Fast algorithms for computing isogenies between elliptic curves

Bostan, A.; Morain, F.; Salvy, B.; Schost, É.

doi:10.1090/S0025-5718-08-02066-8

Fast algorithms for computing isogenies between elliptic curves
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by A. Bostan, F. Morain, B. Salvy and É. Schost PDF

Math. Comp. 77 (2008), 1755-1778 Request permission

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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