A Practical Solution to Yao's Millionaires' Problem and Its Application in Designing Secure Combinatorial Auction

Abstract: The emergence of e-commerce and e-voting platforms has resulted in the rise in the volume of sensitive information over the Internet. This has resulted in an increased demand for secure and private means of information computation. Towards this, the Yao's Millionaires' problem, i.e., to determine the richer among two millionaires' securely, finds an application. In this work, we present a new solution to the Yao's Millionaires' problem namely, Privacy Preserving Comparison (PPC). We show that PPC achieves this comparison in constant time as well as in one execution. PPC uses semi-honest third parties for the comparison who do not learn any information about the values. Further, we show that PPC is collusion-resistance. To demonstrate the significance of PPC, we present a secure, approximate single-minded combinatorial auction, which we call TPACAS, i.e., Truthful, Privacy-preserving Approximate Combinatorial Auction for Single-minded bidders. We show that TPACAS, unlike previous works, preserves the following privacies relevant to an auction: agent privacy, the identities of the losing bidders must not be revealed to any other agent except the auctioneer (AU), bid privacy, the bid values must be hidden from the other agents as well as the AU and bid-topology privacy, the items for which the agents are bidding must be hidden from the other agents as well as the AU. We demonstrate the practicality of TPACAS through simulations. Lastly, we also look at TPACAS' implementation over a publicly distributed ledger, such as the Ethereum blockchain.