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Construction of Rational Points on Elliptic Curves over Finite Fields

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Algorithmic Number Theory (ANTS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4076))

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Abstract

We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the curve. For this, we reduce the problem to the task of finding a rational point on a curve of genus zero.

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Author information

Authors and Affiliations

  1. Mathematics Department, University of Wisconsin-Madison, 480 Lincoln Dr, Madison, WI, 53706-1388, USA

    Andrew Shallue

  2. Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden, The Netherlands

    Christiaan E. van de Woestijne

Authors
  1. Andrew Shallue
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  2. Christiaan E. van de Woestijne
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Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Florian Hess

  2. Institut für Mathematik, MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Sebastian Pauli

  3. Institut für Mathematik, Technische Universität Berlin, Fakultät II, MA 8-1, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Michael Pohst

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© 2006 Springer-Verlag Berlin Heidelberg

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Shallue, A., van de Woestijne, C.E. (2006). Construction of Rational Points on Elliptic Curves over Finite Fields. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_36

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  • DOI: https://doi.org/10.1007/11792086_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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