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.
This work was partially supported by MSRC
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Choie, Y., Yun, D. (2002). Isomorphism Classes of Hyperelliptic Curves of Genus 2 over \( \mathbb{F}_q \) . In: Batten, L., Seberry, J. (eds) Information Security and Privacy. ACISP 2002. Lecture Notes in Computer Science, vol 2384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45450-0_16
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DOI: https://doi.org/10.1007/3-540-45450-0_16
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