Paper 2007/110 Original: eprint.iacr.org/2007/110 ↗
Construction of Pairing-Friendly Elliptic Curves
Abstract
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}.
Metadata
- Available format(s)
PDF- Category
- Implementation
- Publication info
- Preprint.
- History
- 2007-05-18: last updated
- 2007-03-26: published
- Short URL
- https://ia.cr/2007/110
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2007/110,
author = {Woo Sug Kang},
title = {Construction of Pairing-Friendly Elliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2007/110},
year = {2007},
url = {https://eprint.iacr.org/2007/110}
}