Is it possible to abuse elliptic curve pairings as a kind of Diffie Hellman Oracle?

I have a the following equation: e(G,a×G) which is of course is equivalent to e(G,G)^(a) but where a is an unknown discrete logarithm.

Now as an attacker, I need to compute e(G,G)^(a×a).

Is there a way to abuse pairing to do this?