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Allerton Conference on Communication, Control, and Computing

Wireless network secrecy with public feedback

Etienne Perron, Suhas N. Diggavi, Emre Telatar

Published Sep 1, 2008• 1 citation
Publisher

Abstract

In this paper we consider secret communication between two special nodes (ldquosourcerdquo and ldquodestinationrdquo) in a wireless network with authenticated relays: the message communicated to the destination is to be kept information-theoretically (unconditionally) secret from any eavesdropper within a class. A public feedback channel from the destination to all nodes may or may not be available. We focus on a one-relay network with a bottleneck link between the source and the relay to illustrate the ideas. For this particular network, we derive the rate-equivocation capacity region when the public feedback channel is absent, and an achievable secret key rate when public feedback is present.

DOI
10.1109/allerton.2008.4797633

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Xiang He, Aylin Yener

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. A class of relay channels with orthogonal components is considered and an upper bound on the secrecy rate is derived. For the class of relay channels in consideration, we prove the relay and the eavesdropper can be separated to obtain an ‘enhanced’ channel in terms of secrecy capacity. We then consider two special cases of this channel model: (i) the Gaussian orthogonal relay channel, and (ii) the Gaussian Cover-Kim deterministic relay channel. For the former, the upper bound found is tighter than the previously known bound. For the latter, we show that the bound yields the secrecy capacity when the source-destination link is not worse than the source-relay link. This second case also provides the first example where secrecy capacity is achieved with compress and-forward at the relay.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2008•23 citations
In this paper we consider secret communication between two special nodes (ldquosourcerdquo and ldquodestinationrdquo) in a wireless network with authenticated relays: the message communicated to the destination is to be kept information-theoretically (unconditionally) secret from any eavesdropper within a class. A public feedback channel from the destination to all nodes may or may not be available. We focus on a one-relay network with a bottleneck link between the source and the relay to illustrate the ideas. For this particular network, we derive the rate-equivocation capacity region when the public feedback channel is absent, and an achievable secret key rate when public feedback is present.
The aim of information-theoretic secrecy is to ensure that an eavesdropper who listens to the wireless transmission of a message can only collect an arbitrarily small number of information bits about this message. In contrast to cryptography, there are no assumptions on the computational power of the eavesdropper. Information-theoretically secret communication has been studied for many particular wireless network topologies. In the main part of this thesis, we consider such communication for arbitrary acyclic wireless network topologies. We provide lower and upper bounds on the strong perfect secrecy capacity for the case when the channels of the network are either Gaussian or deterministic. These results are based on the recent understanding of the capacity of wireless networks (without secrecy constraints) by Avestimehr, Diggavi and Tse. As a side result, we give inner and outer bounds on the capacity region for the multisource problem in arbitrary wireless networks with Gaussian or deterministic signal interaction. For linear deterministic signal interaction, we find the exact capacity region. For Gaussian signal interaction, we are able to bound the gap between the two bounds on the capacity region. This gap depends only on the network topology, but not on the signal-to-noise ratio (SNR), which leads to an approximation of the capacity region for the high SNR regime. We further consider a particular network topology, called the fan-network, in which we assume that an eavesdropper has physical access to every node in a subset of the relay nodes. We give a general upper bound on the perfect secrecy capacity, and we characterize the perfect secrecy capacity for two special cases. In the second part of the thesis, we consider interactive secrecy, i.e., secrecy in the presence of a public feedback link from the destination to the source. We focus on the problem of secret key generation rather than secret communication. The benefit of public discussion for secret key generation in a broadcast channel was first shown by Maurer. We extend his ideas to a relay network called the line network, leading to a lower bound on the strongly secret key capacity for this network topology. Finally, we introduce a new channel coding setup called the interference-multiple access (IMA) channel. This channel is a variant of the interference channel where one of the receivers is required to decode the messages from both transmitters. We derive an inner bound on the capacity region of the IMA channel, as well as an outer bound for the so-called structured IMA channel. In a semi-deterministic version of the structured IMA channel, the bounds match, providing a characterization of the capacity region. In the Gaussian case, we obtain a 1 bit-approximation of the capacity region. We also show an inner bound on the equivocation-capacity region for the IMA channel, where we require that part of the private message for one receiver is kept information-theoretically secret from the other receiver.
Given that wireless communication occurs in a shared and inherently broadcast medium, the transmissions are vulnerable to undesired eavesdropping. This occurs even when a point-to-point communication is sought, and hence a fundamental question is whether we can utilize the wireless channel properties to establish secrecy. In this paper we consider secret communication between two special nodes ("source" and "destination") in a wireless network with authenticated relays: the message communicated to the destination is to be kept information-theoretically (unconditionally) secret from any eavesdropper within a class. Since the transmissions are broadcast and interfere with each other, complex signal interactions occur. We develop cooperative schemes which utilize these interactions in wireless communication over networks with arbitrary topology, and give provable unconditional secrecy guarantees.
We study secret communication for broadcast channels with two legitimate receivers and one eavesdropper. The transmitter sends two independent confidential messages to the legitimate receivers which have to be kept secret from the eavesdropper. Here, each legitimate receiver is interested in one confidential message having the other one already as side information available. This problem arises for example in the broadcast phase in a bidirectional relay network, where a relay node establishes a bidirectional communication between two nodes while keeping the communication secure from an eavesdropper outside the network. We provide achievable rate regions and an outer bound on the secrecy capacity region.
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.
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. A class of relay channels with orthogonal components is considered and an upper bound on the secrecy rate is derived. For the class of relay channels in consideration, we prove the relay and the eavesdropper can be separated to obtain an ‘enhanced’ channel in terms of secrecy capacity. We then consider two special cases of this channel model: (i) the Gaussian orthogonal relay channel, and (ii) the Gaussian Cover-Kim deterministic relay channel. For the former, the upper bound found is tighter than the previously known bound. For the latter, we show that the bound yields the secrecy capacity when the source-destination link is not worse than the source-relay link. This second case also provides the first example where secrecy capacity is achieved with compress and-forward at the relay.