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
PairingsMiller’s algorithmfinite field arithmeticTate pairingate 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2010/123}},
      url = {https://eprint.iacr.org/2010/123}
}
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