Enhanced Physical Layer Secret Key Generation via Beyond-Diagonal Reconfigurable Intelligent Surfaces in Multi-User MIMO Systems

Physical Layer Key Generation (PLKG) provides a promising approach for establishing secure cryptographic keys between legitimate parties. However, in static and quasi-static environments, the key generation rate is significantly limited due to the low entropy of the wireless channel. To overcome this, Reconfigurable Intelligent Surfaces (RIS) have been proposed to enhance the channel entropy by altering the phase of incident electromagnetic waves. This paper addresses this challenge by proposing a security architecture that integrates a Multi-Input Multi-Output (MIMO) base station with a Beyond-Diagonal Reconfigurable Intelligent Surface (BD-RIS) in multi-user scenarios, in the presence of an eavesdropper. Unlike conventional RIS, BD-RIS not only modifies the phase but also the magnitude of the impinging signals, introducing an additional degree of freedom that further enhances channel randomness. The secret key capacity of the proposed system is compared with that of conventional RIS in two scenarios: firstly, when a direct link exists alongside the BD-RIS-assisted link. Secondly, when the direct link is completely obstructed by an obstacle. Simulation results demonstrate that the proposed BD-RIS architecture outperforms conventional diagonal RIS (D-RIS) in all scenarios. Furthermore, the generated keys undergo randomness tests, successfully passing all National Institute of Standards and Technology (NIST) randomness subtests as well as the Autocorrelation (AC) test, confirming their suitability for secure communications. These findings establish BD-RIS as a promising technology for enhancing physical layer security in static environments for 5G/6G networks and IoT applications.