Computing Canonical Heights on Elliptic Curves in Quasi-linear Time
نویسنده
چکیده
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.
منابع مشابه
Computing canonical heights with little (or no) factorization
Let E/Q be an elliptic curve with discriminant ∆, and let P ∈ E(Q). The standard method for computing the canonical height ĥ(P ) is as a sum of local heights ĥ(P ) = λ̂∞(P ) + ∑ p λ̂p(P ). There are well-known series for computing the archimedean height λ̂∞(P ), and the non-archimedean heights λ̂p(P ) are easily computed as soon as all prime factors of ∆ have been determined. However, for curves wi...
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