Constructing Brezing-Weng pairing friendly elliptic curves using elements in the cyclotomic field

Ezekiel J.  Kachisa; Edward F.  Schaefer; Michael Scott

Paper 2007/452 Original: eprint.iacr.org/2007/452 ↗

Constructing Brezing-Weng pairing friendly elliptic curves using elements in the cyclotomic field

Ezekiel J. Kachisa

Edward F. Schaefer

Michael Scott

Abstract

We describe a new method for constructing Brezing-Weng-like pairing-friendly elliptic curves. The new construction uses the minimal polynomials of elements in a cyclotomic field. Using this new construction we present new ``record breaking'' families of pairing-friendly curves with embedding degrees of $k \in \{16,18,36,40\}$, and some interesting new constructions for the cases $k \in \{8,32\}$

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2007-12-14: last updated; 2007-12-05: published
Short URL: https://ia.cr/2007/452
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2007/452,
      author = {Ezekiel J.  Kachisa and Edward F.  Schaefer and Michael Scott},
      title = {Constructing Brezing-Weng pairing friendly elliptic curves using elements in the cyclotomic field},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/452},
      year = {2007},
      url = {https://eprint.iacr.org/2007/452}
}