  Protecting the parameters, states, and input/output signals of a dynamic
controller is essential for securely outsourcing its computation to an
untrusted third party. Although a fully homomorphic encryption scheme allows
the evaluation of controller operations with encrypted data, an encrypted
dynamic controller with the encryption scheme destabilizes a closed-loop system
or degrades the control performance due to overflow. This paper presents a
novel controller representation based on input-output history data to implement
an encrypted dynamic controller that operates without destabilization and
performance degradation. Implementation of this encrypted dynamic controller
representation can be optimized via batching techniques to reduce the time and
space complexities. Furthermore, this study analyzes the stability and
performance degradation of a closed-loop system caused by the effects of
controller encryption. A numerical simulation demonstrates the feasibility of
the proposed encrypted control scheme, which inherits the control performance
of the original controller at a sufficient level.
