Paper 2014/427 Original: eprint.iacr.org/2014/427 ↗
Fast point multiplication algorithms for binary elliptic curves with and without precomputation
Abstract
In this paper we introduce new methods for computing constant-time variable-base point multiplications over the Galbraith-Lin-Scott (GLS) and the Koblitz families of elliptic curves. Using a left-to-right double-and-add and a right-to-left halve-and-add Montgomery ladder over a GLS curve, we present some of the fastest timings yet reported in the literature for point multiplication. In addition, we combine these two procedures to compute a multi-core protected scalar multiplication. Furthermore, we designed for the first time a regular $\tau$-adic scalar expansion for Koblitz curves. As a result, using the regular recoding approach, we set the speed record for a single constant-time point multiplication on standardized binary elliptic curves at the $128$-bit security level.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2014-07-31: last updated
- 2014-06-06: published
- Short URL
- https://ia.cr/2014/427
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2014/427,
author = {Thomaz Oliveira and Diego F. Aranha and Julio López and Francisco Rodríguez-Henríquez},
title = {Fast point multiplication algorithms for binary elliptic curves with and without precomputation},
howpublished = {Cryptology {ePrint} Archive, Paper 2014/427},
year = {2014},
url = {https://eprint.iacr.org/2014/427}
}