Construction of Rational Points on Elliptic Curves over Finite Fields
- 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
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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