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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2017/350}},
      url = {https://eprint.iacr.org/2017/350}
}
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