\(e(aU,bV) = e(U,V)^{ab} = e(abU, V) = e(U, abV ) = e(bU,aV)\)
In this case Alice gets Bob's ID (\(Q_{id}\)). The trust server then selects a secret (\(s\)) and creates a public key of \(sU\), and where \(U\) is a point on the curve.
Alice then selects a random value (\(r\)) and creates a pairing of \(e(sU,Q_{id})^r\). Bob uses a private key of \(sQ_{id}\) and generates the same key with \(e(rU,sQ_{id})\).