Secrecy Capacity Region of Some Classes of Wiretap Broadcast Channels

This work investigates the secrecy capacity of the Wiretap Broadcast Channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a Broadcast Channel (BC) while keeping them secret from the eavesdropper. We derive a non-trivial outer bound on the secrecy capacity region of this channel which, in absence of security constraints, reduces to the best known outer bound to the capacity of the standard BC. An inner bound is also derived which follows the behavior of both the best known inner bound for the BC and the Wiretap Channel. These bounds are shown to be tight for the deterministic BC with a general eavesdropper, the semi-deterministic BC with a more-noisy eavesdropper and the Wiretap BC where users exhibit a less-noisiness order between them. Finally, by rewriting our outer bound to encompass the characteristics of parallel channels, we also derive the secrecy capacity region of the product of two inversely less-noisy BCs with a more-noisy eavesdropper. We illustrate our results by studying the impact of security constraints on the capacity of the WBC with binary erasure (BEC) and binary symmetric (BSC) components.Comment: 19 pages, 8 figures, To appear in IEEE Trans. on Information Theor

Capacity Bounds for Broadcast Channels with Confidential Messages

In this paper, we study capacity bounds for discrete memoryless broadcast channels with confidential messages. Two private messages as well as a common message are transmitted; the common message is to be decoded by both receivers, while each private message is only for its intended receiver. In addition, each private message is to be kept secret from the unintended receiver where secrecy is measured by equivocation. We propose both inner and outer bounds to the rate equivocation region for broadcast channels with confidential messages. The proposed inner bound generalizes Csisz\'{a}r and K\"{o}rner's rate equivocation region for broadcast channels with a single confidential message, Liu {\em et al}'s achievable rate region for broadcast channels with perfect secrecy, Marton's and Gel'fand and Pinsker's achievable rate region for general broadcast channels. Our proposed outer bounds, together with the inner bound, helps establish the rate equivocation region of several classes of discrete memoryless broadcast channels with confidential messages, including less noisy, deterministic, and semi-deterministic channels. Furthermore, specializing to the general broadcast channel by removing the confidentiality constraint, our proposed outer bounds reduce to new capacity outer bounds for the discrete memory broadcast channel.Comment: 27 pages, 1 figure, submitted to IEEE Transaction on Information Theor

Wiretap and Gelfand-Pinsker Channels Analogy and its Applications

An analogy framework between wiretap channels (WTCs) and state-dependent point-to-point channels with non-causal encoder channel state information (referred to as Gelfand-Pinker channels (GPCs)) is proposed. A good sequence of stealth-wiretap codes is shown to induce a good sequence of codes for a corresponding GPC. Consequently, the framework enables exploiting existing results for GPCs to produce converse proofs for their wiretap analogs. The analogy readily extends to multiuser broadcasting scenarios, encompassing broadcast channels (BCs) with deterministic components, degradation ordering between users, and BCs with cooperative receivers. Given a wiretap BC (WTBC) with two receivers and one eavesdropper, an analogous Gelfand-Pinsker BC (GPBC) is constructed by converting the eavesdropper's observation sequence into a state sequence with an appropriate product distribution (induced by the stealth-wiretap code for the WTBC), and non-causally revealing the states to the encoder. The transition matrix of the state-dependent GPBC is extracted from WTBC's transition law, with the eavesdropper's output playing the role of the channel state. Past capacity results for the semi-deterministic (SD) GPBC and the physically-degraded (PD) GPBC with an informed receiver are leveraged to furnish analogy-based converse proofs for the analogous WTBC setups. This characterizes the secrecy-capacity regions of the SD-WTBC and the PD-WTBC, in which the stronger receiver also observes the eavesdropper's channel output. These derivations exemplify how the wiretap-GP analogy enables translating results on one problem into advances in the study of the other

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

Information-theoretic secrecy for wireless networks

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