Paper 2017/840
Fast Scalar Multiplication for Elliptic Curves over Binary Fields by Efficiently Computable Formulas
Saud Al Musa and Guangwu Xu
Abstract
This paper considers efficient scalar multiplication of elliptic curves over binary fields with a twofold purpose. Firstly, we derive the most efficient $3P$ formula in $\lambda$-projective coordinates and $5P$ formula in both affine and $\lambda$-projective coordinates. Secondly, extensive experiments have been conducted to test various multi-base scalar multiplication methods (e.g., greedy, ternary/binary, multi-base NAF, and tree-based) by integrating our fast formulas. The experiments show that our $3P$ and $5P$ formulas had an important role in speeding up the greedy, the ternary/binary, the multi-base NAF, and the tree-based methods over the NAF method. We also establish an efficient $3P$ formula for Koblitz curves and use it to construct an improved set for the optimal pre-computation of window TNAF.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- binary elliptic curvespoint multiplicationlambda coordinatesefficient formulasDBNSMBNS
- Contact author(s)
- gxu4uwm @ uwm edu
- History
- 2017-09-06: received
- Short URL
- https://ia.cr/2017/840
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2017/840,
author = {Saud Al Musa and Guangwu Xu},
title = {Fast Scalar Multiplication for Elliptic Curves over Binary Fields by Efficiently Computable Formulas},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/840},
year = {2017},
url = {https://eprint.iacr.org/2017/840}
}
