In this paper we investigate the issues concerning with the use of a single server across a network, the Key Distribution Center, to enable private communications within groups of users. After providing several motivations, showing the advantages related to the distribution of the task accomplished by this server, we describe a model for such a distribution, and present bounds on the amount of resources required in a real-world implementation: random bits, memory storage, and messages to be exchanged. Moreover, we introduce a linear algebraic approach to design optimal schemes distributing a Key Distribution Center and we show that some known previous constructions belong to the proposed framework.