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Full-Text Articles in Number Theory
Construction Of Rational Points On Elliptic Curves Over Finite Fields, Andrew Shallue, Christiaan Van De Woestijne
Construction Of Rational Points On Elliptic Curves Over Finite Fields, Andrew Shallue, Christiaan Van De Woestijne
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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.