Privacy in Feedback: The Differentially Private LQG

Hale, Matthew; Jones, Adam G.; Leahy, Kevin

doi:10.23919/acc.2018.8431397

Cited by 26 publications

(21 citation statements)

References 12 publications

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“…Specifically, we will consider that a zero‐mean Gaussian random noise

y_{k}^{a} \in ℝ^{m}

is added to the output y k with the understanding that

y_{k}^{a} \sim 𝒩 (0, \sum_{y}^{a})

with

\sum_{y}^{a} = σ_{y}^{2} I_{m}

and I m is an m th‐order identity matrix. By following the work of Reference 1, in order to meet the

(ϵ, δ)

‐differential privacy requirements we select,

σ_{y} \geq \frac{d_{y}}{2 ϵ} (K_{δ} + \sqrt{K_{δ}^{2} + 2 ϵ})

, where

K_{δ} = {(\frac{1}{\sqrt{2 π}} \int_{δ}^{\infty} e^{- \frac{t^{2}}{2}} d t)}^{- 1}

ϵ, δ \in ℝ^{+}

and

d_{y} \in ℝ^{+}

stands for the 2‐norm sensitivity, which represents the difference between systems with and without the added noise 34 …”

Section: Problem Formulationmentioning

confidence: 99%

A data‐based private learning framework for enhanced security against replay attacks in cyber‐physical systems

Zhai

Vamvoudakis

2020

Intl J Robust & Nonlinear

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Summary This article develops a data‐based and private learning framework of the detection and mitigation against replay attacks for cyber‐physical systems. Optimal watermarking signals are added to assist in the detection of potential replay attacks. In order to improve the confidentiality of the output data, we first add a level of differential privacy. We then use a data‐based technique to learn the best defending strategy in the presence of worst case disturbances, stochastic noise, and replay attacks. A data‐based Neyman‐Pearson detector design is also proposed to identify replay attacks. Finally, simulation results show the efficacy of the proposed approach along with a comparison of our data‐based technique to a model‐based one.

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“…Specifically, we will consider that a zero‐mean Gaussian random noise

y_{k}^{a} \in ℝ^{m}

is added to the output y k with the understanding that

y_{k}^{a} \sim 𝒩 (0, \sum_{y}^{a})

with

\sum_{y}^{a} = σ_{y}^{2} I_{m}

and I m is an m th‐order identity matrix. By following the work of Reference 1, in order to meet the

(ϵ, δ)

‐differential privacy requirements we select,

σ_{y} \geq \frac{d_{y}}{2 ϵ} (K_{δ} + \sqrt{K_{δ}^{2} + 2 ϵ})

, where

K_{δ} = {(\frac{1}{\sqrt{2 π}} \int_{δ}^{\infty} e^{- \frac{t^{2}}{2}} d t)}^{- 1}

ϵ, δ \in ℝ^{+}

and

d_{y} \in ℝ^{+}

stands for the 2‐norm sensitivity, which represents the difference between systems with and without the added noise 34 …”

Section: Problem Formulationmentioning

confidence: 99%

A data‐based private learning framework for enhanced security against replay attacks in cyber‐physical systems

Zhai

Vamvoudakis

2020

Intl J Robust & Nonlinear

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“…Techniques from works such as Kalman Filter with DP [23] and LQG with DP [17] can be used to augment the output privacy of a secure filter and controller. However, such techniques reduce the accuracy of the result and stability is difficult to guarantee.…”

Section: Related Workmentioning

confidence: 99%

Encrypted LQG using labeled homomorphic encryption

Alexandru

Pappas

2019

Proceedings of the 10th ACM/IEEE International Conference on Cyber-Physical Systems

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We consider the problem of implementing a Linear Quadratic Gaussian (LQG) controller on a distributed system, while maintaining the privacy of the measurements, state estimates, control inputs and system model. The component subsystems and actuator outsource the LQG computation to a cloud controller and encrypt their signals and matrices. The encryption scheme used is Labeled Homomorphic Encryption, which supports the evaluation of degree-2 polynomials on encrypted data, by attaching a unique label to each piece of data and using the fact that the outsourced computation is known by the actuator. We write the state estimate update and control computation as multivariate polynomials in the encrypted data and propose an extension to the Labeled Homomorphic Encryption scheme that achieves the evaluation of low-degree polynomials on encrypted data, with degree larger than two. We showcase the numerical results of the proposed protocol for a temperature control application that indicates competitive online times. CCS CONCEPTS • Security and privacy → Public key encryption; Privacypreserving protocols; • Information systems → Process control systems; • Computer systems organization → Embedded and cyber-physical systems.

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“…We can bound ∆ ℓ2 y via ∆ ℓ2 y ≤ s 1 (C)B [16], where s 1 (•) is the maximum singular value of a matrix. Various mechanisms have been developed for enforcing differential privacy in the literature [6].…”

Section: Definition 3 (Sensitivity For Input Perturbation Privacy)mentioning

confidence: 99%

Error Bounds and Guidelines for Privacy Calibration in Differentially Private Kalman Filtering

Yazdani¹,

Hale²

2019

Preprint

Self Cite

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Differential privacy has emerged as a formal framework for protecting sensitive information in control systems.One key feature is that it is immune to post-processing, which means that arbitrary post-hoc computations can be performed on privatized data without weakening differential privacy. It is therefore common to filter private data streams. To characterize this setup, in this paper we present error and entropy bounds for Kalman filtering differentially private state trajectories. We consider systems in which an output trajectory is privatized in order to protect the state trajectory that produced it. We provide bounds on a priori and a posteriori error and differential entropy of a Kalman filter which is processing the privatized output trajectories. Using the error bounds we develop, we then provide guidelines to calibrate privacy levels in order to keep filter error within pre-specified bounds. Simulation results are presented to demonstrate these developments.

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Privacy in Feedback: The Differentially Private LQG

Cited by 26 publications

References 12 publications

A data‐based private learning framework for enhanced security against replay attacks in cyber‐physical systems

A data‐based private learning framework for enhanced security against replay attacks in cyber‐physical systems

Encrypted LQG using labeled homomorphic encryption

Error Bounds and Guidelines for Privacy Calibration in Differentially Private Kalman Filtering

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