A method for constructing a self-dual normal basis in odd characteristic extension fields

Yasuyuki Nogami, Hiroaki Nasu, Yoshitaka Morikawa, Satoshi Uehara

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This paper proposes a useful method for constructing a self-dual normal basis in an arbitrary extension field Fpm such that 4p does not divide m (p - 1) and m is odd. In detail, when the characteristic p and extension degree m satisfies the following conditions (1) and either (2a) or (2b); (1) 2 k m + 1 is a prime number, (2a) the order of p in F2 k m + 1 is 2 k m, (2b) 2 {does not divide} k m and the order of p in F2 k m + 1 is km, we can consider a class of Gauss period normal bases. Using this Gauss period normal basis, this paper shows a method to construct a self-dual normal basis in the extension field Fpm.

Original languageEnglish
Pages (from-to)867-876
Number of pages10
JournalFinite Fields and their Applications
Volume14
Issue number4
DOIs
Publication statusPublished - Nov 1 2008

Keywords

  • Extension field
  • Gauss period normal basis
  • Self-dual normal basis

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

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