Computing isogenies between elliptic curves over đš_{đâż} using Couveignesâs algorithm
Reynald Lercier, François Morain ¡ Mathematics of Computation ¡ 1999
The heart of the improvements by Elkies to Schoofâs algorithm for computing the cardinality of elliptic curves over a finite field is the ability to compute isogenies between curves. Elkiesâ approach is well suited for the case where the characteristic of the field is large. Couveignes showed how to compute isogenies in small characteristic. The aim of this paper is to describe the first successful implementation of Couveignesâs algorithm. In particular, we describe the use of fast algorithms for performing incremental operations on series. We also insist on the particular case of the characteristic 2.