{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T14:23:34Z","timestamp":1780496614270,"version":"3.54.1"},"reference-count":15,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,14]],"date-time":"2021-11-14T00:00:00Z","timestamp":1636848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61602143, 61772166"],"award-info":[{"award-number":["61602143, 61772166"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Zhejiang Province of China","award":["No.LZ17F020002"],"award-info":[{"award-number":["No.LZ17F020002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Lattices used in cryptography are integer lattices. Defining and generating a \u201crandom integer lattice\u201d are interesting topics. A generation algorithm for a random integer lattice can be used to serve as a random input of all the lattice algorithms. In this paper, we recall the definition of the random integer lattice given by G. Hu et al. and present an improved generation algorithm for it via the Hermite normal form. It can be proven that with probability \u22650.99, this algorithm outputs an n-dim random integer lattice within O(n2) operations.<\/jats:p>","DOI":"10.3390\/e23111509","type":"journal-article","created":{"date-parts":[[2021,11,14]],"date-time":"2021-11-14T20:48:36Z","timestamp":1636922916000},"page":"1509","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Random Integer Lattice Generation via the Hermite Normal Form"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3061-2388","authenticated-orcid":false,"given":"Gengran","family":"Hu","sequence":"first","affiliation":[{"name":"School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China"},{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2049-8961","authenticated-orcid":false,"given":"Lin","family":"You","sequence":"additional","affiliation":[{"name":"School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3698-2005","authenticated-orcid":false,"given":"Liang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0640-0956","authenticated-orcid":false,"given":"Liqin","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6620-3319","authenticated-orcid":false,"given":"Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,14]]},"reference":[{"key":"ref_1","unstructured":"Miller, G. 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A Course in Computational Algebraic Number Theory, Springer-Verlag.","DOI":"10.1007\/978-3-662-02945-9"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1107\/S0108767397009781","article-title":"Alternative formulae for the number of sublattices","volume":"A53","author":"Gruber","year":"1997","journal-title":"Acta Cryst."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/11\/1509\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:29:58Z","timestamp":1760167798000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/11\/1509"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,14]]},"references-count":15,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["e23111509"],"URL":"https:\/\/doi.org\/10.3390\/e23111509","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,14]]}}}