PP-VCA: A Privacy-Preserving and Verifiable Combinatorial Auction Mechanism

Algorithm 4

Privacy-preserving and verifiable payment determination (PPVPD).

Input: the auctioneer AUCT has and the winner’s and .

Output: obtains the payment .

 1: AUCT removes the winner from bidders and modifies to , where is the set of auctioned goods and is the bundle of . Then, through Algorithm 3, AUCT chooses a freshful winner , who is the candidate of . AUCT notifies to send average value and to AUCT

 2: If the candidate of can be successfully found, AUCT computes and sends and to . If no candidate is found, AUCT sets as the agreed default value and notifies that is the default value

 3: If is not the default value, can recover from and verify whether is correct through . If they are not equal to each other, knows that the payment is not correct