Transmitting multiple secrets securely in broadcasting networks

A method is presented which permits a broadcasting mechanism to securely transmit a single ciphertext with multiple messages. These messages will only be readable by those users who have the appropriate read key(s). The other messages will be undecipherable. This is a generalization of the secure broadcasting problem stated by G. H. Chiou and W. T. Chen (1989) and C. C. Chang and C. H. Lin (1988). The proposed generalized secure broadcasting cryptosystem is based on Newton´s interpolating polynomials and the Chinese remainder theorem. It is observed that the key management by a Central Authority is simple. In order to broadcast distinct messages to different users, one is only required to construct a polynomial and to compute a constant. To reveal a message, the authorized receiver only has to reveal his key by taking the constant modulo his identification number, evaluate the received polynomial with the obtained key, and then decrypt the resulting ciphertext by using his secret key. The sender can randomly choose any number of users who are authorized to know distinct messages within one broadcast