{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T05:03:26Z","timestamp":1771391006586,"version":"3.50.1"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T00:00:00Z","timestamp":1771372800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T00:00:00Z","timestamp":1771372800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100014718","name":"Innovative Research Group Project of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 62062009"],"award-info":[{"award-number":["No. 62062009"]}],"id":[{"id":"10.13039\/100014718","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015401","name":"Key Research and Development Projects of Shaanxi Province","doi-asserted-by":"publisher","award":["No.AB24010340"],"award-info":[{"award-number":["No.AB24010340"]}],"id":[{"id":"10.13039\/501100015401","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cybersecurity"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In dynamic multi-key Fully Homomorphic Encryption (MFHE) scheme, homomorphic operations on ciphertexts encrypted under different keys are allowed. Moreover, the resulting ciphertext can be further computed with ciphertexts under other keys. In 2016, Peikert and Shiehian presented a dynamic MFHE scheme that relies on using a Common Reference String (CRS) and circular security assumptions. Subsequently, various variants of dynamic MFHE schemes were proposed based on this scheme, but these variant schemes still rely on a CRS and circular security assumption. Therefore, constructing a MFHE GSW scheme relies solely on the LWE assumption and does not require a CRS remains a valuable challenge. This paper introduces a new dynamic MFHE scheme. Compared to existing solutions, our scheme does not require the circular security assumption and depends solely on the LWE assumption, which theoretically provides an enhanced level of security. Additionally, it eliminates the need for a shared CRS but instead replaces the CRS with each party independently generate random matrices. This decentralized approach enhances the ability of users to generate keys independently. The size of ciphertexts and public keys in our scheme is comparable to other existing solutions, thus maintaining efficiency in both computation and ciphertext extension.<\/jats:p>","DOI":"10.1186\/s42400-025-00431-z","type":"journal-article","created":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T03:02:44Z","timestamp":1771383764000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Dynamic multi-key FHE without CRS from LWE"],"prefix":"10.1186","volume":"9","author":[{"given":"Junjie","family":"Wang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0006-7463-6193","authenticated-orcid":false,"given":"Ruwei","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Xiaolong","family":"Tang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,2,18]]},"reference":[{"key":"431_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/s12652-021-02980-w","author":"C Biswas","year":"2022","unstructured":"Biswas C, Dutta R (2022) Dynamic multi-key FHE in symmetric key setting from LWE without using common reference matrix. J Ambient Intell Humaniz Comput. https:\/\/doi.org\/10.1007\/s12652-021-02980-w","journal-title":"J Ambient Intell Humaniz Comput"},{"key":"431_CR5","first-page":"190","volume-title":"Annual international cryptology conference","author":"Z Brakerski","year":"2016","unstructured":"Brakerski Z, Perlman R (2016) Lattice-based fully dynamic multi-key FHE with short ciphertexts. Annual international cryptology conference. Springer, Berlin, pp 190\u2013213"},{"issue":"3","key":"431_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2633600","volume":"6","author":"Z Brakerski","year":"2014","unstructured":"Brakerski Z, Gentry C, Vaikuntanathan V (2014) (Leveled) fully homomorphic encryption without bootstrapping. 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Hong Kong, China, December 3\u20137, 2017, Proceedings, Part I 23.\u00a0Springer, pp 409\u2013437","DOI":"10.1007\/978-3-319-70694-8_15"},{"issue":"5","key":"431_CR10","doi-asserted-by":"publisher","first-page":"1052","DOI":"10.1109\/TIFS.2015.2398359","volume":"10","author":"JH Cheon","year":"2015","unstructured":"Cheon JH, Kim J (2015) A hybrid scheme of public-key encryption and somewhat homomorphic encryption. IEEE Trans Inf Forensics Secur 10(5):1052\u20131063","journal-title":"IEEE Trans Inf Forensics Secur"},{"key":"431_CR12","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1007\/978-3-662-48000-7_31","volume-title":"Advances in cryptology\u2013CRYPTO 2015: 35th annual cryptology conference, Santa Barbara, CA, USA, August 16\u201320, 2015, Proceedings, part II 35","author":"M Clear","year":"2015","unstructured":"Clear M, McGoldrick C (2015) Multi-identity and multi-key leveled FHE from learning with errors. Advances in cryptology\u2013CRYPTO 2015: 35th annual cryptology conference, Santa Barbara, CA, USA, August 16\u201320, 2015, Proceedings, part II 35. Springer, Berlin, pp 630\u2013656"},{"key":"431_CR13","doi-asserted-by":"crossref","unstructured":"Gentry C, Sahai A, Waters B (2013) Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based. In: Advances in Cryptology\u2013CRYPTO 2013: 33rd annual cryptology conference, Santa Barbara, CA, USA, August 18\u201322, 2013. Proceedings, Part I. Springer, Berlin, pp 75\u201392","DOI":"10.1007\/978-3-642-40041-4_5"},{"key":"431_CR14","doi-asserted-by":"crossref","unstructured":"Gentry C (2009) Fully homomorphic encryption using ideal lattices. 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