# Table 3 Computation and Communcitaion efficiency comparison

Scheme Computation Communcitaion
PEKS Trapdoor Test |C| |T| |Pk|
Huang and Li [8] Hp+3E P+HP+E 2P+M 2$$\vert \mathbb {G}_{1} \vert$$ $$\vert \mathbb {G}_{2} \vert$$ $$\vert \mathbb {G}_{1} \vert$$
Li et al. [12] 2P+2Hp+3E+H P+2Hp+2E+M 2P+2E+M 2$$\vert \mathbb {G}_{1} \vert$$ + $$\vert \mathbb {G}_{2} \vert$$ 2$$\mathbb {G}_{1}$$ *
Baek et al. [3] 2P+Hp+2E+M+H Hp+E P+M+E+H $$\vert \mathbb {G}_{1} \vert \,+\,\vert q \vert$$ $$\vert \mathbb {G}_{2} \vert$$ 2$$\vert \mathbb {G}_{1} \vert$$
Rhee et al. [4] P+Hp+2E+H Hp+3E+M P+Hp+2E $$\vert \mathbb {G}_{1} \vert$$ 2$$\vert \mathbb {G}_{1} \vert$$ 2$$\vert \mathbb {G}_{1} \vert$$
Pan and Li [10] Hp+3E+H P+Hp+3E 2P+M 2 $$\vert \mathbb {G}_{1} \vert$$ 2$$\vert \mathbb {G}_{1} \vert$$ + $$\vert \mathbb {G}_{2} \vert$$ $$\vert \mathbb {G}_{1} \vert$$
Our Scheme P+4E+2H 4E+2H+M 2P+M+E 2$$\vert \mathbb {G}_{1} \vert \,+\,\vert \mathbb {G}_{2} \vert$$ 2$$\vert \mathbb {G}_{1} \vert$$ $$\vert \mathbb {G}_{1} \vert$$