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Satoh’s algorithm in characteristic 2. (English) Zbl 1027.11045

The author gives an algorithm for counting points on arbitrary ordinary elliptic curves over finite fields of characteristic 2, extending the \(O(\log^5q)\) method given by T. Satoh [J. Ramanujan Math. Soc. 15, 247-270 (2000; Zbl 1009.11051)], giving the asymptotically fastest point counting algorithm known to date.

MSC:

11G20 Curves over finite and local fields
14G50 Applications to coding theory and cryptography of arithmetic geometry

Citations:

Zbl 1009.11051
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References:

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[8] Takakazu Satoh, The canonical lift of an ordinary elliptic curve over a finite field and its point counting, J. Ramanujan Math. Soc. 15 (2000), no. 4, 247 – 270. · Zbl 1009.11051
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