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In the state-of-the-art literature on cryptography and control theory, therehas been no systematic methodology of constructing cyber-physical systems thatcan achieve desired control performance while being protected againsteavesdropping attacks. In this paper, we tackle this challenging problem. Wefirst propose two novel notions referred to as sample identifying complexityand sample deciphering time in an encrypted-control framework. The formerexplicitly captures the relation between the dynamical characteristics ofcontrol systems and the level of identifiability of the systems while thelatter shows the relation between the computation time for the identificationand 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 lengthto prevent system identification with a given precision within a given lifespan of systems, and of an optimal controller to maximize both of the controlperformance and the difficulty of the identification. The efficiency of theproposed method in terms of security level and realtime-ness is investigatedthrough numerical simulations. To the best of our knowledge, this paper firstconnect the relationship between the security of cryptography and dynamicalsystems from a control-theoretic perspective.

Designing Optimal Key Lengths and Control Laws for Encrypted Control Systems based on Sample Identifying Complexity and Deciphering Time