Table 3 Computation and communication complexities
Protocol | Total number of messages required | Total number of sequential scalar multiplications | The number of pairings |
|---|---|---|---|
HKAP [25] | \(5(l + r) - 6\) | \(5\left( {l + r} \right) - 12\) | – |
GKA-CH [21] | \(2l\, + \,5r\, + \,8\) | \(6\left( {l + 1} \right)\) | – |
PB-GKA HGM [31] | \(2r\, + \,3l\, + \,1\) | \(2\left( {l + r + 5} \right)\) | – |
AP-1/AP-2 [33] | \(2l\, + \,4r\) | \(\left( {3l + 6r} \right)\) | – |
ACEKA [26] | \(3\left( {n/2} \right)\, + \,3\) | \(\left( {5\left( {n/2} \right) + 18} \right)\) | \(21(n/2\, + \,1)\) |
A-DTGKA [20] | \((13n{-}7)/3\) | \(\left( {5n + 1} \right)\) | \(\left( {5n + 1} \right)\) |
ACBGKA [18] | \(4n\) | \(\left( {5n} \right)\) | \(11/2\;\left( n \right)\) |
ECDH-SKDM [43] | r + 1 | \(n\) | – |
NM-setup [16] | \(2\left( {l \cdot r - 2} \right)\) | \(2\left( {l \cdot r} \right)\) | – |
OUR-protocol (NM-CHH-GKA) | \(2\left( {l + r - 2} \right)\) | \(2\left( {l + r} \right)\) | – |