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IEEE Transactions on Information Forensics and Security

Automatic Secret Keys From Reciprocal MIMO Wireless Channels: Measurement and Analysis

Jon W. Wal, R. K. Sharma

Published Jun 16, 2010• 256 citations
Publisher

Abstract

Information theoretic limits for random key generation in multiple-input multiple-output (MIMO) wireless systems exhibiting a reciprocal channel response are investigated experimentally with a new three-node MIMO measurement campaign. As background, simple expressions are presented for the number of available key bits, as well as the number of bits that are secure from a close eavesdropper. Two methods for generating secret keys are analyzed in the context of MIMO channels and their mismatch rate and efficiency are derived. A new wideband indoor MIMO measurement campaign in the 2.51- to 2.59-GHz band is presented, whose purpose is to study the number of available key bits in both line-of-sight and nonline-of-sight environments. Application of the key generation methods to measured propagation channels indicates key generation rates that can be obtained in practice for four-element arrays.

DOI
10.1109/tifs.2010.2052253

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Information theoretic limits for random key generation in multiple-input multiple-output (MIMO) wireless systems exhibiting a reciprocal channel response are investigated experimentally with a new three-node MIMO measurement campaign. As background, simple expressions are presented for the number of available key bits, as well as the number of bits that are secure from a close eavesdropper. Two methods for generating secret keys are analyzed in the context of MIMO channels and their mismatch rate and efficiency are derived. A new wideband indoor MIMO measurement campaign in the 2.51- to 2.59-GHz band is presented, whose purpose is to study the number of available key bits in both line-of-sight and nonline-of-sight environments. Application of the key generation methods to measured propagation channels indicates key generation rates that can be obtained in practice for four-element arrays.
There is growing interest in physical-layer key generation schemes that provide very strong or even perfect security in wireless communication systems. One such scheme is reciprocal channel key generation, where two nodes quantize reciprocal channel state information to generate keys. Although the use of multiple-input multiple-output (MIMO) techniques is interesting in this case since the number of random parameters available for rapid key generation is increased, MIMO techniques may also provide more information to an eavesdropper. This work presents a new MIMO measurement campaign performed in LOS and NLOS indoor environments that studies the correlation of the channel between legitimate users with the eavesdropper channel, revealing what key generation rates can be attained in practice and what fraction of generated key bits are safe from eavesdroppers. The effect of eavesdropper separation, number of antennas, eavesdropper advantage, and covariance separability are studied.
There is growing interest in physical-layer security methods that exploit the random nature of the physical propagation channel to strengthen existing crypto-systems. In reciprocal channel key generation (RCKG), legitimate nodes (Alice and Bob) observe a common fluctuating channel to generate keys that are safe from the eavesdropper (Eve). Previous work [1, 2] derived expressions for the available key bits and those safe from an eavesdropper for MIMO systems with correlated complex Gaussian statistics. This paper applies these expressions to new MIMO measurements in indoor LOS and NLOS environments, indicating how propagation effects limit secure key generation and what key generation rates can be expected in practice.
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.
Secret key generation based on channel measurements has emerged as a meaningful approach to enhance the security of wireless links. The key generation mechanism takes advantage of wireless channel reciprocity and uses the mutual information between legitimate users' channel measurements. However, the rate at which key bits are generated depends on the channel coherence time. Furthermore, eavesdroppers may obtain information to generate the secret key bits if their channels become correlated to the legitimate channels. In this paper, we propose a new approach for key generation that uses MIMO precoding and role switching by legitimate users during the key generation process in order to prevent an eavesdropper whose channel is correlated with the legitimate channel to acquire information that can be used to generate the encryption key, while also ensuring that the rate at which uncorrelated key bits are generated does not depend on the channel coherence time. The proposed approach is supported by an information theoretic analysis and is illustrated with numerical results obtained from simulations showing that, even when the legitimate and eavesdropper channels are correlated, the bit mismatch rate at the eavesdropper does not improve with increasing SNR, while that at the legitimate users improves.
The potential of automatically generating secret keys by randomly changing the state of a reconfigurable antenna is investigated through direct measurement. Measurements are performed with a 5×5 parasitic reconfigurable aperture (RECAP) antenna at 2.54 GHz in an indoor laboratory environment, illustrating that keys can be generated with physical-layer reciprocal channel key generation (RCKG) even in static or line-of-sight (LOS) conditions. Details of the parasitic array, varactor-diode reconfigurable elements, and network-analyzer based measurement setup are presented. Analysis of the data shows that secure key bits is lower when an eavesdropper is in the LOS path between legitimate nodes as opposed to a direction perpendicular to that path. It is also illustrated that the statistics of fading induced with the reconfigurable array are not strictly Gaussian for LOS channels. Encouragingly, measurements show that around 80% of generated key bits are secure even in the worst case conditions.
Extracting secret key from the common randomness of wireless channel has gained significant interest as a mechanism for providing secure point-to-point communications. Current works focus on the methods of exploiting channel characterizations based on Received Signal Strength Indication (RSSI), channel phase and Channel Impulse Response (CIR) under different propagation environments. However, when the channel fading is static or quasi-static, the secret key bits derived from the channel may be identical or nearly identical. In this paper, we propose a method to solve this problem in multiple-input multiple-output (MIMO) systems based on random beamforming. Compared with single antenna systems, MIMO systems offer more randomness available. Furthermore we consider the worst scenario where the eavesdropper Eve knows perfect knowledge of the legitimate channel. The quantization error probability at Eve is simulated to assess the security of the proposed method.