  In this paper, we investigate the physical layer security in the
reconfigurable intelligent surface (RIS)-aided cell-free networks. A maximum
weighted sum secrecy rate problem is formulated by jointly optimizing the
active beamforming (BF) at the base stations and passive BF at the RISs. To
handle this non-trivial problem, we adopt the alternating optimization to
decouple the original problem into two sub-ones, which are solved using the
semidefinite relaxation and continuous convex approximation theory. To decrease
the complexity for obtaining overall channel state information (CSI), we extend
the proposed framework to the case that only requires part of the RIS' CSI.
This is achieved via deliberately discarding the RIS that has a small
contribution to the user's secrecy rate. Based on this, we formulate a mixed
integer non-linear programming problem, and the linear conic relaxation is used
to obtained the solutions. Finally, the simulation results show that the
proposed schemes can obtain a higher secrecy rate than the existing ones.
