Sensor networks have a wide spectrum of military and civil applications, particularly with respect to security and secure keys for encryption and authentication. This thesis presents a new centralized approach which focuses on the group key distribution with revocation capability for Wireless Sensor Networks. We propose a new personal key share distribution. When utilized, this approach proves to be secure against k-number of illegitimate colluding nodes. In contrast to related approaches, our scheme can overcome the security shortcomings while keeping the small overhead requirements per node. It will be shown that our scheme is unconditionally secure and achieves both forward secrecy and backward secrecy. The analysis is demonstrated in terms of communication and storage overheads.