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Digest - IEEE Antennas and Propagation Society. International Symposium

Encryption key establishment using space-time correlated MIMO channels

Chan Chen, Michael A. Jensen

Published Jul 1, 2010• 2 citations
Publisher

Abstract

This paper investigates the establishment of secret encryption keys from temporally and spatially correlated MIMO channel matrices. The discussion first examines the influence of correlation on the secret key rate with the help of a simple SISO channel model that generates samples with correlation behavior that can be described in closed-form. This analysis reveals that an optimal sampling approach can be devised that minimizes the total time required to achieve a key with a specified length. The presentation also examines the decorrelation of measured channel samples, and demonstrates that independently removing spatial and temporal correlations fails to produce random variables that are truly decorrelated. Finally, attention turns to a method for quantizing the uncorrelated channel samples. Simulations using real channel measurements reconfirm the observations made using the simple channel model and demonstrate that while existing algorithms for channel quantization can be effective, their performance falls short of that predicted by the upper bound.

DOI
10.1109/aps.2010.5561266

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This paper investigates the establishment of secret encryption keys from temporally and spatially correlated MIMO channel matrices. The discussion first examines the influence of correlation on the secret key rate with the help of a simple SISO channel model that generates samples with correlation behavior that can be described in closed-form. This analysis reveals that an optimal sampling approach can be devised that minimizes the total time required to achieve a key with a specified length. The presentation also examines the decorrelation of measured channel samples, and demonstrates that independently removing spatial and temporal correlations fails to produce random variables that are truly decorrelated. Finally, attention turns to a method for quantizing the uncorrelated channel samples. Simulations using real channel measurements reconfirm the observations made using the simple channel model and demonstrate that while existing algorithms for channel quantization can be effective, their performance falls short of that predicted by the upper bound.
Encryption of confidential data with a secret key has become a widespread technique for securing wireless transmissions. However, existing key distribution methods that either deliver the secret key with a key distribution center or exchange the secret key using public-key cryptosystems are unable to establish perfect secret keys necessary for symmetric encryption techniques. This research considers secret key establishment, under the broad research area of information theoretic security, using the reciprocal wireless channel as common randomness for the extraction of perfect secret keys in multiple-input multiple-output (MIMO)communication systems. The presentation discusses the fundamental characteristics of the time-variant MIMO wireless channel and establishes a realistic channel simulation model useful for assessing key establishment algorithms. Computational examples show the accuracy and applicability of the model. The discussion then turns to an investigation of the influence of the spatial and temporal correlation of the channel coefficients on the bound of the key size generated from the common channel, and it is found that a sampling approach exists that can generate a key using the minimum sampling time. A practical key generation protocol is then developed based on an enhancement of a published channel coefficient quantization method that incorporates flexible quantization levels, public transmission of the correlation eigenvector matrix and low-density parity-check (LDPC) coding to improve key agreement. This investigation leads to the development of improved channel quantization techniques that dynamically shift the quantization boundaries at one node based on the information provided by the other node. Analysis based on a closed-form bound for the key error rate (KER) and simulations based on the channel model and measurement data show that the enhanced algorithms are able to dramatically reduce key mismatch and asymptotically approach the KER bound. Finally, other secret key generation algorithms based on channel-encryption rather than quantization are discussed, leading to a new concept for secret key generation using the common wireless channel.
This paper discusses the concept of using the physics associated with multipath propagation and multiple antennas to establish secure encryption keys between two wireless nodes in a network. The presentation includes a proposed algorithm for generating uncorrelated keys despite the fact that the random numbers generated by the propagation channel exhibit spatial and temporal correlation. It further briefly discusses some of the measures that must be taken to make the algorithm implementation practical as well as the theoretically-achievable performance of the algorithm. Simulation results using a physical path-based time-variant MIMO model demonstrate that the length of the established key grows as antennas are added. Furthermore, for high SNR environments, the algorithm is able to achieve a key length versus SNR curve whose slope matches that of the theoretically achievable bound.
Secret key generation based on channel reciprocity is an important branch of wireless physical layer security which provides strong or even theoretically perfect secret. With the pursuit of higher secret key rate, the time-frequency joint key extraction schemes have been recently considered, which can exploit simultaneously the resources contained in the frequency and time domains. However, the strong correlation existing between the broadband time-variant channel samples makes the decorrelation process indispensable before quantization. Due to the large size of these channel sample matrices, decorrelation methods based on full channel covariance matrix corresponding to high calculation complexity are difficult to deploy in realistic mobile communication systems. In this work, we propose a method which separates the decorrelation of time-frequency correlated channel characteristics into two steps. The performance of this proposed method is evaluated through both standardized channel model and practical measurements. It is shown that the decorrelation of samples with the two-step method could be close to that based on the full channel covariance matrix, as well as leading to a dramatical reduction on the calculation complexity. The impact of the signal-to-noise-ratio (SNR) on the secret key rate is analyzed, and no distinct difference is shown in this aspect between these two methods.
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.
This paper proposes a practical protocol useful for establishing encryption keys between nodes in a wireless network. The method is designed to enable creation of long keys by extracting the increased randomness inherent in reciprocal time-variant multiple-input multiple-output wireless channels. The presentation provides a strategy for exploiting the degrees of freedom existing in the protocol to decorrelate the information in the public discussion from the key information as well as the channel state information. The paper further discusses several error reduction techniques that can efficiently enhance key agreement between the multiple-antenna nodes. Simulations based on a realistic time-variant channel model demonstrate the efficiency of the key establishment as well as the probability of key agreement for the protocol.
Keys for symmetric encryption can be established by generating key bits from the mutually-observed randomness present within estimates of a reciprocal wireless channel. We consider this approach for key establishment in multiple-input multiple-output (MIMO) systems and provide a channel estimation strategy that increases the key rate, or the mutual information between the channel estimates at the two nodes. The technique applies MIMO transmit and receive beamformers derived from the eigenvectors of the covariance matrix and then iteratively optimizes the power allocated to each transmit beamformer. Simulation results demonstrate the iterative behavior and the achieved performance of the proposed algorithm.