Strong Security and Separated Code Constructions for the Broadcast Channel with confidential Messages

The strong security criterion in the information theoretic security is to require that the UNDIVIDED mutual information between the secret message and the eavesdropper’s message converges to zero as n goes to the infinity. The capacity region of the broadcast channel with confidential messages with the strong security criterion has not been clarified as far as the authors’ knowledge. We shall show that the capacity region does not change even if the weak security requirement is changed to the strong one. Our security proof attaches the inverse of two-universal hash functions to a random coding argument for the broadcast channel with degraded message sets, which has no security requirement, and adds the secrecy. In that sense the proof for secrecy is separated from the proof for error correction. The exponential decreasing speed of the mutual information is also given, which seems novel.

On the other hand, for practical construction of codes, it is convenient if we can add secrecy to an arbitrary given channel code for the broadcast channel with degraded message sets, by just attaching the inverse of a hash function. We shall also show that such a construction is possible by introducing a new form of the privacy amplification theorem. This is the second separated code construction for the broadcast channel with confidential messages.