Construction of Rational Points on Elliptic Curves over Finite Fields | Zendy

Andrew Shallue | Zendy; Christiaan E. van de Woestijne | Zendy

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Construction of Rational Points on Elliptic Curves over Finite Fields

Author(s) -

Andrew Shallue,

Christiaan E. van de Woestijne

Publication year - 2006

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

ISBN - 3-540-36075-1

DOI - 10.1007/11792086_36

Subject(s) - elliptic curve , rational point , hessian form of an elliptic curve , schoof's algorithm , finite field , point (geometry) , tripling oriented doche–icart–kohel curve , jacobian curve , genus , computer science , polynomial and rational function modeling , polynomial , counting points on elliptic curves , task (project management) , mathematics , discrete mathematics , pure mathematics , mathematical analysis , geometry , quarter period , botany , management , biology , economics , algebraic number

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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