{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T08:03:05Z","timestamp":1768896185921,"version":"3.49.0"},"reference-count":43,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,19]],"date-time":"2021-06-19T00:00:00Z","timestamp":1624060800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Reversible data hiding in the encrypted domain (RDH-ED) is a technique that protects the privacy of multimedia in the cloud service. In order to manage three-dimensional (3D) models, a novel RDH-ED based on prediction error expansion (PEE) is proposed. First, the homomorphic Paillier cryptosystem is utilized to encrypt the 3D model for transmission to the cloud. In the data hiding, a greedy algorithm is employed to classify vertices of 3D models into reference and embedded sets in order to increase the embedding capacity. The prediction value of the embedded vertex is computed by using the reference vertex, and then the module length of the prediction error is expanded to embed data. In the receiving side, the data extraction is symmetric to the data embedding, and the range of the module length is compared to extract the secret data. Meanwhile, the original 3D model can be recovered with the help of the reference vertex. The experimental results show that the proposed method can achieve greater embedding capacity compared with the existing RDH-ED methods.<\/jats:p>","DOI":"10.3390\/sym13061090","type":"journal-article","created":{"date-parts":[[2021,6,20]],"date-time":"2021-06-20T21:50:15Z","timestamp":1624225815000},"page":"1090","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Novel Reversible Data Hiding Method for 3D Model in Homomorphic Encryption Domain"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1762-148X","authenticated-orcid":false,"given":"Ting","family":"Luo","sequence":"first","affiliation":[{"name":"Collage of Science and Technology, Ningbo University, Ningbo 315000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Hangzhou Dianzi University, Hangzhou 330018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shanqin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Hangzhou Dianzi University, Hangzhou 330018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shenxian","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Hangzhou Dianzi University, Hangzhou 330018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Gu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Anhui University, Hefei 230039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,19]]},"reference":[{"key":"ref_1","unstructured":"He, X.W., Huang, T.T., Bai, S., and Bai, X. (November, January 27). View N-Gram network for 3D object retrieval. Proceedings of the IEEE\/CVF International Conference on Computer Vision (ICCV), Seoul, Korea."},{"key":"ref_2","first-page":"1","article-title":"Exploring deep learning for view-based 3D model retrieval. ACM Transactions on Multimedia Computing","volume":"16","author":"Gao","year":"2020","journal-title":"Commun. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.cag.2019.05.003","article-title":"Shrubbery-shell inspired 3D model stylization","volume":"82","author":"Zhang","year":"2019","journal-title":"Comput. Graph."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Lee, C.F., Shen, J.J., Agrawal, S., and Li, Y.H. (2021). High-capacity embedding method based on double-layer octagon-shaped shell matrix. Symmetry, 13.","DOI":"10.3390\/sym13040583"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1109\/TVCG.2005.71","article-title":"Blind robust data hiding schemes for copyright protection of 3D mesh objects","volume":"11","author":"Zafeiriou","year":"2005","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1016\/j.ijleo.2018.12.130","article-title":"Hiding clinical information in medical images: An encrypted dual-image reversible data hiding algorithm with base-3 numeral framework","volume":"181","author":"Bhardwaj","year":"2019","journal-title":"Optik"},{"key":"ref_7","unstructured":"Fridrich, J., Goljan, M., and Du, R. (2002, January 19\u201323). Lossless data embedding for all image formats. Proceedings of the SPIE 4675, Security and Watermarking of Multimedia Contents IV, San Jose, CA, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1109\/TCSVT.2003.815962","article-title":"Reversible Data embedding using a difference expansion","volume":"13","author":"Tian","year":"2003","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1109\/TCSVT.2006.869964","article-title":"Reversible data hiding","volume":"16","author":"Ni","year":"2006","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/TIP.2006.891046","article-title":"Expansion embedding techniques for reversible data hiding","volume":"16","author":"Thodi","year":"2007","journal-title":"IEEE Trans. Image Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.jvcir.2019.03.017","article-title":"Convolutional neural networks-based stereo image reversible data hiding method","volume":"61","author":"Luo","year":"2019","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5010","DOI":"10.1109\/TIP.2013.2281422","article-title":"Pairwise prediction-error expansion for efficient reversible data hiding","volume":"22","author":"Ou","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1109\/LSP.2019.2909080","article-title":"Reversible data hiding based on multiple two-dimensional histograms modification","volume":"26","author":"Qin","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_14","unstructured":"Dittmann, J., and Benedens, O. (2003, January 20\u201324). Invertible authentication for 3D meshes. Proceedings of the SPIE 5020, Security and Watermarking of Multimedia Contents V, Santa Clara, CA, USA."},{"key":"ref_15","unstructured":"Wu, H., and Ming, Y. (2005, January 19\u201322). A Reversible Data Hiding Approach to Mesh Authentication. Proceedings of the IEEE\/WIC\/ACM International Conference on Web Intelligence, Compiegne, France."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Jhou, C., Pan, J., and Chou, D. (2007, January 26\u201328). Reversible data hiding base on histogram shift for 3D vertex. Proceedings of the Third International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP 2007), Kaohsiung, Taiwan.","DOI":"10.1109\/IIH-MSP.2007.268"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Sun, Z., Lu, Z., and Li, Z. (2006, January 18\u201320). Reversible data hiding for 3D meshes in the PVQ-compressed domain. Proceedings of the IEEE International Conference on Intelligent Information Hiding and Multimedia Signal Processing, Pasadena, CA, USA.","DOI":"10.1109\/IIH-MSP.2006.265072"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Lu, Z., and Li, Z. (2008, January 19\u201321). High capacity reversible data hiding for 3D meshes in the PVQ domain. Proceedings of the International Workshop on Digital Data Hiding, Sana Barbara, CA, USA.","DOI":"10.1007\/978-3-540-92238-4_18"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wu, D., and Wang, G. (2009, January 22\u201324). A reversible watermarking scheme for 3D meshes. Proceedings of the International Conference on Active Media Technology, Beijing, China.","DOI":"10.1007\/978-3-642-04875-3_52"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wu, H., and Dugelay, J. (2008, January 8\u201310). Reversible watermarking of 3D mesh models by prediction-error expansion. Proceedings of the IEEE 10th Workshop on Multimedia Signal Processing, Queensland, Australia.","DOI":"10.1109\/MMSP.2008.4665183"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5263","DOI":"10.1007\/s11042-017-4430-6","article-title":"Reversible data hiding for 3D mesh models with three-dimensional prediction-error histogram modification","volume":"77","author":"Jiang","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"29713","DOI":"10.1007\/s11042-018-6219-7","article-title":"Reversible data hiding for 3D mesh models with hybrid prediction and multilayer strategy","volume":"78","author":"Zhang","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_23","first-page":"13906","article-title":"Secret sharing approaches for 3D object encryption","volume":"38","author":"Elsheh","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"115632","DOI":"10.1016\/j.image.2019.115632","article-title":"High-capacity reversible data hiding in encrypted image based on specific encryption process","volume":"80","author":"Huang","year":"2020","journal-title":"Signal Proces. Image Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"81412","DOI":"10.1109\/ACCESS.2020.2990903","article-title":"Separable reversible data hiding scheme in homomorphic encrypted domain based on ntru","volume":"8","author":"Zhou","year":"2020","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1109\/TCSVT.2015.2416591","article-title":"Secure reversible image data hiding over encrypted domain via key modulation","volume":"26","author":"Zhou","year":"2015","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_27","unstructured":"Gentry, C. (June, January 31). Fully homomorphic encryption using ideal lattices. Proceedings of the 41st ACM Symposium on Theory of Computing, Bethesda, MD, USA."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1137\/120868669","article-title":"Effificient fully homomorphic encryption from (standard) LWE","volume":"43","author":"Brakershi","year":"2014","journal-title":"Siam J. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.sigpro.2019.05.036","article-title":"Reversible data hiding in encrypted images with additive and multiplicative public-key homomorphism","volume":"164","author":"Chen","year":"2019","journal-title":"Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.sigpro.2013.06.023","article-title":"Reversibility improved data hiding in encrypted images","volume":"94","author":"Zhang","year":"2014","journal-title":"Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.image.2015.09.014","article-title":"Encrypted image-based reversible data hiding with public key cryptography from difference expansion","volume":"39","author":"Shiu","year":"2015","journal-title":"Signal Process. Image Commun."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1109\/TCYB.2015.2423678","article-title":"High capacity reversible data hiding in encrypted images by patch-level sparse representation","volume":"46","author":"Cao","year":"2016","journal-title":"IEEE Trans. Cybern."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1109\/LSP.2011.2114651","article-title":"Reversible data hiding in encrypted image","volume":"18","author":"Zhang","year":"2011","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1109\/LSP.2012.2187334","article-title":"An improved reversible data hiding in encrypted images using side match","volume":"19","author":"Hong","year":"2012","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1109\/TIFS.2011.2176120","article-title":"Separable reversible data hiding in encrypted image","volume":"16","author":"Zhang","year":"2012","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3099","DOI":"10.1109\/TCSVT.2017.2742023","article-title":"Reversible data hiding in homomorphic encrypted domain by mirroring ciphertext group","volume":"28","author":"Xiang","year":"2017","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.jvcir.2013.11.001","article-title":"Effificient reversible data hiding in encrypted images","volume":"25","author":"Zhang","year":"2014","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1109\/TCSVT.2015.2418611","article-title":"Reversible data hiding in encrypted image with distributed source encoding","volume":"26","author":"Qian","year":"2016","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1186\/s13634-017-0496-6","article-title":"Efficient reversible data hiding in encrypted image with public key cryptosystem","volume":"2017","author":"Xiang","year":"2017","journal-title":"Eurasip J. Adv. Signal Process."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"60635","DOI":"10.1109\/ACCESS.2018.2876036","article-title":"High-capacity reversible data hiding for encrypted multimedia data with somewhat homomorphic encryption","volume":"6","author":"Xiong","year":"2018","journal-title":"IEEE Access"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TMM.2017.2723244","article-title":"Reversible data hiding in encrypted three-dimensional mesh models","volume":"20","author":"Jiang","year":"2018","journal-title":"IEEE Trans. Multimed."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Li, L., Wang, S., Zhang, S., and Luo, T. (2020). Homomorphic encryption-based robust reversible data hiding for 3D model. Symmetry, 12.","DOI":"10.3390\/sym12030347"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Li, L., Wang, S., Luo, T., Chang, C.C., Zhou, Q., and Li, H. (2020). Reversible Data Hiding for Encrypted 3D Model Based on Prediction Error Expansion. J. Sens., 8851999.","DOI":"10.1155\/2020\/8851999"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/6\/1090\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:19:10Z","timestamp":1760163550000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/6\/1090"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,19]]},"references-count":43,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["sym13061090"],"URL":"https:\/\/doi.org\/10.3390\/sym13061090","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,19]]}}}