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

Input-Output History Feedback Controller for Encrypted Control with Leveled Fully Homomorphic Encryption