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Reports (Research Report) Year : 2006

Fast algorithms for computing isogenies between elliptic curves

Abstract

We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree $\ell$ ($\ell$ different from the characteristic) in time quasi-linear with respect to $\ell$. This is based in particular on fast algorithms for power series expansion of the Weierstrass $\wp$-function and related functions.
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Dates and versions

inria-00091441 , version 1 (06-09-2006)

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Alin Bostan, Bruno Salvy, Francois Morain, Eric Schost. Fast algorithms for computing isogenies between elliptic curves. [Research Report] 2006, pp.28. ⟨inria-00091441⟩
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