Algorithm 4. Search.

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

Output: Search results R

1: Parse $\{t_{w_1},t_{w_2},...,t_{w_t},E_1,E_2,..E_{t-1}\}\leftarrow T{K}_{i,Q}$

2: for $t_{w_j}\in T{K}_{j,Q}$ do

3:      $v_{\mathcal{B}}\leftarrow \mathcal{I}[t_{w_j}];{\mathcal{B}}_{w_j}||S{L}_{w_j}^i\leftarrow v_{\mathcal{B}}\oplus H_2(t_{w_j})$

4: end for

5:  $\mathcal{B}={\mathcal{B}}_1\wedge {\mathcal{B}}_2\wedge ...\wedge {\mathcal{B}}_t,r=\mathcal{H}(\mathcal{B},\{\mathrm{\perp }\})$

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

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

8:    $flag=\{\mathrm{000...000}{\}}^{t-1},has{h}_i=H_1(t[{\ell }_i]),\psi =\psi {+}_{\mathcal{H}}\mathcal{H}(r,has{h}_i)$

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

10:   for $d=2\to t$ do

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

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

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

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

15:             break

16:         end if

17:      end for

18:   end for

19:   If all positions of flag are 1

20:   get $C_i\leftarrow T[{\ell }_i]$, $R\leftarrow R\cup C_i$

21: end for

22: Server sends { $\psi$} to the blockchain for verification, and sends R to the data user