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This paper presents a new group key management protocol, CKC (Code for Key Calculation). This protocol is based on logical key hierarchy. When a new member joins the group, server sends only the group key for that member. Then, current members and the new member calculate the necessary keys using node codes and one-way hash function. Node code is a code which is assigned to each node of the key tree. Again at leave, server just sends the new group key to remaining members. By this key, members calculate necessary keys using node codes and one-way hash function. The security of the keys is based on one-wayness of hash function. The results show that CKC reduces computational and communication overhead and message size at join while it keeps minimized the overhead of key update at leave.