Paper 2008/008 Original: eprint.iacr.org/2008/008 ↗
Factoring Polynomials for Constructing Pairing-friendly Elliptic Curves
Abstract
In this paper we present a new method to construct a polynomial $u(x) \in \mathbb{Z}[x]$ which will make $\mathrm{\Phi}_{k}(u(x))$ reducible. We construct a finite separable extension of $\mathbb{Q}(\zeta_{k})$, denoted as $\mathbb{E}$. By primitive element theorem, there exists a primitive element $\theta \in \mathbb{E}$ such that $\mathbb{E}=\mathbb{Q}(\theta)$. We represent the primitive $k$-th root of unity $\zeta_{k}$ by $\theta$ and get a polynomial $u(x) \in \mathbb{Q}[x]$ from the representation. The resulting $u(x)$ will make $\mathrm{\Phi}_{k}(u(x))$ factorable.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2008-05-13: last updated
- 2008-01-07: published
- Short URL
- https://ia.cr/2008/008
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2008/008,
author = {Zhitu su and Hui Li and Jianfeng Ma},
title = {Factoring Polynomials for Constructing Pairing-friendly Elliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/008},
year = {2008},
url = {https://eprint.iacr.org/2008/008}
}