Table 2.

Computational cost.

Schemes	Signing	Verifying	Total
Yu and Tate [25] scheme 1	1E + 3BPM	3E + 4BPM	4E + 7BPM
Yu and Tate [25] scheme 2	2E + 3BPM	3E + 3BPM	5E + 6BPM
Wu et al. [26]	3BPM	2P + 2BPM	2P + 5BPM
Addobea et al. [27]	3 BPM	3P + 4BPM	3P + 7BPM
Proposed	4HM	3HM	7HM