed secure multiple watermarking technique based on DWT, DCT and SVD for application in medicine","volume":"77","author":"Zear","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"30523","DOI":"10.1007\/s11042-018-7115-x","article-title":"Robust and distortion control dual watermarking in LWT domain using DCT and error correction code for color medical image","volume":"78","author":"Singh","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_35","first-page":"629","article-title":"Zero watermarking scheme based on U and V matrices of quaternion singular value decomposition for color images","volume":"9","author":"Liu","year":"2018","journal-title":"J. Inf. Hiding Multimed. Signal Process."},{"key":"ref_36","first-page":"1391","article-title":"Zero-watermarking algorithm in transform domain based on RGB channel and voting strategy","volume":"16","author":"Zheng","year":"2020","journal-title":"J. Inf. Process. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"8024","DOI":"10.1016\/j.eswa.2010.12.129","article-title":"An intelligent watermarking method based on particle swarm optimization","volume":"38","author":"Wang","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_38","first-page":"107","article-title":"Zero-watermarking algorithm for color image based on DWT-DCT-SVD","volume":"33","author":"Jiang","year":"2016","journal-title":"Microelectron. Comput."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"4449","DOI":"10.7498\/aps.58.4449","article-title":"A novel zero-bit watermarking algorithm based on Logistic chaotic system and singular value decomposition","volume":"58","author":"Song","year":"2009","journal-title":"Acta Phys. Sin."},{"key":"ref_40","first-page":"2810","article-title":"Novel blind image watermarking based on pseudo Zernike moments","volume":"33","author":"Chen","year":"2016","journal-title":"Appl. Res. Comput."},{"key":"ref_41","first-page":"494","article-title":"Fast Zero-Watermarking Algorithm Based on Schur Decomposition","volume":"13","author":"Liu","year":"2019","journal-title":"J. Front. Comput. Sci. Technol."},{"key":"ref_42","first-page":"3387","article-title":"Research on zero watermarking algorithm for hyper-chaos-based image","volume":"36","author":"Zhang","year":"2019","journal-title":"Appl. Res. Comput."},{"key":"ref_43","first-page":"399","article-title":"A zero-watermark algorithm of color image based on DWT and SVD","volume":"31","author":"Pan","year":"2011","journal-title":"J. Guilin Univ. Electron. Technol."}],"container-title":["Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2410-387X\/9\/3\/49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:02:39Z","timestamp":1760032959000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2410-387X\/9\/3\/49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,1]]},"references-count":43,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["cryptography9030049"],"URL":"https:\/\/doi.org\/10.3390\/cryptography9030049","relation":{},"ISSN":["2410-387X"],"issn-type":[{"type":"electronic","value":"2410-387X"}],"subject":[],"published":{"date-parts":[[2025,7,1]]}}}