Secrecy measures for broadcast channels with receiver side information: Joint vs individual

Abstract

We study the transmission of a common message and three confidential messages over a broadcast channel with two legitimate receivers and an eavesdropper. Each legitimate receiver is interested in decoding two of the three confidential messages, while having the third one as side information. In order to measure the ignorance of the eavesdropper about the confidential messages, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide a general achievable rate region. We establish both the joint and individual secrecy capacity if the two legitimate receivers are less noisy than the eavesdropper. We further investigate the scenario where the eavesdropper is less noisy than the two legitimate receivers. It is known that the joint secrecy constraints can not be fulfilled under this scenario, however, we manage to establish a non vanishing capacity region for the individual secrecy case. ar and K¨ orner extended Wyner's result to the general broadcast channel (BC) with confidential messages. In (4), Kang and Liu generalized the previous two approaches by studying the presence of a shared secret key in the wiretap channel. They derived the secrecy capacity for this scenario by combining the wiretap coding principle along with Shannon's one-time pad idea. The problem of secure communication in BC with more than two receivers remains an open topic. In (5), Chia and El Gamal investigated the secrecy capacity for transmitting one common and one confidential message over a BC with two receivers and one eavesdropper. They provided a general achievable region and managed to establish the capacity when the two receivers are less noisy than the eavesdropper. In this paper, we study a related problem. However, in stead of having only one confidential message to both legitimate receivers, we extend the system such that each legitimate receiver has an extra individual confidential message. This extension allows us to differentiate between joint and individual secrecy. Our setup has an additional feature, that each legitimate receiver possesses the individual confidential message of the other one as side information as shown in Figure 1. In (6) the