Construction of Rational Points on Elliptic Curves over Finite Fields

  • Andrew Shallue
  • Christiaan E. van de Woestijne
Conference paper

DOI: 10.1007/11792086_36

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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andrew Shallue
    • 1
  • Christiaan E. van de Woestijne
    • 2
  1. 1.Mathematics DepartmentUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Mathematisch InstituutUniversiteit LeidenLeidenThe Netherlands

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