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A simple point counting algorithm for Hessian elliptic curves in characteristic three. (English) Zbl 1099.14011
Summary: 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.

MSC:
14G50 Applications to coding theory and cryptography of arithmetic geometry
94A60 Cryptography
Software:
PARI/GP
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