[Resource Topic] 2002/088: Constructing Elliptic Curves with Prescribed Embedding Degrees

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Constructing Elliptic Curves with Prescribed Embedding Degrees

Authors: Paulo S. L. M. Barreto, Ben Lynn, Michael Scott


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.

ePrint: https://eprint.iacr.org/2002/088

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