Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/148080
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- Title
- Efficient arithmetic on Hessian curves
- Related
- International Workshop on Practice and Theory in Public Key Cryptography (13th : 2010) (26 - 28 May 2010 : Paris)
- Related
- Nguyen, Phong Q. and Pointcheval, David. Public key cryptography--PKC 2010 : 13th International Conference on Practice and Theory in Public Key Cryptography, Paris, France, May 26-28, 2010 : proceedings, p.243-260
- DOI
- 10.1007/978-3-642-13013-7_15
- Related
- Lecture notes in computer science Vol. 6056
- Publisher
- Berlin ; New York : Springer
- Date
- 2010
- FoR/RFCD Code(s)
-
010100 Pure Mathematics
- Author/Creator
- Farashahi, Reza R
- Author/Creator
- Joye, Marc
- Description
- 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 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.
- Description
- 18 page(s)
- Subject Keyword
- 010100 Pure Mathematics
- Subject Keyword
- Elliptic curves
- Subject Keyword
- Hessian curves
- Subject Keyword
- cryptography
- Resource Type
- conference paper
- Organisation
- Macquarie University. Dept. of Computing
- Identifier
- http://hdl.handle.net/1959.14/148080
- Identifier
- ISBN:9783642130137
- Identifier
- mq-rm-2009011824
- Language
- eng
- Reviewed
