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The Group Law on Elliptic Curves on Hesse form

In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas

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  • Hege Reithe Frium

    (HQDC Norway)

Abstract

In this paper I will give an introduction to elliptic curves on Hesse form. The embedding of these curves in the projective plane make their symmetries especially nice. If we pick a point p in the projective plane s.t. p is not a 3-torsion point, p is the parametrization of the curve that contains p. We will also see that the division polynomials are independent of chosen elliptic curve on Hesse form.

Suggested Citation

  • Hege Reithe Frium, 2002. "The Group Law on Elliptic Curves on Hesse form," Springer Books, in: Gary L. Mullen & Henning Stichtenoth & Horacio Tapia-Recillas (ed.), Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pages 123-151, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59435-9_10
    DOI: 10.1007/978-3-642-59435-9_10
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