Efficient four-dimensional GLV curve with high security

Olivier Bernard; Renaud Dubois; Simon Masson

Paper 2018/305

Efficient four-dimensional GLV curve with high security

Olivier Bernard, Renaud Dubois, and Simon Masson

Abstract

We apply Smith's construction to generate four-dimensional GLV curves with fast arithmetic in the group law as well as in the base field. As Costello and Longa did in [5] for a 128-bit security level, we btained an interesting curve for fast GLV scalar multiplication, providing a high level of security (254 bits). Our curve is defined over a well-known finite field: $\mathbb{F}_{p^2}$ where $p = 2^{255} - 19$. We finally explicit the two endomorphisms used during GLV decomposition.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Contact author(s): simon masson @ loria fr
History: 2018-04-03: received
Short URL: https://ia.cr/2018/305
License: CC BY

BibTeX

@misc{cryptoeprint:2018/305,
      author = {Olivier Bernard and Renaud Dubois and Simon Masson},
      title = {Efficient four-dimensional {GLV} curve with high security},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/305},
      year = {2018},
      url = {https://eprint.iacr.org/2018/305}
}