Paper 2008/008
Factoring Polynomials for Constructing Pairingfriendly Elliptic Curves
Zhitu su, Hui Li, and Jianfeng Ma
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 PS
 Category
 Publickey cryptography
 Publication info
 Published elsewhere. Unknown where it was published
 Keywords
 pairingfriendly curvespolynomial factoringprimitive element theorem
 Contact author(s)
 ztsu @ mail xidian edu cn
 History
 20080513: last of 3 revisions
 20080107: received
 See all versions
 Short URL
 https://ia.cr/2008/008
 License

CC BY
BibTeX
@misc{cryptoeprint:2008/008, author = {Zhitu su and Hui Li and Jianfeng Ma}, title = {Factoring Polynomials for Constructing Pairingfriendly Elliptic Curves}, howpublished = {Cryptology ePrint Archive, Paper 2008/008}, year = {2008}, note = {\url{https://eprint.iacr.org/2008/008}}, url = {https://eprint.iacr.org/2008/008} }