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IEEE Wireless Communications Letters

Phase Shift Matrix Design With Vector Quantization in RIS-Aided Physical Layer Key Generation

Yufan Song, Liquan Chen, Tianyu Lu, Peng Zhang

Published Jun 10, 2024• 3 citations
Publisher

Abstract

The key generation rate (KGR) of physical layer key generation (PLKG) is severely restricted in quasi-static environments due to a lack of entropy. To address the problem, a reconfigurable intelligent surface (RIS) is introduced. In this letter, we consider the design of phase shift matrix with vector quantization to fully exploit the randomness of the RIS. In order to reduce the bit disagreement ratio (BDR), we design a vector quantizer to fully exploit the quantization range of the RIS channel. Additionally, we provide the design strategy for the phase shift matrix that aligns with the vector quantizer. Furthermore, we present a closed-form solution for the phase shift matrix. Meanwhile, to balance the tradeoff between high KGR and low BDR, we calculate the BDR in different quantization orders and propose an adaptive quantization order selection. Simulations validate that our proposed scheme obtain a higher KGR than the existing schemes under a certain BDR threshold.

DOI
10.1109/lwc.2024.3411878

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arXiv:2208.00218•IEEE Transactions on Information Forensics and Security•Jan 1, 2023•29 citations
The key generation rate (KGR) of physical layer key generation (PLKG) is severely restricted in quasi-static environments due to a lack of entropy. To address the problem, a reconfigurable intelligent surface (RIS) is introduced. In this letter, we consider the design of phase shift matrix with vector quantization to fully exploit the randomness of the RIS. In order to reduce the bit disagreement ratio (BDR), we design a vector quantizer to fully exploit the quantization range of the RIS channel. Additionally, we provide the design strategy for the phase shift matrix that aligns with the vector quantizer. Furthermore, we present a closed-form solution for the phase shift matrix. Meanwhile, to balance the tradeoff between high KGR and low BDR, we calculate the BDR in different quantization orders and propose an adaptive quantization order selection. Simulations validate that our proposed scheme obtain a higher KGR than the existing schemes under a certain BDR threshold.
In quasi-static environments, the key generation rate (KGR) of wireless physical layer key generation (PLKG) can be greatly limited. In this paper, we aim to improve the KGR by reconfigurable intelligent surface (RIS) and jointly design the quantizer and phase shift matrix. We give a reconfiguration strategy able to quantify both real and imaginary parts at the same time and give its closed-form solution of the phase shift matrix. To reduce the bit disagreement ratio (BDR), we design a quantizer suitable for RIS-assisted PLKG which uses non-uniform quantization. To achieve high KGR while maintain low BDR, we analyze the BDR in different quantization levels and realize an adaptive quantization selection. Meanwhile, the simulation results verify that the KGR of the proposed scheme is more than twice that of the existing scheme under a certain BDR threshold.
Abstract In quasi-static environment, the performance of physical-layer key generation (PKG) is limited by low entropy. Deploying reconfigurable intelligent surface (RIS) is a mainstream method to solve this problem. However, the secret key performance (SKP) is generally insufficient at low signal-to-noise ratio (SNR). In this paper, we propose an RIS-assisted adaptive PKG scheme. Specifically, we design phase based uniform quantization to enhance the randomness of the RIS channel while simplifying computations. Then, we present an RIS phase shift matrix design based on rejection sampling to adapt the quantization algorithm, which can reduce bit disagreement rate (BDR) and improve key generation rate (KGR). Furthermore, to balance the system’s requirements for low BDR and high KGR, we derive a theoretical model for estimating the BDR probability. By computing the theoretical BDR, we determine the maximum quantization order for different SNRs. Combined with a discard strategy, this enables adaptive selection of the quantization order. Simulation results demonstrate that the proposed scheme achieves lower BDR and higher KGR than existing approaches. Moreover, it does not require complex algorithms, making it suitable for resource-constrained internet of things scenarios. (RIS_Assist_PKG: https://github.com/GQQ1206/RIS_Assist_PKG )
Physical-layer key generation (PLKG) is an information-theoretic security technique aimed at addressing key distribution challenges among resource-constrained legitimate users in the Internet of Things (IoT). However, in quasi-static or blocked environments, key generation faces significant limitations owing to its low entropy. To overcome this challenge, we propose leveraging a simultaneously transmitting and reflecting (STAR) reconfigurable intelligent surface (RIS). In this study, we introduce a STAR-RIS-aided multiuser PLKG framework and formulate an optimization problem focused on minimizing the average bit disagreement ratio through optimal phase-shift matrix adjustments. Initially, we derive closed-form solutions for optimal phase shifts, simplifying the problem to depend solely on amplitude coefficients. We then employ a Newton-Raphson algorithm under the energy-splitting (ES) protocol and a traversal method under the mode-switching (MS) and time-switching (TS) protocols to solve the optimization problem. Simulation results confirm the efficacy of our proposed schemes by comparison with existing benchmark schemes.
The key generation rate (KGR) performance of wireless physical layer (PHY) key generation can be limited by the quasi-static slow fading environment. In this work, we aim to exploit the radio environment reconfiguration ability enabled by reconfigurable intelligent surface (RIS) to improve KGR of PHY key generation. By rapidly changing the RIS configurations, the randomness or entropy rate of the wireless channel can be significantly increased, thus improving the KGR. To achieve high KGR while keeping low bit disagreement ratio (BDR), for the first time, we propose a machine learning (ML) based adaptive quantization level prediction scheme to decide an optimal quantization level based on channel state information (CSI). Simulation results show that with a prediction accuracy as high as 98.2%, the proposed ML-based prediction model tends to assign high quantization levels in the high SNR regime to reduce BDR, while adopting low quantization levels under low SNRs to maintain a low BDR.
Physical-layer key generation (PLKG) can significantly enhance the security of classic encryption schemes by efficiently providing secret keys in resource-limited network like the Internet of Things (IoT). However, reaching a high key generation rate (KGR) is challenging in applications like smart home or remote area sensing with quasi-static channels. Recently, exploiting reconfigurable intelligent surface (RIS) to induce randomness in quasi-static wireless channels has received significant research interest. However, the inherent spatial correlation among the RIS elements is rarely studied, which can alter the optimum physical-layer key generation (PLKG) approach in terms of KGR and randomness in the key sequence. Specifically, for the first time, in this contribution, we take into account a spatially correlated RIS, which intends to enhance the KGR in a quasi-static medium. Novel closed-form analytical expressions for KGR are derived for the two cases of random phase shift (RPS) and our proposed equal phase shift (EPS) in the RIS elements. We also analyze the correlation between the channel samples to ensure the randomness of the generated secret key sequence. It is shown that the EPS scheme can effectively exploit the inherent spatial correlation between the RIS elements and it leads to a higher KGR compared to the widely used RPS strategy. We further formulate an optimization problem in which we determine the optimal portion of time dedicated to direct and indirect channel estimation, which has never been addressed in previous studies. We show the accuracy and the fast convergence of our sequential convex programming (SCP)-based algorithm and discuss the various parameters affecting spatially correlated RIS-assisted PLKG.
Physical layer key generation (PLKG) is a promising technique to establish symmetric keys between resource-constrained legitimate users. However, PLKG suffers from a low key rate in harsh environments where channel randomness is limited. To address the problem, reconfigurable intelligent surfaces (RISs) are introduced to reshape the channels by controlling massive reflecting elements, which can provide more channel diversity. In this paper, we design a channel probing protocol to fully extract the randomness from the cascaded channel, i.e., the channels through reflecting elements. We derive the analytical expressions of the key rate and design a water-filling algorithm based on the Karush-Kuhn-Tucker (KKT) conditions to find the upper bound. To find the optimal precoding and phase shift matrices, we propose an algorithm based on the Grassmann manifold optimization methods. The system is evaluated in terms of the key rate, bit disagreement rate (BDR) and randomness. Simulation results show that our protocols significantly improve the key rate as compared to existing protocols. Compared to multiple-antennas systems without a RIS, our proposed method achieves an average 9.51 dB performance gain when the side length of an element is 1/4 wavelength and the Rician factor is 0 dB.