Quadratic Optimization Using Additive Homomorphic Encryption in CPS

In this paper, we propose a secure protocol to compute the quadratic optimization in a three-party outsourcing architecture in cyber-physical systems. To enable the real-world implementation, a fixed-point expression is given to represent the input of the protocol. Based on this, we define the recovery operations for decryption, addition, and multiplication. Considering the three-party-involved computation, we thoroughly analyze the privacy issues during the interaction processes. Then, the secure protocol is developed by designing encrypted addition, multiplication, and comparison based on the additive homomorphic encryption scheme. Finally, we propose a sufficient condition only related to the parameters of the fixed-point expression to guarantee that the recovered result is correct.