International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: The Eta Pairing Revisited

F. Hess
Nigel P. Smart
F. Vercauteren
Search ePrint
Search Google
Abstract: In this paper we simplify and extend the Eta pairing, originally discovered in the setting of supersingular curves by Baretto et al., to ordinary curves. Furthermore, we show that by swapping the arguments of the Eta pairing, one obtains a very efficient algorithm resulting in a speed-up of a factor of around six over the usual Tate pairing, in the case of curves which have large security parameters, complex multiplication by $D=-3$, and when the trace of Frobenius is chosen to be suitably small. Other, more minor savings are obtained for more general curves.
  title={The Eta Pairing Revisited},
  booktitle={IACR Eprint archive},
  keywords={implementation /},
  note={ 13315 received 22 Mar 2006, last revised 16 Jun 2006},
  author={F. Hess and Nigel P. Smart and F. Vercauteren},