Renewal of the group key on the mobile communication needs it can be not re-shared by all members of the group with the exception of excluded members but also prevented from making a fraudulent use of group key due to leakage of security information for terminal. In this paper, we propose an efficient renewal mechanism of group key in order for all members of the group to be able to get digital information and to perform the renewal of group key employing the Fiat-Shamir method. It can guarantee the security of a group key since a terminal renews a group key by using security information of an excluded terminal and the previous group key.