International Association
for Cryptologic Research

We clarify and generalize a cube root algorithm in $\\mathbb F_q$ proposed by Pocklington, and later rediscovered by Padr\\\'o and S\\\'aez. We correct some mistakes in the result of Padr\\\'o and S\\\'aez 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.