With pairing-based cryptography we have two cyclic groups (\(G_1\) and \(G_2\)), and which are of an order of a prime number (\(n\)). A pairing on \((G_1,G_2,G_T)\) defines the function \(e:G_1 \times G_2 \rightarrow G_T\), and where \(g_1\) is a generator for \(G_1\) and \(g_2\) is a generator for \(G_2\). If we have the points of \(U_1\) and \(U_2\) on \(G_1\) and \(V_1\) and \(V_2\) on \(G_2\), we get the bilinear mapping of:
\(e(aU,V) =e(U,aV)\)
In this case we will match \(e((X+M \times Y) V,h U) = e(V,(x+y \times m)h U) \), and where \(x\) and \(y\) are secret values.