  In the state-of-the-art literature on cryptography and control theory, there
has been no systematic methodology of constructing cyber-physical systems that
can achieve desired control performance while being protected against
eavesdropping attacks. In this paper, we tackle this challenging problem. We
first propose two novel notions referred to as sample identifying complexity
and sample deciphering time in an encrypted-control framework. The former
explicitly captures the relation between the dynamical characteristics of
control systems and the level of identifiability of the systems while the
latter shows the relation between the computation time for the identification
and the key length of a cryptosystem. Based on these two tractable new notions,
we propose a systematic method for designing the both of an optimal key length
to prevent system identification with a given precision within a given life
span of systems, and of an optimal controller to maximize both of the control
performance and the difficulty of the identification. The efficiency of the
proposed method in terms of security level and realtime-ness is investigated
through numerical simulations. To the best of our knowledge, this paper first
connect the relationship between the security of cryptography and dynamical
systems from a control-theoretic perspective.
