Secure and private control using semi-homomorphic encryption

Networked control systems with encrypted sensors measurements is considered. Semi-homomorphic encryption, specifically the Paillier encryption, is used so that the controller can perform the required computation on the encrypted data. Conditions on the parameters of the encryption technique are provided that guarantee the stability and the performance of the closed-loop system. The results are subsequently extended Laplacian based distributed systems, such as formation-seeking algorithms. It is shown that the problem of figuring out the state measurements of the neighbouring agents of a compromised agent upon using the proposed algorithm is numerically intractable.