Counting Points on Genus 2 Curves with Real Multiplication

  • Pierrick Gaudry
  • David Kohel
  • Benjamin Smith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7073)


We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm reduces the complexity of genus 2 point counting over a finite field \(\mathbb{F}_{q}\) of large characteristic from \({\widetilde{O}}(\log^8 q)\) to \({\widetilde{O}}(\log^5 q)\). Using our algorithm we compute a 256-bit prime-order Jacobian, suitable for cryptographic applications, and also the order of a 1024-bit Jacobian.


Modulus Space Class Number Minimal Polynomial Principal Ideal Hyperelliptic Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Pierrick Gaudry
    • 1
  • David Kohel
    • 2
  • Benjamin Smith
    • 3
  1. 1.LORIACNRS / INRIA / Nancy UniversitéVandoeuvre lès NancyFrance
  2. 2.Institut de Mathématiques de LuminyUniversité de la MéditerranéeMarseille Cedex 9France
  3. 3.INRIA Saclay–Île-de-France, Laboratoire d’Informatique de l’École polytechnique (LIX)Palaiseau CedexFrance

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