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 achievable rate we present.

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Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured codes are useful for providing secrecy, and show how to compute the secrecy rate when structured codes are used. In particular, we solve the problem of bounding equivocation rates with one important class of structured codes, i.e., nested lattice codes. Having established this result, we next demonstrate the use of structured codes for secrecy in two-user Gaussian channels. In particular, with structured codes, we prove that a positive secure degree of freedom is achievable for a large class of fully connected Gaussian channels as long as the channel is not degraded. By way of this, for these channels, we establish that structured codes outperform Gaussian random codes at high SNR. This class of channels include the two-user multiple access wiretap channel, the two-user interference channel with confidential messages and the two-user interference wiretap channel. A notable consequence of this result is that, unlike the case with Gaussian random codes, using structured codes for both transmission and cooperative jamming, it is possible to achieve an arbitrary large secrecy rate given enough power.

We consider a source-destination pair that can only communicate through an untrusted intermediate relay node. The intermediate node is willing to employ a designated relaying scheme to facilitate reliable communication between the source and the destination. Yet, the information it relays needs to be kept secret from it. In this two-hop communication scenario, where the use of the untrusted relay node is essential, we find that a positive secrecy rate is achievable. The center piece of the achievability scheme is the help provided by either the destination node with transmission capability, or an external "good samaritan" node. In either case, the helper performs cooperative jamming that confuses the eavesdropping relay and disables it from being able to decipher what it is relaying. We next derive an upper bound on the secrecy rate for this system. We observe that the gap between the upper bound and the achievable rate vanishes as the power of the relay node goes to infinity. Overall, the paper presents a case for intentional interference, i.e., cooperative jamming, as an enabler for secure communication.

We consider a Gaussian two-hop network where the source and the destination can communicate only via a relay node who is both an eavesdropper and a Byzantine adversary. Both the source and the destination nodes are allowed to transmit, and the relay receives a superposition of their transmitted signals. We propose a new coding scheme that satisfies two requirements simultaneously: the transmitted message must be kept secret from the relay node, and the destination must be able to detect any Byzantine attack that the relay node might launch reliably and fast. The three main components of the scheme are the nested lattice code, the privacy amplification and the algebraic manipulation detection (AMD) code. Specifically, for the Gaussian two-hop network, we show that lattice coding can successfully pair with AMD codes enabling its first application to a noisy channel model. We prove, using this new coding scheme, that the probability that the Byzantine attack goes undetected decreases exponentially fast with respect to the number of channel uses, while the loss in the secrecy rate, compared to the rate achievable when the relay is honest, can be made arbitrarily small. In addition, in contrast with prior work in Gaussian channels, the notion of secrecy provided here is strong secrecy.

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