Coding Schemes for Securing Cyber-Physical Systems Against Stealthy Data Injection Attacks

Fei Miao, Quanyan Zhu, Miroslav Pajic, George J. Pappas

Research output: Contribution to journalArticlepeer-review


This paper considers a method of coding the sensor outputs in order to detect stealthy false data injection attacks. An intelligent attacker can design a sequence of data injection to sensors and actuators that pass the state estimator and statistical fault detector, based on knowledge of the system parameters. To stay undetected, the injected data should increase the state estimation errors while keep the estimation residues small. We employ a coding matrix to change the original sensor outputs to increase the estimation residues under intelligent data injection attacks. This is a low-cost method compared with encryption schemes over all sensor measurements in communication networks. We show the conditions of a feasible coding matrix under the assumption that the attacker does not have knowledge of the exact coding matrix. An algorithm is developed to compute a feasible coding matrix, and, we show that in general, multiple feasible coding matrices exist. To defend against attackers who estimates the coding matrix via sensor and actuator measurements, time-varying coding matrices are designed according to the detection requirements. A heuristic algorithm to decide the time length of updating a coding matrix is then proposed.

Original languageEnglish (US)
Article number7478650
Pages (from-to)106-117
Number of pages12
JournalIEEE Transactions on Control of Network Systems
Issue number1
StatePublished - Mar 2017


  • Coding
  • detection
  • feasible coding matrix
  • state estimator
  • stealthy data injection attacks
  • time-varying coding

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Control and Optimization


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