Ring-LWE-Based Encrypted Controller With Unlimited Number of Recursive Multiplications and Effect of Error Growth
Yeongjun Jang, Joowon Lee, Seonhong Min, Hyesun Kwak, Junsoo Kim, Yongsoo Song · IEEE Transactions on Control of Network Systems · 2025
In this paper, we propose an encrypted dynamic controller that executes an unlimited number of recursive homomorphic multiplications on a Ring Learning With Errors (Ring-LWE) based cryptosystem without bootstrapping. The proposed controller exhibits lower computational complexity compared to existing encrypted controllers implemented on LWE based schemes due to the polynomial structure of Ring-LWE. However, the structural difference introduces additional difficulties in analyzing the effect of error growth; Ring-LWE based schemes inject multiple error coefficients when encrypting a single message, which accumulate under recursive homomorphic multiplications. We show that their effect on the control performance can be arbitrarily bounded by the closed-loop stability, thus recovering the performance of the unencrypted controller. Furthermore, a novel method to “pack” a vector into a polynomial is presented, which enhances computational and memory efficiency when applied to the proposed encrypted controller. The effectiveness of the proposed design is demonstrated through numerical simulations.