{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T18:41:12Z","timestamp":1771612872009,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,11]],"date-time":"2025-05-11T00:00:00Z","timestamp":1746921600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Homomorphic encryption is an important means for cloud computing to ensure information security when outsourcing data. Among them, threshold fully homomorphic encryption (ThFHE) is a key enabler for homomorphic encryption and, from a wider perspective, secure distributed computing. However, current ThFHE schemes are unsatisfactory in terms of security and efficiency. In this paper, a novel ThFHE is proposed for the first time based on an NTRU-based GSW-like scheme of symmetric encryption\u2014Th-S-NGS scheme. Additionally, the threshold structure is realized by combining an extended version of the linear integer secret sharing scheme such that the scheme requires a predetermined number of parties to be online, rather than all the parties being online. The Th-S-NGS scheme is not only more attractive in terms of ciphertext size and computation time for homomorphic multiplication, but also does not need re-linearization after homomorphic multiplication, and thus does not require the computing key, which can effectively reduce the communication burden in the scheme and thus simplify the complexity of the scheme.<\/jats:p>","DOI":"10.3390\/sym17050737","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T03:59:26Z","timestamp":1747108766000},"page":"737","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Threshold Fully Homomorphic Encryption Scheme Based on NGS of Symmetric Encryption"],"prefix":"10.3390","volume":"17","author":[{"given":"Xu","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Cyber Science and Technology, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zheng","family":"Yuan","sequence":"additional","affiliation":[{"name":"China StarNet Network Application Research Institute Co., Ltd., Beijing 100020, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1145\/1364782.1364786","article-title":"Cloud computing","volume":"51","author":"Hayes","year":"2008","journal-title":"ACM."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s00354-008-0081-5","article-title":"Cloud Computing: A Perspective Study","volume":"28","author":"Wang","year":"2010","journal-title":"New Gener. 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