q-SDH assumption

For a randomly chosen element \(x \in \mathbb{Z}_{p}\) and random generators \(g_{1} \in \mathbb{G}_{1}\), \(g_{2} \in \mathbb{G}_{2}\), the q-strong Diffie-Hellman Problem is, given \((g_{1}, g_{1}^{x}, g_{1}^{x^{2}} ,\ldots, g_{1}^{x^{q}}, g_{2}, g_{2}^{x}) \in \mathbb{G}_{1}^{q} \times\mathbb{G}_{2}\), to compute a pair \((g_{1}^{1/(x+c)}, c) \in \mathbb{G}_{1} \times \mathbb{Z}_{p}\).