  A Private Set Operation (PSO) protocol involves at least two parties with
their private input sets. The goal of the protocol is for the parties to learn
the output of a set operation, i.e. set intersection, on their input sets,
without revealing any information about the items that are not in the output
set. Commonly, the outcome of the set operation is revealed to parties and
no-one else. However, in many application areas of PSO the result of the set
operation should be learned by an external participant whom does not have an
input set. We call this participant the decider. In this paper, we present new
variants of multi-party PSO, where there is a decider who gets the result. All
parties expect the decider have a private set. Other parties neither learn this
result, nor anything else about this protocol. Moreover, we present a generic
solution to the problem of PSO.

Cryptography and Security