Single-dimensional encryption against innovation-based stealthy attacks on remote state estimation

Abstract

Remote state estimation through a wireless communication network is usually vulnerable to malicious cyber-attacks, which can manipulate transmitted data without even being detected. This paper presents a countermeasure based on single-dimensional encryption to defend against stealthy attacks. Instead of encrypting one entry of the original measurements, a linear or nonlinear transformation of them is encrypted in order to enhance the security level of the system. It is proved that for most systems, single-dimensional encryption can completely resist innovation-based stealthy attacks. For other special cases, the worst-case constrained attack that yields the greatest estimation error is analyzed. Accordingly, a suboptimal encryption strategy can reduce the influence of attacks effectively. In addition, a new type of innovation-based stealthy attack is proposed. This attack model does not require the calculation of the nominal innovation and can usually lead to greater estimation errors. The worst-case attack for this model is derived analytically. The effectiveness of single-dimensional encryption against the proposed attack is also analyzed. For the above two innovation-based stealthy attacks, the proposed single-dimensional encryption scheme provides an effective defense.