Paper 2017/350
The Montgomery ladder on binary elliptic curves
Thomaz Oliveira, Julio López, and Francisco Rodríguez-Henríquez
Abstract
In this survey paper we present a careful analysis of the Montgomery ladder procedure applied to the computation of the constant-time point multiplication operation on elliptic curves defined over binary extension fields. We give a general view of the main improvements and formula derivations that several researchers have contributed across the years, since the publication of Peter Lawrence Montgomery seminal work in 1987. We also report a fast software implementation of the Montgomery ladder applied on a Galbraith-Lin-Scott (GLS) binary elliptic curve that offers a security level close to 128 bits. Using our software we can execute the ephemeral Diffie-Hellman protocol in just 95,702 clock cycles when implemented on an Intel Skylake machine running at 4 GHz.
Metadata
- Available format(s)
-
PDF
- Publication info
- Published elsewhere. Minor revision. To appear in Journal of Cryptographic Engineering
- Keywords
- Montgomery ladderScalar multiplicationbinary elliptic curves
- Contact author(s)
- francisco @ cs cinvestav mx
- History
- 2017-07-03: last of 2 revisions
- 2017-04-26: received
- See all versions
- Short URL
- https://ia.cr/2017/350
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2017/350,
author = {Thomaz Oliveira and Julio López and Francisco Rodríguez-Henríquez},
title = {The Montgomery ladder on binary elliptic curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/350},
year = {2017},
url = {https://eprint.iacr.org/2017/350}
}
