International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Woo Sug Kang

Publications

Year
Venue
Title
2007
EPRINT
Construction of Pairing-Friendly Elliptic Curves
Woo Sug Kang
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}.