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IEEE Access

An Upper Bound on PHY-Layer Key Generation for Secure Communications Over a Nakagami-M Fading Channel With Asymmetric Additive Noise

Abdulsahib Albehadili, Khair A. Al Shamaileh, Ahmad Y. Javaid, Jared Oluoch, Vijay Devabhaktuni

Published Jan 1, 2018• 19 citations
Publisher

Abstract

The establishment of convenient and reliable cryptographic keys is not always feasible, especially in low-powered wireless devices where a complex key management infrastructure is unaffordable. Physical layer-based key generation approaches, on the other hand, allow two legitimate users to establish a common secret key by exploiting the parameters of the wireless channel, such as the underlying impulse response. In this paper, a fundamental bound on the maximum achievable key generation rate (KGR) over wireless fading channels with asymmetric additive white Gaussian noise (AWGN) is derived. A Nakagami-mfading channel is considered, and the effect of non-reciprocity on the forward and reverse channels correlation is demonstrated. We validate the theoretical platform through simulations using a key generation protocol based on the level crossing rate (LCR) of the fading process. The proposed LCR protocol models the Nakagami channel by utilizing the sum-of-sinusoids approach, where Doppler shift, fading severity, and number-of-paths are taken into account. The proposed protocol also incorporates a two-level quantizer to extract keys, where the channel estimates between a wireless transmitter and receiver can be used as the basis. Besides providing an upper bound on the KGR, the analytical and simulation results intertwine the effect of channel reciprocity with the key generation process.

DOI
10.1109/access.2018.2827925

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The establishment of convenient and reliable cryptographic keys is not always feasible, especially in low-powered wireless devices where a complex key management infrastructure is unaffordable. Physical layer-based key generation approaches, on the other hand, allow two legitimate users to establish a common secret key by exploiting the parameters of the wireless channel, such as the underlying impulse response. In this paper, a fundamental bound on the maximum achievable key generation rate (KGR) over wireless fading channels with asymmetric additive white Gaussian noise (AWGN) is derived. A Nakagami-mfading channel is considered, and the effect of non-reciprocity on the forward and reverse channels correlation is demonstrated. We validate the theoretical platform through simulations using a key generation protocol based on the level crossing rate (LCR) of the fading process. The proposed LCR protocol models the Nakagami channel by utilizing the sum-of-sinusoids approach, where Doppler shift, fading severity, and number-of-paths are taken into account. The proposed protocol also incorporates a two-level quantizer to extract keys, where the channel estimates between a wireless transmitter and receiver can be used as the basis. Besides providing an upper bound on the KGR, the analytical and simulation results intertwine the effect of channel reciprocity with the key generation process.
The multipath-rich wireless environment associated with typical wireless usage scenarios is characterized by a fading channel response that is time-varying, location-sensitive, and uniquely shared by a given transmitter-receiver pair. The complexity associated with a richly scattering environment implies that the short-term fading process is inherently hard to predict and best modeled stochastically, with rapid decorrelation properties in space, time, and frequency. In this paper, we demonstrate how the channel state between a wireless transmitter and receiver can be used as the basis for building practical secret key generation protocols between two entities. We begin by presenting a scheme based on level crossings of the fading process, which is well-suited for the Rayleigh and Rician fading models associated with a richly scattering environment. Our level crossing algorithm is simple, and incorporates a self-authenticating mechanism to prevent adversarial manipulation of message exchanges during the protocol. Since the level crossing algorithm is best suited for fading processes that exhibit symmetry in their underlying distribution, we present a second and more powerful approach that is suited for more general channel state distributions. This second approach is motivated by observations from quantizing jointly Gaussian processes, but exploits empirical measurements to set quantization boundaries and a heuristic log likelihood ratio estimate to achieve an improved secret key generation rate. We validate both proposed protocols through experimentations using a customized 802.11a platform, and show for the typical WiFi channel that reliable secret key establishment can be accomplished at rates on the order of 10 b/s.
Due to the broadcast nature of wireless channels, wireless communication is vulnerable to eavesdropping, message modification, and node impersonation. Securing the wireless communication requires the shared secret keys between the communicating entities. Traditional security schemes rely on public key infrastructures and cryptographic algorithms to manage secret keys. Recently, many physical-layer-based methods have been proposed as alternative solutions for key generation in wireless networks. These methods exploit the inherent randomness of the wireless fading channel to generate secret keys while providing information-theoretical security without intensive cryptographic computations. This article provides an overview of the existing PHY-based key generation schemes exploiting the randomness of the wireless channels. Specifically, we first introduce the fundamental and general framework of the PHY-based key generation schemes and then categorize them into two classes: received-signal-strength-based and channel- phase-based protocols. Finally, we present a performance comparison of them in terms of key disagreement probability, key generation rate, key bit randomness, scalability, and implementation issues.
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.
Physical layer security (PLS) techniques hold promise for augmenting secure communications in the 5thgeneration of mobile wireless networks. Secret key generation (SKG) is a PLS technique which exploits the wireless propagation channel's randomness to generate symmetric key bits for information encryption and decryption. This work proposes symmetric key generation based on non-uniform quantization of the received signal strength (RSS) samples of a Nakagami-mmm fading channel. The proposed strategy for non-uniform quantization for SKG aims to set quantization thresholds for maximal key randomness and high values of key generation rate (KGR) and key agreement probability (KAP). Finally, a framework is proposed to use single node RSS measurements, readily available in the literature, to generate RSS samples at the other link end. This framework facilitates the testing of new SKG algorithms that require simultaneous RSS measurements by the legitimate nodes, which are not readily available in the open literature. The effectiveness of the proposed SKG scheme is validated through Monte Carlo methods and the National Institute of Standards and Technology (NIST) test suite for assessing the randomness of the generated key sequence.
With the advent of innovative wireless technologies and the rapid growth of diverse connected devices, ensuring communication security has become a critical challenge for the future massively connected beyond 5th generation (B5G) wireless networks. The physical layer security (PLS) approach leverages the inherent physical medium characteristics of communication networks to provide secure communications. In particular, the wireless channel-based secret key generation (SKG) is a PLS approach that creates symmetric keys for message encryption/decryption by exploiting the randomness inherent in wireless channels while relying on the channel to be reciprocal between the nodes. This work proposes a novel SKG algorithm that emphasizes the pre-processing and quantization stages with the aim to increase the key generation rate (KGR) and the key agreement rate (KAR) between the legitimate nodes. The algorithm employs biasing of selective samples and sliding-window weighted averaging of the Generalized Gamma fading channel samples based on the channel’s average contiguous duration (ACD) metric, a second-order fading statistic, to enhance the channel reciprocity. The proposed scheme may also be used to improve the key randomness rate (KRR) by using a non-contiguous multi-level quantization strategy that evenly sets the quantization intervals to accommodate a similar number of channel samples across these intervals. Thus, a desired trade-off between the KGR, KAR, and KRR to meet operational requirements can be achieved with the proposed scheme. Finally, a comprehensive analysis of the performance gains of the proposed scheme in relation to other notable works is conducted by investigating the impact of several channel and algorithmic parameters on the KGR, KAR, and KRR of these schemes.
By exploiting multipath fading channels as a source of common randomness, physical layer (PHY) based key generation protocols allow two terminals with correlated observations to generate secret keys with information-theoretical security. The state of the art, however, still suffers from major limitations,e.g., low key generation rate, lower entropy of key bits and a high reliance on node mobility. In this paper, a novel cooperative key generation protocol is developed to facilitate high-rate key generation in narrowband fading channels, where two keying nodes extract the phase randomness of the fading channel with the aid of relay node(s). For the first time, we explicitly consider the effect of estimation methods on the extraction of secret key bits from the underlying fading channels and focus on a popular statistical method - maximum likelihood estimation (MLE). The performance of the cooperative key generation scheme is extensively evaluated theoretically. We successfully establish both a theoretical upper bound on the maximum secret key rate from mutual information of correlated random sources and a more practical upper bound from Cramer-Rao bound (CRB) in estimation theory. Numerical examples and simulation studies are also presented to demonstrate the performance of the cooperative key generation system. The results show that the key rate can be improved by a couple of orders of magnitude compared to the existing approaches.