Current-state opacity modelling and verification in partially observed Petri nets

Saadaoui, Ikram; Li, Zhiwu; Wu, Naiqin

doi:10.1016/j.automatica.2020.108907

Cited by 25 publications

(15 citation statements)

References 17 publications

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“…Unfortunately, it has been proved that opacity verification is generally undecidable for unbounded Petri nets [197,24,126]. On the other hand, for bounded Petri nets, many computationally efficient approaches have been developed recently by utilizing structural properties and modularity of Petri nets to overcome the issue of state-space explosion; see, e.g., [120,198,42,162,103,195]. However, all these results can only be applied to finite systems.…”

Section: 4mentioning

confidence: 99%

Secure-by-Construction Synthesis of Cyber-Physical Systems

Liu¹,

Trivedi²,

Yin³

2022

Preprint

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Correct-by-construction synthesis is a cornerstone of the confluence of formal methods and control theory towards designing safety-critical systems. Instead of following the time-tested, albeit laborious (re)design-verify-validate loop, correct-by-construction methodology advocates the use of continual refinements of formal requirements-connected by chains of formal proofs-to build a system that assures the correctness by design. A remarkable progress has been made in scaling the scope of applicability of correct-byconstruction synthesis-with a focus on cyber-physical systems that tie discrete-event control with continuous environment-to enlarge control systems by combining symbolic approaches with principled state-space reduction techniques. Unfortunately, in the security-critical control systems, the security properties are verified ex post facto the design process in a way that undermines the correct-by-construction paradigm. We posit that, to truly realize the dream of correct-by-construction synthesis for security-critical systems, security considerations must take center-stage with the safety considerations. Moreover, catalyzed by the recent progress on the opacity sub-classes of security properties and the notion of hyperproperties capable of combining security with safety properties, we believe that the time is ripe for the research community to holistically target the challenge of secure-by-construction synthesis. This paper details our vision by highlighting the recent progress and open challenges that may serve as bricks for providing a solid foundation for secure-by-construction synthesis of cyber-physical systems.The revolution in miniaturized communication devices in the beginning of this millennium contributed towards a revolution in the internet-of-things (IoT) and the networked systems woven around them: the cyber-physical systems (CPS). CPS are marked by a close-knit interaction of discrete computation and continuous control over a network and are playing critical roles in virtually every aspect of our modern experience ranging from consumer electronics to implantable medical devices, from smart cars to smart hospitals, and from controlling our power systems to safeguarding our nuclear rectors. These systems are clearly safety-critical as a bug in their design could be life threatening, but given their societal implications, they are also security-critical where a bug in their design may have the potential to jeopardize the privacy, trust, and economic interests of society built around them." We believe that the security considerations should be elevated as primary design drivers along with safety ones to tackle the design challenge of modern CPS and call for a need to expand the correct-byconstruction paradigm of designing safety-critical systems to encompass security: we call this paradigm secure-by-construction. This paper synthesizes ideas from three research communities: discrete event systems (DES), control systems (CS), and formal methods (FM) to pose and study central problems supporting...

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Section: 4mentioning

confidence: 99%

Secure-by-Construction Synthesis of Cyber-Physical Systems

Liu¹,

Trivedi²,

Yin³

2022

Preprint

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“…Many of the existing studies on DESs pay particular attention to the opacity problem. Various methods have investigated the issue of state-based opacity verification in DESs 27 , 28 . In 10 , the authors report a necessary and sufficient criterion using a non-deterministic finite automaton (NFA) by building an observer, i.e., transforming an NFA into a deterministic finite automaton (DFA) with a complexity of 29 , where n is the number of states in the NFA.…”

Section: Introductionmentioning

confidence: 99%

Current-state opacity verification in discrete event systems using an observer net

Labed

Saadaoui

et al. 2022

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Due to the proliferation of contemporary computer-integrated systems and communication networks, there is more concern than ever regarding privacy, given the potential for sensitive data exploitation. A recent cyber-security research trend is to focus on security principles and develop the foundations for designing safety-critical systems. In this work, we investigated the problem of verifying current-state opacity in discrete event systems using labeled Petri nets. A system is current-state opaque provided that the current-state estimate cannot be revealed as a subset of secret states. We introduced a new sub-model of the system, named an observer net. The observer net have the same structure as the plant, but it is distinguished by the use of colored markers as well as simultaneous and recursive transition enabling and firing, which offer an efficient state estimation. We considered two settings of the proposed approach: an on-line setting, in which a current-state opacity algorithm is proposed. The algorithm waits for the occurrence of an observable event and determines if the current observation of a plant reveals the secret behaviour, as well as, an off-line setting, where the verification problem is solved based on a state estimator called a colored estimator. In this context, necessary and sufficient conditions for verifying opacity are developed with illustrative examples to demonstrate the presented approach.

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“…In the context of DES, opacity has been studied very extensively in the past few years; see, e.g., some recent works [2], [5], [12], [13], [21], [25], [27], [30]- [33], [36], [42], [55] and the survey papers [18], [22]. Especially, to characterize different types of security requirements, different notions of opacity are proposed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Optimal Synthesis of Opacity-Enforcing Supervisors for Qualitative and Quantitative Specifications

Xie¹,

Yin²,

Li³

2021

Preprint

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In this paper, we investigate both qualitative and quantitative synthesis of optimal privacy-enforcing supervisors for partially-observed discrete-event systems. We consider a dynamic system whose information-flow is partially available to an intruder, which is modeled as a passive observer. We assume that the system has a "secret" that does not want to be revealed to the intruder. Our goal is to synthesize a supervisor that controls the system in a least-restrictive manner such that the closed-loop system meets the privacy requirement. For the qualitative case, we adopt the notion of infinite-step opacity as the privacy specification by requiring that the intruder can never determine for sure that the system is/was at a secret state for any specific instant. If the qualitative synthesis problem is not solvable or the synthesized solution is too restrictive, then we further investigate the quantitative synthesis problem so that the secret is revealed (if unavoidable) as late as possible. Effective algorithms are provided to solve both the qualitative and quantitative synthesis problems. Specifically, by building suitable information structures that involve information delays, we show that the optimal qualitative synthesis problem can be solved as a safety-game. The optimal quantitative synthesis problem can also be solved as an optimal total-cost control problem over an augmented information structure. Our work provides a complete solution to the standard infinite-step opacity control problem, which has not been solved without assumption on the relationship between controllable events and observable events. Furthermore, we generalize the opacity enforcement problem to the numerical setting by introducing the secret-revelation-time as a new quantitative measure.

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Current-state opacity modelling and verification in partially observed Petri nets

Cited by 25 publications

References 17 publications

Secure-by-Construction Synthesis of Cyber-Physical Systems

Secure-by-Construction Synthesis of Cyber-Physical Systems

Current-state opacity verification in discrete event systems using an observer net

Optimal Synthesis of Opacity-Enforcing Supervisors for Qualitative and Quantitative Specifications

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