Low complexity bit-parallel multiplier for F-2n defined by repeated polynomials
- Authors
- Chang, Nam Su; Kang, Eun Sook; Hong, 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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