Construction of Rational Points on Elliptic Curves over Finite Fields

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.

• Type: Conference
• Year: 2006
• Where: ANTS
• Authors: Andrew Shallue, Christiaan van de Woestijne
• Keywords: Algorithms, ANTS 2006, Deterministic Polynomial-time Algorithm, Nontrivial Rational Point, Rational Point