Counting Points on Hyperelliptic Curves over Finite Fields

  • Pierrick Gaudry
  • Robert Harley
Conference paper

DOI: 10.1007/10722028_18

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1838)
Cite this paper as:
Gaudry P., Harley R. (2000) Counting Points on Hyperelliptic Curves over Finite Fields. In: Bosma W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg

Abstract

We describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an algorithm à la Schoof for genus 2 using Cantor’s division polynomials. These are combined with a birthday paradox algorithm to calculate the cardinality. Our methods are practical and we give actual results computed using our current implementation. The Jacobian groups we handle are larger than those previously reported in the literature.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Pierrick Gaudry
    • 1
  • Robert Harley
    • 2
  1. 1.LIXÉcole PolytechniquePalaiseau CedexFrance
  2. 2.Projet Cristal, INRIADomaine de Voluceau – RocquencourtLe ChesnayFrance

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