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arXiv:2208.00218 · IEEE Transactions on Information Forensics and Security

Joint Precoding and Phase Shift Design in Reconfigurable Intelligent Surfaces-Assisted Secret Key Generation

Tianyu Lu, Liquan Chen, Junqing Zhang, Chen Chen, Aiqun Hu

Published Jan 1, 2023• 29 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/tifs.2023.3268881

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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.
Physical-layer key generation (PKG) exploits the reciprocity and randomness of wireless channels to generate a symmetric key between two legitimate communication ends. However, in multi-cell systems, PKG suffers from severe pilot contamination due to the reuse of pilots in different cells. In this paper, we invoke multiple reconfigurable intelligent surfaces (RISs) for adaptively shaping the environment and enhancing the PKG performance. To this end, we formulate an optimization problem to maximize the weighted sum key rate (WSKR) by jointly optimizing the precoding matrices at the base stations (BSs) and the phase shifts at the RISs. To address the non-convexity of the problem, we adopt an alternating optimization (AO)-based algorithm that divides the joint optimization problem into two subproblems. For the subproblem of precoding matrices, we apply the Lagrangian dual approach based on the Karush-Kuhn-Tucker (KKT) conditions. As for the subproblem of phase shifts, we adopt a projected gradient ascent (PGA) algorithm. Simulation results validate the effectiveness of the proposed scheme, demonstrating significant gains in WSKR. Moreover, compared with a single-RIS case, deploying multiple RISs offer spatial diversity so as to improve the PKG performance of multicell systems.
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.
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.
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.
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.
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 )