  Encrypted control is a promising method for the secure outsourcing of
controller computation to a public cloud. However, a feasible method for
security proofs of control has not yet been developed in the field of encrypted
control systems. Additionally, cryptography does not consider certain types of
attacks on encrypted control systems; therefore, the security of such a system
cannot be guaranteed using a secure cryptosystem. This study proposes a novel
security definition for encrypted control under attack for control systems
using cryptography. It applies the concept of provable security, which is the
security of cryptosystems based on mathematical proofs, to encrypted control
systems. Furthermore, this study analyzes the relation between the proposed
security and the conventional security of cryptosystems. The results of the
analysis demonstrated that the security of an encrypted control system can be
enhanced by employing secure homomorphic encryption.
