A new approach for electronic sealed-bid auctions that preserve the privacy of losing bids is presented. It reduces the number of operations performed by the auctioneers to O(log ); previous protocols require O(N ) or O(N log ) where the number of bidders is N and that of available bidding prices is . Namely, the number of auctioneers' operations in our auction protocol is independent of the number of bidders. This feature offers strong advantages in massive auctions. We also propose a new scheme that checks the equality of two values without disclosing them. The scheme enhances our basic auction protocol, in terms of security and communication costs.

This paper describes simple and efficient (linear-preserving) reductions between the Decision Diffie-Hellman problem and related problems.