# An extension of Satoh's algorithm and its implementation

Abstract : We describe a fast algorithm for counting points on elliptic curves defined over finite fields of small characteristic, following Satoh. Our main contribution is an extension to characteristics two and three. We give a detailed description with the optimisations necessary for an efficient implementation. Finally we give the number of points we have computed on a random'' curve defined over the field Fq with q=2^8009.
Document type :
Journal articles

https://hal.inria.fr/inria-00512791
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Submitted on : Tuesday, August 31, 2010 - 3:56:56 PM
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satoh.pdf
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• HAL Id : inria-00512791, version 1

### Citation

Mireille Fouquet, Pierrick Gaudry, Robert Harley. An extension of Satoh's algorithm and its implementation. Journal of the Ramanujan Mathematical Society, Ramanujan Mathematical Society, 2000, 15, pp.281-318. ⟨inria-00512791⟩

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