Cryptography miracles, secure auctions, matching problem verification

In this article, we extend the methods of Rabin et al.^10,11 in a major way and provide a solution to the long-standing important problem of preventing collusion in secondprice (Vickrey) auctions. The new tools presented are deniable revelation of a secret value and uncontrollable deniable bidding. In Rabin et al.,10,11 new highly efficient methods for proving correctness of announced results of computations were introduced. These proofs completely conceal input values and intermediate results of the computation. One application was to enable an Auctioneer to announce outcome of a sealed bid auction and provide verification of correctness of the outcome, while keeping bid values informationtheoretically secret. We quickly survey these methods for completeness of the discussion and because of their wide applicability. Another example of an application is to prove to participants of a stable matching process such as the assignment residents to hospitals, of the correctness of the announced assignment without revealing any preferences of residents with respect to hospitals and vice-versa.