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Paper: Constructing Brezing-Weng pairing friendly elliptic curves using elements in the cyclotomic field

Authors:
Ezekiel J. Kachisa
Edward F. Schaefer
Michael Scott
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URL: http://eprint.iacr.org/2007/452
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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 $k \in \{16,18,36,40\}$, and some interesting new constructions for the cases $k \in \{8,32\}$
BibTeX
@misc{eprint-2007-13732,
  title={Constructing Brezing-Weng pairing friendly elliptic curves using elements in the cyclotomic field},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Pairing-based cryptography, Tate Pairing, Eta pairing, Ate pairing},
  url={http://eprint.iacr.org/2007/452},
  note={ mike@computing.dcu.ie 13861 received 5 Dec 2007, last revised 14 Dec 2007},
  author={Ezekiel J. Kachisa and Edward F. Schaefer and Michael Scott},
  year=2007
}