Fast point multiplication algorithms for binary elliptic curves with and without precomputation

Thomaz Oliveira; Diego F.  Aranha; Julio López; Francisco Rodríguez-Henríquez

Paper 2014/427

Fast point multiplication algorithms for binary elliptic curves with and without precomputation

Thomaz Oliveira, Diego F. Aranha, Julio López, and Francisco Rodríguez-Henríquez

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. MINOR revision.
Keywords: binary elliptic curves scalar multiplication software implementation
Contact author(s): thomaz figueiredo @ gmail com
History: 2014-07-31: last of 2 revisions; 2014-06-06: received; See all versions
Short URL: https://ia.cr/2014/427
License: CC BY

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}
}