Broadcasting with secrecy of messages is important in a situation such as pay television. In pay television only a broadcasting station broadcasts a message. On the other hand, broadcast communication is also important. Broadcast communication means any user in a whole group can broadcast a message to any subset of the group. In this paper the efficiency of secure broadcast communication is discussed in terms of the length of messages sent and the encryption speed. We prove that the length of the broadcast messages is not kept less than O(n), where n is the number of receivers, when a broadcast system has a form of a single system which is defined as the generalized form of an individual key method and a master key method. In contrast, the proposed secure broadcast communication method, a multi-dimension method, keeps the length of messages sent O(mmn), where m is the number of the dimension used in the multi-dimension method. At the same time the encryption speed was reduced from O(n(log(n+C2)+C3)) of the master key method to O(mn(logmn+C1)) of the multi-dimension method.