Secure and Private Implementation of Dynamic Controllers Using Semihomomorphic Encryption

This article presents a secure and private implementation of linear time-invariant dynamic controllers using Paillier's encryption, a semihomomorphic encryption method. To avoid overflow or underflow within the encryption domain, the state of the controller is reset periodically. A control design approach is presented to ensure stability and optimize performance of the closed-loop system with encrypted controller.

[1]  Iman Shames,et al.  Secure and private control using semi-homomorphic encryption , 2017 .

[2]  Mohamed Boutayeb,et al.  Static output feedback stabilization with H/sub /spl infin// performance for linear discrete-time systems , 2005, IEEE Transactions on Automatic Control.

[3]  W. Marsden I and J , 2012 .

[4]  Dragan Nesic,et al.  Input-output stability properties of networked control systems , 2004, IEEE Transactions on Automatic Control.

[5]  Craig Gentry,et al.  Fully homomorphic encryption using ideal lattices , 2009, STOC '09.

[6]  George A. Perdikaris Computer Controlled Systems , 1991 .

[7]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[8]  Yehuda Lindell,et al.  Introduction to Modern Cryptography , 2004 .

[9]  Hyungbo Shim,et al.  Need for Controllers Having Integer Coefficients in Homomorphically Encrypted Dynamic System , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[10]  James Lam,et al.  Static Output Feedback Stabilization: An ILMI Approach , 1998, Autom..

[11]  Dragan Nesic,et al.  Secure Control of Nonlinear Systems Using Semi-Homomorphic Encryption , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[12]  Isaac Horowitz,et al.  Synthesis of a non-linear feedback system with significant plant-ignorance for prescribed system tolerances† , 1974 .

[13]  J. Moore,et al.  Stable realization of fixed-lag smoothing equations for continuous-time signals , 1974 .

[14]  Iman Shames,et al.  Secure and Private Cloud-Based Control Using Semi-Homomorphic Encryption* , 2016 .

[15]  Orhan Beker,et al.  Fundamental properties of reset control systems , 2004, Autom..

[16]  Sandip C. Patel,et al.  Improving the cyber security of SCADA communication networks , 2009, CACM.

[17]  Adam J. Elbirt Understanding and Applying Cryptography and Data Security , 2009 .

[18]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[19]  Hyungbo Shim,et al.  Encrypting Controller using Fully Homomorphic Encryption for Security of Cyber-Physical Systems* , 2016 .

[20]  Manfred Morari,et al.  Cloud-Based MPC with Encrypted Data , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[21]  Elisa Bertino,et al.  Homomorphic Encryption and Applications , 2014, SpringerBriefs in Computer Science.

[22]  Karl Johan Åström,et al.  Computer-controlled systems (3rd ed.) , 1997 .

[23]  Takahiro Fujita,et al.  Cyber-security enhancement of networked control systems using homomorphic encryption , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[24]  P. Olver Nonlinear Systems , 2013 .

[25]  Daniel E. Quevedo,et al.  Encrypted cloud-based MPC for linear systems with input constraints , 2018 .

[26]  Farhad Farokhi,et al.  Towards Encrypted MPC for Linear Constrained Systems , 2018, IEEE Control Systems Letters.

[27]  Dragan Nesic,et al.  A Lyapunov Proof of an Improved Maximum Allowable Transfer Interval for Networked Control Systems , 2007, IEEE Transactions on Automatic Control.

[28]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[29]  Lihua Xie,et al.  Stability analysis and design of reset control systems with discrete-time triggering conditions , 2012, Autom..

[30]  Yehuda Lindell,et al.  Introduction to Modern Cryptography (Chapman & Hall/Crc Cryptography and Network Security Series) , 2007 .

[31]  Peter F. Al-Hokayem Stability Analysis of Networked Control Systems , 2003 .

[32]  Hyungbo Shim,et al.  Dynamic Controller that Operates over Homomorphically Encrypted Data for Infinite Time Horizon , 2019, ArXiv.

[33]  Asgeir J. Sørensen,et al.  Lyapunov-Based Integrator Resetting With Application to Marine Thruster Control , 2008, IEEE Transactions on Control Systems Technology.

[34]  J. C. Clegg A nonlinear integrator for servomechanisms , 1958, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[35]  Isabelle Queinnec,et al.  Analysis and Synthesis of Reset Control Systems , 2018, Found. Trends Syst. Control..

[36]  Taher El Gamal A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, IEEE Trans. Inf. Theory.