{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T16:54:02Z","timestamp":1783788842719,"version":"3.55.0"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,21]],"date-time":"2023-01-21T00:00:00Z","timestamp":1674259200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Council of the Republic of China","award":["MOST 110-2221-E-153-002-MY2"],"award-info":[{"award-number":["MOST 110-2221-E-153-002-MY2"]}]},{"name":"National Science and Technology Council of the Republic of China","award":["MOST 111-2221-E-153-005"],"award-info":[{"award-number":["MOST 111-2221-E-153-005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Reversible Data Hiding in Encrypted Image (RDHEI) is a technology for embedding secret information in an encrypted image. It allows the extraction of secret information and lossless decryption and the reconstruction of the original image. This paper proposes an RDHEI technique based on Shamir\u2019s Secret Sharing technique and multi-project construction technique. Our approach is to let the image owner hide the pixel values in the coefficients of the polynomial by grouping the pixels and constructing a polynomial. Then, we substitute the secret key into the polynomial through Shamir\u2019s Secret Sharing technology. It enables the Galois Field calculation to generate the shared pixels. Finally, we divide the shared pixels into 8 bits and allocate them to the pixels of the shared image. Thus, the embedded space is vacated, and the generated shared image is hidden in the secret message. The experimental results demonstrate that our approach has a multi-hider mechanism and each shared image has a fixed embedding rate, which does not decrease as more images are shared. Additionally, the embedding rate is improved compared with the previous approach.<\/jats:p>","DOI":"10.3390\/e25020209","type":"journal-article","created":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T02:27:45Z","timestamp":1674440865000},"page":"209","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Reversible Data Hiding in Encrypted Image Using Multiple Data-Hiders Sharing Algorithm"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0619-1966","authenticated-orcid":false,"given":"Chi-Yao","family":"Weng","sequence":"first","affiliation":[{"name":"Department of Computer Science and Artificial Intelligence, National Pingtung University, Pingtung 900, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheng-Hsing","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Artificial Intelligence, National Pingtung University, Pingtung 900, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1109\/TIFS.2009.2035975","article-title":"Reversible image watermarking using interpolation technique","volume":"5","author":"Luo","year":"2010","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"3000","DOI":"10.1016\/j.sigpro.2012.05.034","article-title":"Reversible image watermarking on prediction errors by efficient histogram modification","volume":"92","author":"Wu","year":"2012","journal-title":"Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Xuan, G., Yao, Q., Yang, C., Gao, J., Chai, P., Shi, Y.Q., and Ni, Z. (2006, January 8\u201310). Lossless Data Hiding Using Histogram Shifting Method Base on Integer Wavelets. Proceedings of the International Workshop on Digital Watermarking, LNCS, Jeju Island, Republic of Korea.","DOI":"10.1007\/11922841_26"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1109\/TCSVT.2009.2017409","article-title":"Reversible data hiding based on histogram modification of pixel differences","volume":"19","author":"Tai","year":"2009","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1109\/TIP.2004.840686","article-title":"Lossless generalized-LSB data embedding","volume":"14","author":"Celik","year":"2005","journal-title":"IEEE Trans. Image Process."},{"key":"ref_8","unstructured":"Fridrich, J., Goljan, M., and Du, R. (2002, January 19). Lossless data embedding for all image formats. Proceedings of the SPIE- International Society for Optical Engineering, San Jose, CA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.image.2019.115715","article-title":"Reversible data hiding based on RSBEMD coding and adaptive multi-segment left and right histogram shifting","volume":"81","author":"Peng","year":"2020","journal-title":"Signal Process. Image Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sigpro.2020.107817","article-title":"Reversible data hiding with automatic contrast enhancement for medical images","volume":"178","author":"Gao","year":"2021","journal-title":"Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1109\/TIFS.2013.2248725","article-title":"Reversible data hiding in encrypted images by reserving room before encryption","volume":"8","author":"Ma","year":"2013","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1109\/TCYB.2015.2423678","article-title":"High capacity reversible data hiding in encrypted image by patch-level sparse representation","volume":"46","author":"Cao","year":"2016","journal-title":"IEEE Trans. Cybern."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1670","DOI":"10.1109\/TIFS.2018.2799381","article-title":"An efficient MSB prediction-based method for high -capacity reversible data hiding in encrypted images","volume":"13","author":"Puteaux","year":"2018","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"62361","DOI":"10.1109\/ACCESS.2019.2916355","article-title":"High-capacity reversible data hiding in encrypted images by bit plane partition and MSB prediction","volume":"7","author":"Wu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Yi, S., and Zhou, Y. (2017, January 17\u201320). Adaptive code embedding for reversible data hiding in encrypted images. Proceedings of the IEEE International Conference on Image Processing (ICIP), Beijing, China.","DOI":"10.1109\/ICIP.2017.8297098"},{"key":"ref_16","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_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sigpro.2021.108146","article-title":"Reversible data hiding in encrypted images based on pixel prediction and multi-MSB planes rearrangement","volume":"187","author":"Yin","year":"2021","journal-title":"Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.ins.2019.03.008","article-title":"An efficient coding scheme for reversible data hiding in encrypted image with redundancy transfer","volume":"487","author":"Qin","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"175671","DOI":"10.1109\/ACCESS.2019.2957143","article-title":"A New High Capacity Separable Reversible Data Hiding in Encrypted Images Based on Block Selection and Block-Level Encryption","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.sigpro.2017.09.017","article-title":"Adopting secret sharing for reversible data hiding in encrypted images","volume":"143","author":"Wu","year":"2018","journal-title":"Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3332","DOI":"10.1109\/TIFS.2019.2914557","article-title":"A new reversible data hiding in encrypted image based on multi-secret sharing and lightweight cryptographic algorithms","volume":"14","author":"Chen","year":"2019","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_22","first-page":"978","article-title":"Secret sharing based reversible data hiding in encrypted images with multiple data-hiders","volume":"19","author":"Chen","year":"2022","journal-title":"IEEE Trans. Dependable Secur. 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