Advances, Systems and Applications
Table 4 Computation cost comparison
From: A threshold hybrid encryption method for integrity audit without trusted center
Scheme | KeyGen | File Pre-processing | ProofGen | Verifying | Re-signing |
|---|---|---|---|---|---|
Ref. [4] | 1Exp | \(\phantom {\dot {i}\!}2{N_{U}}{\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{1}}}} + {N_{U}}{\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{1}}}}\) | \(\phantom {\dot {i}\!}{N_{U}}{\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{1}}}} + (2{N_{U}} - 1){\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{1}}}}\) | - | - |
Ref. [8] | - | - | - | \(\phantom {\dot {i}\!}({N_{U}} + R){\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{1}}}} + ({N_{U}} + 2R){\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{1}}}} + (R + 1){\text {Pair}} + R{\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{2}}}} + {N_{U}}{\text {Has}}{{\mathrm {h}}_{{{\mathrm {G}}_{1}}}}\) | \(\phantom {\dot {i}\!}2{\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{1}}}} + {\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{1}}}} + 2{\text {Pair + Has}}{{\mathrm {h}}_{{{\mathrm {G}}_{1}}}}\) |
Ref. [31] | \(\phantom {\dot {i}\!}1{\text {Has}}{{\mathrm {h}}_{{{\mathrm {G}}_{1}}}} + 1{\text {Mu}}{{\mathrm {l}}_{{\mathbb {Z}_{q}}}} + 1{\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{1}}}}\) | - | \(\phantom {\dot {i}\!}{N_{U}}{\text {Mu}}{{\mathrm {l}}_{{\mathbb {Z}_{q}}}} + {N_{U}}{\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{1}}}} + {N_{U}}{\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{1}}}} + 1{\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{2}}}} + 1{\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{2}}}} + 1{\text {Pair}}\) | \(\phantom {\dot {i}\!}2{\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{2}}}} + 1{\text {Pair}} + {N_{U}}{\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{1}}}} + {N_{U}}{\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{1}}}}\) | \(\phantom {\dot {i}\!}2{\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{1}}}} + 1{\text {Has}}{{\mathrm {h}}_{{{\mathrm {G}}_{1}}}} + 1{\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{1}}}} + 2{\text {Pair}}\) |
Ref. [36] | - | - | \(\phantom {\dot {i}\!}(K + R{N_{U}}){\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{1}}}} + R{N_{U}}{\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{1}}}} + {N_{U}}K{\text {Mu}}{{\mathrm {l}}_{\Bbb Z}}_{_{p}} + K{\text {Has}}{{\mathrm {h}}_{\Bbb Z}}_{_{p}}\) | \(\phantom {\dot {i}\!}(2K + {N_{U}}){\text {Ex}}{{\mathrm {p}}_{{{\mathrm {G}}_{1}}}} + (2K + {N_{U}}){\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{1}}}} + R{\text {Mu}}{{\mathrm {l}}_{{{\mathrm {G}}_{2}}}} + {N_{U}}{\text {Has}}{{\mathrm {h}}_{{{\mathrm {G}}_{1}}}} + (R + 2){\text {Pair}}\) | - |
Ours | \(\phantom {\dot {i}\!}(t+3){\mathrm {Mul_{G_{1}}}}+(t-2){\mathrm {Exp_{G_{1}}}}\) | \(\phantom {\dot {i}\!}{\text {Pair}}+4{\mathrm {Mul_{G_{1}}}}+2{\mathrm {Exp_{G_{1}}}}\) | \(\phantom {\dot {i}\!}{N_{U}}{\mathrm {Exp_{G_{1}}}}+(2N_{U}-1){\mathrm {Mul_{G_{1}}}}\) | \(\phantom {\dot {i}\!}(3{N_{U}} - 2){\mathrm {Mul_{G_{1}}}}+{N_{U}}{\text {Pair}}\) | \(\phantom {\dot {i}\!}{\mathrm {2Mul_{G_{1}}}}+4{\mathrm {Exp_{G_{1}}}}+{\mathrm {2Pair}}\) |