## CryptoDB

### Paper: Optimal Pairings

Authors: F. Vercauteren URL: http://eprint.iacr.org/2008/096 Search ePrint Search Google In this paper we introduce the concept of an \emph{optimal pairing}, which by definition can be computed using only $\log_2 r/ \varphi(k)$ basic Miller iterations, with $r$ the order of the groups involved and $k$ the embedding degree. We describe an algorithm to construct optimal ate pairings on all parametrized families of pairing friendly elliptic curves. Finally, we conjecture that any non-degenerate pairing on an elliptic curve without efficiently computable endomorphisms different from powers of Frobenius requires at least $\log_2 r/ \varphi(k)$ basic Miller iterations.
##### BibTeX
@misc{eprint-2008-17773,
title={Optimal Pairings},
booktitle={IACR Eprint archive},
keywords={public-key cryptography /  Tate pairing, ate pairing, elliptic curves, finite fields},
url={http://eprint.iacr.org/2008/096},
note={ frederik.vercauteren@esat.kuleuven.be 13945 received 2 Mar 2008, last revised 7 Mar 2008},
author={F. Vercauteren},
year=2008
}