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.b160769
Published online 2019 Mar 01
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
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