Ring-LWE based encrypted controller with unlimited number of recursive multiplications and effect of error growth
<|reference_start|>Ring-LWE based encrypted controller with unlimited number of recursive multiplications and effect of error growth: 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.<|reference_end|>
@article{jang2024ring-lwe,
    title={Ring-LWE based encrypted controller with unlimited number of recursive
  multiplications and effect of error growth},
    author={Yeongjun Jang, Joowon Lee, Seonhong Min, Hyesun Kwak, Junsoo Kim,
  Yongsoo Song},
    journal={arXiv preprint arXiv:2406.14372},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.14372},
    primaryClass={eess.SY cs.SY}
}