bilinear pairing between special groups

Hi,

usually the bilinear pairing (like the Tate or Weil pairing) is defined the following way:
e: G_1 x G_1 -> G_2
where G_1 is an additive group of order q and G_2 is a multiplicative group or order q.

Now I wonder, if it is possible to let be G_2 the group Z^*_n^{2} = {a | a \in Z_{n^2} AND gcd(a,n^2)=1}. Can you help me to figure this out correctly?

Thanks in advance,
Zsuzsi
.