Phase-Shift Matrices Optimization in STAR-RIS-Aided Physical-Layer Key Generation

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.