  Inventory matching is a standard mechanism/auction for trading financial
stocks by which buyers and sellers can be paired. In the financial world, banks
often undertake the task of finding such matches between their clients. The
related stocks can be traded without adversely impacting the market price for
either client. If matches between clients are found, the bank can offer the
trade at advantageous rates. If no match is found, the parties have to buy or
sell the stock in the public market, which introduces additional costs. A
problem with the process as it is presently conducted is that the involved
parties must share their order to buy or sell a particular stock, along with
the intended quantity (number of shares), to the bank. Clients worry that if
this information were to leak somehow, then other market participants would
become aware of their intentions and thus cause the price to move adversely
against them before their transaction finalizes. We provide a solution, Prime
Match, that enables clients to match their orders efficiently with reduced
market impact while maintaining privacy. In the case where there are no
matches, no information is revealed. Our main cryptographic innovation is a
two-round secure linear comparison protocol for computing the minimum between
two quantities without preprocessing and with malicious security, which can be
of independent interest. We report benchmarks of our Prime Match system, which
runs in production and is adopted by J.P. Morgan. The system is designed
utilizing a star topology network, which provides clients with a centralized
node (the bank) as an alternative to the idealized assumption of point-to-point
connections, which would be impractical and undesired for the clients to
implement in reality. Prime Match is the first secure multiparty computation
solution running live in the traditional financial world.
