Example 2

$Setup(1^{\lambda},N)$: This function outputs $pp=PC.Setup(1^{\lambda},d)$ where if $n_g=4$ , $n_i=32$ and $b=2$ then $d=\{d_{AHP}(N,i,j)\}_{i\in[k_{AHP}]\bigcup\{0\},j\in[s_{AHP}(i)]}=\{8,8,8,8,8,8,8,8,8,4,39,39,39,40,75,36,38,36,36,7,42\}$

Run $KZG.\hspace{1mm}Setup(1^{\lambda},d)$ as following:

If the computation be done in $\mathbb{F}$ of order Goldilock prime $p=Q^2-Q+1$ with $Q=2184$ that is $p=4767673$, a generator of $\mathbb{F}$ is $g=5$.

$KZG.Setup(1^{\lambda},138)=(ck,vk)=(\{g\tau^i\}_{i=0}^{137},g\tau)$ that for secret element $\tau=119$ and generator $g=5$ outputs $ck=\{g\tau^i\}_{i=0}^{137}=(5,)$ and $vk=$.

$KZG.Setup(1^{\lambda},4)=(ck,vk)=(\{g\tau^i\}_{i=0}^{3},g\tau)$ that for secret element $\tau=119$ and generator $g=5$ outputs $ck=\{g\tau^i\}_{i=0}^{3}=(5,)$ and $vk=$.

$KZG.Setup(1^{\lambda},39)=(ck,vk)=(\{g\tau^i\}_{i=0}^{38},g\tau)$ that for secret element $\tau=119$ and generator $g=5$ outputs $ck=\{g\tau^i\}_{i=0}^{38}=(5,)$ and $vk=$.

$KZG.Setup(1^{\lambda},40)=(ck,vk)=(\{g\tau^i\}_{i=0}^{39},g\tau)$ that for secret element $\tau=119$ and generator $g=5$ outputs $ck=\{g\tau^i\}_{i=0}^{39}=(5,)$ and $vk=$.

$KZG.Setup(1^{\lambda},75)=(ck,vk)=(\{g\tau^i\}_{i=0}^{74},g\tau)$ that for secret element $\tau=119$ and generator $g=5$ outputs $ck=\{g\tau^i\}_{i=0}^{74}=(5,)$ and $vk=$.