Table 2. Compare with existing schemes.

Scheme	Index building	Trapdoor generation	Query	Verification	Round
VPS	$O(MN)$	$O(|q|\ast |F_w|)$	$O(|F_w|\ast |F_j{|}^{|q|})$	$O(|q|\ast |F_w|)$	2
VPS-IoT	$O(MN)+O({\sum }_{j=1}^{M}N|F_j|)$	$O(2|q|+|F_w|+|q|\ast |F_w|)$	$O(|F_w|\ast |F_j{|}^{|q|}+|q|)$	$O(|q|\ast |F_q|)$	2
Our Scheme	$O(MN)$	$O(|q|\ast |F_w|)$	$O(|F_w|\ast |F_j{|}^{|q|})$	$O(|F_w|)$	1

Note:

$|F_j|$ is the number of keywords contained in the file $F_j$; $w_j$ is a collection of different keywords in the file $F_j$; $|q|$ is the number of query keywords; $|F_w|$ is the number of files containing query keywords; $|F_q|$ is the size of the returned result file.