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arXiv:2212.01563

Intelligent Reflecting Surface Assisted Secret Key Generation Under Spatially Correlated Channels in Quasi-Static Environments

Vahid Shahiri, Hamid Behroozi, Ali Kuhestani

Published Dec 3, 2022• 2 citations
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Abstract

Physical layer key generation (PLKG) can significantly enhance the security of classic encryption schemes by enabling them to change their secret keys significantly faster and more efficient. However, due to the reliance of PLKG techniques on channel medium, reaching a high secret key rate is challenging in static environments. Recently, exploiting intelligent reflecting surface (IRS) as a means to induce randomness in static wireless channels has received significant research interest. However, the impact of spatial correlation between the IRS elements is rarely studied. To be specific, for the first time, in this contribution, we take into account a spatially correlated IRS which intends to enhance the secret key generation (SKG) rate in a static medium. Closed form analytical expressions for SKG rate are derived for the two cases of random phase shift and equal random phase shift for all the IRS elements. We also analyze the temporal correlation between the channel samples to ensure the randomness of the generated secret key sequence. We further formulate an optimization problem in which we determine the optimal portion of time within a coherence interval dedicated for the direct and indirect channel estimation. We show the accuracy and the fast convergence of our proposed sequential convex programming (SCP) based algorithm and discuss the various parameters affecting spatially correlated IRS assisted PLKG.

DOI
10.48550/arxiv.2212.01563

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Physical layer key generation (PLKG) can significantly enhance the security of classic encryption schemes by enabling them to change their secret keys significantly faster and more efficient. However, due to the reliance of PLKG techniques on channel medium, reaching a high secret key rate is challenging in static environments. Recently, exploiting intelligent reflecting surface (IRS) as a means to induce randomness in static wireless channels has received significant research interest. However, the impact of spatial correlation between the IRS elements is rarely studied. To be specific, for the first time, in this contribution, we take into account a spatially correlated IRS which intends to enhance the secret key generation (SKG) rate in a static medium. Closed form analytical expressions for SKG rate are derived for the two cases of random phase shift and equal random phase shift for all the IRS elements. We also analyze the temporal correlation between the channel samples to ensure the randomness of the generated secret key sequence. We further formulate an optimization problem in which we determine the optimal portion of time within a coherence interval dedicated for the direct and indirect channel estimation. We show the accuracy and the fast convergence of our proposed sequential convex programming (SCP) based algorithm and discuss the various parameters affecting spatially correlated IRS assisted PLKG.
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 secret key generation is a promising candidate to achieve one-time-pad encryption approach for the wireless communication system. However, in a static environment, the secret key rate is low due to the lack of channel time-variation. To solve this problem, this letter proposes a novel secret key generation scheme assisted by an intelligent reflecting surface with discrete phase shifts. In the scheme, legitimate nodes construct the dynamic time-varying channel by rapidly and randomly switching the phase of IRS elements. Then, channel coefficients are used to generate the secret key. Based on the IRS channel model, we derive the probability distribution of the channel coefficient and the expressions of the secret key rate. Furthermore, we optimize the secret key rate by adjusting the switching time of the IRS phase. Monte Carlo simulation and numerical results show that our proposed scheme can update the secret key in a static environment.
Physical-layer key generation (PKG) based on wireless channels is a lightweight technique to establish secure keys between legitimate communication nodes. Recently, intelligent reflecting surfaces (IRSs) have been leveraged to enhance the performance of PKG in terms of secret key rate (SKR), as it can reconfigure the wireless propagation environment and introduce more channel randomness. In this paper, we investigate an IRS-assisted PKG system, taking into account the channel spatial correlation at both the base station (BS) and the IRS. Based on the considered system model, the closed-form expression of SKR is derived analytically considering correlated eavesdropping channels. Aiming to maximize the SKR, a joint design problem of the BS’s precoding matrix and the IRS’s phase shift vector is formulated. To address this high-dimensional non-convex optimization problem, we propose a novel unsupervised deep neural network (DNN)-based algorithm with a simple structure. Different from most previous works that adopt iterative optimization to solve the problem, the proposed DNN-based algorithm directly obtains the BS precoding and IRS phase shifts as the output of the DNN. Simulation results reveal that the proposed DNN-based algorithm outperforms the benchmark methods with regard to SKR.
Physical-layer key generation (PKG) based on wireless channels is a lightweight technique to establish secure keys between legitimate communication nodes. Recently, intelligent reflecting surfaces (IRSs) have been leveraged to enhance the performance of PKG in terms of secret key rate (SKR), as it can reconfigure the wireless propagation environment and introduce more channel randomness. In this paper, we investigate an IRS-assisted PKG system, taking into account the channel spatial correlation at both the base station (BS) and the IRS. Based on the considered system model, the closed form expression of SKR is derived analytically. Aiming to maximize the SKR, a joint design problem of the BS precoding matrix and the IRS reflecting coefficient vector is formulated. To address this high-dimensional non-convex optimization problem, we propose a novel unsupervised deep neural network (DNN) based algorithm with a simple structure. Different from most previous works that adopt the iterative optimization to solve the problem, the proposed DNN based algorithm directly obtains the BS precoding and IRS phase shifts as the output of the DNN. Simulation results reveal that the proposed DNN-based algorithm outperforms the benchmark methods with regard to SKR.
Physical-layer key generation (PKG) based on wireless channels is a lightweight technique to establish secure keys between legitimate communication nodes. Recently, intelligent reflecting surfaces (IRSs) have been leveraged to enhance the performance of PKG in terms of secret key rate (SKR), as it can reconfigure the wireless propagation environment and introduce more channel randomness. In this paper, we investigate an IRS-assisted PKG system, taking into account the channel spatial correlation at both the base station (BS) and the IRS. Based on the considered system model, the closed-form expression of SKR is derived analytically. Aiming to maximize the SKR, a joint design problem of the BS's precoding matrix and the IRS's reflecting coefficient vector is formulated. To address this high-dimensional non-convex optimization problem, we propose a novel unsupervised deep neural network (DNN) based algorithm with a simple structure. Different from most previous works that adopt the iterative optimization to solve the problem, the proposed DNN based algorithm directly obtains the BS precoding and IRS phase shifts as the output of the DNN. Simulation results reveal that the proposed DNN-based algorithm outperforms the benchmark methods with regard to SKR.
Physical layer secret key generation (SKG) is a promising supplement for high-level encryption, which leverages the channel reciprocity and the natural randomness of wireless channel. However, practical implementations often exhibit static environment. To solve this problem, this paper proposes a novel secret key generation scheme assisted by an intelligent reflecting surface (IRS) which can smartly reconfigure the radio signal propagation to improve the secret key rate of SKG. Specially, we formulate the minimum achievable secret key capacity in the IRS-assisted multiple-input single-output (MISO) system with multiple eavesdroppers. Then, an optimization framework for designing IRS reflecting coefficients based on the secret key capacity lower bound is proposed. Numerical results show that our optimal IRS-assisted SKG scheme can achieve much higher achievable secret key capacity when compared with two benchmark schemes.