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Digest - IEEE Antennas and Propagation Society. International Symposium

Optimal array patterns for encryption key establishment in LOS channels

Rashid Mehmood, Jon W. Wallace, Michael A. Jensen

Published Jul 1, 2014• 3 citations
Publisher

Abstract

While the establishment of secret encryption keys based on reciprocal electromagnetic propagation has received recent attention, very limited work has appeared regarding how multiantenna radios should conduct the required channel estimation in the presence of an eavesdropper. This paper demonstrates array beamforming that maximizes the number of bits that can be established when an eavesdropper observes the channel estimation process.

DOI
10.1109/aps.2014.6904570

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While the establishment of secret encryption keys based on reciprocal electromagnetic propagation has received recent attention, very limited work has appeared regarding how multiantenna radios should conduct the required channel estimation in the presence of an eavesdropper. This paper demonstrates array beamforming that maximizes the number of bits that can be established when an eavesdropper observes the channel estimation process.
Establishing secret keys from the commonly-observed randomness of reciprocal wireless propagation channels has recently received considerable attention. We consider such key establishment between two multiantenna nodes that use beamforming for communication, showing that the upper bound on the number of key bits that can be generated from the channel observations can be maximized by properly probing the channel. Specifically, we demonstrate that the eigenvectors of the channel spatial covariance matrix should be used as beamformer weights during channel estimation and we optimize the energy allocated to channel estimation for each beamformer weight under a total energy constraint. Finally, by assuming that the channel covariance is separable, we illustrate implementation of the technique for practical beamforming systems and more advanced signal models that incorporate antenna mutual coupling.
This paper explores optimal array beamforming for establishing secret encryption keys through bidirectional channel estimation in multipath propagation environments. The problem is cast as a convex optimization of the average secure key rate achieved in the presence of a passive eavesdropper, and the optimization is performed using semi-definite programming. Representative results demonstrate that, compared to a conventional but suboptimal beamforming solution, the optimal solution achieves significantly higher key establishment performance, with the relative performance improvement increasing with the transmit correlation.
The performance of techniques for establishing secret encryption keys from the reciprocal electromagnetic propagation between two wireless radios is generally measured by comparing the number of key bits generated to the key rate, or the information theoretic bound on the number of key bits that can be determined for a single independent channel estimate. While typically this bound is computed by assuming that the radios have no information regarding the channel, recent work has demonstrated an approach for computing this bound for nodes using beamformed antenna arrays that know the spatial covariance of a wide-sense stationary channel. Since this bound does not directly indicate how to perform practical channel estimation to obtain estimates that can achieve the bound, the prior work demonstrates an approximation that indicates a practical channel estimation procedure while yielding a mutual information near that of the key rate in rich multipath fading environments. This paper demonstrates appreciable degradation in the mutual information achieved using this approximation when the channel includes a line-of-sight component and proposes a modified approximation technique that performs well over a broad range of propagation conditions.
While conventional antenna array synthesis determines the beamforming weights that create a specified antenna radiation pattern, secure array synthesis formulates the beamforming weights that enhance security for wireless transmission of sensitive data. This paper focuses on creating beamformers that improve the generation of secret encryption keys based on bidirectional estimation of the reciprocal electromagnetic propagation channel between two radios. The technique uses semidefinite programming to determine the array weights that maximize the average secure key rate under a constraint on the total transmit power. The numerical implementation of the technique incorporates array mutual coupling, and the results demonstrate that the technique outperforms a conventional beamforming solution, with the improvement becoming significant for certain channel correlation conditions.