On the arithmetic operations over finite fields of characteristic three with low complexity

In this paper, the Hermite polynomial representation is adapted as a new way to represent certain finite fields of characteristic three. We give the multiplication method to multiply two elements of F3n in the Hermite polynomial representation with subquadratic computational complexity by using a di...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 259; pp. 546 - 554
Main Authors Akleylek, S., Özbudak, F., Özel, C.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.03.2014
Subjects
Finite field representation
Hermite polynomials
Matrix vector product method
Modular multiplication
Matrix vector product method
Hermite polynomials
Modular multiplication
Finite field representation
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ISSN0377-0427
1879-1778
1879-1778
DOI10.1016/j.cam.2013.08.011

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Summary:In this paper, the Hermite polynomial representation is adapted as a new way to represent certain finite fields of characteristic three. We give the multiplication method to multiply two elements of F3n in the Hermite polynomial representation with subquadratic computational complexity by using a divide-and-conquer idea. We show that in some cases there is a set of irreducible binomials in the Hermite polynomial representation to obtain modular reduction with a lower addition complexity than the standard polynomial representation. We also investigate the matrix vector product method for the multiplication of the field elements represented by Hermite polynomials.
ISSN:0377-0427
1879-1778
1879-1778
DOI:10.1016/j.cam.2013.08.011