We describe a second-price sealed-bid auction protocol which has the potential to be t-private and t-resilient, and which is efficient enough for use in large auctions. All polynomials used during the protocol are secret sharing polynomials from (the set of polynomials over the field of integers less than a prime p). The prime p should be chosen to support the assumption that the sum of several random non-zero elements from is very unlikely to be zero (i.e. that is very small). They are stored in a point-value representation, with each of the m auctioneers (who are indexed by i) holding the value at one point. Let be the point held by the auctioneer. These polynomials are manipulated by means of their evaluations at these m points.
Each of the n bidders (indexed by j) computes a set of secret sharing polynomials whose secrets encode her bid. The bidders distribute the shares of these polynomials among the auctioneers. The auctioneers then perform a multi-round computation to determine the selling price. The winning bidder is then determined by combining certain information from the auctioneers.