Providing security for messages in group communication is more essential and critical nowadays. In group oriented applications such as Video conferencing and entertainment applications, it is necessary to secure the confidential data in such a way that intruders are not able to modify or transmit the data. Key transfer protocols fully rely on trusted Key Generation Center (KGC) to compute group key and to transport the group keys to all communication parties in a secured and secret manner. In this paper, an efficient key generation and key transfer protocol has been proposed where KGC can broadcast group key information to all group members in a secure way. Hence, only authorized group members will be able to retrieve the secret key and unauthorized members cannot retrieve the secret key. Hence, inorder to maintain the forward and backward secrecy, the group keys are updated whenever a new member joins or leaves the communication group. The proposed algorithm is more efficient and relies on NP class. In addition, the keys are distributed to the group users in a safe and secure way. Moreover, the key generated is also very strong since it uses cryptographic techniques which provide efficient computation.