Fast algorithms for computing isogenies between elliptic curves
计算复杂性
2013-06-19 v1 符号计算
数论
摘要
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 ( different from the characteristic) in time quasi-linear with respect to . This is based in particular on fast algorithms for power series expansion of the Weierstrass -function and related functions.
引用
@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}
}