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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.
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https://hal.inria.fr/inria-00512791
Contributor : Pierrick Gaudry Connect in order to contact the contributor
Submitted on : Tuesday, August 31, 2010 - 3:56:56 PM
Last modification on : Thursday, February 3, 2022 - 11:14:41 AM
Long-term archiving on: : Wednesday, December 1, 2010 - 2:52:34 AM

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  • HAL Id : inria-00512791, version 1

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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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