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Paper 2009/457

A remark on the computation of cube roots in finite fields

Nozomu Nishihara and Ryuichi Harasawa and Yutaka Sueyoshi and 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.

Metadata
Available format(s)
PDF PS
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
cube rootfinite fieldthe Tonelli-Shanks method
Contact author(s)
harasawa @ cis nagasaki-u ac jp
History
2013-09-13: revised
2009-09-20: received
See all versions
Short URL
https://ia.cr/2009/457
License
Creative Commons Attribution
CC BY
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