When Bob Met Alice And Carol: Shared key Over Three Parties with BN-curves

Elliptic curves are used fairly extensively in public key encryption (such as in Bitcoin and Tor). A BN-curve (Barreto-Naehrig curve) [paper] defines an elliptic curve which can be used for pairings that allow for a high security and efficiency level.

So how do we generate a shared key between three parties? This page implements the…