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Computing canonical heights on elliptic curves in quasi-linear time

Title data

Müller, Jan Steffen ; Stoll, Michael:
Computing canonical heights on elliptic curves in quasi-linear time.
In: LMS Journal of Computation and Mathematics. Vol. 19 (January 2016) . - pp. 391-405.
ISSN 1461-1570
DOI: https://doi.org/10.1112/S1461157016000139

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Subject classification: Mathematics Subject Classification Code: 11G50 14G40 11G05 11Y16
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 07 Oct 2016 06:05
Last Modified: 07 Oct 2016 06:05
URI: https://eref.uni-bayreuth.de/id/eprint/34854