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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.
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참고문헌 (9)
참고문헌 신청
L. Adleman / 1977 / On taking roots in nite elds / 18th Annual Symposium on Foundations of Computer Science (Providence, R.I., 1977) :175~178
Z. Cao / 2012 / Information security and cryptology / Springer :77~85
M. Cipolla / 1903 / Rendiconto dell`Accademia Scienze Fisiche e Matematiche :154~163
G. Heo / 2014 / Remarks on the Pocklington and Padro-Saez cube root algorithm in Fq / Electronics Letters 50(14):1002~1003
D. H. Lehmer / 1969 / Studies in Number Theory / Math. Assoc. Amer, Prentice-Hall :117~151
Z. Cao / 2012 / Information security and cryptology / Springer :77~85
M. Cipolla / 1903 / Rendiconto dell`Accademia Scienze Fisiche e Matematiche :154~163
G. Heo / 2014 / Remarks on the Pocklington and Padro-Saez cube root algorithm in Fq / Electronics Letters 50(14):1002~1003
D. H. Lehmer / 1969 / Studies in Number Theory / Math. Assoc. Amer, Prentice-Hall :117~151
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