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Parallelizing the Weil and Tate Pairings

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Cryptography and Coding (IMACC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7089))

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Abstract

In the past year, the speed record for pairing implementations on desktop-class machines has been broken several times. The speed records for asymmetric pairings were set on a single processor. In this paper, we describe our parallel implementation of the optimal ate pairing over Barreto-Naehrig (BN) curves that is about 1.23 times faster using two cores of an Intel Core i5 or Core i7 machine, and 1.45 times faster using 4 cores of the Core i7 than the state-of-the-art implementation on a single core. We instantiate Hess’s general Weil pairing construction and introduce a new optimal Weil pairing tailored for parallel execution. Our experimental results suggest that the new Weil pairing is 1.25 times faster than the optimal ate pairing on 8-core extensions of the aforementioned machines. Finally, we combine previous techniques for parallelizing the eta pairing on a supersingular elliptic curve with embedding degree 4, and achieve an estimated 1.24-fold speedup on an 8-core extension of an Intel Core i7 over the previous best technique.

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Author information

Authors and Affiliations

  1. Institute of Computing, University of Campinas, Brazil

    Diego F. Aranha

  2. Department of Combinatorics & Optimization, University of Waterloo, Canada

    Edward Knapp & Alfred Menezes

  3. Computer Science Department, CINVESTAV-IPN, Mexico

    Francisco Rodríguez-Henríquez

Authors
  1. Diego F. Aranha
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  2. Edward Knapp
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  3. Alfred Menezes
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  4. Francisco Rodríguez-Henríquez
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Editors and Affiliations

  1. Hewlett-Packard Laboratories, UK

    Liqun Chen

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Aranha, D.F., Knapp, E., Menezes, A., Rodríguez-Henríquez, F. (2011). Parallelizing the Weil and Tate Pairings. In: Chen, L. (eds) Cryptography and Coding. IMACC 2011. Lecture Notes in Computer Science, vol 7089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25516-8_17

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  • DOI: https://doi.org/10.1007/978-3-642-25516-8_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25515-1

  • Online ISBN: 978-3-642-25516-8

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