The generalized Redei-matrix for function fields

Cited 7 time in webofscience Cited 0 time in scopus
  • Hit : 405
  • Download : 0
DC FieldValueLanguage
dc.contributor.authorBae, Sung-Hanko
dc.contributor.authorHu, Suko
dc.contributor.authorJung, Hwanyupko
dc.date.accessioned2013-03-12T18:49:00Z-
dc.date.available2013-03-12T18:49:00Z-
dc.date.created2012-10-09-
dc.date.created2012-10-09-
dc.date.issued2012-07-
dc.identifier.citationFINITE FIELDS AND THEIR APPLICATIONS, v.18, no.4, pp.760 - 780-
dc.identifier.issn1071-5797-
dc.identifier.urihttp://hdl.handle.net/10203/103186-
dc.description.abstractLet F be a finite geometric separable extension of the rational function field F-q(T). Let E be a finite cyclic extension of F with degree l, where l is a prime number. Assume that the ideal class number of the integral closure O-F of F-q[T] in F is not divisible by E. In analogy with the number field case [Q. Yue, The generalized Reclei-matrix, Math. Z. 261 (2009) 23-37], we define the generalized Reclei-matrix R-E/F of local Hilbert symbols with coefficients in F-l. Using this generalized Reclei-matrix we give an analogue of the Redei-Reichardt formula for E. Furthermore, we explicitly determine the generalized Reclei-matrices for Kummer extensions, biquadratic extensions and Artin-Schreier extensions of F-q(T). Finally, using the generalized Reclei-matrix given in this paper, we completely determine the 4-ranks of the ideal class groups for a large class of Artin-Schreier extensions. In cryptanalysis, this class of Artin-Schreier extensions has been used in [P. Gaudry, F. Hess, N.P. Smart, Constructive and destructive facets of Well descent on elliptic curves, J. Cryptology 15 (2002) 19-46] to perform the Well descent, which may lead to a possible method of attack against the ECDLP, so-called GHS attack. (C) 2012 Elsevier Inc. All rights reserved.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.subjectTAME KERNELS-
dc.subjectGENUS THEORY-
dc.subjectBODIES-
dc.titleThe generalized Redei-matrix for function fields-
dc.typeArticle-
dc.identifier.wosid000305817100010-
dc.identifier.scopusid2-s2.0-84862232349-
dc.type.rimsART-
dc.citation.volume18-
dc.citation.issue4-
dc.citation.beginningpage760-
dc.citation.endingpage780-
dc.citation.publicationnameFINITE FIELDS AND THEIR APPLICATIONS-
dc.identifier.doi10.1016/j.ffa.2012.01.004-
dc.contributor.localauthorBae, Sung-Han-
dc.contributor.nonIdAuthorHu, Su-
dc.contributor.nonIdAuthorJung, Hwanyup-
dc.type.journalArticleArticle-
dc.subject.keywordPlusTAME KERNELS-
dc.subject.keywordPlusGENUS THEORY-
dc.subject.keywordPlusBODIES-
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 7 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0