Improving the pocklington and padr Ó-s Áez cube root algorithm

Gook Hwa Cho; Hyang Sook Lee

doi:10.4134/BKMS.b160769

Improving the pocklington and padr Ó-s Áez cube root algorithm

Gook Hwa Cho, Hyang Sook Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we present a cube root algorithm using a recurrence relation. Additionally, we compare the implementations of the Pocklington and Padró-Sáez algorithm with the Adleman-Manders-Miller algorithm. With the recurrence relations, we improve the Pocklington and Padró-Sáez algorithm by using a smaller base for exponentiation. Our method can reduce the average number of Fq multiplications.

Original language	English
Pages (from-to)	277-283
Number of pages	7
Journal	Bulletin of the Korean Mathematical Society
Volume	56
Issue number	2
DOIs	https://doi.org/10.4134/BKMS.b160769
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2019 Korean Mathematical Society.

Keywords

Adleman-Manders-Miller algorithm
Cipolla-Lehmer algorithm
Cube root algorithm
Finite field
Pocklington algorithm

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10.4134/BKMS.b160769

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title = "Improving the pocklington and padr {\'O}-s {\'A}ez cube root algorithm",

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 Fq multiplications.",

keywords = "Adleman-Manders-Miller algorithm, Cipolla-Lehmer algorithm, Cube root algorithm, Finite field, Pocklington algorithm",

author = "Cho, \{Gook Hwa\} and Lee, \{Hyang Sook\}",

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doi = "10.4134/BKMS.b160769",

language = "English",

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AB - In this paper, we present a cube root algorithm using a recurrence relation. Additionally, we compare the implementations of the Pocklington and Padró-Sáez algorithm with the Adleman-Manders-Miller algorithm. With the recurrence relations, we improve the Pocklington and Padró-Sáez algorithm by using a smaller base for exponentiation. Our method can reduce the average number of Fq multiplications.

KW - Adleman-Manders-Miller algorithm

KW - Cipolla-Lehmer algorithm

KW - Cube root algorithm

KW - Finite field

KW - Pocklington algorithm

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JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

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ER -

Improving the pocklington and padr Ó-s Áez cube root algorithm

Abstract

Bibliographical note

Keywords

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