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

Algorithm 3

Privacy-preserving winner determination (PPWD).

Input: CSP has a pair of ElGamal key: , ; the auctioneer AUCT has ; has and .

Output: AUCT obtains the winner set and corresponding bundle set .

 1: CSP:

  (a) Select a large number , calculate , and select s.t.

  (b) Randomly choose noise from

  (c) Send , and to

 2: :

  (a) Compute the average value

  (b) Compute

  (c) Send to AUCT

 3: AUCT and jointly perform:

  (a) AUCT picks the largest and records the corresponding bidder as . is the bundle of

  (b) On input (, , , ), perform privacy-preserving scalar product protocol (PPSP) to obtain

  (c) AUCT receives

 4: AUCT:

  (a) If , is the winner. Inform to send , bundle and and put into the winner set and mark s bundle as auctioned in

  (b) Otherwise, remove from bidders

Repeat Steps 3–4 until no set can be updated