Fast algorithms for computing isogenies between elliptic curves

Details Fast algorithms for computing isogenies between elliptic curves Fast algorithms for computing isogenies between elliptic curves

2006-09-06

arxiv.org/abs/cs/0609020v1

Computer Science

Computational Complexity

Scientific paper

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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