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Paper: Constructing Elliptic Curves with Prescribed Embedding Degrees

Authors:
Paulo S. L. M. Barreto
Ben Lynn
Michael Scott
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URL: http://eprint.iacr.org/2002/088
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Abstract: Pairing-based cryptosystems depend on the existence of groups where the Decision Diffie-Hellman problem is easy to solve, but the Computational Diffie-Hellman problem is hard. Such is the case of elliptic curve groups whose embedding degree is large enough to maintain a good security level, but small enough for arithmetic operations to be feasible. However, the embedding degree is usually enormous, and the scarce previously known suitable elliptic groups had embedding degree $k \leqslant 6$. In this note, we examine criteria for curves with larger $k$ that generalize prior work by Miyaji et al. based on the properties of cyclotomic polynomials, and propose efficient representations for the underlying algebraic structures.
BibTeX
@misc{eprint-2002-11611,
  title={Constructing Elliptic Curves with Prescribed Embedding Degrees},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / elliptic curve cryptosystem},
  url={http://eprint.iacr.org/2002/088},
  note={Accepted for presentation at SCN'02 (to be published in LNCS) pbarreto@larc.usp.br 12836 received 2 Jul 2002, last revised 22 Feb 2005},
  author={Paulo S. L. M. Barreto and Ben Lynn and Michael Scott},
  year=2002
}