On conditions for \rho-value is 1 or not of complete family of pairing-friendly elliptic curves

TL;DR

This paper investigates the conditions under which a complete family of pairing-friendly elliptic curves has a -value of 1, providing insights into when this value cannot be achieved.

Contribution

It identifies specific cases where the -value of a complete family of pairing-friendly elliptic curves is not equal to 1.

Findings

Certain cases prevent the -value from being 1

Provides theoretical conditions for -value not equal to 1

Abstract

We study whether a complete family of pairing friendly elliptic curves has a \rho-value 1 or not. We show that, in some cases, \rho-values are not to be 1.