Construction of Rational Points on Elliptic Curves over Finite Fields

  • Andrew Shallue
  • Christiaan E. van de Woestijne
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4076)


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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