Algorithm 2 Procedure of Encryption

1:functionEncrypt($\mathit{M}={[{\mathit{m}}_{\mathbf{1}},\dots ,{\mathit{m}}_{\mathit{n}}]}^T$,$S{K}_1$) 2:    Pick random $i,j$ ($1\le i,j\le n$) 3:    Construct matrices             ${\mathit{M}}_{\mathbf{1}}={[{\mathit{m}}_{\mathbf{1}},\dots {\mathit{m}}_{\mathit{i}}^{\prime }\dots ,{\mathit{m}}_{\mathit{n}}]}^T$;             ${\mathit{M}}_{\mathbf{2}}={[{\mathit{m}}_{\mathbf{1}},\dots {\mathit{m}}_{\mathit{i}}^{″}\dots ,{\mathit{m}}_{\mathit{n}}]}^T$;             ${\mathit{M}}_{\mathbf{3}}={[{\mathit{m}}_{\mathbf{1}},\dots {\mathit{m}}_{\mathit{j}}^{\prime }\dots ,{\mathit{m}}_{\mathit{n}}]}^T$;             ${\mathit{M}}_{\mathbf{4}}={[{\mathit{m}}_{\mathbf{1}},\dots {\mathit{m}}_{\mathit{j}}^{″}\dots ,{\mathit{m}}_{\mathit{n}}]}^T$;             satisfying Equations (3) and (4). 4:    ${\mathit{Y}}_{\mathbf{1}}\leftarrow {\mathit{P}}_{\mathbf{1}}{\mathit{M}}_{\mathbf{1}}{\mathit{Q}}_{\mathbf{1}}$. 5:    ${\mathit{Y}}_{\mathbf{2}}\leftarrow {\mathit{P}}_{\mathbf{2}}{\mathit{M}}_{\mathbf{2}}{\mathit{Q}}_{\mathbf{2}}$. 6:    ${\mathit{Y}}_{\mathbf{3}}\leftarrow {\mathit{P}}_{\mathbf{3}}{\mathit{M}}_{\mathbf{3}}{\mathit{Q}}_{\mathbf{3}}$. 7:    ${\mathit{Y}}_{\mathbf{4}}\leftarrow {\mathit{P}}_{\mathbf{4}}{\mathit{M}}_{\mathbf{4}}{\mathit{Q}}_{\mathbf{4}}$. 8:    return ${\sigma }_x=\{{\mathit{Y}}_{\mathbf{1}},{\mathit{Y}}_{\mathbf{2}},{\mathit{Y}}_{\mathbf{3}},{\mathit{Y}}_{\mathbf{4}}\}$ 9: end function