English

Fast algorithms for computing isogenies between elliptic curves

Computational Complexity 2013-06-19 v1 Symbolic Computation Number Theory

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.

Keywords

Cite

@article{arxiv.cs/0609020,
  title  = {Fast algorithms for computing isogenies between elliptic curves},
  author = {Alin Bostan and Bruno Salvy and Francois Morain and Eric Schost},
  journal= {arXiv preprint arXiv:cs/0609020},
  year   = {2013}
}