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 CryptosystemElliptic 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2005/302}},
      url = {https://eprint.iacr.org/2005/302}
}
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