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

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

Heuristics on pairing-friendly abelian varieties

We discuss heuristic asymptotic formulae for the number of pairing-friendly abelian varieties over prime fields, generalizing previous work of one of the authors arXiv:math1107.0307Comment: Pages 6-7 rewritten, other minor changes mad