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Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field

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Pairing-Based Cryptography – Pairing 2008 (Pairing 2008)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5209))

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Abstract

We describe a new method for constructing Brezing-Weng-like pairing-friendly elliptic curves. The new construction uses the minimal polynomials of elements in a cyclotomic field. Using this new construction we present new “record breaking” families of pairing-friendly curves with embedding degrees of k ∈ {16,18,36,40}, and some interesting new constructions for the cases k ∈ {8,32}.

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Authors and Affiliations

  1. School of Computing, Dublin City University, Ireland

    Ezekiel J. Kachisa & Michael Scott

  2. Department of Mathematics and Computer Science of Santa Clara University, USA

    Edward F. Schaefer

Authors
  1. Ezekiel J. Kachisa
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  2. Edward F. Schaefer
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  3. Michael Scott
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Steven D. Galbraith Kenneth G. Paterson

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© 2008 Springer-Verlag Berlin Heidelberg

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Kachisa, E.J., Schaefer, E.F., Scott, M. (2008). Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field. In: Galbraith, S.D., Paterson, K.G. (eds) Pairing-Based Cryptography – Pairing 2008. Pairing 2008. Lecture Notes in Computer Science, vol 5209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85538-5_9

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  • DOI: https://doi.org/10.1007/978-3-540-85538-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85503-3

  • Online ISBN: 978-3-540-85538-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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