Table 4 Comparison on computation cost of related schemes.
Schemes | Sign one message (ms) | Authentication \(n(n>1)\) messages (ms) | Total cost (ms) |
|---|---|---|---|
Zhu et al.1 | \(1{{T}_{sm-ecc}}+2{{T}_{h}}=0.4422\) | \((2n+3){{T}_{sm-ecc}}+(3n-3){{T}_{sm-ecc-s}}+(3n+1){{T}_{pa-ecc}}\) \(+3n{{T}_{h}}=0.9311n+1.2864\) | \(0.9311n+1.7286\) |
Wu et al.7 | \(3{{T}_{sm-ecc}}+1{{T}_{mtp}}+1{{T}_{h}}=9.5331\) | \(3{{T}_{bp}}+3n{{T}_{sm-bp}}+2n{{T}_{mtp}}+n{{T}_{h}}=13.9391n+12.633\) | \(13.9391n+22.1661\) |
Zhu et al.8 | \(1{{T}_{sm-ecc}}+1{{T}_{h}}=0.4421\) | \((n+2){{T}_{sm-ecc}}+3n{{T}_{pa-ecc}}+2n{{T}_{h}}=0.4476n+0.884\) | \(0.4476n+1.3261\) |
Zhou et al.18 | \(1{{T}_{sm-ecc}}+2{{T}_{h}}=0.4422\) | \((2n+2){{T}_{sm-ecc}}+3n{{T}_{pa-ecc}}+3n{{T}_{h}}=0.8897n+0.884\) | \(0.8897n+1.3262\) |
Yang et al.29 | \(1{{T}_{sm-ecc}}+2{{T}_{h}}=0.4422\) | s\((4n+1){{T}_{sm-ecc}}+3n{{T}_{pa-ecc}}+4n{{T}_{h}}=1.7738n+0.442\) | \(1.7738n+0.8842\) |
Our scheme | \(1{{T}_{sm-ecc}}+2{{T}_{h}}=0.4422\) | \((2n+3){{T}_{sm-ecc}}+(3n+1){{T}_{pa-ecc}}+(3n+1){{T}_{h}}\) \(= 0.8897n+1.3279\) | \(0.8897n+1.7701\) |
