Attractive Subfamilies of BLS Curves for Implementing High-Security Pairings

Craig Costello; Kristin Lauter; Michael Naehrig

Paper 2011/465 Original: eprint.iacr.org/2011/465 ↗

Attractive Subfamilies of BLS Curves for Implementing High-Security Pairings

Craig Costello

Kristin Lauter

Michael Naehrig

Abstract

Barreto-Lynn-Scott (BLS) curves are a stand-out candidate for implementing high-security pairings. This paper shows that particular choices of the pairing-friendly search parameter give rise to four subfamilies of BLS curves, all of which offer highly efficient and implementation- friendly pairing instantiations. Curves from these particular subfamilies are defined over prime fields that support very efficient towering options for the full extension field. The coefficients for a specific curve and its correct twist are automat- ically determined without any computational effort. The choice of an extremely sparse search parameter is immediately reflected by a highly efficient optimal ate Miller loop and final exponentiation. As a resource for implementors, we give a list with examples of implementation-friendly BLS curves through several high-security levels.

Metadata

Available format(s): PDF
Publication info: Preprint.
History: 2011-10-14: last updated; 2011-08-29: published
Short URL: https://ia.cr/2011/465
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2011/465,
      author = {Craig Costello and Kristin Lauter and Michael Naehrig},
      title = {Attractive Subfamilies of BLS Curves for Implementing High-Security Pairings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/465},
      year = {2011},
      url = {https://eprint.iacr.org/2011/465}
}