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IEEE Transactions on Information Forensics and Security

On Maximizing the Sum Secret Key Rate for Reconfigurable Intelligent Surface-Assisted Multiuser Systems

Guyue Li, Chen K. Sun, Wei Xu, Marco Di Renzo, Aiqun Hu

Published Dec 24, 2021• 79 citations
Publisher

Abstract

Channel reciprocity-based key generation (CRKG) has recently emerged as a new technique to address the problem of key distribution in wireless networks. However, as this approach relies upon the characteristics of fading channels, the corresponding secret key rate may be low when the communication link is blocked. To enhance the applicability of CRKG in harsh propagation scenarios, this paper introduces a novel multiuser key generation scheme, which is referred to as RIS-assisted multiuser key generation (RMK) that leverages the reconfigurable intelligent surface (RIS) technology for appropriately shaping the environment and enhancing the sum secret key rate between an access point and multiple users. In the RMK scheme, an RIS-induced channel, rather than the direct channel, serves as the key source. We derive a general closed-form expression of the secret key rate and optimize the configuration of the RIS to maximize the sum secret key rate over independent and correlated fading channels in the presence of multiple users. In the presence of independent fading, we introduce a low-complexity algorithm based on the Karush-Kuhn-Tucker (KKT) condition. In the presence of correlated fading, the optimization problem is non-convex and challenging to solve. To tackle it, we propose a new optimization algorithm based on the semi-definite relaxation (SDR) and successive convex approximation (SCA) methods. Simulation results demonstrate that the proposed RMK scheme outperforms existing RIS-assisted algorithms and achieves a near-optimal sum secret key rate over independent and correlated fading channels.

DOI
10.1109/tifs.2021.3138612

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Channel reciprocity-based key generation (CRKG) has recently emerged as a new technique to address the problem of key distribution in wireless networks. However, as this approach relies upon the characteristics of fading channels, the corresponding secret key rate may be low when the communication link is blocked. To enhance the applicability of CRKG in harsh propagation scenarios, this paper introduces a novel multiuser key generation scheme, which is referred to as RIS-assisted multiuser key generation (RMK) that leverages the reconfigurable intelligent surface (RIS) technology for appropriately shaping the environment and enhancing the sum secret key rate between an access point and multiple users. In the RMK scheme, an RIS-induced channel, rather than the direct channel, serves as the key source. We derive a general closed-form expression of the secret key rate and optimize the configuration of the RIS to maximize the sum secret key rate over independent and correlated fading channels in the presence of multiple users. In the presence of independent fading, we introduce a low-complexity algorithm based on the Karush-Kuhn-Tucker (KKT) condition. In the presence of correlated fading, the optimization problem is non-convex and challenging to solve. To tackle it, we propose a new optimization algorithm based on the semi-definite relaxation (SDR) and successive convex approximation (SCA) methods. Simulation results demonstrate that the proposed RMK scheme outperforms existing RIS-assisted algorithms and achieves a near-optimal sum secret key rate over independent and correlated fading channels.
By exploiting the entropy of wireless channels, physical layer key generation (PLKG) has gained considerable attention in recent years. Due to the characteristic of dynamic controlling of wireless channels, reconfigurable intelligent surface (RIS) can improve the key generation rate (KGR). Simultaneous transmission and reflection reconfigurable intelligent surface (STAR- RIS) can extend the half-space coverage to full-space coverage. This paper proposes a STAR-RIS-assisted physical layer key generation (SRKG) scheme in a multi-user case. The objective is to maximize the sum KGR by jointly designing the transmitting and reflecting coefficients (TARCs). We propose an iterative algorithm based on alternating optimization (AO), utilizing successive convex approximation (SCA) and semi-definite relaxation (SDR) methods, to solve the non-convex optimization problem in the presence of correlated channels. We also propose a low-complexity algorithm based on Lagrange multipliers to jointly optimize TARCs considering independent fading. Finally, the simulation results validate that, compared with the PLKG scheme assisted by traditional RIS (T-RIS), the proposed SRKG scheme can achieve higher sum KGR in a wider range under correlated and independent channel conditions.
Abstract Reconfigurable intelligent surface (RIS)‐assisted physical layer key generation plays an important role in the eavesdropping problem on a typical multi‐user scenario of wireless networks. Existing RIS‐assisted physical key generation technology mainly solved the security issues in the single‐antenna and multi‐user scenario, which is based on the idealistic assumption of a spatially independent channel model at the RIS. It limits the degrees of freedom and neglects the existence of channel spatial correlation, which would possibly degrade the sum key generation rate (SKGR). To solve the above problem, this paper proposes a secret key generation scheme for RIS‐assisted multiple‐input single‐output multi‐user system. This scheme establishes a spatial correlation channel model, which comprehensively considers the influence of spatial correlation among antennas of the base station (BS), multi‐user, and RIS elements on SKGR. Based on this, a key generation framework is designed to generate a more secure secret key with the maximum SKGR. Specifically, a closed‐form SKGR expression and an optimization problem formulation are obtained to obtain the joint optimal coefficient of the BS and RIS. Then, the difference convex‐successive convex approximation based alternating optimization algorithm is proposed to solve this optimization problem. The simulation results show that the proposed scheme has improved 10‐bit/channel use compared with the randomization scheme of BS precoding and RIS reflection coefficient. It also has an improvement of 12‐bit/channel use compared with the spatially independent scheme.
This paper investigates the simultaneously transmitting and reflecting reconfigurable surface (STAR-RIS) assisted physical layer key generation (PKG) for multiuser networks. We propose a novel STAR-RIS-assisted PKG protocol and formulate a sum secret key rate maximization problem by jointly optimizing the active and passive beamforming. To address the non-convex problem, a block coordinate descent (BCD) algorithm is developed, using both semidefinite relaxation (SDR) and successive convex approximation (SCA) methods to optimize active and passive precoding alternately. Simulation results demonstrate the key generation performance of the proposed algorithm outperforms schemes that STAR-RISs using the random configuration and conventional reflecting/transmitting-only RISs.
Physical-layer security (PLS) is superior to classical cryptography techniques due to its notion of perfect secrecy and independence to an eavesdropper's computational power. One form of PLS arises when Alice and Bob (the legitimate users) exchange signals to extract a common key from the random common channels. The drawback of extracting keys from wireless channels is the ample dependence on the dynamicity and fluctuations of the radio channel. However, some radio channels are constant such as line-of-sight (LoS) and can be estimated by Eve (an illegitimate user), or can be quite static in behavior due to the presence low-mobility users thus restricting the amount of randomness. This in turn lowers the secret key rate (SKR) defined as the number of bits of key generated per channel use. In this work, we aim to address this challenge by using a reconfigurable intelligent surface (RIS) to produce random phases at certain carefully curated intervals such that it disrupts the channel in low-entropy environments. We propose an RIS assisted key generation method, study its performance, and compare with benchmarks to observe the benefit of using an RIS while considering various important metrics such as key mismatch rate and average secret key throughput. Simulations are made to validate our theoretical findings showing an improvement in performance when an RIS is deployed.
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.
Reconfigurable intelligent surface (RIS) has been widely studied as a promising approach in improving secret key rate (SKR) for physical layer (PHY) secret key generation (SKG). Existing RIS-assisted PHY SKG studies mainly focus on improving the SKR by optimizing RIS phase. However, RIS can also be exploited by active attackers to contaminate the channel probing. As a result, there is a trade-off between the increased randomness and the improved correlation between legitimate channels and eavesdropping channels in a RIS-assisted SKG system under channel contamination. In this paper, we study the impact of RIS on PHY SKG by analyzing the SKR performance. A closed-form expression for the lower-bound of secret key capacity is obtained. Theoretical analysis shows that gains of legitimate channel, eavesdropping channel, and RIS-induced channels are key parameters in determining whether the assisting RIS is beneficial or harmful to the PHY SKG. Further, a SKR maximization problem under channel contamination is proposed and solved. Results show that the assisting RIS is definitely harmful to the SKG when the gain ratio of legitimate channel and eavesdropping channel is reduced with the leverage of RIS, while it can significantly improve the SKR with an optimized RIS phase when the gain ratio is improved with the help of RIS.