In this paper, we shall present a new scheme to solve the problem of secure broadcasting in a network. By the use of the proposed scheme, a sender can send secret messages to a group of users, but only the legitimate receivers can recover the plain messages. Our cryptosystem is based on the EIGamal’s public-key scheme and the security is the same as that of the ELGamal’s Further, all of the computation in the scheme can be performed efficiently.