Algorithm 5 DecryptNode.

Input:

$Y_e^{II}$: defined in Equation (3)

${SK}_{\mathcal{Q}}$: the querier $\mathcal{Q}$’s secret key;

$S_{\mathcal{Q}}$: the querier $\mathcal{Q}$’s attribute set;

u: a node in the access tree $T_P$;

Output:

$pa{r}_u$: a secret parameter;

or ⊥

1: if u is a leaf node then

2:   Set $i=att\left(u\right)$;

3:   if $i\in S_{\mathcal{Q}}$ then

4:     Compute $$pa{r}_u=\frac{e\left(D_i,C_u\right)}{e\left({D^{\prime }}_i,{C^{\prime }}_u\right)}=e{\left(g,g\right)}^{q_u\left(0\right)\sum d_k};$$

5:   else return $pa{r}_u=\perp$;

6:   end if

7: else

8:   Define $F_u=null$;

9:   for all $z\in Children\left(u\right)$ do

10:     Compute $pa{r}_z=DecryptNode\left(Y_e^{II},{SK}_{\mathcal{Q}},S_{\mathcal{Q}},z\right)$;

11:     if $pa{r}_z\ne \perp$ then

12:       Update $F_u=F_u\cup \left\{pa{r}_z\right\}$;

13:     end if

14:   end for

15:   if $|F_u|<k_u$ then return $pa{r}_u=\perp$;

16:   else

17:     Compute $pa{r}_u=e{\left(g_0,g_0\right)}^{q_u\left(0\right)d_0}$ using $F_u$ by polynomial interpolation method;

18:   end if

19: end if

return $pa{r}_u$.