Capacity Results for Relay Channels with Confidential Messages

We consider a communication system where a relay helps transmission of messages from {a} sender to {a} receiver. The relay is considered not only as a helper but as a wire-tapper who can obtain some knowledge about transmitted messages. In this paper we study a relay channel with confidential messages(RCC), where a sender attempts to transmit common information to both a receiver and a relay and also has private information intended for the receiver and confidential to the relay. The level of secrecy of private information confidential to the relay is measured by the equivocation rate, i.e., the entropy rate of private information conditioned on channel outputs at the relay. The performance measure of interest for the RCC is the rate triple that includes the common rate, the private rate, and the equivocation rate as components. The rate-equivocation region is defined by the set that consists of all these achievable rate triples. In this paper we give two definitions of the rate-equivocation region. We first define the rate-equivocation region in the case of deterministic encoder and call it the deterministic rate-equivocation region. Next, we define the rate-equivocation region in the case of stochastic encoder and call it the stochastic rate-equivocation region. We derive explicit inner and outer bounds for the above two regions. On the deterministic/stochastic rate-equivocation region we present two classes of relay channels where inner and outer bounds match. We also evaluate the deterministic and stochastic rate-equivocation regions of the Gaussian RCC.Comment: 31 pages, 8 figure

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical-layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical-layer message authentication is also introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201

The Relay-Eavesdropper Channel: Cooperation for Secrecy

This paper establishes the utility of user cooperation in facilitating secure wireless communications. In particular, the four-terminal relay-eavesdropper channel is introduced and an outer-bound on the optimal rate-equivocation region is derived. Several cooperation strategies are then devised and the corresponding achievable rate-equivocation region are characterized. Of particular interest is the novel Noise-Forwarding (NF) strategy, where the relay node sends codewords independent of the source message to confuse the eavesdropper. This strategy is used to illustrate the deaf helper phenomenon, where the relay is able to facilitate secure communications while being totally ignorant of the transmitted messages. Furthermore, NF is shown to increase the secrecy capacity in the reversely degraded scenario, where the relay node fails to offer performance gains in the classical setting. The gain offered by the proposed cooperation strategies is then proved theoretically and validated numerically in the additive White Gaussian Noise (AWGN) channel.Comment: 33 pages, submitted to IEEE Transactions on Information Theor

Cooperation with an Untrusted Relay: A Secrecy Perspective

We consider the communication scenario where a source-destination pair wishes to keep the information secret from a relay node despite wanting to enlist its help. For this scenario, an interesting question is whether the relay node should be deployed at all. That is, whether cooperation with an untrusted relay node can ever be beneficial. We first provide an achievable secrecy rate for the general untrusted relay channel, and proceed to investigate this question for two types of relay networks with orthogonal components. For the first model, there is an orthogonal link from the source to the relay. For the second model, there is an orthogonal link from the relay to the destination. For the first model, we find the equivocation capacity region and show that answer is negative. In contrast, for the second model, we find that the answer is positive. Specifically, we show by means of the achievable secrecy rate based on compress-and-forward, that, by asking the untrusted relay node to relay information, we can achieve a higher secrecy rate than just treating the relay as an eavesdropper. For a special class of the second model, where the relay is not interfering itself, we derive an upper bound for the secrecy rate using an argument whose net effect is to separate the eavesdropper from the relay. The merit of the new upper bound is demonstrated on two channels that belong to this special class. The Gaussian case of the second model mentioned above benefits from this approach in that the new upper bound improves the previously known bounds. For the Cover-Kim deterministic relay channel, the new upper bound finds the secrecy capacity when the source-destination link is not worse than the source-relay link, by matching with the achievable rate we present.Comment: IEEE Transactions on Information Theory, submitted October 2008, revised October 2009. This is the revised versio

Secure Communication over Parallel Relay Channel

We investigate the problem of secure communication over parallel relay channel in the presence of a passive eavesdropper. We consider a four terminal relay-eavesdropper channel which consists of multiple relay-eavesdropper channels as subchannels. For the discrete memoryless model, we establish outer and inner bounds on the rate-equivocation region. The inner bound allows mode selection at the relay. For each subchannel, secure transmission is obtained through one of two coding schemes at the relay: decoding-and-forwarding the source message or confusing the eavesdropper through noise injection. For the Gaussian memoryless channel, we establish lower and upper bounds on the perfect secrecy rate. Furthermore, we study a special case in which the relay does not hear the source and show that under certain conditions the lower and upper bounds coincide. The results established for the parallel Gaussian relay-eavesdropper channel are then applied to study the fading relay-eavesdropper channel. Analytical results are illustrated through some numerical examples.Comment: To Appear in IEEE Transactions on Information Forensics and Securit