  Encrypted control systems allow to evaluate feedback laws on external servers
without revealing private information about state and input data, the control
law, or the plant. While there are a number of encrypted control schemes
available for linear feedback laws, only few results exist for the evaluation
of more general control laws. Recently, an approach to encrypted polynomial
control was presented, relying on two-party secret sharing and an inter-server
communication protocol using homomorphic encryption. As homomorphic encryptions
are much more computationally demanding than secret sharing, they make up for a
tremendous amount of the overall computational demand of this scheme. For this
reason, in this paper, we demonstrate that multi-party computation enables
secure polynomial control based solely on secret sharing. We introduce a novel
secure three-party control scheme based on three-party computation. Further, we
propose a novel $n$-party control scheme to securely evaluate polynomial
feedback laws of arbitrary degree without inter-server communication. The
latter property makes it easier to realize the necessary requirement regarding
non-collusion of the servers, with which perfect security can be guaranteed.
Simulations suggest that the presented control schemes are many times less
computationally demanding than the two-party scheme mentioned above.
