International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Koray Karabina

Affiliation: University of Waterloo

Publications

Year
Venue
Title
2015
EPRINT
2014
EPRINT
2011
EUROCRYPT
2008
EPRINT
Analyzing the Galbraith-Lin-Scott Point Multiplication Method for Elliptic Curves over Binary Fields
Galbraith, Lin and Scott recently constructed efficiently-computable endomorphisms for a large family of elliptic curves defined over F_{q^2} and showed, in the case where q is prime, that the Gallant-Lambert-Vanstone point multiplication method for these curves is significantly faster than point multiplication for general elliptic curves over prime fields. In this paper, we investigate the potential benefits of using Galbraith-Lin-Scott elliptic curves in the case where q is a power of 2. The analysis differs from the q prime case because of several factors, including the availability of the point halving strategy for elliptic curves over binary fields. Our analysis and implementations show that Galbraith-Lin-Scott offers significant acceleration for curves over binary fields, in both doubling- and halving-based approaches. Experimentally, the acceleration surpasses that reported for prime fields (for the platform in common), a somewhat counterintuitive result given the relative costs of point addition and doubling in each case.
2007
EPRINT
On prime-order elliptic curves with embedding degrees k=3,4 and 6
Koray Karabina Edlyn Teske
We further analyze the solutions to the Diophantine equations from which prime-order elliptic curves of embedding degrees $k=3,4$ or $6$ (MNT curves) may be obtained. We give an explicit algorithm to generate such curves. We derive a heuristic lower bound for the number $E(z)$ of MNT curves with $k=6$ and discriminant $D\le z$, and compare this lower bound with experimental data.

Program Committees

Asiacrypt 2014