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Delaying Mismatched Field Multiplications in Pairing Computations

  • Craig Costello
  • Colin Boyd
  • Juan Manuel Gonzalez Nieto
  • Kenneth Koon-Ho Wong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6087)

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.

Keywords

Pairings Miller’s algorithm finite field arithmetic Tate pairing ate pairing 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Craig Costello
    • 1
  • Colin Boyd
    • 1
  • Juan Manuel Gonzalez Nieto
    • 1
  • Kenneth Koon-Ho Wong
    • 1
  1. 1.Information Security InstituteQueensland University of TechnologyBrisbaneAustralia

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