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Isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2

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Abstract

In this paper we study the computation of the number of isomorphism classes of hyperelliptic curves of genus 2 over finite fields F q with q even. We show the formula of the number of isomorphism classes, that is, for q = 2m, if 4 ∤ m, then the formula is 2q 3 + q 2 − q; if 4 | m, then the formula is 2q 3 + q 2 − q + 8. These results can be used in the classification problems and the hyperelliptic curve cryptosystems.

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Authors and Affiliations

  1. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Deng Yingpu & Liu Mulan

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  1. Deng Yingpu
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  2. Liu Mulan
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Correspondence to Deng Yingpu.

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Deng, Y., Liu, M. Isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2. SCI CHINA SER A 49, 173–184 (2006). https://doi.org/10.1007/s11425-004-0043-4

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  • DOI: https://doi.org/10.1007/s11425-004-0043-4

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