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Computing canonical heights on elliptic curves in quasi-linear time
Published online by Cambridge University Press: 26 August 2016
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.
MSC classification
- Type
- Research Article
- Information
- LMS Journal of Computation and Mathematics , Volume 19 , Special Issue A: Algorithmic Number Theory Symposium XII , 2016 , pp. 391 - 405
- Copyright
- © The Author(s) 2016
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