Paper 2014/212

Remarks on the Pocklington and Padró-Sáez Cube Root Algorithm in $\mathbb F_q$

Geon Heo and Seokhwan Choi and Kwang Ho Lee and Namhun Koo and Soonhak Kwon

Abstract

We clarify and generalize a cube root algorithm in $\mathbb F_q$ proposed by Pocklington, and later rediscovered by Padró and Sáez. We correct some mistakes in the result of Padró and Sáez and give a full generalization of their result. We also give the comparison of the implementation of our proposed algorithm with two most popular cube root algorithms, namely the Adleman-Manders-Miller algorithm and the Cipolla-Lehmer algorithm. To the authors' knowledge, our comparison is the first one which compares three fundamental algorithms together.

Note: Some minor typos are corrected.