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)


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.


Elliptic Curve Smart Card Elliptic Curf Isomorphism Class Hyperelliptic Curve 
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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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