I am looking for a curve with a bilinear pairing of safe prime order.
I.e. a bilinear map $G \times G \rightarrow G_T$ where $|G| = p$, $p = 2q +1$, and $p,q$ are both prime.
Is it feasible to find such a curve?
A potential alternative is to find a curve with a bilinear pairing of Sophie Germain prime order, so that the subgroup of order q has a bilinear pairing but the larger group of order p does not have that requirement.