{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T21:58:41Z","timestamp":1768687121761,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,8]],"date-time":"2019-01-08T00:00:00Z","timestamp":1546905600000},"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>As a popular technology in information security, secret image sharing is a method to guarantee the secret image\u2019s security. Usually, the dealer would decompose the secret image into a series of shadows and then assign them to a number of participants, and only a quorum of participants could recover the secret image. Generally, it is assumed that every participant is equal. Actually, due to their position in many practical applications, some participants are given special privileges. Therefore, it is desirable to give an approach to generate shadows with different priorities shadows. In this paper, an efficient essential secret image sharing scheme using a derivative polynomial is proposed. Compared with existing related works, our proposed scheme can not only create the same-sized shadows with smaller size but also removes the concatenation operation in the sharing phase. Theoretical analysis and simulations confirm the security and effectiveness of the proposed scheme.<\/jats:p>","DOI":"10.3390\/sym11010069","type":"journal-article","created":{"date-parts":[[2019,1,9]],"date-time":"2019-01-09T03:06:06Z","timestamp":1547003166000},"page":"69","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["An Efficient Essential Secret Image Sharing Scheme Using Derivative Polynomial"],"prefix":"10.3390","volume":"11","author":[{"given":"Zhen","family":"Wu","sequence":"first","affiliation":[{"name":"School of Information and Communication, Guilin University of Electronic Technology, Guilin 451000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6487-7595","authenticated-orcid":false,"given":"Yi-Ning","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Information and Communication, Guilin University of Electronic Technology, Guilin 451000, China"},{"name":"Guangxi Key Laboratory of Trusted Software, Guilin University of Electronic Technology, Guilin 451000, China"}]},{"given":"Dong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 451000, China"}]},{"given":"Ching-Nung","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of CISE, National Dong Hwa University, Hualien City 97047, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1145\/359168.359176","article-title":"How to share a secret","volume":"22","author":"Shamir","year":"1979","journal-title":"Commun. ACM"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Liu, Y., Guo, W., Fan, C.I., Chang, L., and Cheng, C. (2018). A practical privacy-preserving data aggregation (3PDA) scheme for smart grid. IEEE Trans. Ind. Inform.","DOI":"10.1109\/TII.2018.2809672"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Liu, Y.N., Wang, Y.P., Wang, X.F., Xia, Z., and Xu, J.F. (2018). Privacy-preserving raw data collection without a trusted authority for IoT. Comput. Netw.","DOI":"10.1016\/j.comnet.2018.11.028"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.ins.2018.09.024","article-title":"A new threshold changeable secret sharing scheme based on the Chinese Remainder Theorem","volume":"473","author":"Jia","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1016\/S0097-8493(02)00131-0","article-title":"Secret image sharing","volume":"26","author":"Thien","year":"2002","journal-title":"Comput. Gr."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1186\/1687-6180-2013-49","article-title":"A secret image sharing scheme for light images","volume":"2013","author":"Wu","year":"2013","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"16369","DOI":"10.1007\/s11042-016-3917-x","article-title":"An efficient (t, n)\u2013threshold secret image sharing scheme","volume":"76","author":"Kanso","year":"2017","journal-title":"Multimed. Tools Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/02533839.2017.1294994","article-title":"A novel image protection scheme using bit-plane compression and secret sharing","volume":"40","author":"Liu","year":"2017","journal-title":"J. Chin. Inst. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6017","DOI":"10.1007\/s11042-017-4512-5","article-title":"A novel multiple-level secret image sharing scheme","volume":"77","author":"Liu","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_10","first-page":"166","article-title":"An improved threshold multi-level image recovery scheme","volume":"40","author":"Liu","year":"2018","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Jia, X., Wang, D., Chu, Q., and Chen, Z. (2018). An efficient XOR-based verifiable visual cryptographic scheme. Multimed. Tools Appl., 1\u201317.","DOI":"10.1007\/s11042-018-6779-6"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/TCSVT.2016.2631404","article-title":"Collaborative visual cryptography schemes","volume":"28","author":"Jia","year":"2018","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Shyu, S.J., Chuang, C.C., Chen, Y.R., and Lai, A.F. (2009, January 13\u201316). Weighted threshold secret image sharing. Proceedings of the Pacific-Rim Symposium on Image and Video Technology, Tokyo, Japan.","DOI":"10.1007\/978-3-540-92957-4_86"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"043011","DOI":"10.1117\/1.3268362","article-title":"Weighted modulated secret image sharing method","volume":"18","author":"Chen","year":"2009","journal-title":"J. Electron. Imaging"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3083","DOI":"10.1002\/sec.1233","article-title":"A novel weighted threshold secret image sharing scheme","volume":"8","author":"Li","year":"2015","journal-title":"Secur. Commun. Netw."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"077008","DOI":"10.1117\/1.3168644","article-title":"Fast-weighted secret image sharing","volume":"48","author":"Lin","year":"2009","journal-title":"Opt. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s00145-006-0334-8","article-title":"Hierarchical threshold secret sharing","volume":"20","author":"Tassa","year":"2007","journal-title":"J. Cryptol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.patrec.2011.09.030","article-title":"A hierarchical threshold secret image sharing","volume":"33","author":"Guo","year":"2012","journal-title":"Pattern Recognit. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1016\/j.jvcir.2014.03.004","article-title":"Secret image sharing scheme with hierarchical threshold access structure","volume":"25","author":"Pakniat","year":"2014","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1016\/j.jvcir.2013.07.005","article-title":"Essential secret image sharing scheme with different importance of shadows","volume":"24","author":"Li","year":"2013","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.image.2014.11.003","article-title":"Reducing shadow size in essential secret image sharing by conjunctive hierarchical approach","volume":"31","author":"Yang","year":"2015","journal-title":"Signal Process. Image Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"013103","DOI":"10.1117\/1.OE.55.1.013103","article-title":"Essential secret image sharing with increasable shadows","volume":"55","author":"Chen","year":"2016","journal-title":"Opt. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1016\/j.jvcir.2016.04.004","article-title":"Two-layered structure for optimally essential secret image sharing scheme","volume":"38","author":"Chen","year":"2016","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.dsp.2015.12.004","article-title":"Essential secret image sharing scheme with the same size of shadows","volume":"50","author":"Li","year":"2016","journal-title":"Digit. Signal Process."},{"key":"ref_25","first-page":"135","article-title":"An Expandable Essential Secret Image Sharing Structure","volume":"7","author":"Chen","year":"2016","journal-title":"J. Inf. Hiding Multimed. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.jvcir.2018.02.006","article-title":"Essential secret image sharing scheme with equal-sized shadows generation","volume":"52","author":"Chen","year":"2018","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.image.2018.04.002","article-title":"A construction method of (t, k, n)-essential secret image sharing scheme","volume":"65","author":"Li","year":"2018","journal-title":"Signal Process. 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