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In this paper, we present a dynamic feedback controller that computes thenext state and the control signal over encrypted data using homomorphicproperties of cryptosystems, whose performance is equivalent to the lineardynamic controllers over real-valued data. Assuming that the input as well asthe output of the plant is encrypted and transmitted back to the controller, itis shown that the state matrix of any linear time-invariant controller can bealways converted to a matrix of integer components. This allows the dynamicfeedback controller to operate for infinite time horizon without decryption orreset of its internal state. For implementation in practice, we illustrate theuse of a cryptosystem that is based on the Learning With Errors problem, whichallows both multiplication and addition over encrypted data. It is also shownthat the effect of injected random numbers during encryption for security canbe maintained within a small bound by way of the closed-loop stability.

Dynamic controller that operates over homomorphically encrypted data for infinite time horizon