Secure Parameter Identification for Multi-Participant ARX Systems via CKKS Cryptosystem-Based Proxy Re-Encryption

摘要

This paper investigates the parameter identification for multi-participant autoregressive exogenous input (ARX) systems while protecting the system input and output. To do so, the discrete Gaussian noise in the standard Cheon-Kim-Kim-Song (CKKS) cryptosystem is replaced with a truncated one. By using the CKKS cryptosystem with the truncated discrete Gaussian noise and the key-switching technique, a proxy re-encryption scheme is developed. Based on this scheme, a secure parameter identification algorithm is proposed for multi-participant ARX systems. By rigorously proving that the statistical distance between the discrete Gaussian noise and the truncated one is negligible, the polynomial-time reduction between the standard Ring-Learning with Errors (RLWE) problem and the RLWE problem with the truncated discrete Gaussian noise is established. This result ensures the indistinguishability under chosen-plaintext attacks (IND-CPA) security of the algorithm. By giving a lower bound condition on the size of the plaintext space, the computational overflow in encryption is avoided. Based on this condition, the mean square convergence and convergence rate of the algorithm are given. The trade-off between the security level and the convergence of the algorithm is presented. Finally, a numerical example is given to verify the effectiveness of the algorithm.