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Constructing Brezing-Weng pairing friendly elliptic curves using elements in the cyclotomic field
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Abstract: | We describe a new method for constructing Brezing-Weng-like pairing-friendly elliptic curves. The new construction uses the minimal polynomials of elements in a cyclotomic field. Using this new construction we present new ``record breaking'' families of pairing-friendly curves with embedding degrees of $k \in \{16,18,36,40\}$, and some interesting new constructions for the cases $k \in \{8,32\}$ |
BibTeX
@misc{eprint-2007-13732, title={Constructing Brezing-Weng pairing friendly elliptic curves using elements in the cyclotomic field}, booktitle={IACR Eprint archive}, keywords={public-key cryptography / Pairing-based cryptography, Tate Pairing, Eta pairing, Ate pairing}, url={http://eprint.iacr.org/2007/452}, note={ mike@computing.dcu.ie 13861 received 5 Dec 2007, last revised 14 Dec 2007}, author={Ezekiel J. Kachisa and Edward F. Schaefer and Michael Scott}, year=2007 }