Welcome to the resource topic for 2009/457
Title:
A remark on the computation of cube roots in finite fields
Authors: Nozomu Nishihara, Ryuichi Harasawa, Yutaka Sueyoshi, Aichi Kudo
Abstract:We consider the computation of cube roots in finite fields. For the computation of square roots in finite fields, there are two typical methods; the Tonelli-Shanks method and the Cipolla-Lehmer method. The former can be extended easily to the case of r-th roots, which is called the Adleman-Manders-Miller method, but it seems to be difficult to extend the latter to more general cases. In this paper, we propose two explicit algorithms for realizing the Cipolla-Lehmer method in the case of cube roots for prime fields \mathbb{F}_{p} with p \equiv 1 \ ({\rm mod} \ {3}). We implement these methods and compare the results.
ePrint: https://eprint.iacr.org/2009/457
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