Secure motion control of micro-spacecraft using semi-homomorphic encryption

This paper studies the secure motion control problem for micro-spacecraft systems. A novel semi-homomorphic encrypted control framework, consisting of a logarithmic quantizer, two uniform quantizers, and an encrypted control law based on the Paillier cryptosystem is developed. More specifically, a logarithmic quantizer is adopted as a digitizer to convert the continuous relative motion information to digital signals. Two uniform quantizers with different quantization sensitivities are designed to encode the control gain matrix and digitized motion information to integer values. Then, we develop an encrypted state-feedback control law based on the Paillier cryptosystem, which allows the controller to compute the control input using only encrypted data. Using the Lyapunov stability theory and the homomorphic property of the Paillier cryptosystem, we prove that all signals in the closed-loop system are uniformly ultimately bounded. Different from the traditional motion control laws of spacecraft, the proposed encrypted control framework ensures the security of the exchanged data over the communication network of the spacecraft, even when communication channels are eavesdropped by malicious adversaries. Finally, we verify the effectiveness of the proposed encrypted control framework using numerical simulations.