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PKC
2010
Springer
210views Cryptology» more  PKC 2010»
13 years 5 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 ...
Reza Rezaeian Farashahi, Marc Joye
PKC
1998
Springer
123views Cryptology» more  PKC 1998»
13 years 7 months ago
Two Efficient Algorithms for Arithmetic of Elliptic Curves Using Frobenius Map
In this paper, we present two efficient algorithms computing scalar multiplications of a point in an elliptic curve defined over a small finite field, the Frobenius map of which ha...
Jung Hee Cheon, Sung-Mo Park, Sangwoo Park, Daeho ...
DCC
2000
IEEE
13 years 3 months ago
Efficient Arithmetic on Koblitz Curves
It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: ta...
Jerome A. Solinas
EUROCRYPT
2003
Springer
13 years 8 months ago
Improved Algorithms for Efficient Arithmetic on Elliptic Curves Using Fast Endomorphisms
Mathieu Ciet, Tanja Lange, Francesco Sica, Jean-Ja...
FOCM
2002
97views more  FOCM 2002»
13 years 3 months ago
On the Riemannian Geometry Defined by Self-Concordant Barriers and Interior-Point Methods
We consider the Riemannian geometry defined on a convex set by the Hessian of a selfconcordant barrier function, and its associated geodesic curves. These provide guidance for the...
Yu. E. Nesterov, Michael J. Todd