{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T01:44:17Z","timestamp":1768009457058,"version":"3.49.0"},"reference-count":21,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T00:00:00Z","timestamp":1757980800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of Kazakhstan","award":["AP 23487787"],"award-info":[{"award-number":["AP 23487787"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>This paper examines the properties of classical secret sharing schemes used in information protection systems, including the protection of valuable and confidential data. It addresses issues such as implementation complexity, limited flexibility, vulnerability to new types of attacks, the requirements for such schemes, and analyzes existing approaches to their solutions. A new secret sharing scheme is proposed as a potential solution to these challenges. The developed scheme is based on multivariable functions. The shares distributed among participants represent the values of these functions. Secret reconstruction is reduced to solving a system of linear equations composed of such functions. The structure and mathematical foundation of the scheme are presented, along with an analysis of its properties. A key feature of the proposed scheme is the incorporation of functions aimed at authenticating participants and verifying the integrity of the distributed shares. The paper also provides a cryptanalysis of the scheme, evaluates its resistance to various types of attacks, and discusses the results obtained. Thus, this work contributes to the advancement of information security methods by offering a modern and reliable solution for the secure storage and joint use of secret data.<\/jats:p>","DOI":"10.3390\/computers14090393","type":"journal-article","created":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T10:06:25Z","timestamp":1758017185000},"page":"393","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Secret Sharing Scheme with Share Verification Capability"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9743-9981","authenticated-orcid":false,"given":"Nursulu","family":"Kapalova","sequence":"first","affiliation":[{"name":"Information Security Laboratory, Institute of Information and Computational Technologies, Almaty 050010, Kazakhstan"},{"name":"Faculty of Information Technology, Al-Farabi Kazakh National University, Almaty 050010, Kazakhstan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1670-2520","authenticated-orcid":false,"given":"Armanbek","family":"Haumen","sequence":"additional","affiliation":[{"name":"Information Security Laboratory, Institute of Information and Computational Technologies, Almaty 050010, Kazakhstan"},{"name":"Faculty of Information Technology, Al-Farabi Kazakh National University, Almaty 050010, Kazakhstan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3670-2170","authenticated-orcid":false,"given":"Kunbolat","family":"Algazy","sequence":"additional","affiliation":[{"name":"Information Security Laboratory, Institute of Information and Computational Technologies, Almaty 050010, Kazakhstan"},{"name":"Faculty of Information Technology, Al-Farabi Kazakh National University, Almaty 050010, Kazakhstan"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"\u010cu\u0159\u00edk, P., Ploszek, R., and Zajac, P. (2022). Practical Use of Secret Sharing for Enhancing Privacy in Clouds. Electronics, 11.","DOI":"10.3390\/electronics11172758"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Huang, C.-W., and Juan, J.S.-T. (2025). New (t, n)-Threshold P-VSS Schemes Using Fewer Types of Polarizers. Eng. Proc., 92.","DOI":"10.3390\/engproc2025092049"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Tsai, Y.-Y., Jhou, J.-Y., You, T.-Y., and Lu, C.-T. (2025). Advancing Secret Sharing in 3D Models Through Vertex Index Sharing. Electronics, 14.","DOI":"10.3390\/electronics14081675"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Chang, J.J.-Y., Huang, B.-Y., and Juan, J.S.-T. (2018). A New Visual Multi-Secrets Sharing Scheme by Random Grids. Cryptography, 2.","DOI":"10.3390\/cryptography2030024"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"207","DOI":"10.54254\/2755-2721\/88\/20241746","article-title":"A review of research on secret sharing","volume":"88","author":"Chen","year":"2024","journal-title":"Appl. Comput. Eng."},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1109\/LCOMM.2022.3144375","article-title":"A Modified Shamir Secret Sharing Scheme with Efficient Encoding","volume":"26","author":"Hineman","year":"2022","journal-title":"IEEE Commun. Lett."},{"key":"ref_8","first-page":"13","article-title":"Constructing and implementing some perfect verifiable secret sharing schemes","volume":"2","author":"Gusarova","year":"2021","journal-title":"Avtom. Protsessov Upr."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Blakley, G.R. (1979, January 4\u20137). Safeguarding cryptographic keys. Proceedings of the 1979 International Workshop on Managing Requirements Knowledge (MARK), New York, NY, USA.","DOI":"10.1109\/MARK.1979.8817296"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"\u00c7alkavur, S., and Sol\u00e9, P. (2020). Some Multisecret-Sharing Schemes over Finite Fields. Mathematics, 8.","DOI":"10.3390\/math8050654"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Feldman, P. (1987, January 12\u201314). A practical scheme for non-interactive verifiable secret sharing. Proceedings of the 28th Annual Symposium on Foundations of Computer Science (SFCS 1987), Los Angeles, CA, USA.","DOI":"10.1109\/SFCS.1987.4"},{"key":"ref_12","first-page":"133","article-title":"Efficient (k, n) Threshold Secret Sharing Schemes Secure Against Cheating from n\u22121 Cheaters","volume":"Volume 4586","author":"Araki","year":"2007","journal-title":"Information Security and Privacy, Proceedings of the ACISP 2007, Townsville, Australia, 2\u20134 July 2007"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1049\/cje.2016.08.014","article-title":"GOMSS: A Simple Group Oriented (t, m, n) Multi-secret Sharing Scheme","volume":"26","author":"Miao","year":"2017","journal-title":"Chin. J. Electron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"15749","DOI":"10.1007\/s11227-022-04467-7","article-title":"New attacks on secret sharing-based data outsourcing: Toward a resistant scheme","volume":"78","author":"Rahmani","year":"2022","journal-title":"J. Supercomput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3","DOI":"10.18523\/2617-7080720243-8","article-title":"Secret sharing scheme based on the Goldwasser-Goldrich-Halevi cryptosystem","volume":"7","author":"Likhachov","year":"2025","journal-title":"Mohyla Math. J."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Alam, I., Alali, A., Ali, S., Mohd, A., and Muhammad, S. (2024). A Verifiable Multi-Secret Sharing Scheme for Hierarchical Access Structure. Axioms, 13.","DOI":"10.20944\/preprints202405.2061.v1"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Farahi, S., Noorallahzadeh, M., and Vahedi, S. (2025). Two Verifiable Essential Secret Image Sharing schemes((t,k,n) and (t,s,k,n)-VESIS). Res. Sq., 1\u201329. preprint.","DOI":"10.21203\/rs.3.rs-6799097\/v1"},{"key":"ref_18","first-page":"17","article-title":"The development of an evaluation model for user authentication methods with security, usability, and usage frequency","volume":"3","author":"Ussatova","year":"2025","journal-title":"East.-Eur. J. Enterp. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s00145-024-09536-z","article-title":"Improved Universal Thresholdizer from Iterative Shamir Secret Sharing","volume":"38","author":"Cheon","year":"2025","journal-title":"J. Cryptol."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Chen, J., Deng, H., Su, H., Yuan, M., and Ren, Y. (2024). Lattice-Based Threshold Secret Sharing Scheme and Its Applications: A Survey. Electronics, 13.","DOI":"10.3390\/electronics13020287"},{"key":"ref_21","first-page":"6","article-title":"Development of a new lightweight encryption algorithm","volume":"3","author":"Kapalova","year":"2023","journal-title":"East.-Eur. J. Enterp. 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