{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:48:23Z","timestamp":1776394103287,"version":"3.51.2"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T00:00:00Z","timestamp":1776384000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T00:00:00Z","timestamp":1776384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Beijing Natural Science Foundation","award":["4232034"],"award-info":[{"award-number":["4232034"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["3282025039"],"award-info":[{"award-number":["3282025039"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["3282024052"],"award-info":[{"award-number":["3282024052"]}],"id":[{"id":"10.13039\/501100012226","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>Homomorphic signatures have important potential in cloud computing and data privacy protection, but there are still problems such as low signature efficiency, high overhead, and difficulty in instantiation. To solve these problems, an efficient leveled fully homomorphic signature scheme LFHSS with shortened signature values is constructed. The scheme is based on the GPV framework and the RSIS problem on the NTRU lattice. By using the Fast Fourier Sampling algorithm, it achieves efficient signatures with smaller size. It introduces a homomorphic trapdoor function and designs three basic evaluations: homomorphic addition, multiplication, and scalar multiplication. These operations enable the LFHSS scheme to support homomorphic evaluations of functions consisting of addition, multiplication, and scalar multiplication within a certain circuit depth. Additionally, it is proven to be strongly unforgeable, and the scheme is implemented in software with correctness testing and performance analysis conducted. The experimental results show that the security level of LFHSS is 1.14 times higher than that of BCFL23, and the signature generation speed is 300+ times faster, the homomorphic evaluation speed is 7.8 times faster, and the verification speed is 48K times faster than that of BCFL23. The signature length of LFHSS is only 4.86% of BCFL23. The work in this paper is of great significance to the design and application of homomorphic signatures.<\/jats:p>","DOI":"10.1186\/s42400-025-00409-x","type":"journal-article","created":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:02:01Z","timestamp":1776391321000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Lfhss:(a more efficient) leveled fully homomorphic signature scheme with shortened signature size"],"prefix":"10.1186","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0174-0997","authenticated-orcid":false,"given":"Yatao","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haopeng","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siu Ming","family":"Yiu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,17]]},"reference":[{"key":"409_CR1","doi-asserted-by":"publisher","unstructured":"Agrawal S, Boneh D, Boyen X (2010) Efficient lattice (H)IBE in the standard model. In: Gilbert H (ed) Advances in Cryptology - EUROCRYPT 2010, 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Monaco \/ French Riviera, May 30 - June 3, 2010. Proceedings, Lecture Notes in Computer Science, vol 6110. Springer, pp 553\u2013572, https:\/\/doi.org\/10.1007\/978-3-642-13190-5_28","DOI":"10.1007\/978-3-642-13190-5_28"},{"key":"409_CR2","doi-asserted-by":"publisher","unstructured":"Attrapadung N, Libert B, Peters T (2012) Computing on authenticated data: New privacy definitions and constructions. In: Wang X, Sako K (eds) Advances in Cryptology - ASIACRYPT 2012 - 18th International Conference on the Theory and Application of Cryptology and Information Security, Beijing, China, December 2-6, 2012. Proceedings, Lecture Notes in Computer Science, vol 7658. Springer, pp 367\u2013385, https:\/\/doi.org\/10.1007\/978-3-642-34961-4_23","DOI":"10.1007\/978-3-642-34961-4_23"},{"key":"409_CR3","doi-asserted-by":"publisher","unstructured":"Balb\u00e1s D, Catalano D, Fiore D, et\u00a0al (2023) Chainable functional commitments for unbounded-depth circuits. In: Rothblum GN, Wee H (eds) Theory of Cryptography - 21st International Conference, TCC 2023, Taipei, Taiwan, November 29 - December 2, 2023, Proceedings, Part III, Lecture Notes in Computer Science, vol 14371. Springer, pp 363\u2013393, https:\/\/doi.org\/10.1007\/978-3-031-48621-0_13","DOI":"10.1007\/978-3-031-48621-0_13"},{"issue":"1","key":"409_CR4","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/0022-0000(89)90010-4","volume":"38","author":"DA Barrington","year":"1989","unstructured":"Barrington DA (1989) Bounded-width polynomial-size branching programs recognize exactly those languages in nc1. J Comput Syst Sci 38(1):150\u2013164. https:\/\/doi.org\/10.1016\/0022-0000(89)90010-4","journal-title":"J Comput Syst Sci"},{"issue":"6","key":"409_CR5","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.1109\/TDSC.2018.2867462","volume":"17","author":"R Behnia","year":"2020","unstructured":"Behnia R, Ozmen MO, Yavuz AA (2020) Lattice-based public key searchable encryption from experimental perspectives. IEEE Trans Depend Secur Comput 17(6):1269\u20131282. https:\/\/doi.org\/10.1109\/TDSC.2018.2867462","journal-title":"IEEE Trans Depend Secur Comput"},{"key":"409_CR6","first-page":"1","volume":"1","author":"DJ Bernstein","year":"2009","unstructured":"Bernstein DJ (2009) Introduction to post-quantum cryptography. Post-Quantum Cryptogr 1:1\u201310","journal-title":"Post-Quantum Cryptogr"},{"key":"409_CR7","doi-asserted-by":"publisher","unstructured":"Boneh D, Freeman DM, Katz J, et\u00a0al (2009) Signing a linear subspace: Signature schemes for network coding. In: Jarecki S, Tsudik G (eds) Public Key Cryptography - PKC 2009, 12th International Conference on Practice and Theory in Public Key Cryptography, Irvine, CA, USA, March 18-20, 2009. Proceedings, Lecture Notes in Computer Science, vol 5443. Springer, pp 68\u201387, https:\/\/doi.org\/10.1007\/978-3-642-00468-1_5","DOI":"10.1007\/978-3-642-00468-1_5"},{"key":"409_CR8","doi-asserted-by":"publisher","unstructured":"Boneh D, Gentry C, Gorbunov S, et\u00a0al (2014) Fully key-homomorphic encryption, arithmetic circuit ABE and compact garbled circuits. In: Nguyen PQ, Oswald E (eds) Advances in Cryptology - EUROCRYPT 2014 - 33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Copenhagen, Denmark, May 11-15, 2014. Proceedings, Lecture Notes in Computer Science, vol 8441. Springer, pp 533\u2013556, https:\/\/doi.org\/10.1007\/978-3-642-55220-5_30","DOI":"10.1007\/978-3-642-55220-5_30"},{"key":"409_CR9","doi-asserted-by":"publisher","unstructured":"Brakerski Z, Vaikuntanathan V (2014) Lattice-based FHE as secure as PKE. In: Naor M (ed) Innovations in Theoretical Computer Science, ITCS\u201914, Princeton, NJ, USA, January 12-14, 2014. ACM, pp 1\u201312, https:\/\/doi.org\/10.1145\/2554797.2554799","DOI":"10.1145\/2554797.2554799"},{"key":"409_CR10","doi-asserted-by":"crossref","unstructured":"Carnemolla D, Catalano D, Raimondo MD, et\u00a0al (2024) Implementation and performance analysis of homomorphic signature schemes. IACR Cryptol ePrint Arch p 655","DOI":"10.21203\/rs.3.rs-4793409\/v1"},{"key":"409_CR11","doi-asserted-by":"publisher","unstructured":"Cash D, Hofheinz D, Kiltz E, et\u00a0al (2010) Bonsai trees, or how to delegate a lattice basis. In: Gilbert H (ed) Advances in Cryptology - EUROCRYPT 2010, 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Monaco \/ French Riviera, May 30 - June 3, 2010. Proceedings, Lecture Notes in Computer Science, vol 6110. Springer, pp 523\u2013552, https:\/\/doi.org\/10.1007\/978-3-642-13190-5_27","DOI":"10.1007\/978-3-642-13190-5_27"},{"key":"409_CR12","doi-asserted-by":"publisher","unstructured":"Catalano D, Fiore D, Tucker I (2022) Additive-homomorphic functional commitments and applications to homomorphic signatures. In: Agrawal S, Lin D (eds) Advances in Cryptology - ASIACRYPT 2022 - 28th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, December 5-9, 2022, Proceedings, Part IV, Lecture Notes in Computer Science, vol 13794. Springer, pp 159\u2013188, https:\/\/doi.org\/10.1007\/978-3-031-22972-5_6","DOI":"10.1007\/978-3-031-22972-5_6"},{"key":"409_CR13","doi-asserted-by":"publisher","unstructured":"Ducas L, Lyubashevsky V, Prest T (2014) Efficient identity-based encryption over NTRU lattices. In: Sarkar P, Iwata T (eds) Advances in Cryptology - ASIACRYPT 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security, Kaoshiung, Taiwan, R.O.C., December 7-11, 2014, Proceedings, Part II, Lecture Notes in Computer Science, vol 8874. Springer, pp 22\u201341, https:\/\/doi.org\/10.1007\/978-3-662-45608-8_2","DOI":"10.1007\/978-3-662-45608-8_2"},{"key":"409_CR14","doi-asserted-by":"publisher","unstructured":"Gennaro R, Katz J, Krawczyk H, et\u00a0al (2010) Secure network coding over the integers. In: Nguyen PQ, Pointcheval D (eds) Public Key Cryptography - PKC 2010, 13th International Conference on Practice and Theory in Public Key Cryptography, Paris, France, May 26-28, 2010. Proceedings, Lecture Notes in Computer Science, vol 6056. Springer, pp 142\u2013160, https:\/\/doi.org\/10.1007\/978-3-642-13013-7_9","DOI":"10.1007\/978-3-642-13013-7_9"},{"key":"409_CR15","doi-asserted-by":"publisher","unstructured":"Gentry C, Peikert C, Vaikuntanathan V (2008) Trapdoors for hard lattices and new cryptographic constructions. In: Dwork C (ed) Proceedings of the 40th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, May 17-20, 2008. ACM, pp 197\u2013206, https:\/\/doi.org\/10.1145\/1374376.1374407","DOI":"10.1145\/1374376.1374407"},{"key":"409_CR16","doi-asserted-by":"publisher","unstructured":"Gorbunov S, Vaikuntanathan V, Wee H (2015) Predicate encryption for circuits from LWE. In: Gennaro R, Robshaw M (eds) Advances in Cryptology - CRYPTO 2015 - 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2015, Proceedings, Part II, Lecture Notes in Computer Science, vol 9216. Springer, pp 503\u2013523, https:\/\/doi.org\/10.1007\/978-3-662-48000-7_25","DOI":"10.1007\/978-3-662-48000-7_25"},{"key":"409_CR17","doi-asserted-by":"publisher","unstructured":"Jiayu Y (2021) Research and application of anti quantum cryptography. https:\/\/doi.org\/10.27389\/d.cnki.gxadu.2021.001765","DOI":"10.27389\/d.cnki.gxadu.2021.001765"},{"key":"409_CR18","doi-asserted-by":"publisher","unstructured":"Lu X, Au MH, Zhang Z (2019) Raptor: A practical lattice-based (linkable) ring signature. In: Deng RH, Gauthier-Uma\u00f1a V, Ochoa M, et\u00a0al (eds) Applied Cryptography and Network Security - 17th International Conference, ACNS 2019, Bogota, Colombia, June 5-7, 2019, Proceedings, Lecture Notes in Computer Science, vol 11464. Springer, pp 110\u2013130, https:\/\/doi.org\/10.1007\/978-3-030-21568-2_6","DOI":"10.1007\/978-3-030-21568-2_6"},{"key":"409_CR19","doi-asserted-by":"crossref","unstructured":"Micciancio D, Regev O (2009) Lattice-based cryptography. In: Post-quantum cryptography. Springer, p 147\u2013191","DOI":"10.1007\/978-3-540-88702-7_5"},{"key":"409_CR20","doi-asserted-by":"publisher","unstructured":"Papamanthou C, Shi E, Tamassia R (2013) Signatures of correct computation. In: Sahai A (ed) Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Tokyo, Japan, March 3-6, 2013. Proceedings, Lecture Notes in Computer Science, vol 7785. Springer, pp 222\u2013242, https:\/\/doi.org\/10.1007\/978-3-642-36594-2_13","DOI":"10.1007\/978-3-642-36594-2_13"},{"key":"409_CR21","doi-asserted-by":"publisher","unstructured":"del Pino R, Lyubashevsky V, Seiler G (2018) Lattice-based group signatures and zero-knowledge proofs of automorphism stability. In: Lie D, Mannan M, Backes M, et\u00a0al (eds) Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, CCS 2018, Toronto, ON, Canada, October 15-19, 2018. ACM, pp 574\u2013591, https:\/\/doi.org\/10.1145\/3243734.3243852","DOI":"10.1145\/3243734.3243852"},{"key":"409_CR22","unstructured":"Prest T, et\u00a0al (2020) Falcon. Tech. rep., National Institute of Standards and Technology, https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/round-3-submissions, technical report"},{"key":"409_CR23","doi-asserted-by":"publisher","unstructured":"R L, F W, R Z, et\u00a0al (2022) Ntru-based fully homomorphic signature. Security and Communication Networks pp 1\u201311. https:\/\/doi.org\/10.1155\/2022\/9942717","DOI":"10.1155\/2022\/9942717"},{"key":"409_CR24","doi-asserted-by":"publisher","first-page":"119431","DOI":"10.1109\/ACCESS.2020.3003685","volume":"8","author":"C Wang","year":"2020","unstructured":"Wang C, Wu B, Yao H (2020) Leveled adaptively strong-unforgeable identity-based fully homomorphic signatures. IEEE Access 8:119431\u2013119447. https:\/\/doi.org\/10.1109\/ACCESS.2020.3003685","journal-title":"IEEE Access"},{"key":"409_CR25","doi-asserted-by":"publisher","unstructured":"Wang F, Wang K, Li B, et\u00a0al (2015) Leveled strongly-unforgeable identity-based fully homomorphic signatures. In: L\u00f3pez J, Mitchell CJ (eds) Information Security - 18th International Conference, ISC 2015, Trondheim, Norway, September 9-11, 2015, Proceedings, Lecture Notes in Computer Science, vol 9290. Springer, pp 42\u201360, https:\/\/doi.org\/10.1007\/978-3-319-23318-5_3","DOI":"10.1007\/978-3-319-23318-5_3"},{"key":"409_CR26","doi-asserted-by":"publisher","unstructured":"Wang Y, Wang M (2020) A new fully homomorphic signatures from standard lattices. In: Yu D, Dressler F, Yu J (eds) Wireless Algorithms, Systems, and Applications - 15th International Conference, WASA 2020, Qingdao, China, September 13-15, 2020, Proceedings, Part I, Lecture Notes in Computer Science, vol 12384. Springer, pp 494\u2013506, https:\/\/doi.org\/10.1007\/978-3-030-59016-1_41","DOI":"10.1007\/978-3-030-59016-1_41"},{"key":"409_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-15-8427-5","volume-title":"Lattice-based cryptosystems - a design perspective","author":"J Zhang","year":"2020","unstructured":"Zhang J, Zhang Z (2020) Lattice-based cryptosystems - a design perspective. Springer, Singapore"},{"key":"409_CR28","doi-asserted-by":"publisher","first-page":"2680","DOI":"10.1109\/TIFS.2023.3347880","volume":"19","author":"RK Zhao","year":"2024","unstructured":"Zhao RK, McCarthy S, Steinfeld R et al (2024) Quantum-safe HIBE: does it cost a latte? IEEE Trans Inf Forensics Secur 19:2680\u20132695. https:\/\/doi.org\/10.1109\/TIFS.2023.3347880","journal-title":"IEEE Trans Inf Forensics Secur"}],"container-title":["Cybersecurity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s42400-025-00409-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s42400-025-00409-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s42400-025-00409-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:02:07Z","timestamp":1776391327000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s42400-025-00409-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,17]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["409"],"URL":"https:\/\/doi.org\/10.1186\/s42400-025-00409-x","relation":{},"ISSN":["2523-3246"],"issn-type":[{"value":"2523-3246","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,17]]},"assertion":[{"value":"26 December 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"56"}}