Algorithm 7. Simulator 7.

Input: $\mathcal{I},T,T{K}_{i,Q}$

Output: Search results R

1: Parse $\mathbf{p}\mathbf{h}(\mathbf{w})$ as $[(t_1,p{f}_1),(t_2,p{f}_2),...,(t_c,p{f}_c)]$

2: Parse $\{\overline{t_{w_1}},\overline{t_{w_2}},...,\overline{t_{w_t}},E_1,E_2,..E_{t-1}\}\leftarrow min\mathbf{s}\mathbf{p}(\overline{T{K}_{i,Q}})$

3: for $\overline{t_{w_j}}\in min\mathbf{s}\mathbf{p}(\overline{T{K}_{i,Q}})$ do

4:    $v_{\mathcal{B}}\stackrel{R}{⟵}\{0,1{\}}^{(l+\lambda )};({\mathcal{B}}_{w_j}||S{L}_{w_j}^i)\stackrel{R}{⟵}\{0,1{\}}^{(l+\lambda )}$

5: end for

6: $\mathcal{B}={\mathcal{B}}_1\wedge {\mathcal{B}}_2\wedge \dots \wedge {\mathcal{B}}_t$

7: Get $I{D}_{\mathcal{B}}=\{{\ell }_1,{\ell }_2,...,{\ell }_p\}$ from $\mathcal{B}$

8:  for ${\ell }_i\in I{D}_{\mathcal{B}}$ do

9:      $flag=\{\mathrm{000...000}{\}}^{t-1}$

10:    if $\hat{X}[i]=\mathrm{\perp }$ then

11:       $\hat{X}[i]\stackrel{R}{⟵}\{0,1{\}}^n$

12:    else

13:        $\hat{X}[i]\leftarrow p{f}_i$

14:    end if

15:    $(E(po{s}_1^1),E(po{s}_2^1),E(po{s}_m^1))\leftarrow S{L}_{w_1}^1$

16:   for $d=2\to t$ do

17:       $(E(po{s}_1^i),E(po{s}_2^i),E(po{s}_n^i))\leftarrow S{L}_{w_j}^i$

18:      for $k=1\to m;k^{\mathrm{\prime }}=1\to n$ do

19:         if $E(po{s}_1^{k^{\mathrm{\prime }}})=E(po{s}_1^k)\times E(d-1)$ then

20:            Set the position $(i-1)$ of flag to 1

21:            break

22:         end if

23:      end for

24:   end for

25:   If all positions of flag are 1

26:   get $c_i\leftarrow T[{\ell }_i]$, $R\leftarrow R\cup c_i$

27: end for

28: Server sends { $\hat{X}$} to the blockchain for verification, and sends R to the data user