Abstract
Evaluation of cube roots in characteristic three finite fields is required for Tate (or modified Tate) pairing computation. The Hamming weight of x1/3 means that the number of nonzero coefficients in the polynomial representation of x1/3 in F3m=F3[x]/(f), where f∈F3[x] is an irreducible polynomial. The Hamming weight of x1/3 determines the efficiency of cube roots computation for characteristic three finite fields. Ahmadi et al. found the Hamming weight of x1/3 using polynomial basis [4]. In this paper, we observe that shifted polynomial basis (SPB), a variation of polynomial basis, can reduce Hamming weights of x1/3 and x2/3. Moreover, we provide the suitable SPB that eliminates modular reduction process in cube roots computation.
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