State Estimation with Secrecy against Eavesdroppers

Tsiamis, Anastasios; Gatsis, Konstantinos; Pappas, George J.

doi:10.1016/j.ifacol.2017.08.1563

Cited by 51 publications

(38 citation statements)

References 28 publications

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“…A control-theoretic approach was recently employed in [21], [22], where the performance metric of both the user and the eavesdropper is minimum mean square error (mmse). This framework does not use any encoding.…”

Section: Introductionmentioning

confidence: 99%

“…This framework does not use any encoding. Instead, a secrecy mechanism is employed, which withholds information, either randomly [21] or deterministically [22]. In the case of unstable systems, under certain conditions, the eavesdropper's expected error can grow to infinity while the user's expected error remains bounded.…”

Section: Introductionmentioning

confidence: 99%

“…The dynamical system is modeled as linear, while the channel, is modeled as a packet drop channel. Similar to [19]- [21], we assume that the system is unstable (see Section II for discussion). Both the user and the eavesdropper know the coding scheme and use minimum mean square error estimators as decoders.…”

Section: Introductionmentioning

confidence: 99%

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State-Secrecy Codes for Networked Linear Systems

Tsiamis

Gatsis

Pappas

2020

IEEE Trans. Automat. Contr.

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In this paper, we study the problem of remote state estimation, in the presence of a passive eavesdropper. An authorized user estimates the state of an unstable linear plant, based on the packets received from a sensor, while the packets may also be intercepted by the eavesdropper. Our goal is to design a coding scheme at the sensor, which encodes the state information, in order to impair the eavesdropper's estimation performance, while enabling the user to successfully decode the sent messages. We introduce a novel class of codes, termed State-Secrecy Codes, which use acknowledgment signals from the user and apply linear time-varying transformations to the current and previously received states. By exploiting the properties of the system's process noise, the channel physical model and the dynamics, these codes manage to be fast, efficient and, thus, suitable for real-time dynamical systems. We prove that under minimal conditions, State-Secrecy Codes achieve perfect secrecy, namely the eavesdropper's estimation error grows unbounded almost surely, while the user's estimation performance is optimal. These conditions only require that at least once, the user receives the corresponding packet while the eavesdropper fails to intercept it. Even one occurrence of this event renders the eavesdropper's error unbounded with asymptotically optimal rate of increase. State-Secrecy Codes are provided and studied for two cases, i) when direct state measurements are available, and ii) when we only have output measurements. The theoretical results are illustrated in simulations.the definition (7) of P k and equation (35), we have P k = Cov {x k |J k (s 0:k )} in C. There exist two cases: Case I: s k = 0. In this case, by the definition (33), we have J k (s 0:k ) = J k (s 0:k−1 ). Therefore:where the third equality follows from (35). Case II: s k = 1. Here, by (35):where z k (s 0:k ) is defined in (33). Since all variables are Gaussian, we can compute the posterior estimation error using the Schur complement formula applied to the covariance matrix of x k and z k (s 0:k ) given J k (s 0:k−1 ) (see [28]). By (35), in C we haveHence, by the Schur's complement formula, we have P k = Σ xx − Σ xz (Σ zz ) † Σ zx in C, when s k = 1.We can describe both cases with one equation:since s k = γ k in C. But this holds for any event C = {g 0:k = s 0:k }. Thus, the result holds everywhere, since the events {g 0:k = s}, s ∈ {0, 1} 2k+1 are a partition of the probability space.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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State-Secrecy Codes for Networked Linear Systems

Tsiamis

Gatsis

Pappas

2020

IEEE Trans. Automat. Contr.

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“…Meanwhile, the user can always decode the packets and has optimal mmse. Related work can be found in [17]- [19], where a noncoding approach is adopted. A simple mechanism which withholds measurements is employed, but with high probability the eavesdropper might have very small estimation error infinitely often.…”

Section: Introductionmentioning

confidence: 99%

“…The confidentiality guarantees for the plant's current state are comparable to the information theoretic ones, overcoming the limitations of[17]-[19]; almost surely the eavesdropper's information matrix converges to the open-loop prediction one. These guarantees do not depend on the computational capabilities of the eavesdropper.…”

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confidence: 96%

An Information Matrix Approach for State Secrecy

Tsiamis

Gatsis

Pappas

2018

2018 IEEE Conference on Decision and Control (CDC)

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This paper studies the problem of remote state estimation in the presence of a passive eavesdropper. A sensor measures a linear plant's state and transmits it to an authorized user over a packet-dropping channel, which is susceptible to eavesdropping. Our goal is to design a coding scheme such that the eavesdropper cannot infer the plant's current state, while the user successfully decodes the sent messages. We employ a novel class of codes, termed State-Secrecy Codes, which are fast and efficient for dynamical systems. They apply linear timevarying transformations to the current and past states received by the user. In this way, they force the eavesdropper's information matrix to decrease with asymptotically the same rate as in the open-loop prediction case, i.e. when the eavesdropper misses all messages. As a result, the eavesdropper's minimum mean square error (mmse) for the unstable states grows unbounded, while the respective error for the stable states converges to the open-loop prediction one. These secrecy guarantees are achieved under minimal conditions, which require that, at least once, the user receives the corresponding packet while the eavesdropper fails to intercept it. Meanwhile, the user's estimation performance remains optimal. The theoretical results are illustrated in simulations. arXiv:1809.07312v2 [cs.SY]

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Optimal event‐triggered transmission scheduling for privacy‐preserving wireless state estimation

Leong

Quevedo

2020

Intl J Robust & Nonlinear

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SummaryWe consider a remote state estimation problem in the presence of an eavesdropper over packet dropping links. A smart sensor transmits its local estimates to a legitimate remote estimator, in the course of which an eavesdropper can randomly overhear the transmission. This problem has been well studied for unstable dynamical systems, but seldom for stable systems. In this article, we target at stable and marginally stable systems and aim to design an event‐triggered scheduling strategy by minimizing the expected error covariance at the remote estimator and keeping that at the eavesdropper above a user‐specified lower bound. To this end, we model the evolution of the error covariance as an infinite recurrent Markov chain and develop a recurrence relation to describe the stationary distribution of the state at the eavesdropper. Monotonicity and convergence properties of the expected error covariance are further investigated and employed to solve the optimization problem. Numerical examples are provided to validate the theoretical results.

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State Estimation with Secrecy against Eavesdroppers

Cited by 51 publications

References 28 publications

State-Secrecy Codes for Networked Linear Systems

State-Secrecy Codes for Networked Linear Systems

An Information Matrix Approach for State Secrecy

Optimal event‐triggered transmission scheduling for privacy‐preserving wireless state estimation

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