Table 5.

A comparison of signature generation time and verification time for the proposed authentication methods and the previous methods in single-zone and multi-zone scenarios.

Security Methods	Signature Generation Time Per Message for Single Zone Case (ms)	Signature Verification Time Per Message for Single Zone Case (ms)	Signature Generation Time Per Message for n Receivers in n Multi-Zones (ms)	Signature Verification Time Per Message for Each Receiver in n Multi-Zones (ms)
(1) Horng et al. [19]	2TMG1 + 2TAG1 = 0.9594	3TP + TMG1 + TM2P = 7.8305	0.9594n	3 nTP + nTMG1 + nTM2P = 952.7n
(2) Li et al. [20]	TAG1 + 2TMG1 + TM2P = 1.1	3TP + TMG1 + 2TM2P + TAG1 = 8.094	1.1n	3nTP + nTMG1 + 2nTM2P + nTAG1 = 8.094n
(3) Malhi et al. [21]	4TMG1 + 2TAG1 = 1.93	3TP + 3TMG1 + TAG1 = 8.782	1.93n	3nTP + 3nTMG1 + nTAG1 = 8.778n
(4) Lin et al. [22]	3TP + TM2P = 7.473	5TP + 8TMG1 = 16.132	7.473n	5nTP + 8nTMG1 = 16.132n
(5) Bayat et al. [23]	5TMG1 + TAG1 + TH + TM2P = 2.549	3TP + TMG1 + TH + TM2P = 7.8365	2.549n	3n TP + nTMG1 + nTM2P = 7.952n
(6) Boneh et al. [24]	3TP + 5TMG1 = 9.7275	4TP + 2TM2P = 10.054	9.7275n	4nTP + 2nTM2P = 10.054n
The proposed TCA	TM2P + TMG1 = 0.614	2TP + TM2P = 4.9 + 0.135 = 5.035	0.614	2TP = 5.035
The proposed SCA	TM2P + TMG1 = 0.614	2TP + TM2P = 4.9 + 0.135 = 5.035	0.614n	2TP = 5.035
The proposed RCA	$\left(n-1\right)TAFp+\left(n-1\right)\mathrm{TAG}2+\mathrm{TM}2\mathrm{P}+\mathrm{TMG}1$ = 0.600 + 0.014n	$(n-1)$ $\mathrm{TAG}2+\mathrm{TM}2\mathrm{P}+2\mathrm{TP}=0.013\left(n-1\right)+0.135+4.9=5.014+0.013\mathrm{n}$	0.600 + 0.014n	5.014 + 0.013n