Optimal Pairings

F.  Vercauteren

Paper 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 basic Miller iterations, with the order of the groups involved and 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 basic Miller iterations.

Note: Corrected statement of theorem 2

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Tate pairing ate pairing elliptic curves finite fields
Contact author(s): frederik vercauteren @ esat kuleuven be
History: 2008-03-07: last of 5 revisions; 2008-03-03: received; See all versions
Short URL: https://ia.cr/2008/096
License: CC BY

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}
}