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.