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 Improving the Pocklington and Padr\'{o}-S\'{a}ez Cube Root Algorithm Bull. Korean Math. Soc.Published online 2019 Mar 12 Gook Hwa Cho, and Hyang-sook Lee Ewha Womans University Abstract : In the paper, we present a cube root algorithm using recurrence relation. We also give the comparison of the implementation of Pocklington and Padr\'{o}-S\'{a}ez algorithm with Adleman-Manders-Miller algorithm. Our method can reduce the number of exact multiplications over $\mathbb{F}_q$. Keywords : cube root algorithm, finite field, Pocklington algorithm, Adleman-Manders-Miller algorithm, Cipolla-Lehmer algorithm MSC numbers : 11T06,11Y16,68W40 Full-Text :