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Mathematics of Computation

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Satoh's algorithm in characteristic 2

Author: Berit Skjernaa
Journal: Math. Comp. 72 (2003), 477-487
MSC (2000): Primary 11G20, 11T71; Secondary 11G07, 14H52
Published electronically: March 22, 2002
MathSciNet review: 1933832
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Abstract: We give an algorithm for counting points on arbitrary ordinary elliptic curves over finite fields of characteristic $2$, extending the $O(\log^5q)$method given by Takakazu Satoh, giving the asymptotically fastest point counting algorithm known to date.

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Additional Information

Berit Skjernaa
Affiliation: University of Aarhus, Department of Mathematics, Ny Munkegade, 8000 Aarhus C, Denmark

Keywords: Satoh's algorithm, elliptic curves, finite fields, order counting
Received by editor(s): September 4, 2000
Received by editor(s) in revised form: March 15, 2001
Published electronically: March 22, 2002
Additional Notes: Research supported in part by a Ph.D. grant from CRYPTOMAThIC
Article copyright: © Copyright 2002 American Mathematical Society