Delaying mismatched field multiplications in pairing computations

  • Authors:

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

  • Affiliations:

  • Information Security Institute, Queensland University of Technology, Brisbane, QLD, Australia;Information Security Institute, Queensland University of Technology, Brisbane, QLD, Australia;Information Security Institute, Queensland University of Technology, Brisbane, QLD, Australia;Information Security Institute, Queensland University of Technology, Brisbane, QLD, Australia

  • Venue:
  • WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
  • Year:
  • 2010

  • Fixed argument pairings

    LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America

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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 Fpk are multiplied by elements contained in proper subfields Fpk/d, and by elements in the base field Fp. 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.