Table 6 Comparison of computation cost (in ms) of proposed schemes with similar recent schemes.

From: Two secure authentication protocols for mitigating vulnerabilities in IoD

Schemes

\(D_j/Device_j\)

\(U_i\)/\(GWN_i\)

Server

Total (ms)

Tanveer et al.10

\(3T_{cmap}+2T_s+4T_h\)

\(T_{fe}+5T_{cmap}+4T_s+6T_h\)

\(3T_{cmap}+T_s+3T_h\)

16.453 

Irshad et al.11

\(3T_{mp}+8T_h+1T_{pa}\)

\(T_{fe}+3T_{mp}+15T_h+T_{pa}\)

\(2T_{s}+3T_{mp}+9T_h+T_{pa}\)

47.097 

Zhang et al.22

\(7T_h\)

\(10T_h\)

\(7T_h\)

0.519 

Gupta et al.23

\(4T_h\)

\(7T_h\)

\(5T_h\)

0.341 

Choi et al.24

\(2T_{PUF} + 13T_h\)

\(12T_h\)

\(17T_h\)

1.077 

Modarres and Sarbishaei26

\(T_{PUF} +7T_h\)

\(8T_h\)

\(2T_{PUF} +11T_h\)

0.631 

Nyangaresi et al.27

\(T_{PUF} +4T_{mp}+4T_h+2T_{pa}\)

\(5T_{mp}+5T_h+T_{pa}\)

24.424 

Zhang et al.9

\(6T_h+2T_{PUF}\)

\(8T_h\)

\(6T_h\)

0.67 

Proposed scheme (a)

\(8T_h+2T_{PUF}\)

\(12T_h\)

\(8T_h\)

0.848 

Proposed scheme (b)

\(11T_h+2T_{PUF}\)

\(15T_h\)

\(12T_h\)

1.048