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arXiv · 2504.09248

Asymptotic stabilization under homomorphic encryption: A re-encryption free method

Shuai Feng·Qian Ma·Junsoo Kim·Shengyuan Xu
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Abstract

In this paper, we propose methods to encrypted a pre-given dynamic controller with homomorphic encryption, without re-encrypting the control inputs. We first present a preliminary result showing that the coefficients in a pre-given dynamic controller can be scaled up into integers by the zooming-in factor in dynamic quantization, without utilizing re-encryption. However, a sufficiently small zooming-in factor may not always exist because it requires that the convergence speed of the pre-given closed-loop system should be sufficiently fast. Then, as the main result, we design a new controller approximating the pre-given dynamic controller, in which the zooming-in factor is decoupled from the convergence rate of the pre-given closed-loop system. Therefore, there always exist a (sufficiently small) zooming-in factor of dynamic quantization scaling up all the controller's coefficients to integers, and a finite modulus preventing overflow in cryptosystems. The process is asymptotically stable and the quantizer is not saturated.

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Shuai Feng, Qian Ma, Junsoo Kim, Shengyuan Xu. 2025-04-12. Asymptotic stabilization under homomorphic encryption: A re-encryption free method. https://arxiv.org/abs/2504.09248

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