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Secret key establishment using wireless channels as common randomness in time-variant MIMO systems

Chan Chen

Published Jan 1, 2010• 3 citations
OpenAlex

Abstract

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.

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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 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.
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.
As an alternative and appealing approach to providing information security in wireless communication systems, secret key generation at physical layer has demonstrated its potential in terms of efficiency and reliability over traditional cryptographic methods. Without the necessity of a management centre for key distribution or reliance on computational complexity, physical layer key generation protocols enable two wireless entities to extract identical and dynamic keys from the randomness of the wireless channels associated with them.\nIn this thesis, the reliability of secret key generation at the physical layer is examined in practical wireless channels with imperfect channel state information (CSI). Theoretical analyses are provided to relate key match rate with channel's signal-to-noise ratio (SNR), degrees of channel reciprocity, and iterations of information reconciliation.\nIn order to increase key match rate of physical layer secret key generation, improved schemes in the steps of channel estimation and sample quantization are proposed respectively. In the channel estimation step, multiple observations of the wireless channels are integrated with a linear processor to provide a synthesized and more accurate estimation of the wireless channel. In the sample quantization step, a magnitude based quantization method with two thresholds is proposed to quantize partial samples, where specific quantization areas are selected to reduce cross-over errors. Significant improvements in key match rate are proven for both schemes in theoretical analysis and numerical simulations. Key match rate can even achieve 100% in both schemes with the assistance of information reconciliation process.\nIn the end, a practical application of physical layer secret key generation is presented, where dynamic keys extracted from the wireless channels are utilized for securing secret data transmission and providing efficient access control.
Dynamic secret key generation from wireless channel characteristics is a promising technique for physical layer security. One of the important issues in this field is extending the secret key’s length while preserving its uniformity and randomness. This paper proposes a key generation method based on time-varying and the reciprocity of wireless channels for Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) wireless communication systems. In the proposed technique, the complex impulse response (CIR) of the estimated channel state information (CSI) is extracted, and a quantization algorithm is designed to convert the maximum peaks of the CIR into secret key bits. The effectiveness of the proposed key generation technique is assessed in terms of the randomness of the produced key bits with different key lengths by using a statistical test suite of the National Institute of Standards and Technology (NIST). The proposed technique is employed in the MIMO-OFDM systems with different modulation schemes through Additive White Gaussian Noise (AWGN) and Rayleigh channels. The simulation results show that the secret keys with various key lengths generated from the proposed technique for the MIMO-OFDM systems guarantee randomness. Moreover, the proposed CSI-based key generation technique provides better effectiveness in terms of security when compared to some existing techniques.
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.
The generation of secret keys from reciprocal wireless channel by exploiting their randomness nature, is an emerging area of interest to provide secure communication. One of the main challenges in this domain is to increase the secret key length, extracted from the shared channel coefficients between two legitimate communication parties, while maintaining its randomness and uniformity. In this work, we develop a practical key generation method, based on channel quantization with singular value decomposition (CQSVD), which is capable of significantly increasing the generated secret key in MIMO systems. This is achieved through quantizing the phases and amplitudes of the estimated MIMO channel coefficient's matrix by using an alternative form of SVD, where the key sequence is extracted from the orthogonal basis functions of the decomposed channel. In this method, it is shown that for an M ×M antenna system, with M2independent channel fading coefficients, a secret key sequence of length 2M3can be generated. The extracted key sequence is transformed to a random phase sequence, which is then used to manipulate the transmitted data on a symbol level basis rather than bit level-basis, to provide more secure communication. The comparative simulation results show that the proposed CQSVD method outperforms the state of the art secret key generation methods.