Elliptic Curves for Pairing Applications

Angela Murphy; Noel Fitzpatrick

Paper 2005/302

Elliptic Curves for Pairing Applications

Angela Murphy and Noel Fitzpatrick

Abstract

In this paper we address the question of representing the discriminant of an imaginary quadratic field with respect to the basis of a cyclotomic field. This representation allows us to parameterize new families of ordinary elliptic curves over finite prime fields suitable for pairing applications. In particular these curves have small discriminants greater than four and arbitrary embedding degree. Computational results are presented which support the theoretical findings.

Note: Corrected an error in the representation of sqrt{-15} in Q(\zeta_30). Corrected a typo in step 4.b of algorithm 2.3

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Pairing Based Cryptosystem Elliptic Curves.
Contact author(s): noelfitz @ redbrick dcu ie
History: 2005-12-02: last of 2 revisions; 2005-09-02: received; See all versions
Short URL: https://ia.cr/2005/302
License: CC BY

BibTeX

@misc{cryptoeprint:2005/302,
      author = {Angela Murphy and Noel Fitzpatrick},
      title = {Elliptic Curves for Pairing Applications},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/302},
      year = {2005},
      url = {https://eprint.iacr.org/2005/302}
}