  Encrypted control has been introduced to protect controller data by
encryption at the stage of computation and communication, by performing the
computation directly on encrypted data. In this article, we first review and
categorize recent relevant studies on encrypted control. Approaches based on
homomorphic encryption, multi-party computation, and secret sharing are
introduced, compared, and then discussed with respect to computational
complexity, communication load, enabled operations, security, and research
directions. We proceed to discuss a current challenge in the application of
homomorphic encryption to dynamic systems, where arithmetic operations other
than integer addition and multiplication are limited. We also introduce a
homomorphic cryptosystem called ``GSW-LWE'' and discuss its benefits that allow
for recursive multiplication of encrypted dynamic systems, without use of
computationally expensive bootstrapping techniques.
