It is necessary to prevent the leakage of information by attackers during communication via internet. To prevent such risk, the content of the communication is encrypted. This is similar in group communication. It is necessary to distribute the key to each user efficiently so that the group can share the session key in the group communication. In the key sharing, because the participating user is changed at time, hence key update becomes necessary. This process is very expensive. Hence, our research aim is to find an efficient algorithm for key update by utilizing the minimum number of users.