Variants of Bilinear Diffie-Hellman Assumption Could someone point me to the paper/reference where the following variant of q-strong Bilinear Diffie-Hellman assumption was used?

Given $s \in \mathbb{Z}_p^*$ and $g, g^{\frac{1}{s}}, g^{s}, g^{s^2}, \ldots, g^{s^q}$ it is difficult to compute $g^{\frac{1}{s + c}}$ for $c \in \mathbb{Z}_p^*\setminus \{-s\}$.

Essentially, I am looking for the variant which has $g^{\frac{1}{s}}$ as a part of the public parameter.
To the best of my knowledge, this hard assumption is introduced by Boneh and Boyen in this paper. 

But I don't think so the assumption that you mention being hard, because $c=0$ is a simple solution for it. Then the element $g^{\frac{1}{s}}$ should not publish. Also, this assumption is not bilinear because the challenge is an element in the cyclic group of $\mathbb{G}$ and it is not $e(g,g)^{\frac{1}{\alpha+c}}$.