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IEEE Information Theory Workshop (ITW)

A unified framework for key agreement over wireless fading channels

Lifeng Lai, H. Vincent Poor

Published Jan 1, 2009• 18 citations
Publisher

Abstract

A framework that unifies existing source and channel models for key agreement over wireless fading channels is developed in this paper. It is shown that, in general, to fully exploit the resources provided by time-varying channel gains, one needs to combine both the channel model and the source model. Asymptotic analyses suggest that in the long coherence time regime, the channel model is asymptotically optimal. On the other hand, in the high SNR regime, the source model is asymptotically optimal.

DOI
10.1109/itw.2009.5351257

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IEEE Information Theory Workshop (ITW)•Sep 1, 2012•7 citations
A framework that unifies existing source and channel models for key agreement over wireless fading channels is developed in this paper. It is shown that, in general, to fully exploit the resources provided by time-varying channel gains, one needs to combine both the channel model and the source model. Asymptotic analyses suggest that in the long coherence time regime, the channel model is asymptotically optimal. On the other hand, in the high SNR regime, the source model is asymptotically optimal.
The problem of key generation over wireless fading channels is investigated. First, a joint source-channel approach that combines existing source and channel models for key agreement over wireless fading channels is developed. It is shown that, in general, to fully exploit the resources provided by time-varying channel gains, one needs to combine both the channel model, in which Alice sends a key to Bob over a wireless channel, and the source model, in which Alice and Bob generate a key by exploiting the correlated observations obtained from the wireless fading channel. Asymptotic analyses suggest that in the long coherence time regime, the channel model is asymptotically optimal. On the other hand, in the high power regime, the source model is asymptotically optimal. Second, the framework is extended to the scenario with an active attacker. Assuming that the goal of the attacker is to minimize the key rate that can be generated using the proposed protocol and the attacker will employ such an attack strategy, the attacker's optimal attack strategy is identified and the key rate under this attack model is characterized.
Fundamental limits of secret-key agreement over reciprocal wireless channels are investigated. We consider a two-way block-fading channel where the channel gains in the forward and reverse links between the legitimate terminals are correlated. The channel gains between the legitimate terminals are not revealed to any terminal, whereas the channel gains of the eavesdropper are revealed to the eavesdropper. We propose a two-phase transmission scheme, that reserves a certain portion of each coherence block for channel estimation, and the remainder of the coherence block for correlated source generation. The resulting secret-key involves contributions of both channel sequences and source sequences, with the contribution of the latter becoming dominant as the coherence period increases. We also establish an upper bound on the secret-key capacity, which has a form structurally similar to the lower bound. Our upper and lower bounds coincide in the limit of high signal-to-noise-ratio (SNR) and large coherence period, thus establishing the secret-key agreement capacity in this asymptotic regime. Numerical results indicate that the proposed scheme achieves significant gains over training-only schemes, even for moderate SNR and small coherence periods, thus implying the necessity of randomness-sharing in practical secret-key generation systems.
The problem of establishing a key over a wireless fading channel in the presence of an active attacker is considered. A key agreement protocol that combines the existing source model approach and channel model approach is adopted. First, the attacker's optimal attack strategy for this protocol is characterized. Then, the rate of the key that can be generated under this attack strategy is quantified. It is shown that, unlike the corresponding situation in wireline communications, it is possible to establish a key in the presence of an active attacker in wireless fading channels.
Motivated by recent interest in physical-layer secret-key generation over wireless fading channels, we study the non-coherent secret-key generation capacity of a block-fading wireless channel with channel reciprocity and bi-directional (two-way) communication. We assume a non-coherent main channel, i.e., the realization of channel gains on the main channel is not known to any terminal. The eavesdropper is assumed to have both perfect Channel State Information of its own channel and orthogonal observations from the forward and backward channels. As our main result, we establish new upper and lower bounds on the secret-key generation capacity with public discussion, which are structurally similar. The upper bound can be expressed as a sum of three terms-one of the terms arises due to channel reciprocity, while the other two terms correspond to communication on the forward and backward channels, respectively. In the limit of long coherence period, the contribution from channel reciprocity vanishes to zero, whereas the other terms prevail. The lower bound is based on a separation based scheme. In each coherence block, we use the first symbol for training while the remainder of the coherence block is devoted to source emulation, i.e., to generate correlated sources between the terminals. The lower bound expression also consists of three terms and admits an interpretation similar to the upper bound expression. For Rayleigh fading channels, in the high signal-to-noise ratio (SNR) regime, the gap between the upper and lower bounds is shown to vanish inversely with the coherence period. Numerical results indicate significant performance gains over training-only schemes even for moderate values of SNR and small coherence periods.
In this paper, we study the fundamental limits of secret-key agreement over MIMO quasi-static fading channels. We provide closed-form expressions for the secret-key capacity in both the asymptotic high-power and low-power regimes. The optimal signaling strategy for the low-power regime is shown to be independent of the eavesdropper's channel and secret-key capacity is achieved by transmitting random Gaussian symbols along the direction corresponding to the maximal eigenvalue of the legitimate channel matrix. Hence, by beamforming and waterfilling over the main channel alone, one obtains a semi-blind key-agreement strategy in which the knowledge of the eavesdropper's channel is only required for privacy amplification. We also derive the probability that a target secret-key rate is not achieved by the optimal low-power signaling when assuming only statistical CSI about the eavesdropper's channel.
We study secret-key agreement over a non-coherent block-fading multiple input multiple output (MIMO) wiretap channel. We give an achievable scheme based on training and source emulation and analyze the rate in the high SNR regime. Based on this analysis we find the optimal number of antennas to use for training. Our main result is that if the sum of the number of antennas at Alice and Bob is larger than the coherence time of the channel, the achievable rate does not depend on the number of antennas at Eve. In this case source emulation is not needed, and using only training is optimal. We also consider the case when there is no public channel available. In this case we show that secret-key agreement is still possible by using the wireless channel for discussion, giving the same number of secure degrees of freedom as in the case with a public channel.