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

Date

2014-03-15

Author

AKLEYLEK, SEDAT
Özbudak, Ferruh
Özel, Claire Susanna

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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 F-3n 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.

Subject Keywords

Finite field representation, Hermite polynomials, Modular multiplication, Matrix vector product method

URI

https://hdl.handle.net/11511/46286

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2013.08.011

Collections

Department of Mathematics, Article

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Citation Formats

S. AKLEYLEK, F. Özbudak, and C. S. Özel, “On the arithmetic operations over finite fields of characteristic three with low complexity,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 546–554, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46286.