Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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IMPROVING THE POCKLINGTON AND PADRÓ-SÁEZ CUBE ROOT ALGORITHM

  • Received : 2016.09.22
  • Accepted : 2019.03.04
  • Published : 2019.03.31
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Abstract

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.

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TABLE 1. Adleman-Manders-Miller’s cube root algorithm [1]

E1BMAX_2019_v56n2_277_t0001.png 이미지

TABLE 2. Pocklington and Padro-Saez cube root algorithm [4]

E1BMAX_2019_v56n2_277_t0002.png 이미지

TABLE 3. Theoretical estimation (average number of $\mathbb{F}_q$ multiplications)

E1BMAX_2019_v56n2_277_t0003.png 이미지

TABLE 4. Running time (in seconds) for cube root computa-tion with p ≈ 22000

E1BMAX_2019_v56n2_277_t0004.png 이미지

TABLE 5. Running time (in seconds) for cube root computa-tion with p ≈ 23000

E1BMAX_2019_v56n2_277_t0005.png 이미지

References

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