Computing isogenies between elliptic curves over using Couveignes's algorithm |
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Authors: | R Lercier F Morain |
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Institution: | CELAR/SSIG, Route de Laillé, F-35170 Bruz, France ; Laboratoire d'Informatique de l'École polytechnique (LIX - UMR 7650), F-91128 Palaiseau Cedex, France |
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Abstract: | The heart of the improvements by 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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Keywords: | Elliptic curves finite fields isogenies formal groups Schoof's algorithm |
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