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Encrypted control has been introduced to protect controller data byencryption at the stage of computation and communication, by performing thecomputation directly on encrypted data. In this article, we first review andcategorize recent relevant studies on encrypted control. Approaches based onhomomorphic encryption, multi-party computation, and secret sharing areintroduced, compared, and then discussed with respect to computationalcomplexity, communication load, enabled operations, security, and researchdirections. We proceed to discuss a current challenge in the application ofhomomorphic encryption to dynamic systems, where arithmetic operations otherthan integer addition and multiplication are limited. We also introduce ahomomorphic cryptosystem called ``GSW-LWE'' and discuss its benefits that allowfor recursive multiplication of encrypted dynamic systems, without use ofcomputationally expensive bootstrapping techniques.

Comparison of encrypted control approaches and tutorial on dynamic systems using LWE-based homomorphic encryption