Electron Commer Res (2010) 10: 291–311 DOI 10.1007/s10660-010-9057-x On server trust in private proxy auctions Giovanni Di Crescenzo · Javier Herranz · Germán Sáez Published online: 9 October 2010 © Springer Science+Business Media, LLC 2010 Abstract We investigate proxy auctions, an auction model which is proving very successful for on-line businesses (e.g., http://www.ebay.com), where a trusted server manages bids from clients by continuously updating the current price of the item and the currently winning bid as well as keeping private the winning client’s maximum bid. We propose techniques for reducing the trust in the server by defining and achiev- ing a security property, called server integrity. Informally, this property protects clients from a novel and large class of attacks from a corrupted server by allow- ing them to verify the correctness of updates to the current price and the currently winning bid. Our new auction scheme achieves server integrity and satisfies two im- portant properties that are not enjoyed by previous work in the literature: it has min- imal interaction, and only requires a single trusted server. The main ingredients of our scheme are two minimal-round implementations of zero-knowledge proofs for proving lower bounds on encrypted values: one based on discrete logarithms that is more efficient but uses the random oracle assumption, and another based on quadratic residuosity that only uses standard intractability assumptions but is less efficient. G. Di Crescenzo: Part of this work done while visiting UPC, Spain. J. Herranz and G. Sáez: Work partially supported by Spanish MICINN Ministry, project TSI2006-02731. G. Di Crescenzo ( ) Telcordia Technologies, Piscataway, NJ, USA e-mail: giovanni@research.telcordia.com J. Herranz · G. Sáez Dept. Matemàtica Aplicada IV, Universitat Politècnica de Catalunya C. Jordi Girona, 1-3, Mòdul C3, Campus Nord, 08034 Barcelona, Spain J. Herranz e-mail: jherranz@ma4.upc.edu G. Sáez e-mail: german@ma4.upc.edu