{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T18:03:50Z","timestamp":1772906630809,"version":"3.50.1"},"reference-count":24,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,3,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Encrypted controllers using homomorphic encryption have proven to guarantee the privacy of measurement and control signals, as well as system and controller parameters, while regulating the system as intended. However, encrypting dynamic controllers has remained a challenge due to growing noise and overflow issues in the encoding. In this paper, we review recent approaches to dynamic encrypted control, such as bootstrapping, periodic resets of the controller state, integer reformulations, and FIR controllers, and equip them with a stability and performance analysis to evaluate their suitability. We complement the analysis with a numerical performance comparison on a benchmark system.<\/jats:p>","DOI":"10.1515\/auto-2025-0110","type":"journal-article","created":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T01:00:46Z","timestamp":1772845246000},"page":"233-242","source":"Crossref","is-referenced-by-count":0,"title":["Comparison and performance analysis of dynamic encrypted control approaches"],"prefix":"10.1515","volume":"74","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8022-472X","authenticated-orcid":false,"given":"Sebastian","family":"Schlor","sequence":"first","affiliation":[{"name":"Institute for Systems Theory and Automatic Control, University of Stuttgart , Stuttgart , Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3702-3658","authenticated-orcid":false,"given":"Frank","family":"Allg\u00f6wer","sequence":"additional","affiliation":[{"name":"Institute for Systems Theory and Automatic Control, University of Stuttgart , Stuttgart , Germany"}]}],"member":"374","published-online":{"date-parts":[[2026,3,9]]},"reference":[{"key":"2026030702044186037_j_auto-2025-0110_ref_001","doi-asserted-by":"crossref","unstructured":"J. H. Cheon, A. Kim, M. Kim, and Y. Song, \u201cHomomorphic encryption for arithmetic of approximate numbers,\u201d in Advances in Cryptology \u2013 ASIACRYPT 2017, Hong Kong, China, Springer Cham, 2017, pp.\u00a0409\u2013437.","DOI":"10.1007\/978-3-319-70694-8_15"},{"key":"2026030702044186037_j_auto-2025-0110_ref_002","doi-asserted-by":"crossref","unstructured":"K. Kogiso and T. Fujita, \u201cCyber-security enhancement of networked control systems using homomorphic encryption,\u201d in Proc. 54th IEEE Conf. Decision and Control (CDC), 2015.","DOI":"10.1109\/CDC.2015.7403296"},{"key":"2026030702044186037_j_auto-2025-0110_ref_003","doi-asserted-by":"crossref","unstructured":"A. B. Alexandru, A. Tsiamis, and G. J. Pappas, \u201cTowards private data-driven control,\u201d in Proc. 59th IEEE Conf. Decision and Control (CDC), 2020, pp.\u00a05449\u20135456.","DOI":"10.1109\/CDC42340.2020.9304149"},{"key":"2026030702044186037_j_auto-2025-0110_ref_004","doi-asserted-by":"crossref","unstructured":"M. Schulze Darup, \u201cEncrypted model predictive control in the cloud,\u201d in Privacy in Dynamical Systems, Singapore, Springer, 2019, pp.\u00a0231\u2013265.","DOI":"10.1007\/978-981-15-0493-8_11"},{"key":"2026030702044186037_j_auto-2025-0110_ref_005","doi-asserted-by":"crossref","unstructured":"N. Schl\u00fcter, M. Neuhaus, and M. Schulze Darup, \u201cEncrypted extremum seeking for privacy-preserving PID tuning as-a-service,\u201d in Proc. 2022 European Control Conf. (ECC), 2022.","DOI":"10.23919\/ECC55457.2022.9838380"},{"key":"2026030702044186037_j_auto-2025-0110_ref_006","doi-asserted-by":"crossref","unstructured":"N. Schl\u00fcter, P. Binfet, and M. Schulze Darup, \u201cA brief survey on encrypted control: From the first to the second generation and beyond,\u201d Annu. Rev. 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Schulze Darup, \u201cOn the design of stabilizing FIR controllers,\u201d in Proc. 10th Int. Conf. Control, Decision and Information Technologies (CoDIT), 2024, pp.\u00a02037\u20132042.","DOI":"10.1109\/CoDIT62066.2024.10708593"},{"key":"2026030702044186037_j_auto-2025-0110_ref_010","doi-asserted-by":"crossref","unstructured":"C. Gentry, A Fully Homomorphic Encryption Scheme, Ph.D. thesis, Stanford University, 2009.","DOI":"10.1145\/1536414.1536440"},{"key":"2026030702044186037_j_auto-2025-0110_ref_011","doi-asserted-by":"crossref","unstructured":"J. H. Cheon, K. Han, A. Kim, M. Kim, and Y. Song, \u201cBootstrapping for approximate homomorphic encryption,\u201d in Advances in Cryptology \u2013 EUROCRYPT 2018, Tel Aviv, Israel, Springer Cham, 2018, pp.\u00a0360\u2013384.","DOI":"10.1007\/978-3-319-78381-9_14"},{"key":"2026030702044186037_j_auto-2025-0110_ref_012","unstructured":"A. Al Badawi and Y. Polyakov. Demystifying bootstrapping in fully homomorphic encryption. 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