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Model-Free Undetectable Attacks on Linear Systems Using LWE-Based Encryption
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).ORCID iD: 0000-0001-6558-3807
Seoul Natl Univ Sci & Technol, Dept Elect & Informat Engn, Seoul 01811, South Korea..
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).ORCID iD: 0000-0003-1835-2963
2023 (English)In: IEEE Control Systems Letters, E-ISSN 2475-1456, Vol. 7, p. 1249-1254Article in journal (Refereed) Published
Abstract [en]

We show that the homomorphic property, a desired property in encrypted control, can lead to failure in the cyber defense of a dynamical control system from undetectable attacks, even though individual signal sequences remain unknown to the attacker. We consider an encryption method based on the Learning with Errors (LWE) problem and demonstrate how model-free undetectable attacks on linear systems over integers can be computed from sampled inputs and outputs that are encrypted. Previous work has shown that computing such attacks is possible on nonencrypted systems. Applying this earlier work to our scenario, with minor modifications, typically amplifies the error in encrypted messages unless a short vector problem is solved. Given that an attacker obtains a short vector, we derive the probability that the attack is detected and show how it explicitly depends on the encryption parameters. Finally, we simulate an attack obtained by our method on an encrypted linear system over integers and conduct an analysis of the probability that the attack will be detected.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE) , 2023. Vol. 7, p. 1249-1254
Keywords [en]
Detectors, Trajectory, Encryption, Linear systems, Dynamical systems, Control systems, Sensors, Sampled-data control, quantized systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-324532DOI: 10.1109/LCSYS.2023.3234004ISI: 000917748200002Scopus ID: 2-s2.0-85147205024OAI: oai:DiVA.org:kth-324532DiVA, id: diva2:1741776
Note

QC 20230307

Available from: 2023-03-07 Created: 2023-03-07 Last updated: 2023-08-25Bibliographically approved

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Alisic, RijadSandberg, Henrik

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