Upper-Bound Analysis of Performance Degradation in Encrypted Control System

This study analyzes the impact of encrypting controllers by public-key cryptography on the control performances. Particular public-key cryptography enables the concealment of signals over the communication links and the controller parameters. The encryption process requires their values to be changed into integers that form the ciphertext. This process causes quantization errors, and it leads to degradation of the control performance. This encryption-induced quantization error is related to a key length that is set before generating the public and private keys, and its length represents the size of a ciphertext space. This study presents a theorem that states that the performance degradation caused by the quantized error has an upper bound that is a function of the key length and as the key length incrementally increases, encryption-induced performance degradation of the control system exponentially decreases. A numerical example is used to verify the attributes of the theorem.