  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.
