Fundamental Limits of Obfuscation for Linear Gaussian Dynamical Systems: An Information-Theoretic Approach

In this paper, we study the fundamental limits of obfuscation in terms of privacy-distortion tradeoffs for linear Gaussian dynamical systems via an information-theoretic approach. Particularly, we obtain analytical formulas that capture the fundamental privacy-distortion tradeoffs when privacy masks are to be added to the outputs of the dynamical systems, while indicating explicitly how to design the privacy masks in an optimal way: The privacy masks should be colored Gaussian with power spectra shaped specifically based upon the system and noise properties.

[1]  Quanyan Zhu,et al.  Channel Leakage, Information-Theoretic Limitations of Obfuscation, and Optimal Privacy Mask Design for Streaming Data , 2020 .

[2]  Jerome Le Ny,et al.  Differential Privacy for Dynamic Data , 2020 .

[3]  Privacy in Dynamical Systems , 2020 .

[4]  Quanyan Zhu,et al.  Generic Variance Bounds on Estimation and Prediction Errors in Time Series Analysis: An Entropy Perspective , 2019, 2019 IEEE Information Theory Workshop (ITW).

[5]  Karl Henrik Johansson,et al.  Information-theoretic approaches to privacy in estimation and control , 2019, Annu. Rev. Control..

[6]  Minghui Zhu,et al.  A control-theoretic perspective on cyber-physical privacy: Where data privacy meets dynamic systems , 2019, Annu. Rev. Control..

[7]  George J. Pappas,et al.  Privacy in Control and Dynamical Systems , 2018 .

[8]  Karl Henrik Johansson,et al.  Directed information and privacy loss in cloud-based control , 2017, 2017 American Control Conference (ACC).

[9]  Jie Chen,et al.  Towards Integrating Control and Information Theories , 2017 .

[10]  Ufuk Topcu,et al.  Event-based information-theoretic privacy: A case study of smart meters , 2016, 2016 American Control Conference (ACC).

[11]  Paul Cuff,et al.  Information Theoretic Security and Privacy of Information Systems , 2016 .

[12]  Parv Venkitasubramaniam,et al.  Information-Theoretic Security in Stochastic Control Systems , 2015, Proceedings of the IEEE.

[13]  Ruoheng Liu,et al.  Securing Wireless Communications at the Physical Layer , 2014 .

[14]  Ali Makhdoumi,et al.  Privacy-utility tradeoff under statistical uncertainty , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[15]  H. Vincent Poor,et al.  Utility-Privacy Tradeoffs in Databases: An Information-Theoretic Approach , 2011, IEEE Transactions on Information Forensics and Security.

[16]  Carles Padró,et al.  Information Theoretic Security , 2013, Lecture Notes in Computer Science.

[17]  H. Vincent Poor,et al.  Smart Meter Privacy: A Theoretical Framework , 2013, IEEE Transactions on Smart Grid.

[18]  Flávio du Pin Calmon,et al.  Privacy against statistical inference , 2012, 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[19]  Matthieu R. Bloch,et al.  Physical-Layer Security: From Information Theory to Security Engineering , 2011 .

[20]  H. Vincent Poor,et al.  Competitive privacy in the smart grid: An information-theoretic approach , 2011, 2011 IEEE International Conference on Smart Grid Communications (SmartGridComm).

[21]  Josep Domingo-Ferrer,et al.  From t-Closeness-Like Privacy to Postrandomization via Information Theory , 2010, IEEE Transactions on Knowledge and Data Engineering.

[22]  Pedro M. Crespo,et al.  Asymptotically Equivalent Sequences of Matrices and Hermitian Block Toeplitz Matrices With Continuous Symbols: Applications to MIMO Systems , 2008, IEEE Transactions on Information Theory.

[23]  Raymond W. Yeung,et al.  Information Theory and Network Coding , 2008 .

[24]  Matthieu R. Bloch,et al.  Wireless Information-Theoretic Security , 2008, IEEE Transactions on Information Theory.

[25]  Thomas M. Cover,et al.  Network Information Theory , 2001 .

[26]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[27]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[28]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[29]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .