### 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.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Keywords
pairing-friendlygenus 2 curveprime fields
Contact author(s)
geek @ cerias net
History
2010-12-01: last of 2 revisions
See all versions
Short URL
https://ia.cr/2010/529

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}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.