Multiplication and Squaring on Pairing-Friendly Fields

Augusto Jun Devegili; Colm Ó~hÉigeartaigh; Michael Scott; Ricardo Dahab

Paper 2006/471

Multiplication and Squaring on Pairing-Friendly Fields

Augusto Jun Devegili, Colm Ó~hÉigeartaigh, Michael Scott, and Ricardo Dahab

Abstract

Pairing-friendly fields are finite fields that are suitable for the implementation of cryptographic bilinear pairings. In this paper we review multiplication and squaring methods for pairing-friendly fields $\fpk$ with $k \in \{2,3,4,6\}$. For composite $k$, we consider every possible towering construction. We compare the methods to determine which is most efficient based on the number of basic $\fp$ operations, as well as the best constructions for these finite extension fields. We also present experimental results for every method.

Note: Correction of a typo in the formula for squaring in cubic extensions and reordering of the author list.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: finite fields pairings efficient implementation
Contact author(s): augusto @ ic unicamp br
History: 2007-02-20: revised; 2006-12-14: received; See all versions
Short URL: https://ia.cr/2006/471
License: CC BY

BibTeX

@misc{cryptoeprint:2006/471,
      author = {Augusto Jun Devegili and Colm Ó~hÉigeartaigh and Michael Scott and Ricardo Dahab},
      title = {Multiplication and Squaring on Pairing-Friendly Fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/471},
      year = {2006},
      url = {https://eprint.iacr.org/2006/471}
}