Generating Pairing-friendly Parameters for the CM Construction of Genus 2 Curves over Prime Fields

Kristin Lauter; Ning Shang

Paper 2010/529

Generating Pairing-friendly Parameters for the CM Construction of Genus 2 Curves over Prime Fields

Kristin Lauter and Ning Shang

Abstract

We present two contributions in this paper. First, we give a quantitative analysis of the scarcity of pairing-friendly genus 2 curves. This result is an improvement relative to prior work which estimated the density of pairing-friendly genus 2 curves heuristically. Second, we present a method for generating pairing-friendly parameters for which $\rho\approx 8$, where $\rho$ is a measure of efficiency in pairing-based cryptography. This method works by solving a system of equations given in terms of coefficients of the Frobenius element. The algorithm is easy to understand and implement.

Note: Revised paper incorporating Igor Shparlinski's comments.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: pairing-friendly genus 2 curve prime fields
Contact author(s): geek @ cerias net
History: 2010-12-01: last of 2 revisions; 2010-10-19: received; See all versions
Short URL: https://ia.cr/2010/529
License: CC BY

BibTeX

@misc{cryptoeprint:2010/529,
      author = {Kristin Lauter and Ning Shang},
      title = {Generating Pairing-friendly Parameters for the CM Construction of Genus 2 Curves over Prime Fields},
      howpublished = {Cryptology ePrint Archive, Paper 2010/529},
      year = {2010},
      note = {\url{https://eprint.iacr.org/2010/529}},
      url = {https://eprint.iacr.org/2010/529}
}