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Attractive Subfamilies of BLS Curves for Implementing High-Security Pairings

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Progress in Cryptology – INDOCRYPT 2011 (INDOCRYPT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7107))

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Abstract

Barreto-Lynn-Scott (BLS) curves are a stand-out candidate for implementing high-security pairings. This paper shows that particular choices of the pairing-friendly search parameter give rise to four subfamilies of BLS curves, all of which offer highly efficient and implementation-friendly pairing instantiations.

Curves from these particular subfamilies are defined over prime fields that support very efficient towering options for the full extension field. The coefficients for a specific curve and its correct twist are automatically determined without any computational effort. The choice of an extremely sparse search parameter is immediately reflected by a highly efficient optimal ate Miller loop and final exponentiation. As a resource for implementors, we give a list with examples of implementation-friendly BLS curves through several high-security levels.

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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

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

    Craig Costello, Kristin Lauter & Michael Naehrig

  3. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, Netherlands

    Michael Naehrig

Authors
  1. Craig Costello
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  2. Kristin Lauter
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  3. Michael Naehrig
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Illinois at Chicago, 60607–7053, Chicago, IL, USA

    Daniel J. Bernstein

  2. Indian Institute of Science, India

    Sanjit Chatterjee

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Costello, C., Lauter, K., Naehrig, M. (2011). Attractive Subfamilies of BLS Curves for Implementing High-Security Pairings. In: Bernstein, D.J., Chatterjee, S. (eds) Progress in Cryptology – INDOCRYPT 2011. INDOCRYPT 2011. Lecture Notes in Computer Science, vol 7107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25578-6_23

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  • DOI: https://doi.org/10.1007/978-3-642-25578-6_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25577-9

  • Online ISBN: 978-3-642-25578-6

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