Resilient Homomorphic Encryption Scheme for Cyber-Physical Systems

Abstract

In this paper, a resilient homomorphic encryption scheme for cyber-physical systems (CPS) is presented. The proposed approach allows the calculation process of feedback controllers to be carried out in an encrypted environment. Moreover, the proposed approach is able to neutralize the effect of attacks injected in the encrypted signals sent over the network, so that the controller can still get the true sensor information. We shall first show that the proposed resilient homomorphic encryption scheme can calculate the multiplication of a matrix with a vector directly based on the ciphertexts, whose result after decryption is the same as the matrix-vector product got based on plaintexts. By transforming the control law into a matrix-vector product, the evaluation of the controller can be carried out with ciphertexts. As a result, the resilient homomorphic encryption scheme ensures the confidentiality of both the signals sent over the network and the controller parameters. In addition, a CPS utilizing the proposed encryption scheme is resilient to additive attacks, as long as the attacks are inside the resilience range. The proposed approach is illustrated through the well-established quadruple-tank benchmark process.