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,
$e : G_0 \times G_0 β G_1$
and let $πΆ_{1} = π^{π½π _{1}} $, $ πΆ_{2} = π^{π½π _{2}} $ , ... , $ πΆ_{π}= π^{π½π _{π}} $; $ π·=π^{(πΌ+π)/π½} $
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: $πΆ_{1}$, $πΆ_{2}$, ..., $πΆ_{n}$, $πΆ_{x}$, $e(C_{1},D)$, $e(C_{2},D)$, ..., $e(C_{n},D)$.
If it is not possible, how to prove that?