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An Analysis of Affine Coordinates for Pairing Computation

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Pairing-Based Cryptography - Pairing 2010 (Pairing 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6487))

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Abstract

In this paper we analyze the use of affine coordinates for pairing computation. We observe that in many practical settings, e. g. when implementing optimal ate pairings in high security levels, affine coordinates are faster than using the best currently known formulas for projective coordinates. This observation relies on two known techniques for speeding up field inversions which we analyze in the context of pairing computation. We give detailed performance numbers for a pairing implementation based on these ideas, including timings for base field and extension field arithmetic with relative ratios for inversion-to-multiplication costs, timings for pairings in both affine and projective coordinates, and average timings for multiple pairings and products of pairings.

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Author information

Authors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA, 98052, USA

    Kristin Lauter, Peter L. Montgomery & Michael Naehrig

Authors
  1. Kristin Lauter
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  2. Peter L. Montgomery
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  3. Michael Naehrig
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Editor information

Editors and Affiliations

  1. Technicolor, Security and Content Protection Labs, 1 avenue de Belle Fontaine, 35576, Cesson-Sévigné Cedex, France

    Marc Joye

  2. Japan Advanced Institute of Science and Technology (JAIST), 923-1292, Nomi, Ishikawa, Japan

    Atsuko Miyaji

  3. National Institute of Advanced Industrial Science and Technoloy (AIST), 101-0021, Tokyo, Japan

    Akira Otsuka

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Lauter, K., Montgomery, P.L., Naehrig, M. (2010). An Analysis of Affine Coordinates for Pairing Computation. In: Joye, M., Miyaji, A., Otsuka, A. (eds) Pairing-Based Cryptography - Pairing 2010. Pairing 2010. Lecture Notes in Computer Science, vol 6487. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17455-1_1

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  • DOI: https://doi.org/10.1007/978-3-642-17455-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17454-4

  • Online ISBN: 978-3-642-17455-1

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