Efficient Arithmetic on Hessian Curves

@inproceedings{Farashahi2010EfficientAO,
  title={Efficient Arithmetic on Hessian Curves},
  author={Reza Rezaeian Farashahi and Marc Joye},
  booktitle={Public Key Cryptography},
  year={2010}
}
This paper considers a generalized form for Hessian curves. The family of generalized Hessian curves covers more isomorphism classes of elliptic curves. Over a finite field $\mathbb{F}_q$, it is shown to be equivalent to the family of elliptic curves with a torsion subgroup isomorphic to ℤ/3ℤ. This paper provides efficient unified addition formulas for generalized Hessian curves. The formulas even feature completeness for suitably chosen parameters. This paper also presents extremely fast… 
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