Algorithm 3 Verify

Input:  $Tran{s}_t=({\sigma }_t,{\pi }_t^{vrf},r_t,{\pi }_t,in{p}_t)$, $PP$ Output:  $b\in \{0,1\}$   1:Parse $in{p}_t$ as $(i,t,p{k}_i,p{k}_i^{vrf},C_{i,t},opt,{\theta }_t,y_t,\mathsf{\Delta }{\epsilon }_t,{\epsilon }_t,k,id{x}_t,re{c}_t)$   2:$ms{g}_t\leftarrow i\Vert t\Vert C_{i,t}\Vert y_t\Vert id{x}_t\Vert re{c}_t$   3:Step 1: Source authenticity   4:if $\mathrm{Sign}.\mathrm{Verify}(p{k}_i,{\sigma }_t,ms{g}_t)=0$ then   5:    return 0              ▹ Invalid signature   6:end if   7:Step 2: Index uniqueness   8:if $\mathrm{VRF}.\mathrm{Verify}(p{k}_i^{vrf},(i,t),r_t,{\pi }_t^{vrf})=0$ or $id{x}_t\ne H(i\Vert t\Vert r_t)$ then   9:    return 0           ▹ Invalid VRF proof or index 10:end if 11:Step 3: Computational integrity 12:if $\mathrm{ZK}.\mathrm{Verify}(PP,\mathcal{R},in{p}_t,{\pi }_t)=0$ then 13:    return 0               ▹ Invalid ZK proof 14:end if 15:return 1