Algorithm 2.  $Kyber\_CPA\_En(bi=(f,\mu ),y\in O):encryption$

1. $\gamma \leftarrow {\left\{0,1\right\}}^{256}$

2. ${\mathrm{f}:=\mathrm{Decomp}}_t(f,d_f)$

3. $N~R_t^{i\times i}:=S(\mu )$

4. $(\gamma ,e_1,e_2)~{\beta }_{\eta }^i\times {\beta }_{\eta }^i\times {\beta }_{\eta }:=S(\gamma )$ 5. $\alpha :=Com{p}_t(N^T\gamma +e_1,q_{\alpha })$

6. $\beta :=Com{p}_t(f^T\gamma +e_2+⌈\frac{t}{2}⌉)\cdot y,t_{\beta })$ 7: return $d:=(\alpha ,\beta )$