Paper 2008/334
Analyzing the Galbraith-Lin-Scott Point Multiplication Method for Elliptic Curves over Binary Fields
Darrel Hankerson, Koray Karabina, and Alfred Menezes
Abstract
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.
Note: Minor revision; updated data from eprint 2008/194.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- elliptic curvepoint multiplicationGLV methodisogeny
- Contact author(s)
- hankedr @ auburn edu
- History
- 2008-10-07: revised
- 2008-08-03: received
- See all versions
- Short URL
- https://ia.cr/2008/334
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2008/334,
author = {Darrel Hankerson and Koray Karabina and Alfred Menezes},
title = {Analyzing the Galbraith-Lin-Scott Point Multiplication Method for Elliptic Curves over Binary Fields},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/334},
year = {2008},
url = {https://eprint.iacr.org/2008/334}
}
