In this paper, the encryption-decryption-based set-membership filtering issue is considered for a class of networked two-dimensional systems with unknown-but-bounded noises. In order to preserve data privacy and reduce communication burden, an encryption-decryption mechanism is put forward based on the exclusive or logical operation technique and the one-time pad method, under which the data is encrypted into a ciphertext with finite bits before being transmitted through the networks. The aim of the addressed problem is to develop an encryption-decryption-based set-membership filter (EDSMF) that is capable of generating an ellipsoidal set that contains the true system state and ensuring the security performance. Sufficient conditions are established for the existence of the desired ellipsoidal set, and the corresponding EDSMF gains are obtained by applying the Lagrange multiplier method. Moreover, the uniform boundedness of the ellipsoidal shape-defining matrix is thoroughly studied. Finally, the effectiveness of the proposed filter design method is demonstrated by a practical example of a heat exchanger.