Algorithm 2 Query

Input:  $i,t,x_{i,t},opt,{\theta }_t,{\epsilon }_{t-1},k,re{c}_{t-1},s{k}_i,s{k}_i^{vrf},p{k}_i,p{k}_i^{vrf},PP$ Output:  Transmission package $Tran{s}_t$, Updated state ${\epsilon }_t,re{c}_t$   1: $\mathsf{\Delta }{\epsilon }_t\leftarrow {\epsilon }_{opt,{\theta }_t}$   2:if ${\epsilon }_{t-1}<\mathsf{\Delta }{\epsilon }_t$ then   3:    return ⊥   4: end if   5: ${\eta }_t{\leftarrow }_R{\{0,1\}}^{*}$   6: $y_t\leftarrow \mathrm{Mechanism}(x_{i,t},opt,{\theta }_t,{\eta }_t)$   7: ${\epsilon }_t\leftarrow {\epsilon }_{t-1}-\mathsf{\Delta }{\epsilon }_t$   8: ${\rho }_t{\leftarrow }_R{\{0,1\}}^{\lambda }$   9:$C_{i,t}\leftarrow \mathrm{Com}(x_{i,t};{\rho }_t)$       ▹ Dynamic Commitment 10: $r_t,{\pi }_t^{vrf}\leftarrow \mathrm{VRF}.\mathrm{Eval}(s{k}_i^{vrf},i,t)$ 11: $id{x}_t\leftarrow H(i\Vert t\Vert r_t)$ 12: $met{a}_t\leftarrow (opt,{\theta }_t,\mathsf{\Delta }{\epsilon }_t,{\epsilon }_t)$ 13: $re{c}_t\leftarrow H(re{c}_{t-1}\Vert id{x}_t\Vert met{a}_t)$ 14:$ms{g}_t\leftarrow i\Vert t\Vert C_{i,t}\Vert y_t\Vert id{x}_t\Vert re{c}_t$      ▹ Sign context including t 15: ${\sigma }_t\leftarrow \mathrm{Sign}(s{k}_i,ms{g}_t)$ 16: $in{p}_t\leftarrow (i,t,p{k}_i,p{k}_i^{vrf},C_{i,t},opt,{\theta }_t,y_t,\mathsf{\Delta }{\epsilon }_t,{\epsilon }_t,k,id{x}_t,re{c}_t)$ 17: $wi{t}_t\leftarrow (x_{i,t},{\rho }_t,{\eta }_t,{\epsilon }_{t-1})$ 18: ${\pi }_t\leftarrow \mathrm{ZK}.\mathrm{Prove}(PP,\mathcal{R},in{p}_t,wi{t}_t)$ 19: $Tran{s}_t\leftarrow ({\sigma }_t,{\pi }_t^{vrf},r_t,{\pi }_t,in{p}_t)$ 20:return $Tran{s}_t,{\epsilon }_t,re{c}_t$