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In this work, we compute the condition number of a generator matrix of the ideal lattice from the whole ring of integers of any odd prime degree cyclic number field using canonical embedding.<\/jats:p>","DOI":"10.1515\/jmc-2024-0022","type":"journal-article","created":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T20:33:40Z","timestamp":1738701220000},"source":"Crossref","is-referenced-by-count":1,"title":["The condition number associated with ideal lattices from odd prime degree cyclic number fields"],"prefix":"10.1515","volume":"19","author":[{"given":"Robson Ricardo","family":"de Araujo","sequence":"first","affiliation":[{"name":"Federal Institute of S\u00e3o Paulo, Av. Pastor Jos\u00e9 Dutra de Moraes , 239 - Distrito Industrial Ant\u00f4nio Z\u00e1caro - Catanduva - SP , 15808-305 , Brazil"}]}],"member":"374","published-online":{"date-parts":[[2025,2,4]]},"reference":[{"key":"2025122009205601999_j_jmc-2024-0022_ref_001","doi-asserted-by":"crossref","unstructured":"Stehl\u00e9 D, Steinfeld R, Tanaka K, Xagawa K. Efficient public key encryption based on ideal lattices. Adv Cryptol-ASIACRYPT 2009 Lecture Notes in Comput Sci. 2009;5912:617\u201335. https:\/\/doi.org\/10.1007\/978-3-642-10366-7_36.","DOI":"10.1007\/978-3-642-10366-7_36"},{"key":"2025122009205601999_j_jmc-2024-0022_ref_002","doi-asserted-by":"crossref","unstructured":"Lyubashevsky V, Peikert C, Regev O. On ideal lattices and learning with errors over rings. J Assoc Comput Mach. 2013;60:1\u201335. https:\/\/doi.org\/10.1145\/2535925.","DOI":"10.1145\/2535925"},{"key":"2025122009205601999_j_jmc-2024-0022_ref_003","doi-asserted-by":"crossref","unstructured":"Micciancio D. 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