{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T14:08:43Z","timestamp":1764079723179},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T00:00:00Z","timestamp":1634601600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T00:00:00Z","timestamp":1634601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Front. Comput. Sci."],"published-print":{"date-parts":[[2022,2]]},"DOI":"10.1007\/s11704-021-0479-5","type":"journal-article","created":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T08:30:41Z","timestamp":1634632241000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multi-key FHE without ciphertext-expansion in two-server model"],"prefix":"10.1007","volume":"16","author":[{"given":"Bingbing","family":"Jiang","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,19]]},"reference":[{"key":"479_CR1","doi-asserted-by":"crossref","unstructured":"L\u00f3pez-Alt A, Tromer E, Vaikuntanathan V. On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: Proceedings of the 44th Symposium on Theory of Computing Conference. 2012, 1219\u20131234","DOI":"10.1145\/2213977.2214086"},{"key":"479_CR2","doi-asserted-by":"crossref","unstructured":"Hoffstein J, Pipher J, Silverman J H. NTRU: a ring-based public key cryptosystem. In: Proceedings of the 3rd International Symposium on Algorithmic Number Theory. 1998, 267\u2013288","DOI":"10.1007\/BFb0054868"},{"key":"479_CR3","doi-asserted-by":"crossref","unstructured":"Mukherjee P, Wichs D. Two round multiparty computation via multi-key FHE. In: Proceedings of the 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques. 2016, 735\u2013763","DOI":"10.1007\/978-3-662-49896-5_26"},{"key":"479_CR4","doi-asserted-by":"crossref","unstructured":"Clear M, McGoldrick C. Multi-identity and multi-key leveled FHE from learning with errors. In: Proceedings of the 35th Annual International Cryptology Conference. 2015, 630\u2013656","DOI":"10.1007\/978-3-662-48000-7_31"},{"key":"479_CR5","doi-asserted-by":"crossref","unstructured":"Peikert C, Shiehian S. Multi-key FHE from lwe, revisited. In: Proceedings of the 14th International Conference on Theory of Cryptography. 2016, 217\u2013238","DOI":"10.1007\/978-3-662-53644-5_9"},{"key":"479_CR6","doi-asserted-by":"crossref","unstructured":"Brakerski Z, Perlman R. Lattice-based fully dynamic multi-key FHE with short ciphertexts. In: Proceedings of the 36th Annual International Cryptology Conference. 2016, 190\u2013213","DOI":"10.1007\/978-3-662-53018-4_8"},{"key":"479_CR7","doi-asserted-by":"crossref","unstructured":"Chen L, Zhang Z F, Wang X Q. Batched multi-hop multi-key FHE from ring-lwe with compact ciphertext extension. In: Proceedings of the 15th International Conference on Theory of Cryptography. 2017, 597\u2013627","DOI":"10.1007\/978-3-319-70503-3_20"},{"key":"479_CR8","doi-asserted-by":"crossref","unstructured":"Chongcjitmate W, Ostrovsky R. Circuit-private multi-key FHE. In: Proceedings of the 20th IACR International Conference on Pratice and Theory in Public-Key Cryptography. 2017, 241\u2013270","DOI":"10.1007\/978-3-662-54388-7_9"},{"issue":"2","key":"479_CR9","first-page":"1","volume":"61","author":"Z P Li","year":"2018","unstructured":"Li Z P, Ma C G, Zhou H S. Multi-key FHE for multi-bit messages. Science China Information Science, 2018, 61(2): 1\u20133","journal-title":"Science China Information Science"},{"key":"479_CR10","doi-asserted-by":"crossref","unstructured":"Chen H, Chillotti I, Song Y. Multi-key homomorphic encryption from TFHE. In: Proceedings of International Conference on the Theory and Application of Cryptology and Information Security. 2019, 446\u2013472","DOI":"10.1007\/978-3-030-34621-8_16"},{"key":"479_CR11","first-page":"1054","volume":"2018","author":"T P Zhou","year":"2018","unstructured":"Zhou T P, Li N B, Yang X Y, Han Y L, Liu W C. Efficient multi-key FHE with short extended ciphertexts and less public parameters. IACR Cryptogology ePrint Archive. 2018, 2018: 1054","journal-title":"IACR Cryptogology ePrint Archive"},{"key":"479_CR12","doi-asserted-by":"crossref","unstructured":"Jiang B B, Zhang Y. Privacy-preserving min and kth min computations with fully homomorphic encryption. In: Proceedings of the 34th IEEE International Performance Computing and Communications Conference. 2015, 1\u20138","DOI":"10.1109\/PCCC.2015.7410266"},{"issue":"5","key":"479_CR13","first-page":"1","volume":"61","author":"B B Jiang","year":"2018","unstructured":"Jiang B B, Zhang Y. Securely min and kth min computations with fully homomorphic encryption. Science China Information Science, 2018, 61(5): 1\u20133","journal-title":"Science China Information Science"},{"key":"479_CR14","doi-asserted-by":"crossref","unstructured":"Boyle E, Giboa N, Ishai Y. Breaking the circuit size barrier for secure computation under DDH. In: Proceedings of the 36th Annual International Cryptology Conference. 2016, 509\u2013539","DOI":"10.1007\/978-3-662-53018-4_19"},{"key":"479_CR15","doi-asserted-by":"crossref","unstructured":"Boyle E, Giboa N, Ishai Y. Group-based secure computation: optimizing rounds, communication and computation. In: Proceedings of the 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques. 2017, 163\u2013193","DOI":"10.1007\/978-3-319-56614-6_6"},{"key":"479_CR16","doi-asserted-by":"crossref","unstructured":"Boyle E, Couteau G, Giboa N, Ishai Y, Orr\u00f9 M. Homomorphic secret sharing: optimizations and applications. In: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security. 2017, 2105\u20132122","DOI":"10.1145\/3133956.3134107"},{"key":"479_CR17","doi-asserted-by":"crossref","unstructured":"Boyle E, Kohl L, Scholl P. Homomorphic secret sharing from lattices without FHE. In: Proceedings of the 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques. 2019, 3\u201333","DOI":"10.1007\/978-3-030-17656-3_1"},{"key":"479_CR18","doi-asserted-by":"crossref","unstructured":"Brakerski Z, Halevi S, Polychroniadou A. Four round secure computation without setup. In: Proceedings of the 15th International Conference on Theory of Cryptography. 2017, 645\u2013677","DOI":"10.1007\/978-3-319-70500-2_22"},{"key":"479_CR19","doi-asserted-by":"crossref","unstructured":"Peikert C. Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing. 2009, 333\u2013342","DOI":"10.1145\/1536414.1536461"}],"container-title":["Frontiers of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11704-021-0479-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11704-021-0479-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11704-021-0479-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T04:54:51Z","timestamp":1725944091000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11704-021-0479-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,19]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["479"],"URL":"https:\/\/doi.org\/10.1007\/s11704-021-0479-5","relation":{},"ISSN":["2095-2228","2095-2236"],"issn-type":[{"type":"print","value":"2095-2228"},{"type":"electronic","value":"2095-2236"}],"subject":[],"published":{"date-parts":[[2021,10,19]]},"assertion":[{"value":"26 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 February 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 October 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"161809"}}