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?
Is Square DH hard in Bilinear Groups?
reference request;cr.crypto security
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.