Secure broadcasting using multiple antennas

Abstract

Abstract:We consider three different secure broadcasting scenarios: i) Broadcast channels with common and confidential messages (BCC), ii) multi-receiver wiretap channels with public and confidential messages, and iii) compound wiretap channels. The BCC is a broadcast channel with two users, where in addition to the common message sent to both users, a private message, which needs to be kept hidden as much as possible from the other user, is sent to each user. In this model, each user treats the other user as an eavesdropper. The multi-receiver wiretap channel is a broadcast channel with two legitimate users and an external eavesdropper, where the transmitter sends a pair of public and confidential messages to each legitimate user. Although there is no secrecy concern about the public messages, the confidential messages need to be kept perfectly secret from the eavesdropper. The compound wiretap channel is a compound broadcast channel with a group of legitimate users and a group of eavesdroppers. In this model, the transmitter sends a common confidential message to the legitimate users, and this confidential message needs to be kept perfectly secret from all eavesdroppers. In this paper, we provide a survey of the existing information-theoretic results for these three forms of secure broadcasting problems, with a closer look at the Gaussian multiple-input multiple-output (MIMO) channel models. We also present the existing results for the more general discrete memoryless channel models, as they are often the first step in obtaining the capacity results for the corresponding Gaussian MIMO channel models.Index Terms: Broadcast channels, information theoretic security, multiple antennas.

Secure degrees of freedom of the Gaussian wiretap channel with helpers

“…The capacityequivocation region was originally found for the degraded wiretap channel by Wyner [1], then generalized to the general wiretap channel by Csiszar and Korner [2], and extended to the Gaussian wiretap channel by Leung-YanCheong and Hellman [3]. Multi-user versions of the wiretap channel have been studied recently, e.g., broadcast channels with confidential messages [4], [5], multi-receiver wiretap channels [6]- [8] (see also a survey on extensions of these to MIMO channels [9]), two-user interference channels with confidential messages [4], [10], multiple access wiretap channels [11]- [15], relay eavesdropper channels [16]- [21], compound wiretap channels [22], [23]. Since in most multiuser scenarios it is difficult to obtain the exact secrecy capacity region, achievable secure degrees of freedom (d.o.f.)…”

A Survey of Optimization Approaches for Wireless Physical Layer Security

“…In the downlink, the transmitter transmits confidential messages to the legitimate users while preventing from overhearing of the eavesdroppers. This broadcast channel can be equivalent to a compound wiretap channel which is defined as [3], [23]…”

“…In existing literature, there are two kinds of power constraints in the problem of secrecy rate maximization. One is the sum power constraints of all nodes specified by the constraint P (23), and the other is the individual power constraint of each node specified by the constraints 0 ≤ P (23). Noteworthily, beamforming may be more effective for maximizing secrecy rate by strengthening signals on a desired direction and suppressing/eliminating signals on undesired directions.…”

Degraded Gaussian MIMO multi-receiver wiretap channel with public and confidential messages

“…One particular multi-user extension of the wiretap channel, that is relevant to our work here, is the multi-receiver wiretap channel considered in [3]- [5]. A recent survey on the secure broadcasting problem (including the multi-receiver wiretap channel) can be found in [6].…”