With pairing-based cryptography we have two cyclic groups (\(G_1\) and \(G_2\)), and which are of an order of a prime number (\(n\)).
If \(P\) is a point on \(G_1\), and \(Q\) is a point on \(G_2\), we get a bilinear mapping for the pairing: \(e(aP,bQ)=e(bP,aQ)\).
In this example, we will reduce the security strength of elliptic curve method, and use a pairing of \(e(xP,Q)=e(P,Q)^x\).