Security proof in pairing based cryptography Let : 

$G_{0}$ and $G_{1}$ be two multiplicative cyclic groups of prime order $p$,  $g$ be a generator of $G_{0}$ and $e$ be a bilinear map,

$e : G_0 \times G_0 → G_1$

and let $_{1} = ^{_{1}} $, $ _{2} = ^{_{2}} $ , ... , $ _{}= ^{_{}} $; 
$ =^{(+)/} $

such that $\alpha, \beta, r, s_{1}, s_{2}, ..., s_{n} \in Z_{p}$

Given $s_{x} \in Z_{p}$ ($x \neq i, i=1, ..., n$), and knowing $e\left( C_{1}, D\right), e\left( C_{2}, D\right), ..., e\left( C_{n}, D\right)$. I would like to know if it is possible to compute the value of $e(C_{x},D)$ and/or $D$.

Secret elements: $D$, $e(C_{x},D)$.

Public elements: $_{1}$, $_{2}$, ..., $_{n}$, $_{x}$, $e(C_{1},D)$, $e(C_{2},D)$, ..., $e(C_{n},D)$.

If it is not possible, how to prove that?
The only way i can see to evaluate $e(C_x,D)$ is to recover $D$ from a previous known pairing $e(C_i,D)$. However due to the Fixed Argument Pairing Inversion 1 assumption this is computationally hard.