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Paper: A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties

Authors:
David Freeman
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URL: http://eprint.iacr.org/2008/155
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Abstract: We give an algorithm that produces families of Weil numbers for ordinary abelian varieties over finite fields with prescribed embedding degree. The algorithm uses the ideas of Freeman, Stevenhagen, and Streng to generalize the Brezing-Weng construction of pairing-friendly elliptic curves. We discuss how CM methods can be used to construct these varieties, and we use our algorithm to give examples of pairing-friendly ordinary abelian varieties of dimension 2 and 3 that are absolutely simple and have smaller $\rho$-values than any previous such example.
BibTeX
@misc{eprint-2008-17832,
  title={A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Abelian varieties, hyperelliptic curves, pairing-based cryptosystems, embedding degree, pairing-friendly varieties},
  url={http://eprint.iacr.org/2008/155},
  note={ dfreeman@math.berkeley.edu 13974 received 4 Apr 2008, last revised 5 Apr 2008},
  author={David Freeman},
  year=2008
}