Anzeige
Erschienen in:
2010 | OriginalPaper | Buchkapitel
Efficient Arithmetic on Hessian Curves
verfasst von : Reza R. Farashahi, Marc Joye
Erschienen in: Public Key Cryptography – PKC 2010
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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 addition formulas for generalized binary Hessian curves. The fastest projective addition formulas require 9
M
+ 3
S
, 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 5
M
+ 4
S
when the curve is chosen with small curve parameters.