Computing Canonical Heights on Elliptic Curves in Quasi-Linear Time

22 Dec 2015  ·  Müller J. Steffen, Stoll Michael ·

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. read more

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Number Theory