Computing Canonical Heights on Elliptic Curves in Quasi-Linear Time
Number Theory
2019-02-20 v2
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.
Cite
@article{arxiv.1509.08748,
title = {Computing Canonical Heights on Elliptic Curves in Quasi-Linear Time},
author = {J. Steffen Müller and Michael Stoll},
journal= {arXiv preprint arXiv:1509.08748},
year = {2019}
}
Comments
15 pages. v2: Fixed an inaccuracy in Algorithm 6.1 pointed out by E. Wells. Minor changes in Sections 4 and 6. Updated timings