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Delaying Mismatched Field Multiplications in Pairing Computations

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Arithmetic of Finite Fields (WAIFI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6087))

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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.

The first author acknowledges funding from the Queensland Government Smart State PhD Scholarship. This work has been supported in part by the Australian Research Council through Discovery Project DP0666065.

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Author information

Authors and Affiliations

  1. Information Security Institute, Queensland University of Technology, GPO Box 2434, Brisbane, QLD, 4001, Australia

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

Authors
  1. Craig Costello
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  2. Colin Boyd
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  3. Juan Manuel Gonzalez Nieto
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  4. Kenneth Koon-Ho Wong
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    M. Anwar Hasan

  2. Department of Informatics, HIB, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

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Costello, C., Boyd, C., Gonzalez Nieto, J.M., Wong, K.KH. (2010). Delaying Mismatched Field Multiplications in Pairing Computations. In: Hasan, M.A., Helleseth, T. (eds) Arithmetic of Finite Fields. WAIFI 2010. Lecture Notes in Computer Science, vol 6087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13797-6_14

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  • DOI: https://doi.org/10.1007/978-3-642-13797-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13796-9

  • Online ISBN: 978-3-642-13797-6

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