  Fully Homomorphic Encryption (FHE) has made it possible to perform addition
and multiplication operations on encrypted data. Using FHE in control thus has
the advantage that control effort for a plant can be calculated remotely
without ever decrypting the exchanged information. FHE in its current form is
however not practically applicable for real-time control as its computational
load is very high compared to traditional encryption methods. In this paper a
reformulation of the Gentry FHE scheme is proposed and applied on an FPGA to
solve this problem. It is shown that the resulting FHE scheme can be
implemented for real-time stabilization of an inverted double pendulum using
discrete time control.
