Is it possible to build a bilinear map where the underlying group is of unknown order?
To maintain context, the original question appears below. As per poncho's excellent answer, my original idea is infeasible:
Is it possible to build a bilinear map where the underlying group is an RSA group? I.e. $e: \mathbb{Z}_N \times \mathbb{Z}_N \rightarrow \mathbb{Z}_N$ where N is an RSA modulo?
Alternatively, a bilinear map where the underlying group is of unknown order?