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Paper: Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10

Authors:
David Freeman
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URL: http://eprint.iacr.org/2006/026
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Abstract: We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham. We show that our framework incorporates existing constructions for k = 3, 4, 6, and 12, and we give evidence that the method is unlikely to produce infinite families of curves with embedding degree k > 12.
BibTeX
@misc{eprint-2006-21519,
  title={Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / elliptic curves, embedding degree, pairings},
  url={http://eprint.iacr.org/2006/026},
  note={ dfreeman@math.berkeley.edu 13167 received 19 Jan 2006},
  author={David Freeman},
  year=2006
}