Encrypting Controller using Fully Homomorphic Encryption for Security of Cyber-Physical Systems**The work of J. Kim, C. Lee, and H. Shim was supported by ICT R & D program of MSIP/IITP Grant number 14-824-09-013, Resilient Cyber-Physical Systems Research. The work of J. H. Cheon, A. Kim, M. Kim, and Y. Song was supported by IT R & D program of MSIP/KEIT [No. 0450-21060006] and Samsung Electronics Co., Ltd. (No. 0421-20150074).

Amin, 2009, Safe and secure networked control systems under denial-of-service attacks, Hybrid Systems: Computation and Control, 31

Applebaum, 2009, Public-key cryp-tosystems from the worst-case shortest vector problem: Extended abstract, Proc. of CRYPTO’09, 595

Cheon, 2016, Floating-point homomor-phic encryption, IACR Cryptology ePrint Archive, 2016, 421

Cheon, 2015, Fully homomorphic encryption over the integers revisited, Proc. of EUROCRYPT’15, 513

Dijk, 2010, Fully ho-momorphic encryption over the integers, Proc. of EURO-CRYPT’10, 24

Ducas, 2015, FHEW: Bootstrapping homomorphic encryption in less than a second, Proc. of EUROCRYPT’15, 617

ElGamal, 1984, A public key cryptosystem and a signature scheme based on discrete logarithms, Proc. of CRYPTO’84, 10

C. Gentry. A fully homomorphic encryption scheme. Ph.D. dissertation, Stanford University, 2009.

Johansson, 2000, The quadruple-tank process: A multivariable laboratory process with an adjustable zero, IEEE trans. on Control Systems Technology, 8, 456, 10.1109/87.845876

Kogiso, 2015, Cyber-security enhancement of networked control systems using homomorphic encryption, In Proc. of IEEE 54th Conf. on Decision and Control, 6836

Langner, 2011, Stuxnet: Dissecting a cyberwarfare weapon, IEEE Security & Privacy, 9, 49, 10.1109/MSP.2011.67

Lee, 2015, Secure and robust state estimation under sensor attacks, measurement noise and process disturbances: Observer-based combinatorial approach, Proc. of 14th European Control Conf, 1872

Li, 2010, Secure information aggregation for smart grids using homomorphic encryption, Proc. of 1st IEEE Int. Conf. on SmartGridComm, 327

Lindner, 2011, Better key sizes (and attacks) for LWE-based encryption, Proc. of CT-RSA’11, 319

Micciancio, 2009, Lattice-based Cryptography, Post-Quantum Cryptography, 147, 10.1007/978-3-540-88702-7_5

G. Park, H. Shim, C. Lee, Y. Eun, K. H. Johansson. When adversary encounters uncertain cyber-physical systems: Robust zero-dynamics attack with disclosure resources. To be presented at IEEE Conf. on Decision and Control, Las Vegas, 2016.

Pasqualetti, 2013, Attack detection and identification in cyber-physical systems, IEEE Trans. on Automatic Control, 58, 2715, 10.1109/TAC.2013.2266831

C. Peikert. Public-key cryptosystems from the worst-case shortest vector problem: Extended abstract. In Proc. of STOC’09, pp. 333– 342, 2009.

Regev, 2005, On lattices, learning with errors, random linear codes, and cryptography, Proc. of STOC’05, 84

Sandberg, 2015, Cyberphysical security in networked control systems: An introduction to the issue, IEEE Control Systems Magazine, 35, 20, 10.1109/MCS.2014.2364708

Slay, 2007

Sundaram, 2011, Distributed function calculation via linear iterative strategies in the presence of malicious agents, IEEE Trans. on Automatic Control, 56, 1498, 10.1109/TAC.2010.2088690

A. Teixeira, I. Shames, H. Sandberg, and K. H. Johansson. Revealing stealthy attacks in control systems. In Proc. 50th Annu. Aller-ton Conf. Communication, Control, Computing, pp. 1806-–1813, 2012.

Teixeira, 2015, A secure control framework for resource-limited adversaries, Automatica, 51, 135, 10.1016/j.automatica.2014.10.067

Zhu, 2015, Game-theoretic methods for robustness, security, and resilience of cyberphysical control systems: Games-in-games principle for optimal cross-layer resilient control systems, IEEE Control Systems Magazine, 35, 46, 10.1109/MCS.2014.2364710