Paper 2010/123

Delaying Mismatched Field Multiplications in Pairing Computations

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


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.

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Publication info
Published elsewhere. Unknown where it was published
PairingsMiller’s algorithmfinite field arithmeticTate pairingate pairing.
Contact author(s)
craig costello @ qut edu au
2010-04-08: revised
2010-03-06: received
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      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{}},
      url = {}
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