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PKC
2010
Springer

Efficient Arithmetic on Hessian Curves

9 years 4 months ago
Efficient Arithmetic on Hessian Curves
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 filed Fq, 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 addition formulas for generalized binary Hessian curves. The fastest projective addition formulas require 9M + 3S, where M is the cost of a field multiplication and S is the cost of a field squaring. Moreover, very fast differential addition and doubling formulas are provided that need only 5M + 4S when the curve is chosen with small curve parameters.
Reza Rezaeian Farashahi, Marc Joye
Added 14 Oct 2010
Updated 14 Oct 2010
Type Conference
Year 2010
Where PKC
Authors Reza Rezaeian Farashahi, Marc Joye
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