BA²P : Bidirectional and Anonymous Auction Protocol with Dispute-Freeness

Table 1

Comparison of bidding schemes.

Scheme	Technique	Auctioneer	Hidden bids	Opener of bids
Our work	Chameleon hash	Distrusted	Yes	Bidder
Franklin and Reiter [16]	Verifiable signature sharing	Distrusted	No	Auctioneer
Kikuchi et al. [17]	Secret sharing	Trusted	Yes	Auctioneer
Sako. [18]	Standard cryptographic algorithms	Trusted	Yes	Auctioneer
Suzuki and Kobayashi [19]	Verifiable encryption	Distrusted	Yes	Auctioneer
Suzuki and Yokoo [20]	Homomorphic encryption	Distrusted	Yes	Bidder
Peng et al. [21]	Secret sharing	Distrusted	Yes	Auctioneer
Xiong et al. [8]	Ring signature	Trusted	Yes	Bidder
Galal and Youssef et al. [22]	Commitment and zero-knowledge proof	Distrusted	Yes	Auctioneer