Anne Wolf

Resource allocation for the wire-tap multi-carrier broadcast channel

Resource allocation for the multi-carrier broadcast channel is well understood for a broad class of utility functions, under various quality-of-service constraints, and for different channel models. In this work, we also take security on the physical layer into account. We use the secrecy rate as the objective function for resource allocation and show the similarities and differences to the traditional power and sub-carrier allocations for sum capacity optimization. The sub-carrier selection is similar for both methods whereas the spectral power allocation shows different behavior. Finally, we demonstrate that rich multipath fading decreases the cost of security. All results are illustrated by numerical simulations and discussions.

Secrecy on the Physical Layer in Wireless Networks

This chapter provides a comprehensive state-of-the-art description of the emerging field of physical layer security. We will consider wireless security from an information theoretic view, which allows us to talk about provable secrecy and to derive ultimate secrecy limits. Our main focus is on the optimization of transmit strategies and resource allocation schemes under secrecy constraints. We will consider the following scenario, which is illustrated in Figure 1: Alice wants to send a private message to Bob, which should be kept perfectly secret from Eve. Eve listens and tries to decode the message that Alice sends to Bob.

Beamforming for fading wiretap channels with partial channel information

Secrecy on the physical layer receives increased research interest. Especially in the wireless communication scenarios, the interest in confidentiality of messages increases. In this paper, we discuss the effectiveness of the beamforming strategies maximum ratio transmission (MRT), zero forcing (ZF), and an optimized beamforming (BF) strategy for the transmission under secrecy constraints. The applied channel model is the flat-fading MISO (multiple-input singleoutput) wiretap channel, where the channel to the eavesdropper is only partly known at the transmitter. The scenario with perfect and no channel information to the eavesdropper are included as special cases. We show that under certain conditions the achievable secrecy rates for the transmission with optimized beam-forming can be increased by transmitting artificial noise (AN) in the null space of the channel to the intended receiver, which produces additional interference only at the eavesdropper. We provide a characterization of the optimal beamforming and artificial noise beamforming and analyze the optimal power allocation for asymptotic cases (low and high SNR as well as no and perfect channel information). Numerical simulations illustrate the results.

On the zero forcing optimality for friendly jamming in MISO wiretap channels

We study beamforming strategies for a friendly jammer (or helper) in a MISO wiretap channel. We characterize the beamforming strategy for the maximization of the secrecy rate and analyze the optimality of zero forcing. We show that zero forcing is optimal up to a small constant for high SNR. For low SNR, we derive optimal beamforming strategies for transmitter and helper in terms of minimum Eb/N0 and wideband slope.

Secret key generation from reciprocal spatially correlated MIMO channels

Secret key generation from reciprocal multi-antenna channels is an interesting alternative to cryptographic key management in wireless systems without infrastructure access. In this work, we study the secret key rate for the basic source model with a MIMO channel. First, we derive an expression for the secret key rate under spatial correlation modelled by the Kronecker model and with spatial precoding at both communication nodes. Next, we analyze the result for uncorrelated antennas to understand the optimal precoding for this special case, which is equal power allocation. Then, the impact of correlation is characterized using Majorization theory. Surprisingly for small SNR, spatial correlation increases the secret key rate. For high SNR, the maximum secret key rate is achieved for uncorrelated antennas. The results indicate that a solid system design for reciprocal MIMO key generation is required to establish the secret key rate gains.

Maximization of worst-case secrecy rates in MIMO wiretap channels

We study a multi-antenna wiretap channel, where the transmitter does not have perfect knowledge about the channels to the eavesdropper. The transmitter only knows that the logical location of the eavesdropper is drawn from a certain set. We characterize the worst-case secrecy rate in this scenario for given transmit strategies and derive an upper and a lower bound for the worst-case secrecy rate that is maximized under a sum power constraint at the transmitter. Finally, we discuss strategies for the high and low SNR regime and illustrate our results.

Maximization of worst-case secret key rates in MIMO systems with eavesdropper

A multi-antenna (MIMO) system with eavesdropper is studied, where the transmitter has no perfect knowledge about the channel to the eavesdropper. The transmitter only knows that the channel matrix of the eavesdropper is drawn from a certain set. For this scenario, the worst-case secret key rate and the worst-case channel matrix of the eavesdropper are characterized. It is shown that the maximization of this rate under a sum power constraint at the transmitter is a saddle point problem. Upper and lower bounds for the maximized worst-case secret key rate are derived. Strategies for the high and low SNR regime are presented and the results are finally illustrated and discussed in comparison with the maximized worst-case secrecy rate.

Precoding for secret key generation in multiple antenna channels with statistical channel state information

In future wireless communication systems, more and more small low-power mobile devices will communicate without infrastructure and internet access. In order to provide a lightweight yet powerful security mechanism, physical layer parameters can be used to generate secret keys for perfect secrecy. In this paper, we study the optimal operation of a multiple antenna link with statistical channel state information at all nodes for secret key generation. The impact of spatial correlation on the achievable secret key rates is characterized. Furthermore, the optimal pilot precoding during channel estimation is computed. Numerical simulations illustrate the results for selected scenarios.

End-to-End Key Establishment with Physical Layer Key Generation and Specific Attacker Models

Physical layer key generation got much attention during the last time. However, the need of a common physical channel implies that only point-to-point keys can be generated. In this chapter, we investigate approaches how these point-to-point keys can be used for a secure establishment of end-to-end keys between two users who can only communicate over a multi-hop network. We start with a review of physical layer key generation taking different attacker models into account. Subsequently, we introduce general approaches for the end-to-end key establishment in the presence of various attackers who differ in their behavior and their area of control. We discuss four different path selection algorithms for the key establishment and evaluate their performance by means of simulations. The results show that the end-to-end key establishment can be protected by means of physical layer keys with a reasonable effort if suitable path selection is applied.

Secure Communication in Wiretap Channels with Partial and Statistical CSI at the Transmitter

One major challenge in physical layer security for confidential communication is the lack of channel state information at the transmitter about the channel to the passive eavesdropper. Depending on the attacker and channel assumptions, the statistical or deterministic channel uncertainty model is applied. The chapter reviews recent results for both uncertainty models and compares different signaling and pre-coding schemes and their achievable average and outage secrecy rates in fast and slow-fading wiretap channels. In addition to wiretap coding, artificial noise and non-Gaussian layered signaling are necessary to guarantee non-zero secrecy rates in scenarios where Gaussian wiretap codebooks do not work.