• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.277-283
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• 2019

In this paper, we present a cube root algorithm using a recurrence relation. Additionally, we compare the implementations of the Pocklington and $Padr{\acute{o}}-S{\acute{a}}ez$ algorithm with the Adleman-Manders-Miller algorithm. With the recurrence relations, we improve the Pocklington and $Padr{\acute{o}}-S{\acute{a}}ez$ algorithm by using a smaller base for exponentiation. Our method can reduce the average number of ${\mathbb{F}}_q$ multiplications.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1523-1537
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• 2022

We present a new square root algorithm in finite fields which is a variant of the Pocklington-Peralta algorithm. We give the complexity of the proposed algorithm in terms of the number of operations (multiplications) in finite fields, and compare the result with other square root algorithms, the Tonelli-Shanks algorithm, the Cipolla-Lehmer algorithm, and the original Pocklington-Peralta square root algorithm. Both the theoretical estimation and the implementation result imply that our proposed algorithm performs favorably over other existing algorithms. In particular, for the NIST suggested field P-224, we show that our proposed algorithm is significantly faster than other proposed algorithms.