An Efficient Electronic English Auction System with a Secure On-Shelf Mechanism and Privacy Preserving

Table 2

Comparison in computational cost of the three schemes.

Property	Proposal
	Our proposal	Chang et al.’s proposal [14]	Xiong et al.’s proposal [13]	Chung et al.’s proposal [18]
Registration phase	8PM + H	9PM	4PM + 2H	5PM + 3H
On-shelf phase	7PM + 2E + 2D + 2H	10PM + 2E + 2D + 2H	×	×
Bidding phase	(10 + 2)PM + 3E + 2D + 5H	12PM + 2E + 2D	(4 + 1)PM + 3BM + 2H	(8 + 2)PM + (3 + 1)H
Product claiming phase	2PM + E + D + 1H	6PM	×	×
Dispute phase (bidder/auctioneer)	6PM + E + 1D + 3H/6PM + E + 2D + 3H	3PM + 2H/3PM + E + D	0.5BM/×	×