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High-Confidence Computing

A low-complexity decorrelation method for PHY-based key generation

Gökhan Şahin

Published May 1, 2025• 0 citations
Publisher

Abstract

Physical layer characteristics of a wireless channel, which can be measured independently by the two communicating parties and yield near-identical results due to the channel reciprocity property, have been shown to be an important source of shared secrecy generation. Various types of channel state information (CSI), such as the received signal strength (RSS) and the channel impulse response (CIR) can be utilized for this purpose. Through periodic probing of the CSI, a continuous cycle of secret bit generation and key renewal can be maintained. However, many forms of wireless CSI inherently have substantial temporal correlation, which may hinder the secrecy generation process. Accordingly, various autocorrelation reduction (decorrelation) methods have been proposed, using either sub-sampling approaches that discard potentially valuable CSI data, or, computationally expensive transform domain approaches such as the Discrete Cosine Transform (DCT), Karhunen–Loeve Transform (KLT), and principal component analysis (PCA) that may not be feasible or desirable for resource and energy constrained devices. This paper proposes a low-complexity method for reducing the autocorrelation of the CSI measurements through a reordering of the data based on integer sequences such as the Fibonacci sequences, and applies it to various types of CSI data that represent both the individual path level CIR and the aggregate level multipath gain or RSS. We evaluate the performance of the method in three standard multipath ITU channel models. Fibonacci sequences are observed to be an effective means of decorrelating the channel measurement data, thereby eliminating the need for computationally intensive methods.

DOI
10.1016/j.hcc.2025.100323

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Physical layer characteristics of a wireless channel, which can be measured independently by the two communicating parties and yield near-identical results due to the channel reciprocity property, have been shown to be an important source of shared secrecy generation. Various types of channel state information (CSI), such as the received signal strength (RSS) and the channel impulse response (CIR) can be utilized for this purpose. Through periodic probing of the CSI, a continuous cycle of secret bit generation and key renewal can be maintained. However, many forms of wireless CSI inherently have substantial temporal correlation, which may hinder the secrecy generation process. Accordingly, various autocorrelation reduction (decorrelation) methods have been proposed, using either sub-sampling approaches that discard potentially valuable CSI data, or, computationally expensive transform domain approaches such as the Discrete Cosine Transform (DCT), Karhunen–Loeve Transform (KLT), and principal component analysis (PCA) that may not be feasible or desirable for resource and energy constrained devices. This paper proposes a low-complexity method for reducing the autocorrelation of the CSI measurements through a reordering of the data based on integer sequences such as the Fibonacci sequences, and applies it to various types of CSI data that represent both the individual path level CIR and the aggregate level multipath gain or RSS. We evaluate the performance of the method in three standard multipath ITU channel models. Fibonacci sequences are observed to be an effective means of decorrelating the channel measurement data, thereby eliminating the need for computationally intensive methods.
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.
The reciprocity nature of a wireless channel has been leveraged to generate and establish secret keys between two devices communicating over the channel. This is typically done by having the two devices exchange probing signals to measure their channel state information (CSI), which each then uses to derive secret keys. While extensive research on secret key generation primarily focuses on theoretical and simulation analyses, the practical implementation and adoption of key generation encounter obstacles arising from hardware constraints and varying channel conditions. To address this research gap, we experimentally investigate the channel measurements by collecting CSI data using resource-constrained devices. Our experiments reveal a significant degradation in the correlation between the collected CSI from two low-cost devices limiting the key generation performance. Through our experimental investigations, we first demonstrate that wavelet coherence provides insights on the reciprocity of the channel measurements on both time and frequency. We then propose a new wavelet coherence-based CSI data reconstruction technique that uses wavelet coherence and time-lagged cross-correlation to reconstruct CSI data that is consistent between the two participating devices, resulting in significant improvement in the channel measurements. Additionally, we propose a secret-key generation scheme that exploits the proposed wavelet coherence-based CSI data reconstruction, yielding a significant reduction in the bit error rates and an increase in the key generation rates.
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.
Providing secure communication links between devices of low computational power has been increasingly investigated during recent years. The need for fast and easy-to-implement security for computationally weak wireless devices has lead to the development of physical layer based key generation approaches. The generation of symmetric cryptographic keys out of wireless channel properties turned out to be a promising approach comprising advantages of symmetric as well as asymmetric cryptography. Numerous quantization schemes have been proposed in previous works to increase the Key Generation Rate (KGR). Also by increasing the sampling rate, the input data can be generated faster. However, due to fast sampling rates, redundancy of subsequent bits will increase. This lowers the quality, that is, the randomness of the generated secret key and makes the system more vulnerable to brute-force attacks. We present and analyze different techniques for transforming a temporally correlated sequence into a compressed sequence of decorrelated bits and, therefore, assure non-redundant key sequences.
Key generation is essential for protecting wireless networks. Based on wireless channel reciprocity, transceivers can generate shared secret keys by measuring their communicating channels. However, due to non-simultaneous measurements, asymmetric noises and other interferences, channel measurements collected by different transceivers are highly correlated but not identical and thus might have some discrepancies. Further, these discrepancies might lead to mismatches of bit sequences after quantization. The referred mismatches significantly affect the efficiency of key generation. In this paper, an efficient key generation scheme leveraging wireless channel reciprocity is proposed. To reduce the bit mismatch rate and enhance the efficiency of key generation, the involved transceivers separately apply discrete cosine transform (DCT) and inverse discrete cosine transform (IDCT) to pre-process their measurements. Then, the outputs of IDCT are quantified and encoded to establish the bit sequence. With the implementations of information reconciliation and privacy amplification, the shared secret key can be generated. Several experiments in real environments are conducted to evaluate the proposed scheme. During each experiment, the shared key is established from the received signal strength (RSS) of heterogeneous devices. The results of experiments demonstrate that the proposed scheme can efficiently generate shared secret keys between transceivers.
Due to the reciprocity of wireless channels, the communication parties can directly extract the shared key from channel. This solution were verified through several schemes. However, in real situations, channel sampling of legitimate transceivers might be impacted by noises and other interferences, which makes the channel states obtained by initiator and responder might be obvious different. The efficiency and even availability of physical layer key generation are thus reduced. In this paper, we propose a lightweight and efficient physical layer key generation scheme, which extract shared secret keys from channel state information (CSI). To improve the key generation process, the discrete cosine transform (DCT) is employed to reduce differences of channel states of legitimate transceivers. Then, these outputs are quantified and encoded through multi-bit adaptive quantization(MAQ) quantizer and gray code to generate binary bit sequence, which can greatly reduce the bit error rate. Moreover, the low density parity check (LDPC) code and universal hashing functions are used to achieve information reconciliation and privacy amplifification. By adding preprocessing methods in the key generation process and using the rich information of CSI, the security of communications can be increased on the basis of improving the key generation rate. To evaluate this scheme, a number of experiments in various real environments are conducted. The experimental results show that the proposed scheme can effificiently generate shared secret keys for nodes and protect their communication.