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Computing canonical heights on elliptic curves in quasi-linear time

  • J. Steffen Müller (a1) and Michael Stoll (a2)
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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References
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LMS Journal of Computation and Mathematics
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  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
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