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Turkish Journal of Mathematics

DOI

10.3906/mat-1503-84

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 $\mathbb{F}_{q^p}$ over $\mathbb{F}_q$ where $q=p^n$. 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.

Keywords

Finite field representation, conversion of field elements, transition matrix, normal basis, polynomial basis

First Page

96

Last Page

109

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