Is Square DH hard in Bilinear Groups? Let $G$ be a group, $g ∈_R G, x ∈_R Z_q$, and  $e: G \times G \rightarrow G_T$ be a bilinear paring.

Then, given $g, g^x$, is it still hard to compute $g^{x^2}$?

1. In other words is Square Diffie-Hellman hard in Bilinear Groups? 

I am trying to look for references that have used this problem or a reduction which proves this is hard.

[I am aware of a variant of this called the Flexible Square Diffie-Hellman  [Laguillaumie et al], which asks to compute $(h,h^x,h^{x^2})$ given $g^x$.]

2. What about the decisional version of the same problem?
This assumption has been used in cryptographic constructions.  Both the computational and decisions are generally believed hard by the provable security community, but I doubt a reduction to, e.g., DH will be found.  See http://homepage.ruhr-uni-bochum.de/Eike.Kiltz/papers/dh_full.pdf for discussion and references.