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Computing canonical heights on elliptic curves in quasi-linear time

Published online by Cambridge University Press:  26 August 2016

J. Steffen Müller
Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany email
Michael Stoll
Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany email


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We introduce an algorithm that can be used to compute the canonical height of a point on an elliptic curve over the rationals in quasi-linear time. As in most previous algorithms, we decompose the difference between the canonical and the naive height into an archimedean and a non-archimedean term. Our main contribution is an algorithm for the computation of the non-archimedean term that requires no integer factorization and runs in quasi-linear time.

Research Article
© The Author(s) 2016 


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