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Constructing Elliptic Curves with Prescribed Embedding Degrees
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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 }