Joint Precoding and Phase Shift Design in Reconfigurable Intelligent Surfaces-Assisted Secret Key Generation

Key generation is a promising technique to establish symmetric keys between resource-constrained legitimate users. However, key generation suffers from low secret key rate (SKR) in harsh environments where channel randomness is limited. To address the problem, reconfigurable intelligent surfaces (RISs) are introduced to reshape the channels by controlling massive reflecting elements, which can provide more channel diversity. In this paper, we design a channel probing protocol to fully extract the randomness from the cascaded channel, i.e., the channel through reflecting elements. We derive the analytical expressions of SKR and design a water-filling algorithm based on the Karush-Kuhn-Tucker (KKT) conditions to find the upper bound. To find the optimal precoding and phase shift matrices, we propose an algorithm based on the Grassmann manifold optimization methods. The system is evaluated in terms of SKR, bit disagreement rate (BDR) and randomness. Simulation results show that our protocols significantly improve the SKR as compared to existing protocol.