Asymptotic stabilization under homomorphic encryption: A re-encryption free method
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915240021590016 |
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| author | Feng, Shuai Ma, Qian Kim, Junsoo Xu, Shengyuan |
| author_facet | Feng, Shuai Ma, Qian Kim, Junsoo Xu, Shengyuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09248 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic stabilization under homomorphic encryption: A re-encryption free method Feng, Shuai Ma, Qian Kim, Junsoo Xu, Shengyuan Systems and Control Cryptography and Security 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. |
| title | Asymptotic stabilization under homomorphic encryption: A re-encryption free method |
| topic | Systems and Control Cryptography and Security |
| url | https://arxiv.org/abs/2504.09248 |