Optimal Pairings

F.  Vercauteren

Paper 2008/096 Original: eprint.iacr.org/2008/096 ↗

Optimal Pairings

F. Vercauteren

Abstract

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2008-03-07: last updated; 2008-03-03: published
Short URL: https://ia.cr/2008/096
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2008/096,
      author = {F.  Vercauteren},
      title = {Optimal Pairings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/096},
      year = {2008},
      url = {https://eprint.iacr.org/2008/096}
}