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arXiv · 1509.08748

Computing Canonical Heights on Elliptic Curves in Quasi-Linear Time

J. Steffen Müller·Michael Stoll
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Abstract

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.

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J. Steffen Müller, Michael Stoll. 2015-09-29. Computing Canonical Heights on Elliptic Curves in Quasi-Linear Time. https://doi.org/10.1112/s1461157016000139

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