## CryptoDB

### Paper: Construction of Pairing-Friendly Elliptic Curves

Authors: Woo Sug Kang URL: http://eprint.iacr.org/2007/110 Search ePrint Search Google We explain a method of finding the polynomials representing $\sqrt{-D}$ and $\zeta_k$ over the field containing $\sqrt{-D}$ and $\zeta_k$ and how to construct a pairing friendly elliptic curves over the cyclotomic fields containing ${\mathbb Q} (\zeta_k, \sqrt{-D})$ for arbitrary $k$ and $D$ by CP method. By using the factorization of the cyclotomic polynomial combined some polynomial, we extend the construction over cyclotomic fields to the construction over some extensions of the cyclotomic fields containing ${\mathbb Q} (\zeta_k, \sqrt{-D})$. We explain the limitation of finding more families of pairing friendly elliptic curves with embedding degree 10. For all computation, we use the PARI-GP \cite{GP}.
##### BibTeX
@misc{eprint-2007-13392,
title={Construction of Pairing-Friendly Elliptic Curves},
booktitle={IACR Eprint archive},
keywords={implementation / elliptic curves, embedding degree, pairing based cryptography},
url={http://eprint.iacr.org/2007/110},
note={ wsgkang@korea.ac.kr 13651 received 23 Mar 2007, last revised 18 May 2007},
author={Woo Sug Kang},
year=2007
}