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 cryptographyTate PairingEta pairingAte 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2007/452}},
      url = {https://eprint.iacr.org/2007/452}
}
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