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Generating Pairing-friendly Parameters for the CM Construction of Genus 2 Curves over Prime Fields
Authors: Kristin Lauter, Ning ShangAbstract:
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.
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