Heuristics on pairing-friendly elliptic curves

Abstract

We present a heuristic asymptotic formula as $x\to \infty$ for the number of isogeny classes of pairing-friendly elliptic curves with fixed embedding degree $k\ge 3$, with fixed discriminant, with rho-value bounded by a fixed ${\rho }_0$ such that $1<{\rho }_0<2$, and with prime subgroup order at most $x$.

arXiv commenttext substantially rewritten, tables corrected