Algorithmic Number Theory

Volume 4076 of the series Lecture Notes in Computer Science pp 510-524

Construction of Rational Points on Elliptic Curves over Finite Fields

  • Andrew ShallueAffiliated withMathematics Department, University of Wisconsin-Madison
  • , Christiaan E. van de WoestijneAffiliated withMathematisch Instituut, Universiteit Leiden

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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.