Assume that we have an already assigned Multiplicative Cyclic Group $\mathbb Z_p^*$ with order $q=p-1$, and $p$ is a prime number, is it possible to create a bilinear function $\hat{e}: \mathbb Z_p^* \times \mathbb Z_p^* \rightarrow \mathbb G_2$ with the property that follows:
$$\hat{e}(g^{a},g^{sb})=\hat{e}(g^{b},g^{sa})$$
$g$ is a generator for $\mathbb Z_p^*$, and $\mathbb G_2$ is also a Multiplicative Cyclic Group with order $q$
it seems that if the creation of this function is practical in polynomial time then there should be new attacks on some cryptographic protocols with security property of anonymity.