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Isomorphism Classes of Hyperelliptic Curves of Genus 2 over \( \mathbb{F}_q \)

  • Y. Choie
  • D. Yun
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2384)

Abstract

We present a simple and direct method of counting the number of the isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic different from 5. In this case it turns out that the number of isomorphism classes of genus-2 hyperelliptic curve over a given field \( \mathbb{F}_q \) is on the order of q 3. These results have applications to hyperelliptic curve cryptography.

Keywords

Elliptic Curve Smart Card Elliptic Curf Isomorphism Class Hyperelliptic Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Y. Choie
    • 1
  • D. Yun
    • 1
  1. 1.Department of MathematicsPohang University of Science and TechnologyPohangKorea

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