Remarks on the Pocklington and Padró-Sáez cube root algorithm in Fq

Abstract

A cube root algorithm in Fq proposed by Pocklington and later rediscovered by Padró and Sáez is clarified and generalised. Some errors in the result of Padró and Sáez are corrected and a full generalisation of their result is given. A comparison of the implementation of the proposed algorithm with the two most popular cube root algorithms is also given, namely the Adleman-Manders-Miller algorithm and the Cipolla-Lehmer algorithm. To the authors' knowledge, this comparison is the first one which compares three fundamental algorithms together. © The Institution of Engineering and Technology 2014.