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Key generation is a promising technique to establish symmetric keys betweenresource-constrained legitimate users. However, key generation suffers from lowsecret key rate (SKR) in harsh environments where channel randomness islimited. To address the problem, reconfigurable intelligent surfaces (RISs) areintroduced to reshape the channels by controlling massive reflecting elements,which can provide more channel diversity. In this paper, we design a channelprobing protocol to fully extract the randomness from the cascaded channel,i.e., the channel through reflecting elements. We derive the analyticalexpressions of SKR and design a water-filling algorithm based on theKarush-Kuhn-Tucker (KKT) conditions to find the upper bound. To find theoptimal precoding and phase shift matrices, we propose an algorithm based onthe Grassmann manifold optimization methods. The system is evaluated in termsof SKR, bit disagreement rate (BDR) and randomness. Simulation results showthat our protocols significantly improve the SKR as compared to existingprotocol.

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