Construction of Pairing-Friendly Elliptic Curves

Woo Sug Kang

Paper 2007/110

Construction of Pairing-Friendly Elliptic Curves

Woo Sug Kang

Abstract

We explain a method of finding the polynomials representing $\sqrt{- D}$ and $ζ_{k}$ over the field containing $\sqrt{- D}$ and $ζ_{k}$ and how to construct a pairing friendly elliptic curves over the cyclotomic fields containing $Q (ζ_{k}, \sqrt{- D})$ for arbitrary $k$ and $D$ by CP method. By using the factorization of the cyclotomic polynomial combined some polynomial, we extend the construction over cyclotomic fields to the construction over some extensions of the cyclotomic fields containing $Q (ζ_{k}, \sqrt{- D})$ . We explain the limitation of finding more families of pairing friendly elliptic curves with embedding degree 10. For all computation, we use the PARI-GP \cite{GP}.

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Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: elliptic curves embedding degree pairing based cryptography
Contact author(s): wsgkang @ korea ac kr
History: 2007-05-18: last of 5 revisions; 2007-03-26: received; See all versions
Short URL: https://ia.cr/2007/110
License: CC BY

BibTeX

@misc{cryptoeprint:2007/110,
      author = {Woo Sug Kang},
      title = {Construction of Pairing-Friendly Elliptic Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/110},
      year = {2007},
      url = {https://eprint.iacr.org/2007/110}
}