{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:29:14Z","timestamp":1766269754800,"version":"3.46.0"},"reference-count":6,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2020,11,25]],"date-time":"2020-11-25T00:00:00Z","timestamp":1606262400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,11,25]]},"abstract":"Abstract<\/jats:title>\n \n Recently, Blanco-Chac\u00f3n proved the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for some families of cyclotomic number fields by giving some upper bounds for the condition number Cond(\n \n V\n n<\/jats:sub>\n <\/jats:italic>\n ) of the Vandermonde matrix\n \n V\n n<\/jats:sub>\n <\/jats:italic>\n associated to the\n n<\/jats:italic>\n th cyclotomic polynomial. We prove some results on the singular values of\n \n V\n n<\/jats:sub>\n <\/jats:italic>\n and, in particular, we determine Cond(\n \n V\n n<\/jats:sub>\n <\/jats:italic>\n ) for\n n<\/jats:italic>\n = 2\n \n k<\/jats:sup>\n p\n \u2113<\/jats:sup>\n <\/jats:italic>\n , where\n k<\/jats:italic>\n ,\n \u2113<\/jats:italic>\n \u2265 0 are integers and\n p<\/jats:italic>\n is an odd prime number.\n <\/jats:p>","DOI":"10.1515\/jmc-2020-0009","type":"journal-article","created":{"date-parts":[[2020,11,30]],"date-time":"2020-11-30T15:54:44Z","timestamp":1606751684000},"page":"174-178","source":"Crossref","is-referenced-by-count":8,"title":["On the condition number of the Vandermonde matrix of the\n n<\/i>\n th cyclotomic polynomial"],"prefix":"10.1515","volume":"15","author":[{"given":"Antonio J. Di","family":"Scala","sequence":"first","affiliation":[{"name":"Politecnico di Torino, Department of Mathematical Sciences , Corso Duca degli Abruzzi 24 , Torino , Italy"}]},{"given":"Carlo","family":"Sanna","sequence":"additional","affiliation":[{"name":"Politecnico di Torino, Department of Mathematical Sciences , Corso Duca degli Abruzzi 24 , Torino , Italy"}]},{"given":"Edoardo","family":"Signorini","sequence":"additional","affiliation":[{"name":"Telsy Elettronica e Telecomunicazioni S.p.A. , Corso Svizzera 185 , Torino , Italy"}]}],"member":"374","published-online":{"date-parts":[[2020,11,25]]},"reference":[{"key":"2025120600333869201_j_jmc-2020-0009_ref_001","doi-asserted-by":"crossref","unstructured":"V. Lyubashevsky, C. Peikert, and O. Regev, On ideal lattices and learning with errors over rings, Advances in cryptology\u2014EUROCRYPT 2010, Lecture Notes in Comput. Sci., vol. 6110, Springer, Berlin, 2010, pp. 1\u201323.","DOI":"10.1007\/978-3-642-13190-5_1"},{"key":"2025120600333869201_j_jmc-2020-0009_ref_002","doi-asserted-by":"crossref","unstructured":"O. Regev, On lattices, learning with errors, random linear codes, and cryptography, J. ACM 56 (2009), no. 6, Art. 34, 40.","DOI":"10.1145\/1568318.1568324"},{"key":"2025120600333869201_j_jmc-2020-0009_ref_003","doi-asserted-by":"crossref","unstructured":"D. Stehl\u00e9, R. Steinfeld, K. Tanaka, and K. Xagawa, Efficient public key encryption based on ideal lattices (extended abstract), Advances in cryptology\u2014ASIACRYPT 2009, Lecture Notes in Comput. Sci., vol. 5912, Springer, Berlin, 2009, pp. 617\u2013635.","DOI":"10.1007\/978-3-642-10366-7_36"},{"key":"2025120600333869201_j_jmc-2020-0009_ref_004","unstructured":"I. Blanco-Chac\u00f3n, On the RLWE\/PLWE equivalence for cyclotomic number fields, Appl. Algebra Engrg. Comm. Comput. (accepted)."},{"key":"2025120600333869201_j_jmc-2020-0009_ref_005","doi-asserted-by":"crossref","unstructured":"M. Rosca, D. Stehl\u00e9, and A. Wallet, On the ring-LWE and polynomial-LWE problems, Advances in cryptology\u2014EUROCRYPT 2018. Part I, Lecture Notes in Comput. Sci., vol. 10820, Springer, Cham, 2018, pp. 146\u2013173.","DOI":"10.1007\/978-3-319-78381-9_6"},{"key":"2025120600333869201_j_jmc-2020-0009_ref_006","doi-asserted-by":"crossref","unstructured":"G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, sixth ed., Oxford University Press, Oxford, 2008, Revised by D. R. Heath-Brown and J. H. Silverman, With a foreword by Andrew Wiles.","DOI":"10.1093\/oso\/9780199219858.002.0002"}],"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/jmc\/15\/1\/article-p174.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2020-0009\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2020-0009\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:35:38Z","timestamp":1764981338000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2020-0009\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,25]]},"references-count":6,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,4,20]]},"published-print":{"date-parts":[[2021,4,20]]}},"alternative-id":["10.1515\/jmc-2020-0009"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2020-0009","relation":{},"ISSN":["1862-2984"],"issn-type":[{"type":"electronic","value":"1862-2984"}],"subject":[],"published":{"date-parts":[[2020,11,25]]}}}