A distributed application may be considered as a set of nodes which are spread across the network, and need to communicate with each other. The design and implementation of these distributed applications is greatly simplified using Group Communication Systems (GCSs) which provide multipoint to multipoint communication. Hence, GCSs can be used as building blocks for implementing distributed applications. The GCS is responsible for reliable delivery of group messages and management of group membership. The peer-to-peer model and the client-server model are the two models of distributed systems for implementing GCSs. In this thesis, our focus is on improving the capability of GCS based on the client-server model. Security is an important requirement of many distributed applications. For such applications, security has to be provided m the GCS itself. The security of a GCS includes confidentiality, authentication and non-repudiation of messages, and ensuring that the GCS is properly meeting its guarantees. The complexity and cost of implementation of the above three types of security guarantees greatly depend on whether the GCS servers are trusted by the group members or not. Making use of the GCS services provided by untrusted GCS servers becomes necessary when the GCS servers are managed by a third party. In this thesis, we have proposed algorithms for ensuring the above three security guarantees for GCSs in which servers are not trusted. As part of the solution, we have proposed a new digital multisignature scheme which allows group members to verify that a message has indeed been signed by all group members. The various group key management algorithms proposed in literature differ from each other with respect to the following four metrics: communication overhead, computational overhead, storage at each member and distribution of load among group members. We identify the need for a distributed group key management algorithm which minimizes the computational overhead on group members and propose an algorithm to achieve it.