In this paper, we present a method to encrypt dynamic controllers that can be implemented through most homomorphic encryption schemes, including somewhat, leveled fully, and fully homomorphic encryption. To this end, we represent the output of the given controller as a linear combination of a fixed number of previous inputs and outputs. As a result, the encrypted controller involves only a limited number of homomorphic multiplications on every encrypted data, assuming that the output is re-encrypted and transmitted back from the actuator. A guidance for parameter choice is also provided, ensuring that the encrypted controller achieves predefined performance for an infinite time horizon. Furthermore, we propose a customization of the method for Ring-Learning With Errors (Ring-LWE) based cryptosystems, where a vector of messages can be encrypted into a single ciphertext and operated simultaneously, thus reducing computation and communication loads. Unlike previous results, the proposed customization does not require extra algorithms such as rotation, other than basic addition and multiplication. Simulation results demonstrate the effectiveness of the proposed method.

翻译：摘要：本文提出一种方法，可通过大多数同态加密方案（包括部分同态、层次全同态和全同态加密）实现动态控制器的加密。为此，我们将给定控制器的输出表示为固定数量先前输入与输出的线性组合。由此，假设输出经重新加密后从执行器回传，加密控制器针对每个加密数据仅涉及有限次同态乘法。本文还提供了参数选择指南，确保加密控制器在无限时域内达到预定义性能。此外，我们针对基于环误差学习（Ring-LWE）的密码系统提出方法定制，其中消息向量可加密为单一密文并同步操作，从而降低计算与通信负载。与以往结果不同，本定制方法除基本加法和乘法外，无需轮转等额外算法。仿真结果验证了所提方法的有效性。