Benign and Malicious Reconfigurable Intelligent Surfaces in MISO Wiretap Channels

Reconfigurable intelligent surface (RIS) has been developed as an efficient technology to make the electromagnetic environment programmable by adjusting the passive reflecting elements. Despite its benefits, the RIS may serve as a passive jammer by manipulating the environment when utilized by an adversary. In this paper, we investigate the impact of benign and malicious RISs on multiple-input single-output (MISO) wiretap channels. In particular, we design an efficient joint transmit beamforming and benign RIS phase shifting strategy under the worst-case secrecy rate achieved by optimizing the malicious RIS’s phase shifting strategy. In doing so, we formulate a max-min secrecy rate problem, and propose a suboptimal algorithm based on alternating optimization (AO) with two inner gradient-descent-ascent (GDA) algorithms. Numerical results show that a positive secrecy rate is guaranteed when the benign RIS’s reflecting channel dominates the malicious RIS’s reflecting channel.

I. Introduction

Reconfigurable intelligent surface (RIS) is an enabling technology to tune radio signal propagation in wireless networks [1]. By smartly tuning the signal reflection via a large number of low-cost passive reflecting elements, the RIS is capable of dynamically altering wireless channels to strengthen the desired signal and/or suppress the undesired signal [2], [3]. RIS has advantages in enhancing the secure transmission of wireless communications via physical layer security (PLS). For example, the transmitter (Alice) can deploy low-cost RISs, called benign RISs, to improve the secrecy rate, e.g., [4]- [7]. The eavesdropper (Eve) can also use RISs, called malicious RISs, to deteriorate the PLS of wireless communications [8]. There are few works on PLS with the interplay between benign and malicious RISs on the secrecy rate. In [9], the authors consider a wiretap channel, where Eve uses an RIS to degrade the legitimate receiver’s (Bob’s) reception and to improve the illegitimate receiver’s (Eve’s) reception by passive jamming. In [10], a new scenario is studied: Bob and Eve use independent RISs under perfect channel state information (CSI). Moreover, compared to [9], the work in [10] considers a benign RIS as well. In [10], the beamforming strategy (Alice’s strategy) as well as the design of the benign RIS (Bob’s strategy) are available to Eve when she is tuning her own RISs (Eve’s strategy). The beamforming is suboptimal due to employing the closed form expression in [11] without considering the worst-case secrecy rate achieved by optimizing the malicious RIS’s strategy. In this way, the system’s robustness against the malicious RIS’s attacks as well as the convergence of GDA cannot be guaranteed. Our contributions are summarized as follows: