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

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

Paper 2007/452

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

Ezekiel J. Kachisa, Edward F. Schaefer, and 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 $k \in \{8,32\}$

Note: Minor corrections

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Pairing-based cryptography Tate Pairing Eta pairing Ate pairing
Contact author(s): mike @ computing dcu ie
History: 2007-12-14: revised; 2007-12-05: received; See all versions
Short URL: https://ia.cr/2007/452
License: CC BY

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}
}