Factoring Polynomials for Constructing Pairing-friendly Elliptic Curves

Zhitu su; Hui Li; Jianfeng Ma

Paper 2008/008

Factoring Polynomials for Constructing Pairing-friendly Elliptic Curves

Zhitu su, Hui Li, and Jianfeng Ma

Abstract

In this paper we present a new method to construct a polynomial $u (x) \in Z [x]$ which will make $Φ_{k} (u (x))$ reducible. We construct a finite separable extension of $Q (ζ_{k})$ , denoted as $E$ . By primitive element theorem, there exists a primitive element $θ \in E$ such that $E = Q (θ)$ . We represent the primitive -th root of unity by and get a polynomial from the representation. The resulting will make factorable.

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: pairing-friendly curves polynomial factoring primitive element theorem
Contact author(s): ztsu @ mail xidian edu cn
History: 2008-05-13: last of 3 revisions; 2008-01-07: 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 Pairing-friendly Elliptic Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/008},
      year = {2008},
      url = {https://eprint.iacr.org/2008/008}
}