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.


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