A Privacy-Preserving Quadratic Optimisation with Additive Homomorphic Encryption in Cyber-Physical Systems

In this paper, we propose a secure protocol to compute the quadratic optimisation problem under a three-party outsourcing architecture in the scenario of cyber-physical systems. To enable real-world implementation, we propose an encoding framework that uses a fixed-point expression and a truncated-mapping scheme to map real numbers into multiple data blocks, improving the protocol’s efficiency. Based on this, we define the recovery operations for decryption, addition, and multiplication. Considering computations involving three parties to solve the quadratic optimisation problem, we thoroughly analyse privacy issues during the interaction process. Then, a secure protocol is developed by designing privacy-preserving addition, multiplication, and comparison protocols based on the additive homomorphic encryption scheme. The data blowup and “0”-privacy leakage problems are addressed specifically for the gradient descent process by designing a secure addition protocol for block data and a secure comparison protocol. The efficiency and security of the proposed protocol are formally analysed in depth. Finally, through intensive experiments, we demonstrate the efficiency and security of our protocol.