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A Simple Point Counting Algorithm for Hessian Elliptic Curves in Characteristic Three

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Abstract

Given an ordinary elliptic curve on Hesse form over a finite field of characteristic three, we give a sequence of elliptic curves which leads to an effective construction of the canonical lift, and obtain an algorithm for computing the number of points. Our methods are based on the study of an explicitly and naturally given 3-isogeny between elliptic curves on Hesse form.

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Authors and Affiliations

  1. Department of Mathematics, University of Oslo, P.O. Box 1053, 0316, Oslo, Norway

    Trond Stølen Gustavsen & Kristian Ranestad

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  1. Trond Stølen Gustavsen
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  2. Kristian Ranestad
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Correspondence to Trond Stølen Gustavsen.

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Gustavsen, T.S., Ranestad, K. A Simple Point Counting Algorithm for Hessian Elliptic Curves in Characteristic Three. AAECC 17, 141–150 (2006). https://doi.org/10.1007/s00200-006-0013-x

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  • DOI: https://doi.org/10.1007/s00200-006-0013-x

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