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Low complexity bit-parallel multiplier for F-2n defined by repeated polynomials

Authors
Chang, Nam SuKang, Eun SookHong, Seokhie
Issue Date
31-May-2018
Publisher
ELSEVIER SCIENCE BV
Keywords
Finite field; Irreducible polynomial; Polynomial basis; Multiplication
Citation
DISCRETE APPLIED MATHEMATICS, v.241, pp 2 - 12
Pages
11
Indexed
SCI
SCIE
SCOPUS
Journal Title
DISCRETE APPLIED MATHEMATICS
Volume
241
Start Page
2
End Page
12
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/75476
DOI
10.1016/j.dam.2016.07.014
ISSN
0166-218X
1872-6771
Abstract
Wu recently proposed three types of irreducible polynomials for low-complexity bit-parallel multipliers over F-2n. In this paper, we consider new classes of irreducible polynomials for low-complexity bit-parallel multipliers over F-2n, namely, repeated polynomial (RP). The complexity of the proposed multipliers is lower than those based on irreducible pentanomials. A repeated polynomial can be classified by the complexity of bit-parallel multiplier based on RPs, namely, C1, C2 and C3. If we consider finite fields that have neither a ESP nor a trinomial as an irreducible polynomial when n <= 1000, then, in Wu's result, only 11 finite fields exist for three types of irreducible polynomials when n <= 1000. However, in our result, there are 181, 232(52.4%), and 443(100%) finite fields of class Cl, C2 and C3, respectively. (C) 2016 Elsevier B.V. All rights reserved.
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