Almost k-Step Opacity Enforcement in Stochastic Discrete-Event Systems via Differential Privacy

Zhao R., UZAM M., Li Z.

Mathematics, vol.13, no.8, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 8
  • Publication Date: 2025
  • Doi Number: 10.3390/math13081255
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: differential privacy, discrete event system, finite state automaton, k-step opacity
  • Yozgat Bozok University Affiliated: Yes

Abstract

This paper delves into current-state opacity enforcement in partially observed discrete event systems through an innovative application of differential privacy, which is fundamental for security-critical cyber–physical systems. An opaque system implies that an external agent cannot infer the predefined system secret via its observational output, such that the important system information flow cannot be leaked out. Differential privacy emerges as a robust framework that is pivotal for the protection of individual data integrity within these systems. Motivated by the differential privacy mechanism for information protection, this research proposes the secret string adjacency relation as a novel concept, assessing the similarity between potentially compromised strings and system-generated alternatives, thereby shielding the system’s confidential data from external observation. The development of secret string differential privacy is achieved by substituting sensitive strings. These substitution strings are generated by a modified Levenshtein automaton, following exponentially distributed generation probabilities. The verification and illustrative examples of the proposed mechanism are provided.