A Note on the Ate Pairing

Chang-An Zhao; Fangguo Zhang; Jiwu Huang

Paper 2007/247 Original: eprint.iacr.org/2007/247 ↗

A Note on the Ate Pairing

Chang-An Zhao

Fangguo Zhang

Jiwu Huang

Abstract

The Ate pairing has been suggested since it can be computed efficiently on ordinary elliptic curves with small values of the traces of Frobenius $t$. However, not all pairing-friendly elliptic curves have this property. In this paper, we generalize the Ate pairing and find a series of variations of the Ate pairing. We show that the shortest Miller loop of the variations of the Ate pairing can possibly be as small as $r^{1/\varphi(k)}$ on more pairing-friendly curves generated by the method of complex multiplications, and hence speed up the pairing computation significantly.

Metadata

Available format(s): PDF
Publication info: Preprint.
History: 2008-01-02: last updated; 2007-06-20: published
Short URL: https://ia.cr/2007/247
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2007/247,
      author = {Chang-An Zhao and Fangguo Zhang and Jiwu Huang},
      title = {A Note on the Ate Pairing},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/247},
      year = {2007},
      url = {https://eprint.iacr.org/2007/247}
}