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IEEE Communications Letters

On the Key Generation From Correlated Wireless Channels

Junqing Zhang, Biao He, Trung Q. Duong, Roger Woods

Published Jan 9, 2017• 87 citations
Publisher

Abstract

This letter investigates the secret key capacity of key generation from correlated wireless channels in a source model. We systematically study a practical scenario by taking into account all relevant parameters including sampling delay, eavesdroppers' location, qualities of legitimate and eavesdropping channels, Doppler spread, and pilot length. Our findings indicate that secret key capacity is determined by the cross correlation of the channel measurements, and a better legitimate channel is not necessary when the correlation between legitimate channels is higher than correlation between legitimate and eavesdropping channels. We also find that it is possible to tune the secret key capacity by carefully designing the sampling delay, pilot length, and channel qualities. This letter offers practical design guidelines on secure key generation systems.

DOI
10.1109/lcomm.2017.2649496

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This letter investigates the secret key capacity of key generation from correlated wireless channels in a source model. We systematically study a practical scenario by taking into account all relevant parameters including sampling delay, eavesdroppers' location, qualities of legitimate and eavesdropping channels, Doppler spread, and pilot length. Our findings indicate that secret key capacity is determined by the cross correlation of the channel measurements, and a better legitimate channel is not necessary when the correlation between legitimate channels is higher than correlation between legitimate and eavesdropping channels. We also find that it is possible to tune the secret key capacity by carefully designing the sampling delay, pilot length, and channel qualities. This letter offers practical design guidelines on secure key generation systems.
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This letter examines the optimal pilot length for key generation in correlated wireless channels. We first deduce the secret key capacity as a function of the pilot length N and other system parameters. Then, derive two fixed-point equations to identify the optimal N with and without an eavesdropper. Our analysis and numerical results confirm the existence of the optimal N that maximizes the secret key capacity, and both results for optimal N are consistent. Furthermore, the optimal N generally decreases with average signal-to-noise ratio and maximum Doppler shift. Our examination can provide useful guidelines in designing practical key generation systems.
Key generation technique generates symmetric keys based on the temporal variation, reciprocity and spatial decorrelation of the wireless channel. Most key generation schemes, however, assume that the eavesdropping channels are independent of the main channel and neglect the influence of the eavesdroppers. In this paper, we analyze the secret key capacity taking into account the information leaked to eavesdroppers, and the security analysis shows the eavesdropping channel correlation will reduce the secret key capacity. Then we propose a security channel estimating (SCE) scheme to resist eavesdroppers and the scheme is shown to be efficient. Finally, we use the Monte Carlo simulation verifies the theoretical analysis results.
This paper investigates the role of the eavesdropper's statistics in the implementation of a practical secret-key generation system. We carefully conduct the information-theoretic analysis of a secret-key generation system from wireless channel gains measured with software-defined radios. In particular, we show that it is inaccurate to assume that the eavesdropper gets no information because of decorrelation with distance. We also provide a bound for the achievable secret-key rate in the finite key-length regime that takes into account the presence of correlated eavesdropper's observations. We evaluate this bound with our experimental gain measurements to show that operating with a finite number of samples incurs a loss in secret-key rate on the order of 20%.
There is growing interest in wireless security methods that provide strong or even perfect secrecy by taking advantage of features of the physical propagation channel. In advantage-based methods, high channel quality in an average or opportunistic sense is exploited between two legitimate nodes, such that nonzero secrecy capacity can be achieved. Since such methods require bounds on the quality of the eavesdropper channel, they are somewhat impractical. Secret key generation based on tracking channel evolution in time division duplex systems is a more attractive option, where two nodes generate secret key bits based on a mutually known random channel. Since the eavesdropper channel is typically independent of the legitimate channel, the key can only be broken by brute force attacks, which are difficult when new keys are continuously generated. In this paper, the information theoretic limits of key generation schemes are investigated, based on the level of estimation error, temporal correlation, and dependence of the eavesdropper and legitimate channels. Three practical candidate key generation schemes are also considered: channel quantization and channel quantization with guardband.
Abstract—We study the secret-key capacity in a joint source-channel coding setup—the terminals are connected over a discrete memoryless channel and have access to side information, modelled as a pair of discrete memoryless source sequences. As our main result, we establish the upper and lower bounds on the secret-key capacity. In the lower bound expression, the equivocation terms of the source and channel components are functionally additive even though the coding scheme generates a single secret-key by jointly taking into account the source and channel equivocations. Our bounds coincide, thus establishing the capacity, when the underlying wiretap channel can be decomposed into a set of independent, parallel, and reversely degraded channels. For the case of parallel Gaussian channels and jointly Gaussian sources we show that Gaussian codebooks achieve the secret-key capacity. In addition, when the eavesdropper also observes a correlated side information sequence, we establish the secret-key capacity when both the source and channel of the eavesdropper are a degraded version of the legitimate receiver. We finally also treat the case when a public discussion channel is available, propose a separation based coding scheme, and establish its optimality when the channel output symbols of the legitimate receiver and eavesdropper are conditionally independent given the input. Index Terms—Information theoretic security, joint sourcechannel coding, public discussion, secret-key agreement, wiretap channel. I.