Abstract

We present a practical protocol based on homomorphic cryptography for conducting provably fair sealed-bid auctions. The system preserves the secrecy of the bids, even after the announcement of auction results, while also providing for public verifiability of the correctness and trustworthiness of the outcome. No party, including the auctioneer, receives any information about bids before the auction closes, and no bidder is able to change or repudiate any bid. The system is illustrated through application to first-price, uniform-price and second-price auctions, including multi-item auctions. Empirical results based on an analysis of a prototype demonstrate the practicality of our protocol for real-world applications.

Highlights

  • In recent years, auctions and electronic marketplaces have been used to facilitate trillions of dollars in trade in the world economy [10]

  • We have developed a practical protocol for sealed bid auctions that prevents such manipulations

  • We have carefully examined the role of all parties in a sealed-bid auction and formalized their role in a cryptographically sound protocol

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Summary

INTRODUCTION

Auctions and electronic marketplaces have been used to facilitate trillions of dollars in trade in the world economy [10]. A secrecy-preserving verification protocol allows anyone, including bidders and third parties, to verify that the auction was correct: the auctioneer correctly determined the winner(s) and associated payment(s) according to published rules. With specially designed hardware and software audited by third parties for correctness, and installed in physically secure locations with ongoing monitoring and auditing, can prevent the leaking of information with high assurance [33]. With such deliberately opaque servers it is of the utmost import that an auction participant can independently verify the correctness of the outcome of an auction and be assured that there is no fraud. Because our method is parallelizable, it is possible to accommodate even tens of thousands of bidders in at most a day of computation on a 64-node network

Related Work
Real-World Components
Notaries
Overall Flow and Main Steps of Auction
Cryptographic Tools
Public Key Infrastructure
Commitments
Sources of Randomness
Delayed private key revelation
Verifiable and Confidential Comparisons
SINGLE-ITEM AUCTIONS
Protocol
Verification
MULTI-ITEM AUCTIONS
Payment
EMPIRICAL RESULTS
CONCLUSIONS AND FUTURE WORK
Decryption
Decryption with random help value r
Uniqueness of Encryptions
Mathematical Operations on Encrypted Values
BULK VERIFICATION OF TEST SETS

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