Delaying Mismatched Field Multiplications in Pairing Computations

Craig Costello; Colin Boyd; Juan Manuel Gonzalez Nieto; Kenneth Koon-Ho Wong

Paper 2010/123

Delaying Mismatched Field Multiplications in Pairing Computations

Craig Costello, Colin Boyd, Juan Manuel Gonzalez Nieto, and Kenneth Koon-Ho Wong

Abstract

Miller's algorithm for computing pairings involves performing multiplications between elements that belong to different finite fields. Namely, elements in the full extension field $\mathbb{F}_{p^k}$ are multiplied by elements contained in proper subfields $\mathbb{F}_{p^{k/d}}$, and by elements in the base field $\mathbb{F}_{p}$. We show that significant speedups in pairing computations can be achieved by delaying these ``mismatched'' multiplications for an optimal number of iterations. Importantly, we show that our technique can be easily integrated into traditional pairing algorithms; implementers can exploit the computational savings herein by applying only minor changes to existing pairing code.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Pairings Miller’s algorithm finite field arithmetic Tate pairing ate pairing.
Contact author(s): craig costello @ qut edu au
History: 2010-04-08: revised; 2010-03-06: received; See all versions
Short URL: https://ia.cr/2010/123
License: CC BY

BibTeX

@misc{cryptoeprint:2010/123,
      author = {Craig Costello and Colin Boyd and Juan Manuel Gonzalez Nieto and Kenneth Koon-Ho Wong},
      title = {Delaying Mismatched Field Multiplications in Pairing Computations},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/123},
      year = {2010},
      url = {https://eprint.iacr.org/2010/123}
}