CKKS Cryptosystem-Based Secure Parameter Identification for Multi-Participant ARX Systems

Abstract

This paper investigates parameter identification for multi-participant autoregressive systems with exogenous input (ARX systems) while protecting the system input and output. A novel Cheon-Kim-Kim-Song (CKKS) cryptosystem-based secure parameter identification algorithm is proposed. By combining a modified CKKS cryptosystem and a proxy re-encryption scheme, the algorithm enables the fusion center to perform homomorphic operations on the ciphertexts which are encrypted using different secret keys. A sufficient condition on the truncation value of the truncated discrete Gaussian noise is derived to ensure the indistinguishability under chosen-plaintext attack (IND-CPA) security of the algorithm under collusion and quantum attacks. For convergence analysis, an auxiliary plaintext sequence is constructed to characterize the encryption noise and quantization error in the encrypted estimate. Using this sequence, a criterion for avoiding plaintext overflow is given, based on which the mean square convergence and convergence rate of the algorithm are given. A numerical example demonstrates the effectiveness and superior performance of the algorithm.