We present a secure network service for sovereign information sharing whose only trusted component is an off-theshelf secure coprocessor. The participating data providers send encrypted relations to the service that sends the encrypted results to the recipients. The technical challenge in implementing such a service arises from the limited capability of the secure coprocessors: they have small memory, no attached disk, and no facility for communicating directly with other machines in the network. The internal state of an ongoing computation within the secure coprocessor cannot be seen from outside, but its interactions with the server can be exploited by an adversary. We formulate the problem of computing join in this setting where the goal is to prevent information leakage through patterns in I/O while maximizing performance. We specify criteria for proving the security of a join algorithm and provide provably safe algorithms. These algorithms can be used to compute general joins involving arbitrary predicates and multiple sovereign databases. We thus enable a new class of applications requiring query processing across sovereign entities such that nothing apart from the result is revealed to the recipients.