Reynald Lercier

R. Lercier and F. Morain. Computing isogenies between elliptic curves over GF(pⁿ) using Couveignes's algorithm. Mathematics of Computation, 69(229):351-370, January 2000.

The heart of the improvements of Elkies to Schoof's algorithm for computing the cardinality of elliptic curves over a finite field is the ability to compute isogenies between curves. Elkies' 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 Couveignes's 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.

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