Formulas for cube roots in F3m using shifted polynomial basis

Authors:
Young In Cho;Nam Su Chang;Seokhie Hong
Affiliations:
CIST (Center for Information Security Technologies), Korea University, Anam-dong, Seongbuk-gu, Seoul, 136-713, Korea;Department of Information Security Systems, Sejong Cyber University, Seoul, Korea;CIST (Center for Information Security Technologies), Korea University, Anam-dong, Seongbuk-gu, Seoul, 136-713, Korea
Venue:
Information Processing Letters
Year:
2014

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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@?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.