  In this paper, we propose a method to encrypt linear dynamic controllers that
enables an unlimited number of recursive homomorphic multiplications on a Ring
Learning With Errors (Ring-LWE) based cryptosystem without bootstrapping.
Unlike LWE based schemes, where a scalar error is injected during encryption
for security, Ring-LWE based schemes are based on polynomial rings and inject
error as a polynomial having multiple error coefficients. Such errors
accumulate under recursive homomorphic operations, and it has been studied that
their effect can be suppressed by the closed-loop stability when dynamic
controllers are encrypted using LWE based schemes. We show that this also holds
for the proposed controller encrypted using a Ring-LWE based scheme.
Specifically, only the constant terms of the error polynomials affect the
control performance, and their effect can be arbitrarily bounded even when the
noneffective terms diverge. Furthermore, a novel packing algorithm is applied,
resulting in reduced computation time and enhanced memory efficiency.
Simulation results demonstrate the effectiveness of the proposed method.
