Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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POINTS COUNTING ALGORITHM FOR ONE-DIMENSIONAL FAMILY OF GENUS 3 NONHYPERELLIPTIC CURVES OVER FINITE FIELDS

  • Sohn, Gyo-Yong (School of Electrical Engineering and Computer Science, Kyungpook National University)
  • 투고 : 2011.09.15
  • 심사 : 2011.11.16
  • 발행 : 2012.01.30
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초록

In this paper, we present an algorithm for computing the number of points on the Jacobian varieties of one-dimensional family of genus 3 nonhyperelliptic curves over finite fields. We also provide the explicit formula of the characteristic polynomial of the Frobenius endomorphism of the Jacobian of $C:y^3=x^4+{\alpha}$ over a finite field $\mathbb{F}_p$ with $p{\equiv}1$ (mod 3) and $p{\neq}1$ (mod 4). Moreover, we give some implementation results using Gaudry-Schost method. A 162-bit order is computed in 97 s on a Pentium IV 2.13 GHz computer using our algorithm.

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참고문헌

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