Matthieu R. Bloch

Wireless Information-Theoretic Security

This paper considers the transmission of confidential data over wireless channels. Based on an information-theoretic formulation of the problem, in which two legitimates partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through a second independent quasi-static fading channel, the important role of fading is characterized in terms of average secure communication rates and outage probability. Based on the insights from this analysis, a practical secure communication protocol is developed, which uses a four-step procedure to ensure wireless information-theoretic security: (i) common randomness via opportunistic transmission, (ii) message reconciliation, (iii) common key generation via privacy amplification, and (iv) message protection with a secret key. A reconciliation procedure based on multilevel coding and optimized low-density parity-check (LDPC) codes is introduced, which allows to achieve communication rates close to the fundamental security limits in several relevant instances. Finally, a set of metrics for assessing average secure key generation rates is established, and it is shown that the protocol is effective in secure key renewal-even in the presence of imperfect channel state information.

Physical-Layer Security: From Information Theory to Security Engineering

This complete guide to physical-layer security presents the theoretical foundations, practical implementation, challenges and benefits of a groundbreaking new model for secure communication. Using a bottom-up approach from the link level all the way to end-to-end architectures, it provides essential practical tools that enable graduate students, industry professionals and researchers to build more secure systems by exploiting the noise inherent to communications channels. The book begins with a self-contained explanation of the information-theoretic limits of secure communications at the physical layer. It then goes on to develop practical coding schemes, building on the theoretical insights and enabling readers to understand the challenges and opportunities related to the design of physical layer security schemes. Finally, applications to multi-user communications and network coding are also included.

Quantum key distribution over 25 km with an all-fiber continuous-variable system

We report on the implementation of a reverse-reconciliated coherent-state continuous-variable quantum key distribution system, with which we generated secret keys at a rate of more than 2 kb/s over 25 km of optical fiber. Time multiplexing is used to transmit both the signal and phase reference in the same optical fiber. Our system includes all experimental aspects required for a field implementation of a quantum key distribution setup. Real-time reverse reconciliation is achieved by using fast and efficient low-density parity check error correcting codes.

Strong Secrecy From Channel Resolvability

We analyze physical-layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability. Instead of considering capacity-based constructions, which associate to each message a subcode that operates just below the capacity of the eavesdroppers channel, we consider channel-resolvability-based constructions, which associate to each message a subcode that operates just above the resolvability of the eavesdroppers channel. Building upon the work of Csiszár and Hayashi, we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels. Specifically, we show that at least for symmetric wiretap channels, random capacity-based constructions fail to achieve the strong secrecy capacity, while channel-resolvability-based constructions achieve it. We then leverage channel resolvability to establish the secrecy-capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics. Finally, we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information (CSI), mixed channels, and compound channels with receiver CSI, as well as the secret-key capacity of source models for secret-key agreement. By tying secrecy to channel resolvability, we obtain achievable rates for strong secrecy metrics with simple proofs.

Cooperative Security at the Physical Layer: A Summary of Recent Advances

Wireless communications systems are particularly vulnerable to security attacks because of the inherent openness of the transmission medium. In this article, we focus on guaranteeing confidentiality against eavesdropping attacks where an unauthorized entity aims to intercept an ongoing wireless communication, and we provide a comprehensive summary of recent advances in the area of physical-layer security that guarantees confidentiality by using cooperative techniques unique to the wireless medium. These cooperative techniques consist of carefully designed coding and signaling schemes that are able to harness the properties of the physical layer and to ensure some level of information-theoretic security.

Wireless Secrecy Regions With Friendly Jamming

Inspired by recent results on information-theoretic security, we consider the transmission of confidential messages over wireless networks, in which the legitimate communication partners are aided by friendly jammers. We characterize the security level of a confined region in a quasi-static fading environment by computing the probability of secrecy outage in connection with two new measures of physical-layer security: the jamming coverage and the jamming efficiency. Our analysis for various jamming strategies based on different levels of channel state information provides insight into the design of optimal jamming configurations and shows that a single jammer is not sufficient to maximize both figures of merit simultaneously. Moreover, a single jammer requires full channel state information to provide security gains in the vicinity of the legitimate receiver.

On the secrecy capacity of arbitrary wiretap channels

We investigate the fundamental secrecy limits of arbitrary wiretap channels using the information-spectrum approach and we provide a random coding theorem for the secrecy capacity under various secrecy metrics. We show how our result specializes to several recent results, e.g., compound channels, parallel channels, and fading channels. As a side benefit, our analysis shows that earlier results hold under more stringent secrecy metrics than previously established.

Strong Secrecy on the Binary Erasure Wiretap Channel Using Large-Girth LDPC Codes

For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at least three, we show using density evolution analysis that the expected bit-error probability of these ensembles, when passed through a binary erasure channel with erasure probability ϵ, decays as <i>O</i>(exp(-(<i>c</i>₁)<i>n(c</i>₂))) with the block-length <i>n</i> for positive constants <i>c</i>₁ and <i>c</i>₂, as long as ϵ is less than the erasure threshold ϵ_th of the DDP. This guarantees that the coset coding scheme using the dual sequence provides strong secrecy over the binary erasure wiretap channel for erasure probabilities greater than 1-ϵ_th.

Covert Communication Over Noisy Channels: A Resolvability Perspective

We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel, while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals through another discrete memoryless channel. We develop a coding scheme based on the principle of channel resolvability, which generalizes and extends prior work in several directions. First, it shows that irrespective of the quality of the channels, it is possible to communicate on the order of √n reliable and covert bits over n channel uses if the transmitter and the receiver share on the order of √n key bits. This improves upon earlier results requiring on the order of √n log n key bits. Second, it proves that if the receivers channel is better than the wardens channel in a sense that we make precise, it is possible to communicate on the order of √n reliable and covert bits over n channel uses without a secret key. This generalizes earlier results established for binary symmetric channels. We also identify the fundamental limits of covert and secret communications in terms of the optimal asymptotic scaling of the message size and key size, and we extend the analysis to Gaussian channels. The main technical problem that we address is how to develop concentration inequalities for low-weight sequences. The crux of our approach is to define suitably modified typical sets that are amenable to concentration inequalities.

Strongly Secure Communications Over the Two-Way Wiretap Channel

We consider the problem of secure communications over the two-way wiretap channel under a strong secrecy criterion. We improve existing results by developing an achievable region based on strategies that exploit both the interference at the eavesdroppers terminal and cooperation between legitimate users. We leverage the notion of channel resolvability for the multiple-access channel to analyze cooperative jamming and we show that the artificial noise created by cooperative jamming induces a source of common randomness that can be used for secret-key agreement. We illustrate the gain provided by this coding technique in the case of the Gaussian two-way wiretap channel, and we show significant improvements for some channel configurations.