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Isomorphism Classes of Genus-2 Hyperelliptic Curves Over Finite Fields

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

We propose a reduced equation for hyperelliptic curves of genus 2 over finite fields ? q of q elements with characteristic different from 2 and 5. We determine the number of isomorphism classes of genus-2 hyperelliptic curves having an ? q -rational Weierstrass point. These results have applications to hyperelliptic curve cryptography.

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Authors and Affiliations

  1. Instituto de Física Aplicada, CSIC, C/ Serrano 144, 28006 Madrid, Spain (e-mail: {luis, jaime}@iec.csic.es), , , , , , ES

    L. Hernández Encinas & J. Muñoz Masqué

  2. Department of C&O, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 (e-mail: ajmeneze@uwaterloo.ca), , , , , , CA

    Alfred J. Menezes

Authors
  1. L. Hernández Encinas
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  2. Alfred J. Menezes
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  3. J. Muñoz Masqué
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Received: May 2, 2001

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Encinas, L., Menezes, A. & Masqué, J. Isomorphism Classes of Genus-2 Hyperelliptic Curves Over Finite Fields. AAECC 13, 57–65 (2002). https://doi.org/10.1007/s002000100092

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  • DOI: https://doi.org/10.1007/s002000100092