## CryptoDB

### Paper: Constructing Brezing-Weng pairing friendly elliptic curves using elements in the cyclotomic field

Authors: Ezekiel J. Kachisa Edward F. Schaefer Michael Scott URL: http://eprint.iacr.org/2007/452 Search ePrint Search Google 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
}