We present protocols for distributed computation of relational intersections and equi-joins such that each site gains no information about the tuples at the other site that do not intersect or join with its own tuples. Such protocols form the building blocks of distributed information systems that manage sensitive information, such as patient records and financial transactions, that must be shared in only a limited manner. We discuss applications of our protocols, outlining the ramifications of assumptions such as semi-honesty. In addition to improving on the efficiency of earlier protocols, our protocols are asymmetric, making them especially applicable to applications in which a low-powered client interacts with a server in a privacy-preserving manner. We present a brief experimental study of our protocols. (UMIACS-TR-2004-09)