Privacy for the Stock Market

We investigate the problem of performing Stock Market operations, such as buying or selling shares of a certain stock, in a private way, which had recently been left open. We present a formal definition for a private stock purchase protocol, addressing several privacy and security concerns on usual on-line stock market operations. According to our definition, a client would not reveal how many shares she is buying or selling (not even which of these two cases is happening), and what price she is offering for those. We then present an efficient protocol meeting this definition, based on the hardness of the decisional Diffie–Hellman problem. Our protocol requires no interaction between the clients, can be executed in a constant number of rounds between the clients and the server, and requires several technical contributions, such as a new and efficient zero-knowledge protocol for proving sum-related statements about encrypted values, which is of independent interest.