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)
- 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
- 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}, url = {https://eprint.iacr.org/2010/529} }