Formulas for cube roots in F-3(m) using shifted polynomial basis
- Authors
- Cho, Young In; Chang, Nam Su; Hong, Seokhie
- Issue Date
- 6월-2014
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Cryptography; Shifted polynomial basis; Cube roots; Finite field arithmetic
- Citation
- INFORMATION PROCESSING LETTERS, v.114, no.6, pp.331 - 337
- Indexed
- SCIE
SCOPUS
- Journal Title
- INFORMATION PROCESSING LETTERS
- Volume
- 114
- Number
- 6
- Start Page
- 331
- End Page
- 337
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/98461
- DOI
- 10.1016/j.ipl.2014.01.001
- ISSN
- 0020-0190
- Abstract
- Evaluation of cube roots in characteristic three finite fields is required for Tate (or modified Tate) pairing computation. The Hamming weight of x(1/3) means that the number of nonzero coefficients in the polynomial representation of x(1/3) in F-3(m) = F-3[x]/(f), where f is an element of F-3[x] is an irreducible polynomial. The Hamming weight of x(1/3) determines the efficiency of cube roots computation for characteristic three finite fields. Ahmadi et al. found the Hamming weight of x(1/3) using polynomial basis [4]. In this paper, we observe that shifted polynomial basis (SPB), a variation of polynomial basis, can reduce Hamming weights of x(1/3) and x(2/3). Moreover, we provide the suitable SPB that eliminates modular reduction process in cube roots computation. (c) 2014 Elsevier B.V. All rights reserved.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - School of Cyber Security > Department of Information Security > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.