Free storage basis conversion over finite fields

AKYILDIZ E., Harold N. Y., SINAK A.

Turkish Journal of Mathematics, vol.41, no.1, pp.96-109, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.3906/mat-1503-84
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.96-109
  • Keywords: Conversion of field elements, Finite field representation, Normal basis, Polynomial basis, Transition matrix
  • Akdeniz University Affiliated: No

Abstract

Representation of a field element plays a crucial role in the efficiency of field arithmetic. If an efficient representation of a field element in one basis exists, then field arithmetic in the hardware and/or software implementations becomes easy. Otherwise, a basis conversion to an efficient one is searched for easier arithmetic. However, this conversion often brings a storage problem for transition matrices associated with these bases. In this paper, we study this problem for conversion between normal and polynomial bases in the extension field Fqp over Fq where q = pn . We construct transition matrices that are of a special form. This provides free storage basis conversion algorithms between normal and polynomial bases, which is crucial from the implementation point of view.