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 Improving the Pocklington and Padr\'{o}-S\'{a}ez cube root Algorithm Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 277-283 https://doi.org/10.4134/BKMS.b160769Published online March 1, 2019 Gook Hwa Cho, Hyang-Sook Lee Ewha Womans University; Ewha Womans University Abstract : In this paper, we present a cube root algorithm using a recurrence relation. Additionally, we compare the implementations of the Pocklington and Padr\'{o}-S\'{a}ez algorithm with the Adleman-Manders-Miller algorithm. With the recurrence relations, we improve the Pocklington and Padr\'{o}-S\'{a}ez algorithm by using a smaller base for exponentiation. Our method can reduce the average number of $\mathbb F_q$ multiplications. Keywords : cube root algorithm, finite field, Pocklington algorithm, Adleman-Manders-Miller algorithm, Cipolla-Lehmer algorithm MSC numbers : 11T06, 11Y16, 68W40 Full-Text :