We present a practical system for conducting sealed-bid auctions that preserves the secrecy of the bids while providing for verifiable correctness and trustworthiness of the auction. The auctioneer must accept all bids submitted and follow the published rules of the auction. No party receives any useful information about bids before the auction closes and no bidder is able to change or repudiate her 1 bid. Our solution uses Paillier’s homomorphic encryption scheme [25] for zero knowledge proofs of correctness. Only minimal cryptographic technology is required of bidders; instead of employing complex interactive protocols or multi-party computation, the single auctioneer computes optimal auction results and publishes proofs of the results ’ correctness. Any party can check these proofs of correctness via publicly verifiable computations on encrypted bids. The system is illustrated through application to firstprice, uniform-price and second-price auctions, including multiitem auctions. Our empirical results demonstrate the practicality of our method: auctions with hundreds of bidders are within reach of a single PC, while a modest distributed computing network can accommodate auctions with thousands of bids. 1.

We investigate whether it is possible to preserve privacy in sealed-bid auctions to a maximal extent. In particular, this paper focuses on unconditional full privacy, i.e., privacy that relies neither on trusted third parties (like auctioneers), nor on computational intractability assumptions (like the hardness of factoring). These constraints imply a scenario in which bidders exchange messages according to some predefined protocol in order to jointly determine the auction outcome without revealing any additional information. It turns out that the first-price sealed-bid auction can be emulated by an unconditionally fully private protocol. However, the protocol’s round complexity is exponential in the bid size, and there is no more efficient protocol. On the other hand, we prove the impossibility of privately emulating the second-price sealed-bid auction for more than two bidders. This impossibility holds even when relaxing various privacy constraints such as allowing the revelation of all but one losing bid (while maintaining anonymity) or allowing the revelation of the second highest bidder’s identity.

Abstract. Securecomputationisapromisingapproachtobusinessproblems in which several parties want to run a joint application and cannot reveal their inputs. Secure computation preserves the privacy of input data using cryptographic protocols, allowing the parties to obtain the benefits of data sharing and at the same time avoid the associated risks. These business applications need protocols that support all the primitive data types and allow secure protocol composition and efficient application development. Secure computation with rational numbers has been a challenging problem. We present in this paper a family of protocols for multiparty computation with rational numbers using fixed-point representation. This approach offers more efficient solutions for secure computation than other usual representations.

Privacy and anonymity have become two factors of increasing importance in auction protocol. This paper provides an efficient sealed-bid electronic auction protocol based on the technique of ring signature and verifiable technique of encryption key chain. The peculiar characteristics of our protocol are non-repudiation of bidders but preserving their anonymity and allowing the auctioneer to determine the wining bid without revealing the losing bid. Our protocol has additional characteristics such as public verifiability, unforgeability, correctness and fairness.

Abstract. We present a cryptographic protocol for conducting efficient, provably-correct and secrecy-preserving combinatorial clock-proxy auctions. The “clock phase ” functions as a trusted auction despite price discovery: bidders submit encrypted bids, and prove for themselves that they meet activity rules, and can compute total demand and thus verify price increases without revealing any information about individual demands. In the sealed-bid “proxy phase”, all bids are revealed the auctioneer via time-lapse cryptography and a branch-and-bound algorithm is used to solve the winner-determination problem. Homomorphic encryption is used to prove the correctness of the solution, and establishes the correctness of the solution to any interested party. Still an NP-hard optimization problem, the use of homomorphic enryption imposes additional computational time on winner-determination that is linear in the size of the branch-and-bound search tree, and thus roughly linear in the original (search-based) computational time. The result is a solution that avoids, in the usual case, the exponential complexity of previous cryptographically-secure combinatorial auctions. 1

tography service ” that produces public encryption keys and guarantees decryption at a particular time by constructing and releasing the corresponding decryption key after a specific interval. This service functions as a new cryptographic commitment primitive with binding, hiding, and nonrepudiation. Provided with these tools, we construct four new mechanisms for electronic commerce: a cryptographic sealed-bid auction protocol for one or more identical items, a cryptographic combinatorial auction protocol based on the “clock-proxy ” auction, a cryptographic securities exchange that conducts a continuous double auction for a particular security, and a cryptographic combinatorial securities exchange that provides for efficient atomic exchange of baskets of many securities. Along the way, we develop useful building blocks of independent interest, most notably a novel cryptographic mechanism to efficiently prove a solution to a linear or integer program is optimal based on its encrypted inputs and encrypted constraints; this provides unprecedented efficiency in proving the correctness of winner and price determination in our combinatorial clock-proxy auction. Contents

Abstract—Secure auctions have many potential uses including eVoting, computational resource allocation and FCC spectrum auctions.The SGVA privacy preserving auction scheme is able to conduct combinatorial auctions and keep the losing bid values secret. However, SVGA is a black box so users have no means to assure themselves that the auction has actually taken place and that their bid has been included in the computation of the result. We have designed a verification scheme composed of zero knowledge proofs that extends the basic SGVA secure auction protocol to permit users to verify offline that the protocol has been executed correctly. This is especially useful in environments where participants have no pre-existing trust, such as the Internet. Figure 2 shows Alice holding a privacy preserving sealed bid auction on her web site hosted by Sam. Bob and Jim submit encrypted bids to the auctioneer. I.