Cryptology ePrint Archive: Report 2004/015

An AGM-type elliptic curve point counting algorithm in characteristic three

Trond St{\o}len Gustavsen and Kristian Ranestad

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.

Category / Keywords: foundations / elliptic curve cryptosystems, point counting

Date: received 26 Jan 2004

Contact author: stolen at math uio no

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Version: 20040127:083026 (All versions of this report)

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