A Secure Broadcasting Scheme with Network Coding

We consider the secure broadcasting network coding problem over an acyclic network with single source node and two sink nodes. The secret message consists of two private messages and one common message. Secure means that no information about the secret message leaks to the adversary, that is, it achieves the perfect secure and belongs to information theoretic secure. Broadcasting means that different sink nodes receive different parts of the secret message. Given a network topology and network codes, a secure broadcasting scheme is proposed based on the signal space of sink nodes. The secret message is perfect secure if a limited number of edges are wiretapped by adversary. Analysis shows that our scheme is admissible. And the upper bound of the secrecy broadcasting capacity region can be achieved by our scheme. Besides, the sufficient condition of existence for our scheme, i.e., the lower bound of the coding field size, is also derived.