Algorithm 4 KeyGenerate.

Input:

$MK$: TA’s master key;

$PK$: the public parameter;

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

Output:

$S{K}_{\mathcal{Q}}$: a secret key;

1: Compute $D=MK·g_0^{d_0}$, where $d_0\in {\mathbb{Z}}_p$;

2: for all $i\in S_{\mathcal{Q}}$ do

3:   Compute $D_i=H{\left(i\right)}^{r_i}·g_0^{d_0}$, ${D^{\prime }}_i=g_0^{r_i}$, where $r_i\in {\mathbb{Z}}_p$;

4: end for

return ${SK}_{\mathcal{Q}}=\left\{D,\forall i\in S_{\mathcal{Q}}:D_i,{D^{\prime }}_i\right\}$.