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. 2016 Dec 14;16(12):2123. doi: 10.3390/s16122123

Table 4.

Comparisons of the computation costs.

Scheme		Computation Cost
Scheme		Registration	Login & Authentication	Total
Kim et al.’s [13]	User	$2 T_{h} + T_{x}$	$9 T_{h} + 9 T_{x}$	$11 T_{h} + 10 T_{x}$
	$G W N$	$6 T_{h} + 3 T_{x}$	$8 T_{h} + 8 T_{x}$	$14 T_{h} + 11 T_{x}$
	Sensor	0	$2 T_{h} + 2 T_{x}$	$2 T_{h} + 2 T_{x}$
Chang et al.’s [14]	User	$2 T_{h} + T_{x}$	$9 T_{h} + 5 T_{x}$	$11 T_{h} + 6 T_{x}$
	$G W N$	$5 T_{h} + 3 T_{x}$	$10 T_{h} + 4 T_{x}$	$15 T_{h} + 7 T_{x}$
	Sensor	0	$4 T_{h} + T_{x}$	$4 T_{h} + T_{x}$
Yoon and Yoo’s [15]	User	$T_{h}$	$3 T_{h} + 2 T_{x} + 2 T_{E}$	$4 T_{h} + 2 T_{x} + 2 T_{E}$
	$G W N$	$2 T_{h} + 2 T_{x}$	$4 T_{h}$	$6 T_{h} + 2 T_{x}$
	Sensor	0	$3 T_{h} + 2 T_{E}$	$3 T_{h} + 2 T_{E}$
Choi et al.’s [18]	User	$T_{h} + T_{F}$	$10 T_{h} + 2 T_{x} + T_{F} + T_{e n c} + 2 T_{E}$	$11 T_{h} + 2 T_{x} + 2 T_{F} + T_{e n c} + 2 T_{E}$
	$G W N$	$3 T_{h} + 3 T_{x}$	$10 T_{h} + T_{x} + 2 T_{e n c}$	$13 T_{h} + 4 T_{x} + 2 T_{e n c}$
	Sensor	0	$6 T_{h} + T_{e n c} + 2 T_{E}$	$6 T_{h} + T_{e n c} + 2 T_{E}$
Proposed	User	$T_{h} + T_{F}$	$9 T_{h} + 4 T_{x} + T_{F} + 2 T_{E}$	$10 T_{h} + 4 T_{x} + 2 T_{F} + 2 T_{E}$
	$G W N$	$5 T_{h} + 3 T_{x}$	$11 T_{h} + 4 T_{x}$	$16 T_{h} + 7 T_{x}$
	Sensor	0	$4 T_{h} + T_{x} + 2 T_{E}$	$4 T_{h} + T_{x} + 2 T_{E}$